RE: [tuning] Re: single generator scales with symmetry at the hal f-octave

I wrote,

>> Many of the third of each set seems to have L/s = sqrt(2)+1, rather
>>than L/s = sqrt(2). Right? Or am I misunderstanding what you mean by
>>L/s here?

Dan wrote,

>No, your right. It should have read "They are given in a Golden,
>Equal, Silver, "Apical" order; that is the first of each group has L/s
>= Phi; the second L/s = 2, and the third L/s = sqrt(2)+1." Sorry.

But the third of some groups did have L/s = sqrt(2) . . .

Paul H. Erlich wrote,

> But the third of some groups did have L/s = sqrt(2) . . .

Hmm, shouldn't. Which ones exactly? It's all pretty tedious manual
labor so a mistake is certainly possible, but I was pretty careful.
Let me know.

--Dan Stearns

I wrote,

>> But the third of some groups did have L/s = sqrt(2) . . .

Dan wrote,

>Hmm, shouldn't. Which ones exactly? It's all pretty tedious manual
>labor so a mistake is certainly possible, but I was pretty careful.
>Let me know.

The entries under 10-tone symmetrical scales where "P" = 600¢ (which, of
course, are most interesting to me) seemed to have L/s = phi, L/s = 1.5
(rather than 2), and L/s = sqrt(2) (rather than sqrt(2)+1). Perhaps this has
something to do with what I pointed out in my post on Pell-icans -- the Pell
generators produce a series of MOS scales which alternate between L/s =
sqrt(2) and L/s = sqrt(2)+1 . . .?

Paul H. Erlich wrote,

> The entries under 10-tone symmetrical scales where "P" = 600�
(which, of course, are most interesting to me) seemed to have L/s =
phi, L/s = 1.5 (rather than 2), and L/s = sqrt(2) (rather than
sqrt(2)+1). Perhaps this has something to do with what I pointed out
in my post on Pell-icans -- the Pell generators produce a series of
MOS scales which alternate between L/s = sqrt(2) and L/s = sqrt(2)+1 .
. .?

No, just human error -- mine. I just checked 'em all, and the entry
under "[2s & 8L]" should have read:

0 80 210 340 470 600 680 810 940 1070 1200
0 130 260 390 520 600 730 860 990 1120 1200
0 130 260 390 470 600 730 860 990 1070 1200
0 130 260 340 470 600 730 860 940 1070 1200
0 130 210 340 470 600 730 810 940 1070 1200

0 67 200 333 467 600 667 800 933 1067 1200
0 133 267 400 533 600 733 867 1000 1133 1200
0 133 267 400 467 600 733 867 1000 1067 1200
0 133 267 333 467 600 733 867 933 1067 1200
0 133 200 333 467 600 733 800 933 1067 1200

0 56 192 328 464 600 656 792 928 1064 1200
0 136 272 408 544 600 736 872 1008 1144 1200
0 136 272 408 464 600 736 872 1008 1064 1200
0 136 272 328 464 600 736 872 928 1064 1200
0 136 192 328 464 600 736 792 928 1064 1200

All the rest are as they should be though. Thanks for spotting this
Paul, I appreciate it.

-- Dan Stearns

Dan wrote,

>All the rest are as they should be though.

Umm . . . the [4s & 6L] ones seem to have the phi, 1.5, and sqrt(2) L/s
ratios as well . . .

Paul H. Erlich wrote,

> Umm . . . the [4s & 6L] ones seem to have the phi, 1.5, and sqrt(2)
L/s ratios as well . . .

No, check again. Human error on your side this time I think. <I'll
still call you "eagle eye" though!>

--Dan Stearns

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Dan wrote,

>No, check again. Human error on your side this time I think.

Oops, you're right!