15/14: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = septimal diatonic semitone, septimal major semitone | |||
| Color name = ry1, ruyo unison | |||
| Name = septimal diatonic semitone, | |||
| Color name = ry1, ruyo | |||
| 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]] | ||
* [[7/6]] and [[5/4]] | * [[7/6]] and [[5/4]] | ||
* [[6/5]] and [[9/7]] | * [[6/5]] and [[9/7]] | ||
* [[4/3]] and [[10/7]] | * [[4/3]] and [[10/7]] | ||
* [[7/5]] and [[3/2]] | * [[7/5]] and [[3/2]] | ||
* [[14/9]] and [[5/3]] | * [[14/9]] and [[5/3]] | ||
* [[8/5]] and [[12/7]] | * [[8/5]] and [[12/7]] | ||
* [[7/4]] and [[15/8]] | * [[7/4]] and [[15/8]] | ||
It also arises in higher limits as: | |||
* [[14/13]] and [[15/13]] | |||
* [[14/11]] and [[15/11]] | |||
* [[22/15]] and [[11/7]] | |||
* [[26/15]] and [[13/7]] | |||
== 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 [[ | 15/14 is traditionally called a ''diatonic semitone'', perhaps for its proximity (and conflation in systems such as septimal [[meantone]] and [[marvel]]) with the classic diatonic semitone [[16/15]]. However, 15/14 is a ''[[Wikipedia:chromatic semitone|chromatic semitone]]'' in both [[Helmholtz–Ellis notation]] and the [[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>Marc Sabat. [https://masa.plainsound.org/pdfs/crystal-growth.pdf ''Three Crystal Growth Algorithms in 23-limit constrained Harmonic Space'']. Plainsound Music Edition, 2008.</ref>. | ||
== 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. | |||
< | In combination with [[19/17]] it forms a good approximation of [[golden meantone]]. The untempered combination of five 19/17's and two 15/14's leads to an interval that is sharp to an octave by the [[mercurial comma]]: (19/17)<sup>5</sup> × (15/14)<sup>2</sup> = 2 / (mercurial comma). | ||
== | == Temperaments == | ||
15/14 is | The following [[linear temperament]]s are [[generate]]d by a [[~]]15/14: | ||
* [[Septidiasemi]] | |||
* [[Subsedia]] | |||
In addition, this [[fractional-octave temperament]] is generated by a ~15/14: | |||
* [[Tertiosec]] (1\3) | |||
Several [[10th-octave temperaments]] treat ~15/14 as the period, including [[decoid]] and [[linus]]. | |||
{{todo|complete list}} | |||
== See also == | == See also == | ||
| Line 38: | Line 45: | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
== References == | |||
<references/> | |||
[[Category:Semitone]] | [[Category:Semitone]] | ||
[[Category:Chroma]] | [[Category:Chroma]] | ||
[[Category:Mercurial]] | [[Category:Mercurial]] | ||