5L 5s: Difference between revisions

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However, if one insists on using only the versions of the diatonic scale that have the maximum number of consonant triads available, then it turns out all of these scales will be 7-note subsets of Blackwood[10]. They will also be the most compact arrangement of those five consonant triads possible on the 5-limit triangular lattice, which is just a fancy way of saying those five chords will be maximally connected to each other by common tones. This suggests that one can approach melody in Blackwood[10] by treating it not as one 10-note scale, but as several related 7-note scales, each of which functions like a 5-limit untempered version of the diatonic scale.

This approach allows one to apply the usual principles of diatonic tonality and modality, with the caveat that each familiar mode of the diatonic scale will come in two flavors, depending which of the 7 notes one wants to build consonant triads on. The two flavors will share six notes in common, but one of the seven will differ by 81/80 (i.e. one step of 15edo). Interesting relationships do arise if one maintains the tonic but switches through its different modes (i.e. 1 mixolydian to 1 ionian to 1 lydian), and an "extra" mode appears, because ~~of the fact that 256/243 is tempered out~~ (~~a way to understand 256/243 vanishing in musical terms is that~~ V/V/V/V = IV, unlike in meantone where V/V/V/V = iii). All together, there are 14 modes of the 7-note diatonic to be found in Blackwood[10] if we keep the same tonic, and 20 if we allow alterations of the tonic.

This approach allows one to apply the usual principles of diatonic tonality and modality, with the caveat that each familiar mode of the diatonic scale will come in two flavors, depending which of the 7 notes one wants to build consonant triads on. The two flavors will share six notes in common, but one of the seven will differ by 81/80 (i.e. one step of 15edo). Interesting relationships do arise if one maintains the tonic but switches through its different modes (i.e. 1 mixolydian to 1 ionian to 1 lydian), and an "extra" mode appears, because five fifths close (hence V/V/V/V = IV, unlike in meantone where V/V/V/V = iii). All together, there are 14 modes of the 7-note diatonic to be found in Blackwood[10] if we keep the same tonic, and 20 if we allow alterations of the tonic.

== MODMOSes ==

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 However, if one insists on using only the versions of the diatonic scale that have the maximum number of consonant triads available, then it turns out all of these scales will be 7-note subsets of Blackwood[10]. They will also be the most compact arrangement of those five consonant triads possible on the 5-limit triangular lattice, which is just a fancy way of saying those five chords will be maximally connected to each other by common tones. This suggests that one can approach melody in Blackwood[10] by treating it not as one 10-note scale, but as several related 7-note scales, each of which functions like a 5-limit untempered version of the diatonic scale.
-This approach allows one to apply the usual principles of diatonic tonality and modality, with the caveat that each familiar mode of the diatonic scale will come in two flavors, depending which of the 7 notes one wants to build consonant triads on. The two flavors will share six notes in common, but one of the seven will differ by 81/80 (i.e. one step of 15edo). Interesting relationships do arise if one maintains the tonic but switches through its different modes (i.e. 1 mixolydian to 1 ionian to 1 lydian), and an "extra" mode appears, because of the fact that 256/243 is tempered out (a way to understand 256/243 vanishing in musical terms is that V/V/V/V = IV, unlike in meantone where V/V/V/V = iii). All together, there are 14 modes of the 7-note diatonic to be found in Blackwood[10] if we keep the same tonic, and 20 if we allow alterations of the tonic.
+This approach allows one to apply the usual principles of diatonic tonality and modality, with the caveat that each familiar mode of the diatonic scale will come in two flavors, depending which of the 7 notes one wants to build consonant triads on. The two flavors will share six notes in common, but one of the seven will differ by 81/80 (i.e. one step of 15edo). Interesting relationships do arise if one maintains the tonic but switches through its different modes (i.e. 1 mixolydian to 1 ionian to 1 lydian), and an "extra" mode appears, because five fifths close (hence V/V/V/V = IV, unlike in meantone where V/V/V/V = iii). All together, there are 14 modes of the 7-note diatonic to be found in Blackwood[10] if we keep the same tonic, and 20 if we allow alterations of the tonic.
 == MODMOSes ==