784/783: Difference between revisions
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[[Tempering out]] this comma in the 2.3.7.29 subgroup results in the rank-3 '''biminoric''' temperament, a.k.a. '''spoogalactic''' temperament. It tempers 28/27 and 29/28 together, as well as [[49/27]] and [[29/16]] together. [[7/6]] and [[29/24]] are separated by 29/28 as are [[36/29]] and [[9/7]], where 9/7 is 28/27 below [[4/3]] and 7/6 is 28/27 above [[9/8]], so tempering out this comma to extend the 2.3.7 subgroup to the 2.3.7.29 subgroup is of very high accuracy, yielding obviously distinct flavours of thirds, as a third-tone lies between the two minor thirds and between the two major thirds. | [[Tempering out]] this comma in the 2.3.7.29 subgroup results in the rank-3 '''biminoric''' temperament, a.k.a. '''spoogalactic''' temperament. It tempers 28/27 and 29/28 together, as well as [[49/27]] and [[29/16]] together. [[7/6]] and [[29/24]] are separated by 29/28 as are [[36/29]] and [[9/7]], where 9/7 is 28/27 below [[4/3]] and 7/6 is 28/27 above [[9/8]], so tempering out this comma to extend the 2.3.7 subgroup to the 2.3.7.29 subgroup is of very high accuracy, yielding obviously distinct flavours of thirds, as a third-tone lies between the two minor thirds and between the two major thirds. | ||
The optimal ET sequence is well-supplied with relatively efficient [[edo]]s that [[support]] it. Some | The optimal ET sequence is well-supplied with relatively efficient [[edo]]s that [[support]] it. Some alternative tunings not appearing in the optimal ET sequence are [[55edo]], [[63edo]], and their sum, [[118edo]]. 63edo is notable as a multiple of 7edo (for ~32/29 = 1\7) and 9edo (for ~7/6 = 2\9), while 55edo is a flat-tending meantone system (using ~8/7 = 1\5) that is in terms of errors not much more inefficient than 58edo or 41edo. | ||
A [[catakleismic]] extension is available in the 2.3.5.7.13.29 subgroup, with the notable [[S-expression]] of {S25, S26, S27, S28}. It is also tempered out in [[miracle]], [[magic]], [[newt]] extensions, and a [[septischismic]] extension. | A [[catakleismic]] extension is available in the 2.3.5.7.13.29 subgroup, with the notable [[S-expression]] of {S25, S26, S27, S28}. It is also tempered out in [[miracle]], [[magic]], [[newt]] extensions, and a [[septischismic]] extension. | ||
Latest revision as of 15:03, 18 October 2026
| Interval information |
Twenuzozo comma
reduced
784/783, the biminorisma, is an unnoticeable 29-limit comma measuring about 2.21 cents. It is the distance between the intervals 29/28 and 28/27 (thus having the S-expression S28).
Temperaments
Tempering out this comma in the 2.3.7.29 subgroup results in the rank-3 biminoric temperament, a.k.a. spoogalactic temperament. It tempers 28/27 and 29/28 together, as well as 49/27 and 29/16 together. 7/6 and 29/24 are separated by 29/28 as are 36/29 and 9/7, where 9/7 is 28/27 below 4/3 and 7/6 is 28/27 above 9/8, so tempering out this comma to extend the 2.3.7 subgroup to the 2.3.7.29 subgroup is of very high accuracy, yielding obviously distinct flavours of thirds, as a third-tone lies between the two minor thirds and between the two major thirds.
The optimal ET sequence is well-supplied with relatively efficient edos that support it. Some alternative tunings not appearing in the optimal ET sequence are 55edo, 63edo, and their sum, 118edo. 63edo is notable as a multiple of 7edo (for ~32/29 = 1\7) and 9edo (for ~7/6 = 2\9), while 55edo is a flat-tending meantone system (using ~8/7 = 1\5) that is in terms of errors not much more inefficient than 58edo or 41edo.
A catakleismic extension is available in the 2.3.5.7.13.29 subgroup, with the notable S-expression of {S25, S26, S27, S28}. It is also tempered out in miracle, magic, newt extensions, and a septischismic extension.
Biminoric
Subgroup: 2.3.7.29
Comma list: 784/783
Subgroup-val mapping: [⟨1 0 0 4], ⟨0 1 0 -3], ⟨0 0 1 2]]
- mapping generators: ~2, ~3, ~7
- WE: ~2 = 1199.9057 ¢, ~3/2 = 702.2269 ¢, ~7/4 = 968.6429 ¢
- error map: ⟨-0.094 +0.178 -0.372 +0.556]
- CWE: ~2 = 1200.0000 ¢, ~3/2 = 702.2309 ¢, ~7/4 = 968.5643 ¢
- error map: ⟨0.000 +0.276 -0.262 +0.859]
Optimal ET sequence: 14, 17, 19, 22, 36, 41, 58, 77, 99, 135, 311, 446, 1027j, 1126j, 1261jj
Badness (Sintel): 0.0387
Scales
Biminordene
Designed and named by Scott Dakota, the JI pre-image is:
28/27 9/8 7/6 9/7 4/3 81/56 3/2 14/9 12/7 7/4 27/14 2/1
Which can be tempered using one's preferred tuning of Biminoric. For example, using the POTE tuning yields:
61.8726 204.5643 266.4369 435.8452 497.7179 640.4095 702.2821 764.1548 933.5631 968.7190 1138.1274 1200.0000
Etymology
This comma was named for the two kinds of minor thirds discussed above. It was not named bimajorisma to further distance from association with the unrelated temperament named bisupermajor.
Trivia
A form of this temperament is used in the song "Into The Spoogalaxy!" by members of the XA Discord server for the 2023 Server vs. Server music competition, from which was invented a light-hearted alternative name "spoogalactic comma" thus implying a "spoogalactic temperament", but it is recommended to use the formal names biminoric and biminorisma, the name proposed prior by Scott Dakota, who had also spent time using the rank-3 temperament prior to suggesting names for the comma (of which biminorisma was favoured by other members of the XA Discord).