Diachrome: Difference between revisions
Added interpretations |
→Lattice: Fix typo in lattice interval: 2L + m → 2L + s |
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== Structure == | == Structure == | ||
=== Lattice === | === Lattice === | ||
5sC has two chains of "fifths" (the 7-step 3L + m + 3s) both having 6 notes and offset by 3L + m + 2s. The interval L + s is thus reached by stacking two fifths and reducing, and m is reached by stacking -5 fifths and reducing. The three leftmost notes of the lower chain (the one not offset by 3L + m + 2s) are joined to the three rightmost notes of the upper chain by 2L + | 5sC has two chains of "fifths" (the 7-step 3L + m + 3s) both having 6 notes and offset by 3L + m + 2s. The interval L + s is thus reached by stacking two fifths and reducing, and m is reached by stacking -5 fifths and reducing. The three leftmost notes of the lower chain (the one not offset by 3L + m + 2s) are joined to the three rightmost notes of the upper chain by 2L + s. 5sL (resp. 5sR) similarly has two chains of fifths, but the lower chain has 7 (resp. 5) notes and the upper chain 5 (resp. 7) notes. | ||
=== As substitution scale === | === As substitution scale === | ||
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=== 2.3.7.11.13 parapyth === | === 2.3.7.11.13 parapyth === | ||
Diachrome can be given a [[parapyth]] (2.3.7.11.13[29 & 41 & 46]) tempering: | Diachrome can be given a [[parapyth]] (2.3.7.11.13[29 & 41 & 46]) tempering: | ||
* The L step becomes 12/11 | * The L step becomes 12/11; | ||
* The m step becomes 22/21~104/99~256/243 | * The m step becomes 22/21~104/99~256/243; | ||
* The s step becomes 28/27~33/32~1053/1024 | * The s step becomes 28/27~33/32~1053/1024. | ||
The tempered tuning thus has the mappings | The tempered tuning thus has the mappings | ||
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=== 2.3.11.19.23/5.31 [17 & 24] === | === 2.3.11.19.23/5.31 [17 & 24] === | ||
There's also a diachrome tempered by an extension of [[Rastmic_clan#Neutral | neutral]] (2.3.11.19.23/5.31[17 & 24]): | There's also a diachrome tempered by an extension of [[Rastmic_clan#Neutral | neutral]] (2.3.11.19.23/5.31[17 & 24]): | ||
* The L step is 12/11 | * The L step is 12/11; | ||
* The m step is 256/243~128/121~93/88~19/18 | * The m step is 256/243~128/121~93/88~19/18; | ||
* The s step is 33/32~32/31~95/92 | * The s step is 33/32~32/31~95/92. | ||
The tempered tuning thus has the mappings | The tempered tuning thus has the mappings | ||
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=== 2.3.7.13.19.23 [17 & 19 & 41] === | === 2.3.7.13.19.23 [17 & 19 & 41] === | ||
A diachrome is also available in the 2.3.7.13.19.23[17 & 19 & 41] tempering: | A diachrome is also available in the 2.3.7.13.19.23[17 & 19 & 41] tempering: | ||
* The L step is 13/12 | * The L step is 13/12; | ||
* The m step is 256/243~96/91~19/18 | * The m step is 256/243~96/91~19/18; | ||
* The s step is 28/27~27/26 | * The s step is 28/27~27/26. | ||
The tempered tuning has the mappings | The tempered tuning has the mappings | ||
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=== Pele temperament === | === Pele temperament === | ||
In the [[pele]] | In the [[pele]] temperament ([41 & 46 & 58]), following interpretations are available: | ||
* L = 10/9, m = 21/20~22/21~256/243, s = 56/55~64/63~66/65~81/80 | * L = 10/9, m = 21/20~22/21~256/243, s = 56/55~64/63~66/65~81/80; | ||
* L = 11/10, m = 21/20~22/21~256/243, s = 40/39~45/44~50/49 | * L = 11/10, m = 21/20~22/21~256/243, s = 40/39~45/44~50/49; | ||
* L = 12/11, m = 21/20~22/21~256/243, s = 28/27~33/32~65/63. | * L = 12/11, m = 21/20~22/21~256/243, s = 28/27~33/32~65/63; | ||
* L = 13/12, m = 21/20~22/21~104/99~256/243, s = 27/26. | |||
== External links == | == External links == | ||