Where the twelve notes come from, and everything they build. One tool open at a time.
the course as a dependency spine · a node lights when you earn it
1 · ORIGIN. WHERE THE TWELVE NOTES COME FROM
Start with one note. Stack a pure fifth, the ratio 3/2, and keep stacking. The twelve notes are not a design decision. They are what stacking fifths does.
0 fifths stacked. Press the button.
The spiral does not close. (3/2)^12 = 129.746338 2^7 = 128 twelve pure fifths = 8423.46 cents seven octaves = 8400 cents the miss = 23.46 cents
That miss is the Pythagorean comma. The twelfth note up is B#, and B# is not C.
"Every note is changed just a little bit so that they fit in the 7 octaves while still being the same distance apart."Elijah, Music Curriculum
"The biggest downside is that the only perfect interval is the octave."Elijah, Music Curriculum
Hear the 1.955 cents
Two notes a fifth apart share a partial: the third harmonic of the low note and the second harmonic of the high one. When the fifth is pure they land on the same frequency and the sound sits still. When it is tempered they miss, and the sound beats. That beat is the price of the circle closing.
Pure 440 and 660. Tempered 440 and 659.255. Shared partial 1320.000 against 1318.510, so the tempered fifth beats about 1.49 times a second.
The third is where you hear it, not the fifth. Just 386.31 cents against tempered 400 cents, a miss of 13.69 cents, beating about 8.7 times a second. The fifth in the same chord is only 1.955 cents off.
440 held against the note twelve pure fifths up folded back into the octave, 446.003. About 6 wobbles a second. That wobble is the whole reason 12TET exists.
earned by stacking all twelve fifths and tempering them
2 · BUILD A SCALE FROM THREE CHORDS
Drag the window across the circle. Three chords in a row: the root chord, the chord a perfect fifth down, and the chord a perfect fifth up. Their notes are a scale.
"Just like basic chords are built with three notes, scales are built with three chords."Elijah, Music Curriculum
Drag on the wheel to move the window, or use the buttons.
The pattern is the last thing you learn here, not the first. Unfold a major scale and a minor scale to earn this one.
earned by unfolding one major scale and one minor scale
3 · THE MODE ROTATOR
Seven notes are selected on the circle. They never change. All that changes is which one is home.
"Rotate the selection of the seven notes so that the outside intervals will change."Elijah, Music Curriculum
the rule underneath, and how it was checked
Take three chords in a row on the circle and root on the flattest of the three. Rotate the window one step and you get the next mode down the ladder of brightness. Every row below was derived from scratch before this tool was written, and every row matched.
The three chords
Notes it produces
Rooted on
Mode
On the first five rows the root really is the flattest of the three, exactly as the one line rule says. On the last two the window runs off the sharp end of the selection and picks F back up, so those three no longer run flat to sharp and the root is the chord the window starts on. That is the only place the rule needs the reading spelled out.
earned by rotating through all seven modes
4 · LEAN AND DIRECTION
The circle is not a set of positions. It is a set of forces. Every step has a direction and every interval has a lean.
Two axes, one diagram.
Up a fifth: brighter. Down a fifth: darker.
The sharp side is the major side, the flat side is the minor side.
Close together on the circle is consonant, far apart is dissonant.
"Even though P5s and P4s are perfect, P5s are more towards major and P4s are more towards minor."Elijah, Music Curriculum
"Octaves are perfectly pure, they are not major or minor."Elijah, Music Curriculum
"Up a major interval is down a minor interval and vice versa."Elijah, Music Curriculum
A P4 up is a P5 down folded back. That is why it darkens, and it is the same sentence as the quote above it.
The overtone series is major, the undertone series is minor
The overtone series is the stack of pitches hiding inside every single note, and it is where the major triad comes from. Mirror it downward and you get the undertone series, and it is minor. Up the overtone series is more major, down the undertone series is more minor.
overtone 1 : 2 : 3 : 4 : 5 : 6 going up gives the major triad undertone 1 : 1/2 : 1/3 : 1/4 : 1/5 : 1/6 going down gives the minor triad
Negative harmony
Reflect the music across the circle's axis and the major side trades places with the minor side: the same level of tension, but on the minor side now. The mirror on this wheel runs between the 1 and the 5 of the key.
Pick a chord above to mirror it.
earned by mirroring a chord and hearing both series
5 · KEY RECOGNITION DRILL
One or two chords, and you name the key. Not by guessing. By the giveaways.
Press Deal to begin.
0 right · 0 wrong
Name the major key. Every key is on the pad in circle order, C at the top left.
his giveaway table, the logic this drill runs on
One chord giveaways. Some single chords are so rare that their scale position is unique. Phrygian = 3 · Lydian = 4 · Dom7 = 5 · Dim = 7
Two chord giveaways. Certain pairs can only sit in one place in a major key. 2m + 3m (tone apart) · 3m + 4 (semitone) · 4 + 5 (tone) · 5 to 2m
Relative minors. If a major chord is in a major scale, its relative minor is also in that scale, and vice versa, so every confirmed chord confirms its relative too.
Sharps and flats. Look at which sharps or flats are actually being played and find them on the circle of fifths.
Accidentals. "Listen for where it resolves to: that is probably the tonic chord."
earned at six right
SHARPEN
A miss mints a card. Trigger, then what it is, then why. Nothing here is a scolding; it is the shape you want in your hands when the chord goes by.
No cards yet. Miss one in the drill and it lands here.
Your progress
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