135/128: Difference between revisions
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it's not just close, it's a semiconvergent |
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== Temperaments == | == Temperaments == | ||
If 135/128 is treated as a comma to be tempered out, it may be called the '''pelogic comma'''. It represents the difference between three [[4/3|perfect fourth]]s and a [[5/4|just major third]] (plus an [[octave]]). Tempering it out results in [[mavila temperament]]. | If 135/128 is treated as a comma to be tempered out, it may be called the '''pelogic comma'''. It represents the difference between three [[4/3|perfect fourth]]s and a [[5/4|just major third]] (plus an [[octave]]). Tempering it out results in [[mavila temperament]]. | ||
135/128 is very close to one step of [[13edo]], in fact being a [[Wikipedia:Continued_fraction|semiconvergent]]. [[Aluminium]] temperament realizes this through a regular temperament lens. | |||
== See also == | == See also == | ||
* [[256/135]] – its [[octave complement]] | * [[256/135]] – its [[octave complement]] | ||
* [[Aluminium comma]] - the difference between 13 stacks of this interval and [[2/1]] | |||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
* [[Medium comma]] | * [[Medium comma]] | ||
Revision as of 22:36, 17 May 2023
| Interval information |
major limma,
major chroma,
pelogic comma
Layobi comma
reduced harmonic
[sound info]
The 5-limit interval 135/128, about 92.2 cents in size, is called the ptolemaic chromatic semitone, major limma or major chroma. It is a syntonic comma away from the Pythagorean chromatic semitone 2187/2048, and so is tuned justly in 1/7 comma meantone. Flattening by another syntonic comma reaches the even simpler 25/24. In regular 5-limit diatonic systems, it is the chromatic semitone that compliments 16/15, as the two semitones add up to 9/8.
Temperaments
If 135/128 is treated as a comma to be tempered out, it may be called the pelogic comma. It represents the difference between three perfect fourths and a just major third (plus an octave). Tempering it out results in mavila temperament.
135/128 is very close to one step of 13edo, in fact being a semiconvergent. Aluminium temperament realizes this through a regular temperament lens.
See also
- 256/135 – its octave complement
- Aluminium comma - the difference between 13 stacks of this interval and 2/1
- Gallery of just intervals
- Medium comma
- File:Ji-135-128-csound-foscil-220hz.mp3 – another sound example