273/272: Difference between revisions

 

'''273/272''', the '''tannisma''', or 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]].  

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>.

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.5638, ~5/4, ~7/4 = 967.5985, ~11/8, ~13/8 = 838.3951

[[Subgroup]]: 2.3.7.13.17

 

{{Mapping|legend=1| 1 0 0 0 -4 | 0 1 0 0 1 | 0 0 1 0 1 | 0 0 0 1 1 }}

 

: mapping generators: ~2, ~3, ~7, ~13

 

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.5638, ~7/4 = 967.5985, ~13/8 = 838.3951

 

{{Optimal ET sequence|legend=1| 10, 17g, 24, 26, 31, 36, 113, 149 }}

== Etymology ==

This comma was named by Scott Dakota, who also devised tannic temperament, as the ''tannisma'' no later than 2017. The name ''tannisma'' does not adhere to the wiki comma logging standard that a comma name "X-isma" should not be associated to a temperament "X-ic" that is a weak extension of the temperament that the comma induces, since 17-limit tannic is a weak extension of 2.3.7.13.17 prototannic (see above). ''Prototannisma'' has thus been proposed as an alternative name.