352/351: Difference between revisions

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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 [[16/13]] and [[27/22]]; and

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== 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 ==

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 ~~down~~). The upward version is called '''11/13k''' or '''13/11k up''' and is represented (in a secondary role) by {{sagittal| |( }}.

=== 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| |( }}.

== 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 ==

* [[Small comma]]

* [[List of superparticular intervals]]

== Notes ==

[[Category:Major minthmic]]

[[Category:Commas named for the intervals they stack]]

[[Category:Commas named for the generator of their temperament]]

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 | 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:
+'''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 [[16/13]] and [[27/22]]; and
@@ Line 12: / Line 12: @@
 == 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 ==
-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 down). The upward version is called '''11/13k''' or '''13/11k up''' and is represented (in a secondary role) by {{sagittal| |( }}.
+=== 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| |( }}.
 == 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 ==
-* [[Small comma]]
 * [[List of superparticular intervals]]
+== Notes ==
 [[Category:Major minthmic]]
+[[Category:Commas named for the intervals they stack]]
+[[Category:Commas named for the generator of their temperament]]