135/128: Difference between revisions

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The [[5-limit]] interval '''135/128''', about 92.2 [[cent]]s 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]].
The [[5-limit]] interval '''135/128''', about 92.2 [[cent]]s 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]].


As a [[comma]], it is known as the '''pelogic comma''', and it represents the difference between three [[4/3|perfect fourths]] and a [[5/4|just major third]] (plus an [[octave]]).
== 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]]).


== See also ==
== See also ==

Revision as of 19:37, 28 January 2023

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,
pelogic 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
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, 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).

See also

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