User:FloraC/Quick reference: Difference between revisions

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== Important prime limits ==
== Important prime limits ==
; 2-limit (rank-2):
* 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
; 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
; 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: tonal and microtonal
* Tonality: microtonal
* Categorical characteristics: pivotal, ambitonal, and semiambitonal
* Categorical characteristics: ambitonal and semiambitonal
* Mode 8
* Completes the harmonic series for the first 4 octaves


; 23-limit (rank-9):  
; 23-limit (rank-9):  
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* Tonality: pseudotonal and pseudomicrotonal
* Tonality: pseudotonal and pseudomicrotonal
* Categorical characteristics: pseudoambitonal
* Categorical characteristics: pseudoambitonal
* Mode 12
* 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)
* Mode 16
* Completes the harmonic series for the first 5 octaves
 
; 37-limit (rank-12)
; 37-limit (rank-12)


; 47-limit (rank-15)
; 47-limit (rank-15)
* Mode 24
* Completes the harmonic series for the first 5 octaves and a fifth


; 61-limit (rank-18)
; 61-limit (rank-18)
* Mode 32
* Completes the harmonic series for the first 6 octaves


; 89-limit (rank-24)
; 89-limit (rank-24)
* Mode 48
* Completes the harmonic series for the first 6 octaves and a fifth
* Followed by a record prime gap
* Followed by a record prime gap