Re: Lilypond help - arbitrary accidental glyphs

[Hans Aberg]

On 30 Oct 2013, at 14:09, Clive So <address@hidden> 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