15/14: Difference between revisions
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Although called ''septimal diatonic semitone'' for its proximity (and conflation in systems such as septimal [[meantone]]) with the classic diatonic semitone [[16/15]], 15/14 is a ''[[Wikipedia:chromatic semitone|chromatic semitone]]'' in both [[Helmholtz-Ellis notation]] and [[Functional Just System]] because it is [[5120/5103]] larger than the apotome [[2187/2048]]. | Although called ''septimal diatonic semitone'' for its proximity (and conflation in systems such as septimal [[meantone]]) with the classic diatonic semitone [[16/15]], 15/14 is a ''[[Wikipedia:chromatic semitone|chromatic semitone]]'' in both [[Helmholtz-Ellis notation]] and [[Functional Just System]] because it is [[5120/5103]] larger than the apotome [[2187/2048]]. | ||
In combination with [[19/17]] it forms a good approximation of [[golden meantone]]. | In combination with [[19/17]] it forms a good approximation of [[golden meantone]]. The untempered combination of five 19/17 and two 15/14 leads to an interval that is sharp to an octave by the [[mercurial comma]]: <code>((19/17)^5 * (15/14)^2 = (2/1) / (mercurial comma))</code> | ||
== See also == | == See also == | ||
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[[Category:Superparticular]] | [[Category:Superparticular]] | ||
[[Category:Listen]] | [[Category:Listen]] | ||
[[Category:Mercurial]] | |||
Revision as of 00:54, 17 December 2020
| Interval information |
reduced
[sound info]
15/14 is a superparticular ratio with a numerator which is the fifth triangular number.
It may be found as the interval between many 7-limit ratios, including:
- 16/15 and 8/7
- 14/13 and 15/13
- 7/6 and 5/4
- 6/5 and 9/7
- 14/11 and 15/11
- 4/3 and 10/7
- 7/5 and 3/2
- 22/15 and 11/7
- 14/9 and 5/3
- 8/5 and 12/7
- 26/15 and 13/7
- 7/4 and 15/8
Although called septimal diatonic semitone for its proximity (and conflation in systems such as septimal meantone) with the classic diatonic semitone 16/15, 15/14 is a chromatic semitone in both Helmholtz-Ellis notation and Functional Just System because it is 5120/5103 larger than the apotome 2187/2048.
In combination with 19/17 it forms a good approximation of golden meantone. The untempered combination of five 19/17 and two 15/14 leads to an interval that is sharp to an octave by the mercurial comma: ((19/17)^5 * (15/14)^2 = (2/1) / (mercurial comma))