Angel: Difference between revisions

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If the [[~]][[5/1]] is required to be pure, then the fifths will be exactly the same size as the fifths of quarter-comma meantone (namely, the fourth root of five), but the octaves will be slightly flat (by less than half a cent). On the other hand, if the octaves are made perfect (making it close to [[31edo]]), the ~5/1 will be slightly sharp. Both options are perceptually very close to one another.

More specifically, the term angel may refer to various [[MOS scale|mosses]] and [[MODMOS scale|modmosses]] that are derived from this setting. There are mosses with 3, 4, 7, and 11 notes per period; these have 5, 7, 12, and 19 notes per octave and so may be considered the angel equivalents of the [[~~Diatonic, Chromatic, Enharmonic, Subchromatic~~|pentic, diatonic, chromatic, and enharmonic]] scales respectively.

More specifically, the term angel may refer to various [[MOS scale|mosses]] and [[MODMOS scale|modmosses]] that are derived from this setting. There are mosses with 3, 4, 7, and 11 notes per period; these have 5, 7, 12, and 19 notes per octave and so may be considered the angel equivalents of the [[meantone #Scales|pentic, diatonic, chromatic, and enharmonic]] scales respectively.

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 do not even have to train yourself to hear the 5th harmonic as [[equivalence|equivalent]], since the octave can still be thought of as a "pseudo-equivalency" due to its being the generator.

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 If the [[~]][[5/1]] is required to be pure, then the fifths will be exactly the same size as the fifths of quarter-comma meantone (namely, the fourth root of five), but the octaves will be slightly flat (by less than half a cent). On the other hand, if the octaves are made perfect (making it close to [[31edo]]), the ~5/1 will be slightly sharp. Both options are perceptually very close to one another.
-More specifically, the term angel may refer to various [[MOS scale|mosses]] and [[MODMOS scale|modmosses]] that are derived from this setting. There are mosses with 3, 4, 7, and 11 notes per period; these have 5, 7, 12, and 19 notes per octave and so may be considered the angel equivalents of the [[Diatonic, Chromatic, Enharmonic, Subchromatic|pentic, diatonic, chromatic, and enharmonic]] scales respectively.
+More specifically, the term angel may refer to various [[MOS scale|mosses]] and [[MODMOS scale|modmosses]] that are derived from this setting. There are mosses with 3, 4, 7, and 11 notes per period; these have 5, 7, 12, and 19 notes per octave and so may be considered the angel equivalents of the [[meantone #Scales|pentic, diatonic, chromatic, and enharmonic]] scales respectively.
 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 do not even have to train yourself to hear the 5th harmonic as [[equivalence|equivalent]], since the octave can still be thought of as a "pseudo-equivalency" due to its being the generator.