Coleman 16

[Jim Coleman, Sr.]

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 )
>