Ed9

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Equal Divisions of the Double Tritave -- frequency ratio 9/1, aka "Nonuple" -- are closely related to Equal Divisions of the Tritave -- frequency ratio 3/1, aka "Triple" -- in other words, ED3 or EDT scales. Given any odd-numbered ED3, an ED9 can be generated by taking every other tone of the ED3. For example, given 5ED3 (aka 5edt), two tritaves of which, in cents are:

0 380 761 1141 1522 1902 2282 2663 3043 3424 3804...

...taking every other tone yields:

0 380 761 1141 1522 1902 2282 2663 3043 3424 3804...

0 761 1522 2282 3043 3804...

The resultant scale we can call 5ED9.

This approach yields more useful scales starting with ED3 systems which are larger, where a composer might decide a single degree is too small to be useful. As one example, consider 53ED3 (aka 53edt), which is well known to be an excellent temperament in the 3.4.5.7.11.13.17.19 subgroup, but whose single degree, approximately 35.9¢, might be "too small" in some context (e.g. guitar frets). Taking every other step of 53ED3 produces 53ED9, an equal-stepped scale which repeats at 9/1, the double tritave, and has a single step of 71.8¢.

ED9 scales also have the feature that they ascend the pitch continuum twice as fast as ED3 systems. 53 tones of 53ED3 is one tritave, while 53 tones of 53ED9 is two tritaves. Thus, fewer bars would be needed on a metallophone, fewer keys on a keyboard, etc.

See: Equal Temperaments

Individual pages for ED9s