Pontigailimma: Difference between revisions
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The '''pontigailimma''' is an [[unnoticeable comma|unnoticeable]] [[13-limit]] (specifically [[2.3.5.7.13 subgroup|2.3.5.7.13-subgroup]]) [[comma]] with a [[ratio]] of '''1990656/1990625''' (0.027{{cent}}). It is the difference between two [[7/4]]'s and a stack of [[16/13]] above five [[6/5]]'s. Alternatively, it is the amount by which [[27/25]] exceeds a stack of [[25/24]], [[49/48]], and [[65/64]]. In terms of [[superparticular]] commas, it is the difference between [[4096/4095]] and [[4375/4374]]. | |||
It also appears as the difference between several non-superparticular comma pairs: | |||
* [[15625/15552]] and [[640/637]] | |||
* [[325/324]] and [[6144/6125]] | |||
* [[729/728]] and [[65625/65536]] | |||
It is tempered out in [[hemikleismic]], [[vulture]], [[pontiac]], [[abigail]], [[ennealimmal]], and [[alphatrillium]] temperaments, as well as by [[46edo|46]], [[50edo|50]], [[53edo|53]], [[68edo|68]], [[103edo|103]], [[121edo|121]], [[171edo|171]], [[217edo|217]], [[224edo|224]], [[270edo|270]], [[441edo|441]], [[494edo|494]], [[643edo|643]], [[814edo|814]], [[935edo|935]], [[3125edo|3125]], [[3395edo|3395]], [[6079edo|6079]], [[8539edo|8539]], [[11664edo|11664]], and [[16808edo]]. | |||
[[ | Its name potentially comes from ponti ['''ponti'''ac] + gai [abi'''gai'''l] + limma [from Greek ''λεῖμμα,'' the remnant]. Thus, it is the tiny remnant that is tempered out in pontiac and abigail. | ||
[[Category:Commas named by combining multiple temperament names]] | |||
Latest revision as of 15:27, 22 February 2026
| Interval information |
55⋅72⋅13 atom
The pontigailimma is an unnoticeable 13-limit (specifically 2.3.5.7.13-subgroup) comma with a ratio of 1990656/1990625 (0.027 ¢). It is the difference between two 7/4's and a stack of 16/13 above five 6/5's. Alternatively, it is the amount by which 27/25 exceeds a stack of 25/24, 49/48, and 65/64. In terms of superparticular commas, it is the difference between 4096/4095 and 4375/4374.
It also appears as the difference between several non-superparticular comma pairs:
- 15625/15552 and 640/637
- 325/324 and 6144/6125
- 729/728 and 65625/65536
It is tempered out in hemikleismic, vulture, pontiac, abigail, ennealimmal, and alphatrillium temperaments, as well as by 46, 50, 53, 68, 103, 121, 171, 217, 224, 270, 441, 494, 643, 814, 935, 3125, 3395, 6079, 8539, 11664, and 16808edo.
Its name potentially comes from ponti [pontiac] + gai [abigail] + limma [from Greek λεῖμμα, the remnant]. Thus, it is the tiny remnant that is tempered out in pontiac and abigail.