Lesson 4: Intervals

Key Takeaways

Every interval has two components: generic size (lines/spaces on staff) and specific size (diminished/minor/perfect/major/augmented)
Family I (unisons, 4ths, 5ths, octaves) use dim/perfect/aug; Family II (2nds, 3rds, 6ths, 7ths) use dim/minor/major/aug — never cross families
Inversion rule: specific quality flips (major↔minor, aug↔dim, perfect stays); generic numbers add to 9

Melodic interval: two notes in succession; harmonic interval: two notes sounded simultaneously — measured identically
Simple interval: octave or smaller; compound interval: larger than an octave — treat compound as simple + octave(s)

Melodic and harmonic intervals

Count lines and spaces spanned on the staff (inclusive) → unison through octave
Unaffected by clef changes or accidentals — C♯ to E𝄫 is still some kind of third

Generic interval sizes on staff

Family	Generic Sizes	Available Qualities
I	Unisons, 4ths, 5ths, Octaves	Diminished · Perfect · Augmented
II	2nds, 3rds, 6ths, 7ths	Diminished · Minor · Major · Augmented

Semitone reference chart (use only as fallback):

Semitones	0	1	2	3	4	5	6	7	8	9	10	11	12
Name	P1	m2	M2	m3	M3	P4	d5	P5	m6	M6	m7	M7	P8

Family I (4ths & 5ths): Does the top note appear in both major and minor scales of the bottom note?

Yes → Perfect; No → reckon as ±1 semitone from perfect → aug or dim
Speed tip: matched accidentals (both ♯, both ♭, or both ♮) = Perfect — except B & F, which need mixed accidentals to be perfect

Family II (3rds, 6ths, 7ths): Does the top note appear in the major or minor scale of the bottom note?

In major scale → Major; in minor scale → Minor; neither → modify up/down from the known interval
⚠️ This scale method does not work for 2nds — count semitones instead

Inversion diagram

Practical trick for hard intervals: invert → ID the now-small interval → re-invert using the chart