Re: Eventone tunings (in place of "equitone")

Hello, there, everyone, and in view of the established use of
"equitone" or "equiton" in a different meaning, may I propose another
term for my intended meaning of a regular temperament used in such a
fashion that a usual major third is constructed from two regular
whole-tones of identical size?

My new proposed is "eventone," a term with a linguistic flavor maybe
somewhat closer to "meantone" than my earlier choice of "equitone."

For example:

"As it happens, 46-tone equal temperament (46-tET) is almost identical
to an eventone with major thirds precisely at 14:11."

Most respectfully,

Margo Schulter
mschulter@value.net

Dear Mrs. Margo Schulter,

As concerns the subdivision of a third into two tones, I should like to mention
the work of Robert Tanner, 1972/1982. He found out that musical hearing prefers
two EQUAL tones making up the third. This stipulated equality of tones holds for
meantone, as well as for Pythagorean!

Tanner, Robert: Le probleme des "deux tierces" (Pythagore ou Zarlino), Sa
solution psycharithm�tique et exp�rimentale. Acustica,Vol. 27, 1972, page 335ff.

Tanner, R.: La th�se des n�o-pythagoriciens sur les rapports musicaux, invalid�e
par leur propre m�thode exp�rimentale. Acustica, Vol. 50/1, 1982, page 1-15, en
particulier pp. 8 et 15

In Bach/"wohltemperirt", C-major, C-D and D-E are of equal size - as it "ought
to be".

In Bach/"wohltemperirt", C#-major is the Pythagorean scale; arising from
the descending perfect fifths tuned: c-f-bb-eb-ab-db-gb. Thus, tones of equal
size make up the major thirds.

The Bach-comma is 1/5 of the Pythagorean Comma and amounts to 4.7 cent, because
this musical temperament divides P by 5.

Reference: ha.kellner.bei.t-online.de

Most successive tones within major thirds differ by 4.7 cent - the Bach-comma.

However, the greatest deviation from equality of successive tones of major
thirds in Bach/"wohltemperirt", is 2*4.7 cent (=9.4 cent). Save some exceptions,
I wonder if Bach always tries to avoid setting that sequence of tones within the
exceptional third concerned. I found a few examples but one fabulous
counter-example for the preference of equal tones in a third: in Duetto II of
the Clavier�bung III.

Incidentally, here might be one reason why the sequence (in any temperament) of
C-D-Eb gives its melodically triste, sad impression: The successive tones are
first, one tone, then a semitone.

Kind regards,
Herbert Anton Kellner

mschulter schrieb:
> Hello, there, everyone, and in view of the established use of
> "equitone" or "equiton" in a different meaning, may I propose another
> term for my intended meaning of a regular temperament used in such a
> fashion that a usual major third is constructed from two regular
> whole-tones of identical size?
>
> My new proposed is "eventone," a term with a linguistic flavor maybe
> somewhat closer to "meantone" than my earlier choice of "equitone."
>
> For example:
>
> "As it happens, 46-tone equal temperament (46-tET) is almost identical
> to an eventone with major thirds precisely at 14:11."
>
> Most respectfully,
>
> Margo Schulter
> mschulter@value.net
>
>
>
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On Wed, 4 Jul 2001 19:31:10 -0700 (PDT), mschulter <MSCHULTER@VALUE.NET>
wrote:

>My new proposed is "eventone," a term with a linguistic flavor maybe
>somewhat closer to "meantone" than my earlier choice of "equitone."
>
>For example:
>
>"As it happens, 46-tone equal temperament (46-tET) is almost identical
>to an eventone with major thirds precisely at 14:11."

Could this also be applied to scales that split the minor third in half?
Some of my favorite tunings (including 15-TET) have this property. In fact,
it might be a useful property of scales in general to be able to split
consonant intervals into a small number (2 or 3) of equal parts.