Coleman 16

[Richard Brekne]

Hi Jim and others.

I cant help launching a little finger in the air about the insistance of useing
only "cents deviations" in describing temperaments. Ear tuners dont really use
cents actively very much at all. Most ear tuners probably think of cents only
when relating to starting pitch, and from then on its beats per second. Thats
what we deal in, and as such our awareness of cents doesnt permit us to auralize
(visa vi visualize) what these figures below really imply.

Is it  (and I am asking out of genuine curiousity) so difficult to also relate
these temperaments in terms of beats per second for various intervals ??

"Jim Coleman, Sr." wrote:

> 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)
>

Richard Brekne
RPT, N.P.T.F.
Bergen, Norway