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 >
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