135/128

Interval information

Ratio	135/128
Factorization	2-7 × 33 × 5
Monzo	[-7 3 1⟩
Size in cents	92.17872¢
Names	ptolemaic chromatic semitone, major limma, major chroma, mavila comma
Color name	Ly1, layo unison, Layobi comma
FJS name	[math]\displaystyle{ \text{A1}^{5} }[/math]
Special properties	reduced, reduced harmonic
Tenney height (log2 nd)	14.0768
Weil height (log2 max(n, d))	14.1536
Wilson height (sopfr(nd))	28
Harmonic entropy (Shannon, [math]\displaystyle{ \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