Aural Pure 5ths Equal Temperament

[Jim]

Hi Dennis:

Thanks for your well reasoned response. I have not yet dealt with the
difference between the 3/2 fifths and the 6/4 fifths. This is still
quite new to me.  However, I do not relate this temperament to any of
the historical temperaments at this time.  You will notice that I refer
to this as an equal temperament which includes tempering the octaves as
well. When you actually try this temperament on a piano, you will find
that all the 5ths stay pure, all the 4ths stay in even progression, all
the 3rds stay in even progression, all the 6ths stay in even progression.
Therefore, this is not anywhere near an historical temperament except that
equal temperament was also developed historically.

I have a great respect for your depth of understanding of the historical
temperaments. For years I used an aural temperament which I tho't was
equal temperament, but which was closer to Marpurg I.  I liked the idea
of balancing the 3 3rds of an octave first and then I could tune all but
3 notes in the octave as either a 4th or a 5th from those balanced 3rds.
I called those my primary 4ths and 5ths. Then I could tune the last 3
notes from some of the primary 4ths or 5ths. Steve Brady was the first to
suggest to me that I was tuning strangely close to the Marpurg.

In this current tuning, I stress that this is more equal temperament than
that which we normally call equal temperament, because it also tempers
the octaves so that they match better thoughout the whole piano. Let me
know what you find after you have had a chance to try it. I may have to
alter my estimate of the 1.5 beat 4ths and octaves a little after I have
more experience in tuning different pianos. At the time of the writing,
I had only tuned my Steinway L and one Yamaha console with this system.
Now I have tuned a few more pianos including a Yamaha CFIII. The results
still make the piano sound bigger.

Jim Coleman, Sr.

On Wed, 21 May 1997, Dennis Johnson wrote:

>
>
> Jim,
>
> If I understand your temperament correctly, you are setting something
> very close to a 1/5 ditonic comma meantone, with the comma divided
> regularly between four fifths and the octave. Your language does not
> necessarily imply regularly tempered divisions, but if your thirds are
> of equal size then these divisions of the ditonic comma would need to be
> equal as well. This is something different from anything I have tried, but
> I have come to respect your interests.  Actually, it would not be so far
> removed from the Marpurg I temperament, which is a 1/6 comma ditonic
> division, all of them being fifths. In your temperament, the telling
> triads would be D Maj, B Maj, E Maj, and Eb Maj, but there can be no
> argument that all other keys are improved over both the standard ET
> and the traditional Pythagorean triads for two reasons. First, the fifths
> are pure which implies the triads to be proportionally beating (actually,
> 6:4 fifths are strictly proportional but that is not worth picking over)
> and second, the thirds within these triads would beat identical to, or very
> similar to, beat speeds of standard ET thirds. It then becomes an aesthetic
> question as to whether one prefers this color, or something else.
>
> I eventually tired of the Marpurg I temperament because I felt that the
> color of a 1/6 ditonic fifth matched with an ET third did not appeal to
> me. That is why I must wonder about these keys mentioned because a 1/5
> ditonic fifth would beat slightly faster than a 1/6 fifth. This
> is not to say that a fifth beating 1.5 bs is too fast. To the contrary.
> 1/4 syntonic fifths beat even faster, and they can be glorious. The
> aesthetic issue, IMO, is one of balancing beat speeds in a complimentary
> way between fifths and thirds. Generally, the more noticeable a fifth is
> beating, the slower I like the thirds to be, with the clever exception of
> an occasional proportionally beating triad that can hide a faster
> beating fifth. In my experience, when a noticeably beating fifth beats in
> no rhythmic relationship to the thirds, and the thirds are beating as
> fast as standard ET, you get a color much less satisfying than a traditional
> Pythagorean triad with much faster thirds and a pure fifth.
>
> Hope I did not ramble too long, but thanks for sharing this preview of
> your article.
>
>
> Dennis Johnson
> St. Olaf College
>
>