1716/1715: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = lummic comma | | Name = lummic comma | ||
| Color name = 3o1or<sup>3</sup>g-2, tholotriru-agu negative 2nd | |||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
The '''lummic comma''', '''1716/1715''', is | The '''lummic comma''', '''1716/1715''', is an [[unnoticeable comma|unnoticeable]] [[13-limit]] [[superparticular]] [[comma]] measuring about 1.0{{cent}}. It often arises as the difference between simpler commas: ([[176/175]])/([[196/195]]), ([[351/350]])/([[441/440]]), ([[1573/1568]])/([[385/384]]), ([[540/539]])/([[1575/1573]]), and ([[1001/1000]])/([[2401/2400]]). It factors into ([[2080/2079]])⋅([[9801/9800]]). | ||
Tempering | == Temperaments == | ||
[[Tempering out]] this comma leads to the rank-5 '''lummic''' temperament. It is tempered out by several notable edos including [[72edo]], [[270edo]] and [[400edo]] among others. | |||
[[Subgroup]]: 2.3.5.7.11.13 | |||
[[Mapping]]: <br> | |||
{| class="right-all" | |||
|- | |||
| [⟨ || 1 || 0 || 0 || 0 || 0 || -2 || ], | |||
|- | |||
| ⟨ || 0 || 1 || 0 || 0 || 0 || -1 || ], | |||
|- | |||
| ⟨ || 0 || 0 || 1 || 0 || 0 || 1 || ], | |||
|- | |||
| ⟨ || 0 || 0 || 0 || 1 || 0 || 3 || ], | |||
|- | |||
| ⟨ || 0 || 0 || 0 || 0 || 1 || -1 || ]] | |||
|} | |||
: mapping generators: ~2, ~3, ~5, ~7, ~11 | |||
[[Optimal tuning]]s: | |||
: [[WE]]: ~2 = 1199.9814{{c}}, ~3/2 = 701.9502{{c}}, ~5/4 = 386.4011{{c}}, ~7/4 = 969.0830{{c}}, ~11/8 = 551.2624{{c}} | |||
: [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9462{{c}}, ~5/4 = 386.3868{{c}}, ~7/4 = 969.0766{{c}}, ~11/8 = 551.2373{{c}} | |||
{{Optimal ET sequence|legend=1| 22f, 26, 27e, 31, 45ef, 46, 58, 72, 103, 121, 130, 193, 198, 224, 270, 494, 764, 1137, 1258, 1289, 1419, 1559, 1689, 2183d }} | |||
[[Badness]] (Sintel): 0.318 | |||
== Etymology == | |||
This comma was named after [[Carl Lumma]]. Perhaps interestingly, a ''lummisma'' was first proposed by [[Gene Ward Smith]] in 2011 as a name for 1001/1000, but Carl Lumma pointed out that 1716/1715 was "better"<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_97947.html Yahoo! Tuning Group | ''Short commas'']</ref>, which might ultimately led to this comma being named so. | |||
== References == | |||
[[Category:Lummic]] | [[Category:Lummic]] | ||
[[Category:Commas named after composers]] | |||
[[Category:Commas named after music theorists]] | |||
Latest revision as of 08:09, 4 March 2026
| Interval information |
reduced
The lummic comma, 1716/1715, is an unnoticeable 13-limit superparticular comma measuring about 1.0 ¢. It often arises as the difference between simpler commas: (176/175)/(196/195), (351/350)/(441/440), (1573/1568)/(385/384), (540/539)/(1575/1573), and (1001/1000)/(2401/2400). It factors into (2080/2079)⋅(9801/9800).
Temperaments
Tempering out this comma leads to the rank-5 lummic temperament. It is tempered out by several notable edos including 72edo, 270edo and 400edo among others.
Subgroup: 2.3.5.7.11.13
| [⟨ | 1 | 0 | 0 | 0 | 0 | -2 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | -1 | ], |
| ⟨ | 0 | 0 | 1 | 0 | 0 | 1 | ], |
| ⟨ | 0 | 0 | 0 | 1 | 0 | 3 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 1 | -1 | ]] |
- mapping generators: ~2, ~3, ~5, ~7, ~11
- WE: ~2 = 1199.9814 ¢, ~3/2 = 701.9502 ¢, ~5/4 = 386.4011 ¢, ~7/4 = 969.0830 ¢, ~11/8 = 551.2624 ¢
- CWE: ~2 = 1200.0000 ¢, ~3/2 = 701.9462 ¢, ~5/4 = 386.3868 ¢, ~7/4 = 969.0766 ¢, ~11/8 = 551.2373 ¢
Optimal ET sequence: 22f, 26, 27e, 31, 45ef, 46, 58, 72, 103, 121, 130, 193, 198, 224, 270, 494, 764, 1137, 1258, 1289, 1419, 1559, 1689, 2183d
Badness (Sintel): 0.318
Etymology
This comma was named after Carl Lumma. Perhaps interestingly, a lummisma was first proposed by Gene Ward Smith in 2011 as a name for 1001/1000, but Carl Lumma pointed out that 1716/1715 was "better"[1], which might ultimately led to this comma being named so.