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.