Yahoo Tuning Groups Ultimate Backup tuning Circulating temperaments

I was talking to Chris Vaisvil, and he said that although he finds the
theory hard to follow sometimes, if we just send him Scala files he'll
play in any tuning we want. I think that's a good idea, and for
reasons posted on XA I think a great way to start this would be to
send him circulating versions of chromatic-sized MOS's for The Best
Temperaments Ever. He said that if we do that, and just tell him the
fingerings for the albitonic scales within them, he'll play it.

The obvious question is: how the heck do we generate circulating
temperaments? One way to do it is to view a circulating temperament as
a combination of two simpler regular temperaments. For instance, we
might consider Werckmeister to be an amalgamation of meantone and
superpyth. We can perhaps do analogous things by looking at pairs like
porcupine/nusecond[15], magic/mohajira[10], machine/slendric[11],
squares/sensi[11], orwell/huxley[13], orgone/hanson[15],
glacial/tetracot[13], etc.

I'm not entirely sure if all of the above are ideal (I'm sure they're
not), but it gets across the general idea. The question of how to
optimize for these is another matter, though, and now that it's clear
that essentially tempered chords are here to stay I'm not sure that
shooting for an optimum amount of 4:5:6's or whatever is the way to
go. Any ideas?

Of course, we could always just not do this, and instead hand him
chromatic MOS's, but I think this might lead to some better, and more
interesting results. It would be great to have a page of these on the
wiki, with accompanying fingerings for the albitonic scale, and tell
people to just fire away before they've learned the theory at all;
this will capture a lot of the "market" that tends to go right for the
low-numbered EDOs for ease of conceptualization.

-Mike

🔗cityoftheasleep <igliashon@...>

I was thinking about circulating temperaments the other day, and I think they are a great concept that I'll probably never use, but find interesting nonetheless. One way to approach them would be to take a temperament where two consonances are equated, like in (say) Godzilla, the 49/48 and 81/80 temperament. Here the generator is both a 7/6 and an 8/7, and it's not very good at being either; but suppose we warped the generator chain a bit so that in some places, it would be closer to 7/6 and in others it'd be closer to 8/7. If we did it right, we could probably squeeze some rather accurate-sounding otonal and utonal tetrads out of it. Or at least improve on it somewhat. I mean, we could probably think of a million temperaments that could be improved in circulating versions. I remember a circulating 12-note temperament I stumbled across many moons ago where all the major 3rds were near-Just 5/4, 9/7, or 14/11, and all the minor 3rds 6/5, 7/6, or 13/11, and yet all the fifths were close enough to perfect that it gave the whole tuning very strong consonance and immense versatility across keys. Granted, with categorical perception in full swing, it didn't sound even a little bit xenharmonic to me, but it did sound cooler than 12-TET. When I think about it, it was basically playing on how 12-TET in the 11-limit could be said to temper out 36/35 and 56/55 (on top of 81/80 and 128/125 or whatever).

I know George Secor came up with a great 17-tone WT, and there're probably really awesome 19-, 22-, and heck, maybe even 15- and 16-note WT's just waiting to be discovered. Hell, I bet there's even a great 14-note WT that might open up the 14-note world to a lot of people who find 14-ET too discordant.

And here's why I'm suddenly interested in this: much of the divide in this group (and the community at large) centers around disagreements about the relative importance of concordance vs. simplicity. This keeps me from using Sensi[46] as much as it keeps Gene from using Mavila[7]. But when you think about it, meantone and 12-TET, despite being clearly different in concordance, are interchangeable enough in practice that what works musically in one also works more or less as well in the other (unless you're exploiting 12-TET's unique enharmonic equivalences or meantone's lack thereof). All the theory developed in the meantone era (and the Pythagorean era before it) didn't get thrown out when everyone switched to 12-TET. Some people prefer the sound of meantone, some prefer to work in 12-TET, but there's enough commonalities that people can speak the same language about both tunings, and share insights, and develop compositional techniques that work across tunings.

So where I'm at is I think it would be great if we could find a few tunings that on the one hand fit a simple ET and sounds at least alright there, but on the other can be made super-concordant as an unequal temperament or a circulating temperament. I guess the two darlings of the community are Mavila and Porcupine, and maybe we can add Miracle to the list (which, I'll note, could plausibly be manifested in 21-ET for those that don't care about the loss in accuracy). I'm still waiting for the Semaphore wave to hit, but anyway...anybody up to a circulating Mavila[16] temperament? Is there *anything* we can do to Mavila to make it more concordant?

-Igs

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> I was talking to Chris Vaisvil, and he said that although he finds the
> theory hard to follow sometimes, if we just send him Scala files he'll
> play in any tuning we want. I think that's a good idea, and for
> reasons posted on XA I think a great way to start this would be to
> send him circulating versions of chromatic-sized MOS's for The Best
> Temperaments Ever. He said that if we do that, and just tell him the
> fingerings for the albitonic scales within them, he'll play it.
>
> The obvious question is: how the heck do we generate circulating
> temperaments? One way to do it is to view a circulating temperament as
> a combination of two simpler regular temperaments. For instance, we
> might consider Werckmeister to be an amalgamation of meantone and
> superpyth. We can perhaps do analogous things by looking at pairs like
> porcupine/nusecond[15], magic/mohajira[10], machine/slendric[11],
> squares/sensi[11], orwell/huxley[13], orgone/hanson[15],
> glacial/tetracot[13], etc.
>
> I'm not entirely sure if all of the above are ideal (I'm sure they're
> not), but it gets across the general idea. The question of how to
> optimize for these is another matter, though, and now that it's clear
> that essentially tempered chords are here to stay I'm not sure that
> shooting for an optimum amount of 4:5:6's or whatever is the way to
> go. Any ideas?
>
> Of course, we could always just not do this, and instead hand him
> chromatic MOS's, but I think this might lead to some better, and more
> interesting results. It would be great to have a page of these on the
> wiki, with accompanying fingerings for the albitonic scale, and tell
> people to just fire away before they've learned the theory at all;
> this will capture a lot of the "market" that tends to go right for the
> low-numbered EDOs for ease of conceptualization.
>
> -Mike
>

🔗genewardsmith <genewardsmith@...>

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

> The obvious question is: how the heck do we generate circulating
> temperaments? One way to do it is to view a circulating temperament as
> a combination of two simpler regular temperaments. For instance, we
> might consider Werckmeister to be an amalgamation of meantone and
> superpyth. We can perhaps do analogous things by looking at pairs like
> porcupine/nusecond[15], magic/mohajira[10], machine/slendric[11],
> squares/sensi[11], orwell/huxley[13], orgone/hanson[15],
> glacial/tetracot[13], etc.

I just posted about this on XA, but here is better for future reference. I tried this idea with porcupine/nusecond[15], and though I gave nusecond only seven generators and porcupine eight, nusecond ending up kicking porcupine's ass. Chris is welcome to give it a test spin.

! nufip15.scl
!
A 15-note lesfip mutant nusecond, target 11-limit diamond, error limit 12 cents
15
!
44.85398
156.27185
200.77030
312.16415
387.79495
466.95289
544.35733
621.76177
700.91971
776.55051
887.94437
932.44281
1043.86068
1088.71467
1200.00000

🔗Chris Vaisvil <chrisvaisvil@...>

🔗Keenan Pepper <keenanpepper@...>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> I just posted about this on XA, but here is better for future reference. I tried this idea with porcupine/nusecond[15], and though I gave nusecond only seven generators and porcupine eight, nusecond ending up kicking porcupine's ass. Chris is welcome to give it a test spin.
>
> ! nufip15.scl
> !
> A 15-note lesfip mutant nusecond, target 11-limit diamond, error limit 12 cents
> 15
> !
> 44.85398
> 156.27185
> 200.77030
> 312.16415
> 387.79495
> 466.95289
> 544.35733
> 621.76177
> 700.91971
> 776.55051
> 887.94437
> 932.44281
> 1043.86068
> 1088.71467
> 1200.00000

I don't like this resulting scale at all. You must be doing something with your target intervals that's "weird" to me.

BTW, I'm thinking about a more generic way of doing this where the meantone/superpyth split, or porcupine/nusecond split, would hopefully just pop out rather than being put in by hand.

Keenan

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

On Wed, Jan 11, 2012 at 6:00 AM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > The obvious question is: how the heck do we generate circulating
> > temperaments? One way to do it is to view a circulating temperament as
> > a combination of two simpler regular temperaments. For instance, we
> > might consider Werckmeister to be an amalgamation of meantone and
> > superpyth. We can perhaps do analogous things by looking at pairs like
> > porcupine/nusecond[15], magic/mohajira[10], machine/slendric[11],
> > squares/sensi[11], orwell/huxley[13], orgone/hanson[15],
> > glacial/tetracot[13], etc.
>
> I just posted about this on XA, but here is better for future reference. I tried this idea with porcupine/nusecond[15], and though I gave nusecond only seven generators and porcupine eight, nusecond ending up kicking porcupine's ass. Chris is welcome to give it a test spin.

It's definitely an interesting scale; it has relatively pure 4:5:6's
on 1/1, 5/4, 11/8, and 3/2, and relatively pure 10:12:15's on 1/1,
5/4, 5/3, and 9/5. I'm not sure what to make of it, or how to evaluate
that it's more nusecond instead of porcupine, etc.

This originally started because I was hoping to get a circulating
temperament built around porcupine[15], so that in "most keys" you'd
get good porcupine harmony, but then there'd be a string of wolf
generators. And I thought that we could make use of those "wolf"
generators by having them correspond to some other temperament, like
nusecond. But it looks like nusecond's won the war here.

How about this: if you could design the best porcupine[15] circulating
temperament possible, how would you do it? Let's assume our mindset
now is analogous to the one that led to the development of
Werckmeister: we don't want the wanton harmonic debauchery of 15-EDO,
but we want something in which people can play in "all keys" of
porcupine[15] for ease of conceptualization. Well-temperaments are the
answer to this conundrum - (and I bet if we do a good job with a whole
bunch of these then maybe people will start getting their guitars
retuned with curvy frets to well temperaments too).

See, circulating temperaments can save microtonal music!

-Mike

🔗genewardsmith <genewardsmith@...>

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

> It's definitely an interesting scale; it has relatively pure 4:5:6's
> on 1/1, 5/4, 11/8, and 3/2, and relatively pure 10:12:15's on 1/1,
> 5/4, 5/3, and 9/5. I'm not sure what to make of it, or how to evaluate
> that it's more nusecond instead of porcupine, etc.

By the way, despite the fact that it's strictly proper and constant structure, Keenan hates this scale, claiming it is "weird". That may mean, of course, it has xenharmonic potential; I'll see what Chris makes of it. Scala tells me it's best minor thirds form a closed circle, despite the fact that four of those minor thirds are approximate 11/9s, and the rest approximate 6/5s. That actually sounds like it might be neat, and it's the sort of thing you guys were discussing.

> How about this: if you could design the best porcupine[15] circulating
> temperament possible, how would you do it?

I'll think about it. Maybe someone else might give it a try also?

🔗Mike Battaglia <battaglia01@...>

On Jan 11, 2012, at 4:43 PM, genewardsmith <genewardsmith@...>
wrote:

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

By the way, despite the fact that it's strictly proper and constant
structure, Keenan hates this scale, claiming it is "weird". That may mean,
of course, it has xenharmonic potential; I'll see what Chris makes of it.
Scala tells me it's best minor thirds form a closed circle, despite the
fact that four of those minor thirds are approximate 11/9s, and the rest
approximate 6/5s. That actually sounds like it might be neat, and it's the
sort of thing you guys were discussing.

It is neat; I'm sure Chris will come up with something in it. It isn't
objectively bad, but yielded a different result than I was expecting.

> How about this: if you could design the best porcupine[15] circulating
> temperament possible, how would you do it?

I'll think about it. Maybe someone else might give it a try also?

It would help me to do so if I could understand the wiki article on
lesfips.

-Mike

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

On Jan 11, 2012, at 5:11 PM, "genewardsmith" <genewardsmith@...>
wrote:

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Jan 11, 2012, at 4:43 PM, genewardsmith <genewardsmith@...>
> wrote:

> It is neat; I'm sure Chris will come up with something in it. It isn't
> objectively bad, but yielded a different result than I was expecting.

It's basically got three sizes of steps, and could be regularized with
little difficulty. I don't know if that would make Keenan like it better.

I can't speak for Keenan, but something with 8:10:11:12 chords and
10:11:12:15 chords, optimized around the shell of a porcupine structure,
would make me a happy man. Did you see the part where I mentioned that
guitars can be retuned to well temperaments and that this will save music?
Or at least it's a compromise between complexity and error that I can agree
on.

> It would help me to do so if I could understand the wiki article on
> lesfips.

I'll take a look at improving it, but you surprised me by asking for
something more formal.

In general I prefer going as far as I can with the formal stuff and asking
questions, which makes it easier to read more formal stuff, etc.

-Mike

🔗Chris Vaisvil <chrisvaisvil@...>

This seems to be very close to the porcupine 15 I used.

Sounds good.

Chris

On Wed, Jan 11, 2012 at 6:00 AM, genewardsmith
<genewardsmith@sbcglobal.net>wrote:

> **
>
>
>
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > The obvious question is: how the heck do we generate circulating
> > temperaments? One way to do it is to view a circulating temperament as
> > a combination of two simpler regular temperaments. For instance, we
> > might consider Werckmeister to be an amalgamation of meantone and
> > superpyth. We can perhaps do analogous things by looking at pairs like
> > porcupine/nusecond[15], magic/mohajira[10], machine/slendric[11],
> > squares/sensi[11], orwell/huxley[13], orgone/hanson[15],
> > glacial/tetracot[13], etc.
>
> I just posted about this on XA, but here is better for future reference. I
> tried this idea with porcupine/nusecond[15], and though I gave nusecond
> only seven generators and porcupine eight, nusecond ending up kicking
> porcupine's ass. Chris is welcome to give it a test spin.
>
> ! nufip15.scl
> !
> A 15-note lesfip mutant nusecond, target 11-limit diamond, error limit 12
> cents
> 15
> !
> 44.85398
> 156.27185
> 200.77030
> 312.16415
> 387.79495
> 466.95289
> 544.35733
> 621.76177
> 700.91971
> 776.55051
> 887.94437
> 932.44281
> 1043.86068
> 1088.71467
> 1200.00000
>
>
>

🔗Mike Battaglia <battaglia01@...>

🔗Herman Miller <hmiller@...>

On 1/10/2012 11:18 PM, Mike Battaglia wrote:
> I was talking to Chris Vaisvil, and he said that although he finds the
> theory hard to follow sometimes, if we just send him Scala files he'll
> play in any tuning we want. I think that's a good idea, and for
> reasons posted on XA I think a great way to start this would be to
> send him circulating versions of chromatic-sized MOS's for The Best
> Temperaments Ever. He said that if we do that, and just tell him the
> fingerings for the albitonic scales within them, he'll play it.
>
> The obvious question is: how the heck do we generate circulating
> temperaments? One way to do it is to view a circulating temperament as
> a combination of two simpler regular temperaments. For instance, we
> might consider Werckmeister to be an amalgamation of meantone and
> superpyth. We can perhaps do analogous things by looking at pairs like
> porcupine/nusecond[15], magic/mohajira[10], machine/slendric[11],
> squares/sensi[11], orwell/huxley[13], orgone/hanson[15],
> glacial/tetracot[13], etc.

Well, if you think about historical circulating or "well-tempered" tunings, many of them are meantone-based. I don't think superpyth really enters into the equation, except perhaps for some "temperament ordinaire" type tunings that have one or more sharp fifths (and not likely even in those cases). Many of those meantone-based tunings have only two distinct sizes of fifths (Werckmeister nearly but not exactly so): tempered and just, but you could distribute the variation more evenly. Similarly, you could imagine versions of augmented, diminished, injera, and pajara as 12-note circulating temperaments. One of my well-temperaments from back when I was experimenting with those things was based on diminished temperament. Basically you'll start out with one interval per period that's a different size from your generator, take the difference and distribute it over one or more adjacent generators.

🔗Chris Vaisvil <chrisvaisvil@...>

Here you go

http://chrisvaisvil.com/?p=2020

Truth in advertizing - this is played back actual speed - I change about a
dozen pitches / lengths / timing / velocities. Deleted about a dozen more
fat finger flubs.

Chris

On Wed, Jan 11, 2012 at 8:45 PM, Chris Vaisvil <chrisvaisvil@...>wrote:

> I don't know - I'd have to run the same piece through both tunings to hear
> them side by side.
>
> I think I get immersed when I play and don't hear what I'm doing compared
> to another tuning per se.
>
> Got this one coming up in a few minutes.
>
> Chris
>
>
> On Wed, Jan 11, 2012 at 8:33 PM, Mike Battaglia <battaglia01@...>wrote:
>
>> **
>>
>>
>> On Jan 11, 2012, at 8:04 PM, Chris Vaisvil <chrisvaisvil@...>
>> wrote:
>>
>>
>>
>> This seems to be very close to the porcupine 15 I used.
>>
>> Sounds good.
>>
>> Chris
>>
>>
>> Lol, I love it. Perhaps categorical perception has struck again.
>>
>> Chris, how much does 15-EDO sound like these scales?
>>
>>
>>
>>
>
>