Yahoo Tuning Groups Ultimate Backup tuning In Defense of Inequality (was: Tuning psychosis...& Knowsur's awesome new album)

This is in reply to message #23077 on MMM:
--- In MakeMicroMusic@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Tue, Sep 14, 2010 at 5:40 PM, gdsecor <gdsecor@...> wrote:
> >
> > I would have to call that a half-truth. It's not *12* that we want to get away from, but rather *12-equal*. Have we forgotten that there are plenty of *12-unequal* alternatives, many of which have been popular longer than 12-equal?
> >
> > When I read the following, I couldn't help noticing that it's all about alternatives to *12*, without any mention of alternatives to *equal*.
>
> Haha. Well, I admit that I like 12-equal. And I like equal
> temperaments in general. I'm actually pretty surprised that you're
> such a big fan of unequal ones, since I know you have AP, and as
> someone else with AP, the whole concept irritates me.

I don't understand why you would say that. The only reason I can think of is that pitches in 12-unequal differ from 12-equal. However, the pitches in 17-equal, 19-equal, 31-equal, etc. differ from 12-equal by even greater amounts, so you should then be even more irritated with non-12-equal than 12-unequal. In order to cope, we must think of the pitch labels (F, C, G, etc.) as applying to a range of pitches (or pitch "buckets") rather than single (fixed) frequencies.

But if that is not the issue, then what is?

> Not that I can't
> get used to them, but I prefer being able to create any sonority over
> any chroma that I wish.

But in an ET you can't create *any sonority* over any chroma you wish. You're stuck with the limited number of sonorities available in the ET. In an un-ET there are many more sonorities from which to choose, and you choose them by your choice of tonic key.

There is a term, "mood" (coined by Ivor Darreg several decades ago), that applies to the differences that can be heard in one tuning vs. another (e.g., 19-ET vs. 12-ET). (I don't know whether that's the best term for it, but it's distinctive and has been used for a good many years for that purpose.) With an ET the mood does not change with transposition, but with an un-ET the mood does change, often dramatically. At first I thought of these different moods within a single tuning as "good" and "bad" keys, but now I regard contrasting moods as a feature that can be exploited for dramatic effect (see an example below).

> This is, admittedly, a part of microtonal
> music I have not explored so much, and perhaps my ideas will change
> when I mess around with them more.

Well, then, mess away! You'll find Scala files for my favorite tried & true unequal tunings here:
/tuning-math/files/secor/scl/
For 12: Secor5_23TX.scl
For 17: Secor17wt.scl
For 19: Secor19wt.scl
For 19 (with 11's added in 3 keys): Secor19p3.scl
For 34: Secor34wt.scl

> > Not only is there 12-unequal, but also 17-unequal, 19-unequal, 29-unequal, and 34-unequal, which are mentioned far less often around here than JI. I'm not talking about 12-, 17-, or 19-tone MOS's of regular temperaments, but rather circulating tempered tunings that are playable in all keys and optimized, i.e., tuned significantly "better" than equal (whatever that means), in a limited number of keys.
>
> Ah yes, limiting the number of keys... :(

That's another half-truth. Allow me to give an example, using the high-contrast Secor5_23TX.scl tuning for 12-unET:

True: In 12-unET you are limited in the number of keys with a mood similar to 12-ET to two (major triads: E and Eb). However, this is good IMO, because I would rather not be stuck with only that one mood. Once I heard how historical meantone triads sounded, I found (and still find) the heavy tempering of the 3rds of 12-ET rather irritating, and the equalness of the tuning affords me no escape.

False: In 12-ET you are limited in the number of keys in which you can have the historical meantone mood, which is zero, whereas in 12-unEQ, there are 6 (major triads: Bb, F, C, G, D, A) in which the major 3rds are tempered less than 8 cents. In 12-ET you are also limited in the number of keys in which you can have a pythagorean or meta-pythagorean mood, again zero! In 12-unEQ, OTOH, there are 4 (major triads: B, F#, C#, G#/Ab).

For an example of dramatic effect, try a V-i (dominant to tonic) progression in the keys of E minor, B minor, or F# minor, where a relatively dissonant (heavily tempered) dominant triad resolves to a much more consonant (lightly tempered) tonic (minor) triad.

Another difference between 12-ET and this particular 12-unET is that the 24 major & minor triads in the former have irrationally related beating, whereas in the latter all have proportional-beating. (As to how audible is the difference is debatable, but there is a difference.)

> > > > At some point in the future I'd like to do an ET survey and write a
> > > > piece in every tuning from 7 to 22 or something, and if I do, I'm not
> > > > going to skip 12, just for symbolic reasons (and also because I think
> > > > there's a lot of xenharmonic material to squeeze out of it too).
> >
> > Yep, I'd say that just about all the xenharmonic material got squeezed out of 12-unequal when it finally succumbed to equalization in the latter half of the 19th century.
>
> Well, don't forget that 12-equal has good approximations to 17/16 and
> 19/16 as well. So chords like E-F#-D-F sound something like 8:9:14:17.
> There are scales that can be constructed with these sonorities, one of
> which is a mode of the Magen Abot scale I posted on tuning a while
> ago.
>
> There's also the fact that a lot of the really, really hip modern
> stuff I listen to, I think, has amazing and beautiful sonorities that
> have emerged from a radically expanded approach to 12-equal and
> diatonic harmony, which I think hasn't fully crossed back over to
> classical music yet. So to take some of these ideas and put them back
> in a classical setting would be xenharmonic in its own right.
>
> For example, this piece: http://www.youtube.com/watch?v=MMINC9EOZME
>
> Start listening at 4:10. At 4:58 onward, I get chills. If this isn't
> truly xenharmonic, it's at least pseudo-xenharmonic :) I haven't
> worked it out yet, but I strongly suspect that what they're doing here
> is treating 12-equal like a tempered CPS, and modulating all over the
> place, but pedaling it over the Db. That is, they try to modulate
> continuously to a mode that shares a common dyad or two, and do it in
> a way that it keeps sounding unresolved and yet harmonic. Then they
> pedal it over the Eb.

Nicely creative and very tasteful. It would be well worth your while to figure out exactly what's going on with the harmony (which can hold its own against the best of 20th-century "classical" music). But in spite of the progressively thicker textures, I have no trouble telling that it's unmistakably within the 12-ET range of mood and not xenharmonic.

> > > > But
> > > > even this is besides the point, which is that even if you really HATE
> > > > 12...
> >
> > (But not as much as I hate EQUAL ...)
> >
> > > > 7-tet is way further out of tune with JI than 12, and on this
> > > > album, it still sounds great.
> >
> > 18:20:22:24:27:30:33
> > or
> > 17:19:21:23:25:28:31
>
> That is an interesting possibility. That would probably sound really good.

The chords would be smoother and more cohesive due to difference-tone stabilization. One place where JI really shines is in approximating EDO's that do not (in turn) approximate low-harmonic-limit JI. You've probably read this already, (and my apologies if so, since I mentioned it recently, and it's also the wrong time of year), but in case not, here's the underlying principle:
/tuning/files/secor/blarney.txt

> > Gentlemen, it's been a pleasure to seize this opportunity to award your discussion a "rave" review. 8>}
>
> Aaaaaaaaaa HA!
>
> By the way, I sent you an offlist about 68-equal a little bit ago...
> did you by chance get it?

I may have, but I'm not sure. I sometimes delete messages without opening them if I'm not able to identify the sender, but I don't remember reading that one. If you still have a copy, please re-send it, and I'll look for it.

--George

George>"My main point in bringing up unequal tunings is not to establish whether
or not they are "better" than equal ones, but rather to draw attention to the
fact that they are a separate category of alternative tunings different from
JI, ET's, and n-dimension regular temperaments). They ought not to be
neglected, because they can deliver a combination of better intonation (over
ET's), more modulation (over JI), and a greater range of mood within a given
number of tones/octave."

Better intonation is a major reason I now gravitate toward un-equal scales
(if not always un-equal tuning with "transposition" possible)...it seems to make
whatever emotion an interval has "shine" through that beating better (to me
beating is equivalent to fog, minor amounts of it makes things fade in an
interesting way, major amounts mean you can't see much anything).

>"and a greater range of mood within a given number of tones/octave"

This (perhaps) sparks another debate. I have no problem with a couple of
different "versions" of a tone (IE a third being either 5/4 or 11/9 depending on
each root tone is used)...to me this change in MOOD (George...if I'm using the
term correctly) actually
A) Seems to make little difference in the greater scheme of things IE a 1 5/4
3/2 chord doesn't sound much different in "color" than a 1 11/9 3/2 one...it
doesn't kill the overall musical meaning/"color".
B) On the flip side, the slight emotional "tint" you hear may be desirable to
some as it indeed "allows a greater range of mood per a given number of tones"

Some people argue whether JI or ETs or regular temperaments are better. I'd
still vouch for a compromise (with lots of added benefits) being what George is
describing. Which, if I have it right, can also be known as "irregular
temperament".

In Defense of Inequality (was: Tuning psychosis...& Knowsur's awesome new album)

🔗gdsecor <gdsecor@...>

🔗gdsecor <gdsecor@...>

🔗Michael <djtrancendance@...>