expanded temperment (Jim C.)

[Jim]

Congratulations Ralph:

You are only the 3rd person who has actually successfully tried the
widened octaves or approaching pure 5ths temperament. Now, I'm going
to suggest that you might next try widening a little more, say, 1.5
cents addition to the A4 stretch number. This will make your 5ths even
purer and the octaves and 4ths a little wider. You can then actually
measure the widths of the 5ths that are a result of this tuning. They
may not all be perfectly pure, but they will be close to pure. You are
another who confirms what I said in the beginning that many aural tuners
have been doing this accidentally for years and have been judged as
superior tuners perhaps for that very reason.

I just completed reading an article by Mieczyslaw Kolinski from an older
edition of the American Journal of the Musicological Society on this
very subject, so I can not claim originality to this system of tuning.
I must however say that I arrived at it empirically whereas he arrived
at it theoretically. His system does not include a sense of inharmonicity
whereas, mine was developed with that specifically in mind.

Jim Coleman, Sr.

PS I believe that these studies will eventually help us all to arrive at
   a concensus as to the best type of octave stretch to use. It may not be
   perfectly pure 5ths, but something close to it  JWC


On Mon, 14 Jul 1997 rmartin21@juno.com wrote:

> Hi Jim
> 
> Some observations re your recommended expansion.
> 
> The last three pianos I have tuned by adding 1c to the A and using, of
> course, the SAT. Tuned my own 42" yamaha which I had previously tuned
> aurally and was amazed to find that I had to move virtually NOTHING. The
> only variation worth mentioning was that the tuning flattened the bass
> slightly more than I did aurally.
> 
> This AM I tuned a Kawaii KG-2 and figured I'd try the expanded tuning
> here also. Triple octaves sounded great and even 4 octave span was very
> playable. You were quite right when you mentioned that the slightly
> faster 4ths are really not noticable when playing, but the solidity of
> the 5ths were outstanding. Also, the single octaves that I thought would
> be too wide for me ..were actually very comfortable.
> 
> Maybe I like the tuning because I have been tuning aurally quite wide
> right along without really paing much attention to it. In any event, I am
> very pleased with the approach because it sounds like my aural tunings
> without all the work.
> 
> Thank you for all the information "beyond the call of duty"
> 
> Ralph
>