Re: EDO and meantone for faq

There was a thread a year or two ago regardgin various ways
of characterising tuning schemes. EDO seemed to be a fairly
nice one for Equal Division of the Octave without the
presumption of 'temperance'.

Regarding meantone definitions for the faq, Daniels post
"Re: Draft: What is meantone (MT)?" was really excellent. I
have never seen ALL the information I've struggled to
understand over the past few years encapsulated so succinctly.

I nominate Daniel to write everything in the faq (just
kidding).

Regarding EDO approximations of meantone, after staring at
and listenning to chords in 31tet and getting ---><--- close
to orderring a 31tet guitar, I started getting really excited
about the possibilities of 55. Better fifths, sharper thirds
and more 'difference' between major and minor (in other words,
its comma reduction is less and it is more 'normal' for a
12tet hacker). It seems to be unique in 2, 3, 5, 7, 11
identities (31 has collisions on 12/11 and 11/10). It does
have its problems compared to 31. The best 7/5 + the
best 5/4 does not equal the best 7/4. There is also the
interesting fact that the best 10/9 != the best 9/8 BUT
2 * best 9/8 = best 5/4 (making it meantone with an unusual
9 limit identity present, which is probably why those 7's
don't line up properly).

It has the 'soothing exotic' 5EDO and the 'non-soothing
exotic' 11EDO embedded. There is a lot of potential to combine
smooth and crunchy by playing with these two EDOs together
(a quintet of 11-tone rows, internally strident, but comforting
in ensemble) or a minimalist eleptet of 5 EDO instruments where
varius sub-ensembles would have varying levels of mutual
harmony (I've just been back into a mild Steve Reich phase).

Some of the relations also look very interesting. The best
5/4 is 18 steps, giving an interesting via 'cuberoot(best 5/4)'
approximation to

13/12 14/13 15/14
1/1 13/12 7/6 5/4

Also, the best fifth is 32 giving "fourth and eighths of a
fifth" in addition to a neutral third at half a fifth (31 has
a sixth of a fifth in addition to half). The major seventh, at
50 steps, has a "streched whole tone scale" filling it (which
is made up of 4^(1/11) (a two octave 11 tone scale).

Experiences in 55 from list members? (If I get around to
orderring a guitar it will be 31, 55 would be too cramped
and the neat relations I get excited about don't quite
match my guitar playing).

Bob Valentine

Bob Valentine wrote:

> There was a thread a year or two ago regardgin various ways
> of characterising tuning schemes. EDO seemed to be a fairly
> nice one for Equal Division of the Octave without the
> presumption of 'temperance'.

As you may have noticed, I say "-equal". I only recall one occasion
when anybody had to ask me what I meant by "31-equal". I don't know
of any other terminology that is so obvious. It also seems to be how
some people pronounce "TET".

You could always redefine "TET" to mean "tones equal tuning" if you
don't like the "temperament" bit. I don't think we need a term for
referring to ETs that *are* temperaments. You can say how the
tempering is done. Like "31-equal meantone" or "17-equal neutral
third scale" or "41-equal with 2.3.7.9.11".

FWIW, my objections to "TET" are that it's difficult to say, not
obvious to a newbie, confuses with 8TET meaning "octet", and implies
the American definition of "tone".

> Regarding meantone definitions for the faq, Daniels post
> "Re: Draft: What is meantone (MT)?" was really excellent. I
> have never seen ALL the information I've struggled to
> understand over the past few years encapsulated so succinctly.

No arguments here.

> Experiences in 55 from list members? (If I get around to
> orderring a guitar it will be 31, 55 would be too cramped
> and the neat relations I get excited about don't quite
> match my guitar playing).

I've thought about fretting to something like 1/5- or 1/6-comma
meantone. It would be good for "traditional" music, where you don't
use remote keys, and don't expect 7-limit or higher intervals. You
should only need 17 frets to the octave, and you can leave some of
them out when you get away from the nut. Using only the larger gaps
would me more like 12-equal, and the fifths would be purer than
31-equal. If I had multiple fingerboards, one of them would be like
this.

Of course, such a fretting would lose all the interesting properties
of 55 that you outlined. So you end up going for 31-equal. I know
it's boring that it keeps on coming up like this, but as a meantone
with 11-limit consistency it is an obvious one to pick.

I still suggest you consider a 19-fret subset like I have. It doesn't
have much of the 11-limit, but 9-limit chords tend to be much easier
to play than they would be if you had more frets getting in the way.

Graham

List!
Daniel has had more actual experience with actually using various
tunings!

Robert C Valentine wrote:

>
> I nominate Daniel to write everything in the faq (just
> kidding).

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

On Wed, 21 Feb 2001 14:08:31 +0200 (IST), Robert C Valentine
<BVAL@IIL.INTEL.COM> wrote:

>Experiences in 55 from list members? (If I get around to
>orderring a guitar it will be 31, 55 would be too cramped
>and the neat relations I get excited about don't quite
>match my guitar playing).

I've used 1/6-comma meantone, which is very close to 55-TET, but I've only
used 21 notes of it (the diatonic scale with sharps and flats). Its triads
are pleasantly more consonant than 12-TET, without being too exotic to
sound "out of tune" to someone unfamiliar with meantone. "Misspelled"
intervals like D-E# can produce some interesting results.

--
see my music page ---> ---<http://www.io.com/~hmiller/music/index.html>--
hmiller (Herman Miller) "If all Printers were determin'd not to print any
@io.com email password: thing till they were sure it would offend no body,
\ "Subject: teamouse" / there would be very little printed." -Ben Franklin

I nominate Daniel Wolf to be the collector of questions and answers and
the compiler of the FAQ.

-----Original Message-----
From: Kraig Grady [mailto:kraiggrady@anaphoria.com]
Sent: Wednesday, February 21, 2001 6:31 PM
To: tuning@yahoogroups.com
Subject: Re: [tuning] Re: EDO and meantone for faq

List!
Daniel has had more actual experience with actually using various
tunings!

Robert C Valentine wrote:

I nominate Daniel to write everything in the faq (just
kidding).

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com <http://www.anaphoria.com>

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

Yahoo! Groups Sponsor

<http://rd.yahoo.com/M=163100.1330039.2920210.2/D=egroupmail/S=1700022409:N/
A=524804/*http://www.classmates.com/index.tf?s=2629> Classmates.com
Click here for Classmates.com

<http://us.adserver.yahoo.com/l?M=163100.1330039.2920210.2/D=egroupmail/S=17
00022409:N/A=524804/rand=255529267>

You do not need web access to participate. You may subscribe through
email. Send an empty email to one of these addresses:
tuning-subscribe@yahoogroups.com - join the tuning group.
tuning-unsubscribe@yahoogroups.com - unsubscribe from the tuning group.
tuning-nomail@yahoogroups.com - put your email message delivery on hold
for the tuning group.
tuning-digest@yahoogroups.com - change your subscription to daily digest
mode.
tuning-normal@yahoogroups.com - change your subscription to individual
emails.
tuning-help@yahoogroups.com - receive general help information.

Your use of Yahoo! Groups is subject to the Yahoo! Terms of Service
<http://docs.yahoo.com/info/terms/> .

Robert Valentine wrote,

>Experiences in 55 from list members? (If I get around to
>orderring a guitar it will be 31, 55 would be too cramped
>and the neat relations I get excited about don't quite
>match my guitar playing).

Get a fretless guitar with 5-tET markers and 10 "submarkers" in-between each
pair.

>
> > >Experiences in 55 from list members?
>
> just a question here, why isn't 53-ET adressed, basically a extension of
> pythagorean tuning
>

Herman,

Thank you for your (and Pauls) reply re 55. As another step in my
'microtonal history' (which so far has really only been trying to figure
out HOW rather than actually producing any works) I spent a long time
thinking that 53 would be 'the next big thing'.

Basically there is a fundamental line you cross when you stop
confabulating the 81:80 that seems to me to result in a different
approach being necessary. This is based on starting from a muscial
sysem I'm familiar with, where a C ionian mode is

C D E F G A B C

rather than

C D Fb F G Bbb Cb C

which I believe the correct spelling of the schismic major scale is.

I think that Graham and/or Margaret already have, somewhere, a 'classes
of EDOs' worked out. (Regarding EDO, it means what it means, another
acronym was determined for covering BP or 88cet). I have tried working
out classifications and never quite finished, but thought that basic
behaviors should be expressable.

Quasi-Meantone
4 * best(3/2) = best( 5/4 ) = 2 * best( 9/8 )

> cents from just
>
> 9/8 5/4 3/2
> 5 36 94 18
> 7 -32 -43 -16
> 12 -4 14 -2
> 19 -14 -7 -7
> 24 -4 14 -2
> 26 -19 -17 -10
> 31 -10 1 -5
> 36 -4 14 -2
> 38 -14 -7 -7
> 43 -9 4 -4
> 50 -12 -2 -6
> 55 -8 6 -4
> 67 -7 8 -3
>

Quasi-Pythagorean
8 * best( 4/3 ) = best( 5/4 ) < 2 * best( 9/8 )

certainly 15, 22, 27, 29, 34, 41, 53...

Bob Valentine

--- In tuning@y..., Robert C Valentine <BVAL@I...> wrote:

> I think that Graham and/or Margaret already have, somewhere,
a 'classes
> of EDOs' worked out.

See message 311 in the archives for my ET classification system. E-
mail me privately if you have any questions -- I'm unsubscribing very
soon!