From the physics of a single string to jazz harmony. Every stop can be clicked and heard. Your first click on any button turns the sound on.
① The harmonic series: all of music hidden inside one note
Play any single note and a whole series of overtones is actually sounding in the air with it. Pick a fundamental, press play, and watch them emerge one by one — click each to hear it alone.
How to apply it?
① the secret of timbre:each instrument＝ a recipe of overtones. The clarinet's low register has only odd-numbered overtones(hollow wooden),the flute has few overtones(clean and transparent) — key EQ, pick a timbre, tune to exactly this table.
② the overblowing of wind instruments:without changing fingering, only air and embouchure, the note jumps to the next overtone — the flute jumps an octave (2nd overtone), the clarinet jumps a twelfth (3rd overtone),the entire upper-register fingering system is built on the harmonic series.
③ ensemble intonation: the 5th overtone is flat 14¢, overtone 7 the overtone is flat 31¢ — when brass sustains a chord together,the third must be nudged flat to "lock in",This is the intuition of just intonation.
④ the birthplace of chords: overtones 4-5-6 are a major triad! Harmony was not invented by people, is a gift of physics.
What to notice: the 2nd overtone is an octave up; overtone 3 is a perfect fifth; overtone 5 is a major third — the major triad is written straight into nature。
while overtone 7 overtone is ... than on the piano ♭7 flat by about 31 cents — this "flatward ♭7" is the physical source of the loose, mournful quality of blues singing.
So what is equal temperament?Just intonation is beautifully in tune, but every change of key means retuning. Equal temperament slices the octave "evenly into 12 parts",
each cell 100 cents — every key compromises a little, in exchange for 12 keys can all use it.
② Interval: the distance between two notes
First click a starting note on the keyboard (say Re), then choose an interval and hear what leaping up from it sounds like.
Click the keyboard to pick a starting note → click an interval
Where do you use it?Major third＝the sunshine of the major, the minor third＝the melancholy of the minor; the perfect fifth = the power chord and the bass's skeleton;
Augmented fourth (tritone)＝the tension core of the dominant seventh, and also 2-5-1 that makes it want to "resolve".
An interval's quality: major, minor, perfect, augmented, diminished
the interval's name＝degree(the number, from how many lines it spans on the page)＋quality(the adjective, from the actual number of semitones). The same 6 semitones,
written as F→B is an "augmented fourth", written as F→C♭ is a "diminished fifth" — the spelling on the page decides the name, but the ear hears the same thing.
quality
applicable degrees
rule
examples (all starting from C to start)
perfect (Perfect)
1 · 4 · 5 · 8 degree
the most stable family, with no major/minor distinction
C→F perfect fourth, C→G Perfect fifth
Major
2 · 3 · 6 · 7 degree
the version built into the major scale
C→E major third, C→A Major sixth
minor
2 · 3 · 6 · 7 degree
a major interval shrunk by a semitone
C→E♭ minor third, C→B♭ Minor seventh
augmented (Augmented)
any degree
a perfect or major intervalthen stretch widersemitone
C→F♯ augmented fourth, C→G♯ Augmented fifth
diminished (diminished)
any degree
a perfect or minor intervalthen compresssemitone
C→G♭ diminished fifth, C→B𝄫 Diminished seventh
Mnemonic: diminished ← minor ← Major → augmented (2·3·6·7 degrees); diminished ← perfect → augmented (1458 degrees).
each arrow＝ semitones. The three most common quality alterations in jazz: augmented fourth, /diminished fifth (tritone), diminished seventh (dim7 chord), augmented fifth (augmented chord).
③ Seventh-chord field guide: maj7 · 7 · m7 · half-diminished seventh · fully diminished (＋whole-tone scale)
Click the keyboard to pick a root, then choose a chord type. It arpeggiates first (one note at a time), then sounds together, with formula and use shown alongside.
④ Diatonic chords: the seven chords native to a major key
Take each note of the major scale as a root and stack a third, another third, another third — and you get the seven diatonic seventh chords, the raw materials of jazz harmony. Pick a key and try it:
Did you notice?framed by the dashed line iim7、V7、Imaj7 is 2-5-1 's source — it was not invented,
are "the three from the diatonic set most eager to go home". The seventh m7♭5(half-diminished seventh) is the minor key's 2-5-1 's first leg.
How to apply it? — the diatonic chords are the alphabet for writing and figuring out songs
① Roman numerals=a universal language:call the chord I、ii、V rather than C、Dm、G,The same progression holds in any key — musicians rely on it to communicate and to transpose accompaniment.
② pop songs 90% among these seven:hear "which degree we're on now", you can figure out chords and lay down accompaniment.
③ a map for improvising:know that we are now on V7, you know ♭9 is usable, wanting to resolve back to I — the diatonic chords tell you which notes are family in this bar. Click below to hear the three most common progressions: