784/783: Difference between revisions

'''784/783''', the '''biminorisma''', is an [[unnoticeable comma|unnoticeable]] [[29-limit]] [[comma]] measuring about 2.21{{cent}}. 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]].

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. 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.  

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.  

* [[CTE]]: ~2 = 1\1, ~3/2 = 702.169, ~7/4 = 968.378

A form of this temperament is used in the song [https://on.soundcloud.com/fJWXc "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]]).