9/9 9. Cumulative Exercises and Review

A reliable problem-solving sequence

The central method is to move from local details to larger musical meaning. Begin by identifying the clef, key signature, and meter. Then determine the pitches and their scale-degree relationships, check durations and strong beats, identify or construct the chords, label them with Roman numerals, and interpret their harmonic functions.

This order prevents isolated mistakes. For example, an accidental should be understood in relation to the key rather than treated as an unrelated pitch event. Likewise, a chord label is more informative when its inversion, phrase position, and surrounding progression are also considered.

Takeaway: Read a passage from notation and pitch, through rhythm and chords, toward harmonic function and phrase interpretation.

Pitch, keys, and scale relationships

A major scale follows the whole-step and half-step pattern

where $W$ means whole step and $H$ means half step. In G major, the scale is G–A–B–C–D–E–F♯–G. The notes B, E, F♯, and C are scale degrees $3$, $6$, $7$, and $4$, respectively. F♯ is the leading tone because it is scale degree $7$, a half step below the tonic G.

The key signature establishes a recurring collection of accidentals. An isolated accidental normally applies for the rest of the measure at the same staff position. In the examples reviewed here, D major has F♯ and C♯ and its relative minor is B minor; A major has F♯, C♯, and G♯ and its relative minor is F♯ minor; F major has B♭ and its relative minor is D minor; E♭ major has B♭, E♭, and A♭ and its relative minor is C minor.

Minor scales require attention to form. Natural minor uses the unaltered minor collection, while raising the leading tone for harmonic-minor harmony strengthens dominant motion. In A minor, raising G to G♯ changes the dominant harmony from a minor triad to a major triad.

Takeaway: Key signatures define the normal pitch collection, while scale degrees explain how individual pitches behave within that collection.

Intervals, rhythm, and meter

An interval has two parts: generic size and quality. Generic size counts letter names, while quality identifies the exact semitone distance. Thus C–G is a perfect fifth, E–F is a minor second, B♭–D is a major third, F♯–C♯ is a perfect fifth, and A–F is a minor sixth. Intervals are melodic when the pitches occur successively and harmonic when they sound together.

To invert an interval, place the lower note above the upper note or the upper note below the lower note. The generic sizes of an interval and its inversion add to $9$. Perfect intervals remain perfect under inversion; major intervals become minor, and minor intervals become major.

A meter organizes beats into measures. In simple meter, beats divide into two; in compound meter, beats divide into three. A time signature such as $\frac{4}{4}$ indicates four quarter-note beats in a measure, while $\frac{6}{8}$ is commonly understood as compound because its beats divide into groups of three eighth notes. A dot adds half of a note’s original value, and a tie combines durations across notes or bar lines.

When checking a measure, add durations rather than relying on visual appearance. In $\frac{4}{4}$, a quarter note plus a half note leaves a quarter-note duration. In $\frac{3}{4}$, a dotted quarter note leaves three eighth-note units. Three eighth notes plus a dotted quarter note already complete $\frac{6}{8}$.

Takeaway: Interval names describe pitch distance, while meter and duration describe how musical time is organized.

Triads, seventh chords, and inversions

A triad is built by stacking two thirds above a root. In a major key, the diatonic triads follow this pattern:

• $I$: major

• $ii$: minor

• $iii$: minor

• $IV$: major

• $V$: major

• $vi$: minor

• $vii^\circ$: diminished

In C major, these are the complete set of diatonic triad labels. In natural A minor, the pattern is $i$, $ii^\circ$, $III$, $iv$, $v$, $VI$, and $VII$. Raising the leading tone produces a stronger dominant, especially the major $V$ triad and the dominant seventh chord.

Chord identification should include root, quality, and key. For example, E–G–C in C major is a C-major triad in first inversion, so it is $I^6$. D–F♯–A–C in G major is a dominant seventh chord, $V^7$. B♭–D–F in F major is $IV$, A–C♯–E in D minor is $V$, and D–F–A♭ in E♭ major is $vii^\circ$.

Inversion is determined by the bass note, not by the order of the upper voices. C–E–G with E in the bass is first inversion; G–B–D–F with F in the bass is third inversion; A–C–E with A in the bass is root position; and F–A–C with C in the bass is second inversion.

Takeaway: Identify a chord from its pitch collection, then refine the label by considering quality, root, bass note, and key.

Function, progression, and cadence

Harmonic function groups chords according to their tendency within a key. The three broad categories are tonic, predominant, and dominant.

• Tonic: $I$, and often $vi$ or $iii$ in suitable contexts.

• Predominant: $ii$ and $IV$.

• Dominant: $V$ and $vii^\circ$.

A common tonal progression moves from tonic toward predominant, then dominant, and finally back to tonic. In C major, the progression $I–ii–V–I$ demonstrates this path clearly. The final $V–I$ motion supplies the strongest dominant-to-tonic closure.

Function is contextual. The Roman numeral identifies the chord’s relation to the key, but the same chord can have different interpretive weight depending on what precedes and follows it. The chord $vi$, for instance, may act as a tonic substitute, while $ii$ and $IV$ commonly prepare the dominant.

A cadence describes how a phrase ends. An authentic cadence uses dominant-to-tonic motion. A half cadence ends on the dominant, leaving the phrase open. A final $vi$ after $V$ may create a deceptive or non-final ending rather than the full closure expected from $V–I$.

Takeaway: Roman numerals identify chords, but harmonic function and cadence explain what those chords do in a phrase.

From notation to complete harmonic analysis

Integrated analysis combines every preceding skill. Consider the progression in G major:

The first and last chords are tonic, $IV$ and $ii$ are predominant, and $V^7$ is dominant. The final $V^7–I$ creates an authentic-cadence pattern.

For a melody in C major written in $\frac{4}{4}$, verify the number of beats before analyzing pitch. A passage containing C4, D4, and E4 with durations of quarter, quarter, and half note fills one measure. A third measure containing C4 for a half note, G3 for a quarter note, and C4 for a quarter note also fills the measure; if the final note is omitted, the measure is short by one quarter-note beat. Scale-degree analysis then identifies C, D, E, G as $1$, $2$, $3$, and $5$ in C major.

Chord-to-melody matching uses prominent melody notes as evidence, but more than one harmony may be possible. The four-measure pattern C–E–G–E, D–F–A–F, G–B–D–B, C–G–E–C supports $I–ii–V–I$, with $V$ supplying the strongest dominant-to-tonic motion.

Harmonic rhythm concerns when those chord changes occur. The progression

changes harmony once per measure. The progression

changes harmony twice in each of the first three measures, so it has a faster harmonic rhythm while still suggesting predominant–dominant–tonic motion.

For mixed notation, reconstruct incomplete chords from the bass and upper notes. In F major, the bass sequence F–G–C–F with upper notes A–C, B♭–D, E–G, and A–C completes the progression $I–ii–V–I$. The final tonic restores the key and produces closure.

A complete analysis should report the key, meter, scale degrees, intervals, chord roots and qualities, inversions, Roman numerals, harmonic rhythm, functions, and cadence or other phrase ending. A sequence such as $I–iii–IV–V–vi$ may have correct Roman numerals but still be incomplete if it does not explain inversion, function, phrase position, or the potentially deceptive ending on $vi$.

Takeaway: Strong analysis connects notation, pitch, rhythm, harmony, and phrase structure instead of treating each feature as an isolated exercise.

Final synthesis and self-check

A composition-and-analysis task in D major can serve as a final synthesis. Write four measures in $\frac{4}{4}$ using at least four note values, one rest, and one tied or dotted rhythm. Begin with a tonic-related pitch, include a melodic third and a melodic step, and end on scale degree $1$.

Then place at least four different diatonic chords beneath the melody. Include a predominant chord before a dominant chord and aim for an authentic cadence at the end. The written analysis should identify:

1. Key and meter.

2. Scale-degree numbers for the melody.

3. Interval labels for three successive note pairs.

4. Roman numerals for the harmony.

5. Chord inversions.

6. Harmonic rhythm.

7. A brief description of the phrase.

Before accepting the result, check each layer in order: do the durations fill every measure, do the pitches belong to the stated key or have deliberate accidentals, do the chords support important melody notes, does the predominant lead convincingly to the dominant, and does the ending support the intended cadence?

Final checklist:

• What are the key and meter?

• What are the scale degrees and intervals?

• What chords are present, and are any inverted?

• How quickly does the harmony change?

• Which chords function as tonic, predominant, or dominant?

• Does the phrase establish an authentic cadence, a half cadence, or a less conclusive ending?

• Roman-numeral analysis