135/128
Ratio | 135/128 |
Factorization | 2^{-7} × 3^{3} × 5 |
Monzo | [-7 3 1⟩ |
Size in cents | 92.178716¢ |
Names | ptolemaic chromatic semitone, major limma, major chroma, mavila comma |
Color name | Ly1, layo unison, Layobi comma |
FJS name | [math]\text{A1}^{5}[/math] |
Special properties | reduced, reduced harmonic |
Tenney height (log_{2} nd) | 14.0768 |
Weil height (log_{2} max(n, d)) | 14.1536 |
Wilson height (sopfr (nd)) | 28 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~4.3033 bits |
Comma size | medium |
S-expression | S3 / S4 |
[sound info] | |
open this interval in xen-calc |
The 5-limit interval 135/128, about 92.2 cents in size, is called the ptolemaic chromatic semitone, the major limma or the 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 mavila comma. It represents the difference between three perfect fourths and a just major third (plus an octave). Tempering it out results in the 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 a stack of 13 instances of this interval and 2/1
- Gallery of just intervals
- Medium comma
- File:Ji-135-128-csound-foscil-220hz.mp3 – another sound example