Sqrt(25/24): Difference between revisions

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{{Infobox ~~Interval~~

{{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.

| Ratio = \sqrt{25/24}

| ~~Monzo~~ = ~~-3/2 -1/2 1~~

| Cents = 35.~~33621343214121~~

~~| Name = square root of 25/24~~

~~| Calc = sqrt~~(25/24)

}}

~~The~~ '''~~square root of [[25/24]]~~''' ('''~~sqrt(25/24)~~''') is ~~an interval measuring approximately 35.336{{cent}} 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. 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 ==

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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]].

[[34edo~~|34-edo~~]] has such an excellent sqrt(25/24) that the next EDO to have a better one is [[441edo|441]].

[[34edo]] has such an excellent sqrt(25/24) that the next EDO to have a better one is [[441edo|441]].

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-{{Infobox Interval
+{{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.
-| Ratio = \sqrt{25/24}
-| Monzo = -3/2 -1/2 1
-| Cents = 35.33621343214121
-| Name = square root of 25/24
-| Calc = sqrt(25/24)
-}}
-The '''square root of [[25/24]]''' ('''sqrt(25/24)''') is an interval measuring approximately 35.336{{cent}} 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. 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 ==
@@ Line 19: / Line 16: @@
 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|34-edo]] has such an excellent sqrt(25/24) that the next EDO to have a better one is [[441edo|441]].
+[[34edo]] has such an excellent sqrt(25/24) that the next EDO to have a better one is [[441edo|441]].
+<references group="note" />