Sqrt(25/24): Difference between revisions
m VectorGraphics moved page 2ed25/24 to Sqrt(25/24) over redirect: There's precedent for radical intervals having their own pages, and additionally, most of what this page discusses is the radical interval, not the tuning system. |
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Sqrt(25/24), the '''classical semichroma''' or '''ptolemaic semichroma'''<ref group="note">It is not ''diptolemaic'' as it is only flattened by one [[81/80|comma]] from the Pythagorean semichroma of [[sqrt(2187/2048)]].</ref>, is a the difference between a 5-limit major or minor third and a pure neutral third [[Sqrt(3/2)]]. | |||
{{Infobox interval|Ratio=\sqrt{25/24}|Name=classical semichroma, ptolemaic semichroma|Cents=35.336}} | |||
This is an interval that allows to pass from a just major third (5/4) to a just minor third (6/5) by [[equal contrary motion]], and vice versa. Let be two voices forming a 5/4 interval. If the lower voice goes up by a sqrt(25/24) and the upper voice goes down by the same interval, the next interval formed by the two voices will be a 6/5 interval. | This is an interval that allows to pass from a just major third (5/4) to a just minor third (6/5) by [[equal contrary motion]], and vice versa. Let be two voices forming a 5/4 interval. If the lower voice goes up by a sqrt(25/24) and the upper voice goes down by the same interval, the next interval formed by the two voices will be a 6/5 interval. | ||
The interval, when stacked, yields a tuning system close to [[34edo]], which consistently represents it as one step. | |||
== Listen == | == Listen == | ||
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[[34edo|34-edo]] has such an excellent sqrt(25/24) that the next EDO to have a better one is [[441edo|441]]. | [[34edo|34-edo]] has such an excellent sqrt(25/24) that the next EDO to have a better one is [[441edo|441]]. | ||
<references group="note" /> | |||
Revision as of 17:07, 3 June 2025
Sqrt(25/24), the classical semichroma or ptolemaic semichroma[note 1], is a the difference between a 5-limit major or minor third and a pure neutral third Sqrt(3/2).
| Interval information |
ptolemaic semichroma
This is an interval that allows to pass from a just major third (5/4) to a just minor third (6/5) by equal contrary motion, and vice versa. Let be two voices forming a 5/4 interval. If the lower voice goes up by a sqrt(25/24) and the upper voice goes down by the same interval, the next interval formed by the two voices will be a 6/5 interval.
The interval, when stacked, yields a tuning system close to 34edo, which consistently represents it as one step.
Listen
Approximations
EDOs that have both a good 5-odd-limit and a sqrt(25/24) distinct from 25/24 include (among others) 24, 27, 31 and 34.
34-edo has such an excellent sqrt(25/24) that the next EDO to have a better one is 441.
- ↑ It is not diptolemaic as it is only flattened by one comma from the Pythagorean semichroma of sqrt(2187/2048).