User:BudjarnLambeth/12edo as a 2.3.5.17.19 tuning: Difference between revisions
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* nth-b [[Half-prime subgroup|Nth-basis subgroup]] | * nth-b [[Half-prime subgroup|Nth-basis subgroup]] | ||
* frac = [[Subgroup|Other fractional subgroup]] | * frac = [[Subgroup|Other fractional subgroup]] | ||
Technically any fractional subgroup can be said to be nth-basis, so an arbitrary cutoff must be drawn somewhere. This page considers 200th-basis or higher to not be nth-basis, while 199th or lower is accepted. | |||
== How to choose a type == | == How to choose a type == | ||
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# If there are still spots left open, then they should be filled by every prime 13 and up which the EDO approximates with less than 35% relative error, preferencing the lowest primes first, until all spots are filled | # If there are still spots left open, then they should be filled by every prime 13 and up which the EDO approximates with less than 35% relative error, preferencing the lowest primes first, until all spots are filled | ||
== | == List of subgroups by EDO == | ||
Size categories taken from my [[human EDO size categorization]] (HUECAT). | Size categories taken from my [[human EDO size categorization]] (HUECAT). | ||
=== Picnic EDOs (1-4) === | === Picnic EDOs (1-4) === | ||
; 3 basis elements | |||
* [[1edo]]: 2.125.127 (comp) | * [[1edo]]: 2.125.127 (comp) | ||
* [[2edo]]: 2.7/5.17/3 (nth-b) (15th) | * [[2edo]]: 2.7/5.17/3 (nth-b) (15th) | ||
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=== Birthday EDOs (5-19) === | === Birthday EDOs (5-19) === | ||
; 3 basis elements | |||
* [[5edo]]: 2.3.7 (no-n) | * [[5edo]]: 2.3.7 (no-n) | ||
* [[6edo]]: 2.9.5 (comp) | * [[6edo]]: 2.9.5 (comp) | ||
; 5 basis elements | |||
* [[7edo]]: 2.3.11/3.11/5.13 (nth-b) (15th) | * [[7edo]]: 2.3.11/3.11/5.13 (nth-b) (15th) | ||
* [[8edo]]: 2.5/3.11/3.13/5.19 (nth-b) (15th) | * [[8edo]]: 2.5/3.11/3.13/5.19 (nth-b) (15th) | ||
* [[9edo]]: 2.5.7/3.11.13/7 (nth-b) ( | * [[9edo]]: 2.5.7/3.11.13/7 (nth-b) (21st) | ||
* [[10edo]]: 2.3.7.13.17 (no-n) | * [[10edo]]: 2.3.7.13.17 (no-n) | ||
* [[11edo]]: 2.9.15.7.11 (comp) | * [[11edo]]: 2.9.15.7.11 (comp) | ||
* [[12edo]]: 2.3.5.17.19 (no-n) | * [[12edo]]: 2.3.5.17.19 (no-n) | ||
; 6 basis elements | |||
* [[13edo]]: 2.9.5.11.13.17 (comp) | * [[13edo]]: 2.9.5.11.13.17 (comp) | ||
* [[14edo]]: 2.3.7/5.9/5.11/5.13 (nth-b) (5th) | * [[14edo]]: 2.3.7/5.9/5.11/5.13 (nth-b) (5th) | ||
* [[15edo]]: 2.3.5.7.11 ( | * [[15edo]]: 2.3.5.7.11.23 (no-n) | ||
* [[16edo]]: 2.5.7.13.19 (no-n) | * [[16edo]]: 2.5.7.13.19 (no-n) | ||
* [[17edo]]: 2.3.7.11.13 (no-n) | * [[17edo]]: 2.3.7.11.13.19 (no-n) | ||
* [[18edo]]: 2.9.5.7/3.11 (nth-b) ( | * [[18edo]]: 2.9.5.7/3.11.13/7 (nth-b) (21st) | ||
* [[19edo]]: 2.3.5.7.11.13 (lim) | * [[19edo]]: 2.3.5.7.11.13 (lim) | ||
=== Carousel EDOs (20-34) === | === Carousel EDOs (20-34) === | ||
; 6 basis elements | |||
* [[20edo]]: 2.3.7.11.13.17 (no-n) | * [[20edo]]: 2.3.7.11.13.17 (no-n) | ||
* [[21edo]]: 2.3.5.7.13.17 (no-n) | * [[21edo]]: 2.3.5.7.13.17 (no-n) | ||
| Line 103: | Line 110: | ||
* [[26edo]]: 2.3.5.7.11.13 (lim) | * [[26edo]]: 2.3.5.7.11.13 (lim) | ||
* [[27edo]]: 2.3.5.7.11.13 (lim) | * [[27edo]]: 2.3.5.7.11.13 (lim) | ||
; 7 basis elements | |||
* [[28edo]]: 2.3.5.7.11.13.19 (no-n) | * [[28edo]]: 2.3.5.7.11.13.19 (no-n) | ||
* [[29edo]]: 2.3.5.7.11.13.19 (no-n) | * [[29edo]]: 2.3.5.7.11.13.19 (no-n) | ||
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* [[51edo]]: 2.3.5+.5-.7.11+.11- (dual) | * [[51edo]]: 2.3.5+.5-.7.11+.11- (dual) | ||
* [[52edo]]: 2.3+.3-.5.7.11.19 (dual) | * [[52edo]]: 2.3+.3-.5.7.11.19 (dual) | ||
; 8 basis elements | |||
* [[53edo]]: 2.3.5.7.11.13.17.19 (lim) | * [[53edo]]: 2.3.5.7.11.13.17.19 (lim) | ||
* [[54edo]]: 2.3+.3-.5+.5-.7+.7-.11 (dual) | * [[54edo]]: 2.3+.3-.5+.5-.7+.7-.11 (dual) | ||
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=== Double-decker EDOs (55-74) === | === Double-decker EDOs (55-74) === | ||
''(May complete later.)'' | ''(May complete later.)'' | ||
== Notation of dual-3 EDOs == | == Notation of dual-3 EDOs == | ||