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Created page with "Equal Divisions of the Triple Octave -- frequency ratio 8/1, aka "Octuple" -- are closely related to Equal Divisions of the Octave -- frequency ratio 2/1, aka "Duple" -- in ot..." |
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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 31ED2 (aka [[31edo]]), which is well known to be a consistent temperament in the 11-limit, but whose single degree, approximately 38.7¢, might be "too small" in some context (e.g. guitar frets). Taking every third step of 31ED2 produces [[31ed8|31ED8]], an equal-stepped scale which repeats at 8/1, the triple octave, and has a single step of 116.1¢. | 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 31ED2 (aka [[31edo]]), which is well known to be a consistent temperament in the 11-limit, but whose single degree, approximately 38.7¢, might be "too small" in some context (e.g. guitar frets). Taking every third step of 31ED2 produces [[31ed8|31ED8]], an equal-stepped scale which repeats at 8/1, the triple octave, and has a single step of 116.1¢. | ||
ED8 scales also have the feature that they ascend the pitch continuum three times as fast as ED2 systems. 31 tones of 31ED2 is one octave, while | ED8 scales also have the feature that they ascend the pitch continuum three times as fast as ED2 systems. 31 tones of 31ED2 is one octave, while 31 tones of 31ED8 is three octaves. Thus, fewer bars would be needed on a metallophone, fewer keys on a keyboard, etc. | ||
See: [[Equal-step tuning|Equal Temperaments]] | See: [[Equal-step tuning|Equal Temperaments]] | ||