Re: 404, 808 salt;-) 22edo.

Thanks Carl for clarifying my comments, and threatening me with censorship.

At about 8 am GMT this morning when I attempted to follow the link intonationjuste, I got an 808 or 404 (unobtainable url)

I checked it again since I read your message and see that it does actually display now.

Hence my sarcasm, assumed the url to be either a spoof or a typo.

My best linguistic friend tells me that "with a pinch of salt" has a few different meanings:
1) Communications are of a comedic value.
2) Advice for which the integrity or credibility should be questioned.

I trust that you were using the term in the first sense.

I beg to disagree with your recommendation of 22 edo as a good fretting system for guitars.

Although it will produce some interesting intervals, they fail to be those that one would expect to find commonly in a 5L+2s pattern which has been used extensively in Western harmony.

More info. on this tuning and its harmonic potentials and limitations can be found at:

http://en.wikipedia.org/wiki/22_equal_temperament

and for a comparison view for 88edo go to:

http://en.wikipedia.org/wiki/List_of_meantone_intervals

Charles Lucy
lucy@lucytune.com

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

At 10:38 AM 1/15/2008, you wrote:
>Thanks Carl for clarifying my comments, and threatening me with
>censorship.

Count on it.

>I beg to disagree with your recommendation of 22 edo as a good
>fretting system for guitars.
>Although it will produce some interesting intervals, they fail to be
>those that one would expect to find commonly in a 5L+2s pattern which
>has been used extensively in Western harmony.

That's true. It's not the fretting to choose if you want to play
diatonic harmony. But I think it opens up more new worlds in fewer
tones than any other system.

-Carl

--- In tuning-math@yahoogroups.com, Carl Lumma <carl@...> wrote:
>
> At 10:38 AM 1/15/2008, you wrote:
> >Thanks Carl for clarifying my comments, and threatening me with
> >censorship.
>
> Count on it.
>
> >I beg to disagree with your recommendation of 22 edo as a good
> >fretting system for guitars.
> >Although it will produce some interesting intervals, they fail to
be
> >those that one would expect to find commonly in a 5L+2s pattern
which
> >has been used extensively in Western harmony.
>
> That's true. It's not the fretting to choose if you want to play
> diatonic harmony. But I think it opens up more new worlds in fewer
> tones than any other system.

Right, 22t-ET is in the Diaschismic family, IIRC. Of course, you are
familiar with Paul Erlich's Paper "Tonality, Temperament and Twenty-
two Tone Harmony" (22 is also interesting in that M22 is one of the
five Mathieu Groups, but more generally, has some interesting set-
theoretical properties. Oops there I go again...)

PGH

> -Carl
>

--- In tuning-math@yahoogroups.com, "Paul G Hjelmstad"
<phjelmstad@...> wrote:
>
> --- In tuning-math@yahoogroups.com, Carl Lumma <carl@> wrote:
> >
> > At 10:38 AM 1/15/2008, you wrote:
> > >Thanks Carl for clarifying my comments, and threatening me with
> > >censorship.
> >
> > Count on it.
> >
> > >I beg to disagree with your recommendation of 22 edo as a good
> > >fretting system for guitars.
> > >Although it will produce some interesting intervals, they fail
to
> be
> > >those that one would expect to find commonly in a 5L+2s pattern
> which
> > >has been used extensively in Western harmony.
> >
> > That's true. It's not the fretting to choose if you want to play
> > diatonic harmony. But I think it opens up more new worlds in
fewer
> > tones than any other system.
>
> Right, 22t-ET is in the Diaschismic family, IIRC. Of course, you
are
> familiar with Paul Erlich's Paper "Tonality, Temperament and Twenty-
> two Tone Harmony" (22 is also interesting in that M22 is one of the
> five Mathieu Groups, but more generally, has some interesting set-
> theoretical properties. Oops there I go again...)
>
> PGH

For example, 22 tone subsets have this interesting property with
their Z relations. These are when 2 or more set types have the same
interval vector. (A set type is a Tn/TnI type, which would be
a set, its transposes, and inverses, and their transposes).

Notice how the Z-related sets (Doubles, Triples, etc) have a
phenomenon of clustering in multiples of 5. I should get some
sort of award for the most obscure contribution to the understanding
of 22-tET! (11-sets include those with "normal" complementation
(always pairs) plus "strange" Z-relations)

Subset C(22,5) 621 Types

Singles 581 581 0

Doubles 40 20 20
Totals 621 601 20

Subset C(22,6) 1782 Types

Singles 1657 1657 0

Doubles 110 55 55

Triples 15 5 10
Totals 1782 1717 65

Subset C(22,7) 3936 Types

Singles 3241 3241 0

Doubles 620 310 310

Triples 75 25 50
Totals 3936 3576 360

Subset C(22,8) 7440 Types

Singles 6255 6255 0

Doubles 1080 540 540

Triples 105 35 70
Totals 7440 6830 610

Subset C(22,9) 11410 Types

Singles 8435 8435 0

Doubles 2600 1300 1300

Triples 375 125 250
Totals 11410 9860 1550

Subset C(22,10) 14938 Types

Singles 11718 11718 0

Doubles 2860 1430 1430

Triples 360 120 240
Totals 14938 13268 1670

Subset C(22,11) 16159 Types

Singles 554 554 0

Doubles 13970 6985 6985

Triples 15 5 10

Quads 1560 390 1170

Quints 0 0 0

Sextuples 60 10 50
Totals 16159 7944 8215

>> That's true. It's not the fretting to choose if you want to play
>> diatonic harmony. But I think it opens up more new worlds in fewer
>> tones than any other system.
>
>Right, 22t-ET is in the Diaschismic family, IIRC.

22-ET supports (is a tuning of) diaschismic. It also supports
porcupine, pajara, and magic.

-Carl