Kite Guitar originals: Difference between revisions

The octave is divided into 41 equal steps, a tuning called 41-ET or 41edo or 41-equal. Whereas 12-equal has 100¢ steps, 41-equal has steps of 29.27¢. We can round this off to 30¢ for convenience, since a cent or two doesn't matter much in practice. This 30¢ interval is called an arrow, because the little arrows by the noteheads raise or lower the pitch by 30¢. Notes are called up-E, down-F-sharp, etc., written ^E and vF#. A note that has no ups or downs is called plain. The 7 plain natural notes are close to 12-equal, but they do deviate slightly. The pattern is easy to see when the notes are arranged in chain-of-5ths order:

| style="width:40px;" |D

| style="width:40px;" | G#

|0¢

In the table, D is the "anchor note" that agrees with standard tuning exactly. D is an ideal anchor because it makes the table symmetrical. But F, C, G and A have all been used by microtonalists historically. If hired to record a part remotely, always ask what the anchor note is!

Assuming D is the anchor note, let's find some pitches. ^D is 30¢ sharp and vD is 30¢ flat. F# is +10¢, so vF# is -20¢. C is -5¢, so vC is -35¢. In certain situations, double arrows are needed. ^^C is called dup-C and vvC# is dud-C-sharp. Note that ^^C = vvC#. One more equivalence: ^^C = vDb. Thus 3 arrows = a minor 2nd. These equivalences are useful, because if you've already found vDb on your instrument, and you see ^^C on the score, you know what to do.

*one arrow = half a fret = a quarter-sharp or quarter-flat

*two arrows = one fret = half a sharp/flat

*three arrows = 1.5 frets = a minor 2nd

This table lists all the notes and intervals. Mid intervals, written with "~", are midway between major and minor.

! colspan="2" |tuning

!interval from D

|^1

| -41¢

|vD# / Eb

| Eb

| vA1 / m2

|A1 / ^m2

|Eb

| +46¢

|E

| +34¢

| ^M2

| F

|F

|F#

| -49¢

| +39¢

| -32¢

|v4

| G

|P4

| -44¢

| G#

|G#

| +44¢

|A

|A

|P5

| -39¢

| Bb

| vA5 / m6

| Bb

|B

| B

| ^M6

| C

| -46¢

| vM7

| +41¢

|vD

|D

| +0¢

So how exactly would a vocalist or violinist or trombonist tune a precise number of cents sharp or flat? It helps to borrow a Kite guitar and familiarize oneself with the sound of the various intervals. It also helps to understand just intonation. See the [https://kiteguitar.com/what-it-is/ "What it is -- long explanation"] page for an overview. In practice, use the ups and downs as a rough guide, then listen to the other parts and try to blend. For example, the downmajor 3rd from D to vF# is 380¢, very close to the just 5/4 of 386¢. So one simply flattens the F# until the interference beats go away. But wait, should the 3rd be 380¢ or 386¢? In general, deviating slightly from 41-equal is fine, if it makes the chord smoother. The just harmonic 7th is only 3¢ sharp of the 41-equal downminor 7th, so such deviation is even less of an issue.

===Cancelling rules===

TODO: Complete this

Any chord name without ups or downs is exactly what one would expect it to be. Cm7 is still C Eb G Bb. But in practice most chords have ups and downs in them. An up or down between the chord root and the chord type (e.g. C^m7) raises or lowers the 3rd, and also the 6th, 7th or 11th, if present. Thus C down-seven is the usual C7 chord with the 3rd and 7th downed: Cv7 = C vE G vBb. Mnemonic: every other note of a stacked-3rds chord with a 6th below the root is affected: '''6th''' - root - '''3rd''' - 5th - '''7th''' - 9th - '''11th''' - 13th. Note that the 6th is affected, but the 13th is not.

If the 3rd is downed but the minor 7th is not, the chord is named C-down add7, written Cv,7. The comma before the 7 means "add". Analogous to M and m, "a" means augmented and "d" means diminished. Half-diminished chords are named as dim add7 chords. For example, C ^Eb Gb ^Bb is C^d^7.