2187/2048: Difference between revisions

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added main lemma, reworked accordingly, added see-also links
m "Chroma" seems a good category for augmented unisons
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[[Category: 3-limit]]
[[Category:3-limit]]
[[Category: Interval]]
[[Category:Interval]]
[[Category: Interval ratio]]
[[Category:Interval ratio]]
[[Category: Pythagorean]]
[[Category:Large comma]]
[[Category: Semitone]]
[[Category:Pythagorean]]
[[Category: Large comma]]
[[Category:Semitone]]
[[Category:Chroma]]
[[Category:Apotomic]]

Revision as of 10:38, 9 October 2020

Interval information
Ratio 2187/2048
Factorization 2-11 × 37
Monzo [-11 7
Size in cents 113.685¢
Names Apotome,
Pythagorean chromatic semitone
FJS name [math]\displaystyle{ \text{A1} }[/math]
Special properties reduced,
reduced harmonic
Tenney norm (log2 nd) 22.0947
Weil norm (log2 max(n, d)) 22.1895
Wilson norm (sopfr(nd)) 43

[sound info]
Open this interval in xen-calc

2187/2048, the apotome, also known as the Pythagorean chromatic semitone or the Pythagorean major semitone, is the chromatic semitone in the Pythagorean tuning. It is the 3-limit interval between seven perfect just fifths (3/2) and four octaves (2/1): 37/211 = 2187/2048, and measures about 113.7¢. Unlike the situation in meantone tunings, it is larger, not smaller, than the corresponding diatonic semitone, which is the Pythagorean minor second of 256/243.

See also