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{n\cdot d}[/math]) |
~2.41954 bits |
Comma size | unnoticeable |
S-expression | S28 |
open this interval in xen-calc |
784/783, the biminorisma, is a 29-limit interval, and 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 and 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, therefore, tempering this comma adds the prime 29 to the 2.3.7 subgroup with very high accuracy, yielding thirds obviously distinct flavours of thirds, as a third-tone lies between the two minor thirds (and hence the two major thirds). Importantly, this comma was not named the "bimajorisma" to further distance from association with an unrelated temperament named Bisupermajor.
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
Temperaments
Biminoric
Subgroup: 2.3.7.29
Patent EDO tunings with <25% relative error on 7/4 and <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
CTE generators: (2/1,) 3/2 = 702.169 ¢, 7/4 = 968.378 ¢
Trivia
A form of this temperament being 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).