Modal union: Difference between revisions
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{{About|a type of scale|a collection of scales|Dome}} | {{About|a type of scale|a collection of scales|Dome}} | ||
The '''modal union''' of a [[periodic scale]] is the scale obtained by superimposing all its [[mode]]s on the same tonal center. The resulting scale contains every mode of the original scale on | The '''modal union''' of a [[periodic scale]] is the scale obtained by superimposing all its [[mode]]s on the same tonal center. The resulting scale contains every mode of the original scale on the tonic. | ||
The modal union of an ''n''-tone scale has at most 2''n''−1 distinct tones; it has fewer tones if there are enharmonic equivalents. For example, the basic [[5L 2s|diatonic]] scale of [[12edo]] has 7 tones, but its modal union only has 12 tones instead of 13, because the augmented fourth of the lydian mode is enharmonically equivalent to the diminished fifth of the the locrian mode. However, in other tunings of the diatonic scale, such as [[17edo]] (hard diatonic) or [[19edo]] (soft diatonic), the modal union has 13 tones, and the enharmonic notes differ by a [[diesis]]. | The modal union of an ''n''-tone scale has at most 2''n''−1 distinct tones; it has fewer tones if there are enharmonic equivalents. For example, the basic [[5L 2s|diatonic]] scale of [[12edo]] has 7 tones, but its modal union only has 12 tones instead of 13, because the augmented fourth of the lydian mode is enharmonically equivalent to the diminished fifth of the the locrian mode. However, in other tunings of the diatonic scale, such as [[17edo]] (hard diatonic) or [[19edo]] (soft diatonic), the modal union has 13 tones, and the enharmonic notes differ by a [[diesis]]. | ||