Meantones and edo's - response to Gene "Wizard" Smith posting. - people's perception of "microtonality"

On 21 Dec. 2005, at 16:27, tuning@yahoogroups.com wrote:

>
> Message: 5
> Date: Tue, 20 Dec 2005 21:35:19 -0000
> From: "Gene Ward Smith" <gwsmith@svpal.org>
> Subject: Re: enharmonics of different pitches (MMM: people's > perception of "microtonality
>
> --- In tuning@yahoogroups.com, "threesixesinarow" <CACCOLA@N...> > wrote:
>
>> Some French tuning instructions from 1830s here
>>
>> http://geocities.com/threesixesinarow/montalt.htm
>
> This guy wants everything from Fbb to B##, which is the 35 tones of
> Meantone[35]; that beats Mozart's mere 21 tones. No mention is made of
> the possibility of equating Fbb with D##, I see.

The reason that he fails to mention it may have something to do with the fact that;
From A;
Fbb is L+4s = 163.126 cents in LT and
Dx is 4L-s = 159.329

If you wanted to re-enforce your claim that LucyTuning is 88edo you might have been better to use 44 steps in each direction from A.
e.g.
From A;
Gbbbbbb is 8s-2L = 598.3081
Bxxx is 7L-6s = 601.695 cents
Although you can always find edo approximations to meantones, and vice versa -
the simple musical harmonic diatonic logic and the "spiral nature of meantone is lost, by expressing it as edo's.

A simple simultaneous-type equation calculation applied to your stated notenames would, of course, reveal your intended edo and cent values for L and s.

(1)First equation from your note names:
L+4s=4L-s
therefore
5s=3L

(2) Second equation from meantone (5L+2s=octave) diatonic theory:
5L+2s = 1200 cents = one octave.

OK so now you have the equations, I'm sure that you can do the arithmetic.
(Like the constipated mathematician -- who sat down and worked it out with a ......? ;-)
(skoolboy joke - influenced by my now teenage son - the answer is pencil!; although I used an old ball point pen in this case)

or

using equation (1)
L+4s=4L-s
therefore
5s=3L
octave
Let u=units per octave
Therefore 5s=5u
3L=5u

Therefore from equation (2)

(5*3) + (5*2) = 25 units per octave, or 1200/25 cents per unit = 48 cents per unit

etc. etc.

You see what I mean?;-) .......

It's so much easier to conceptualise tunings in musical meantone terms e.g. Large and small interval in octave = 5L+2s.

Charles Lucy - lucy@harmonics.com
------------ Promoting global harmony through LucyTuning -------
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Charles Lucy wrote:

[snip]

> If you wanted to re-enforce your claim that LucyTuning is 88edo

That's a pretty silly claim, because if LucyTuning is 88EDO then pi = 22/7. (Just thought I'd mention that.)

> you > might have been better to use 44 steps in each direction from A.
> e.g.
> From A;
> Gbbbbbb is 8s-2L = 598.3081
> Bxxx is 7L-6s = 601.695 cents
> Although you can always find edo approximations to meantones, and vice > versa - > the simple musical harmonic diatonic logic and the "spiral nature of > meantone is lost, by expressing it as edo's.

I agree. And besides, EDOs higher than like 40 or 50 don't really have any advantages over an open meantone system.

[snip]

Keenan

--- In tuning@yahoogroups.com, Keenan Pepper <keenanpepper@g...> wrote:

> > If you wanted to re-enforce your claim that LucyTuning is 88edo
>
> That's a pretty silly claim, because if LucyTuning is 88EDO then pi
= 22/7.
> (Just thought I'd mention that.)

Need I say here that I didn't make this claim?

> I agree. And besides, EDOs higher than like 40 or 50 don't really
have any
> advantages over an open meantone system.

The cited reference seemed to assume that the theoretical ideal was
55-et, a popular choice. Even thought people didn't use all of it,
they found it advantageous to make use of it as a theoretical tool.

On Thu, 22 Dec 2005, Gene Ward Smith wrote:
>
> --- In tuning@yahoogroups.com, Keenan Pepper
> <keenanpepper@g...> wrote:
>
> > > If you wanted to re-enforce your claim that LucyTuning is 88edo
> >
> > That's a pretty silly claim, because if LucyTuning is 88EDO then pi
> = 22/7.
> > (Just thought I'd mention that.)
>
> Need I say here that I didn't make this claim?

Of course not, Gene! Anyone who thinks
you're silly is just, well, silly!

Compliments of the silly season,
Yahya

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