135/112: Difference between revisions
Make this marvel-ptolemaic until 3645/3584 has an accepted name |
Update thanks to the establishment of the aberschisma |
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{{Infobox Interval | {{Infobox Interval | ||
| Name = septimal wide minor third, marvel-ptolemaic minor third, | | Name = septimal wide minor third, marvel-ptolemaic minor third, aberschismic augmented second | ||
| Color name = ry2, ruyo 2nd | | Color name = ry2, ruyo 2nd | ||
}} | }} | ||
'''135/112''', the '''septimal wide minor third''' | '''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 [[3645/3584]], i.e. a [[81/80|syntonic comma]] plus a [[225/224|marvel comma]]. This interval functionally doubles as a type of augmented second, sharp of the [[19683/16384|Pythagorean augmented second]] by an [[aberschisma]]. 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]] semidiminished fifth – in fact, a stack of two 135/112's differs from [[16/11]] by [[200704/200475]], a comma 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. | This interval has the distinction of being almost half of a [[16/11]] semidiminished fifth – in fact, a stack of two 135/112's differs from [[16/11]] by [[200704/200475]], a comma 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. | ||
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[[Category:Second]] | [[Category:Second]] | ||
[[Category:Augmented second]] | [[Category:Augmented second]] | ||
[[Category: | [[Category:Aberschismic]] | ||
Latest revision as of 19:48, 30 July 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 3645/3584, i.e. a syntonic comma plus a marvel comma. This interval functionally doubles as a type of augmented second, sharp of the Pythagorean augmented second by an aberschisma. 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 semidiminished fifth – in fact, a stack of two 135/112's differs from 16/11 by 200704/200475, a comma 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