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 if we arrange the notes in chain-of-5ths order:

{| class="wikitable"

|Ab

|Eb

|Bb

|F

|C

|G

|D

|A

|E

|B

|F#

|C#

|G#

All the notes with sharps are extra-sharp. All the notes with flats are extra-flat. Note that G# is sharper than Ab by one arrow. Thus G# is also ^Ab, and Ab is also vG#. (Likewise C# = ^Db, vD# = Eb, etc.) Since G# ≠ Ab, the familiar circle of 12 fifths opens up into a spiral. Because this spiral is really a circle of 41 fifths, the innermost and outermost few notes overlap.

[[File:41-edo spiral.png|none|thumb|384x384px]]

* 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

Here's all the notes, with equivalent names:

{| class="wikitable"

!^D

!^^D / vvD# / vEb

!vD# / Eb

!D# / ^Eb

!^D# / ^^Eb / vvE

!vE

!E

!^E

!vF

!^F

!^^F / vvF# / vGb

!vF# / Gb

|F#

!#F / ^Gb

!^F# / ^^Gb / vvG

!vG

!G

!^G

!^^G / vvG# / vAb

!vG# / Ab

| -15¢

!G# / ^Ab

!^G# / ^^Ab / vvA

!vA

!A

!^A

!^^A / vvA# / vBb

!vA# / Bb

!A# / ^Bb

!^A# / ^^Bb / vvB

|Bb

!vB

| +7¢

!^B

!vC

!C

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 "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.