39edo: Difference between revisions

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5 5 3 5 5 3 5 5 3 - [[MOSScales|MOS]] of type [[6L 3s|6L 3s (unfair Augmented nonatonic)]]

5 4 4 5 4 4 5 4 4 - [[MOSScales|MOS]] of type [[3L 6s|3L 6s (fair Augmented nonatonic)]]

5 4 4 5 4 4 5 4 4, 7 3 3 7 3 3 7 3 3 - [[MOSScales|MOS]] of type [[3L 6s|3L 6s (fair Augmented nonatonic)]]

4 4 4 4 4 4 4 4 4 3 - [[MOSScales|MOS]] of type [[9L 1s|9L 1s (Grumpy decatonic)]]

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2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 - [[MOSScales|MOS]] of type [[19L 1s]]

2 2 2 2 2 2 1 2 2 2 2 2 2 1 2 2 2 2 2 2 1 - [[MOS]] of type 18L 3s

2 2 2 1 2 2 2 1 2 2 2 1 2 2 2 2 1 2 2 2 2 1 - [[MOSScales|MOS]] of type [[17L 5s]]

'''2 2 1 2 2 1 2 2 1 2 2 1 2 2 1 2 2 2 1 2 2 2 1''' - [[MOSScales|MOS]] of type [[16L 7s]]

2 1 2 1 2 1 2 2 1 2 1 2 1 2 1 2 2 1 2 1 2 1 2 1 2 - [[MOS]] of type 14L 11s

2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 - [[MOSScales|MOS]] of type [[13L 13s]]

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39edo offers not one, but several different ways to realize the traditional Western diatonic scale. One way is to simply take a chain of fifths (the diatonic MOS: '''7 7 2 7 7 7 2'''). Because 39edo is a superpyth rather than a meantone system, this means that the harmonic quality of its diatonic scale will differ somewhat, since "minor" and "major" triads now approximate 6:7:9 and 14:18:21 respectively, rather than 10:12:15 and 4:5:6 as in meantone diatonic systems. Diatonic compositions translated onto this scale thus acquire a wildly different harmonic character, albeit still very pleasing.

Another option is to use a MODMOS, such as '''7 6 3 7 6 7 3'''; this scale enables us to continue using pental rather than septimal thirds, but it has a false (wolf) fifth. When translating diatonic compositions into this scale, the wolf fifth ~~can be avoided~~ by introducing accidental notes when necessary. There are other MODMOS's that combine both pental and septimal harmonies. As such, a single Western classical or pop composition can be translated into 39edo in ''many'' different ways, acquiring a distinctly different but still harmonious character each time.

Another option is to use a MODMOS, such as '''7 6 3 7 6 7 3'''; this scale enables us to continue using pental rather than septimal thirds, but it has a false (wolf) fifth. When translating diatonic compositions into this scale, it is possible to avoid the wolf fifth by introducing accidental notes when necessary. It is also possible to avoid the wolf fifth by extending the scale to either '''7 3 3 3 7 3 3 7 3''' (a [[MODMOS]] of type 3L 6s) or '''4 3 6 3 4 3 6 4 3 3.''' There are other MODMOS's that combine both pental and septimal harmonies. As such, a single Western classical or pop composition can be translated into 39edo in ''many'' different ways, acquiring a distinctly different but still harmonious character each time.

The MOS and the MODMOS's all have smaller-than-usual semitones, which makes them more effective for melody than their counterparts in 12edo or meantone systems.

@@ Line 604: / Line 604: @@
 5 3 5 5 3 5 5 3 - [[MOSScales|MOS]] of type [[6L 3s|6L 3s (unfair Augmented nonatonic)]]
-4 4 5 4 4 5 4 4 - [[MOSScales|MOS]] of type [[3L 6s|3L 6s (fair Augmented nonatonic)]]
+4 4 5 4 4 5 4 4, 7 3 3 7 3 3 7 3 3 - [[MOSScales|MOS]] of type [[3L 6s|3L 6s (fair Augmented nonatonic)]]
 4 4 4 4 4 4 4 4 3 - [[MOSScales|MOS]] of type [[9L 1s|9L 1s (Grumpy decatonic)]]
@@ Line 627: / Line 627: @@
 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 1 - [[MOSScales|MOS]] of type [[19L 1s]]
+2 2 2 2 2 1 2 2 2 2 2 2 1 2 2 2 2 2 2 1 - [[MOS]] of type 18L 3s
 2 2 1 2 2 2 1 2 2 2 1 2 2 2 2 1 2 2 2 2 1 - [[MOSScales|MOS]] of type [[17L 5s]]
 '''2 2 1 2 2 1 2 2 1 2 2 1 2 2 1 2 2 2 1 2 2 2 1''' - [[MOSScales|MOS]] of type [[16L 7s]]
+1 2 1 2 1 2 2 1 2 1 2 1 2 1 2 2 1 2 1 2 1 2 1 2 - [[MOS]] of type 14L 11s
 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 - [[MOSScales|MOS]] of type [[13L 13s]]
@@ Line 646: / Line 650: @@
 edo offers not one, but several different ways to realize the traditional Western diatonic scale. One way is to simply take a chain of fifths (the diatonic MOS: '''7 7 2 7 7 7 2'''). Because 39edo is a superpyth rather than a meantone system, this means that the harmonic quality of its diatonic scale will differ somewhat, since "minor" and "major" triads now approximate 6:7:9 and 14:18:21 respectively, rather than 10:12:15 and 4:5:6 as in meantone diatonic systems. Diatonic compositions translated onto this scale thus acquire a wildly different harmonic character, albeit still very pleasing.
-Another option is to use a MODMOS, such as '''7 6 3 7 6 7 3'''; this scale enables us to continue using pental rather than septimal thirds, but it has a false (wolf) fifth. When translating diatonic compositions into this scale, the wolf fifth can be avoided by introducing accidental notes when necessary. There are other MODMOS's that combine both pental and septimal harmonies. As such, a single Western classical or pop composition can be translated into 39edo in ''many'' different ways, acquiring a distinctly different but still harmonious character each time.
+Another option is to use a MODMOS, such as '''7 6 3 7 6 7 3'''; this scale enables us to continue using pental rather than septimal thirds, but it has a false (wolf) fifth. When translating diatonic compositions into this scale, it is possible to avoid the wolf fifth by introducing accidental notes when necessary. It is also possible to avoid the wolf fifth by extending the scale to either '''7 3 3 3 7 3 3 7 3''' (a [[MODMOS]] of type 3L 6s) or '''4 3 6 3 4 3 6 4 3 3.''' There are other MODMOS's that combine both pental and septimal harmonies. As such, a single Western classical or pop composition can be translated into 39edo in ''many'' different ways, acquiring a distinctly different but still harmonious character each time.
 The MOS and the MODMOS's all have smaller-than-usual semitones, which makes them more effective for melody than their counterparts in 12edo or meantone systems.