User:MisterShafXen/9edo: Difference between revisions
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Prime factorization
32
Step size
133.333 ¢
Fifth
5\9 (666.667 ¢)
Semitones (A1:m2)
-1:2 (-133.3 ¢ : 266.7 ¢)
Consistency limit
7
Distinct consistency limit
5
Created page with "{{Infobox ET}} {{ED intro}} == Theory == 9edo can be seen as the flattest mavila tuning. Its antidiatonic scale is basic, and its superdiatonic is equalized. If the fifths are flatter than 9's (e.g. 11edo's), the superdiatonic becomes balzano. == Intervals == {{Interval table|9edo|additional=Tritonic note names A A# Bb B B# Cb C C# Ab A ; Antidiatonic notation (mode ssLsssL) A B C C#/Db D E F G G#/Ab A}} == Harmonics == {{Harmonics in equal|steps=9}}" Tags: Visual edit Mobile edit Mobile web edit Advanced mobile edit |
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== Harmonics == | == Harmonics == | ||
{{Harmonics in equal|steps=9}} | {{Harmonics in equal|steps=9}} | ||
Latest revision as of 16:53, 20 August 2025
| ← 8edo | 9edo | 10edo → |
9 equal divisions of the octave (abbreviated 9edo or 9ed2), also called 9-tone equal temperament (9tet) or 9 equal temperament (9et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 9 equal parts of about 133 ¢ each. Each step represents a frequency ratio of 21/9, or the 9th root of 2.
Theory
9edo can be seen as the flattest mavila tuning. Its antidiatonic scale is basic, and its superdiatonic is equalized. If the fifths are flatter than 9's (e.g. 11edo's), the superdiatonic becomes balzano.
Intervals
| Steps | Cents | Approximate ratios | Ups and downs notation | Tritonic note names |
|---|---|---|---|---|
| 0 | 0 | 1/1 | D | A |
| 1 | 133.3 | 11/10, 12/11, 13/12, 14/13, 15/14, 16/15, 17/16 | E | A# |
| 2 | 266.7 | 7/6, 8/7, 13/11, 15/13, 19/16, 20/17, 22/19 | E♯, F♭ | Bb |
| 3 | 400 | 5/4, 9/7, 14/11, 19/15 | F | B |
| 4 | 533.3 | 4/3, 11/8, 15/11, 18/13, 19/14 | G | B# |
| 5 | 666.7 | 3/2, 13/9, 16/11, 19/13, 22/15 | A | Cb |
| 6 | 800 | 8/5, 11/7, 14/9, 19/12, 21/13 | B | C |
| 7 | 933.3 | 7/4, 12/7, 17/10, 19/11, 22/13 | B♯, C♭ | C# |
| 8 | 1066.7 | 11/6, 13/7, 15/8, 20/11 | C | Ab |
| 9 | 1200 | 2/1 | D | A |
Harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -35.3 | +13.7 | -35.5 | +62.8 | -18.0 | -40.5 | -21.6 | +28.4 | -30.8 | +62.6 | +38.4 |
| Relative (%) | -26.5 | +10.3 | -26.6 | +47.1 | -13.5 | -30.4 | -16.2 | +21.3 | -23.1 | +46.9 | +28.8 | |
| Steps (reduced) |
14 (5) |
21 (3) |
25 (7) |
29 (2) |
31 (4) |
33 (6) |
35 (8) |
37 (1) |
38 (2) |
40 (4) |
41 (5) | |