15/14: Difference between revisions
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'''15/14''' is a [[superparticular]] ratio with a numerator which is the fifth [[Wikipedia: | '''15/14''' is a [[superparticular]] ratio with a numerator which is the fifth [[Wikipedia:Triangular number|triangular number]]. It may be found as the interval between many [[7-limit]] ratios, including: | ||
It may be found as the interval between many [[7-limit]] ratios, including: | |||
* [[16/15]] and [[8/7]] | * [[16/15]] and [[8/7]] | ||
* [[14/13]] and [[15/13]] | * [[14/13]] and [[15/13]] | ||
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* [[7/4]] and [[15/8]] | * [[7/4]] and [[15/8]] | ||
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> | |||
== Terminology == | |||
15/14 is traditionally called a ''diatonic semitone'', perhaps for its proximity (and conflation in systems such as septimal [[meantone]]) with the classic diatonic semitone [[16/15]]. However, 15/14 is a ''[[Wikipedia:chromatic semitone|chromatic semitone]]'' in both [[Helmholtz-Ellis notation]] and [[Functional Just System]], viewed as the apotome [[2187/2048]] altered by [[5120/5103]]. [[Marc Sabat]] has taken to call it the ''major chromatic semitone'' in the same material where [[21/20]] is also named as the minor diatonic semitone<ref>[https://marsbat.space/pdfs/crystal-growth.pdf Marc Sabat (2008) Three Crystal Growth Algorithms in 23-limit constrained Harmonic Space]</ref>. | |||
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== See also == | == See also == | ||
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* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
* [[Gallery of Just Intervals]] | * [[Gallery of Just Intervals]] | ||
* [[Wikipedia: | * [[Wikipedia: Septimal diatonic semitone]] | ||
[[Category:7-limit]] | [[Category:7-limit]] | ||
Revision as of 14:32, 3 March 2021
| 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
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))
Terminology
15/14 is traditionally called a diatonic semitone, perhaps for its proximity (and conflation in systems such as septimal meantone) with the classic diatonic semitone 16/15. However, 15/14 is a chromatic semitone in both Helmholtz-Ellis notation and Functional Just System, viewed as the apotome 2187/2048 altered by 5120/5103. Marc Sabat has taken to call it the major chromatic semitone in the same material where 21/20 is also named as the minor diatonic semitone[1].