Correction

Before everyone starts on me:

smallest pitch bend range is 200 cents into 127 parts which is 1.5748 cents maximum deviation from the exact pitch required. If I could use the fine bends I would. Even so, 1.56 cent accuracy is not too bad. Bend 64, is of course the centre - no pitch deviation at all.

I don't subscribe to Tuning anymore - too much to do to read yet more mails. I will say that the 46EDO representation I reject because its chromatic intervals in the 11 note scale are larger than the diatonic ones, within that scale. The diatonic analogy is the 17EDO scale

0 3 6 7 10 13 16 (0 where the chromatic shift is 2 and the diatonic is 1 steps wide.

Alternatives for 11 from 19 are 30, 41 and 49, etc. I leave these for the theoretical minded to work out the pcs.

Mark

--- In MakeMicroMusic@yahoogroups.com, Mark Gould <mark.gould@a...> wrote:

> I don't subscribe to Tuning anymore - too much to do to read yet more
> mails. I will say that the 46EDO representation I reject because its
> chromatic intervals in the 11 note scale are larger than the diatonic
> ones, within that scale.

I'm not sure what you are saying here. In terms of scale steps, your
scale goes [2,2,1,2,2,2,1,2,2,2,1]. The ratio large step/small step is
of course 2. For 46, this would be [5,5,2,5,5,5,2,5,5,5,2], with a
ratio of 2.5; for 65, [7,7,3,7,7,7,3,7,7,7,3] with a ratio of 2.333.

--- In MakeMicroMusic@yahoogroups.com, Mark Gould <mark.gould@a...>
wrote:

> I don't subscribe to Tuning anymore - too much to do to read yet
>more
> mails.

Understood -- though things are very slow there, I can't fault you
for this. I'd love to continue a theory conversation with you
*somewhere*, though, if even in private e-mail -- all I know is that
this isn't the place for it. But I will mix a little theory in below,
so I apologize to all.

> I will say that the 46EDO representation I reject because its
> chromatic intervals in the 11 note scale are larger than the
diatonic
> ones, within that scale. The diatonic analogy is the 17EDO scale
>
> 0 3 6 7 10 13 16 (0 where the chromatic shift is 2 and the diatonic
is
> 1 steps wide.

I just want to say that diatonic melodies, even ones that modulate,
sound absolutely beautiful to me in 17-equal. This is based on
listening to Blackwood and playing myself, but I know George and
Margo agree. Harmony is precarious at best but the melodic and
modulatory properties sound close to ideal to me -- or at least they
evoke some powerful feelings in my heart. Historically and
geographically, the diatonic scale in Pythagorean tuning has been
very important, despite the fact that its chromatic semitone is
slightly larger than its diatonic semitone.

With the semisixths[11] scale, I have a lot less experience, but
semisixths came up as an interesting temperament for 5-limit harmony
and one of the three or four *most* interesting for 7-limit. It looks
to me as if, either way, the harmonically optimal tuning is such that
19-, 27-, and 46-tone 'generalized diatonic' scales from this
temperament have large step : small step approximately in the golden
ratio. The 11-tone scale, though, has harmonically optimal steps of
131 and 50 cents; one mode is
131+50+131+131+131+50+131+131+131+50+131. On Wednesday, I'm going to
try to mess with this *melodically* and see if it doesn't evoke any
feelings for me.

Hopefully I'll also have some 15-equal lunacy to share with the list
at that point.

--- In MakeMicroMusic@yahoogroups.com, "Paul Erlich" <perlich@a...> wrote:

> With the semisixths[11] scale, I have a lot less experience, but
> semisixths came up as an interesting temperament for 5-limit harmony
> and one of the three or four *most* interesting for 7-limit. It looks
> to me as if, either way, the harmonically optimal tuning is such that
> 19-, 27-, and 46-tone 'generalized diatonic' scales from this
> temperament have large step : small step approximately in the golden
> ratio.

The large step of (septimal) Semisixths[11] is 3 generator steps, an
approximate 15/14. The small step is -8 generator steps; it can be
taken as 28/27, 36/35 or 50/49. If you take the ratio of these in the
TOP tuning, you get 2.6278, which is closer to 1+phi; of course this
is assuming flattened octaves. If you use the rms tuning, you get a
ratio of 2.564, if the minimax tuning you get once again the TOP ratio
of 2.6278

> Hopefully I'll also have some 15-equal lunacy to share with the list
> at that point.

You mean a composition??

--- In MakeMicroMusic@yahoogroups.com, "Gene Ward Smith"
<gwsmith@s...> wrote:
> --- In MakeMicroMusic@yahoogroups.com, "Paul Erlich" <perlich@a...>
wrote:
>
> > With the semisixths[11] scale, I have a lot less experience, but
> > semisixths came up as an interesting temperament for 5-limit
harmony
> > and one of the three or four *most* interesting for 7-limit. It
looks
> > to me as if, either way, the harmonically optimal tuning is such
that
> > 19-, 27-, and 46-tone 'generalized diatonic' scales from this
> > temperament have large step : small step approximately in the
golden
> > ratio.
>
> The large step of (septimal) Semisixths[11] is 3 generator steps, an
> approximate 15/14. The small step is -8 generator steps; it can be
> taken as 28/27, 36/35 or 50/49. If you take the ratio of these in
the
> TOP tuning, you get 2.6278, which is closer to 1+phi;

Yup -- that follows because the large step in the 11-note scale is a
large step plus a small step in the 19-note scale I mentioned above,
while the small step is the same size in both the 11-note and 19-note
scales.

> > Hopefully I'll also have some 15-equal lunacy to share with the
list
> > at that point.
>
> You mean a composition??

If you can call it that. I recorded a looping chord progression and
Ara is adding a melody over it. It sounds funny and annoying at the
same time; might as well share it.

Paul,

{you wrote...}
>If you can call it that.

Why not? And you can call it anything you want, since you're the one making it.

>I recorded a looping chord progression and Ara is adding a melody over it.

A lot of music is made this way, but you know that already...

>It sounds funny and annoying at the same time

Like life!

>might as well share it.

Please do - the more we share, the more we learn...

Cheers,
Jon