352/351: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = major minthma, major gentle comma | | Name = major minthma, major gentle comma | ||
| Color name = | | Color name = 3u1oM, thuloma | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
'''352/351''', the '''major minthma''' | '''352/351''', the '''major minthma''' or '''major gentle comma''' 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]]. This means that [[13/8]] plus three [[3/2|perfect fifths]] differs from [[11/8]] by exactly this comma up to [[octave equivalence]]; as such, this comma can be understood as relating harmonics 11 and 13 by a [[chain of fifths]]. Second, it is the difference between various tridecimal intervals and their adjacent undecimal intervals such as between [[11/9]] and [[39/32]], between [[16/13]] and [[27/22]], and between the tridecimal quartertone of [[1053/1024]] and the undecimal quartertone of [[33/32]]. | ||
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 | 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 == | == Temperaments == | ||
Tempering out this comma leads to a form of '''major minthmic | [[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 == | It is tempered out in a large number of notable temperaments such as [[meanpop]], [[srutal]], [[countercata]], [[cassandra]], [[diaschismic]], [[hemififths]], [[amity]], [[rodan]], [[buzzard]] and higher rank temperaments like [[parapyth]], [[Aberschismic family#Overview to extensions|aberschismic extensions]], [[gentle]], [[Catalog of rank-4 temperaments#Akua (352/351, 847/845)|akua]] or [[valinorsmic]]. | ||
== 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| |( }}. | ||
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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''. | 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. | 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]] | ||
== References == | |||
[[Category:Major minthmic]] | [[Category:Major minthmic]] | ||
[[Category:Commas named for the intervals they stack]] | [[Category:Commas named for the intervals they stack]] | ||
[[Category:Commas | [[Category:Commas named for the generator of their temperament]] | ||