Pseudoinverse temperament

I've added pseudoinverse/Frobenius tempering to the latest Scala
version, 2.23p. Also Graham's RMS-TOP and their pure octaves
counterpart (or pure whatever ratio).
See the Modify:Temper dialog. I've tested pseudoinverse with some
values Gene posted to this list and they all agreed. If people test
some more then thanks in advance.

Manuel

--- In tuning-math@yahoogroups.com, "Manuel Op de Coul"
<manuel.op.de.coul@...> wrote:
>
> I've added pseudoinverse/Frobenius tempering to the latest Scala
> version, 2.23p.

Frobenius is now the preferred name.

Manuel Op de Coul wrote:
> I've added pseudoinverse/Frobenius tempering to the latest Scala
> version, 2.23p. Also Graham's RMS-TOP and their pure octaves
> counterpart (or pure whatever ratio).
> See the Modify:Temper dialog. I've tested pseudoinverse with some
> values Gene posted to this list and they all agreed. If people test
> some more then thanks in advance.
> > Manuel

I checked the values for TOP-RMS hedgehog temperament, using the generators from the table at the end of Graham's paper that he recently uploaded to the tuning-math files section (which agree with my calculations). With a period of 599.619 cents and a generator of 164.248 cents, and a generator mapping [<2, 4, 6, 7], <0, -3, -5, -5]> you should get these values for the primes:

2/1: 1199.238
3/1: 1905.732
5/1: 2776.474
7/1: 3376.093

(The actual values I get from my calculations are slightly different, due to the roundoff of the generators in the table: 1199.238, 1905.733, 2776.476, 3376.095)

I tried this in Scala with the pseudoinverse log-weighted option (RMS-TOP), tempering out 50/49 and 245/243, and got:

Wedgie: <<6 10 10 2 -1 -5||
|
0: 1/1 0.000 unison, perfect prime
1: 1198.226 cents 1198.226
2: 1905.811 cents 1905.811
3: 2776.944 cents 2776.944
4: 3376.057 cents 3376.057

The wedgie is correct, but the other values don't agree.

--- In tuning-math@yahoogroups.com, Herman Miller <hmiller@...> wrote:
> (The actual values I get from my calculations are slightly different,
> due to the roundoff of the generators in the table: 1199.238, 1905.733,
> 2776.476, 3376.095)
>
> I tried this in Scala with the pseudoinverse log-weighted option
> (RMS-TOP), tempering out 50/49 and 245/243, and got:
>
> Wedgie: <<6 10 10 2 -1 -5||
> |
> 0: 1/1 0.000 unison, perfect prime
> 1: 1198.226 cents 1198.226
> 2: 1905.811 cents 1905.811
> 3: 2776.944 cents 2776.944
> 4: 3376.057 cents 3376.057
>
> The wedgie is correct, but the other values don't agree.

Thanks Herman. I forgot to square the log(p)'s in the equations, now I
get the same values as you:
1199.23804
1905.73320
2776.47598
3376.09500

I'll upload a new version tomorrow.

Manuel