Hi Jim: Here are the deviation numbers for the Coleman 16 well temperament: C C# D D# E F F# G G# A A# B 6 0 2 2 -2 6 -2 4 1 0 4 -2 This will provide the following interval widths: sharps 5ths 4ths 3rds Flats 5ths 4ths 3rds C -4 2 6 F -2 0 8 G -4 4 8 Bb 0 0 12 D -4 4 10 Eb 0 1 16 A -4 4 14 Ab -1 1 19 E -2 4 17 Db -1 0 20 B -2 2 18 Gb 0 2 20 The normal widths in equal temperament are as follows: 5ths -2 cents from pure (actually -1.95) 4ths 2 " " " M3rds 14 " " " (actually 13.7 varies with inharmonicity) I could have used decimals in the above, but it is easier to visualize this way and .1 cent does not make much difference anyway. In the Coleman 16 the 4ths are very quiet, 1/3 of the 5ths are a little busier, and the M3rds get busier in a rather even manner but start out much slower as one progresses through the key tonalities from few to more sharps or flats in the key signature. In the Coleman 11 which I sent you before, there is in general less deviation from ET and the widest M3rds are not as edgy. I think it is safer for introducing one to Well Temperament. Here are the specs for it: C C# D D# E F F# G G# A A# B 3 0 0 0 -3 4 -2 2 0 -1 2 -4 Interval widths: Sharps side 5ths 4ths M3rds Flats side 5ths 4ths M3rds C -3 3 8 F -3 0 9 G -4 3 8 Bb 0 0 12 D -3 4 12 Eb 0 2 16 A -4 3 15 Ab -2 2 17 E -3 4 17 Db -2 0 18 B 0 3 18 Gb 0 0 18 I hope these figures help you understand better what is going on in these well temperaments. All these temperaments were figured out on a spreadsheet about 3 years ago or more. I started out with the Coleman 2 which had only 2 cent variations from ET in two places. I could do that on the fly by manually deviating from the SAT FAC tunings twice in each octave. You are correct in that with the SAT III it is much easier to make all the deviations with just two button pushes after the basic 12 note variation has been programmed. And, it is much easier to go back to the original ET or another HT with just 2 button pushes. After programming 16 Well temperaments, I have discarded all but the 11 and the 16 for my personal use. If one should want a more stout well temperament, the Young or Valotti would be next in complexity. Next would be the Kirnberger or the Paul Bailey Well T. What I particularly like about the Coleman 11 and 16 is that there are no wild 4ths or 5ths. You must understand that there are some who develop a taste for these greater contrasts. At one of the PTG conventions I saw two people who had embossed wolf emblems on their shirts as a badge of courage. I was told that one has to earn the right to wear them. I am not yet qualified to wear them, but perhaps someday as I grow to appreciate more contrast from the musical perspective, I might be permitted to wear them. Jim Coleman, Sr. On Fri, 17 Nov 2000, Jim Dally wrote: > Hi Jim: You suggested I remind you to send me the Coleman 16 numbers. = > I really enjoyed starting on the Coleman 11 and I do hear the = > differences. I want to be capable of doing an historical temperament if = > one is requested. Someday, I might go for a SAT III. As I understand = > the function of the machine it will greatly simplify an historical = > temperament. Many thanks for your assistance. Jim Dally ( no hurry = > for the 16 ) >
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