15/14: Difference between revisions
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== Terminology == | == 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>. | 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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== Approximation == | == Approximation == | ||
15/14 is very accurately approximated by [[10edo]] (1\10) and all linus temperaments. The [[linus comma]], 5.6¢, is the amount by which a stack of ten 15/14's falls short of the octave. | 15/14 is very accurately approximated by [[10edo|10EDO]] (1\10) and all linus temperaments. The [[15/14ths equal temperament|linus comma]], 5.6¢, is the amount by which a stack of ten 15/14's falls short of the octave. | ||
== See also == | == See also == | ||
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* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
* [[15/14ths equal temperament|AS15/14]] - its ambitonal sequence | |||
* [[Wikipedia: Septimal diatonic semitone]] | * [[Wikipedia: Septimal diatonic semitone]] | ||
Revision as of 22:17, 10 September 2021
| Interval information |
septimal major semitone
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].
Approximation
15/14 is very accurately approximated by 10EDO (1\10) and all linus temperaments. The linus comma, 5.6¢, is the amount by which a stack of ten 15/14's falls short of the octave.
See also
- 28/15 – its octave complement
- 7/5 – its fifth complement
- List of superparticular intervals
- Gallery of just intervals
- AS15/14 - its ambitonal sequence
- Wikipedia: Septimal diatonic semitone