9edo: Difference between revisions

9edo can be notated with conventional notation, including the staff, note names, relative notation, etc. in two ways. The first defines sharp/flat, major/minor and aug/dim in terms of the native antidiatonic scale, such that sharp is higher pitched than flat, and major/aug is wider than minor/dim, as would be expected. Because it does not follow diatonic conventions, conventional interval arithmetic no longer works, e.g. {{nowrap|M2 + M2}} isn't M3, and {{nowrap|D + M2}} isn't E. Because antidiatonic is the sister scale to diatonic, you can solve this by swapping major and minor in interval arithmetic rules. Chord names don't follow diatonic nominals because {{dash|C, E, G|med}} is not {{dash|P1, M3, P5|med}}.

The second approach is to essentially pretend 9edo's antidiatonic scale is a normal diatonic, meaning that sharp is lower in pitch than flat (since the "S" step is larger than the "L" step) and major/aug is narrower than minor/dim. This allows music notated in 12edo or another diatonic system to be directly translated to 9edo "on the fly", and it carries over the way interval arithmetic and chord names work from diatonic notation.

 

In this notation, the [[enharmonic unison]] is the augmented 2nd, e.g. E♭ to F♯.

![[degree]]

![[cent]]s

! colspan="2" | Antidiatonic<br />Major wider than minor

! colspan="2" | Diatonic<br />Major narrower than minor

|[[1/1]]

|[[File:0-0 unison.mp3|frameless]]

|[[14/13]] (+5.035), [[13/12]] (−5.239),<br />[[12/11]] (−17.304)

|[[File:0-133,33 minor second (9-EDO).mp3|frameless]]

|[[7/6]] (−0.204)

|[[File:0-266,67 major 2nd, minor 3rd (9-EDO).mp3|frameless]]

|[[5/4]] (+13.686), [[14/11]] (−17.508),<br />[[9/7]] (−35.084)

|[[File:0-400 major third (12-EDO).mp3|frameless]]

|[[4/3]] (+35.288), [[11/8]] (−17.985)

|[[File:0-533,33 fourth (9-EDO).mp3|frameless]]

|[[16/11]] (+17.985), [[3/2]] (−35.288)

|[[File:0-666,67 fifth (9-EDO).mp3|frameless]]

|[[14/9]] (+35.084) [[11/7]] (+17.508),<br />[[8/5]] (−13.686)

|[[File:0-800 minor sixth (12-EDO).mp3|frameless]]

|[[12/7]] (+0.204)

|[[File:0-933,33 major 6th, minor 7th (9-EDO).mp3|frameless]]

|[[11/6]] (+17.304) [[13/7]] (−5.035)

|[[File:0-1066,67 major seventh (9-EDO).mp3|frameless]]

|[[2/1]]

|[[File:0-1200 octave.mp3|frameless]]