Modern School of Music Entrance Exam Set

The core of this question lies in understanding the principles of counterpoint and harmonic progression as applied in a contrapuntal texture. The scenario describes a two-part invention where the second voice enters after the first. The first voice presents a melodic idea in C minor. The second voice enters a perfect fifth below the initial entry of the first voice, which is a standard practice for imitative counterpoint, often leading to a modulation. Let’s analyze the harmonic implications. The first voice begins on C. If the second voice enters a perfect fifth below C, it would be F. However, the question states the second voice enters *after* the first voice has established its initial melodic material. The key is C minor. A common harmonic progression in C minor would involve moving towards the dominant, G major (or G minor). If the second voice enters in imitation, it typically does so at the octave or the fifth. Entering at the fifth below the *initial* note of the first voice (C) would place the second voice on F. However, the imitation is of the *melodic idea*, not just the starting note. Consider the first voice’s melodic idea. If it starts with C, then D, then Eb, then F, the imitation at the fifth below would mean the second voice starts on F, then G, then Ab, then Bb. This would establish F minor as a potential new tonal center, or at least a strong influence. However, the question specifies the *overall* context is C minor, and the imitation is a “perfect fifth below.” This implies the relationship between the *entries* of the theme. The crucial element is how the imitation at the fifth below functions harmonically within the established key of C minor. If the first voice starts on C, and the second voice imitates at the fifth below, its first note would be F. However, in a two-part invention in C minor, the secondary tonal area often explored is the relative major (Eb major) or the dominant minor (G minor). Imitation at the fifth below the tonic (C) would lead to the subdominant area (F minor). Let’s re-evaluate the “perfect fifth below.” If the first voice starts on C, and the second voice imitates at the fifth *below* the first voice’s *entry point*, and the key is C minor, the most logical harmonic destination for the *imitation itself* to explore, while still being related to C minor, is the dominant. Imitation at the fifth *above* the tonic would be G. Imitation at the fifth *below* the tonic would be F. However, in the context of a two-part invention, the imitation often serves to establish a new tonal center or explore related keys. The question states the second voice enters a “perfect fifth below the initial entry of the first voice.” If the first voice’s initial entry is C, a perfect fifth below is F. However, this would lead to the subdominant. In many contrapuntal forms, especially those derived from Baroque practice, the imitation at the fifth often leads to the dominant. This is because the dominant is the most closely related key to the tonic and provides a strong harmonic pull. Therefore, if the first voice starts on C, and the imitation is at the fifth, the second voice would typically start on G (a fifth above C). If it’s a fifth *below*, it would be F. However, the question is about the *harmonic implication* of the imitation. If the first voice presents a theme in C minor, and the second voice imitates at the fifth, the most common and harmonically functional relationship explored in this context is the dominant. This is because the dominant (G) is a fifth above the tonic (C). If the imitation is at the fifth *below*, it would be F. But the question is framed within the context of a two-part invention in C minor. The typical pattern is to move towards the dominant. Let’s consider the melodic contour. If the first voice starts C-D-Eb, the imitation at the fifth below would be F-G-Ab. This establishes F minor. However, the question asks about the *harmonic implication* for the overall piece in C minor. The most common secondary key area explored in a C minor piece, through imitation at the fifth, is the dominant. This means the second voice would typically enter on G, a fifth above C. If the imitation is strictly “a perfect fifth below,” it would be F. But this is less common for establishing a new tonal center in a typical Baroque invention structure. The key to understanding this question is recognizing that while imitation can occur at various intervals, the most common and harmonically significant interval for establishing a secondary tonal center in a two-part form is the fifth (either above or below, leading to the dominant or subdominant, respectively, but the dominant is more prevalent for forward motion). Given the context of a Modern School of Music Entrance Exam, the expectation is to understand the functional harmonic implications. Imitation at the fifth below the tonic (C) would lead to the subdominant (F). However, in the development of a piece, moving to the dominant is more common. Let’s assume the “perfect fifth below” refers to the interval relationship between the *voices* during the imitation, not necessarily the new tonic. If the first voice starts on C, and the second voice imitates at the fifth below, its first note is F. This F, in the context of C minor, is the subdominant. However, the question is about the *harmonic implication* for the piece’s structure. The most common harmonic area explored through imitation at the fifth in a minor key is the dominant. This implies that the imitation is likely at the fifth *above* the tonic, or that the “fifth below” is being interpreted in a way that leads to the dominant. Let’s consider the standard practice in Baroque inventions. If a piece is in C minor, the second voice often enters in imitation at the fifth. This means the second voice starts on G (a fifth above C). This establishes the dominant key area. If the question states “a perfect fifth below,” and the first voice starts on C, the second voice starts on F. F is the subdominant. However, the question asks about the *harmonic implication* for the overall piece. The most significant harmonic relationship explored through imitation at the fifth in a minor key is the dominant. Therefore, the imitation at the fifth below the initial entry of the first voice, in the context of C minor, is most likely intended to explore the dominant tonal area, even if the literal interval suggests the subdominant. This is a nuanced point about functional harmony in contrapuntal writing. The dominant is the most closely related key and provides the strongest harmonic pull back to the tonic. Therefore, the harmonic implication of imitation at the fifth in C minor is the exploration of the dominant tonal area, which is G minor or G major. The phrasing “perfect fifth below” is a bit of a distractor if interpreted too literally without considering the functional harmonic context of contrapuntal forms. The correct answer focuses on the most common and harmonically significant outcome. The correct answer is the exploration of the dominant tonal area.

The question probes the understanding of harmonic function and its application in creating a sense of resolution within a musical context, specifically as taught at the Modern School of Music Entrance Exam University. The core concept is the dominant-tonic relationship, which is fundamental to Western tonal music. A dominant chord (V) naturally leads to a tonic chord (I) due to the inherent tension created by the tritone interval between the third and seventh of the dominant chord. In the key of C major, the dominant chord is G major (G-B-D). The tonic chord is C major (C-E-G). The resolution from G major to C major is considered the strongest and most common cadence. To analyze the provided harmonic progression, we first identify the key. The presence of F# and C# strongly suggests the key of D major or B minor. However, the final chord being D major (D-F#-A) confirms D major as the tonic. The progression is: Am (vi) – D7 (V7) – G (IV) – C (I) – F#m7b5 (iiø7 in E minor, or viiø7 in G major, or a Neapolitan chord in a minor key if preceded by a diminished chord, but here it functions as a pivot to B minor). The progression then moves to Bm (vi in D major). The crucial part for resolution is the movement from the dominant function to the tonic. In D major, the dominant chord is A major or A7. The progression provided does not explicitly feature a clear dominant-tonic resolution in D major at the end. Let’s re-examine the progression with a focus on creating a strong sense of resolution *towards* D major. A dominant seventh chord built on A (A7: A-C#-E-G) would strongly resolve to D major. The progression presented is Am – D7 – G – C – F#m7b5 – Bm. The D7 chord here functions as a secondary dominant, specifically V7/G, resolving to G. The G then resolves to C, which is V7/F in the key of Bb major, or IV in G major. The F#m7b5 is a diminished chord. The Bm is the relative minor of D major. The question asks about achieving a strong sense of resolution *to the tonic*. In the context of D major, the tonic is D major. The strongest resolution is typically achieved by a dominant chord (A major or A7) preceding the tonic chord (D major). The provided progression does not end with a dominant-tonic resolution in D major. Instead, it ends on B minor. If we consider the possibility of a deceptive cadence, a V chord resolving to vi (A7 to Bm in D major) would create a sense of temporary resolution but not a final tonic resolution. The question is about *achieving* a strong sense of resolution to the tonic. This implies creating the expectation and then fulfilling it. Let’s consider the options in relation to creating a strong resolution to D major. Option 1: A chord with a leading tone to D (C#) and a chord with the subdominant of D (G) in the bass, followed by the tonic. This is not a standard dominant-tonic resolution. Option 2: A chord with the dominant note of D (A) and the leading tone of D (C#) in its structure, followed by the tonic. This describes the dominant chord (A major or A7) resolving to the tonic (D major). The A7 chord (A-C#-E-G) contains the dominant note A and the leading tone C#, and its resolution to D major (D-F#-A) is the hallmark of strong tonal resolution. Option 3: A chord with the subdominant note of D (G) and the tonic note of D (D) in its structure, followed by the tonic. This describes a subdominant-tonic relationship, which is weaker than dominant-tonic. Option 4: A chord with the mediant of D (F#) and the tonic note of D (D) in its structure, followed by the tonic. This describes a mediant-tonic relationship, which is not a primary driver of strong resolution. Therefore, the most effective way to achieve a strong sense of resolution to the tonic D major is by preceding it with its dominant chord, which contains the dominant note and the leading tone.

The core concept tested here is the understanding of harmonic function within a tonal context, specifically how a dominant seventh chord (V7) resolves to the tonic (I). In the key of C major, the V7 chord is G7 (G-B-D-F), and the tonic chord is C major (C-E-G). The most common and structurally sound resolution involves the leading tone (B in G7) ascending by a half step to the tonic (C), and the seventh of the dominant chord (F in G7) descending by step to the third of the tonic chord (E). The root of the dominant chord (G) typically moves to the root of the tonic chord (C), and the fifth of the dominant chord (D) can move to either the root (C) or the third (E) of the tonic chord. Consider the progression G7 to C. The G7 chord contains the notes G, B, D, and F. The C major chord contains the notes C, E, and G. The strongest voice leading occurs when the leading tone (B) resolves to the tonic (C), and the chordal seventh (F) resolves to the third of the tonic (E). This creates smooth, stepwise motion in the inner voices, which is a fundamental principle in tonal harmony taught at institutions like the Modern School of Music Entrance Exam University. The resolution of the G7 to C in root position, with the B moving to C and the F moving to E, exemplifies this principle. The G in the bass of the G7 typically moves to C in the bass of the C chord, and the D can move to either C or E. The specific voicing that emphasizes the leading tone’s resolution to the tonic and the seventh’s resolution to the third is crucial for a strong cadential effect. Therefore, the resolution of the leading tone to the tonic and the seventh to the third of the tonic chord is the most harmonically significant aspect of this progression.

The question probes the understanding of harmonic function and its application in creating a sense of resolution within a musical context, specifically as taught at the Modern School of Music Entrance Exam University. The core concept is the dominant-tonic relationship, which is fundamental to Western tonal music. The dominant chord (V) creates tension that naturally resolves to the tonic chord (I). In this scenario, a C major scale is the reference. The dominant chord in C major is G major (G-B-D). The tonic chord is C major (C-E-G). The question asks about the chord that provides the strongest sense of arrival or resolution to a C major chord. This arrival is most powerfully achieved by the dominant chord. Therefore, a G major chord (or its dominant seventh, G7) is the correct answer. The explanation focuses on the function of the dominant chord in creating a cadence, a harmonic progression that marks the end of a phrase or piece, and how this function is a cornerstone of tonal harmony studied at institutions like the Modern School of Music Entrance Exam University. Understanding this functional harmony is crucial for composition, arrangement, and theoretical analysis, all key areas within the curriculum. The other options represent chords that, while potentially found in C major, do not possess the same inherent tension-resolution relationship with the tonic that the dominant chord does. For instance, the subdominant (IV) chord, F major, creates a different kind of harmonic movement, often leading away from the tonic or towards the dominant, rather than directly resolving to the tonic. The mediant (III) chord, E minor, has a weaker pull towards the tonic. The supertonic (ii) chord, D minor, typically functions as a pre-dominant chord, often leading to the dominant. Thus, the G major chord’s role in establishing the V-I cadence makes it the most appropriate answer for achieving a strong sense of resolution to C major.

The question probes the understanding of harmonic function and its application in creating tension and resolution within a musical context, specifically relevant to advanced composition studies at the Modern School of Music Entrance Exam University. The core concept tested is the role of the dominant seventh chord in leading to the tonic. In a tonal system, the dominant seventh chord (V7) possesses a strong tendency to resolve to the tonic chord (I). This tendency arises from the inherent dissonances within the V7 chord, particularly the tritone formed between the third and seventh of the chord. For instance, in C major, the G7 chord (G-B-D-F) contains the tritone B-F. The B naturally wants to resolve up to C (the tonic), and the F naturally wants to resolve down to E (the third of the C major tonic chord). This strong pull towards resolution is a fundamental principle of Western tonal harmony. Therefore, a composer seeking to create a sense of anticipation and subsequent release would strategically employ the dominant seventh chord in proximity to its tonic resolution. The other options represent harmonic functions that, while important, do not possess the same degree of inherent forward momentum and resolutionary pull as the dominant seventh. The subdominant (IV) chord often leads to the dominant, creating a sense of preparation but not the same immediate tension. The mediant (III) chord offers a different color and can lead to various resolutions but lacks the direct V-I pull. The leading-tone chord (vii°) is closely related to the dominant and also has a strong tendency to resolve to the tonic, but the dominant seventh chord is the more archetypal and commonly utilized harmonic device for this specific purpose in creating predictable yet powerful tension and release. The question requires an understanding of these functional relationships and their psychological impact on the listener, a crucial skill for composers and theorists at the Modern School of Music Entrance Exam University.

The question probes the understanding of harmonic function and its application in creating tension and resolution within a tonal framework, a core concept at the Modern School of Music Entrance Exam. Specifically, it tests the ability to identify the chord that most effectively creates a dominant-seventh relationship leading to a tonic chord, thereby generating the strongest sense of harmonic pull. In a typical Western tonal system, the V7 chord (dominant seventh) has the strongest tendency to resolve to the I chord (tonic). The V7 chord contains the leading tone of the key, which is a half step below the tonic, and the tritone formed by the third and seventh of the dominant seventh chord, which strongly pulls towards the tonic and mediant of the tonic chord, respectively. Therefore, to create the most compelling dominant-tonic resolution, the chord that functions as the dominant seventh of C major (which is G7) would be the most appropriate choice. The G7 chord consists of the notes G, B, D, and F. The B is the leading tone to C, and the F is a half step above E (the third of C major), creating the characteristic tension that resolves to the tonic. While other chords might precede a tonic chord, the V7 chord is paramount for establishing a strong, expected resolution in tonal music, a principle emphasized in the theoretical curriculum at the Modern School of Music Entrance Exam.

The core of this question lies in understanding the principles of harmonic progression and voice leading within a contrapuntal context, specifically as applied in the compositional pedagogy at the Modern School of Music. A common error in harmonic analysis, especially for students transitioning from simpler harmonic concepts, is to misinterpret the function of a diminished seventh chord. In the given scenario, the progression from a G major chord (implied by the context of a dominant function leading to C) to an F# diminished seventh chord, and then to a G major chord, presents a specific harmonic challenge. The F# diminished seventh chord, when functioning as a secondary dominant or a leading-tone chord to a chord a half step above it (G), creates a strong pull towards that chord. However, the subsequent resolution to G major, rather than the expected G minor or a chord derived from G minor, requires careful consideration of voice leading. The F# diminished seventh chord (F#, A, C, Eb) contains dissonant intervals that necessitate smooth resolutions. In a typical resolution to G major, the F# would resolve upwards to G, the A would resolve to G or B, the C would resolve to B, and the Eb would resolve to D. However, the question implies a specific scenario where the F# diminished seventh chord is used to create a particular color or tension before resolving to G major. The most harmonically sound and stylistically appropriate resolution for a diminished seventh chord, particularly in a context aiming for sophisticated harmonic language as taught at the Modern School of Music, involves ensuring that each voice moves by step or a small, consonant leap. Consider the F# diminished seventh chord as a leading-tone chord to G. The leading tone to G is F#. The diminished seventh chord built on the leading tone of a key is the vii°7 chord. In the key of G major, the vii°7 chord would be F#°7 (F#, A, C, Eb). This chord strongly resolves to G major. The question asks about the *most appropriate* resolution for the F# diminished seventh chord *in the context of a Modern School of Music composition exercise*. This implies adherence to established principles of voice leading and harmonic function. The F# diminished seventh chord (F#, A, C, Eb) has a specific intervallic structure: root, minor third, diminished fifth, diminished seventh. When resolving to G major (G, B, D), the most conventional and smoothest voice leading involves: F# resolving to G (up a semitone) A resolving to G (down a whole tone) or to B (up a whole tone) C resolving to B (down a semitone) Eb resolving to D (down a whole tone) The question is designed to test the understanding of how a diminished seventh chord can be used to create chromatic tension and then resolve smoothly. The F# diminished seventh chord, when used as a secondary dominant or leading-tone chord to G, creates a strong chromatic pull. The crucial aspect for advanced students at the Modern School of Music is not just identifying the chord, but understanding its functional role and the expected voice leading. The most common and stylistically sound resolution of an F#°7 to G major involves the F# moving to G, the A moving to G, the C moving to B, and the Eb moving to D. This creates a smooth, stepwise motion in most voices. Let’s analyze the options in terms of voice leading and harmonic function: If the F# diminished seventh chord is functioning as a leading-tone chord to G, the most direct and common resolution is to a G chord. The specific voicing of the F# diminished seventh chord will dictate the exact movement of each voice. However, the underlying principle is that the diminished seventh chord creates a strong tension that resolves by moving voices by step or small leaps to the tonic chord. The F# diminished seventh chord (F#, A, C, Eb) contains the interval of a diminished seventh (F# to Eb), which is enharmonically equivalent to a major sixth. This interval, along with the tritone (F# to C), contributes to its dissonant character and strong pull. The question is about the *most appropriate* resolution in a compositional context at the Modern School of Music. This implies a consideration of both harmonic function and smooth voice leading. The F# diminished seventh chord, when leading to G major, functions as a leading-tone chord. The leading tone (F#) must resolve upwards to the tonic (G). The other tones of the diminished seventh chord also have conventional resolutions. The A can resolve down to G, the C down to B, and the Eb down to D. This creates a smooth resolution to the G major chord. Therefore, the resolution of the F# diminished seventh chord to a G major chord, with appropriate voice leading, is the most harmonically sound and stylistically expected outcome in this context. The specific question asks for the *most appropriate* resolution, implying a consideration of established compositional practices taught at the Modern School of Music. The F# diminished seventh chord is a powerful tool for chromaticism and tension, and its resolution to the tonic chord of the key it is leading to is a fundamental concept. The calculation is conceptual, not numerical. The F# diminished seventh chord is F#-A-C-Eb. The G major chord is G-B-D. Voice leading: F# -> G (up a semitone) A -> G (down a whole tone) C -> B (down a semitone) Eb -> D (down a whole tone) This is a standard and smooth resolution. Final Answer: The most appropriate resolution for an F# diminished seventh chord, particularly in a compositional exercise at the Modern School of Music focusing on harmonic progression and voice leading, is to a G major chord. This is because the F# diminished seventh chord often functions as a leading-tone chord to the tonic of G major, creating strong harmonic tension that resolves smoothly through stepwise motion in the voices. The F# naturally moves up to G, the C moves down to B, and the Eb moves down to D, while the A can resolve to G or B, completing the G major triad with proper voice leading. This resolution exemplifies sophisticated harmonic practice and is a cornerstone of contrapuntal and harmonic studies at institutions like the Modern School of Music.

The question probes the understanding of harmonic function and voice leading principles within a specific contrapuntal context, relevant to advanced music theory at the Modern School of Music Entrance Exam University. The scenario presents a progression that, while seemingly functional, contains a subtle violation of standard voice-leading practice when analyzed through the lens of classical harmony and counterpoint. Consider the progression in C major: I – vi – IV – V. In a four-part texture, a common realization of the vi chord (Am) would involve the notes A, C, E. If the soprano voice is on G (part of the C major chord, the tonic), and the bass is on A (the root of the vi chord), the alto and tenor would typically fill in the remaining notes of the Am chord. A common voicing would place C and E in the inner voices. Now, consider the subsequent IV chord (F major: F, A, C). If the soprano moves from G to F, and the bass moves from A to F, the inner voices need to resolve appropriately. A common error in such a progression, especially when aiming for smooth voice leading and avoiding parallel perfect intervals, is the treatment of the leading tone (B in C major) or other dissonances. Let’s analyze a specific problematic voicing for the vi chord (Am) that leads to an issue in the IV chord (F major). Suppose the soprano is on G, bass on A, alto on E, and tenor on C. When moving to the IV chord (F major), if the soprano moves to F, the bass moves to F, the alto moves to A, and the tenor moves to C, this is a standard F major chord. However, the question implies a scenario where a specific harmonic function is being tested in relation to voice leading. The core of the question lies in identifying a subtle error in voice leading that might arise from a less common or intentionally flawed realization of a standard progression. The progression I-vi-IV-V is fundamental. The error would likely stem from how the leading tone (B) or a dissonant tone is handled across the chord changes, particularly when aiming for a specific textural effect or when a student might misapply a rule. Let’s consider a scenario where the progression is in G major: I (G-B-D) – vi (Em: E-G-B) – IV (C: C-E-G) – V (D: D-F#-A). If the soprano is on D (tonic of G), and the bass moves to E (root of vi), a common voicing for Em would be E, G, B. Now, moving to IV (C major), if the soprano moves to C, and the bass moves to C, the inner voices must form a C major chord (C, E, G). A potential error could occur if, for instance, the alto was on B (leading tone of C major, but also part of the Em chord) and incorrectly resolved to C, while the tenor, also part of the Em chord, moved to G. This is generally acceptable. However, the question is designed to test a more nuanced understanding of voice leading, specifically concerning the resolution of dissonances or the avoidance of parallel perfect intervals. A common pitfall in contrapuntal writing is the parallel fifth or octave. Let’s re-examine the progression in C major: C (C-E-G-C) – Am (A-C-E-A) – F (F-A-C-F) – G (G-B-D-G). Consider a voicing for Am: Soprano G, Alto C, Tenor E, Bass A. Moving to F major: Soprano F, Bass F. If Alto moves to A and Tenor moves to C, this is F major. No parallel fifths or octaves are immediately apparent in this direct movement. The question is likely testing a more subtle error, perhaps related to the treatment of the leading tone or a specific inversion. Let’s consider the progression in terms of melodic contour and voice crossing. A more sophisticated error would involve a situation where a specific chordal tone is treated as a non-chord tone or vice versa, or where a melodic line creates an unintended harmonic consequence. Let’s assume the question is designed around a common error in the resolution of a dominant seventh chord, or a deceptive cadence, but presented within a seemingly simple progression. The prompt states “harmonic function and voice leading principles.” Consider the progression I-vi-IV-V in C major. C Major: C-E-G A minor: A-C-E F Major: F-A-C G Major: G-B-D If the soprano is on G, and the bass moves from C to A. For the Am chord, if the alto is on E and the tenor is on C, this is a complete Am chord. Moving to F major (F-A-C), if the soprano moves to F, the bass is A. For the F major chord, if the alto moves to A and the tenor moves to C, this is an F major chord. The error must be in the *voice leading* between these chords, not just the chord qualities themselves. A common error that advanced students are tested on is the parallel perfect interval. Let’s consider a specific voicing that might lead to this: C Major: Soprano G, Alto E, Tenor C, Bass C. A minor: Soprano F, Alto C, Tenor A, Bass A. Here, the movement from G to F in the soprano and C to A in the tenor creates a parallel fifth (G-C to F-A). This is a direct violation. Therefore, the scenario described in the question, when realized with specific voicings, can lead to a parallel perfect interval, specifically parallel fifths between the tenor and soprano voices. This is a fundamental error in contrapuntal writing that the Modern School of Music Entrance Exam University would expect candidates to identify. The progression itself is standard, but the specific realization of the inner voices and their movement across chord changes is crucial. The error is the creation of parallel perfect fifths between the tenor and soprano voices when moving from a C major chord (voiced G-E-C-C) to an A minor chord (voiced F-C-A-A). The interval between tenor (C) and soprano (G) is a perfect fifth. The interval between tenor (A) and soprano (F) is also a perfect fifth.

The core of this question lies in understanding the principles of counterpoint and harmonic progression as applied in early Baroque music, a foundational element of the Modern School of Music Entrance Exam curriculum. Specifically, it tests the ability to identify a melodic line that adheres to the rules of species counterpoint while also creating a plausible harmonic relationship with an implied bass line. In a two-part setting, the melodic line must avoid parallel fifths and octaves with the implied bass, maintain melodic independence, and resolve dissonances correctly. Consider a scenario where a student is asked to harmonize a given cantus firmus in the bass voice with a new melodic line in the upper voice. The cantus firmus is C-D-E-F-G-A-B-C. To create a correct counterpoint, the upper voice must move in contrary motion or oblique motion where possible, and stepwise motion is preferred. Let’s analyze a potential upper voice: G-F-E-D-C-B-A-G. 1. **C-G:** Perfect fifth (consonant). 2. **D-F:** Major third (consonant). 3. **E-E:** Unison (consonant, but repeated notes in the same voice should be avoided if possible, though not strictly forbidden in all contexts). 4. **F-D:** Major sixth (consonant). 5. **G-C:** Perfect fourth (dissonant, requires resolution). 6. **A-B:** Major second (consonant). 7. **B-A:** Major third (consonant). 8. **C-G:** Perfect fifth (consonant). In this example, the progression from G to C in the upper voice against F to G in the bass creates a perfect fourth, which is a dissonance. The F in the bass moves to G, and the G in the upper voice moves to C. This creates a harmonic interval of a perfect fourth (F-G is a second, F-C is a fifth, G-C is a fourth). The resolution of the perfect fourth (G-C) needs careful consideration. If the bass moves to G and the upper voice moves to C, the interval is a fourth. If the bass moves to A and the upper voice moves to G, it’s a seventh. Let’s re-evaluate the implied harmonic progression. If the bass is C-D-E-F-G-A-B-C, and the upper voice is G-F-E-D-C-B-A-G, the harmonic intervals are: C-G (P5), D-F (M3), E-E (P1), F-D (M6), G-C (P4), A-B (M2), B-A (M3), C-G (P5). The progression F-G in the bass and G-C in the upper voice creates a P4 (F-C) and a P4 (G-C). The interval between the bass (F) and the upper voice (G) is a major second. The interval between the bass (G) and the upper voice (C) is a perfect fourth. The perfect fourth is a dissonance that typically resolves downwards by step. In this case, the G in the bass moves to A, and the C in the upper voice moves to B. The interval G-C is a perfect fourth. The resolution would be A-B (major second). The dissonance is between G (bass) and C (upper voice). The resolution is A (bass) and B (upper voice). The interval A-B is a major second, which is consonant. The critical point is the resolution of the perfect fourth formed by G in the bass and C in the upper voice. The bass moves G to A, and the upper voice moves C to B. The interval G-C is a perfect fourth. The resolution is A-B, which is a major second. The dissonance (perfect fourth) is resolved by step into a consonant interval. A more nuanced understanding involves the harmonic implications. If the bass is C, D, E, F, G, A, B, C, and the upper voice is G, F, E, D, C, B, A, G, the harmonic intervals are: C-G (P5), D-F (M3), E-E (P1), F-D (M6), G-C (P4), A-B (M2), B-A (M3), C-G (P5). The progression F-G in the bass and G-C in the upper voice creates a perfect fourth between the bass and upper voice (G-C). This perfect fourth is a dissonance. The subsequent notes are A in the bass and B in the upper voice, forming a major second. The resolution of the perfect fourth (G-C) to a major second (A-B) is valid. The key is that the perfect fourth is treated as a dissonance and resolved correctly. The melodic contour of the upper voice is also important, featuring stepwise motion and a clear shape. The avoidance of parallel fifths and octaves with the bass is crucial. For instance, if the bass were C-D and the upper voice were G-G, that would be parallel octaves. If the bass were C-E and the upper voice were G-D, that would be parallel fifths. The chosen upper voice G-F-E-D-C-B-A-G, when paired with C-D-E-F-G-A-B-C, avoids these forbidden parallels and resolves the dissonance appropriately, making it a correct example of two-part counterpoint suitable for advanced study at the Modern School of Music Entrance Exam.

The question probes the understanding of harmonic progression and voice leading principles within a specific compositional context relevant to the Modern School of Music Entrance Exam. The scenario presents a progression that, if analyzed strictly by functional harmony in a major key, might appear to lead to an unexpected resolution. However, the core concept being tested is the application of modal interchange and chromaticism to create richer harmonic color and smooth voice leading, particularly in contemporary classical and jazz-influenced styles often explored at the Modern School of Music. Consider the progression in C major: Cmaj7 – F#m7b5 – B7alt – Em7. The F#m7b5 chord functions as a iiø7 in the key of E minor, which is the relative minor of G major. However, the subsequent B7alt chord is a V7alt of E minor. The resolution to Em7 is a standard V-i cadence in E minor. The F#m7b5 to B7alt is a common tritone substitution movement, where F#m7b5 (F#, A, C, Eb) can be seen as a substitute for a chord that would typically precede B7alt, such as a diminished chord or a secondary dominant. More directly, F#m7b5 is enharmonically related to F#dim7, which can function as a leading-tone chord to G major. However, the progression moves to B7alt, which strongly implies E minor. The key to understanding this progression’s effectiveness at the Modern School of Music lies in recognizing the F#m7b5 as a pivot chord or a chromatic passing chord that facilitates a smooth transition to the dominant of E minor. The F#m7b5 contains the notes F#, A, C, and Eb. The B7alt chord contains B, D#, F#, and Ab (or G#). The Eb in the F#m7b5 can resolve enharmonically to D# in the B7alt, creating a smooth chromatic voice leading. Alternatively, the F#m7b5 can be viewed as a borrowed chord from the parallel minor of G major (G minor), where F#m7b5 is the viiø7 of G minor, leading to a dominant chord of G minor (D7). However, the progression then moves to B7alt, the dominant of E minor. A more direct interpretation, and one that aligns with advanced harmonic practice taught at the Modern School of Music, is to view the F#m7b5 as a chord that sets up the B7alt through chromatic voice leading. The A in F#m7b5 can move to G# (enharmonic Ab) in B7alt. The F# remains common. The Eb can chromatally descend to D# in B7alt. This creates a strong chromatic pull towards the E minor tonality. The F#m7b5, in this context, acts as a pre-dominant or a chord that introduces chromaticism, preparing the dominant chord of E minor. The use of modal interchange or chromatic alteration of diatonic chords is a hallmark of sophisticated harmonic writing, and this progression exemplifies that. The F#m7b5, while not strictly diatonic to C major, serves a crucial function in leading to the altered dominant of E minor, which then resolves to E minor. This demonstrates an understanding of how chords from related keys or with altered tones can be integrated to create sophisticated harmonic movement, a core tenet of advanced music theory and composition at the Modern School of Music Entrance Exam. The progression is not simply a series of unrelated chords but a carefully constructed path that utilizes chromaticism and modal borrowing to achieve a desired harmonic effect, specifically preparing a strong dominant-tonic resolution in a closely related key.

The leading tone of the diminished seventh chord resolves upwards by a semitone to the tonic of the destination chord.

The question probes the understanding of harmonic function and voice leading principles within a specific contrapuntal context relevant to advanced music theory at the Modern School of Music Entrance Exam University. The scenario presents a progression that, at first glance, might seem to lead to a standard cadence. However, the critical element is the implied melodic motion and the resulting harmonic implications. Consider the progression: \(Cmaj7 \rightarrow Gsus4 \rightarrow G\). In a typical four-part chorale setting, with the bass line moving \(C \rightarrow G\), and assuming standard voice leading practices where voices move by step or common tone where possible: If the soprano has \(E \rightarrow D \rightarrow D\), the alto has \(G \rightarrow C \rightarrow B\), and the tenor has \(B \rightarrow F \rightarrow G\), the chords are: 1. \(Cmaj7\): \(C, E, G, B\) (Soprano E, Alto G, Tenor B, Bass C) 2. \(Gsus4\): \(G, C, D, F\) (Soprano D, Alto C, Tenor F, Bass G) 3. \(G\): \(G, B, D, G\) (Soprano D, Alto B, Tenor G, Bass G) The transition from \(Cmaj7\) to \(Gsus4\) involves the soprano moving from \(E\) to \(D\), the alto from \(G\) to \(C\), and the tenor from \(B\) to \(F\). The \(Gsus4\) chord contains the notes \(G, C, D, F\). The \(C\) in the alto is a common tone with the \(Cmaj7\) if it were \(Cmaj9\), but here it functions as the 4th of the \(G\) chord, resolving to the 3rd. The tenor’s movement from \(B\) to \(F\) is a descending perfect fifth, which is acceptable. The soprano’s \(E\) to \(D\) is a descending major second. The crucial point is the resolution of the \(Gsus4\) to \(G\). The \(C\) in the alto (the 4th of \(Gsus4\)) must resolve downwards by step to \(B\) (the 3rd of \(G\)). The tenor’s \(F\) (the 7th of \(Gsus4\)) must resolve downwards by step to \(E\) (the 5th of \(G\)) or upwards to \(G\) (the root). If the tenor moves to \(E\), and the soprano holds \(D\), and the bass is \(G\), the resulting \(G\) chord would be \(G, D, E, G\), which is a \(G\) chord with an added 6th (\(G, B, D, E\)). However, the question implies a standard \(G\) major chord. The most harmonically sound and stylistically appropriate resolution of \(Gsus4\) to \(G\) in this context, considering the preceding \(Cmaj7\) and the implied melodic lines, would involve the \(C\) in the alto resolving to \(B\), and the \(F\) in the tenor resolving to \(E\). This creates a \(G\) chord with an added 6th (\(G, B, D, E\)). However, if the goal is a pure \(G\) major triad, the \(F\) in the tenor would need to resolve to \(E\), and the \(C\) in the alto to \(B\). The question asks about the *most likely* harmonic implication given the preceding context and the typical expectations of resolution in tonal music studied at the Modern School of Music Entrance Exam University. The \(Gsus4\) chord strongly implies a resolution to \(G\). The \(C\) in the alto, as the 4th of the \(Gsus4\), is expected to resolve down to \(B\), the 3rd of the \(G\) chord. The \(F\) in the tenor, as the 7th of the \(Gsus4\), is expected to resolve down to \(E\), the 5th of the \(G\) chord. This creates a standard \(G\) major chord with the notes \(G, B, D, E\). The presence of the \(E\) as the 5th of the \(G\) chord is a standard component. The question is about the *function* of the \(C\) in the \(Gsus4\) chord and its resolution. The \(C\) is the 4th scale degree of \(G\), and its resolution to the 3rd scale degree (\(B\)) is a fundamental principle of suspensions and chordal resolutions. Therefore, the most direct and expected harmonic function of the \(C\) in the \(Gsus4\) chord, leading to a \(G\) major chord, is its role as a suspension resolving to the third of the dominant chord. The correct answer is the resolution of the suspension. The \(C\) in the \(Gsus4\) chord, in relation to the implied \(G\) major chord, functions as a suspended 4th (\(Gsus4\)). The resolution of this suspension is to the 3rd of the chord, which is \(B\). This movement from \(C\) to \(B\) is a characteristic and fundamental aspect of tonal harmony and counterpoint, a core concept taught at the Modern School of Music Entrance Exam University. The \(F\) in the tenor, as the 7th of the \(Gsus4\), would typically resolve to \(E\), the 5th of the \(G\) chord. The question focuses on the primary harmonic tension and its resolution.

The question probes the understanding of harmonic function and its application in creating a sense of resolution within a musical context, specifically relevant to the Modern School of Music Entrance Exam’s focus on advanced tonal harmony. The core concept tested is the dominant function, which typically resolves to the tonic. In Western tonal music, the V chord (dominant) has a strong tendency to resolve to the I chord (tonic). This resolution creates a sense of closure and stability. The V7 chord, with its added seventh, intensifies this dominant function due to the tritone interval between the third and seventh of the chord, which strongly pulls towards the tonic chord’s notes. Consider a progression in C Major. The tonic chord is C Major (C-E-G). The dominant chord is G Major (G-B-D), and the dominant seventh chord is G7 (G-B-D-F). The B in the G7 chord is the leading tone and strongly resolves upwards to C. The F in the G7 chord is the seventh and strongly resolves downwards to E. Thus, G7 resolves to C Major. The question asks about a chord that *precedes* a dominant seventh chord, implying a pre-dominant function. Pre-dominant chords prepare the dominant chord. Common pre-dominant chords include the ii chord (supertonic) and the IV chord (subdominant). In C Major, the ii chord is D minor (D-F-A), and the IV chord is F Major (F-A-C). If the dominant seventh chord is G7 (G-B-D-F), a common preceding chord would be D minor (D-F-A). The F in the D minor chord moves to E in the G7 chord (a common tone or a step down), and the A in the D minor chord moves to G in the G7 chord (a step down). This creates a smooth voice leading into the dominant. Alternatively, an F Major chord (F-A-C) could precede G7. The F is a common tone, the A moves to G, and the C moves to B. The question specifically asks what chord *precedes* the dominant seventh chord. Therefore, we are looking for a pre-dominant chord. Among the options, a chord that functions as a pre-dominant leading to a V7 chord is the most appropriate answer. The ii chord (supertonic) is a very common pre-dominant. In the context of C Major, the ii chord is D minor. If the dominant seventh is G7, then D minor (D-F-A) is a strong candidate for preceding it. The F in D minor leads smoothly to E in G7, and the A leads to G. The question asks for a chord that precedes a dominant seventh chord. The dominant seventh chord is the V7. Chords that precede V7 are typically pre-dominant chords, such as the ii or IV. If we consider the ii chord in a major key, it is a minor triad. For example, in C Major, the V7 is G7, and the ii chord is D minor. The D minor chord (D-F-A) leads effectively into G7 (G-B-D-F). The F in D minor moves to E in G7, and the A moves to G in G7. This smooth voice leading makes the ii chord a strong pre-dominant.

The question probes the understanding of harmonic progression and voice leading principles within a specific musical context relevant to advanced composition studies at the Modern School of Music Entrance Exam University. The scenario describes a progression from a tonic chord (C major) to a dominant chord (G major) in root position, followed by a move to the subdominant (F major) and then back to the tonic. The core concept being tested is the avoidance of parallel perfect fifths and octaves, a fundamental rule in traditional Western harmony that still informs much contemporary practice and theoretical analysis. Consider the progression C major (C-E-G) to G major (G-B-D). If the bass moves from C to G, and the inner voices are arranged such that they create parallel fifths or octaves with the bass or each other, this would be considered a violation. For instance, if the alto voice is on G and the tenor voice is on E, moving to the G major chord where the alto remains on G and the tenor moves to D would create parallel octaves between the alto and the bass (G to G) and parallel fifths between the tenor and the bass (G to D, then D to G). The correct approach, therefore, involves ensuring that all voice movements, particularly between adjacent chords, maintain proper spacing and avoid forbidden parallels. This often requires careful consideration of inversions, contrary motion, and the strategic use of leaps or steps in the inner voices. The explanation of why the other options are incorrect would involve demonstrating how they would inevitably lead to such parallel motion or violate other fundamental principles of smooth voice leading, such as excessive leaps or awkward intervals. The emphasis at the Modern School of Music Entrance Exam University is on developing a sophisticated understanding of these foundational elements as a basis for innovative compositional techniques.

The question probes the understanding of harmonic function and its application in creating tension and release within a musical context, specifically relevant to the Modern School of Music Entrance Exam’s focus on advanced compositional techniques. The scenario describes a composer aiming to evoke a sense of unresolved anticipation. In Western tonal harmony, the dominant seventh chord (V7) possesses a strong tendency to resolve to the tonic chord (I). This is due to the inherent tritone interval within the V7 chord (between the 3rd and 7th scale degrees) and the voice-leading tendencies of its individual tones. The leading tone (the 3rd of the V7 chord) naturally resolves up by a half step to the tonic, and the seventh of the V7 chord (the 7th scale degree) typically resolves down by a step to the third of the tonic chord. Therefore, to create the *greatest* sense of unresolved anticipation, a composer would want to emphasize the elements that create this tension and delay the expected resolution. The dominant seventh chord, by its very nature, is the most potent harmonic device for this purpose among the common diatonic chords. While other chords can create tension, the V7 chord’s structural relationship to the tonic makes its resolution the most fundamental expectation in tonal music. The diminished seventh chord, while dissonant, often functions as a substitute or altered dominant, and its resolution can be more ambiguous or lead to different harmonic areas, not necessarily creating the *specific* type of anticipation tied to a direct tonic resolution. The subdominant chord (IV or IV7) typically leads to the dominant or tonic but does not possess the same inherent pull towards the tonic as the dominant seventh. The mediant chord (iii) has a weaker tendency and is less commonly used to create strong, immediate anticipation of the tonic. Thus, the dominant seventh chord is the most direct and powerful tool for generating the described harmonic tension and the expectation of imminent resolution.

The question assesses understanding of harmonic function and voice leading within a specific tonal context, particularly the resolution of dissonances and the establishment of cadential progressions. The scenario describes a progression moving from a dominant seventh chord in second inversion (V6/5) to a tonic chord in first inversion (I6). In C major, the V chord is G major (G-B-D-F), and the dominant seventh is G7 (G-B-D-F). The second inversion of G7 is D-G-B-F. The tonic chord is C major (C-E-G), and the first inversion is E-G-C. The progression is from D-G-B-F to E-G-C. Let’s analyze the voice leading: 1. **Bass:** Moves from D to E. This is a standard leading-tone to tonic bass movement in a first inversion tonic chord. 2. **Soprano:** Let’s assume the soprano is on F (the seventh of the G7 chord). The seventh of a dominant seventh chord typically resolves down by step to the third of the tonic chord. In C major, the third of C major is E. So, F resolving to E is correct. 3. **Alto:** Let’s assume the alto is on B (the third of the G7 chord). The third of the dominant chord often moves to the root or fifth of the tonic chord. Moving from B to C (the root of the tonic) is a common and strong resolution. 4. **Tenor:** Let’s assume the tenor is on G (the fifth of the G7 chord). The fifth of the dominant chord can move to the root or third of the tonic chord. Moving from G to C (the root) or G to E (the third) are both acceptable. If the tenor is on G and resolves to C, this creates parallel octaves with the bass if the bass is also on C, which is generally avoided. However, in a I6 chord, the root C is in the bass. If the tenor moves to E, it creates a correct resolution. The core of the question lies in the function of the chords and the expected resolutions. The progression V6/5 to I6 is a common cadential device. The dissonance in the V6/5 chord is the seventh (F in this case). This seventh must resolve downwards by step to the third of the tonic chord (E). The leading tone (B) in the V chord must resolve upwards to the tonic root (C). The other voices should move smoothly to complete the tonic chord. The scenario describes a situation where the seventh of the dominant seventh chord (F) is in the soprano and resolves down by step to the third of the tonic chord (E). This is a fundamental principle of voice leading in tonal harmony, particularly in cadential contexts. The leading tone (B) in the dominant chord would typically resolve up to the tonic root (C). The remaining voices would fill out the tonic chord (C-E-G). The progression from a dominant seventh in second inversion (V6/5) to a tonic chord in first inversion (I6) is a standard and harmonically sound movement. The resolution of the dissonant seventh (F to E) is the most critical aspect tested here, as it dictates the melodic contour and harmonic clarity. The question emphasizes the *necessity* of this resolution for establishing the tonic’s stability and the overall harmonic coherence, especially in the context of a formal musical composition or performance at the Modern School of Music Entrance Exam University. This type of harmonic analysis is foundational for advanced composition and theory studies.

The question assesses the candidate’s understanding of voice leading principles within the context of Baroque chorale harmonization, a fundamental skill at the Modern School of Music Entrance Exam. Given a specific melodic line in the soprano and a bass line, the task is to select the most appropriate harmonization for the inner voices (alto and tenor). This requires not only identifying the correct chord tones but also ensuring that the movement of the alto and tenor voices is melodically smooth and contrapuntally sound. Specifically, candidates must avoid forbidden parallels (parallel octaves and fifths) between any two voices, including the inner voices themselves and between inner voices and the outer voices. Furthermore, the melodic contour of the alto and tenor should ideally feature stepwise motion or common tones, minimizing awkward leaps. The distribution of chord tones between the alto and tenor also matters; typically, the alto is the higher of the two inner voices. The correct option will be the one that results in a harmonically complete chord with the most elegant and stylistically appropriate voice leading for the alto and tenor, reflecting the rigorous standards of musical composition and performance taught at the Modern School of Music Entrance Exam. This involves a careful evaluation of each option against these contrapuntal and stylistic criteria, demonstrating a nuanced understanding of how to create a cohesive and pleasing harmonic texture.

The question probes the understanding of harmonic function and its application in creating a sense of resolution within a musical context, specifically as taught at the Modern School of Music Entrance Exam University. The core concept tested is the dominant-tonic relationship, which is fundamental to Western tonal harmony. A dominant chord (V) has a strong tendency to resolve to the tonic chord (I). In the key of C major, the dominant chord is G major (G-B-D). The tonic chord is C major (C-E-G). The leading tone, B, in the G major chord creates a strong pull towards C, the tonic note. The subdominant chord (IV) in C major is F major (F-A-C). While the subdominant can lead to the dominant, it does not possess the same inherent tension that demands resolution to the tonic as the dominant chord does. The mediant chord (III) in C major is E minor (E-G-B). This chord shares the leading tone (B) with the dominant, but its overall function is less about creating immediate tension and resolution to the tonic, and more about providing a related, but less forceful, harmonic color. The supertonic chord (ii) in C major is D minor (D-F-A). This chord typically functions as a pre-dominant, often leading to the dominant chord, thereby indirectly contributing to the eventual resolution to the tonic. Therefore, the chord that most directly and strongly creates the expectation of immediate resolution to the tonic in C major is the dominant chord.

The question probes the understanding of harmonic function and voice leading within a specific contrapuntal context, relevant to advanced music theory at the Modern School of Music Entrance Exam University. The scenario presents a progression that, while seemingly functional, contains a subtle violation of standard voice-leading principles when analyzed through the lens of classical harmony and counterpoint. Consider the progression: \(Cmaj \rightarrow G7 \rightarrow Cmaj\). In a typical four-part setting (SATB), if the soprano voice moves from \(E\) in the \(Cmaj\) chord to \(D\) in the \(G7\) chord, and then to \(C\) in the subsequent \(Cmaj\) chord, this is a standard descending melodic line. However, the core of the question lies in the implied harmonic function and the resulting voice leading. The \(G7\) chord, functioning as a dominant, typically resolves to \(Cmaj\). The \(D\) in the \(G7\) chord is the leading tone to \(E\) in the \(Cmaj\) chord. If the \(G7\) chord is voiced with \(G, B, D, F\), and the subsequent \(Cmaj\) chord is \(C, E, G, C\), the movement of the \(B\) in the \(G7\) chord to \(C\) in the \(Cmaj\) chord is a standard leading-tone resolution upwards by a semitone. The \(F\) in the \(G7\) chord typically resolves down by step to \(E\) in the \(Cmaj\) chord. The issue arises if the inner voices create a parallel fifth or octave, or an awkward melodic leap that disrupts the smooth flow expected in advanced counterpoint. The scenario describes a composer at the Modern School of Music Entrance Exam University attempting to create a “sense of unresolved tension” by altering the typical dominant-tonic resolution. The key is to identify which alteration would *most* effectively achieve this while still adhering to fundamental principles of tonal music, albeit with a deliberate twist. Let’s analyze the options in terms of their harmonic and melodic implications: * **Option a) Substituting the dominant seventh chord with a diminished seventh chord built on the leading tone of the dominant:** If the dominant is \(G\), the leading tone to \(G\) is \(F\#\). A diminished seventh chord built on \(F\#\) would be \(F\#, A, C, Eb\). This chord has a strong tendency to resolve. Its relationship to the tonic \(Cmaj\) is complex. While it can function as a secondary dominant or a chromatic passing chord, its inherent instability and the presence of dissonant intervals like the augmented second (or diminished seventh) between \(F\#\) and \(Eb\) create significant tension. When resolving to \(Cmaj\), the \(F\#\) would typically resolve up to \(G\), the \(A\) to \(G\) or \(C\), the \(C\) to \(B\) or \(C\), and the \(Eb\) down to \(D\) or \(C\). This substitution creates a more pronounced and complex tension than a standard dominant seventh, as the diminished seventh chord is inherently more dissonant and its resolution pathways are more varied and often lead to more chromatic alterations. This aligns with the composer’s goal of creating unresolved tension. * **Option b) Introducing a chromatic passing tone in the bass line between the tonic and the dominant:** For example, moving from \(C\) to \(C\#\) then to \(G\). While chromaticism adds color, a simple passing tone in the bass between \(I\) and \(V\) might not create the *most* profound sense of unresolved tension compared to altering the dominant chord itself. The tension is often more palpable when it resides within the dominant harmony’s structure. * **Option c) Employing a plagal cadence (\(IV-I\)) instead of a perfect cadence (\(V-I\)):** A plagal cadence is generally considered weaker and less conclusive than a perfect cadence. While it can create a sense of gentle resolution, it doesn’t typically evoke “unresolved tension” in the same way a modified dominant harmony would. It’s more about a different *type* of resolution, not a lack of it. * **Option d) Doubling the third of the dominant seventh chord in the soprano voice:** Doubling the third of a dominant seventh chord is generally discouraged in strict counterpoint due to potential voice-leading issues, particularly if the doubled third is the leading tone. However, in a modern context, this is a stylistic choice that might create a slightly richer sound but doesn’t inherently create a sense of *unresolved tension* as effectively as a harmonically more complex substitution. The tension is more about the chord’s inherent function and its resolution. Therefore, substituting the dominant seventh with a diminished seventh chord built on the leading tone of the dominant offers the most potent and harmonically sophisticated method to achieve the desired “sense of unresolved tension” within the framework of tonal music, a concept crucial for students at the Modern School of Music Entrance Exam University.

The question probes the understanding of harmonic function and its application in creating a sense of resolution within a musical context, specifically relevant to the Modern School of Music Entrance Exam’s focus on advanced harmonic theory and compositional techniques. The core concept tested is the dominant-to-tonic progression, which is fundamental to Western tonal music. In C major, the tonic chord is C major (C-E-G). The dominant chord is G major (G-B-D) or G dominant seventh (G-B-D-F). The progression from the dominant (V) to the tonic (I) creates the strongest sense of arrival and closure. The diminished seventh chord built on the leading tone (B diminished seventh: B-D-F-Ab) is a highly chromatic and tension-generating chord that functions as a secondary dominant, specifically as a V7/V (dominant of the dominant). In C major, the dominant chord is G major. The leading tone of G major is F#. Therefore, the diminished seventh chord built on F# would be F# diminished seventh (F#-A-C-Eb). This chord, F#dim7, resolves to G major (V in C major). The G major chord then resolves to C major (I). Thus, the sequence F#dim7 – G – C represents a common and effective way to establish the tonic chord through a more elaborate harmonic path, showcasing an understanding of chromaticism and voice leading principles crucial for advanced composition and analysis at the Modern School of Music. The resolution of F#dim7 to G involves specific voice leading: F# typically moves to G, A to G, C to B, and Eb to D. The G chord then resolves to C. This demonstrates a sophisticated grasp of how chromatic chords function to enhance tonal gravity.

The question probes the understanding of harmonic function and its application in creating a sense of resolution within a musical context, specifically as taught at the Modern School of Music Entrance Exam University. The core concept is the dominant function, typically represented by a V chord (or its inversions/extensions), which creates a strong tendency to resolve to the tonic (I chord). In a minor key, the dominant chord is often altered to a major triad (V) or a dominant seventh chord (V7) by raising the leading tone, which is the third of the dominant chord. This raised leading tone creates a stronger melodic pull towards the tonic. Consider a progression in A minor. The tonic chord is Am (i). The dominant chord in natural minor would be Em (v), which is a minor triad. However, to create a stronger cadence, the leading tone (G#) is raised to G natural, making the dominant chord E major (V) or E7 (V7). The resolution of E7 to Am is a very common and strong cadence. The question asks about a situation where a composer *avoids* this typical resolution to create a sense of lingering tension or ambiguity. If a composer uses a ii° chord (diminished triad) in a minor key, such as B diminished in A minor, and resolves it to the tonic (Am), this creates a less conventional resolution than the dominant-tonic relationship. The ii° chord in minor is often part of a ii°–V–i progression, but its direct resolution to i is not as tonally imperative as V–i. The diminished triad itself has a more unstable quality due to the diminished fifth interval. When this diminished triad resolves to the tonic, the specific voice leading can create a feeling of unresolved tension. For instance, if the diminished triad is B-D-F, and it resolves to A-C-E (Am), the F might resolve down to E, and the D might resolve up to E, or the B might resolve to A. The diminished quality of the ii° chord, particularly its tritone interval (B-F), when resolved to the tonic triad, can lead to a more complex harmonic color and a less definitive sense of arrival compared to the strong pull of the V chord. The avoidance of the V chord’s characteristic leading tone resolution is key here. Therefore, the ii° chord’s direct resolution to the tonic in a minor key, while harmonically valid, offers a less pronounced sense of finality and can be used to maintain harmonic interest or suspense, aligning with the Modern School of Music Entrance Exam University’s emphasis on nuanced harmonic exploration.

The core of this question lies in understanding how harmonic function and voice leading principles interact within the context of chromaticism, specifically addressing the potential for parallel perfect intervals when moving from a diatonic chord to one with altered tones. In the given progression, a C major chord (I) moves to a G7 chord with an altered ninth (G7#9). The G7#9 chord contains the notes G, B, D, F, and A#. Consider the movement from C major (C-E-G) to G7#9 (G-B-D-F-A#). The root motion from C to G is a perfect fifth, which is a standard and strong progression. The third of C major is E. In G7#9, the third is B. The movement from E to B is a diminished fifth, a consonant interval. The fifth of C major is G. In G7#9, the fifth is D. The movement from G to D is a perfect fifth, a consonant interval. The critical interval to examine for potential parallel perfect fifths or octaves is between the non-chord tones or altered tones and the existing chord tones. In this scenario, the progression is diatonic to chromatic. The G7#9 chord introduces the A#. Let’s analyze the voice leading from a C major chord to a G7#9 chord, assuming a standard SATB voicing. If C major is voiced C4-E4-G4-C5, and we move to G7#9 (G-B-D-F-A#), we need to avoid parallel perfect fifths and octaves. A common voicing for C major might be C4-E4-G4-C5. A possible voicing for G7#9 could be G3-B3-D4-F4-A#4. Let’s consider a more problematic voicing for C major, for instance, C4-G4-E4-C5. If we move this to G7#9, we need to be careful. Consider the interval between E4 and G4 in the C major chord. This is a minor third. Now consider the interval between the corresponding voices in the G7#9 chord. If the E4 moves to F4 (a common tendency for the 3rd of I moving to the 7th of V), and the G4 moves to A#4 (the altered 9th), the interval between F4 and A#4 is an augmented third, which is enharmonically a perfect fourth. This is not a parallel perfect interval. However, the question is about the *potential* for parallel perfect intervals. The G7#9 chord itself contains a tritone between B and F, which is characteristic of the dominant seventh chord. The addition of A# creates a dissonant interval with G (minor third) and B (augmented second). The critical point is the relationship between the diatonic chord tones and the chromatic alterations. The G7#9 chord is a dominant chord, and its function is to resolve to the tonic. The altered ninth (A#) creates a strong chromatic pull. Let’s re-examine the potential for parallel perfect intervals. If we have a C major chord voiced as C-E-G, and we move to G7#9. Consider the interval between E and G in C major (a minor third). If E moves to F (the seventh of G7), and G moves to A# (the altered ninth of G7), the interval between F and A# is an augmented third. The question asks about the *most likely* or *most problematic* parallel interval. The G7#9 chord is inherently dissonant due to the A#. The interval between the third (B) and the altered ninth (A#) is an augmented second, which is a dissonant interval. The interval between the root (G) and the altered ninth (A#) is a minor third. The most common issue with chromatic alterations in dominant chords, especially when moving from a diatonic chord, is the creation of parallel perfect intervals. The G7#9 chord contains the notes G, B, D, F, and A#. The interval between B and F is a tritone. The interval between G and A# is a minor third. The interval between B and A# is an augmented second. The question is subtly asking about the inherent harmonic relationship and voice-leading implications. The G7#9 chord is a dominant chord with an altered ninth. The altered ninth (A#) creates a specific harmonic color and tension. When moving from a diatonic chord like C major, the voice leading must be carefully managed to avoid parallel perfect intervals. The most common pitfall with altered dominant chords is the parallel perfect fifth or octave. Let’s consider the interval between the root and the fifth of the C major chord (C-G, a perfect fifth). If these voices move to G and D in the G7#9 chord, this is a perfect fifth, but it’s not parallel if the voices are moving correctly. The issue arises when two voices that form a perfect interval in the first chord move to form another perfect interval in the second chord, *and* they move in the same direction. The G7#9 chord is often used to create a bluesy or jazz-like sound. The A# creates a dissonant interval with the root G and the third B. The interval between the root G and the altered ninth A# is a minor third. The interval between the third B and the altered ninth A# is an augmented second. The question is about the *most significant* harmonic or voice-leading consideration when moving from a diatonic tonic to a dominant chord with an altered ninth. The altered ninth introduces a strong chromatic element. The interval between the root and the altered ninth (G to A#) is a minor third. The interval between the third and the altered ninth (B to A#) is an augmented second. The most problematic interval to consider in this context, given the options, is the relationship between the root and the altered ninth, and how it might lead to parallel perfect intervals with other voices. The G7#9 chord’s characteristic sound comes from the A#. The interval between G and A# is a minor third. Let’s consider the possibility of parallel perfect fifths. If we have C-G in the C major chord, and these voices move to G-D in the G7#9 chord, this is a perfect fifth. If the E in the C major chord moves to F in the G7#9, and the C moves to G, we need to check the intervals. The question is designed to test the understanding of how chromatic alterations affect voice leading. The G7#9 chord has a specific intervallic structure. The interval between the root (G) and the altered ninth (A#) is a minor third. The interval between the third (B) and the altered ninth (A#) is an augmented second. The interval between the fifth (D) and the altered ninth (A#) is a diminished sixth. The most direct and significant intervallic relationship created by the altered ninth is its relationship to the root and the third of the dominant chord. The interval between the root (G) and the altered ninth (A#) is a minor third. This is a consonant interval, but its chromatic nature is important. The question is about the *most significant* intervallic relationship introduced by the altered ninth in the context of a dominant chord. The G7#9 chord contains the interval of a minor third between its root (G) and its altered ninth (A#). This interval is a key characteristic of this chord’s sound and its harmonic function. While other intervals exist, the relationship between the root and the altered ninth is fundamental to understanding the chord’s identity and its typical voice-leading resolutions. The presence of the A# creates a specific harmonic tension that is often resolved by moving the A# down by a semitone to G, or by resolving the dominant chord itself. The interval between G and A# is a minor third. Final Answer Calculation: The question asks for the most significant intervallic relationship introduced by the altered ninth in a G7#9 chord. The G7#9 chord consists of the notes G, B, D, F, and A#. The interval between the root (G) and the altered ninth (A#) is a minor third. The interval between the third (B) and the altered ninth (A#) is an augmented second. The interval between the fifth (D) and the altered ninth (A#) is a diminished sixth. The interval between the seventh (F) and the altered ninth (A#) is an augmented fourth (tritone). Among these, the interval between the root and the altered ninth is a fundamental characteristic that defines the “ninth” quality of the chord. While the augmented second and augmented fourth are dissonant and crucial to the chord’s tension, the minor third between the root and the altered ninth is the defining interval of the altered ninth itself. Therefore, the minor third is the most direct and significant intervallic relationship introduced by the altered ninth in relation to the chord’s root. The correct answer is the minor third.

The core of this question lies in understanding the interplay between harmonic function theory and the specific constraints of a modal system, particularly as applied in contemporary compositional contexts often explored at the Modern School of Music Entrance Exam University. A modal interchange, in its broadest sense, involves borrowing chords or melodic material from a parallel mode. However, the question specifies a diatonic context within a single key and then introduces a chromatic alteration that functions as a pivot. The progression from C major to G major is a standard dominant-tonic relationship, often analyzed as V-I in the key of G. The introduction of an F# in the second chord (G major) is diatonic to G major. The crucial element is the preceding chord, Am7b5 (A half-diminished seventh). In C major, Am7b5 is the iiø7 chord. When this chord is followed by G major, the A acts as a common tone, and the C in the Am7b5 moves down to B in the G major chord, while the E remains a common tone. The F# in the G major chord is the leading tone to G. The progression Am7b5 to G major is not a standard diatonic progression within C major. However, if we consider the Am7b5 as a chord that can lead to a dominant chord, and G major is functioning as a dominant in the key of C (which it is, V of C), then the Am7b5 can be seen as a pre-dominant or a substitute for a ii chord. A more nuanced interpretation, relevant to advanced harmonic analysis taught at institutions like the Modern School of Music Entrance Exam University, considers the function of the Am7b5. In C major, Am7b5 is the iiø7. A common progression in jazz and contemporary classical music is ii-V-I. If we were to consider a ii-V in G, it would be Am7-D7-G. The Am7b5 is not the typical ii chord in G. However, the question asks about the *function* of the Am7b5 *in relation to* the subsequent G major chord, within the broader context of C major. The Am7b5 contains the notes A, C, E, G♭. The G major chord contains G, B, D. The common tones are G. The relationship is not a direct diatonic one. Let’s re-evaluate the progression from a modal interchange perspective, even though it’s framed within a single key. If we consider C major as the tonic, the Am7b5 is the iiø7. The G major chord is the V chord. The progression iiø7 – V is not a standard diatonic progression. However, the Am7b5 can be reinterpreted. The notes A, C, E, G♭ can be seen as a subset of other harmonic contexts. Consider the possibility of a Neapolitan chord or a secondary dominant. The Am7b5 does not function as a Neapolitan chord. A secondary dominant to G major would be D7. Let’s focus on the *sound* and *voice leading* that makes this progression plausible in advanced harmonic contexts. The Am7b5 has a dissonant quality due to the tritone between A and E♭ (if it were Am7b5, it would be A, C, E♭, G♭. Assuming it’s Am7b5, the notes are A, C, E♭, G♭. If it’s A half-diminished, it’s A, C, E♭, G. The question states Am7b5, which is A, C, E♭, G♭. This is an augmented diminished seventh chord, not a half-diminished seventh. Let’s assume the question meant A half-diminished seventh, which is A, C, E♭, G. Then the progression is A, C, E♭, G to G, B, D. Common tone is G. E♭ to D is a semitone descent. C to B is a semitone descent. This is a plausible voice leading. However, if we strictly interpret Am7b5 as A, C, E♭, G♭, then the progression is A, C, E♭, G♭ to G, B, D. Common tone is G. E♭ to D is a semitone descent. C to B is a semitone descent. G♭ to D is an augmented sixth interval. This is less conventional. Let’s assume the question intended a common jazz/contemporary harmony concept where Am7b5 functions as a substitute or a chord leading to a dominant. The Am7b5 chord (A, C, E♭, G) can be seen as a iiø7 in B♭ minor (iiø7-V7-i). However, the target chord is G major. A key concept at the Modern School of Music Entrance Exam University is the understanding of altered chords and their functions. The Am7b5, when followed by G major, can be analyzed as a chord that creates chromatic tension leading to the dominant. The E♭ in the Am7b5 (assuming A half-diminished) resolves down to D in the G major chord. The C in the Am7b5 resolves down to B in the G major chord. The G is a common tone. This creates a smooth, albeit chromatic, transition. The most fitting description for this type of progression, where a chord outside the immediate diatonic context is used to lead to a dominant or tonic, is often related to modal interchange or chromatic substitution. Given the options, we need to identify the most accurate harmonic function. Let’s consider the possibility of the Am7b5 being a borrowed chord. If we consider C minor as a parallel minor, the iiø7 in C minor is Dm7b5. This doesn’t fit. Let’s consider the function of the Am7b5 as a pre-dominant. In C major, the ii chord is Dm. The iv chord is Fm. The vi chord is Am. The Am7b5 is a variation of the vi chord, with a flattened fifth. This flattening of the fifth creates a more dissonant, leading quality. When Am7b5 leads to G major (V of C), it functions as a chromatic pre-dominant, adding color and tension before the arrival of the dominant. This is a common technique in jazz harmony and contemporary classical composition, emphasizing the use of altered chords to create richer harmonic movement. The Am7b5 can be seen as a substitute for a ii chord or a chord that prepares the dominant through chromatic voice leading. The E♭ to D and C to B movements are characteristic of chromatic descent towards the dominant. This type of harmonic device is often explored in advanced harmony courses at the Modern School of Music Entrance Exam University to develop sophisticated compositional techniques. The progression Am7b5 to G major, within the context of C major, is best understood as a chromatic pre-dominant function. The Am7b5, with its inherent dissonance and chromatic intervals, creates a strong pull towards the G major chord, acting as a sophisticated way to prepare the dominant. This is not a simple diatonic substitution but a deliberate use of chromaticism to enhance harmonic color and drive. The specific voice leading (E♭ to D, C to B) highlights the chromatic nature of this preparation. This technique is a hallmark of advanced harmonic practice, emphasizing the composer’s ability to manipulate harmonic expectations and create compelling musical narratives, a skill highly valued at the Modern School of Music Entrance Exam University. Final Answer Calculation: The progression is from C major to G major. The chords are Am7b5 and G major. In C major, the diatonic chords are: Cmaj7, Dm7, Em7, Fmaj7, G7, Am7, Bm7b5. Am7b5 (A, C, E♭, G) is not diatonic to C major. G major (G, B, D) is the V chord in C major. The function of Am7b5 leading to G major is to provide a chromatic preparation for the dominant. The E♭ in Am7b5 resolves to D in G major (semitone descent). The C in Am7b5 resolves to B in G major (semitone descent). The G is a common tone. This chromatic movement is characteristic of a pre-dominant function that adds color and tension. Therefore, it acts as a chromatic pre-dominant.

The question probes the understanding of harmonic progression and voice leading principles within a specific contrapuntal context, relevant to advanced music theory studies at the Modern School of Music Entrance Exam University. The scenario describes a two-part invention where a melodic line is presented, and the task is to harmonize it in a manner that adheres to strict contrapuntal rules, particularly concerning the avoidance of parallel fifths and octaves, and the proper resolution of dissonances. Consider the given melodic line in the upper voice. To create a harmonically sound and contrapuntally correct lower voice, one must analyze the intervals created between the upper and lower voices at each beat. The core principle to avoid is the direct or hidden progression of perfect fifths or octaves between the two voices. This means that if two voices are a perfect fifth apart, they cannot both move to a note that is also a perfect fifth away from their new respective pitches. Similarly, if they are an octave apart, they cannot both move to pitches that are an octave apart. Let’s analyze a hypothetical progression. If the upper voice is on C and the lower voice is on G (a perfect fifth), and the next chord has the upper voice moving to D and the lower voice moving to A (also a perfect fifth), this constitutes parallel fifths. The same logic applies to octaves. Furthermore, dissonances, such as seconds, sevenths, and tritones, must be prepared (usually by step or common tone) and resolved by step in the direction that resolves the dissonance. The correct approach involves selecting lower voice notes that create consonant intervals (unisons, thirds, fifths, sixths, octaves) with the upper voice, while ensuring that any movement to new intervals avoids the forbidden parallels. This often requires careful consideration of the underlying harmonic progression and the melodic contour of both parts. For instance, if the upper voice ascends, the lower voice might descend to maintain smooth voice leading and avoid parallels. The selection of the correct option hinges on identifying the progression that most effectively maintains harmonic clarity, contrapuntal integrity, and melodic independence between the two voices, demonstrating a sophisticated understanding of Baroque-era contrapuntal practices, a cornerstone of study at the Modern School of Music Entrance Exam University. The correct option will be the one that demonstrates the most skillful avoidance of parallel perfect intervals and the appropriate handling of any implied dissonances, creating a musically coherent and technically sound two-part texture.

The question probes the understanding of harmonic function and its application in creating a sense of resolution within a musical context, specifically referencing the Modern School of Music Entrance Exam’s emphasis on advanced tonal harmony. The core concept tested is the dominant-to-tonic relationship, which is fundamental to Western tonal music. A V-I cadence, where the dominant chord (V) resolves to the tonic chord (I), is the most common and powerful way to establish the tonic key and create a feeling of finality. In C major, the dominant chord is G major (G-B-D), and the tonic chord is C major (C-E-G). The resolution of the leading tone (B in the G major chord) to the tonic (C) is a crucial element in this cadence. Therefore, a progression that moves from a chord functioning as dominant to a chord functioning as tonic will provide the strongest sense of harmonic closure. Considering the options, a ii-V-I progression in C major (Dm-G-C) is a classic example of this. The Dm (ii) chord often acts as a pre-dominant, leading to the V chord, which then resolves to I. The dominant function is most directly represented by the V chord. The question asks for the progression that *most strongly* establishes the tonic. While other cadences exist, the V-I is the archetypal resolution. The options provided are variations of common progressions. The progression that directly features the dominant chord resolving to the tonic chord will provide the most pronounced sense of tonic establishment.

The question probes the understanding of harmonic function and voice leading principles within a specific contrapuntal context, relevant to advanced music theory at the Modern School of Music Entrance Exam. The scenario presents a progression from a dominant seventh chord in first inversion to a tonic chord in root position. Specifically, it moves from a \(V^6\) to a \(I\). In a four-part texture, the dominant seventh chord in first inversion \(V^6_5\) typically has the seventh in the soprano or alto voice. When resolving to the tonic, the seventh of the dominant chord must resolve downwards by step. If the seventh is in the soprano, it resolves down to the third of the tonic chord. If the seventh is in the alto, it also resolves down to the third of the tonic chord. The leading tone (the third of the dominant chord) must resolve upwards to the tonic. The root of the dominant chord (in the bass) moves to the tonic. The fifth of the dominant chord moves to either the root or the fifth of the tonic chord. Consider the progression \(G^7\) in first inversion (Bass: B, Soprano: F, Alto: D, Tenor: G) resolving to \(C\) major (Bass: C, Soprano: C, Alto: E, Tenor: G). Here, the F (seventh of \(G^7\)) resolves down to E (third of \(C\)). The B (leading tone) resolves up to C (root of \(C\)). The G (root of \(G^7\)) moves to C (root of \(C\)). The D (fifth of \(G^7\)) moves to G (fifth of \(C\)). This is a standard and correct resolution. However, the question asks about a scenario where the leading tone is in the soprano and the seventh is in the alto. Let’s analyze this: \(V^6_5\) in first inversion means the third of the dominant chord is in the bass. For example, \(G^7\) in first inversion with B in the bass. If the leading tone (B) is in the soprano, and the seventh (F) is in the alto, the progression to \(C\) major would involve the soprano B resolving to C. The alto F would resolve down to E. The tenor might have G resolving to G, and the bass B resolving to C. This creates parallel octaves between the bass and soprano if both move to C. More critically, if the leading tone is in the soprano, it *must* resolve upwards to the tonic. If the seventh is in the alto, it *must* resolve downwards by step. The crucial constraint for the leading tone in the soprano is its upward resolution to the tonic. If the seventh is in the alto, it resolves down to the third of the tonic chord. The question implies a potential issue with voice leading. The most common error in this scenario, especially when the leading tone is in the soprano and the seventh is in the alto, is the potential for parallel octaves or fifths, or an awkward resolution of the seventh. The most fundamental rule violated when the leading tone is in the soprano and the seventh is in the alto, and the leading tone does not resolve upwards, is the leading tone’s imperative resolution. If the leading tone is in the soprano, it must resolve up to the tonic. If the seventh is in the alto, it must resolve down by step. The scenario described, with the leading tone in the soprano and the seventh in the alto, presents a specific challenge in maintaining smooth voice leading and avoiding forbidden parallels, particularly if the seventh is not handled correctly. The most direct violation of fundamental voice-leading principles in this specific configuration, when aiming for a tonic chord, is the failure of the leading tone to resolve upwards, or an incorrect resolution of the seventh. The question is designed to test the understanding of the leading tone’s obligatory upward resolution when it appears in the soprano voice, a core tenet of traditional counterpoint taught at the Modern School of Music Entrance Exam. The resolution of the seventh is also critical, but the leading tone’s position in the soprano carries a stronger imperative for upward resolution. Therefore, the most significant voice-leading error would be the failure of the leading tone in the soprano to resolve upwards to the tonic.

The question probes the understanding of harmonic function and voice leading principles within a contrapuntal context, specifically concerning the resolution of dissonances and the establishment of tonal centers. In a four-part chorale setting at the Modern School of Music Entrance Exam, a common challenge is maintaining smooth voice leading while adhering to harmonic conventions. Consider a progression where a diminished seventh chord (e.g., C#dim7: C#, E, G, Bb) precedes a tonic chord (e.g., G major: G, B, D). The diminished seventh chord, due to its inherent instability and tendency to resolve, requires careful handling. The leading tone of the key (B in G major) is often found within the diminished seventh chord, and its resolution is crucial. The diminished seventh interval (e.g., C# to Bb) typically resolves outwards by a semitone (C# to D, Bb to B), or the outer voices resolve in contrary motion. In the context of a chorale, the inner voices must also resolve correctly to avoid parallel perfect intervals and to maintain melodic smoothness. The diminished seventh chord’s tendency to resolve to a dominant chord (or a chord a third above its root) is a key principle. If the diminished seventh chord is built on the leading tone of the dominant (e.g., F#dim7 in G major, which would be F#, A, C, Eb), it would typically resolve to the dominant chord (D major). However, the question presents a scenario where the diminished seventh chord precedes the tonic. The resolution of the diminished seventh chord to the tonic chord requires specific voice leading. The leading tone of the tonic (B in G major) must resolve upwards to the tonic (G). The seventh of the diminished seventh chord (Bb in C#dim7) typically resolves downwards by step to the third of the tonic chord (B in G major). The root of the diminished seventh chord (C#) can resolve up to the fifth of the tonic chord (D), and the third of the diminished seventh chord (E) can resolve down to the root of the tonic chord (G). Alternatively, the diminished seventh chord could be interpreted as a secondary diminished seventh chord, leading to a dominant function. If the diminished seventh chord is C#dim7, it could function as a leading-tone chord to D major (V/V in G). In this case, C#dim7 would resolve to D major (D, F#, A). The question, however, implies a direct resolution to the tonic. The most common and stylistically appropriate resolution of a diminished seventh chord to a tonic chord involves the leading tone of the diminished seventh chord resolving upwards to the tonic, and the seventh of the diminished seventh chord resolving downwards by step to the third of the tonic chord. For instance, if the diminished seventh chord is built on the leading tone of the dominant (e.g., F#dim7 in G major), it resolves to the dominant (D major). If the diminished seventh chord is built on the leading tone of the tonic (e.g., F#dim7 in G major, if G were the tonic, F# is the leading tone), it would resolve to the tonic. However, diminished seventh chords are often used to create chromatic tension. A diminished seventh chord built on the leading tone of the dominant (e.g., C#dim7 in D major, which is the dominant of G) would resolve to D major. The question asks about a diminished seventh chord resolving to a tonic. The critical aspect is the resolution of the dissonant intervals within the diminished seventh chord. The augmented sixth interval (e.g., C# to Bb) typically resolves outwards by semitone. The diminished fifth interval (e.g., E to Bb) resolves inwards by semitone. The diminished seventh chord’s tendency to resolve to a chord a third above its root is a strong indicator. If we consider a diminished seventh chord built on the leading tone of the dominant, it resolves to the dominant. For example, in C major, Bdim7 (B, D, F, Ab) resolves to C major. The leading tone B resolves up to C. The seventh Ab resolves down to G. The F resolves down to E. The D resolves up to F. This is a common resolution. The question asks about a diminished seventh chord resolving to a tonic. The core principle is the resolution of the leading tone and the seventh. The leading tone of the diminished seventh chord (the highest note in root position) typically resolves up by a semitone. The seventh of the diminished seventh chord (the lowest note in root position) typically resolves down by a semitone. The other two notes resolve by step. The most common resolution of a diminished seventh chord is to a dominant chord. However, it can also resolve to a tonic chord, often with specific voice leading. The diminished seventh chord is inherently unstable and seeks resolution. The interval of a diminished seventh (e.g., C#-Bb) resolves outwards to an octave or a sixth. The interval of a diminished fifth (e.g., E-Bb) resolves inwards to a perfect fifth or a third. In the context of a chorale at the Modern School of Music Entrance Exam, the resolution of the leading tone of the diminished seventh chord to the tonic is paramount. The leading tone of the diminished seventh chord (the highest note in root position) must resolve upwards to the tonic. The seventh of the diminished seventh chord must resolve downwards by step. The other two notes resolve by step to complete the tonic chord. The diminished seventh chord functions as a highly chromatic and unstable sonority that strongly pulls towards resolution. Its symmetrical nature (built of minor thirds) allows for enharmonic reinterpretation, but in a functional harmonic context, its resolution is guided by the tendency of its constituent intervals. The leading tone within the diminished seventh chord (the note a semitone below the root of the chord it resolves to) will resolve upwards to the tonic. The seventh of the diminished seventh chord (the note a whole tone below the root of the chord it resolves to) will resolve downwards by step. The remaining two notes will resolve by step to form the tonic chord. Therefore, the most crucial aspect of the resolution of a diminished seventh chord to a tonic chord is the correct stepwise resolution of its dissonant intervals, particularly the leading tone and the seventh, to establish the tonic sonority clearly and avoid awkward leaps or parallel motion. The diminished seventh chord’s ability to function as a leading-tone chord to the dominant, or as a chromatic passing chord, makes its resolution a fundamental concept in tonal harmony. The question tests the understanding of how the inherent tension within the diminished seventh chord is released through specific voice-leading patterns that reinforce the stability of the tonic. The correct answer focuses on the resolution of the leading tone and the seventh of the diminished seventh chord, which are the most critical elements for a smooth and tonally secure progression to the tonic. The diminished seventh chord’s characteristic sound arises from the diminished seventh interval and the diminished fifth interval. These intervals create a strong pull towards resolution. The leading tone of the diminished seventh chord (the note a semitone below the tonic of the chord it resolves to) must resolve upwards to the tonic. The seventh of the diminished seventh chord (the note a whole tone below the tonic of the chord it resolves to) must resolve downwards by step. The other two notes of the diminished seventh chord will resolve by step to complete the tonic chord. This ensures a smooth and tonally coherent progression, which is a cornerstone of harmonic practice taught at the Modern School of Music Entrance Exam.

The question probes the understanding of harmonic function and its application in creating a sense of resolution within tonal music, a core concept at the Modern School of Music Entrance Exam. The progression V-I (dominant to tonic) is the most fundamental cadence in Western tonal harmony, providing the strongest sense of closure. In the key of C major, the dominant chord is G major (G-B-D), and the tonic chord is C major (C-E-G). The resolution from G major to C major involves the leading tone (B) resolving upwards to the tonic (C), and the dominant root (G) typically resolving to the tonic root (C). This movement creates a strong sense of arrival and completion. Other progressions, while harmonically valid, do not offer the same degree of finality. For instance, a ii-V-I progression (Dm-G-C) is common and strong, but the V-I is the final, resolving element. A IV-V-I (F-G-C) is also strong, with the IV chord often acting as a pre-dominant. A iii-vi-ii-V-I (Em-Am-Dm-G-C) is a more complex but still ultimately tonic-resolving progression. The question requires identifying the progression that most definitively establishes the tonic center, which is the V-I cadence.

The question probes the understanding of harmonic function and voice leading principles within a contrapuntal context, specifically concerning the resolution of dissonances and the establishment of tonal centers. In the given scenario, a composer at the Modern School of Music Entrance Exam is exploring a passage that moves from a dominant seventh chord in first inversion (vii°⁶/V) to a tonic chord in root position (I). The dominant seventh chord in first inversion, when resolving to the tonic, often presents a leading tone in the bass. The leading tone (the seventh degree of the scale) has a strong tendency to resolve upwards by a half step to the tonic. The third of the dominant seventh chord (which is the supertonic) typically resolves downwards by step to the tonic. The fifth of the dominant seventh chord (the dominant) resolves downwards by step to the tonic. The seventh of the dominant seventh chord (the leading tone of the dominant chord, which is the sixth of the tonic scale) resolves downwards by step to the tonic. Consider a progression in C major: G7/B (B-D-F-G) resolving to C major (C-E-G). In first inversion (G7/B), the chord tones are B, D, F, G. The bass note is B. The leading tone to C is B. The dominant chord is G7. The leading tone of G is F#. The dominant of C is G. The leading tone of C is B. The chord is G7 in first inversion, meaning B is in the bass. The chord tones are B, D, F, G. The resolution is to C major (C, E, G). Let’s analyze the voice leading from G7/B to C: Bass: B resolves to C (up by half step). This is the leading tone resolving to the tonic. Other voices: If D is in an upper voice, it typically resolves down to C. If F is in an upper voice, it typically resolves down to E. If G is in an upper voice, it typically resolves to G (common tone) or down to E. The question asks about the *most* characteristic resolution of the leading tone within this specific harmonic context. The leading tone, by its very nature, creates melodic tension that demands resolution to the tonic. This upward resolution by a half step is a fundamental principle of tonal harmony and is crucial for establishing the tonic center. While other voices have their own resolutions, the leading tone’s upward movement to the tonic is paramount for structural integrity and harmonic clarity, especially in the context of a strong cadence like V7 to I. The specific inversion of the dominant seventh chord (first inversion) places the leading tone in the bass, emphasizing its role and requiring its characteristic upward resolution to the tonic. This upward resolution of the leading tone is a cornerstone of Western tonal music and a key concept taught at institutions like the Modern School of Music Entrance Exam. The other options represent either incorrect resolutions or resolutions that are less fundamental to the function of the leading tone in this specific progression. For instance, a downward resolution of the leading tone would weaken the sense of arrival on the tonic.

The question probes the understanding of harmonic function and voice leading principles within the context of chromaticism, specifically focusing on the resolution of altered tones in a late Romantic or early 20th-century harmonic language, as is often explored at the Modern School of Music Entrance Exam. The scenario presents a dominant seventh chord in second inversion (V6/5) leading to a tonic chord. The crucial element is the augmented sixth interval created by the altered tone. In a typical dominant function, the leading tone (scale degree 7) resolves upwards by a half step to the tonic (scale degree 1). When this leading tone is chromatically raised (e.g., G# in the key of A minor, functioning as the leading tone to A), it creates an augmented sixth with the tonic note (e.g., G# to A). However, the question specifies a diminished seventh chord in root position, which is often used as a substitute for a dominant seventh chord, particularly in its ability to resolve to multiple tonalities. The diminished seventh chord, when functioning as a pre-dominant or secondary dominant substitute, typically resolves to a dominant chord. The diminished seventh chord built on the leading tone of the dominant (vii°7/V) resolves to V. In the key of C major, the dominant is G major. The leading tone of G is F#. A diminished seventh chord built on F# would be F#-A-C-Eb. This chord resolves to G major. However, the question presents a diminished seventh chord in root position and asks about its resolution to a tonic chord, implying a direct tonicization or a deceptive resolution. A diminished seventh chord built on the leading tone of the tonic (vii°7/I) resolves to I. In C major, the leading tone is B. A diminished seventh chord built on B would be B-D-F-Ab. This chord resolves to C major. The augmented sixth interval within this chord is F-Db (enharmonically F-C#). The resolution of this diminished seventh chord (B-D-F-Ab) to C major would involve B resolving to C, D resolving to C or E, F resolving to E, and Ab resolving to G. The augmented sixth interval F-Db (or F-C#) in the B diminished seventh chord (B-D-F-Ab) is not the primary characteristic interval for tonic resolution. The question is designed to test the understanding of how diminished seventh chords, particularly those derived from the leading tone of the tonic, function and resolve. The diminished seventh chord built on the leading tone of the tonic (vii°7/I) is a common pre-tonic chord. In C major, this chord is B-D-F-Ab. The resolution to C major involves B resolving to C, D resolving to E, F resolving to E, and Ab resolving to G. The interval between F and Ab is a minor third. The interval between D and F is a minor third. The interval between B and D is a minor third. The interval between B and Ab is a diminished seventh. The question asks about the resolution of a diminished seventh chord in root position to a tonic chord, specifically focusing on the augmented sixth interval. A diminished seventh chord built on the leading tone of the tonic (vii°7/I) contains an augmented sixth interval between its third and seventh (e.g., in B°7/C, the interval between D and Ab is a diminished seventh, and between F and Ab is a minor third. The interval between B and F is a diminished fifth. The interval between B and Ab is a diminished seventh). The question is likely referring to the diminished seventh chord that *contains* an augmented sixth interval that resolves outwards. This is the diminished seventh chord built on the lowered supertonic (ii°7) or the leading tone of the dominant (vii°7/V). However, the question specifies resolution to a *tonic* chord. The diminished seventh chord built on the leading tone of the tonic (vii°7/I) is the most direct diminished seventh chord resolution to the tonic. In C major, this is B-D-F-Ab. The interval between F and Ab is a minor third. The interval between D and F is a minor third. The interval between B and D is a minor third. The interval between B and Ab is a diminished seventh. The question is likely referencing the diminished seventh chord built on the lowered sixth scale degree, which functions as a Neapolitan chord’s enharmonic equivalent or a chromatic mediant. However, the most common diminished seventh chord that resolves to a tonic and contains an augmented sixth interval that resolves outwards is the vii°7/I. In C major, this is B-D-F-Ab. The augmented sixth interval is not directly present within this chord in its standard spelling. The question is likely testing the understanding of the diminished seventh chord built on the leading tone of the dominant, which resolves to the dominant, and then the dominant resolves to the tonic. For example, in C major, the dominant is G. The leading tone of G is F#. The diminished seventh chord built on F# is F#-A-C-Eb. This chord resolves to G major. The augmented sixth interval is A-Eb. This resolves outwards to the octave G. The question asks about resolution to a *tonic* chord. The diminished seventh chord that most directly resolves to the tonic and contains an augmented sixth interval that resolves outwards is the diminished seventh chord built on the leading tone of the tonic. In C major, this is B-D-F-Ab. The augmented sixth interval is not explicitly present in this spelling. However, if we consider the enharmonic spelling of the diminished seventh chord, or its function as a pivot, the question might be alluding to the diminished seventh chord built on the lowered third scale degree, which functions as a secondary leading-tone chord. Let’s re-evaluate the premise. The question asks about a diminished seventh chord in root position resolving to a tonic chord, and specifically mentions an augmented sixth interval. The diminished seventh chord built on the leading tone of the tonic (vii°7/I) is the most common diminished seventh chord that resolves directly to the tonic. In C major, this is B-D-F-Ab. The interval between F and Ab is a minor third. The interval between D and F is a minor third. The interval between B and D is a minor third. The interval between B and Ab is a diminished seventh. The augmented sixth interval is not inherent in this spelling. However, the diminished seventh chord built on the lowered supertonic (ii°7) can resolve to the tonic. In C major, this would be D-F-Ab-Cb. This chord resolves to C major. The augmented sixth interval here is Ab-Cb (enharmonically Ab-B). This resolves outwards to C. Therefore, the diminished seventh chord built on the lowered supertonic (ii°7) is the correct answer. The calculation is conceptual: identify the diminished seventh chord built on the lowered supertonic in a given key (e.g., C major), identify the augmented sixth interval within it, and describe its resolution to the tonic. The lowered supertonic in C major is D. The diminished seventh chord built on D is D-F-Ab-Cb. The augmented sixth interval is Ab-Cb. This resolves to C-C (an octave). The question tests a nuanced understanding of chromatic harmony and voice leading, particularly the function and resolution of diminished seventh chords in late tonal music, a core area of study at the Modern School of Music Entrance Exam. Diminished seventh chords are inherently unstable due to their symmetrical structure and the presence of dissonant intervals. Their resolution is crucial for establishing tonal centers. The diminished seventh chord built on the lowered supertonic (ii°7) is a sophisticated chromatic device that often functions as a pre-dominant or a substitute for a dominant chord. In the key of C major, the lowered supertonic is D. The diminished seventh chord built on D is D-F-Ab-Cb. This chord contains the interval of an augmented sixth between Ab and Cb (enharmonically Ab-B). This augmented sixth interval is a hallmark of chromatic harmony and possesses a strong tendency to resolve outwards by a half step to an octave. In this case, Ab resolves up to B, and Cb resolves down to C, forming the octave C-C. The chord D-F-Ab-Cb, when resolving to C major, typically involves D moving to C, F moving to E, Ab moving to G, and Cb resolving to C. This specific resolution of the augmented sixth interval (Ab-Cb to C-C) is a key element in understanding the chord’s function and its ability to lead to the tonic. This type of harmonic progression is frequently encountered in the repertoire studied at the Modern School of Music Entrance Exam and requires a deep grasp of theoretical concepts beyond basic triads and seventh chords. Understanding the enharmonic equivalence of intervals and chords, and how these equivalences facilitate modulation and chromaticism, is vital for advanced musical analysis and composition. The ability to identify and analyze such progressions demonstrates a candidate’s readiness for the rigorous theoretical training at the Modern School of Music Entrance Exam.