Keenan and Catakleismic

Dave is not a fan of complex temperaments, and has cast doubt
specifically on catakleismic, the 53&72 7 and 11-limit temperament, as
being too complex. I was therefore highly interested to note that a
scale called "keenan5" in the Scala archives, which apparently dates
back to Christmas of 1999, could represent the first historical
apperance of what is, in effect, catakleismic tempering.

Below I give a version of keenan5 using the poptimal generator of
71/269; if you compare it to the keenan5 of Dave you can see that the
catakleismic interpretation is clear. The two are quite close. I also
give Catakleismic[34] in the same tuning by way of a comparison. In
the comments at the bottom of keenan5_269 I give the scale in terms of
catakleismic generators.

"Muddles" such as 21;72;269 might be interesting, I suppose.

! keenan5_269.scl
Keenan5 as a catakleismic scale with 71/269 generator
31
! 53&72 catakleismic wedgie = <<6 5 22 -21 -6 18 -54 37 -66-135||
!
35.687732
84.758364
115.985130
151.672862
200.743494
231.970260
267.657993
316.728625
352.416357
383.643123
432.713755
468.401487
499.628253
548.698885
584.386617
615.613383
651.301115
700.371747
731.598513
767.286245
816.356877
852.044610
883.271375
932.342007
968.029740
999.256506
1048.327138
1084.014870
1115.241636
1168.773234
1200.000000
! scale = [-28, -27, -23, -22, -21, -17, -16, -12, -11, -10, -6, -5, -1,
! 0, 1, 5, 6, 10, 11, 12, 16, 17, 21, 22, 23, 27, 28, 33, 34, 38, 39]

! cata34.scl
Catakleismic[34] in 71/269 generator tuning
34
!
17.843866
66.914498
84.758364
133.828996
151.672862
200.743494
249.814126
267.657993
316.728625
334.572491
383.643123
401.486989
450.557621
499.628253
517.472119
566.542751
584.386617
633.457249
651.301115
700.371747
718.215613
767.286245
816.356877
834.200743
883.271375
901.115242
950.185874
968.029740
1017.100372
1034.944238
1084.014870
1133.085502
1150.929368
1200.000000

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
>
> Dave is not a fan of complex temperaments, and has cast doubt
> specifically on catakleismic, the 53&72 7 and 11-limit
temperament, as
> being too complex. I was therefore highly interested to note that a
> scale called "keenan5" in the Scala archives, which apparently
dates
> back to Christmas of 1999, could represent the first historical
> apperance of what is, in effect, catakleismic tempering.
>
> Below I give a version of keenan5 using the poptimal generator of
> 71/269; if you compare it to the keenan5 of Dave you can see that
the
> catakleismic interpretation is clear. The two are quite close. I
also
> give Catakleismic[34] in the same tuning by way of a comparison. In
> the comments at the bottom of keenan5_269 I give the scale in
terms of
> catakleismic generators.
...
> ! scale = [-28, -27, -23, -22, -21, -17, -16, -12, -11, -10, -6, -
5, -1,
> ! 0, 1, 5, 6, 10, 11, 12, 16, 17, 21, 22, 23, 27, 28, 33, 34, 38,
39]

I think the huge gaps in this generators sequence make it clear that
a catakleismic interpretation is entirely unwarranted. I seem to
remember it was a planar temperament, which probably has several
possible non-contiguous linear interpretations.

-- Dave Keenan

--- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...> wrote:

> I think the huge gaps in this generators sequence make it clear that
> a catakleismic interpretation is entirely unwarranted.

You are assuming that linear temperaments always should be used with a
MOS, and it is this which is entirely unwarrented. Linear temperaments
can be treated like planar temperaments, if you wish.

I seem to
> remember it was a planar temperament, which probably has several
> possible non-contiguous linear interpretations.

It almost certainly is 11-limit marvel, the {225/224, 385/384}
temperament which I think we concluded you invented. The relationship
between this and catakleismic is extremely close. Catakleismic is what
you get when you add 4375/4374 to the commas of marvel, and doing this
can be justified in the same way as adding 385/384 to 7-limit marvel:
there is very little tuning damage as a result. In order for the scale
to be natively catakleismic rather than marvel, all you would need
would be a comma pump for it; I havn't found one but I suppose it
might be in there somewhere. Whether or not it is there, there isn't
much percentage in a scale of this size in ignoring the possibility;
the larger the scale, the more likely an unintended equivalency is
lurking anyway. In any event, it makes no sense to me to have invented
11-limit marvel and yet disparage 11-limit catakleismic.

--- In tuning-math@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...>
wrote:
>
> --- In tuning-math@yahoogroups.com, "Dave Keenan" <d.keenan@b...>
wrote:
>
> > I think the huge gaps in this generators sequence make it clear
that
> > a catakleismic interpretation is entirely unwarranted.
>
> You are assuming that linear temperaments always should be used
with a
> MOS, and it is this which is entirely unwarrented.

I'm not assuming MOS.

> Linear temperaments
> can be treated like planar temperaments, if you wish.

Sure, but when I say I find some temperament to be too complex I'm
thinking of how many consonances (and of what accuracy) can be
obtained from a given number of notes in a contiguous (or at least
fairly compact) set on the chain (or lattice) of generators.

> I seem to
> > remember it was a planar temperament, which probably has several
> > possible non-contiguous linear interpretations.
>
> It almost certainly is 11-limit marvel, the {225/224, 385/384}

Yes.

> temperament which I think we concluded you invented.

Discovered may be a better word -- with much help from Carl Lumma,
Paul Erlich and Graham Breed. And I would be very surprized if
Adriaan Fokker hadn't discovered it earlier.

> The relationship
> between this and catakleismic is extremely close. Catakleismic is
what
> you get when you add 4375/4374 to the commas of marvel, and doing
this
> can be justified in the same way as adding 385/384 to 7-limit
marvel:
> there is very little tuning damage as a result. In order for the
scale
> to be natively catakleismic rather than marvel, all you would need
> would be a comma pump for it; I havn't found one but I suppose it
> might be in there somewhere. Whether or not it is there, there
isn't
> much percentage in a scale of this size in ignoring the
possibility;
> the larger the scale, the more likely an unintended equivalency is
> lurking anyway. In any event, it makes no sense to me to have
invented
> 11-limit marvel and yet disparage 11-limit catakleismic.

I certainly can't disparage the fine-tuning of this scale to some
optimal catakleismic, but the choice of which generator-multiples to
include clearly owes nothing to Catakleismic and everything to 11-
limit Marvel.

A contiguous or compact set of Catakleismic to contain the same 11-
limit consonances would be far larger. That's all I mean when I say
catakleismic is too complex.

After all, this scale would probably sound just fine tempered all
the way to 72-ET, but I assume you would not then say that this
scale is "essentially 72-ET".

Anyway, that was 6 years ago and I don't currently consider that
scale to be terribly significant.

-- Dave Keenan