Questions: Perfect vs. Diminished vs. Augmented Intervals

Question 1

A violinist plays C–Ab in a passage where Ab resolves down to G (part of a G-major arrival). A second violinist plays the enharmonically equivalent C–G# in a passage where G# rises to A. Acoustically these two intervals span the same 8 semitones. Musically, how should a trained listener hear them?

• A. As identical — enharmonic equivalents always sound the same in any musical context
• B. As different — same acoustic distance but different resolution tendencies: Ab pulls down toward G while G# pulls up toward A
• C. As different only because of the key signatures written in the score, not from the sound itself
• D. As identical in isolation but distinguishable only because of what precedes them

Answer: (B)

This is the key insight: enharmonic equivalents (augmented fifth C–G# and minor sixth C–Ab) span the same semitones and sound acoustically identical in isolation. But in tonal context, G# is a raised note with upward resolution tendency, while Ab is a lowered note with downward resolution tendency. A trained ear hears not just the raw interval size but the directional pull — which note wants to move, and in which direction. Acoustic size and harmonic function diverge for enharmonic equivalents.

Question 2

Why is the tritone the most useful anchor interval when learning to recognize altered perfect intervals by ear?

• A. It is the easiest interval to sing accurately in tune
• B. It is the only interval that can be spelled as both augmented and diminished
• C. Its extreme instability — splitting the octave exactly in half with no simple frequency ratio — gives it an unmistakable, restless sound unlike any other interval
• D. It is the most frequently occurring interval in Western tonal repertoire

Answer: (C)

The tritone's distinctive sound comes from its lack of any simple frequency ratio: unlike perfect intervals (2:1, 3:2, 4:3) or consonant thirds, the tritone produces maximum dissonance because it has no stable acoustic basis. Splitting the octave exactly in half creates a tense, restless quality that is impossible to confuse with other intervals once heard. The topic recommends it as 'the most distinctive sound' — making it the ideal fixed reference point from which to compare augmented and diminished perfect intervals.

Question 3

An augmented fifth (e.g., C–G#) and a minor sixth (e.g., C–Ab) span the same number of semitones but typically resolve in opposite directions in tonal music.

• T. True
• F. False

Answer: True

Both span 8 semitones — they are enharmonically equivalent in terms of acoustic size. But in tonal context, the raised note G# carries an upward resolution tendency (toward A), while the lowered note Ab carries a downward tendency (toward G). The ear, trained in tonal harmony, hears this directional pull and distinguishes the intervals functionally even though they are acoustically identical in isolation. This is the central ear-training lesson the topic emphasizes.

Question 4

Perfect intervals (fourths, fifths, octaves, unisons) are a subcategory of major intervals — a perfect fifth is simply a type of major fifth.

• T. True
• F. False

Answer: False

Perfect intervals form their own category, entirely separate from the major/minor system. Unisons, fourths, fifths, and octaves have no major or minor versions — they are perfect. Their acoustic stability (simple frequency ratios: 2:1, 3:2, 4:3) sets them apart from the intervals that come in major/minor pairs. The quality system for perfect intervals is perfect/diminished/augmented. Calling a perfect fifth a 'major fifth' is a category error — it conflates two distinct quality systems.

Question 5

Why does the ear need to learn both the raw acoustic size of an interval AND its resolution tendency, and when does this distinction matter most?

Model answer: Raw acoustic size tells you what the interval sounds like in isolation. Resolution tendency tells you how the interval behaves in musical context — which note wants to move and in which direction. These diverge whenever two intervals are enharmonically equivalent: an augmented fifth and a minor sixth sound the same out of context but resolve differently within a progression. The distinction matters most when recognizing chromatic harmony, where enharmonic reinterpretation — respelling a chord to change its apparent resolution — is a central compositional technique.

If you only hear acoustic size, you cannot predict how a melody will continue or how a chord will resolve. Training the ear to hear resolution tendency — the 'directional pull' of raised vs. lowered notes — is what allows a musician to hear harmony as movement rather than as a static stack of intervals. This skill is essential for chromatic and Romantic repertoire, where enharmonic pivots appear constantly and the same sonic object carries different functional meanings depending on its spelling and context.