You’ve been using intervals without naming them. A chord is built from intervals. A melody moves by intervals. Every time you stacked a root and a fifth, or stepped from one note to the next—that was an interval. This lesson names every distance from 1 to 12 semitones, teaches interval quality, and reveals the tritone—the most unstable interval and the reason V7→I resolves.
s(), note(), stack(), cat(), setcpm(35),
mini-notation (~ * [] <> / @),
.gain(), .pan(),
.lpf(), .lpq(), .attack(), .decay(),
.sustain(), .release(),
.room(), .size(),
.delay(), .delaytime(), .delayfeedback(),
.distort(), chord notation [c3,eb3,g3],
progressions with <>,
.every(), .sometimes(), .jux(), .off(),
arrangement with cat() and gain automation,
scales, modes, chords, and the phonk palette from EDM.4–8c.
Two notes at the same time. The distance between them is an interval. Hit play:
First cycle: two C3s. Same pitch, same note—unison. Zero semitones apart. Second cycle: C3 and C4. One octave. Twelve semitones. The widest interval before you repeat the same note name.
Now walk up from C3, one semitone at a time. All 13 intervals from unison to octave:
Thirteen intervals, one per cycle. C3 stays fixed on the bottom. The top note climbs one semitone each time. Some sound smooth—consonant, stable. Others grate—dissonant, tense. Each distance has its own character.
The distance between two pitches, measured in semitones. Every interval has a name based on its size and quality. A chord is intervals stacked from a root. A melody is intervals played in sequence.
The full map. Every interval from 0 to 12 semitones:
| semitones | name | abbr | character | example |
|---|---|---|---|---|
| 0 | Unison | P1 | identical | C–C |
| 1 | Minor 2nd | m2 | tense, close | C–Db |
| 2 | Major 2nd | M2 | step, motion | C–D |
| 3 | Minor 3rd | m3 | dark, sad | C–Eb |
| 4 | Major 3rd | M3 | bright, happy | C–E |
| 5 | Perfect 4th | P4 | open, suspended | C–F |
| 6 | Tritone | TT | unstable, demonic | C–Gb |
| 7 | Perfect 5th | P5 | stable, powerful | C–G |
| 8 | Minor 6th | m6 | bittersweet | C–Ab |
| 9 | Major 6th | M6 | warm, sweet | C–A |
| 10 | Minor 7th | m7 | bluesy, tense | C–Bb |
| 11 | Major 7th | M7 | bright tension | C–B |
| 12 | Octave | P8 | same note, higher | C–C |
In the 13-interval editor, listen for which intervals sound stable and which sound tense. The perfect intervals (0, 5, 7, 12) are the anchors. The tritone (6) is the most restless. Try pausing on one you like—delete the other cat() entries and loop just that pair.
Intervals come in families. Perfect intervals: P1, P4, P5, P8—they’re neither major nor minor, just stable. Major/minor intervals: 2nds, 3rds, 6ths, 7ths—they come in pairs, one semitone apart. And the tritone at 6 semitones, which belongs to no family.
The most important pair: minor 3rd vs major 3rd. This is the interval that decides whether a chord is major or minor:
First cycle: C and Eb. Minor 3rd. Dark. Second cycle: C and E. Major 3rd. Bright. One semitone difference between them. That single semitone is why C minor and C major feel so different. The 3rd is the identity of the chord.
Perfect intervals (P1, P4, P5, P8) are neither major nor minor. 2nds, 3rds, 6ths, 7ths come in major and minor pairs—always one semitone apart. Major = wider = brighter. Minor = narrower = darker. The quality determines the character.
Flip an interval: move the bottom note up an octave. What was a major 3rd becomes something else. Hit play:
C–E is a major 3rd (4 semitones). E–C is a minor 6th (8 semitones). Same two note names, different order, different interval. The sizes add to 12. The qualities swap: major becomes minor. Perfect stays perfect.
Flip an interval by moving the bottom note up an octave. Major becomes minor. Perfect stays perfect. The semitone counts always add to 12. M3 (4) inverts to m6 (8). P4 (5) inverts to P5 (7). m2 (1) inverts to M7 (11).
Invert P4: change [c3,e3] to [c3,f3] and [e3,c4] to [f3,c4]. C–F is P4 (5 semitones). F–C is P5 (7 semitones). Now try m2: [c3,db3] inverts to [db3,c4]—M7. The tightest interval inverts to the widest.
Six semitones. Exactly half an octave. The most unstable interval in tonal music. Hit play:
Tense. Restless. It wants to move somewhere. It doesn’t rest. Historically called “diabolus in musica”—the devil in music.
Now hear what happens when the tritone resolves. B and F live inside a G7 chord. When G7 moves to C major, B pulls up to C and F pulls down to E:
G7 contains B and F—a tritone. They resolve outward: B steps up to C, F steps down to E. That’s why V7→I resolves. The tritone inside the dominant chord creates the tension. The tonic chord releases it. Every V7→I you’ve ever heard works because of this.
6 semitones. Exactly half an octave. The most unstable interval. Found inside every dominant 7th chord—between the 3rd and the 7th of that chord. Its resolution outward is the engine of tonal harmony. V7→I works because the tritone inside the V7 demands resolution.
The phonk progression. Four bars. Listen for the G7 in bar 4—it has the tritone (B and F) that pulls back to Cm in bar 1:
Bar 4: G7 — [g2,b2,d3,f3]. B and F are a tritone apart. When it loops to bar 1, Cm7 — [c3,eb3,g3,bb3] — B resolves up to C, F resolves down to Eb. You’ve been hearing this resolution since EDM.4. Now you know why it works.
Medieval monks avoided the tritone in choral music. The interval was considered so dissonant it was associated with the devil—“diabolus in musica.” Singing it in plainchant was discouraged. The ban was more practical than theological: without a clear resolution context, the tritone destabilized the mode. It sounded wrong with no way to make it right.
What medieval monks avoided, jazz musicians made foundational. Every dominant 7th chord contains a tritone. Every ii–V–I progression depends on it. Tritone substitution—replacing V7 with a chord a tritone away—became one of bebop’s signature moves. The interval that was forbidden became the engine of harmonic motion.
The “blue note” in a blues scale is the b5—a tritone above the root. It’s the note that makes blues sound like blues. Play a C blues scale: C Eb F Gb G Bb C. That Gb is the tritone. It bends, it wails, it doesn’t belong to major or minor. That tension is the point.
The tritone is its own inversion. Flip it and you get another tritone. C to Gb = 6 semitones. Gb to C = 6 semitones. It divides the octave exactly in half. No other interval does this. That symmetry is what makes it so unstable—there’s no “direction” built in. It could resolve either way.
The full phonk track. Drums, 808, pad, and a melody that uses different intervals for different emotional effects. Bar 1 melody: minor 3rds and perfect 5ths—dark, stable. Bar 4 melody: major 3rd and tritone—bright tension pulling toward resolution. The intervals carry the emotion.
The melody in bar 1: C–Eb (m3), Eb–G (M3), G–Eb (m3). Dark minor intervals, stable. Bar 4: G–B (M3), B–D (m3), D–F (m3)—and B to F across the chord is the tritone. Maximum tension. When it loops back to bar 1, the tritone resolves. The intervals do the emotional work.
[g3 ~ c4 ~ e4 ~ c4 ~]. The B→C and F→E resolution happens in the melody itself. Hear the release.[c4 ~ g4 ~ f4 ~ c4 ~] for bar 1. Medieval, hollow, strong.[c4 ~ db4 ~ b3 ~ c4 ~]. Anxious. Claustrophobic. Useful for tension sections.| concept | means | example |
|---|---|---|
| interval | distance between two pitches in semitones | C–Eb = 3 semitones = m3 |
| m2 / M2 | minor 2nd (1) / major 2nd (2) | C–Db / C–D |
| m3 / M3 | minor 3rd (3) / major 3rd (4) — decides major vs minor | C–Eb / C–E |
| P4 / P5 | perfect 4th (5) / perfect 5th (7) — stable, open | C–F / C–G |
| tritone (TT) | 6 semitones, half an octave — most unstable | B–F inside G7 |
| m6 / M6 | minor 6th (8) / major 6th (9) | C–Ab / C–A |
| m7 / M7 | minor 7th (10) / major 7th (11) | C–Bb / C–B |
| P1 / P8 | unison (0) / octave (12) | C–C / C–C |
| quality | perfect, major, or minor — determines character | P4 is open; m3 is dark; M3 is bright |
| inversion | flip bottom note up — sizes add to 12, M↔m | M3 (4) inverts to m6 (8) |
| V7→I resolution | tritone inside V7 resolves outward to tonic | G7 [B,F] → C [C,E] |
13 intervals from unison (0) to octave (12). Perfect intervals: P1, P4, P5, P8. Major/minor pairs: 2nds, 3rds, 6ths, 7ths. The tritone (6) stands alone. Inversion flips M↔m, sizes add to 12. The tritone inside V7 is why dominant chords resolve. Every chord and every melody is built from intervals.
Next: Non-Chord Tones. Every type of tension between the notes that matter.
Tracks that demonstrate this lesson’s concepts.
| artist | track | why |
|---|---|---|
| Akira Yamaoka | Silent Hill 2: Theme of Laura (2001) | (VGM) tritone as dread, industrial meets beauty |
| Beethoven | Symphony No. 5: Opening (1808) | (classical) minor 3rd as the most famous interval in music |
| Burial | Archangel (2007) | (garage) pitched vocal intervals as emotional architecture |
The naming system for intervals is ancient. The emotional associations are not universal — they’re culturally constructed.
The Pythagorean tradition ranked intervals by the simplicity of their frequency ratio: octave (2:1), fifth (3:2), fourth (4:3) = “perfect” consonances. Thirds (5:4 and 6:5) were considered dissonant until the Renaissance. The cultural shift from “thirds are dissonant” to “thirds are the foundation of harmony” took 500 years and reshaped all of Western music.
The augmented fourth / diminished fifth (6 semitones) earned the nickname “diabolus in musica” (the devil in music) — though this attribution is more legend than documented medieval practice. What IS documented is that theorists from Guido d’Arezzo (11th c.) onward treated it with caution. The interval was not literally banned but was avoided in chant and early polyphony. Its rehabilitation began with the development of dominant seventh chords in the Baroque era — the tritone inside V7 became the engine of tonal resolution.
Sources: Tenney, A History of ‘Consonance’ and ‘Dissonance’ (1988); Drabkin, “Tritone” in New Grove (2001).