273/272: Difference between revisions

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{{Infobox Interval

| Name = tannisma

| Name = tannisma, prototannisma

| Color name = 17u3oz1, suthozo 1sn,<br>Suthozo comma

| Comma = yes

}}

'''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]].

'''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 29:

== 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>.

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>.

=== Prototannismic ===

[[Subgroup]]: 2.3.5.7.11.13.17

[[Comma list]]: 273/272

[[Mapping]]: <br>

{| class="right-all"

|-

| [⟨ || 1 || 0 || 0 || 0 || 0 || 0 || -4 || ],

|-

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

|-

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

|-

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

|-

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

|-

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

=== Prototannic ===

[[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 }}

: 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" 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.

== References ==

[[Category:~~Tannismic~~]]

[[Category:Prototannismic]]

[[Category:Commas with unknown etymology]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Name = tannisma
+| Name = tannisma, prototannisma
 | Color name = 17u3oz1, suthozo 1sn,<br>Suthozo comma
 | Comma = yes
 }}
-'''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]].
+'''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 29: / Line 29: @@
 == 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>.
+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>.
+=== Prototannismic ===
+[[Subgroup]]: 2.3.5.7.11.13.17
+[[Comma list]]: 273/272
+[[Mapping]]: <br>
+{| class="right-all"
+|-
+| [⟨ || 1 || 0 || 0 || 0 || 0 || 0 || -4 || ],
+|-
+| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || 1 || ],
+|-
+| ⟨ || 0 || 0 || 1 || 0 || 0 || 0 || 0 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || 1 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || 0 || ],
+|-
+| ⟨ || 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 ET sequence|legend=1| 17cg, 19eg, 22, 26, 27eg, 29g, 31, 41, 46, 72, 103, 130g, 149, 159, 221ef, 262df, 308def, 334cdf }}
+=== Prototannic ===
+[[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 }}
+: 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" 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.
 == References ==
 <references/>
-[[Category:Tannismic]]
+[[Category:Prototannismic]]
+[[Category:Commas with unknown etymology]]