Graham explains clearly why it's mean

[Graham explains why it's callehd *mean*tone:]

>> The distance between 9/8 and 10/9 is a syntonic comma. A
>> whole tone is two steps on the spiral of fifths. So, if you
>
>> temper the fifth by 1/4 comma, the tone will be tempered by
>> 1/2 comma, leaving it halfway between the two values.

[Joe:]

> DUH. THANKS. FINALLY I got this!

> I wish this explanation were up on Kyle Gann's otherwise
> excellent webpage on meantone tuning. It was the one thing
> that wasn't clear!

(( Light goes on ))

So that's why it's called meantone????!!

Wow; thanks Graham. That actually makes sense
for the first time. I feel like a great weight
has been lifted. And Joe thanks for having the
balls to ask this question.

Wow!

I had believed what I had been told be 'others' which I
should not have! That so-called 'official' explanation
is clearly a bunch of hooey -- Graham's explanation
is not only the right one, but simple and easy to
understand. What more could ja ask for?

- Jeff

--
"When the philosopher's argument becomes tedious,
complicated, and opaque, it is usually a sign that he
is attempting to prove as true to the intellect what is
plainly false to common sense. But men of intellect
will believe anything -- if it appeals to their ego,
their vanity, their sense of self-importance."
-- Vox Clamantis in Deserto, Edward Abbey

> From: X. J. Scott <xjscott@earthlink.net>
> To: <tuning@yahoogroups.com>
> Sent: Friday, August 10, 2001 9:51 AM
> Subject: [tuning] Graham explains clearly why it's mean
>
>
> [Graham explains why it's callehd *mean*tone:]
>
> >> The distance between 9/8 and 10/9 is a syntonic comma. A
> >> whole tone is two steps on the spiral of fifths. So, if you
> >
> >> temper the fifth by 1/4 comma, the tone will be tempered by
> >> 1/2 comma, leaving it halfway between the two values.
>
> [Joe:]
>
> > DUH. THANKS. FINALLY I got this!
>
> > I wish this explanation were up on Kyle Gann's otherwise
> > excellent webpage on meantone tuning. It was the one thing
> > that wasn't clear!
>
>
> (( Light goes on ))
>
> So that's why it's called meantone????!!
>
> Wow; thanks Graham. That actually makes sense
> for the first time. I feel like a great weight
> has been lifted. And Joe thanks for having the
> balls to ask this question.
>
> Wow!

You guys must be missing some of my posts.

I sent one on July 13 which explained this, and
another one on August 5 in which I quote that one.

Here's the revelant bit again:

> From: monz <joemonz@yahoo.com>
> To: <tuning@yahoogroups.com>
> Sent: Friday, July 13, 2001 9:28 AM
> Subject: Re: [tuning] trias harmonica - for Margot Schulter
>
>
> Note also that 1/4-comma meantone, the type you describe
> here, where the "5th" is calculated as ( (3/2) / (81/80)^(1/4) )
> = ~696.5784285 cents (nearly identical to 31-EDO), was only
> one early solution. Its "major 3rd" is of course the 5:4
> ratio = ~386.3137139 cents. Its "whole-tone" is ~193.1568569
> cents, which is *precisely* the mean between the 9:8 and 10:9
> ratios. This is the only tuning which can be labeled *exactly*
> as "mesotonic".
>

Herbert Anton Kellner's Greek word "mesotonic" means exactly the
same thing as the English word "meantone".

love / peace / harmony ...

-monz
http://www.monz.org
"All roads lead to n^0"

_________________________________________________________
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--- In tuning@y..., "monz" <joemonz@y...> wrote:

/tuning/topicId_26880.html#26916
> > (( Light goes on ))
> >
> > So that's why it's called meantone????!!
> >
> > Wow; thanks Graham. That actually makes sense
> > for the first time. I feel like a great weight
> > has been lifted. And Joe thanks for having the
> > balls to ask this question.
> >
> > Wow!
>
>
>
> You guys must be missing some of my posts.
>

Hi Monz...

No, I think at least *I* saw those. The point was, it would be great
to include the idea that the two sizes of D are the SECOND FIFTH in
the chain of fifths, and the tempering is thereby ONE HALF of the
syntonic comma that's eliminated by the 4th tempered fifth. I don't
believe that is anyplace in your dictionary or webpage, and it made
things a *lot* clearer for me.

*Of course* I had heard that "meantone" was the placing of the tone
in between, or 1/2 way between the other D tones, but I never
understood why it was 1/2 way before...

I think that would be a nice addition to your dictionary pages, since
it made it so clear for *me.*

Thanks!

_______ _______ ________
Joseph Pehrosn

In posting 26957 Re: nutty professor has me confused (JI)-
I added a relevant P.S., which I repeat here in this thread for your
convenience, as an additional note on the meantone nomenclature, since
the D is not only the mean between two possible pitches tuned justly
to the JI G and A, but the meantone G and A are also MEANS between
two pitches tuned to the meantone D and C and E respectively (which
latter are the same in either JI or meantone):

P.S. Concerning the derivation of the name "meantone" for this
temperament, please note this interesting observation for the most
elegantly simple version, the quarter-comma. Since the comma division
is symmetrical around D in this tuning (assuming C-based tuning), the
temperament for D should be set first. After tuning C and E as a just
5:4 M3, you can set the temperament for D by:

1) tuning A a Perfect 4th above E (and consequently a just M6 above C
if you want to double check)

2) tuning G a Perfect 5th above C

3) tuning D a Perfect 5th below the just A

4) play the D against the just G (it will be flat to the G by a
synontic comma)

5) Observe the beat rate

6) Raise the D till the beat rate is half the initial rate

This sets the tempered D. Now the two remaining tempered core
pitches, G and A, are tuned as mean pitches between C and D, then D
and E respectively, by an analogous procedure.

*!*!*!*!*!*! NOTE THE FOLLOWING: All three notes are tempered as
MEANS between two pitches, and not just the D. All other pitches from
Eb to G#, or wherever else you want to place the "wolf" fifth
(actually a diminished 6th or its inversion, an augmented 3rd), can
be tuned as just 5:4 Major 3rds to these core pitches.

This simplest and most elegantly symmetrical mother of all the other
meantone temperaments has two difficulites beyond the limits it
imposes on harmonic modulation:

1) Unlike 12-EDO, it does not order the degree of pitch error to
align with the order of the intervalic primes. In ET, the fifths are
almost just, the Major 3rds next (as bad as they may be), etc., so
the most dissonant intervals are also the least accurate. Quarter-
comma meantone has the fifths more than twice as mistuned as ET, but
Major 3rds are perfect, inverting the order of primacy for the
intervals.

2) Further, quarter-comma has diatonic half-steps 5.5 cents wider
than the already fat (to modern ears) diatonic half-steps of JI. The
narrow chromatic half-steps of JI are further narrowed by 5.5 cents.
This has mostly a melodic significance, but not a completely
negligible one.

These weaknesses seem to have bothered some quarter-comma users
enough to seek other variants of meantone, many of which did little
or nothing to extend the range of clean modulations, but rather
shifted some of the pitch error of the perfect 5ths and minor 3rds to
the Major 3rds, narrowing the diatonic half-steps and widening the
chromatic half-steps in the bargain.

--- In tuning@y..., jpehrson@r... wrote:
> --- In tuning@y..., "monz" <joemonz@y...> wrote:
>
> /tuning/topicId_26880.html#26916
> > > (( Light goes on ))
> > >
> > > So that's why it's called meantone????!!
> > >
> > > Wow; thanks Graham. That actually makes sense
> > > for the first time. I feel like a great weight
> > > has been lifted. And Joe thanks for having the
> > > balls to ask this question.
> > >
> > > Wow!