Angel: Difference between revisions

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Although angel scales are not octave-repeating, the fact that the generator is an octave makes them far less xenharmonic than one might think. You don't even have to train yourself to hear pentaves as equivalent, since the octave can still be thought of as a "pseudo-equivalency" due to its being the generator.

In particular, the ~~[[Angel/Tuning specifications|~~angel MOS]] with 11 notes per period has long chains of ten octaves, which spans nearly the entire range of human hearing. Many if not most common-practice pieces can be easily translated into this scale, since the deviation from a purely octave-repeating system only becomes apparent for melodies and harmonies spanning several octaves. Compound intervals (spanning more than an octave) are sometimes perceived as more or less consonant than their simple counterparts; this is especially true for high-limit intervals like 11:8 (which is more consonant in compound form). Thus it may actually be beneficial to use a system that doesn't exactly repeat at the octave.

In particular, the angel MOS with 11 notes per period has long chains of ten octaves, which spans nearly the entire range of human hearing. Many if not most common-practice pieces can be easily translated into this scale, since the deviation from a purely octave-repeating system only becomes apparent for melodies and harmonies spanning several octaves. Compound intervals (spanning more than an octave) are sometimes perceived as more or less consonant than their simple counterparts; this is especially true for high-limit intervals like 11:8 (which is more consonant in compound form). Thus it may actually be beneficial to use a system that doesn't exactly repeat at the octave.

Straight-fretted angel guitars would be a possibility; such guitars would have unequally spaced frets and would need to be tuned in [https://en.wikipedia.org/wiki/All_fifths_tuning all-fifths], since the period is a fifth.

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 Although angel scales are not octave-repeating, the fact that the generator is an octave makes them far less xenharmonic than one might think. You don't even have to train yourself to hear pentaves as equivalent, since the octave can still be thought of as a "pseudo-equivalency" due to its being the generator.
-In particular, the [[Angel/Tuning specifications|angel MOS]] with 11 notes per period has long chains of ten octaves, which spans nearly the entire range of human hearing. Many if not most common-practice pieces can be easily translated into this scale, since the deviation from a purely octave-repeating system only becomes apparent for melodies and harmonies spanning several octaves. Compound intervals (spanning more than an octave) are sometimes perceived as more or less consonant than their simple counterparts; this is especially true for high-limit intervals like 11:8 (which is more consonant in compound form). Thus it may actually be beneficial to use a system that doesn't exactly repeat at the octave.
+In particular, the angel MOS with 11 notes per period has long chains of ten octaves, which spans nearly the entire range of human hearing. Many if not most common-practice pieces can be easily translated into this scale, since the deviation from a purely octave-repeating system only becomes apparent for melodies and harmonies spanning several octaves. Compound intervals (spanning more than an octave) are sometimes perceived as more or less consonant than their simple counterparts; this is especially true for high-limit intervals like 11:8 (which is more consonant in compound form). Thus it may actually be beneficial to use a system that doesn't exactly repeat at the octave.
 Straight-fretted angel guitars would be a possibility; such guitars would have unequally spaced frets and would need to be tuned in [https://en.wikipedia.org/wiki/All_fifths_tuning all-fifths], since the period is a fifth.