Diaharmonic: Difference between revisions

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The '''Diaharmonic''' collection is the name proposed by Mason Green for a 9-note scale with step pattern L L S S L L L S S. It is a [[diatonic scale]] where each semitone is divided equally in half.

The '''Diaharmonic''' collection is the name proposed by [[Mason Green]] for a 9-note scale with step pattern L L S S L L L S S. It is a [[diatonic scale]] where each semitone is divided equally in half.

It can also be thought of as a cross between two of the three ancient Greek genera (diatonic and enharmonic) since the diatonic and enharmonic ~~tetrachords~~ "fuse together" nicely. The two whole tones of the diatonic tetrachord nest inside the major third of the enharmonic one, while the two quarter tones of the enharmonic tetrachord fit into the semitone of the diatonic one. This gives us a '''diaharmonic pentachord''' (portmanteau of diatonic and enharmonic), which can then be used to construct a 9-note scale.

It can also be thought of as a cross between two of the three ancient Greek [[genera]] (diatonic and enharmonic) since the diatonic and enharmonic [[tetrachord]]s "fuse together" nicely. The two whole tones of the diatonic tetrachord nest inside the major third of the enharmonic one, while the two quarter tones of the enharmonic tetrachord fit into the semitone of the diatonic one. This gives us a '''diaharmonic pentachord''' (portmanteau of diatonic and enharmonic), which can then be used to construct a 9-note scale.

[[~~19edo|~~19edo]] works extremely well as a tuning for the diaharmonic scale (in which it has step sizes 3 3 1 1 3 3 3 1 1). However, there are other options which include 24edo and 43edo.

[[19edo]] works extremely well as a tuning for the diaharmonic scale (in which it has step sizes 3 3 1 1 3 3 3 1 1). However, there are other options which include [[24edo]] and [[43edo]].

The 19edo diaharmonic scale is interesting because it can combine the melodic advantages of neomedieval systems (like [[~~17edo|~~17edo]] and Pythagorean) with the harmonic advantages of a meantone system. We can do this by shrinking the diatonic semitone in a melodic line while expanding the preceding whole tone. Essentially in major keys, we have a diatonic scale with two extra notes, one which can function either as an "ascending/augmented third" or a "descending/diminished" fourth, and the other which can function either as an "ascending/augmented seventh" or "descending/diminished" octave.

The 19edo diaharmonic scale is interesting because it can combine the melodic advantages of neomedieval systems (like [[17edo]] and [[Pythagorean]]) with the harmonic advantages of a [[meantone]] system. We can do this by shrinking the diatonic semitone in a melodic line while expanding the preceding whole tone. Essentially in major keys, we have a diatonic scale with two extra notes, one which can function either as an "ascending/augmented third" or a "descending/diminished" fourth, and the other which can function either as an "ascending/augmented seventh" or "descending/diminished" octave.

[[Category:19edo]]

[[Category:9-tone scales]]

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-The '''Diaharmonic''' collection is the name proposed by Mason Green for a 9-note scale with step pattern L L S S L L L S S. It is a [[diatonic scale]] where each semitone is divided equally in half.
+The '''Diaharmonic''' collection is the name proposed by [[Mason Green]] for a 9-note scale with step pattern L L S S L L L S S. It is a [[diatonic scale]] where each semitone is divided equally in half.
-It can also be thought of as a cross between two of the three ancient Greek genera (diatonic and enharmonic) since the diatonic and enharmonic tetrachords "fuse together" nicely. The two whole tones of the diatonic tetrachord nest inside the major third of the enharmonic one, while the two quarter tones of the enharmonic tetrachord fit into the semitone of the diatonic one. This gives us a '''diaharmonic pentachord''' (portmanteau of diatonic and enharmonic), which can then be used to construct a 9-note scale.
+It can also be thought of as a cross between two of the three ancient Greek [[genera]] (diatonic and enharmonic) since the diatonic and enharmonic [[tetrachord]]s "fuse together" nicely. The two whole tones of the diatonic tetrachord nest inside the major third of the enharmonic one, while the two quarter tones of the enharmonic tetrachord fit into the semitone of the diatonic one. This gives us a '''diaharmonic pentachord''' (portmanteau of diatonic and enharmonic), which can then be used to construct a 9-note scale.
-[[19edo|19edo]] works extremely well as a tuning for the diaharmonic scale (in which it has step sizes 3 3 1 1 3 3 3 1 1). However, there are other options which include 24edo and 43edo.
+[[19edo]] works extremely well as a tuning for the diaharmonic scale (in which it has step sizes 3 3 1 1 3 3 3 1 1). However, there are other options which include [[24edo]] and [[43edo]].
-The 19edo diaharmonic scale is interesting because it can combine the melodic advantages of neomedieval systems (like [[17edo|17edo]] and Pythagorean) with the harmonic advantages of a meantone system. We can do this by shrinking the diatonic semitone in a melodic line while expanding the preceding whole tone. Essentially in major keys, we have a diatonic scale with two extra notes, one which can function either as an "ascending/augmented third" or a "descending/diminished" fourth, and the other which can function either as an "ascending/augmented seventh" or "descending/diminished" octave.
+The 19edo diaharmonic scale is interesting because it can combine the melodic advantages of neomedieval systems (like [[17edo]] and [[Pythagorean]]) with the harmonic advantages of a [[meantone]] system. We can do this by shrinking the diatonic semitone in a melodic line while expanding the preceding whole tone. Essentially in major keys, we have a diatonic scale with two extra notes, one which can function either as an "ascending/augmented third" or a "descending/diminished" fourth, and the other which can function either as an "ascending/augmented seventh" or "descending/diminished" octave.
 [[Category:19edo]]
 [[Category:9-tone scales]]