273/272: Difference between revisions

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'''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]].

'''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]].

== Commatic relations ==

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== 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 [[~~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 [[marvel ~~temperament~~]]<ref>[https://www.facebook.com/groups/497105067092502/posts/1158638974272438/ Relevant Facebook post by Scott Dakota]</ref>.

[[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 chord]]s called [[prototannismic chords]]. The prototannic temperament has a notable [[weak extension]] to the full 17-limit called [[tannic]]. According to [[Scott Dakota]], tannic is of similar overall utility to [[marvel]]<ref>[https://www.facebook.com/groups/497105067092502/posts/1158638974272438/ Relevant Facebook post by Scott Dakota]</ref>.

=== Prototannic ===

[[Subgroup]]: 2.3.7.13.17

[[Comma list]]: 273/272

{{Mapping|legend=2| 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]]s:

* [[WE]]: ~2 = 1200.4469{{c}}, ~3/2 = 701.2262{{c}}, ~7/4 = 967.0489{{c}}, ~13/8 = 837.6531{{c}}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.2150{{c}}, ~7/4 = 967.0685{{c}}, ~13/8 = 837.7810{{c}}

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

[[Badness]] (Sintel): 0.113

=== Prototannismic ===

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| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 1 || ]]

|}

: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13

[[Optimal tuning]] ([[~~CTE~~]]): ~2 = ~~1\1~~, ~3/2 = 701.~~5638~~, ~5/4, ~7/4 = 967.~~5985~~, ~11/8, ~13/8 = ~~838~~.~~3951~~

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1200.4469{{c}}, ~3/2 = 701.2262{{c}}, ~5/4 = 385.4186{{c}}, ~7/4 = 967.0489{{c}}, ~11/8 = 549.9753{{c}}, ~13/8 = 837.6531{{c}}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.2150{{c}}, ~5/4 = 385.7085{{c}}, ~7/4 = 967.0685{{c}}, ~11/8 = 550.4163{{c}}, ~13/8 = 837.7810{{c}}

{{Optimal ET sequence|legend=1| 17cg, 19eg, 22, 26, 27eg, 29g, 31, 41, 46, 72, 103, 130g, 149, 159, 221ef, 262df, 308def, 334cdf }}

~~=== Prototannic ===~~

[[Badness]] (Sintel): 0.678

[[~~Subgroup~~]]: 2.~~3.7.13.17~~

~~[[Comma list]]: 273/272~~

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

== 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 naming standard as it would induce ''tannic'' as a temperament that tempers out the comma alone in its minimal prime subgroup, 2.3.7.13.17 {273/272}, for which Scott's 17-limit tannic is a weak extension and cannot share the same time. ''Prototannisma'' has thus been proposed as an alternative name.

~~: 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~~ ==

== See also ==

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" if "X-ic" is a weak extension of ~~the temperament induced by the comma, since 17-limit tannic is a weak extension of 2.3.7.13.17[273/272~~] ~~(see above). ''Prototannisma'' has thus been proposed as an alternative name.~~

* [[List of superparticular intervals]]

== References ==

@@ Line 4: / Line 4: @@
 | Comma = yes
 }}
+'''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]].
-'''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]].
 == Commatic relations ==
@@ Line 31: / Line 30: @@
 == 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 [[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 [[marvel temperament]]<ref>[https://www.facebook.com/groups/497105067092502/posts/1158638974272438/ Relevant Facebook post by Scott Dakota]</ref>.
+[[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 chord]]s called [[prototannismic chords]]. The prototannic temperament has a notable [[weak extension]] to the full 17-limit called [[tannic]]. According to [[Scott Dakota]], tannic is of similar overall utility to [[marvel]]<ref>[https://www.facebook.com/groups/497105067092502/posts/1158638974272438/ Relevant Facebook post by Scott Dakota]</ref>.
+=== Prototannic ===
+[[Subgroup]]: 2.3.7.13.17
+[[Comma list]]: 273/272
+{{Mapping|legend=2| 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]]s:
+* [[WE]]: ~2 = 1200.4469{{c}}, ~3/2 = 701.2262{{c}}, ~7/4 = 967.0489{{c}}, ~13/8 = 837.6531{{c}}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.2150{{c}}, ~7/4 = 967.0685{{c}}, ~13/8 = 837.7810{{c}}
+{{Optimal ET sequence|legend=1| 10, 17g, 24, 26, 31, 36, 113, 149 }}
+[[Badness]] (Sintel): 0.113
 === Prototannismic ===
@@ Line 53: / Line 68: @@
 | ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 1 || ]]
 |}
 : mapping generators: ~2, ~3, ~5, ~7, ~11, ~13
-[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.5638, ~5/4, ~7/4 = 967.5985, ~11/8, ~13/8 = 838.3951
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1200.4469{{c}}, ~3/2 = 701.2262{{c}}, ~5/4 = 385.4186{{c}}, ~7/4 = 967.0489{{c}}, ~11/8 = 549.9753{{c}}, ~13/8 = 837.6531{{c}}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.2150{{c}}, ~5/4 = 385.7085{{c}}, ~7/4 = 967.0685{{c}}, ~11/8 = 550.4163{{c}}, ~13/8 = 837.7810{{c}}
 {{Optimal ET sequence|legend=1| 17cg, 19eg, 22, 26, 27eg, 29g, 31, 41, 46, 72, 103, 130g, 149, 159, 221ef, 262df, 308def, 334cdf }}
-=== Prototannic ===
+[[Badness]] (Sintel): 0.678
-[[Subgroup]]: 2.3.7.13.17
-[[Comma list]]: 273/272
-{{Mapping|legend=1| 1 0 0 0 -4 | 0 1 0 0 1 | 0 0 1 0 1 | 0 0 0 1 1 }}
+== 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 naming standard as it would induce ''tannic'' as a temperament that tempers out the comma alone in its minimal prime subgroup, 2.3.7.13.17 {273/272}, for which Scott's 17-limit tannic is a weak extension and cannot share the same time. ''Prototannisma'' has thus been proposed as an alternative name.
-: 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 ==
+== See also ==
-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" if "X-ic" is a weak extension of the temperament induced by the comma, since 17-limit tannic is a weak extension of 2.3.7.13.17[273/272] (see above). ''Prototannisma'' has thus been proposed as an alternative name.
+* [[List of superparticular intervals]]
 == References ==