On 30 Oct 2013, at 14:09, Clive So <cliv...@gmail.com> wrote: >> Note that in E31, the rational interval 7/4 is on the augmented 6th, or 25 >> E31 tonesteps, whereas the minor 7th is on 26 E31 tonesteps, one E31 >> tonestep higher. > > Yes, absolutely! Many people think of the interval 7/4 as a type of 7th > (harmonic, barbershop, etc.) but I strongly believe that it should be > understood as an augmented 6th (125/72 ≈ 7/4). Just because it's a 7-limit > interval, it doesn't make it a 7th. Likewise, you don't call the JI major 3rd > a "5th" because it's a 5-limit interval. This has important implications in > terms of voice leading and harmonic progression.
The 5-limit Just minor 7th 16/9 will though cause beats with the 7/4 if the 7th partial is present though it is suppressed in normal orchestral playing. But I think this has long been known, due to the extensive treatment of the augmented sixth chords [1], which traditionally are always spelled like that, and not enharmonic exchanged with the minor 7th. > Fokker (and hence the "Dutch school"?) happened to have chosen to use flats > exclusively (semi-flat, flat, sesquiflat, double-flat, and even 2½ flat!) for > practical reasons, but I don't agree with that as it obscures the harmonic > function of each note. This has the consequence that the interval 7/4 is > spelt, for example, as C - B-sesquiflat, making it look like a sort of 7th. > Although the "Dutch school" approach doesn't have the same notion of harmonic > function as in the traditional sense, Fokker did consider the interval 7/4 to > be a sort of 7th, and consequently the chord C - E - G - B-sesquiflat a > "dominant 7th". This is in direct contradiction with JI theory. If 7/4 is put on the augmented sixth M6#, with m (resp. M) the minor (resp. major) second, M6# = m + 4M = 5M, so microtonal accidentals may not be needed in E31 for describing 7-limit Just intonation. 1. https://en.wikipedia.org/wiki/Augmented_sixth_chord _______________________________________________ lilypond-user mailing list lilypond-user@gnu.org https://lists.gnu.org/mailman/listinfo/lilypond-user
