Pentatonic Functional Just System: Difference between revisions
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One can see that the ratios of 5 are further from 5edo intervals than ratios of 7. Thus, the 5-limit intervals can now be considered "subminor" and "supermajor", compared to the intervals of 7 in diatonic. Using the <sub>5</sub>fifth construction, we get the [[3:5:9]] subminor and [[5:9:15|1/(9:5:3) = 5:9:15]] supermajor chords, the compact voicings of which are [[9:10:12]] and [[15:18:20]] respectively. | |||
If we try to construct 5-limit triads the normal way, the [[4:5:6]] major triad becomes <sub>5</sub>P1–<sub>5</sub>d3<sup>5</sup>–<sub>5</sub>P4, and the [[10:12:15]] minor triad becomes <sub>5</sub>P1–<sub>5</sub>M2<sub>5</sub>–<sub>5</sub>P4. Augmented and diminished intervals occur way more frequently; thus they are not the best names. From here on we will refer to augmented and diminished as "super" and "sub" (not to be confused with "supermajor" and "subminor"), with symbols "S" and "s" respectively. | |||