In 15 tone equal temperament, as well as all equal divisions of the octave that are multiples of 5, have a 5 tone equal scale. Notation: 5n-ed2s. – which means 5 times some number n – equal divisions of 2 times the base frequency.
This 5 town equal scale works well as a standalone pentatonic scale, and every note sounds good with every other note. It doesn’t have the polished harmony of western romantic music, which is characteristic of near-perfect tuned 3rd harmonics (fifths and fourths) and well tuned 5th harmonics (major and minor thirds). It does however place its characteristic interval between 7:6 and 8:7, making it essentially an embodiment of the 7th harmonic.
Side question: since 15:11 rests between 7:6 and 8:7 (as (7+8)/(6+7) is (15/11), why in this context does this 240¢ interval seems to hold the characteristics of the 7 instead of the 15 or 11?
The Blackwood [10] scale is a combination of two of these 5-equal scales. In 15-edo, there are two modes, a major and a minor mode. The major being a LsLs… symmetrical scale structure, and the minor being a sLsL.. scale structure.
In the major version, you get the leading tones below each of the notes in 5-equal, therefore adding the major 3rd, major 6, and major 7th to the scale set, as well as the large tritone and the neutral 2nd.
In the minor version, the opposite it true, adding the minor 3rd, 6th and 7th, as well as the small semitone and the small tritone.
The 5-equal scale base set can be described as having the large tone (septimal), the 4th, 5th, and harmonic 7th.
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Noah Dean Jordan 