On Mon, Feb 13, 2012 at 10:28 PM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > A temperament is a mathematical object. How you'd like to use that
> > mathematical object for musical purposes is up to you. To say that
> > temperaments with really high error "don't exist" is wrong. If you
> > want to say that they don't accurately model perception or something,
> > just say that.
>
> I think defining temperaments as mathematical objects is stupid. As mappings
or homomorphisms, sure, they're pure math. But "temperament" implies music,
music implies perception, perception implies reality, and in reality, things
either exist or they don't.

OK, so you below agreed that we don't know what's going on, that our
paradigm is still embryonic and/or "broken," and that you don't have
any scientific answer, and that you want to start finding one. Woo
hoo. So I'll move on from this and get into that, because this is
like, new research on the list, for once.

What I suggest is to think hard about how to handle the phrase
"[perceptual] things either exist or they don't" in this field. While
this statement is very obviously true, I've found that it can be a
very limiting factor in studying this stuff. This is because we're
dealing with something as tenuous as the perception of a single person
- actually, we're dealing with the perceptions of large groups of
people. So while it's obvious that things either exist or they don't,
it's very difficult - actually in some cases, I might believe it's
mathematically impossible, for the same sorts of reasons that Turing's
famous "halting problem" is impossible - to know when they do or
don't.

What I've found to be a freeing paradigm is to think instead in terms
of the -probability- that something will exist. We need not talk about
the actual existence of things now, but the likelihood that they
-will- exist when performed. This allows us to completely sidestep all
of the above problems. Furthermore, once you start thinking entirely
in terms of probabilities, you allow yourself to plug into what is
probably the coolest branch of mathematics I know of, and that's
information theory. In this field, "information" is defined as the
outcome of a random variable. Thinking in these terms allows us to
stop worrying about what's being transmitted through these discrete
random variables - what the "meaning" of the information is - and
allows us to start thinking about things like how much information, of
whatever "meaning," is transmitted at all (the Shannon entropy of the
signal), how "clear" the channel is vs how noisy (the mutual
information of the channel), and how clear the channel COULD BE if you
carefully custom-tailor the information you send to avoid "noise" (the
channel capacity), how difficult it is to "guess" at the information
in a noisy channel (the Renyi entropy) and so on.

The above isn't even a fraction of the useful concepts floating around
this field, which was initially designed to handle things like
electrical communication channels despite that the engineers working
on this stuff will ever know what information is being transmitted. In
that case, the quantum leap in thought was to not worrying about what
actual information ("meaning") was being transmitted, but to think
about the overall characteristics of the signal and the channels for
which this meaning is transmitted at all. I think the same leap
applies here, and even though this paradigm isn't going to give you
the hard and fast answer you may be looking for, it's powerful enough
to make a lot of good, real progress with minimal assumptions, which
is good. We can model the "clarity" of scales as the mutual
information of an information channel, the "clarity" of a ratio as a
type of Shannon entropy, the "intelligibility" of a category as a type
of min-entropy, and a ton of other stuff.

I can't say I understand all of the implications of the above paradigm
- I'm still looking for the single unifying theme that ties it al
together. All I can say is it's worth not adopting a philosophy that
rules these sorts of ideas out. (Plus, information theory is easier to
learn and more awesome than exterior algebra anyway.)

> > Part of the problem is that you don't seem to be acknowledging that a
> > "temperament" doesn't imply the POTE version or even a fixed-pitch
> > example at all,
>
> Not true. I suggest that for some temperaments, there are no tunings that will
allow the temperament to be perceived, and that we can possibly deduce what
these are based on an understanding of the limits of interval recognizability.

The only ones I can think of involve tempering out actual consonances
in the chord that's being played. So tempering out 6/5, for instance -
unless you intone one ratio two ways at the same time. Anything else I
can think of some dumb adaptive scheme that would trivially satisfy
that it has some dumb musical use, even though it's dumb. Even dumb
things like tempering out 9/8 have some dumb use.

But since you, below, said you don't mind including categorical
perception in this - I assure you that it's almost impossible to find
anything that's truly impossible to be perceived. Categorical
perception is nuts, especially for someone like me who has AP and has
categorized the pitch spectrum itself. I hear 12-EDO in everything.

> And I'm fine with that. I'd love to have a more nuanced view of temperament
where we allow that it's not the mathematical structure alone that defines the
temperament, but also the effects of musical context on intervallic perception.
As an aside, you're not correct that the hedgehog[8] example demonstrates 9/8
vanishing. We'd have to hear 500 cents as a 3/2 for that. Hearing 600 cents as a
3/2 might be 15/14 vanishing or something, depending on what you want to say 600
cents is.

If we hear 600 cents as 3/2, then 2*600 is 1200 = 2/1 = 9/4 = 9/8 vanishes.

> As am I! Just because I don't believe something exists now, doesn't mean I'm
going to maintain that belief dogmatically when I suddenly find myself staring
it in the face.

Ok, but my point is that I don't think it's a good idea to assume that
things don't exist right now, in 2012.

> > We're talking about probabilities. If something has an improbable
> > chance of happening, then it has a chance of happening.
>
> Sure, anything's possible! There's a non-zero probability that I'll turn into
a bowl of petunias in 30 seconds, or that I'll suddenly gain the ability to fly,
or that the TARDIS will materialize in my bedroom.

Yeah, that seems right to me. Possible, but not likely.

> > They're just ideals you want to work towards. The TE tunings for each
> > will be different.
>
> How's that relevant? Temperaments aren't tied to specific tunings, remember?

My point is that different mappings imply different ideals for the
same scale, and this is partly reflected in that they have different
TE tunings.

> > They're different things you can do with each scale.
>
> Say you're in 8-ED2. How are they different things you can do with 8-ED2?

Consider 6-EDO in the 2.9 subgroup. Now consider it in the 2.5.7.9.11
subgroup. Tune the latter so that the 11/4 is pure. How are these
different things you can do with 6-EDO?

> > Well, 750 cents "sounds kinda like 3/2" to me, and 450 cents "sounds
> > kinda like 5/4," so I'm happy.
>
> That's not father temperament. 750 cents has to sound kinda like 3/2 and kinda
like 8/5. I don't think it sounds like either, I think it sounds like a flat
11/7.

To me it sort of sounds like all three of those things, assuming I
ignore everything I've learned about music in the past year and
equivocate between ratios and categories.

450 cents has to sound like 5/4 and 4/3, but I don't think it sounds
like either, I think it sounds like a sharp 9/7.

To me it sort of sounds like all three of those things, assuming I
ignore everything I've learned about music in the past year and
equivocate between ratios and categories.

> More importantly, 0-450-750 has to sound like a 4:5:6 and a 15:20:24 and a
9:12:16 and a 16:20:25. I don't think it sounds like any of those, I think it
sounds like an out-of-tune 7:9:11.

It's vaguely recognizable as 4:5:6, I'd say, assuming I ignore
everything I've learned about music in the past year and equivocate
between ratios and categories.

> It's possible that you could fool me into thinking those intervals sound like
out-of-tune 5-limit intervals, and if you could, I'd say "great job, you've
shown me how to 'activate' my father temperament perception. Okay, how did you
do it? Great, now we've learned something! Now let's apply this new knowledge
and beef up our theories about music cognition."

You should join XA chat, where we've been talking about this stuff for
months now. (I wish we were documenting it). For starters, I'd say:
play slendroid in 16-EDO, 3 3 1 3 3 3. Just play the first 5 notes
over and over. That makes the 450 cents to me sound like a 5/4, except
I'm actually wantonly equivocating it with "major third" here because
of your totally subjective definition and now I need to go take a
shower to cleanse myself.

> > You are a special case of human being. Everyone alive is unique in
> > their own special way. We all have our own unique fingerprints, DNA,
> > and way of using temperament mappings. What's sensible for you might
> > not be sensible for someone who's using it all differently.
>
> And yet, we are all enough alike that the field of biology is possible, that
the field of medicine is possible, that the field of psychology is possible,
that the field of psychoacoustics is possible...my individual idiosyncrasies are
not so great that I can't make any generalizations from my experience to the
experience of others.

OK, but we're all using temperaments differently and so your
conclusions will only extrapolate to your own personal interpretation.

> > I'm saying that that notion, by itself, isn't something I'd be arguing
> > with. I do think that the whole "x is heard as y" paradigm itself,
> > where we pretend subjective things are objective, is totally crude and
> > coarse and a loaded way of putting it, but if that's all you were
> > saying, I wouldn't be pedantic about it. But, we're talking about
> > dicot.
>
> Then stop being pedantic about it!

I'm not. We're talking about dicot.

> > Musically evoked means what, someone hears it and says "that sounds
> > like 5/4?" I'm pretty sure I could play some stuff in 12-EDO that
> > would leave most people unable to tell me the chord quality of some
> > arbitrary chord in a trippy sequence of chords, so that most
> > effectively wouldn't be able to tell me if a chord was major or minor
> > or "sounds like 4:5:6" or "sounds like 10:12:15" or whatever. Then
> > they won't be able to actively able to compare with some prior,
> > remembered stimulus, thus failing by this definition.
>
> Right. And in doing so, you would have "broken" their sense of temperament,
they wouldn't be perceiving any image of Q in Z^n, so the mapping would break
and the temperament would cease to exist in that moment.

My mom can't figure out what the hell's going on when I play music at
all, but she likes it; this is no different from that.

> > > > What does "objectively absurd" mean?
> > >
> > > Let's say "incompatible with known mechanisms of human music cognition."
> >
> > Can you give an example of such a mechanism and a limitation it would
provide?
>
> You know more about the mechanisms of human music cognition than I do...why
don't you tell me? Maybe I have a totally warped view of how music cognition
works, I never studied this stuff, everything I know I got from you, Paul, and
Carl!

What I know is that this whole notion of "perceiving a ratio as
______" is actually not related to psychoacoustics or music cognition
at all, but just normal, regular, boring old cognition. If I'm exposed
to a stimulus long enough, I'll remember it and be able to gauge how
much other things are the same and different from it. If an interval
has certain defining features which are associated with it being tuned
a certain way, like the usual small-integer ratio features, I'll tend
to remember those things about it.

It doesn't seem to me like you're trying to put a cap on the bounds of
music cognition but on -cognition-. You're now talking about totally
subjective measures of when an interval "resembles" another. In the
sense you're talking now, I don't think that these basic entities
which are being resembled have anything to do with small-integer
ratios. And lastly, as far as resemblances are concerned, what I know
is that the mind is a really, really weird place.

> > It's ridiculous! First off, again, temperaments imply NO TUNING AT
> > ALL. You can tune them however. You don't even need to use fixed pitch
> > instruments. We haven't even finished inventing all of the clever ways
> > to use mappings. But we're going to use the word "existence" to
> > describe an abstract regular temperament which doesn't seem musically
> > useful under all of the circumstances that we've thought of so far?
> > That seems like this crazy statement to make.
>
> Tell me, Mike...does a song exist before it's written? Does a picture exist
before it's painted?

No, but a temperament exists before you write music in it, because
that's how Gene defined everything, and I happen to like it.

> Again, I think that's a short-sighted and misleading definition of
temperaments. The mathematical objects can be defined without any identification
with musical intervals, and I would argue that they are only temperaments if
they can be identified with musical intervals. That means that you need to be
able to do more than mathematically define a temperament to assert its
reality--you have to be able to connect it to music in some meaningful way.

The mathematical objects are always defined with respect to musical
intervals; that's what the Z^n business is all about. Temperaments are
ideals for how to to intone Z^n.

> Yep. Hypothesize, test, conclude, modify. You just saw it happen. I posited
that dicot temperament doesn't exist, you showed me a case where it does,
thereby falsifying my hypothesis, and my hypothesis was rejected.

I'm not going to be able to falsify all of your hypotheses just
because I'm not infinitely creative. This seems obvious to me and I
don't see why you or anyone else would pretend that I'm the arbiter of
good or bad temperaments. You should have more of a healthy self-doubt
about writing stuff off.

> > You keep talking about how you don't want to assume that these crazy
> > novel musical circumstances could exist unless you have evidence for
> > them. Well, is the above example not sufficient evidence for the
> > existence of musical circumstances that you of I or nobody is
> > currently thinking of? I'm sure if I'm clever enough I could even
> > figure out a way to make the temperament eliminating 9/8 work. Would
> > that convince you that it's bad to write things off at this point in
> > time?
>
> No. Why should it?

Because you missed something once and you might miss something else?

> > Why is it not better to admit that we haven't thought of all the
> > clever and offbeat ways we could use these temperaments, rather than
> > assuming we currently have the capability to declare various
> > mathematical objects as being musically useless?
>
> Because *everything* is useless until a use is found for it!

I disagree.

> Well, there we have it--context. You determine whether it's dicot vs. mohajira
according to the nearest JI chord that a given tempered chord sounds like. So if
I'm playing around in 24-ED2, playing a bunch of
0-700-1200-1900-2400-2600-2750-3100 chords, you're going to go "oh, dicot,
totally"; but if I should happen to drop in a 0-700-1200-1400-1750 chord, you'll
go "oh, that's a 4:6:8:9:11 chord, this is mohajira". It's only dicot so long as
the chords are sounding to you like what the mapping says. As soon as you hear a
chord that doesn't fit the mapping, your perception switches over to a mapping
that fits the chord.

Under your scheme, which I hate. I think that dicot is something more
abstract than any mode of perception and refers to a certain tuning
ideal for a scalar structure.

> ...and play a bunch of 0-542.971-697.189 triads, you'd have to say "that's
mohajira, not dicot." Right?

I'd probably say that just for the sake of communication, sure. Or an
11-limit higher extension of dicot.

> This is a big problem in our paradigm right now, in that we really haven't
pinned down what it means to "use" a temperament. It's not enough to just load
up the POTE or TOP or TE scala file of some scale derived from the temperament.
You have to do specific things with the music to "activate" perception of the
mapping--you have to create the image of Q with Z^n--or you're just using Z^n,
no mapping is taking place, and no temperament is being invoked.

Look, it's not a big problem for me, because I went through this
little crisis already. Yes, the paradigm is incomplete. Temperaments
aren't everything they should be. You're right, we can't go claim how
great and complete and scientific and perfect and finished the theory
is. But, they're still useful as conceptual tools, and I'm happy to
know exactly what their limitations are and use the theory anyway.

> > Or don't use a fixed pitch tuning at all. The whole point of a
> > "mapping," which is also called an "abstract regular temperament," is
> > that it's larger than any single tuning.
>
> And yet, a temperament is only usable in the form of some tuning. Pretending
we can leave tuning out of it altogether is a grievous error.

Then it makes even less sense to invalidate a temperament before it's
been given a tuning.

-Mike