273/272: Difference between revisions
+commatic relations and temperaments |
Tannisma -> prototannisma since {273/272, 441/440, 561/560} is a weak extension of {273/272} and weak extension never share the same name |
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{{Infobox Interval | {{Infobox Interval | ||
| Name = | | Name = prototannisma | ||
| Color name = 17u3oz1, suthozo 1sn,<br>Suthozo comma | | Color name = 17u3oz1, suthozo 1sn,<br>Suthozo comma | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
'''273/272''', the ''' | '''273/272''', the '''prototannisma''', is a [[small comma|small]] [[17-limit]] (also 2.3.7.13.17 [[subgroup]]) [[comma]] with a value of roughly 6.35 [[cent]]s. It forms the difference between [[21/17]] and [[16/13]], and the difference between [[39/32]] and [[17/14]], as well as the difference between [[17/13]] and [[21/16]]. | ||
== Commatic relations == | == Commatic relations == | ||
| Line 29: | Line 29: | ||
== Temperaments == | == Temperaments == | ||
Tempering out this comma in the 17-limit leads to the rank-6 ''' | Tempering out this comma in the 17-limit leads to the rank-6 '''prototannismic temperament''', or in the 2.3.7.13.17 subgroup, the rank-4 '''prototannic temperament''', both characterized by the equivalences introduced above, and lead to a type of essentially tempered chords called [[prototannismic chords]]. The prototannic temperament has a notable [[extension|weak extension]] to the full 17-limit called [[tannic]]. However, that is not all, as according to [[Scott Dakota]], tannic is actually of similar overall utility to those that temper out the [[marvel comma]]<ref>[https://www.facebook.com/groups/497105067092502/posts/1158638974272438/ Relevant Facebook post by Scott Dakota]</ref>. | ||
== Etymology == | |||
This comma was named by Scott Dakota, who also devised the tannic temperament, as the ''tannisma'' no later than 2017. The community decided that it was necessary to distinguish the associated subgroup temperament from its weak extension, so the prefix ''proto-'' was later added. | |||
== References == | == References == | ||
<references/> | <references/> | ||
[[Category: | [[Category:Prototannismic]] | ||
Revision as of 07:58, 21 July 2023
| Interval information |
Suthozo comma
reduced
273/272, the prototannisma, is a small 17-limit (also 2.3.7.13.17 subgroup) comma with a value of roughly 6.35 cents. It forms the difference between 21/17 and 16/13, and the difference between 39/32 and 17/14, as well as the difference between 17/13 and 21/16.
Commatic relations
This comma is the difference between the following superparticular pairs:
- 35/34 and 40/39
- 52/51 and 64/63
- 65/64 and 85/84
- 91/90 and 136/135
- 154/153 and 352/351
- 169/168 and 442/441
- 221/220 and 1156/1155
- 225/224 and 1275/1274
- 256/255 and 4096/4095
It factors into the following superparticular pairs:
- 441/440 and 715/714
- 385/384 and 936/935
- 375/374 and 1001/1000
- 364/363 and 1089/1088
- 351/350 and 1225/1224
- 325/324 and 1701/1700
- 289/288 and 4914/4913
Temperaments
Tempering out this comma in the 17-limit leads to the rank-6 prototannismic temperament, or in the 2.3.7.13.17 subgroup, the rank-4 prototannic temperament, both characterized by the equivalences introduced above, and lead to a type of essentially tempered chords called prototannismic chords. The prototannic temperament has a notable weak extension to the full 17-limit called tannic. However, that is not all, as according to Scott Dakota, tannic is actually of similar overall utility to those that temper out the marvel comma[1].
Etymology
This comma was named by Scott Dakota, who also devised the tannic temperament, as the tannisma no later than 2017. The community decided that it was necessary to distinguish the associated subgroup temperament from its weak extension, so the prefix proto- was later added.