37&49 for 2.3.5.7.9'.11

37&49 makes for a plausible 2.3.5.7.9'.11 which does not temper out the consistency pseudocomma, 9'/9. It has a low complexity for 9', since 9'/8 is two generator steps, and a 12-note MOS for those into retuning 12edo. 3\37 is a good tuning.

On Wed, Apr 13, 2011 at 4:57 PM, genewardsmith
<genewardsmith@...> wrote:
>
> 37&49 makes for a plausible 2.3.5.7.9'.11 which does not temper out the consistency pseudocomma, 9'/9. It has a low complexity for 9', since 9'/8 is two generator steps, and a 12-note MOS for those into retuning 12edo. 3\37 is a good tuning.

So how does this work? Tempering out 9'/9 brings us to rank 1. Do we
get 12-equal? And also, if we temper out 135/128, does that somehow
imply a tempering out of 9'/9? I guess so...

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> So how does this work? Tempering out 9'/9 brings us to rank 1. Do we
> get 12-equal? And also, if we temper out 135/128, does that somehow
> imply a tempering out of 9'/9? I guess so...

I posted a response to this which didn't appear. I'll repeat that it doesn't temper out either 135/128 or 9'/9, but does temper out 64/63 and 3125/3087, as well as 100/99 and 176/175 in the 11-limit, plus 128 * 9'/1125. The 37&49 temperament is already meantone's eccentric uncle who lives in the attic and plays with his sharp fifths; adding in the inconsisent 9' means we get to use meantone 9/8s. Here's a version of the 12 note MOS:

! moantone12.scl
!
Moantone[12] in 86edo
12
!
97.67442
195.34884
293.02326
390.69767
488.37209
586.04651
711.62791
809.30233
906.97674
1004.65116
1102.32558
2/1

Gene, I hate to rely on you to answer all my dumb questions, but what
do you mean by "37&49 temperament"?

Thanks,
Jake

On 4/13/11, genewardsmith <genewardsmith@...> wrote:
>
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
>> So how does this work? Tempering out 9'/9 brings us to rank 1. Do we
>> get 12-equal? And also, if we temper out 135/128, does that somehow
>> imply a tempering out of 9'/9? I guess so...
>
> I posted a response to this which didn't appear. I'll repeat that it doesn't
> temper out either 135/128 or 9'/9, but does temper out 64/63 and 3125/3087,
> as well as 100/99 and 176/175 in the 11-limit, plus 128 * 9'/1125. The 37&49
> temperament is already meantone's eccentric uncle who lives in the attic and
> plays with his sharp fifths; adding in the inconsisent 9' means we get to
> use meantone 9/8s. Here's a version of the 12 note MOS:
>
> ! moantone12.scl
> !
> Moantone[12] in 86edo
> 12
> !
> 97.67442
> 195.34884
> 293.02326
> 390.69767
> 488.37209
> 586.04651
> 711.62791
> 809.30233
> 906.97674
> 1004.65116
> 1102.32558
> 2/1
>
>
>
>
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--- In tuning@yahoogroups.com, Jake Freivald <jdfreivald@...> wrote:
>
> Gene, I hate to rely on you to answer all my dumb questions, but what
> do you mean by "37&49 temperament"?

I always mean patent vals. Thus, for me 7-limit 37&49 temperament combines [<37 59 86 104|, <49 78 114 138|], where the numbers for the N-edo patent val are obtained by multiplying N * <1 log2(3) log2(5) log2(7)| and rounding to the nearest integer. This can then be computed to have a 16/15~21/20 semitone generator in a temperament where (16/15)/(21/20) = 64/63 is tempered out. As in meantone, four generators brings you to a major third, and ten to a 7/4, though of course the generators are not fifths. Five generators gets you to a fourth, eighteen to an 11/4.

On Wed, Apr 13, 2011 at 8:11 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > So how does this work? Tempering out 9'/9 brings us to rank 1. Do we
> > get 12-equal? And also, if we temper out 135/128, does that somehow
> > imply a tempering out of 9'/9? I guess so...
>
> I posted a response to this which didn't appear. I'll repeat that it doesn't temper out either 135/128 or 9'/9, but does temper out 64/63 and 3125/3087, as well as 100/99 and 176/175 in the 11-limit, plus 128 * 9'/1125. The 37&49 temperament is already meantone's eccentric uncle who lives in the attic and plays with his sharp fifths; adding in the inconsisent 9' means we get to use meantone 9/8s. Here's a version of the 12 note MOS:

Ack, sorry, I meant 128/125. If you temper out 128/125, that should
bring you to 12-equal, right? And so does tempering out 9'/9. The two
must be offset from one another by some comma that's already being
tempered in moantone.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> The two must be offset from one another by some comma that's already
> being tempered in moantone.

Moantone, the best temperament for expressing lamentation, pain
and grief.

Kalle

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> > I posted a response to this which didn't appear. I'll repeat that it doesn't temper out either 135/128 or 9'/9, but does temper out 64/63 and 3125/3087, as well as 100/99 and 176/175 in the 11-limit, plus 128 * 9'/1125. The 37&49 temperament is already meantone's eccentric uncle who lives in the attic and plays with his sharp fifths; adding in the inconsisent 9' means we get to use meantone 9/8s. Here's a version of the 12 note MOS:
>
> Ack, sorry, I meant 128/125. If you temper out 128/125, that should
> bring you to 12-equal, right? And so does tempering out 9'/9. The two
> must be offset from one another by some comma that's already being
> tempered in moantone.

That's the 128 * 9'/1125 comma mentioned above.

Not p0rn groove?

(sorry ;-) )

Chris

On Thu, Apr 14, 2011 at 10:29 AM, Kalle Aho <kalleahomappi.helsinki.fi> wrote:

In tuningyahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

The two must be offset from one another by some comma that's already
being tempered in moantone.

Moantone, the best temperament for expressing lamentation, pain
and grief.

Kalle

>

Yeah, that too! :)

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> Not p0rn groove?
>
> (sorry ;-) )
>
> Chris
>
> On Thu, Apr 14, 2011 at 10:29 AM, Kalle Aho <kalleahomappi.helsinki.fi> wrote:
>
>
>
> In tuningyahoogroups.com, Mike Battaglia <battaglia01@> wrote:
>
> The two must be offset from one another by some comma that's already
> being tempered in moantone.
>
> Moantone, the best temperament for expressing lamentation, pain
> and grief.
>
> Kalle
>
> >
>