How consistent are cents?

If you want an idea of what a randomly chosen consistent badness
measure looks like, chew on this:

Cons(w, 1200) for w from 2 to 49

3 53.998800
5 12.42619668
7 5.183728199
9 5.183728199
11 2.895954014
13 3.263002903
15 3.263002903
17 2.576191158
19 2.216354953
21 2.216354953
23 1.952782773
25 2.703605969
27 2.703605969
29 2.450061526
31 2.264455891
33 2.264455891
35 2.264455891
37 2.123104197
39 2.180931116
41 2.066877882
43 1.975042642
45 1.975042642
47 1.899581355
49 1.899581355

--- In tuning-math@y..., genewardsmith@j... wrote:
> If you want an idea of what a randomly chosen consistent badness
> measure looks like, chew on this:
>
> Cons(w, 1200) for w from 2 to 49
>
> 3 53.998800
> 5 12.42619668
> 7 5.183728199
> 9 5.183728199
> 11 2.895954014
> 13 3.263002903
> 15 3.263002903
> 17 2.576191158
> 19 2.216354953
> 21 2.216354953
> 23 1.952782773
> 25 2.703605969
> 27 2.703605969
> 29 2.450061526
> 31 2.264455891
> 33 2.264455891
> 35 2.264455891
> 37 2.123104197
> 39 2.180931116
> 41 2.066877882
> 43 1.975042642
> 45 1.975042642
> 47 1.899581355
> 49 1.899581355

Again, I don't know what you mean by consistent here. 1200-tET is
consistent through the 9-limit, but not the 11-limit.

Paul wrote:
>Again, I don't know what you mean by consistent here. 1200-tET is
>consistent through the 9-limit, but not the 11-limit.

Are you sure? According to my calculation, 1200-tET is 12-limit
consistent (hey, funny). This is the integer limit, Paul
prefers to use the odd limit which is one less for octave
divisions. The 12-limit region is 1199.97488 - 1200.01221 tET.
The margin is very small, 11/7 is almost halfway between two
steps: 782.49 cents.

Manuel

In-Reply-To: <OF6575791C.83BBE7D8-ONC1256ADA.004B4ECC@ezh.nl>
I agree with Manuel: 1200-equal is 11-limit consistent.

Graham

--- In tuning-math@y..., <manuel.op.de.coul@e...> wrote:
>
> Paul wrote:
> >Again, I don't know what you mean by consistent here. 1200-tET is
> >consistent through the 9-limit, but not the 11-limit.
>
> Are you sure? According to my calculation, 1200-tET is 12-limit
> consistent (hey, funny). This is the integer limit, Paul
> prefers to use the odd limit which is one less for octave
> divisions. The 12-limit region is 1199.97488 - 1200.01221 tET.
> The margin is very small, 11/7 is almost halfway between two
> steps: 782.49 cents.
>
> Manuel

Hi Manuel, you are right. 1200-tET is 11-limit consistent, but not 13-
limit consistent. I typed "1" instead of "11" in my program and got
an error, so I mistakenly concluded that 11 didn't work. It does.

--- In tuning-math@y..., "Paul Erlich" <paul@s...> wrote:

> Hi Manuel, you are right. 1200-tET is 11-limit consistent, but not
13-
> limit consistent. I typed "1" instead of "11" in my program and got
> an error, so I mistakenly concluded that 11 didn't work. It does.

In any case, what I gave was not a measure of consistency, but a
consistent measure. I enforce consistency, and then simply give a
measure of how far out of tune the result is in a relative sense.