The Biosphere: Difference between revisions

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 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.

This lattice can also be extended to deal with "higher primes", as can 5-limit JI. However, we instead expand the subgroup outward from the center, so that the "higher primes" we look at are things like like 5, 11, and 13. However, it may prove more useful at first to think purely within the 2.3.7.13/5 subgroup, so as to first come to understand the xenharmonic possibilities of the system.

Subgroup: 2.3.7.13/5

{{val| 0 0 1 -1 }}

Comma list: 91/90

{{val| 0 0 0 0 1 0 }}

Oceanfront is very similar to the familiar 7-limit superpyth temperament, in which 16/9 is equated with 7/4, 32/27 equated with 7/6, and 81/64 with 9/7. Oceanfront aims to equate 81/64 with 13/10 instead, however, so the fifths are even sharper than those of superpyth - 713.910 cents is the optimal POTE generator. The general structure of this scale is similar to that of meantone[7], except that the "major" triads in this scale are 10:13:15, and the minor triads are 6:7:9.

Subgroup: 2.3.7.13/5

[[POTE generator]]: ~4/3 = 486.090

{{see also| Archytas clan #Superpyth }}

Extends 11-limit superpyth as 22&49.

[[Comma list]]: 64/63, 78/77, 91/90, 100/99

[[POTE generator]]: ~4/3 = 489.521

{{see also| Archytas clan #Ultrapyth }}

[[Comma list]]: 55/54, 64/63, 91/90, 1573/1568

[[POTE generator]]: ~4/3 = 486.500

{{see also| Porcupine family #Porcupinefish }}

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.

[[Comma list]]: 55/54, 64/63, 91/90, 100/99

[[POTE generator]]: ~10/9 = 162.277

[[Badness]]: 0.025314

Tropic is the merger of the biosphere and the [[The Archipelago|archipelago]]. It is also a subgroup relative of semaphore temperament, since [[49/48]] vanishes. Of note is that [[676/675]] vanishes, so that two 7/6's (or 15/13)'s is equated with 4/3. While this temperament doesn't take advantage of the nearly pure harmonies that biome tempering can offer, particularly where 7/4 is involved, it still has some use, particularly for those who don't mind a bit more error in their tunings.

[[Comma list]]: 49/48, 91/90

[[POTE generator]]: ~7/6 = 251.507

{{see also| Diaschismic family #Echidnic }}

13-limit echidnic temperament, the 10&46 temperament, is about as accurate as a biosphere temperament can get.

[[Category:Biome]]

[[Category:Biosphere]]