15/14: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 15/14 | | Ratio = 15/14 | ||
| Monzo = -1 1 1 -1 | | Monzo = -1 1 1 -1 | ||
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| Sound = jid_15_14_pluck_adu_dr220.mp3 | | Sound = jid_15_14_pluck_adu_dr220.mp3 | ||
}} | }} | ||
{{Wikipedia|Septimal diatonic semitone}} | |||
'''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: | '''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]] | * [[16/15]] and [[8/7]] | ||
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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>. | ||
== Approximation == | |||
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. | |||
== | == References == | ||
<references/> | |||
== See also == | == See also == | ||
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* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
* [[15/14ths equal temperament|AS15/14]] - its ambitonal sequence | * [[15/14ths equal temperament|AS15/14]] - its ambitonal sequence | ||
[[Category:7-limit]] | [[Category:7-limit]] | ||
[[Category:Semitone]] | [[Category:Semitone]] | ||
[[Category:Chroma]] | [[Category:Chroma]] | ||
[[Category:Superparticular]] | [[Category:Superparticular]] | ||
[[Category:Mercurial]] | [[Category:Mercurial]] | ||