352/351: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = minthma, 11/13-kleisma | | Name = major minthma, major gentle comma, 11/13-kleisma | ||
| Color name = 3u1o1, thulo 1sn,<br>Thulo comma | | Color name = 3u1o1, thulo 1sn,<br>Thulo comma | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
'''352/351''', the '''major minthma''', '''major gentle comma''' or '''11/13-kleisma''', is a [[small comma|small]] [[13-limit]] (also 2.3.11.13 [[subgroup]]) [[comma]] measuring about 4.9{{cent}}. This comma can be described in a number of ways. First, it is the difference between the tridecimal minor third of [[13/11]] and the Pythagorean minor third of [[32/27]], hence the name ''11/13''-kleisma. Second, it is the difference between various tridecimal intervals and their adjacent undecimal intervals such as | |||
* between the tridecimal quartertone of [[1053/1024]] and the undecimal quartertone of [[33/32]]; | * between the tridecimal quartertone of [[1053/1024]] and the undecimal quartertone of [[33/32]]; | ||
* between [[16/13]] and [[27/22]]; and | * between [[16/13]] and [[27/22]]; and | ||
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352/351 and [[351/350]], the ratwolfsma, are extremely close in size and make up a consecutive pair of 13-limit [[superparticular]] commas. Their difference is [[chalmersia|123201/123200]], the chalmersma, the smallest 13-limit superparticular comma; their sum is [[176/175]], the valinorsma, an 11-limit superparticular comma. | 352/351 and [[351/350]], the ratwolfsma, are extremely close in size and make up a consecutive pair of 13-limit [[superparticular]] commas. Their difference is [[chalmersia|123201/123200]], the chalmersma, the smallest 13-limit superparticular comma; their sum is [[176/175]], the valinorsma, an 11-limit superparticular comma. | ||
== History and etymology == | |||
This comma was known as the ''minthma'' from 2011. In 2022, [[Margo Schulter]] requested it should be changed to ''major''/''greater minthma'' to distinguish it from [[364/363]], which would gain the name ''minor''/''lesser minthma''. The ''major gentle comma'' was also added to this comma in contrast to the ''minor gentle comma'' of 364/363. Both commas were essential to define the [[gentle]] temperament. | |||
== See also == | == See also == | ||
* [[ | * [[Major minthmic chords]] | ||
* [[Small comma]] | * [[Small comma]] | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
[[Category: | [[Category:Major minthmic]] | ||
Revision as of 13:35, 15 January 2024
| Interval information |
major gentle comma,
11/13-kleisma
Thulo comma
reduced
352/351, the major minthma, major gentle comma or 11/13-kleisma, is a small 13-limit (also 2.3.11.13 subgroup) comma measuring about 4.9 ¢. This comma can be described in a number of ways. First, it is the difference between the tridecimal minor third of 13/11 and the Pythagorean minor third of 32/27, hence the name 11/13-kleisma. Second, it is the difference between various tridecimal intervals and their adjacent undecimal intervals such as
- between the tridecimal quartertone of 1053/1024 and the undecimal quartertone of 33/32;
- between 16/13 and 27/22; and
- between 39/32 and 11/9.
352/351 and 351/350, the ratwolfsma, are extremely close in size and make up a consecutive pair of 13-limit superparticular commas. Their difference is 123201/123200, the chalmersma, the smallest 13-limit superparticular comma; their sum is 176/175, the valinorsma, an 11-limit superparticular comma.
History and etymology
This comma was known as the minthma from 2011. In 2022, Margo Schulter requested it should be changed to major/greater minthma to distinguish it from 364/363, which would gain the name minor/lesser minthma. The major gentle comma was also added to this comma in contrast to the minor gentle comma of 364/363. Both commas were essential to define the gentle temperament.