Ed4: Difference between revisions

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The resultant scale we can call 5ed4.

Odd ed4s are [[nonoctave]] systems, but even ed4s are not and ~~are identical~~ to ~~EDOs~~.

Odd-numbered ed4s are [[nonoctave]] systems (in fact ones with the highest attainable relative error for the octave), but even-numbered ed4s are not and exactly correspond to [[EDO]]s (2ed4 to [[1edo]], 4ed4 to [[2edo]], 6ed4 to [[3edo]] and so on).

This approach yields more useful scales starting with edo systems which are larger, where a composer might decide a single degree is too small to be useful. As one example, consider 37edo, which is known to be an excellent temperament in the 2.5.7.11.13.27 [[subgroup]], but whose single degree, approximately 32.4¢, might be "too small" in some context (e.g. guitar frets). Taking every other step of 37edo produces [[37ed4]], an equal-stepped scale which repeats at 4/1, the double octave, and has a single step of 64.9¢. (See also [[65cET]].)

@@ Line 10: / Line 10: @@
 The resultant scale we can call 5ed4.
-Odd ed4s are [[nonoctave]] systems, but even ed4s are not and are identical to EDOs.
+Odd-numbered ed4s are [[nonoctave]] systems (in fact ones with the highest attainable relative error for the octave), but even-numbered ed4s are not and exactly correspond to [[EDO]]s (2ed4 to [[1edo]], 4ed4 to [[2edo]], 6ed4 to [[3edo]] and so on).
 This approach yields more useful scales starting with edo systems which are larger, where a composer might decide a single degree is too small to be useful. As one example, consider 37edo, which is known to be an excellent temperament in the 2.5.7.11.13.27 [[subgroup]], but whose single degree, approximately 32.4¢, might be "too small" in some context (e.g. guitar frets). Taking every other step of 37edo produces [[37ed4]], an equal-stepped scale which repeats at 4/1, the double octave, and has a single step of 64.9¢. (See also [[65cET]].)