Sqrt(25/24): Difference between revisions
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relation to sqrtP5 probably more important than voice leading, also plan to reformat this as a radical interval page rather than an ET page at some point |
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It is almost equal to [[34edo]]. | It is almost equal to [[34edo]]. | ||
==Theory== | ==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. | One step of this tuning, the '''classical semichroma''', is the difference between a 5-limit major or minor third and a pure neutral third [[Sqrt(3/2)]]. | ||
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. | |||
== Listen == | == Listen == | ||
Revision as of 11:56, 3 June 2025
| ← 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, the classical semichroma, is the difference between a 5-limit major or minor third and a pure neutral third Sqrt(3/2).
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.
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.