1053/1024: Difference between revisions
Cmloegcmluin (talk | contribs) add section for this comma's use in Sagittal notation |
Dave Keenan (talk | contribs) →Sagittal notation: Added downward version |
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== Sagittal notation == | == Sagittal notation == | ||
In the [[Sagittal]] system, this comma (possibly tempered) is represented (in a secondary role) by the sagittal {{sagittal | /|) }} and is called the '''13 medium diesis''', or '''13M''' for short, because the simplest ratio it notates is 8:13, as for example in A:F{{sagittal | /|) }}. The primary role of {{ sagittal | /|) }} is [[36/35#Sagittal notation | 36/35]] (35M up). | In the [[Sagittal]] system, this comma (possibly tempered) is represented (in a secondary role) by the sagittal {{sagittal | /|) }} and is called the '''13 medium diesis''', or '''13M''' for short, because the simplest ratio it notates is 8:13, as for example in A:F {{sagittal | /|) }}. The primary role of {{ sagittal | /|) }} is [[36/35#Sagittal notation | 36/35]] (35M up). The downward version is called '''1/13M''' or '''13M down''' and is represented (in a secondary role) by {{sagittal| \!) }}. | ||
== Functional Just System and Helmholtz-Ellis notation == | == Functional Just System and Helmholtz-Ellis notation == | ||
Revision as of 12:42, 9 October 2024
| Interval information |
tridecimal comma
Latho comma
reduced harmonic
1053/1024, the tridecimal quartertone, tridecimal comma or Hunt minor submediant comma, is a 13-limit interval of about 48.3 cents. It is the interval between the Pythagorean major third of 81/64 and the tridecimal neutral third of 16/13. It can be considered a type of quartertone. It is 4096/4095 smaller than 36/35, and 352/351 smaller than 33/32.
Sagittal notation
In the Sagittal system, this comma (possibly tempered) is represented (in a secondary role) by the sagittal and is called the 13 medium diesis, or 13M for short, because the simplest ratio it notates is 8:13, as for example in A:F . The primary role of is 36/35 (35M up). The downward version is called 1/13M or 13M down and is represented (in a secondary role) by .
Functional Just System and Helmholtz-Ellis notation
1053/1024 is significant in Functional Just System as the tridecimal formal comma which translates a Pythagorean interval to a nearby tridecimal interval, analogous to 64/63 and 33/32 for septimal and undecimal, respectively. However, in Helmholtz-Ellis notation, that role is taken by 27/26.