784/783

Interval information

Ratio	784/783
Subgroup monzo	2.3.7.29 [4 -3 2 -1⟩
Size in cents	2.209616¢
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 (log2 nd)	19.2276
Weil height (log2 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
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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]]

Optimal tunings:

• 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).