135/112: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = septimal wide minor third, marvel-ptolemaic minor third, aberschismic augmented second | |||
| Color name = ry2, ruyo 2nd | |||
| Name = septimal wide minor third, | |||
| Color name = | |||
}} | }} | ||
'''135/112''', conventionally known as the '''septimal wide minor third''' or '''marvel-ptolemaic minor third''', is a [[7-limit]] interval that is sharp of the [[32/27|Pythagorean minor third]] by an [[3645/3584|aberdiesis (3645/3584)]], i.e. a [[81/80|syntonic comma (81/80)]] plus a [[225/224|marvel comma (225/224)]]. This interval functionally doubles as a type of augmented second, sharp of the [[19683/16384|Pythagorean augmented second (19683/16384)]] by an [[5120/5103|aberschisma (5120/5103)]]. This gives rise to the more precise name '''aberschismic augmented second'''. In fact it forms the difference between [[9/7]] and [[16/15]]. | |||
This interval has the distinction of being almost half of a [[16/11|undecimal semidiminished fifth (16/11)]] – in fact, a stack of two <u>135/112</u>'s differs from [[16/11]] by a [[200704/200475|"reef comma" (200704/200475)]], which is less than two cents in size. Because of the relationship between <u>135/112</u> and [[16/11]], one can easily form a triad consisting of 1–135/112–16/11, to which one can then add [[135/77]] as a seventh. | |||
== See also == | == See also == | ||
* [[224/135]] – its octave complement | |||
* [[224/135]] | * [[56/45]] – its fifth complement | ||
* [[56/45]] | |||
* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
[[Category:Third]] | [[Category:Third]] | ||
[[Category:Minor third]] | [[Category:Minor third]] | ||
[[Category: | [[Category:Second]] | ||
[[Category:Augmented second]] | |||
[[Category:Aberschismic]] | |||
Latest revision as of 13:22, 31 August 2026
| Interval information |
marvel-ptolemaic minor third,
aberschismic augmented second
135/112, conventionally known as the septimal wide minor third or marvel-ptolemaic minor third, is a 7-limit interval that is sharp of the Pythagorean minor third by an aberdiesis (3645/3584), i.e. a syntonic comma (81/80) plus a marvel comma (225/224). This interval functionally doubles as a type of augmented second, sharp of the Pythagorean augmented second (19683/16384) by an aberschisma (5120/5103). This gives rise to the more precise name aberschismic augmented second. In fact it forms the difference between 9/7 and 16/15.
This interval has the distinction of being almost half of a undecimal semidiminished fifth (16/11) – in fact, a stack of two 135/112's differs from 16/11 by a "reef comma" (200704/200475), which is less than two cents in size. Because of the relationship between 135/112 and 16/11, one can easily form a triad consisting of 1–135/112–16/11, to which one can then add 135/77 as a seventh.
See also
- 224/135 – its octave complement
- 56/45 – its fifth complement
- Gallery of just intervals