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'''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: | '''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. This means that when this comma is [[tempering out|tempered out]], 11/8 plus three perfect fourths octave reduces to 13/8; as such, this comma can be understood as relating harmonics 11 and 13 by a chain of fourths. 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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== Temperaments == | == Temperaments == | ||
Tempering out this comma leads to a form of '''major minthmic temperament''' (full 13-limit rank-5) or '''majorminth temperament''' (2.3.11.13 subgroup rank-3), which enables [[major minthmic chords]]. | Tempering out this comma leads to a form of '''major minthmic temperament''' (full 13-limit rank-5) or '''majorminth temperament''' (2.3.11.13 subgroup rank-3), which enables [[major minthmic chords]]. Mintha was a nymph turned into a mint plant by a goddess whom she got in the way of<ref>[https://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0104%3Aalphabetic+letter%3DM%3Aentry+group%3D26%3Aentry%3Dmintha-bio-1 ''Dictionary of Greek and Roman Biography and Mythology''] – William Smith (1849)</ref><ref>[https://web.archive.org/web/20221230130135/http://mythandreligion.upatras.gr/english/__trashed/ ''Dictionary of Classical Mythology''] – M. R. Wright (2012)</ref><ref>[https://www.greekboston.com/culture/mythology/minthe ''All About Minthe – Myth of Greek Mythology''] – Greek Boston (2024)</ref>, and major minthmic tempering has the slightly sharp, minty-fresh fifths some people appreciate. [[Margo Schulter]] has expressed great fondness for this comma, for example. | ||
== Sagittal notation == | == Notation == | ||
=== Sagittal notation === | |||
In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented (in a secondary role) by the sagittal {{sagittal | !( }} and is called the '''13/11 kleisma''', or '''13/11k''' for short, because the simplest interval it notates is 13/11, as for example in D-F{{nbhsp}}{{sagittal | !( }}. The primary role of {{ sagittal | !( }} is [[5120/5103#Sagittal notation | 5103/5120]] (7/5k). The upward version is called '''11/13k''' or '''13/11k up''' and is represented (in a secondary role) by {{sagittal| |( }}. | In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented (in a secondary role) by the sagittal {{sagittal | !( }} and is called the '''13/11 kleisma''', or '''13/11k''' for short, because the simplest interval it notates is 13/11, as for example in D-F{{nbhsp}}{{sagittal | !( }}. The primary role of {{ sagittal | !( }} is [[5120/5103#Sagittal notation | 5103/5120]] (7/5k). The upward version is called '''11/13k''' or '''13/11k up''' and is represented (in a secondary role) by {{sagittal| |( }}. | ||
== History and etymology == | == History and etymology == | ||
This comma was known as the ''minthma'' from 2011. The word ''minthma'' is a contraction of ''minor thirds comma'' into a single word. 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. | This comma was known as the ''minthma'' from 2011. The word ''minthma'' is a contraction of ''minor thirds comma'' into a single word. 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. Gentle was named for the [[gentle region|gentle fifth]], a mild version of the [[superpyth]] fifth. | |||
== See also == | == See also == | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
== Notes == | |||
[[Category:Major minthmic]] | [[Category:Major minthmic]] | ||
[[Category:Commas named for the intervals they stack]] | |||
[[Category:Commas named for the generator of their temperament]] | |||
Latest revision as of 14:34, 20 March 2025
| 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. This means that when this comma is tempered out, 11/8 plus three perfect fourths octave reduces to 13/8; as such, this comma can be understood as relating harmonics 11 and 13 by a chain of fourths. 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 chalmersia, the smallest 13-limit superparticular comma; their sum is 176/175, the valinorsma, an 11-limit superparticular comma.
Temperaments
Tempering out this comma leads to a form of major minthmic temperament (full 13-limit rank-5) or majorminth temperament (2.3.11.13 subgroup rank-3), which enables major minthmic chords. Mintha was a nymph turned into a mint plant by a goddess whom she got in the way of[1][2][3], and major minthmic tempering has the slightly sharp, minty-fresh fifths some people appreciate. Margo Schulter has expressed great fondness for this comma, for example.
Notation
Sagittal notation
In the Sagittal system, the downward version of this comma (possibly tempered) is represented (in a secondary role) by the sagittal and is called the 13/11 kleisma, or 13/11k for short, because the simplest interval it notates is 13/11, as for example in D-F . The primary role of is 5103/5120 (7/5k). The upward version is called 11/13k or 13/11k up and is represented (in a secondary role) by .
History and etymology
This comma was known as the minthma from 2011. The word minthma is a contraction of minor thirds comma into a single word. 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. Gentle was named for the gentle fifth, a mild version of the superpyth fifth.
See also
Notes
- ↑ Dictionary of Greek and Roman Biography and Mythology – William Smith (1849)
- ↑ Dictionary of Classical Mythology – M. R. Wright (2012)
- ↑ All About Minthe – Myth of Greek Mythology – Greek Boston (2024)