User:Pailiaq/Tritone substitution: Difference between revisions

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In 26-EDO, the semioctave is 13\26 = 600¢, but the diatonic augmented fourth is only 12\26 ≈ 554¢. A diatonic dominant seventh chord therefore lacks a true tritone, breaking the substitution mechanism of the 3rd and 7th swapping.

The solution is to use the '''harmonic seventh chord''' ((0, 8, 15, 21)\26 approximating 4:5:6:7) as your dominant. In 26-EDO, the harmonic seventh (7/4) lands at 21\26 ≈ 969¢, which is ~0.4¢ from just. With a major third at 8\26, the interval from third to seventh is exactly 13 steps = 600¢. This nondiatonic chord produces a perfect tritone substitution, with the caveat that you must step outside your scale (playing a downminor 7) when playing a V-I progression if you want consistency in sound for when also using tritone substitutions.

The solution is to use the '''harmonic seventh chord''' ((0, 8, 15, 21)\26 approximating 4:5:6:7) as your dominant V. In 26-EDO, the harmonic seventh (7/4) lands at 21\26 ≈ 969¢, which is ~0.4¢ from just. With a major third at 8\26, the interval from third to seventh is exactly 13 steps = 600¢. This nondiatonic chord produces a perfect tritone substitution, with the caveat that you must step outside your scale (playing a downminor 7) when playing a V-I progression if you want consistency in sound for when also using tritone substitutions.

Howewever, using the diatonic, tritoneless dominant 7th chord also can work; the only difference being that the third and 7ths don't perfectly swap positions, as one of them will drift up or down by an edostep.

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 In 26-EDO, the semioctave is 13\26 = 600¢, but the diatonic augmented fourth is only 12\26 ≈ 554¢. A diatonic dominant seventh chord therefore lacks a true tritone, breaking the substitution mechanism of the 3rd and 7th swapping.
-The solution is to use the '''harmonic seventh chord''' ((0, 8, 15, 21)\26 approximating 4:5:6:7) as your dominant. In 26-EDO, the harmonic seventh (7/4) lands at 21\26 ≈ 969¢, which is ~0.4¢ from just. With a major third at 8\26, the interval from third to seventh is exactly 13 steps = 600¢. This nondiatonic chord produces a perfect tritone substitution, with the caveat that you must step outside your scale (playing a downminor 7) when playing a V-I progression if you want consistency in sound for when also using tritone substitutions.
+The solution is to use the '''harmonic seventh chord''' ((0, 8, 15, 21)\26 approximating 4:5:6:7) as your dominant V. In 26-EDO, the harmonic seventh (7/4) lands at 21\26 ≈ 969¢, which is ~0.4¢ from just. With a major third at 8\26, the interval from third to seventh is exactly 13 steps = 600¢. This nondiatonic chord produces a perfect tritone substitution, with the caveat that you must step outside your scale (playing a downminor 7) when playing a V-I progression if you want consistency in sound for when also using tritone substitutions.
 Howewever, using the diatonic, tritoneless dominant 7th chord also can work; the only difference being that the third and 7ths don't perfectly swap positions, as one of them will drift up or down by an edostep.