9edo
UNDER CONSTRUCTION
9edo, or 9 equal divisions of the octave (sometimes called 9-TET or 9-tone equal temperament), is the equal tuning featuring steps of (1200/9) = 133.333… cents exactly, 9 of which stack to the perfect octave 2/1.
[Overview of tuning properties for key intervals]
General theory
Derivation
[Derivation by equal division of various key intervals or of interval qualities]
JI approximation
[Overview of viable vals, tuning tendencies, and accurate/structurally interesting subgroups. Always cover the patent val alongside any notable non-patent vals.]
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | 0.0 | -35.3 | +13.7 | -35.5 | -18.0 | -40.5 | +28.4 | -30.8 | +38.4 | +37.1 | +55.0 |
| Relative (%) | 0.0 | -26.5 | +10.3 | -26.6 | -13.5 | -30.4 | +21.3 | -23.1 | +28.8 | +27.8 | +41.2 | |
| Steps (reduced) |
9 (0) |
14 (5) |
21 (3) |
25 (7) |
31 (4) |
33 (6) |
37 (1) |
38 (2) |
41 (5) |
44 (8) |
45 (9) | |
Edostep interpretations
[Cover these in a list]
Intervals and notation
| Edostep | Cents | Intervals | Notation | Bame (optional) | ||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Group 1 | Additional groups | Notation 1 (usually ups and downs) | Notation 2 (usually neutral diatonic notation, if different)) | Additional notations | System 1 (usually ADIN) | System 2 (usually ups and downs, if meaningfully different) | System 3 (usually neutral diatonic, if different) | Additional systems | ||
| 0 | XXX | XX/XX | XX/XX | D | D | J | ... | ... | ... | ... |
| ... | ... | ... | ... | ... | ... | ... | ||||
[Add solfege in a separate table, if applicable]
Tempering properties
Tempered commas
[List commas with S-expressions and examples of what they equate]
Arithmetic progressions
Notable structural chains
[Generator chains]
Compositional theory
Tertian structure
[Describe]
| Quality (ADIN) | Mosdiatonic Quality | Quality |
|---|---|---|
| Cents | XXX | XXX |
| Just interpretation | X/X | X/X |
| Steps | X | X |
Diatonic thirds are bolded.
Scales
[if edo is composite, link to subset edos and discuss scales of subset edos there]
[List scales and scale descriptions including structure (generators if applicable), notable intervals available, associated temperaments, relationships to other scales, and logic for derivation.]
[Explain more complex scale theory topics here]
Tables of scales
Harmony
[explain notable JI and DR chords. TRY TO PROVIDE COHERENT CHORD SYSTEMS RATHER THAN JUST LISTING RANDOM CHORDS WITH NO RELATION. Explain tunings of familiar chords]
[Explain systems of harmony here, this is how you put the chords together to make music]
[Sections such as "functional harmony", "modal harmony", etc - varies based on the edo and the personal composition style]
[Use individual voices maybe?]
Tables of chords
Instruments
[Put instruments and isomorphic layouts here]
