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== Temperaments == | == 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 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>. | [[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 === | === Prototannismic === | ||
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: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13 | : mapping generators: ~2, ~3, ~5, ~7, ~11, ~13 | ||
[[Optimal tuning]] | [[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 }} | {{Optimal ET sequence|legend=1| 17cg, 19eg, 22, 26, 27eg, 29g, 31, 41, 46, 72, 103, 130g, 149, 159, 221ef, 262df, 308def, 334cdf }} | ||
[[Badness]] (Sintel): 0.678 | |||
[[ | |||
== Etymology == | == 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. | 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. | ||
== See also == | |||
* [[List of superparticular intervals]] | |||
== References == | == References == | ||