784/783: Difference between revisions

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'''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~~]].

'''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]].

== Temperaments ==

=== Biminoric ===

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.

[[Subgroup]]: 2.3.7.29

[[Comma list]]: 784/783

[[Optimal tuning]]s:

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

== Scales ==

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1200.0000

</pre>

~~== 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{{cent}}, 7/4 = 968.378{{cent}}~~

== Trivia ==

A form of this temperament being 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]]).

A form of this temperament being 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]]).

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 }}
-'''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]].
+'''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]].
+== Temperaments ==
+=== Biminoric ===
+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.
+[[Subgroup]]: 2.3.7.29
+[[Comma list]]: 784/783
+{{Mapping|legend=2| 1 0 0 4 | 0 1 0 -3 | 0 0 1 2 }}
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1\1, ~3/2 = 702.169}, ~7/4 = 968.378
 == Scales ==
@@ Line 39: / Line 52: @@
 .0000
 </pre>
-== 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{{cent}}, 7/4 = 968.378{{cent}}
 == Trivia ==
-A form of this temperament being 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]]).
+A form of this temperament being 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]]).