Sqrt(25/24): Difference between revisions
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Sqrt(25/24) is | {{Infobox interval|Ratio=\sqrt{25/24}|Name=classical semichroma, ptolemaic semichroma|Cents=35.336}}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 (hemi-)Pythagorean semichroma of [[sqrt(2187/2048)]].</ref>, is a the difference between a 5-limit major or minor third and a neutral third [[sqrt(3/2)]] dividing the [[3/2|perfect fifth]] in two. | ||
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. Any [[edo]] that maps [[25/24]] to an even number of steps, and thus any edo that contains a true neutral third, contains a representation of this interval. | ||
[ | Rational intervals that are close to this interval include [[49/48]] and [[50/49]], which stack to 25/24. The difference between 49/48 and 50/49 is [[2401/2400]], and tempering it out leads to the super-accurate [[Breed (temperament)|breed]] temperament. | ||
This interval, when stacked, yields a tuning system close to [[34edo]], which consistently represents it as one step. | |||
== Listen == | == Listen == | ||
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EDOs that have both a good [[5-odd-limit]] and a sqrt(25/24) distinct from [[25/24]] include (among others) [[24edo#Counterpoint|24]], [[27edo|27]], [[31edo|31]] and [[34edo|34]]. | EDOs that have both a good [[5-odd-limit]] and a sqrt(25/24) distinct from [[25/24]] include (among others) [[24edo#Counterpoint|24]], [[27edo|27]], [[31edo|31]] and [[34edo|34]]. | ||
[[34edo | [[34edo]] has such an excellent sqrt(25/24) that the next EDO to have a better one is [[441edo|441]]. | ||
<references group="note" /> | |||
Latest revision as of 09:56, 30 December 2025
| Interval information |
ptolemaic semichroma
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 neutral third sqrt(3/2) dividing the perfect fifth in two.
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. Any edo that maps 25/24 to an even number of steps, and thus any edo that contains a true neutral third, contains a representation of this interval.
Rational intervals that are close to this interval include 49/48 and 50/49, which stack to 25/24. The difference between 49/48 and 50/49 is 2401/2400, and tempering it out leads to the super-accurate breed temperament.
This 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.
34edo 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 (hemi-)Pythagorean semichroma of sqrt(2187/2048).