784/783: Difference between revisions

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{{Infobox Interval

| Name = ~~spoogalactic comma~~

| Name = biminorisma

| Color name = twenuzozo 2nd, 29uzz2,<br>Twenuzozo comma}}

| Color name = twenuzozo 2nd, 29uzz2,<br>Twenuzozo comma

| Comma = yes

}}

'''784/783''', the '''~~spoogalactic comma~~''', is a [[29-limit]] ~~interval, and~~ is the distance between the intervals [[29/28]] and [[28/27]]. ~~Tempering it~~ out ~~results in~~ [[~~spoogalactic~~ temperament]], the rank-3 temperament ~~in the~~ 2.3.7.29 ~~subgroup~~. ~~The names~~ of the ~~comma and temperament were proposed due to a~~ form of this temperament ~~being~~ used in the song [https://on.soundcloud.com/fJWXc "Into The Spoogalaxy!"] by members of the ~~Xenharmonic Alliance~~ Discord server for the 2023 Server vs. Server music competition.

'''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 ==

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

[[Optimal tuning]]s:

* [[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:

<pre>

28/27

9/8

7/6

9/7

4/3

81/56

3/2

14/9

12/7

7/4

27/14

2/1

</pre>

Which can be tempered using one's preferred tuning of [[#Biminoric|Biminoric]]. For example, using the [[POTE]] tuning yields:

<pre>

61.8726

204.5643

266.4369

435.8452

497.7179

640.4095

702.2821

764.1548

933.5631

968.7190

1138.1274

1200.0000

</pre>

== Trivia ==

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]]).

[[Category:Commas named for the intervals they stack]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Name = spoogalactic comma
+| Name = biminorisma
-| Color name = twenuzozo 2nd, 29uzz2,<br>Twenuzozo comma}}
+| Color name = twenuzozo 2nd, 29uzz2,<br>Twenuzozo comma
+| Comma = yes
+}}
-'''784/783''', the '''spoogalactic comma''', is a [[29-limit]] interval, and is the distance between the intervals [[29/28]] and [[28/27]]. Tempering it out results in [[spoogalactic temperament]], the rank-3 temperament in the 2.3.7.29 subgroup. The names of the comma and temperament were proposed due to a form of this temperament being used in the song [https://on.soundcloud.com/fJWXc "Into The Spoogalaxy!"] by members of the Xenharmonic Alliance Discord server for the 2023 Server vs. Server music competition.
+'''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 ==
+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
+{{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 ==
+=== Biminordene ===
+Designed and named by [[Scott Dakota]], the JI pre-image is:
+<pre>
+/27
+/8
+/6
+/7
+/3
+/56
+/2
+/9
+/7
+/4
+/14
+/1
+</pre>
+Which can be tempered using one's preferred tuning of [[#Biminoric|Biminoric]]. For example, using the [[POTE]] tuning yields:
+<pre>
+.8726
+.5643
+.4369
+.8452
+.7179
+.4095
+.2821
+.1548
+.5631
+.7190
+.1274
+.0000
+</pre>
+== Trivia ==
+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]]).
+[[Category:Commas named for the intervals they stack]]