Xenharmonic Reference:EDO page skeleton

This page is to be used as a template for making EDO pages.

Xedo, or X equal divisions of the octave (sometimes called X-TET or X-tone equal temperament), is the equal tuning featuring steps of (1200/X) = Y cents exactly, X 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.]

Approximation of prime harmonics in 0edo

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan	-nan
	Relative (%)	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0	0.0
Steps (reduced)		0 (0)	0 (0)	0 (0)	0 (0)	0 (0)	0 (0)	0 (0)	0 (0)	0 (0)	0 (0)	0 (0)

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]

Notable structural chains

[Generator chains]

Compositional theory

Tertian structure

[Describe]

Thirds in Xedo

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]

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?]

Instruments

[Put instruments and isomorphic layouts here]