Scales for the 19-et

Joseph has remarked that the 19-et seems weird to him. The obvious
cure to that is the meantone diatonic scale; and to that we can add
the 12-note meantone scale; with a 5-limit complexity of 4 these
specialize in triads, as we would expect. The 12-note scale is
usually thought of as 1/3-comma meantone temperament, but 12 meantone
fifths are a small enough number that it can be treated as a scale of
pattern 121212212122, with modulation and all the rest of it. Does
anyone know if this is what Yasser advocated?

The 19-et also has its chain-of-major-sixths, which is interesting
partly because the 19-et has such good major sixths/minor thirds, and
partly because it has a low 7-complexity at 6 and hence a high amount
of 7-harmony. As an alternative to diatonic, there is therefore the
7-note scale with pattern 1414144 in the 19-et. Also, 11-note scales
have been discussed a little of late on the math list, and we have a
fine one here: 11311311313; containing both of these is the
15-note scale 111211121112112.

The generator 2/19, with a 7-limit complexity of 7 and a 9 and
11-limit complexity of 11 gives nice 9 and 10 note scales, with
pattern 222222223 and 2222222221.

We also do well with 4/19, with a 9-limit complexity of 8, and a
different 9-note scale, with pattern 131313133, as well as a nice
14-note scale with pattern 11211211211212.

--- In tuning@y..., genewardsmith@j... wrote:
> Joseph has remarked that the 19-et seems weird to him. The obvious
> cure to that is the meantone diatonic scale; and to that we can add
> the 12-note meantone scale; with a 5-limit complexity of 4 these
> specialize in triads, as we would expect. The 12-note scale is
> usually thought of as 1/3-comma meantone temperament, but 12
meantone
> fifths are a small enough number that it can be treated as a scale
of
> pattern 121212212122, with modulation and all the rest of it. Does
> anyone know if this is what Yasser advocated?

It is, but I'm sure you wouldn't like his suggestion for the basic
chords of this system.

> The 19-et also has its chain-of-major-sixths, which is interesting
> partly because the 19-et has such good major sixths/minor thirds,
and
> partly because it has a low 7-complexity at 6 and hence a high
amount
> of 7-harmony. As an alternative to diatonic, there is therefore the
> 7-note scale with pattern 1414144 in the 19-et. Also, 11-note
scales
> have been discussed a little of late on the math list, and we have
a
> fine one here: 11311311313;

All of this is covered in more detail at
http://www.uq.net.au/~zzdkeena/Music/ChainOfMinor3rds.htm

> The generator 2/19, with a 7-limit complexity of 7 and a 9 and
> 11-limit complexity of 11

I'd be hesitant speaking of the 11-limit complexity, since 19-tET is
not consistent in the 11-limit.