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The Biosphere: Difference between revisions

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= Parent Temperaments =
= Parent Temperaments =
== Biome ==
== Biome ==
Subgroup: 2.3.7.13/5
Subgroup: 2.3.7.13/5


Comma: 91/90
Comma list: 91/90


Map:
Mapping:  


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


<0 1 0 2|
{{val| 0 1 0 2 }}


<0 0 1 -1|
{{val| 0 0 1 -1 }}


EDOs: 14, 17, 22, 27, 32, 46
{{Val list|legend=1| 14, 17, 22, 27, 32, 46 }}


== Biosphere ==
== Biosphere ==
Subgroup: Full 13-limit
Subgroup: Full 13-limit


Comma: 91/90
Comma list: 91/90


Map:
Mapping:  


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


<0 1 0 0 0 2|
{{val| 0 1 0 0 0 2 }}


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


<0 0 0 1 0 -1|
{{val| 0 0 0 1 0 -1 }}


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


EDOs: 46
{{Val list|legend=1| 46 }}


= Rank two temperaments =
= Rank two temperaments =
== Oceanfront ==
== Oceanfront ==
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.
The sharp fifths of this scale can be a little more dissonant than meantone ears are used to, as can the flat fifths of something like mavila. This scale is very much like a brighter cousin of mavila in that regard.
Subgroup: 2.3.7.13/5
Subgroup: 2.3.7.13/5


Commas: 91/90, 64/63
Comma list: 91/90, 64/63


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


Map: [<1 2 2 3|, < 0 -1 2 -4|]
Mapping: [<1 2 2 3|, < 0 -1 2 -4|]


EDOs: 27, 32
{{Val list|legend=1| 27, 32 }}


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.
== Oceanfront Children ==
=== Superpyth ===


The sharp fifths of this scale can be a little more dissonant than meantone ears are used to, as can the flat fifths of something like mavila. This scale is very much like a brighter cousin of mavila in that regard.
Extends 11-limit superpyth as 22&49.


== Oceanfront Children ==
=== Superpyth ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Commas: 91/90, 64/63, 78/77, 245/243
Comma list: 91/90, 64/63, 78/77, 245/243


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


Map: [< 1 2 6 2 10 9|, <0 -1 -9 2 -16 -13|]
Mapping: [< 1 2 6 2 10 9|, <0 -1 -9 2 -16 -13|]


EDOs: 22, 27e, 32c, 37e, 49, 76bcde
{{Val list|legend=1| 22, 27e, 32c, 37e, 49, 76bcde }}


Badness: 0.0247
Badness: 0.0247


Extends 11-limit superpyth as 22&49.
=== 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.


=== Porcupinefish ===
Subgroup: 13-limit
Subgroup: 13-limit


Commas: 91/90, 64/63, 250/243, 121/120
Comma list: 91/90, 64/63, 250/243, 121/120


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


Map: [<1 2 3 2 4 6|, <0 -3 -5 6 -4 -17|]
Mapping: [<1 2 3 2 4 6|, <0 -3 -5 6 -4 -17|]


EDOs: 15, 22, 37, 59
{{Val list|legend=1| 15, 22, 37, 59 }}


Badness: 0.0253
Badness: 0.0253


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.
== Tropic ==
 
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.


== Tropic ==
Subgroup: 2.3.7.13/5
Subgroup: 2.3.7.13/5


Commas: 91/90, 49/48
Comma list: 91/90, 49/48


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


Map: [<1 2 3 2|, <0 -2 -1 -3|]
Mapping: [<1 2 3 2|, <0 -2 -1 -3|]


EDOs: 19, 24
{{Val list|legend=1| 19, 24 }}
 
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.


== Avian ==
== Avian ==
Subgroup: 2.3.5.7.13
Subgroup: 2.3.5.7.13


Commas: 91/90, 245/243
Comma list: 91/90, 245/243


[[POTE_tuning|POTE generator]]: 443.322
[[POTE generator]]: 443.322


Map: [<1 -1 -1 -2 0|, <0 7 9 13 10|]
Mapping: [<1 -1 -1 -2 0|, <0 7 9 13 10|]


EDOs: 19, 27, 46
{{Val list|legend=1| 19, 27, 46 }}


== Echidnic ==
== Echidnic ==
Retrieved from "https://en.xen.wiki/w/The_Biosphere"