273/272: Difference between revisions

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'''273/272''', the '''tannisma''', is a [[small comma|small]] [[17-limit]] 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]]. ~~Equating these three sets of intervals~~ is ~~characteristic of~~ '''tannismic ~~temperaments~~''', ~~however~~, that's not all, as according to Scott Dakota, ~~such temperaments are~~ 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>~~, and lead to a type of essentially tempered chord called the '''tannic chord'''~~.

'''273/272''', the '''tannisma''', 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 ==

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 '''tannismic temperament''', or in the 2.3.7.13.17 subgroup, the rank-4 '''tannic temperament''', both characterized by the equivalences introduced above, and lead to a type of essentially tempered chord called the [[tannismic chord]]. However, that is not all, as according to [[Scott Dakota]], the tannic temperament 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>.

== References ==

[[Category:Tannismic]]

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-'''273/272''', the '''tannisma''', is a [[small comma|small]] [[17-limit]] 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]].  Equating these three sets of intervals is characteristic of '''tannismic temperaments''', however, that's not all, as according to Scott Dakota, such temperaments are 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>, and lead to a type of essentially tempered chord called the '''tannic chord'''.
+'''273/272''', the '''tannisma''', 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 ==
+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 '''tannismic temperament''', or in the 2.3.7.13.17 subgroup, the rank-4 '''tannic temperament''', both characterized by the equivalences introduced above, and lead to a type of essentially tempered chord called the [[tannismic chord]]. However, that is not all, as according to [[Scott Dakota]], the tannic temperament 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>.
 == References ==
 <references/>
+[[Category:Tannismic]]