Sqrt(25/24): Difference between revisions
m Eliora moved page Sqrt(25/24) to 2ed25/24: There is no need for pages about individual ET steps when they can be perfectly doubled by the same edonoi. |
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{{Infobox | {{Infobox ET}} | ||
2ed25/24 is a tuning system created by dividing the interval of [[25/24]] logarithmically into steps of about 35.336 cents each. Each step represents a frequency ratio of the square root of 25/24. | |||
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. | It is almost equal to [[34edo]]. | ||
==Theory== | |||
One step of this tuning 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. | |||
== Listen == | == Listen == | ||
Revision as of 16:24, 26 November 2022
| ← 11edo | Sqrt(25/24) | 13edo → |
(convergent)
2ed25/24 is a tuning system created by dividing the interval of 25/24 logarithmically into steps of about 35.336 cents each. Each step represents a frequency ratio of the square root of 25/24.
It is almost equal to 34edo.
Theory
One step of this tuning 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.
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.