The Biosphere: Difference between revisions
Dogwithabome (talk | contribs) m i assume that "9-limit" was an error so i corrected it to 7-limit |
m replaced "full 13-limit" with 2.3.5.7.11.13 |
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The '''biosphere''' is the name given to the collection of temperaments that are children of or related to '''biome temperament''', the rank-3 2.3.7.13/5 subgroup temperament eliminating the biome comma [[91/90]], and '''biosphere temperament''', its rank-5 full 13-limit extension. The term "biome" loosely means "ecosystem" or "climate." | The '''biosphere''' is the name given to the collection of temperaments that are children of or related to '''biome temperament''', the rank-3 2.3.7.13/5 subgroup temperament eliminating the biome comma [[91/90]], and '''biosphere temperament''', its rank-5 full 13-limit extension. The term "biome" loosely means "ecosystem" or "climate." | ||
The next low-numbered triad after 4:5:6 with a 3/2 on the outside is 6:7:9, but its inversion, 14:18:21, can sound extremely dissonant to those not used to | The next low-numbered triad after 4:5:6 with a 3/2 on the outside is 6:7:9, but its inversion, 14:18:21, can sound extremely dissonant to those not used to [[9-odd-limit]] harmony. On the other hand, you also have 10:13:15, which is another standout triad of low complexity with a fifth on the outside, but its inversion, 26:30:39, is also relatively complex. Tempering out 91/90 makes both of these problems disappear by connecting the two together, such that the utonal inverse of 6:7:9 becomes 10:13:15. | ||
The rank-3 biome temperament is of particular theoretical interest because it generates a rank-3 lattice that is analogous to the 5-limit JI lattice. As 5-limit JI is the basis for which all 5-limit linear temperaments are derived, the rank-3 biome temperament can serve as a basis to derive useful 2.3.7.13/5 linear temperaments. Instead of our base triads being 4:5:6 and its utonal inversion 10:12:15, we instead treat 6:7:9 and its utonal inversion 10:13:15 as fundamental to the system. The three dimensions of the system can be thought of as 2/1, 3/2, and 7/6 (or 9/7, or 13/10). 46EDO is a great tuning for biome, giving nearly-pure harmonies all around, somewhat analogous to the accuracy of 34EDO or 53EDO in approximating 5-limit JI. | The rank-3 biome temperament is of particular theoretical interest because it generates a rank-3 lattice that is analogous to the 5-limit JI lattice. As 5-limit JI is the basis for which all 5-limit linear temperaments are derived, the rank-3 biome temperament can serve as a basis to derive useful 2.3.7.13/5 linear temperaments. Instead of our base triads being 4:5:6 and its utonal inversion 10:12:15, we instead treat 6:7:9 and its utonal inversion 10:13:15 as fundamental to the system. The three dimensions of the system can be thought of as 2/1, 3/2, and 7/6 (or 9/7, or 13/10). 46EDO is a great tuning for biome, giving nearly-pure harmonies all around, somewhat analogous to the accuracy of 34EDO or 53EDO in approximating 5-limit JI. | ||
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=== Biosphere === | === Biosphere === | ||
Subgroup: | Subgroup: 2.3.5.7.11.13 | ||
Comma list: 91/90 | Comma list: 91/90 | ||
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{{Optimal ET sequence|legend=1| 27, 32 }} | {{Optimal ET sequence|legend=1| 27, 32 }} | ||
Scales: [[Oceanfront scales]] | |||
==== Superpyth ==== | ==== Superpyth ==== | ||
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Extends 11-limit superpyth as 22&49. | Extends 11-limit superpyth as 22&49. | ||
Subgroup: | Subgroup: 2.3.5.7.11.13 | ||
[[Comma list]]: 64/63, 78/77, 91/90, 100/99 | [[Comma list]]: 64/63, 78/77, 91/90, 100/99 | ||
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{{see also| Archytas clan #Quasisuper }} | {{see also| Archytas clan #Quasisuper }} | ||
Subgroup: | Subgroup: 2.3.5.7.11.13 | ||
[[Comma list]]: 64/63, 78/77, 91/90, 121/120 | [[Comma list]]: 64/63, 78/77, 91/90, 121/120 | ||
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===== Full 13-limit ultrapyth ===== | ===== Full 13-limit ultrapyth ===== | ||
Subgroup: | Subgroup: 2.3.5.7.11.13 | ||
[[Comma list]]: 55/54, 64/63, 91/90, 1573/1568 | [[Comma list]]: 55/54, 64/63, 91/90, 1573/1568 | ||
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===== Ultramarine ===== | ===== Ultramarine ===== | ||
Subgroup: | Subgroup: 2.3.5.7.11.13 | ||
[[Comma list]]: 64/63, 91/90, 100/99, 847/845 | [[Comma list]]: 64/63, 91/90, 100/99, 847/845 | ||
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Porcupinefish is the 13-limit extension of [[Porcupine|porcupine]] that you get by adding 91/90 to the usual mix of porcupine temperaments. Its name is derived from that it is a combination of the porcupine and oceanfront temperaments. | Porcupinefish is the 13-limit extension of [[Porcupine|porcupine]] that you get by adding 91/90 to the usual mix of porcupine temperaments. Its name is derived from that it is a combination of the porcupine and oceanfront temperaments. | ||
Subgroup: | Subgroup: 2.3.5.7.11.13 | ||
[[Comma list]]: 55/54, 64/63, 91/90, 100/99 | [[Comma list]]: 55/54, 64/63, 91/90, 100/99 | ||
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===== Full 13-limit godzilla ===== | ===== Full 13-limit godzilla ===== | ||
Subgroup: | Subgroup: 2.3.5.7.11.13 | ||
[[Comma list]]: 45/44, 49/48, 78/77, 81/80 | [[Comma list]]: 45/44, 49/48, 78/77, 81/80 | ||
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===== Varan ===== | ===== Varan ===== | ||
Subgroup: | Subgroup: 2.3.5.7.11.13 | ||
[[Comma list]]: 49/48, 66/65, 77/75, 81/80 | [[Comma list]]: 49/48, 66/65, 77/75, 81/80 | ||
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===== Baragon ===== | ===== Baragon ===== | ||
Subgroup: | Subgroup: 2.3.5.7.11.13 | ||
[[Comma list]]: 49/48, 56/55, 81/80, 91/90 | [[Comma list]]: 49/48, 56/55, 81/80, 91/90 | ||
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{{see also| Diaschismic family #Anguirus }} | {{see also| Diaschismic family #Anguirus }} | ||
Subgroup: | Subgroup: 2.3.5.7.11.13 | ||
[[Comma list]]: 49/48, 56/55, 91/90, 352/351 | [[Comma list]]: 49/48, 56/55, 91/90, 352/351 | ||
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13-limit echidnic temperament, the 10&46 temperament, is about as accurate as a biosphere temperament can get. | 13-limit echidnic temperament, the 10&46 temperament, is about as accurate as a biosphere temperament can get. | ||
Subgroup: | Subgroup: 2.3.5.7.11.13 | ||
[[Comma list]]: 91/90, 169/168, 385/384, 441/440 | [[Comma list]]: 91/90, 169/168, 385/384, 441/440 | ||