Ed4: Difference between revisions

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This approach yields more useful scales starting with ED2 systems which are larger, where a composer might decide a single degree is too small to be useful. As one example, consider 37ED2 (aka [[37edo]]), which is well 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 37ED2 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]].)

ED4 scales also have the feature that they ascend the pitch continuum twice as fast as ED2 systems. 37 tones of 37ED2 is one octave, while 37 tones of ~~ED4~~ is 2 octaves. Thus, fewer bars would be needed on a metallophone, fewer keys on a keyboard, etc.

ED4 scales also have the feature that they ascend the pitch continuum twice as fast as ED2 systems. 37 tones of 37ED2 is one octave, while 37 tones of 37ED4 is 2 octaves. Thus, fewer bars would be needed on a metallophone, fewer keys on a keyboard, etc.

See: [[Equal-step tuning|Equal Temperaments]]

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*[[57ed4]]

*[[59ed4]]

*[[61ed4]]

*[[63ed4]]

*[[65ed4]]

*[[67ed4]]

*[[69ed4]]

*[[71ed4]]

*[[73ed4]]

*[[75ed4]]

*[[77ed4]]

*[[79ed4]]

*[[81ed4]]

*[[83ed4]]

*[[85ed4]]

*[[87ed4]]

*[[89ed4]]

*[[91ed4]]

*[[93ed4]]

*[[95ed4]]

*[[97ed4]]

*[[99ed4]]

[[Category:Ed4| ]]

[[Category:Equal-step tuning]]

@@ Line 13: / Line 13: @@
 This approach yields more useful scales starting with ED2 systems which are larger, where a composer might decide a single degree is too small to be useful. As one example, consider 37ED2 (aka [[37edo]]), which is well 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 37ED2 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]].)
-ED4 scales also have the feature that they ascend the pitch continuum twice as fast as ED2 systems. 37 tones of 37ED2 is one octave, while 37 tones of ED4 is 2 octaves. Thus, fewer bars would be needed on a metallophone, fewer keys on a keyboard, etc.
+ED4 scales also have the feature that they ascend the pitch continuum twice as fast as ED2 systems. 37 tones of 37ED2 is one octave, while 37 tones of 37ED4 is 2 octaves. Thus, fewer bars would be needed on a metallophone, fewer keys on a keyboard, etc.
 See: [[Equal-step tuning|Equal Temperaments]]
@@ Line 47: / Line 47: @@
 *[[57ed4]]
 *[[59ed4]]
+*[[61ed4]]
+*[[63ed4]]
+*[[65ed4]]
+*[[67ed4]]
+*[[69ed4]]
+*[[71ed4]]
+*[[73ed4]]
+*[[75ed4]]
+*[[77ed4]]
+*[[79ed4]]
+*[[81ed4]]
+*[[83ed4]]
+*[[85ed4]]
+*[[87ed4]]
+*[[89ed4]]
+*[[91ed4]]
+*[[93ed4]]
+*[[95ed4]]
+*[[97ed4]]
+*[[99ed4]]
 [[Category:Ed4| ]]
 [[Category:Equal-step tuning]]