User:FloraC/Quick reference: Difference between revisions
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== Important prime limits == | == Important prime limits == | ||
; 2-limit (rank-1): | |||
* Essential equivalence | |||
* Completes the harmonic series for the first octave | |||
; 3-limit (rank-2): | ; 3-limit (rank-2): | ||
* Essential interval functions | * Essential interval functions | ||
* Completes the harmonic series for the first 2 octaves | |||
* Rank is a highly composite number | |||
; 5-limit (rank-3): | |||
* Completes the harmonic series for the first 2 octaves and a fifth | |||
; 7-limit (rank-4): | |||
* Tonality: tonal | |||
* Categorical characteristics: pivotal and semiambitonal | |||
* Completes the harmonic series for the first 3 octaves | |||
* Rank is a highly composite number | |||
; 11-limit (rank-5): | |||
* Completes the harmonic series for the first 3 octaves and a fifth | |||
; 13-limit (rank-6): | ; 13-limit (rank-6): | ||
* Essential interval colors | * Essential interval colors | ||
* Tonality: | * Tonality: microtonal | ||
* Categorical characteristics: | * Categorical characteristics: ambitonal and semiambitonal | ||
* | * Completes the harmonic series for the first 4 octaves | ||
* Rank is a highly composite number | |||
; 23-limit (rank-9): | ; 23-limit (rank-9): | ||
| Line 26: | Line 45: | ||
* Tonality: pseudotonal and pseudomicrotonal | * Tonality: pseudotonal and pseudomicrotonal | ||
* Categorical characteristics: pseudoambitonal | * Categorical characteristics: pseudoambitonal | ||
* | * Completes the harmonic series for the first 4 octaves and a fifth | ||
* Followed by a record prime gap | * Followed by a record prime gap | ||
; 31-limit (rank-11) | ; 31-limit (rank-11) | ||
* | * Completes the harmonic series for the first 5 octaves | ||
; 37-limit (rank-12) | ; 37-limit (rank-12) | ||
* Rank is a highly composite number | |||
; 47-limit (rank-15) | ; 47-limit (rank-15) | ||
* | * Completes the harmonic series for the first 5 octaves and a fifth | ||
; 61-limit (rank-18) | ; 61-limit (rank-18) | ||
* | * Completes the harmonic series for the first 6 octaves | ||
; 89-limit (rank-24) | ; 89-limit (rank-24) | ||
* | * Completes the harmonic series for the first 6 octaves and a fifth | ||
* Followed by a record prime gap | * Followed by a record prime gap | ||
* Rank is a highly composite number | |||
== Edo sizes == | == Edo sizes == | ||
* Exo: 0–9 | * Exo: 0–9 | ||
* Small: | * Small: 10–38 | ||
* Medium: | ** Semitonic: 10–14 | ||
* Large: | ** Subsemitonic: 15–26 | ||
* Mega: | ** Dietic: 27–38 | ||
* Medium: 39–79 | |||
** Commatic: 39–67 | |||
** Subcommatic: 68–79 | |||
* Large: 80–190 | |||
** Hemicommatic: 80–132 | |||
** Codettic: 133–137 | |||
** Kleismatic: 138–190 | |||
* Mega: 191+ | |||
** Subkleismatic | |||
** Hemikleismatic | |||
** … | |||