784/783
Ratio | 784/783 |
Subgroup monzo | 2.3.7.29 [4 -3 2 -1⟩ |
Size in cents | 2.2096162¢ |
Name | biminorisma |
Color name | twenuzozo 2nd, 29uzz2, Twenuzozo comma |
FJS name | [math]\text{m2}^{7,7}_{29}[/math] |
Special properties | square superparticular, reduced |
Tenney height (log_{2} nd) | 19.2276 |
Weil height (log_{2} max(n, d)) | 19.2294 |
Wilson height (sopfr (nd)) | 60 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.24293 bits |
Comma size | unnoticeable |
S-expression | S28 |
open this interval in xen-calc |
784/783, the biminorisma, is an unnoticeable 29-limit comma measuring about 2.21 ¢. It is the distance between the intervals 29/28 and 28/27 (thus having the S-expression S28). The name comes from that 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, and therefore, tempering out this comma adds the prime 29 to the 2.3.7 subgroup with 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. This comma was not named the bimajorisma to further distance from association with the unrelated temperament named bisupermajor.
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. Edos that support it include 36edo, 41edo, 58edo, 118edo, and 135edo. Patent edo tunings with less than 25% relative error on 7/4 and less than 20% relative error on 29/16: 22, 27, 36, 41, 63, 77, 99, 113, 135, 140, 162, 176, 198, 203, 212, 217, 239, 275, 297, 302, 311, 316, 338, 352, 374, 379, 415, 437, 451, 473, 478, 487, 492, 514, 550, 555, 577, 591, 613, 627, 649, 654, 690, 726, 731, 767, 789, 825, 830, 866, 902, 1001.
Biminoric
Subgroup: 2.3.7.29
Comma list: 784/783
Sval mapping: [⟨1 0 0 4], ⟨0 1 0 -3], ⟨0 0 1 2]]
- CTE: ~2 = 1\1, ~3/2 = 702.169, ~7/4 = 968.378
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
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).