Yahoo Tuning Groups Ultimate Backup tuning 5L3s in 13-equal is Father[8].

Here's what Graham's temperament finder spits out for 13-equal:

http://x31eq.com/cgi-bin/rt.cgi?ets=13&limit=5
http://x31eq.com/cgi-bin/rt.cgi?ets=13&limit=7
http://x31eq.com/cgi-bin/rt.cgi?ets=13&limit=11

For the 5-limit, the val with the lowest TE error is the one mapping
5/4 to 369 cents. For the 7-limit on up, it's the one mapping 5/4 to
462 cents. For the 11-limit, 11/8 is mapped to 646 cents, despite that
the nearest direct match to 11/8 in 13-equal is the 554 cent interval.

These vals are in a race with one another. What does this mean? Does
the auditory system actually change depending on what limit you're
working within?

Of course not. For one thing, it means that the patent val, where you
just round each prime off to the nearest match, is often not the one
with the lowest TE error. It also means that none of this has anything
at all to do with music cognition, where you're free to identify as
many mistuned 5/4's in a scale that you want.

We're dealing with ambiguous ETs here, where a few different vals
produce similar TE errors. How do you pick one? Igs suggests a scheme
based effectively on consistency, which Paul suggested, which I
believe was first put forward by Herman. But, now that we have TE
error to go by, why are we supposed to stick with consistency?

It seems that the argument is being made that the algorithm being
presented - which is "round each prime off to the nearest match only
in the albitonic scale you're working with" is superior because it
gets away from math and linear algebra, and supposedly holds some
resemblance to music cognition. The idea that if no better match to
5/4 exists in the specific albitonic scale in which you are working,
then you might as well just give 5/4 to the nearest match, and when
you go to a deep enough MOS that you get a better match, you switch
the mapping. But since when does music cognition work this way? Since
when is there actually "just one 5/4" with your brain switching VF
processing as soon as it gets a better match?

There is no good way to pick names for extremely ambiguous scales like
this, so in lieu of that, we should just let people do what they want.
If they want to call it Father[8], then that's as good a name as any.
But to assert that it's -not- Father because Uncle is a better mapping
isn't necessarily true, nor is it true that Uncle is the only
cognitively relevant mapping for 5L3s in 13-equal.

-Mike

🔗cityoftheasleep <igliashon@...>

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

> There is no good way to pick names for extremely ambiguous scales like
> this, so in lieu of that, we should just let people do what they want.
> If they want to call it Father[8], then that's as good a name as any.

No, it's not. Father refers to a specific temperament. Even if people are hearing this scale occasionally as fitting the mapping, it is misleading to say that it "is" Father temperament when there are other mappings which are relevant (at least some of the time, if you don't buy that they're relevant most of the time). The name "Father" specifies one. single. specific. mapping. in the 5-limit.

> But to assert that it's -not- Father because Uncle is a better mapping
> isn't necessarily true, nor is it true that Uncle is the only
> cognitively relevant mapping for 5L3s in 13-equal.

It doesn't mater whether the Uncle mapping is always better or not, what matters is that sometimes the Uncle mapping fits what we hear, and maybe it does this a majority of the time (I think it does, anyway). Calling it Father means ignoring the ambiguity. Why use any of these names? What use is it to generate terminology if we're just going use it inconsistently? The name "Father" means something. It has a definition. It has a mapping, a comma, a particular TOP and POTE optimization, a particular complexity, a particular badness measure related to the optimal tunings...all of which are different from those of Uncle.

I guess we could just re-define Father temperament as a 2.3.3'.5.5' temperament instead, since the original Father temperament is pretty much confined to 8-EDO and is of questionable relevance. That should satisfy everyone. Then people can go on calling 13-EDO Father and we can address the fact that intervallic perception in this temperament is very ambiguous and flexible and I don't have to fume about how the Father mapping only pertains under certain circumstances.

But I'm not budging on the 11-EDO/Hanson thing. If we can call 11-EDO Hanson, the sky's the limit. We could call 7-EDO Hanson, and why stop there? Why not call 10-EDO Hanson, too? Why not let Mavila absorb Meantone while we're at it?

-Igs

🔗Graham Breed <gbreed@...>

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> What do we call the MOS family then? A few years ago,
> somebody (I think it was you) asked for names of MOS
> families. I suggested 3L 2s be called "father" and 5L 3s
> "unfair father". Those names are still on the xenwiki:
>
> http://xenharmonic.wikispaces.com/MOSNamingScheme
>
> I still stand by this. "Father" is a contraction of
> "fourth-third". Anything with a generator between a fourth
> and a third could be called "father". Yes, it refers to a
> specific 5-limit mapping as well. "Father temperament"
> should refer to that mapping. But note that you're
> confusing the issue by bringing in "father temperament"
> when Mike's quote only mentioned "father" -- no
> "temperament".

I've never accepted that MOS naming scheme. When I originally asked for a naming scheme, I wanted something transparent, systematic, single-denotative, and obvious. I wanted names that would tell you exactly what the scale was, rather than just being a "clever", "fanciful", and/or "free-associated" word whose meaning is not intelligible without access to a glossary of names. The MOS scheme that resulted is full of gobbledegook--"Rice", "Bicycle", "Mosh", "Mish", and the few remaining dwarves, are among the worst offenders.

Instead of that goofy mess, I use a simple notation: #L+#s. The scale being debated in 13-EDO is simply 5L+3s (or 5L3s if you don't like the plus sign; I use the plus sign to remind people that it is in fact an equation, 5L+3s=1200 cents). It is more compact, more single-denotative, more transparent, and more obvious than the whole MOS naming scheme that was proposed back then, and much less confusing. Rather than requiring a glossary and memorization of several nonsensical names, the whole nomenclature can be explained in one sentence, and any MOS of arbitrary size can be referenced consistently using the same format.

I have come to accept that some flights of fancy are necessary for the naming of temperaments, as there are just too many variations and parameters to admit a single concise and transparent taxonomy, but MOS scales are simple and straightforward, and also don't rest on any debatable psychoacoustic or perceptual qualities (the way some temperaments do). There is no need to resort to the same fanciful tactics in naming them. Neither is there any need to borrow temperament names and apply them to MOS families. Furthermore, at least a few people are catching on with the #L#s nomenclature, and with a little more effort on my part, perhaps even more will catch on.

-Igs

🔗Mike Battaglia <battaglia01@...>

On Fri, Jun 3, 2011 at 3:55 AM, cityoftheasleep <igliashon@...> wrote:
>
> > There is no good way to pick names for extremely ambiguous scales like
> > this, so in lieu of that, we should just let people do what they want.
> > If they want to call it Father[8], then that's as good a name as any.
>
> No, it's not. Father refers to a specific temperament. Even if people are hearing this scale occasionally as fitting the mapping, it is misleading to say that it "is" Father temperament when there are other mappings which are relevant (at least some of the time, if you don't buy that they're relevant most of the time). The name "Father" specifies one. single. specific. mapping. in the 5-limit.

I have no idea how you can determine if a listener is "hearing
something as" 5/4 or not. We just had a huge conversation a few weeks
ago about how the entire thing is the Big Masturbatory Theoretical
Question. If someone is hearing something as a "major third," are they
hearing it as 5/4?

If so, then the perception of Father seems to be multistable and
switches between what you'd call Father and Uncle, and perhaps Dicot
and Tetracot sometimes too. (That's why I made this example, in fact.)
Or you could define a new temperament called Funcle or something,
which is a 2.3.3b.5.5c temperament or whatever you want to call it.

But if the two aren't the same thing, then I have no idea how you're
going to make claims about people "hearing things" as a 5/4, based on
a simple but somewhat arbitrary algorithm involving rounding 5/4 off
to its nearest approximation without taking into account the other
notes in the chord. As you can see in my links above, TE error
disagrees with you above the 5-limit and sets the "Father" mapping as
the optimal one. But what does any of this have to do with music
cognition?

> > But to assert that it's -not- Father because Uncle is a better mapping
> > isn't necessarily true, nor is it true that Uncle is the only
> > cognitively relevant mapping for 5L3s in 13-equal.
>
> It doesn't mater whether the Uncle mapping is always better or not, what matters is that sometimes the Uncle mapping fits what we hear, and maybe it does this a majority of the time (I think it does, anyway). Calling it Father means ignoring the ambiguity. Why use any of these names? What use is it to generate terminology if we're just going use it inconsistently? The name "Father" means something. It has a definition. It has a mapping, a comma, a particular TOP and POTE optimization, a particular complexity, a particular badness measure related to the optimal tunings...all of which are different from those of Uncle.

I have no idea what it is we hear, and I don't think you do either.
And I don't want to impose requirements on people about the
terminology they're supposed to use when it's based on unfounded
assumptions involving big masturbatory theoretical questions about
what we hear. That's the last thing this group of noobs needs.

> I guess we could just re-define Father temperament as a 2.3.3'.5.5' temperament instead, since the original Father temperament is pretty much confined to 8-EDO and is of questionable relevance. That should satisfy everyone. Then people can go on calling 13-EDO Father and we can address the fact that intervallic perception in this temperament is very ambiguous and flexible and I don't have to fume about how the Father mapping only pertains under certain circumstances.

This again assumes that the perception of a "major third" is really
the perception of 5/4, and that distortions of categorical interval
perception are actually distortions of f0 estimation. Which is a fine
assumption to make, except the more I go on the less I know how true
it is.

> But I'm not budging on the 11-EDO/Hanson thing. If we can call 11-EDO Hanson, the sky's the limit. We could call 7-EDO Hanson, and why stop there? Why not call 10-EDO Hanson, too? Why not let Mavila absorb Meantone while we're at it?

Welcome to the world of slang. I'm all for it :)

-Mike

🔗Steve Parker <steve@...>

🔗Mike Battaglia <battaglia01@...>

On Tue, Jun 7, 2011 at 7:19 AM, Steve Parker <steve@...> wrote:
>
> but I really don't understand calling anything a 5/4 that is not a five four?
> It seems sensible to have 'Major Third' as a category and say that something maps to or is heard as a major third -
> you could then be more specific as to which major third.
> But a 5/4 is not something to be subjectively, psychologically or philosophically determined - it is a ratio??
> Something 5 cents away from a 5/4 does not sound like a 5/4 to me. It may well sound like a major third but not possibly a 5/4.
> What am I missing? Is it just conventional to describe in this way - if so it seems flawed.
> Steve P.

There are multiple things that go on when you hear a justly tuned interval:

1) The part of your brain that tries to reframe a harmonic series of
sine waves as a single note goes into action and tries to "fuse" the
interval. (Look up the "missing fundamental" phenomenon for more of
this)
2) You won't hear any beating, as the partials will all be in
alignment with one another.
3) You'll hear a sort of "buzzing" effect with the interval, which if
memory serves I believe is more pronounced if the partials of the
timbre are harsher. If you've been following my posts on the subject
then you'll know that I believe that this is abstractly related to
beating.
4) Your brain will try to cognize it according to some kind of learned
interval template, e.g. is this a "major third?" Is it a "minor
third?" How about a "perfect fourth?" etc.

All of these things might go into your conscious recognition of an
interval. So if, to you, a 5/4 means that it's so perfectly tuned that
it incorporates all of the above, then to mistune the interval so as
to destroy one of those effects, it won't really be what you were
thinking of as 5/4 anymore. However, the generally accepted convention
around here is to focus on #1, which is the virtual fundamental that
your brain tries to squeeze out of the interval you're playing.

#1 is much less easily destroyed than #2 or 3. Small degrees of
mistuning can pretty much destroy the buzzing effect, and beating is
pretty easy to create. The virtual fundamental effect, on the other
hand, is pretty resilient and can handle a decent amount of mistuning.
In that sense, a mistuned 5/4 might still be "heard as a 5/4,"
although it won't have all of the aural properties that a justly tuned
5/4 would have.

The million dollar question here is whether #4 is actually a special
case of #1, or if it's something else entirely. That is, if I say I'm
hearing a "major third," does that somehow mean I'm hearing 5/4? I
don't think anyone knows, and is what we're presently discussing.

-Mike

🔗Steve Parker <steve@...>

🔗Mike Battaglia <battaglia01@...>

🔗cityoftheasleep <igliashon@...>

In other words, what Mike is saying is that rational intervals may describe a discrete mathematical or even physical identity, but due to uncertainties in our perceptual faculties, they do not describe our perceptual reality. Under most normal musical circumstances a mildly-tempered "version" of a Just interval will be functionally indistinguishable from the "real thing", and in other circumstances a Just interval may even fail to sound Just.

This is the psychoacoustic validation of the practice of temperament: we can achieve a similar-enough musical effect to JI by using accurate temperaments, and this allows us to "convey" the same "musical information" in a tempered tuning as in a Just one, with the added benefit in the increase in number of available consonances, and the overall simplification of the system of pitch relationships.

However, the exploration of so-called "exotemperaments", wherein the tempering out of large commas over a short space in the circle of generative intervals leads to a massive reduction in accuracy, has brought us to new territory. For example, if you temper a 3/2 heavily so that it "approximates" BOTH a 3/2 and an 8/5, and is tuned so as to minimize the error of approximation to both intervals, you end up with an interval around 750 cents. This is clearly not a 3/2, and is clearly not an 8/5, either, in fact it's just about right in the middle between them. It is an ambiguous interval to Western listeners used to distinguishing between a perfect fifth and a minor sixth. Because the brain "hates" ambiguity, there is a tendency to "force" or "round" the perception this interval into a familiar category, based on other available perceptual cues. Thus we are beginning to discover--and I think we here on this list may be the first to discover this, actually--that perceptual cues unrelated to frequency relationships can bias the perception of ambiguously-tuned intervals, and even some unambiguously-tuned intervals. In other words, we are experiencing phenomena of single intervals--that is, singular frequency relationships--triggering multiple perceptual categorizations depending on musical context.

Prior to these experiences, it was generally assumed that proximity to certain Just identities dictated intervallic categorical perception. That is to say, anything within a certain "field of attraction" of a 5/4 was presumed to sound like a major 3rd, and the identity of "major 3rd" was conflated with "proximity to 5/4". This is now being challenged. The current debate is whether this whole "one interval played, multiple intervals heard" experience means that 1) perceptual cues can bias our "harmonic series detector" allowing us to perceive a "played" 9/7 or 13/10 (or whatever) as a "heard" 5/4 (for example), or that 2) our harmonic series detector is not actually our source of intervallic categorical perception. The latter view holds that a "major 3rd" actually has nothing to do with approximation of a 5/4 ratio, but some other (as yet unknown) factor or set of factors. I think of this latter view as "the null hypothesis coming back for revenge" against the long-held experimental hypothesis that proximity to certain JI identities dictates categorical intervallic perception.

Hope that helps,

-Igliashon

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Jun 7, 2011, at 7:47 AM, Steve Parker <steve@...> wrote:
>
>
>
> Can you explain more how/why no-one knows?
>
> The relationship between cognitive and learned factors is a matter of
> continued investigation.
>
> If I here a 12ET major third I never think it is a 5/4. Above F I call it
> 'piano A'.
> A 5/4 A above F is an entirely different pitch. I never hear these notes as
> the same, nor the interval they make with F as the same.
>
>
> In a certain sense, I do hear them as fitting into the same perceptual
> category.
>
> I'm still missing something. A major third category has wiggle room in it,
> but a 5/4 is a fact, no? Even if I couldn't hear it, if the interval was out
> by half a cent it would no longer be a 5/4.
>
>
> Don't forget that frequency ratios, or even the concept of frequency at all,
> isn't something you can take for granted - the brain has to expend effort to
> divine exactly what these frequencies in the signal are. And whatever
> algorithm the brain uses to put the signal into the "frequency domain"
> doesn't actually put it into the true, classical frequency domain, which
> means infinite precision along the frequency axis and zero time resolution.
> Rather, the brain settles on a mixed time-frequency representation of the
> signal, which has degrees of freedom both in frequency and in time. The
> introduction of time resolution means you have to sacrifice frequency
> resolution, which downstream creates an uncertainty in the perception of
> pitch.
>
> -Mike
>

🔗cityoftheasleep <igliashon@...>

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

> I have no idea how you can determine if a listener is "hearing
> something as" 5/4 or not. We just had a huge conversation a few weeks
> ago about how the entire thing is the Big Masturbatory Theoretical
> Question. If someone is hearing something as a "major third," are they
> hearing it as 5/4?

Let's say you're walking down the street, and some old guy walks past you and you think "hey, that guy looked like my Uncle Steve!" What does that mean? Presumably, it means you saw his appearance, registered that he had many features that were near-identical to your uncle but possessed some that were different. You might have thoughts like "he's like my Uncle Steve, but fatter, with glasses, and he's not bald", meaning that if you could eliminate all the differences, he would look *just like* your uncle, i.e. by visibly indistinguishable from him.

Let's take this into music. Let's say you've been playing around with your monochords and canons for a few years and have discovered the wonderful sonorous sound of 5/4. You know what it sounds like pretty well at this point, maybe you can even sing it perfectly as a harmony with the hum of the refrigerator or something. Then you go visit your Uncle Steve and listen to him play the piano. Something sounds a little familiar to you and you ask him to hold down C and E together for a minute, and you go "AHA! That sounds like a 5/4, except there's a bit of beating going on!" Meaning that if you could eliminate that beating, it would sound *just like* a 5/4. You don't get this when he plays C-F or C-Eb.

This is the only way I know how to meaningfully interpret the idea that we can hear intervals "as" other intervals. Clearly, my understanding of this concept implies that we can't hear one interval as another interval unless we already know what the "heard as" interval sounds like, which (to me) suggests that no one is hearing anything as 5/4 unless they already know what a 5/4 sounds like. Imagine, continuing the above example, you invite Uncle Steve over to hear you play your monochord, and when you play a 5/4, he reacts just like you did to the piano, only instead of saying "that major 3rd sounds like a 5/4", he says, "that 5/4 sounds like a major 3rd, except that it's not beating!"

> If so, then the perception of Father seems to be multistable and
> switches between what you'd call Father and Uncle, and perhaps Dicot
> and Tetracot sometimes too. (That's why I made this example, in fact.)
> Or you could define a new temperament called Funcle or something,
> which is a 2.3.3b.5.5c temperament or whatever you want to call it.

How about "Daddy?" LOL.

> But if the two aren't the same thing, then I have no idea how you're
> going to make claims about people "hearing things" as a 5/4, based on
> a simple but somewhat arbitrary algorithm involving rounding 5/4 off
> to its nearest approximation without taking into account the other
> notes in the chord. As you can see in my links above, TE error
> disagrees with you above the 5-limit and sets the "Father" mapping as
> the optimal one. But what does any of this have to do with music
> cognition?

Well, that's the problem with the regular mapping paradigm. It's not anchored in anything to do with liminal music cognition. The paradigm becomes unstable near certain boundary conditions. It works excellently for high-accuracy temperaments, but when we move toward exotemperaments everything goes up in the air and I wonder what the use is anymore of applying the paradigm. I've said this for a long time, actually. I've objected many times that when it comes to inaccurate temperaments, multiple mappings can be applied simultaneously and there is no clear way to differentiate which mapping is valid.

Take 14-EDO's 5L+4s scale: is it Semaphore? Godzilla? Bug? Beep? Some subgroup with a 15/13 generator that equates two of them with 4/3? Some other subgroup with a 37/32 generator that equates two of them with 43/32? Depending on who you ask, you might get an argument in favor of any of these--or all, or none of these--mappings. It all depends on how you're hearing the intervals, and there is no clear way to determine how any of us are really "hearing" intervals like these. What if you really *can* hear the identities of high harmonics? 14-EDO excellently renders harmonics 25, 29, 37, 39, 41, 43, 55, and 61. We ignore that here because most of us are conservative about what we consider JI, and we don't consider these to be "Just", but that doesn't invalidate them as targets of approximation. These harmonics all have a "sound" to them that we can come to recognize, and there are people like Johnny Reinhard who like to work with these harmonics (though usually in a purely-Rational setting).

The question we always come back to is, "is it possible to hear something like 26:32:39 as an identity, or does it always sound like an 'out-of-tune' 4:5:6". People like Kraig and JR who work with extended JI almost always say "the former is true", whereas people like Paul who have studied psychoacoustics more in-depth tend to say "the latter is true". So for me it's a question of who to trust--the practitioners or the theorists.

> I have no idea what it is we hear, and I don't think you do either.
> And I don't want to impose requirements on people about the
> terminology they're supposed to use when it's based on unfounded
> assumptions involving big masturbatory theoretical questions about
> what we hear. That's the last thing this group of noobs needs.

Which is why I'm now proposing that we drop the temperament-related names all together when we're in boundary territory.

-Igs

🔗Graham Breed <gbreed@...>

"cityoftheasleep" <igliashon@...> wrote:
> --- In tuning@yahoogroups.com, Mike Battaglia
> <battaglia01@...> wrote:
>
> > I have no idea how you can determine if a listener is
> > "hearing something as" 5/4 or not. We just had a huge
> > conversation a few weeks ago about how the entire thing
> > is the Big Masturbatory Theoretical Question. If
> > someone is hearing something as a "major third," are
> > they hearing it as 5/4?
>
> Let's say you're walking down the street, and some old
> guy walks past you and you think "hey, that guy looked
> like my Uncle Steve!" What does that mean? Presumably,
> it means you saw his appearance, registered that he had
> many features that were near-identical to your uncle but
> possessed some that were different. You might have
> thoughts like "he's like my Uncle Steve, but fatter, with
> glasses, and he's not bald", meaning that if you could
> eliminate all the differences, he would look *just like*
> your uncle, i.e. by visibly indistinguishable from him.

But if he said "Ah, Uncle Steve -- he was like a father to
me" the meaning would be entirely different. Mike didn't
say anything about sounding like a 5/4.

> This is the only way I know how to meaningfully interpret
> the idea that we can hear intervals "as" other
> intervals. Clearly, my understanding of this concept
> implies that we can't hear one interval as another
> interval unless we already know what the "heard as"
> interval sounds like, which (to me) suggests that no one
> is hearing anything as 5/4 unless they already know what
> a 5/4 sounds like. Imagine, continuing the above example,
> you invite Uncle Steve over to hear you play your
> monochord, and when you play a 5/4, he reacts just like
> you did to the piano, only instead of saying "that major
> 3rd sounds like a 5/4", he says, "that 5/4 sounds like a
> major 3rd, except that it's not beating!"

You show a certain lack of imagination, then. Another
interpretation is that the interval can stand in for a 5/4
in some context or another. Or that we have an innate
sense of 5/4-ness that this interval evokes. It's possible
to be frightened by something that looks like a snake even
if you don't know what a snake looks like.

Let's say Uncle Steve plays a tune on his monochord that's
imitates the song of a purple breasted reed warbler.
You've never been keen on birds. You wouldn't be able to
identify the song of a common reed warbler, let alone the
purple breasted variety. But it happens that purple
breasted read warblers were common where you grew up. As
Uncle Steve plays his monochord, it takes you back to those
long evenings when you watched the sun set behind the
chemical weapons factory. Clearly, although you can't
identify it, this sounds like a purple breasted reed
warbler to you. But there's no way you'd ever confuse the
sound of a monochord with a bird.

> Well, that's the problem with the regular mapping
> paradigm. It's not anchored in anything to do with
> liminal music cognition. The paradigm becomes unstable
> near certain boundary conditions. It works excellently
> for high-accuracy temperaments, but when we move toward
> exotemperaments everything goes up in the air and I
> wonder what the use is anymore of applying the paradigm.
> I've said this for a long time, actually. I've objected
> many times that when it comes to inaccurate temperaments,
> multiple mappings can be applied simultaneously and there
> is no clear way to differentiate which mapping is valid.

Questioning the validity of exotemperaments is hardly an
original argument. Still, they stumble on because
musicians find them useful things to talk about. You
aren't the first to suggest multiple mapping may apply
simultaneously either. You may be the first to describe
that as an objection.

Graham

🔗Graham Breed <gbreed@...>

"cityoftheasleep" <igliashon@...> wrote:

> Prior to these experiences, it was generally assumed that
> proximity to certain Just identities dictated intervallic
> categorical perception. <snip>

It was? I can't have been paying attention, then. I
thought categorical perception was as a (subconscious)
statistical analysis of the things you were perceiving. So
on hearing an interval of 440 cents, you'd associate it
with a major third, very sharp, because you'd heard a lot
of intervals of around 400 cents (or flatter) before, but
not many between, say, 420 and 480 cents. If you'd been
exposed to quartertones, maybe you'd have heard that 440
cents as a slightly flat example of a quartertone-expanded
major third. If you were familiar with 9-limit harmony,
where 5/4 and 9/7 are distinct intervals, that 440 cents
would almost certainly be heard as belonging to the 9/7
category.

If the 440 cents resolved onto 400 (or even 386)
cents, you'd hear a release of tension, because it fits
a traditional idea of tuning better. You'd describe that as
a single interval becoming better tuned. If you heard an
interval of 500 cents resolve onto 400 cents you may also
hear a release of tension, depending on how much you've
internalized common practice harmony. But you'd describe
it as consisting of two different intervals, because
they're clearly distinct on a 12 note scale. It's
categorical perception that allows you to distinguish a
wrong note from a mistuning. In both cases, though, you can
say that the larger interval is within the field of
attraction of the major third.

One of the points of alternative temperament classes is
that they play with your existing categories of pitch.
It's possible that, after being exposed to a lot of
near-just music, you'd find 5/4 being the archetype of a
major third instead of 400 cents. The point of
exotemperaments is then that they confuse even these
categories. The number of pitch categories is likely to
be reduced when you consider exotemperaments -- not 12
pitches to the octave, but maybe 7 or 5. At this point,
what may be a wrong note on a chromatic scale may well be
categorized as a mistuning -- and a mistuning of an
identifiable ratio.

I don't see any object in constraining what musicians can
talk about as approximations within reasonable bounds --
and I think it's quite reasonable to consider an interval
with a natural tendency to resolve as approximating the
interval it sounds like it should resolve onto. Whether
it's really heard as that interval is the BMTQ.

Graham

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:

> But if he said "Ah, Uncle Steve -- he was like a father to
> me" the meaning would be entirely different.

And yet the analogy would remain as effective. Because being like a father is different than being a father, and the awareness of these differences is what prompts one to compare rather than equate.

> Mike didn't say anything about sounding like a 5/4.

Now this looks like a game of semantics to me. Surely if we hear something as a 5/4, that means we hear it as "sounding like" a 5/4 as well. It would be an odd phenomenon indeed if we heard something *as* a 5/4 but did not hear it *sounding like* a 5/4.

> You show a certain lack of imagination, then. Another
> interpretation is that the interval can stand in for a 5/4
> in some context or another.

I think that's pretty obviously implied within my description of my understanding, if two intervals sound alike then clearly they should be able to stand in for one another in some context or another.

> Or that we have an innate
> sense of 5/4-ness that this interval evokes. It's possible
> to be frightened by something that looks like a snake even
> if you don't know what a snake looks like.

That's not a valid analogy. A valid analogy would be that it's possible to know that something that looks like a snake *is* a "snake" without ever having seen or heard of a snake before. In any case I haven't seen a shred of evidence anywhere that Just intervals form the basis for some innate musical categorical perception that is universal to the human species.

> Let's say Uncle Steve plays a tune on his monochord that's
> imitates the song of a purple breasted reed warbler.
> You've never been keen on birds. You wouldn't be able to
> identify the song of a common reed warbler, let alone the
> purple breasted variety. But it happens that purple
> breasted read warblers were common where you grew up. As
> Uncle Steve plays his monochord, it takes you back to those
> long evenings when you watched the sun set behind the
> chemical weapons factory. Clearly, although you can't
> identify it, this sounds like a purple breasted reed
> warbler to you. But there's no way you'd ever confuse the
> sound of a monochord with a bird.

While this is a lovely analogy, it really has no bearing on the discussion. For one, you weren't born knowing what the purple breasted reed warbler sounds like. It's an experience you were subjected to post-natally that has since been buried in the subconsciousness. So what we have hear is a new stimulus triggering a subconscious association with a *memory* by virtue of some similarity between the stimulus and the memory. That is not at all the same as a familiar stimulus achieving perceptual categorization according some innately-defined categorization schema based on never-before-experienced acoustic properties. Most Western-trained musicians do not experience pure intervals as such until someone introduces them to JI, and so never have the opportunity to form a memory of what a 5/4 sounds like, which is then subconsciously invoked every time they hear a major 3rd.

For two, you have never been aware that the song belongs to something known as a "purple breasted reed warbler", so it's not true to say that Uncle Steve's monochord tune sounds to you like a purple breasted reed warbler (I wish you had picked a bird with a shorter name!). It sounds like "that birdsong you used to hear watching the sun set behind the chemical weapons factory". To most musicians, there is no cognitive intervallic perceptual category of "5/4", except perhaps as a time-signature. So nobody is hearing anything "as" a 5/4 unless they know what a 5/4 is. They're just hearing a beatless major 3rd.

> Questioning the validity of exotemperaments is hardly an
> original argument. Still, they stumble on because
> musicians find them useful things to talk about. You
> aren't the first to suggest multiple mapping may apply
> simultaneously either. You may be the first to describe
> that as an objection.

Multiple mappings always apply everywhere, now that I think about it, so long as we are looking only at tunings and not at pieces of music. There are infinite ways to use the regular mapping paradigm to describe the workings of any given tuning. But there is nothing built into the regular mapping paradigm to tell us which mappings are valid, and under what musical circumstances they may be valid. This is why we can debate whether 13-EDO is Father or not, and also why there is no way to settle that debate without appealing to something outside the paradigm. Not that it matters in the grand scheme of things, I suppose...the artistic merit of the music matters much more than how it could be described in terms of JI.

I guess, at that, I'm just going to let it go. I don't really know why I got so involved in this in the first place, as the regular mapping paradigm is mostly useful for finding optimizations, while I let my options be dictated by the EDOs available within my range of acceptable size. I suppose I should have taken Paul's advice long ago, which was "if you're not concerned with approximating JI, why bother with regular temperament?" There are other ways of looking at music that surely suit me better anyway.

Yep, I'm done talking about temperaments.

-Igs

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

On Tue, Jun 7, 2011 at 12:23 PM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> This is the only way I know how to meaningfully interpret the idea that we can hear intervals "as" other intervals. Clearly, my understanding of this concept implies that we can't hear one interval as another interval unless we already know what the "heard as" interval sounds like, which (to me) suggests that no one is hearing anything as 5/4 unless they already know what a 5/4 sounds like. Imagine, continuing the above example, you invite Uncle Steve over to hear you play your monochord, and when you play a 5/4, he reacts just like you did to the piano, only instead of saying "that major 3rd sounds like a 5/4", he says, "that 5/4 sounds like a major 3rd, except that it's not beating!"

Right, except we don't know if that particular percept is actually
what it means to hear an interval "as" 5/4, or if that's just what it
means to hear an interval as a "major third." You know, another option
that we haven't discussed is that there's just more than one harmonic
percept that's lumped into this "major third" category - maybe we're
aware that it's some kind of 5/4 above the root, and also aware that
it's a "whole step" above a "whole step," where a whole step means
9/8. And we're also aware how it's accessible by fifths, and we know
that fifths are 3/2. It could just be that every single one of these
things comprises the "Major third" gestalt, and if you get rid of 3/2
the others are still strong enough to activate the relevant schema
nonetheless. And melodically, I'd assume that the knowledge of how to
get to a "major third" by way of compound intervals - e.g. whole steps
on top of wholesteps - is more important than the knowledge of how to
get to it directly, e.g. by 5/4. I would, in fact, assume that the
brain gathers as much information as possible about what's going on.

Lastly, the idea really isn't that the brain actually identifies
specific chunks of the harmonic series - it's not really like "oh,
this is two notes in a '5/4' ratio." It's more like, this sound is
actually a high-pass or band-pass filtered part of *INSERT LOW-PITCHED
SOUND HERE*. The actual thing that's going on is the generation of a
phantom low note, not the identification of a specific dyad in the
series.

> How about "Daddy?" LOL.

LOL, this whole thing is f*cked.

> Well, that's the problem with the regular mapping paradigm. It's not anchored in anything to do with liminal music cognition. The paradigm becomes unstable near certain boundary conditions. It works excellently for high-accuracy temperaments, but when we move toward exotemperaments everything goes up in the air and I wonder what the use is anymore of applying the paradigm. I've said this for a long time, actually. I've objected many times that when it comes to inaccurate temperaments, multiple mappings can be applied simultaneously and there is no clear way to differentiate which mapping is valid.

What exactly do you view as "the paradigm?" Keep in mind that it
doesn't seem that people can agree on what the paradigm is. You seem
to be endorsing Carl's specific interpretation, but it's not the only
one out there, and he's been known to change his mind every now and
then anyway.

> Take 14-EDO's 5L+4s scale: is it Semaphore? Godzilla? Bug? Beep? Some subgroup with a 15/13 generator that equates two of them with 4/3? Some other subgroup with a 37/32 generator that equates two of them with 43/32? Depending on who you ask, you might get an argument in favor of any of these--or all, or none of these--mappings. It all depends on how you're hearing the intervals, and there is no clear way to determine how any of us are really "hearing" intervals like these. What if you really *can* hear the identities of high harmonics? 14-EDO excellently renders harmonics 25, 29, 37, 39, 41, 43, 55, and 61. We ignore that here because most of us are conservative about what we consider JI, and we don't consider these to be "Just", but that doesn't invalidate them as targets of approximation. These harmonics all have a "sound" to them that we can come to recognize, and there are people like Johnny Reinhard who like to work with these harmonics (though usually in a purely-Rational setting).

The issue is that there are just multiple percepts that occur when you
hear a dyad. That's it, plain and simple. Higher-limit identities may
very well have a role when you start talking about optimizing things
for periodicity buzz, which if I ever work it out will probably be
very similar to Erv Wilson's stuff on recurrent sequences. You
remember the RI-ified Father chords I posted a while ago.

Then you also have the VF mechanism, and you also have beating. The
present question is whether or not the bulk of musical "information"
really is communicated via the VF mechanism. If not, then it isn't
worth exalting on a massive theoretical pedestal, such that when we
talk about "perception of ratios" that we have to always assume this
means VF perception. But if it is, then it is very much worth focusing
on.

It could also be that the basic idea is to pick nicely-tuned harmonies
just to get the VF mechanism in the brain to stop complaining, so that
you can smoothly communicate information some other way - just like we
want to pick timbres to get the cochlea to stop complaining about
roughness and beating. Or the whole thing could just be comprised of
interlocking parts that hand information off to one another.

> The question we always come back to is, "is it possible to hear something like 26:32:39 as an identity, or does it always sound like an 'out-of-tune' 4:5:6". People like Kraig and JR who work with extended JI almost always say "the former is true", whereas people like Paul who have studied psychoacoustics more in-depth tend to say "the latter is true". So for me it's a question of who to trust--the practitioners or the theorists.

Paul has a much more nuanced interpretation of what's going on than
you wrote above. Paul's interpretation is more like, if you were to
play this to a baby, with no learned factors at all, and also you're
playing it after like an hour of silence, so that there's no biasing
from previously played chords, how would your brain naturally sort
this triad out? What would it sound like? What possible "fits" could
there be? What would the relative distribution of probabilities be?
That's it. The age-old debate on the tuning list over whether or not
you can learn with enough training to hear 26:32:39 as a chunk of the
harmonic series isn't something that seems to fit into Paul's current
paradigm. In fact, I'd hope that the Frere Jacques example would put
this debate to rest, because we saw that people were able to resolve
15:16:17 once they knew what notes they were supposed to "look for."
However, you have to keep in mind that there is a difference between
being able to "identify" 26:32:39 by hearing its particular pattern of
beating, buzz pattern, mixture of 4:5:6-ness and other things - and
being able to "identify" it by hearing a VF pop out 1/26 down from the
root. People ought to be specific when they talk about which meaning
they mean. Cameron, for example, I sometimes think means the former
meaning, whereas Carl tends to talk about the latter. Whether the
latter should take precedence has to do with what I wrote in my
previous paragraph about how important the VF mechanism is.

Much has been made of the interpretation that the curve is supposed to
represent a "hard" psychoacoustic limitation on hearing, but that's
not what Paul endorses. He specifically doesn't endorse the view that
a low-numbered triad has a "field of attraction" that dominates
everything around it, irrespective of training or cultural upbringing.
To do so would make an assumption about the futility of learning in
influencing F0 estimation, and that isn't what he intended for HE to
demonstrate. He intended for it to make no claims about learning at
all, and just model what things would be like for a tabula rasa baby
or something like that. The only sense in which 4:5:6 has a "field of
attraction" is that it has a strong probability that will influence
the perception triads in its vicinity - for an untrained listener -
outside of any musical context with things like leading tones that
could bias f0 estimation - that's it. It isn't supposed to be the tool
that proves to artists that they're stuck in a world of placebo
effect.

Go ask him about it on XA if you want, I just had a phone conversation
with him about this like a week ago. He thinks that the paradigm where
people can't learn to hear mistuned 4:5:6's as being anything but
4:5:6 isn't what the point of HE is supposed to be. And if you ever
delve into some information theory enough to understand his idea, it
actually makes much more sense that way. He's not convinced about the
hypothesis about categorical perception really being harmonic series
detection, but once I work out some listening tests that debate will
end too.

> > I have no idea what it is we hear, and I don't think you do either.
> > And I don't want to impose requirements on people about the
> > terminology they're supposed to use when it's based on unfounded
> > assumptions involving big masturbatory theoretical questions about
> > what we hear. That's the last thing this group of noobs needs.
>
> Which is why I'm now proposing that we drop the temperament-related names all together when we're in boundary territory.

Or we could just pick the most common, notorious, all-purpose, general
temperament for some MOS, and give that the name, which is what people
want to do. Like how you're never going to hear anyone calling 2L5s
anything but mavila, except for maybe "pelog" or something like that.
So in that case you have "father," the scale, and then also "father,"
the temperament. If you're talking about father, the scale, then it's
assumed you're also talking about the temperament unless you be more
specific. Sure, why not?

-Mike

🔗Mike Battaglia <battaglia01@...>

On Tue, Jun 7, 2011 at 4:50 PM, Graham Breed <gbreed@...> wrote:
>
> It was? I can't have been paying attention, then. I
> thought categorical perception was as a (subconscious)
> statistical analysis of the things you were perceiving. So
> on hearing an interval of 440 cents, you'd associate it
> with a major third, very sharp, because you'd heard a lot
> of intervals of around 400 cents (or flatter) before, but
> not many between, say, 420 and 480 cents. If you'd been
> exposed to quartertones, maybe you'd have heard that 440
> cents as a slightly flat example of a quartertone-expanded
> major third. If you were familiar with 9-limit harmony,
> where 5/4 and 9/7 are distinct intervals, that 440 cents
> would almost certainly be heard as belonging to the 9/7
> category.

Which is another good option. We need to find ways to test all of these.

I note that the 240 cent intervals in 15-equal are definitely
something new, something between secondness and thirdness. You can
squeeze them into the major second box, but it's a tough fit. You can
also put them into the minor third box, but there's too much room. I
meditated on that for a little bit last night and came to the
conclusion that this is what "8/7-ness" was. But I also note that
"major secondness" seems to correlate with 9/8-ness, though, which is
interesting. I'm still not sure what minor thirdness correlates with.

Whatever it is, it doesn't seem to actually have anything to do with
whether it really is the "third" scale degree or not, because major
thirds in diminished[8] or the altered scale are actually diminished
fourths, but they work just fine. Conversely, the minor third in the
altered scale is also generally used as a #9, although you can always
just treat it as a minor third in a half diminished chord or
something.

There does seem to be something that can make an interval "function
differently" in different circumstances, but scalar position doesn't
look like the magic bullet.

> One of the points of alternative temperament classes is
> that they play with your existing categories of pitch.
> It's possible that, after being exposed to a lot of
> near-just music, you'd find 5/4 being the archetype of a
> major third instead of 400 cents.

Another interesting thing - when I move from 12-equal to 31-equal, at
first, the major thirds sound flat and the major seconds even worse.
Once I play a segment of the circle of fifths, however, something in
my brain rewires itself to make it all right again. So if I play
C-G-D-A-E, just notes, not chords, then I go play C-E again, suddenly
the 5/4 sounds correct. Then, when I move back to 12-equal, the same
process fixes it over there. So perhaps part of the perception of the
common practice major third is an awareness of how it's reachable by
fifth, which is to say an internalization of the 81/80 comma pump.

This also highlights another idea I've been throwing around, which is
that of the perception of "compound" intervals. Just like you can have
an awareness of 5/4 as a prime interval, as well as a composite
interval being reachable by meantone fifth, 9/8 has two modes of
perception - that of being an actual 9/8 from the root, and that of
being two fifths up and an octave down from the root. Play around in
an inconsistent temperament sometime where you have 9/8 as being
distinct from 3/2 * 3/2 - once you really internalize the fact that
the 9/8 doesn't have anything to do with "fifths" anymore, it can
sometimes start to take on a very different character; cold and
resonant, like 11/8 or something like that. It becomes a higher-limit
prime both in terms of its mapping and in terms of its perception. To
me, this signifies that we are very much aware of how intervals fit
together to make other intervals, and that this awareness is learned,
not innate. So when you say that we'll learn to hear 5/4 as being
correct over 400 cents with enough exposure, all I can say is that I
hear it as correct if the fifths are at like 697 cents and I play a
lick around the scale first.

-Mike

🔗cityoftheasleep <igliashon@...>

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

> Right, except we don't know if that particular percept is actually
> what it means to hear an interval "as" 5/4, or if that's just what it
> means to hear an interval as a "major third." You know, another option
> that we haven't discussed is that there's just more than one harmonic
> percept that's lumped into this "major third" category - maybe we're
> aware that it's some kind of 5/4 above the root, and also aware that
> it's a "whole step" above a "whole step," where a whole step means
> 9/8. And we're also aware how it's accessible by fifths, and we know
> that fifths are 3/2. It could just be that every single one of these
> things comprises the "Major third" gestalt, and if you get rid of 3/2
> the others are still strong enough to activate the relevant schema
> nonetheless. And melodically, I'd assume that the knowledge of how to
> get to a "major third" by way of compound intervals - e.g. whole steps
> on top of wholesteps - is more important than the knowledge of how to
> get to it directly, e.g. by 5/4. I would, in fact, assume that the
> brain gathers as much information as possible about what's going on.

I'm done. I can't go any further with this. I've been following this line of inquiry all this time in hopes of reaching some firm foundation on which to build up my understanding of tuning, but the longer I'm embroiled in this, the further backward I feel like I'm getting. I don't care what's going on with the auditory processing, I don't care what's happening in my cochlea, I don't care where my definition of a "major 3rd" comes from. I care about moods and colors and textures, and nothing we've talked about is moving me forward in understanding those aspects. Maybe it's true that much of the harmonic series fetishizing that goes on in some circles is numerology, but that's no reason to dismiss it. I think religion is all mythology, too, but if it inspires people to do good things, therein lies its value.

I'm done with thinking in terms of temperament, I'm done with thinking about psychoacoustics, I'm done with trying to reconcile inconsistencies and enforce rigorous terminologies. It's gotten me nowhere, and my input has gotten the community nowhere, so it's time for me to stop beating my head against the wall and get back to doing stuff that actually might have some benefit for others--like making music.

-Igs

🔗Mike Battaglia <battaglia01@...>

On Tue, Jun 7, 2011 at 11:27 PM, cityoftheasleep
<igliashon@...> wrote:
>
> I'm done. I can't go any further with this. I've been following this line of inquiry all this time in hopes of reaching some firm foundation on which to build up my understanding of tuning, but the longer I'm embroiled in this, the further backward I feel like I'm getting. I don't care what's going on with the auditory processing, I don't care what's happening in my cochlea, I don't care where my definition of a "major 3rd" comes from. I care about moods and colors and textures, and nothing we've talked about is moving me forward in understanding those aspects.

I agree that moods and colors are textures are what's important,
except I feel like understanding all of this is moving me forward in
those aspects. But to be honest, I like it best when I observe what
people do naturally, figure out "what they're doing," and then just
describe it. That way you avoid theoretical incest, where people say
that the theory should work xyz way, and then go on learning how to
make it work that way. So go do what you want to do naturally and work
out the theory later, I say.

> Maybe it's true that much of the harmonic series fetishizing that goes on in some circles is numerology, but that's no reason to dismiss it. I think religion is all mythology, too, but if it inspires people to do good things, therein lies its value.

Wait, hold on, now you're saying the opposite!

> I'm done with thinking in terms of temperament, I'm done with thinking about psychoacoustics, I'm done with trying to reconcile inconsistencies and enforce rigorous terminologies.

No, wait, now it's the un-opposite again. Well, I think I agree with
at least one of the things you wrote above, but I'm too confused to
know which. Either way, can I just call 5L3s "father" now?

This will all get a lot more interesting when it stops being a Big
Masturbatory Theoretical Question and becomes a Tangible Concrete
Scientific Hypothesis, which will happen when I develop some Specific
Elegant Listening Tests. Stay tuned for those. You might have to stay
tuned for a while, though, because moving to NYC is rough.

-Mike

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

🔗cityoftheasleep <igliashon@...>

🔗genewardsmith <genewardsmith@...>

🔗Carl Lumma <carl@...>

🔗genewardsmith <genewardsmith@...>

🔗Daniel Nielsen <nielsed@...>

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

🔗bobvalentine1 <bob.valentine@...>

🔗Carl Lumma <carl@...>

🔗cityoftheasleep <igliashon@...>

Seriously, I know you're NOT a homophobe, Carl, but honestly that usage of the word "gay" just doesn't fly after high school. Maybe you see it as homosexuals trying to "ban" a word and censor your speech, but hey, guess what, they don't actually have the power to do that. The only thing stopping you is your own awareness that any self-respecting liberal is going to look down on you for using the term that way. Not because "ooh it's a bad word, like 'fuck' 'shit' 'bitch' etc.", but because gay people are getting a tough time of it from society pretty much everywhere and it seems immature and insensitive to go on using the term that way if you actually give a shit about what gay people are going through.

To me I refrain from it voluntarily because I have a lot of gay friends and even in San Francisco they are frequent targets of harassment and derision. If I were to persist in the naive grade-school usage of the term around my gay friends, they would probably find it hurtful and insensitive. I think it's fair to say that gay people, especially gay men and boys, are some of the most heavily-persecuted people in this country (to say nothing of the countries where homosexuality is a crime punishable by death). Regardless of the fact that you were ignorant of the origins of that usage of the term when you were a kid, you're not now. Millions of people all over the country use the term "gay" as a homophobia-based pejorative, because the majority of society is still more or less homophobic. When I hear an educated adult use the term "gay" negatively or pejoratively, my thoughts are "either this person hasn't matured since high school, or they're a homophobe". I like to think neither pertains to you, but you are showing a surprising lack of maturity about this particular issue.

-Igs

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
>
> > My imagination?? It's a well-known pejorative term.
>
> I learned that usage before I had a clue what sex was.
> That some group is going to call themselves gay and then
> attempt to ban any negative usage of the word is pathetic.
>
> -Carl
>

🔗genewardsmith <genewardsmith@...>

🔗lobawad <lobawad@...>

Admiral Jones, have you ever stopped and stepped back to take a gander at the larger picture of the "the regular temperament paradigm" in terms of who is actually doing what?

Who is deliberately excercising the RTP on a regular basis, early and often, to make music for people to hear? Hm. There is you, working at one extreme of the RTP in "exotemperaments", which can be likened to attempting a syncretism in athletics by combining the sports of badminton and autoerotic asphyxiation, and Gene Ward Smith, working at the other extreme of the RTP in "microtemperaments", which can be likened to being tossed into the deep end with a copy of Jane's Fighting Ships superglued to one's nose. (these are descriptions in neon hyperbole, not value judgements).

Who else? In the RTP MOR, AFIK, you'll find only Joseph McPherson and myself, both clearly something of an embarrassment to the online community responsible for articulating the RTP, so that doesn't count.

Hm.

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
>
> > Right, except we don't know if that particular percept is actually
> > what it means to hear an interval "as" 5/4, or if that's just what it
> > means to hear an interval as a "major third." You know, another option
> > that we haven't discussed is that there's just more than one harmonic
> > percept that's lumped into this "major third" category - maybe we're
> > aware that it's some kind of 5/4 above the root, and also aware that
> > it's a "whole step" above a "whole step," where a whole step means
> > 9/8. And we're also aware how it's accessible by fifths, and we know
> > that fifths are 3/2. It could just be that every single one of these
> > things comprises the "Major third" gestalt, and if you get rid of 3/2
> > the others are still strong enough to activate the relevant schema
> > nonetheless. And melodically, I'd assume that the knowledge of how to
> > get to a "major third" by way of compound intervals - e.g. whole steps
> > on top of wholesteps - is more important than the knowledge of how to
> > get to it directly, e.g. by 5/4. I would, in fact, assume that the
> > brain gathers as much information as possible about what's going on.
>
> I'm done. I can't go any further with this. I've been following this line of inquiry all this time in hopes of reaching some firm foundation on which to build up my understanding of tuning, but the longer I'm embroiled in this, the further backward I feel like I'm getting. I don't care what's going on with the auditory processing, I don't care what's happening in my cochlea, I don't care where my definition of a "major 3rd" comes from. I care about moods and colors and textures, and nothing we've talked about is moving me forward in understanding those aspects. Maybe it's true that much of the harmonic series fetishizing that goes on in some circles is numerology, but that's no reason to dismiss it. I think religion is all mythology, too, but if it inspires people to do good things, therein lies its value.
>
> I'm done with thinking in terms of temperament, I'm done with thinking about psychoacoustics, I'm done with trying to reconcile inconsistencies and enforce rigorous terminologies. It's gotten me nowhere, and my input has gotten the community nowhere, so it's time for me to stop beating my head against the wall and get back to doing stuff that actually might have some benefit for others--like making music.
>
> -Igs
>

🔗lobawad <lobawad@...>

"Pehrson" not McPherson, sorry (I was just contemplating whether to take my son to a coupla-times-a-year McDonald's "meal" today, and got discombobulated).

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
> Admiral Jones, have you ever stopped and stepped back to take a gander at the larger picture of the "the regular temperament paradigm" in terms of who is actually doing what?
>
> Who is deliberately excercising the RTP on a regular basis, early and often, to make music for people to hear? Hm. There is you, working at one extreme of the RTP in "exotemperaments", which can be likened to attempting a syncretism in athletics by combining the sports of badminton and autoerotic asphyxiation, and Gene Ward Smith, working at the other extreme of the RTP in "microtemperaments", which can be likened to being tossed into the deep end with a copy of Jane's Fighting Ships superglued to one's nose. (these are descriptions in neon hyperbole, not value judgements).
>
> Who else? In the RTP MOR, AFIK, you'll find only Joseph McPherson and myself, both clearly something of an embarrassment to the online community responsible for articulating the RTP, so that doesn't count.
>
> Hm.
>
>
>
> --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@> wrote:
> >
> > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > > Right, except we don't know if that particular percept is actually
> > > what it means to hear an interval "as" 5/4, or if that's just what it
> > > means to hear an interval as a "major third." You know, another option
> > > that we haven't discussed is that there's just more than one harmonic
> > > percept that's lumped into this "major third" category - maybe we're
> > > aware that it's some kind of 5/4 above the root, and also aware that
> > > it's a "whole step" above a "whole step," where a whole step means
> > > 9/8. And we're also aware how it's accessible by fifths, and we know
> > > that fifths are 3/2. It could just be that every single one of these
> > > things comprises the "Major third" gestalt, and if you get rid of 3/2
> > > the others are still strong enough to activate the relevant schema
> > > nonetheless. And melodically, I'd assume that the knowledge of how to
> > > get to a "major third" by way of compound intervals - e.g. whole steps
> > > on top of wholesteps - is more important than the knowledge of how to
> > > get to it directly, e.g. by 5/4. I would, in fact, assume that the
> > > brain gathers as much information as possible about what's going on.
> >
> > I'm done. I can't go any further with this. I've been following this line of inquiry all this time in hopes of reaching some firm foundation on which to build up my understanding of tuning, but the longer I'm embroiled in this, the further backward I feel like I'm getting. I don't care what's going on with the auditory processing, I don't care what's happening in my cochlea, I don't care where my definition of a "major 3rd" comes from. I care about moods and colors and textures, and nothing we've talked about is moving me forward in understanding those aspects. Maybe it's true that much of the harmonic series fetishizing that goes on in some circles is numerology, but that's no reason to dismiss it. I think religion is all mythology, too, but if it inspires people to do good things, therein lies its value.
> >
> > I'm done with thinking in terms of temperament, I'm done with thinking about psychoacoustics, I'm done with trying to reconcile inconsistencies and enforce rigorous terminologies. It's gotten me nowhere, and my input has gotten the community nowhere, so it's time for me to stop beating my head against the wall and get back to doing stuff that actually might have some benefit for others--like making music.
> >
> > -Igs
> >
>

🔗Carl Lumma <carl@...>

🔗lobawad <lobawad@...>

🔗cityoftheasleep <igliashon@...>

Upon further consideration, I don't really believe I use exotemperaments as such. I do actually consider all the scales I use to be rich in good harmonies, so it's more that I treat them as subgroup temperaments. 16-EDO I treat as a 2.5.7.11/3.19 subgroup, for instance. I guess 20-EDO I treat as a 7-limit temperament but it's not an exotemperament, just a sub-optimal 5-limit temperament. I could use it as a decent 2.7.11.13.15.19 subgroup if I was more keen on exploiting its accuracies. Also I use 19-EDO with increasing frequency and there's nothing exo about it (except perhaps in the ratios of 7). But I can't say the paradigm really guides me in composition, either...I don't exploit comma pumps except by accident, I don't map out lattices or periodicity blocks describing the JI relationships within the temperaments, etc. I just load up the scale and go to town with it. I really only use the paradigm as an analytical tool to describe what intervals in the tuning or scale I'm treating as basic consonances.

Oh, and you forgot to mention Petr. He's made plenty of music using the RTP as well, some of which is arguably the best of any of ours. His winning entry for the 2009 UnTwelve competition, for instance, fairly blew my mind. And I'm sure Mike B. will be inundating us with RTP music as soon as his life settles down. Perhaps so will Paul--word on the street is he's building a recording studio in his basement.

-Igs

🔗lobawad <lobawad@...>

Okay. It would be interesting to know who is deliberately using regular temperament (and I don't mean fanciful post factum interpretations of 12-tET, that's pathetic), and how specifically they're doing so.

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> Upon further consideration, I don't really believe I use exotemperaments as such. I do actually consider all the scales I use to be rich in good harmonies, so it's more that I treat them as subgroup temperaments. 16-EDO I treat as a 2.5.7.11/3.19 subgroup, for instance. I guess 20-EDO I treat as a 7-limit temperament but it's not an exotemperament, just a sub-optimal 5-limit temperament. I could use it as a decent 2.7.11.13.15.19 subgroup if I was more keen on exploiting its accuracies. Also I use 19-EDO with increasing frequency and there's nothing exo about it (except perhaps in the ratios of 7). But I can't say the paradigm really guides me in composition, either...I don't exploit comma pumps except by accident, I don't map out lattices or periodicity blocks describing the JI relationships within the temperaments, etc. I just load up the scale and go to town with it. I really only use the paradigm as an analytical tool to describe what intervals in the tuning or scale I'm treating as basic consonances.
>
> Oh, and you forgot to mention Petr. He's made plenty of music using the RTP as well, some of which is arguably the best of any of ours. His winning entry for the 2009 UnTwelve competition, for instance, fairly blew my mind. And I'm sure Mike B. will be inundating us with RTP music as soon as his life settles down. Perhaps so will Paul--word on the street is he's building a recording studio in his basement.
>
> -Igs
>
> --- In tuning@yahoogroups.com, "lobawad" <lobawad@> wrote:
> >
> > Admiral Jones, have you ever stopped and stepped back to take a gander at the larger picture of the "the regular temperament paradigm" in terms of who is actually doing what?
> >
> > Who is deliberately excercising the RTP on a regular basis, early and often, to make music for people to hear? Hm. There is you, working at one extreme of the RTP in "exotemperaments", which can be likened to attempting a syncretism in athletics by combining the sports of badminton and autoerotic asphyxiation, and Gene Ward Smith, working at the other extreme of the RTP in "microtemperaments", which can be likened to being tossed into the deep end with a copy of Jane's Fighting Ships superglued to one's nose. (these are descriptions in neon hyperbole, not value judgements).
> >
> > Who else? In the RTP MOR, AFIK, you'll find only Joseph McPherson and myself, both clearly something of an embarrassment to the online community responsible for articulating the RTP, so that doesn't count.
> >
> > Hm.
> >
> >
> >
> > --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@> wrote:
> > >
> > > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> > >
> > > > Right, except we don't know if that particular percept is actually
> > > > what it means to hear an interval "as" 5/4, or if that's just what it
> > > > means to hear an interval as a "major third." You know, another option
> > > > that we haven't discussed is that there's just more than one harmonic
> > > > percept that's lumped into this "major third" category - maybe we're
> > > > aware that it's some kind of 5/4 above the root, and also aware that
> > > > it's a "whole step" above a "whole step," where a whole step means
> > > > 9/8. And we're also aware how it's accessible by fifths, and we know
> > > > that fifths are 3/2. It could just be that every single one of these
> > > > things comprises the "Major third" gestalt, and if you get rid of 3/2
> > > > the others are still strong enough to activate the relevant schema
> > > > nonetheless. And melodically, I'd assume that the knowledge of how to
> > > > get to a "major third" by way of compound intervals - e.g. whole steps
> > > > on top of wholesteps - is more important than the knowledge of how to
> > > > get to it directly, e.g. by 5/4. I would, in fact, assume that the
> > > > brain gathers as much information as possible about what's going on.
> > >
> > > I'm done. I can't go any further with this. I've been following this line of inquiry all this time in hopes of reaching some firm foundation on which to build up my understanding of tuning, but the longer I'm embroiled in this, the further backward I feel like I'm getting. I don't care what's going on with the auditory processing, I don't care what's happening in my cochlea, I don't care where my definition of a "major 3rd" comes from. I care about moods and colors and textures, and nothing we've talked about is moving me forward in understanding those aspects. Maybe it's true that much of the harmonic series fetishizing that goes on in some circles is numerology, but that's no reason to dismiss it. I think religion is all mythology, too, but if it inspires people to do good things, therein lies its value.
> > >
> > > I'm done with thinking in terms of temperament, I'm done with thinking about psychoacoustics, I'm done with trying to reconcile inconsistencies and enforce rigorous terminologies. It's gotten me nowhere, and my input has gotten the community nowhere, so it's time for me to stop beating my head against the wall and get back to doing stuff that actually might have some benefit for others--like making music.
> > >
> > > -Igs
> > >
> >
>

🔗Mike Battaglia <battaglia01@...>

On Thu, Jun 9, 2011 at 4:17 AM, lobawad <lobawad@...> wrote:
>
> Admiral Jones, have you ever stopped and stepped back to take a gander at the larger picture of the "the regular temperament paradigm" in terms of who is actually doing what?

What exactly is the RTP? All of the things that we've been discussing
in the last week are very modern extensions of the RTP, often to
address its perceived flaws, but what exactly is "it?" "It" seems to
be many different things to many different people - Carl has a certain
very strict interpretation of it, Graham has a different one that
allows more room for Sethares, Gene has yet another one which allows
for ratios to occur in maqam melodies and prefers microtemperament,
Paul Erlich has yet another one which leaves almost everything open to
learning, you have yet another one which has lots of good merits, and
I've been generally floating around trying to figure out which bits
and pieces from each viewpoint I agree and disagree with, which is
where Mr. Jones seems to be at as well.

But where do these nuances of interpretation stop being "the RTP" and
just start being someone's interpretation of the larger picture of
music cognition? If anything, the RTP doesn't associate with any of
them, but rather allows for the expression of all of these viewpoints;
it is a branch of pure mathematics that has nothing to do with
psychoacoustics.

So when you say who in the community espouses the RTP, meaning just
these regularly-tempered scales that you then map back to mistuned
constituent primes - Ron Sword is almost a collector of regularly
tempered scales, I had a nice conversation with Jacob Barton about
Father[8] the other day, Chris Vaisvil's been known to throw some
regularly tempered scales into his improvs, etc. When people talk
about mavila as having a "flat 3/2," and "5/4's and 6/5's that switch
places in the circle of fifths," that implies that they're mapping a
certain note in mavila to 3/2 and two others to 5/4 and 6/5, and is
hence an application of regular mapping. The more interesting question
for me is why some scales seem to "catch on" right away, and others
don't.

-Mike

🔗cityoftheasleep <igliashon@...>

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

> But where do these nuances of interpretation stop being "the RTP" and
> just start being someone's interpretation of the larger picture of
> music cognition? If anything, the RTP doesn't associate with any of
> them, but rather allows for the expression of all of these viewpoints;
> it is a branch of pure mathematics that has nothing to do with
> psychoacoustics.

Yep. The paradigm is indeed not at all concerned with psychoacoustics. It is apparently a messy and contentious process to try to anchor the paradigm into something more related to musical cognition. I suppose you could say it's really this attempt at anchoring I'm giving up on; I've been meditating a lot in the last few days about the "point" of any paradigm of alternative tuning systems. It seems to me that the purpose of any paradigm is just to help guide musicians through the infinite possibilities available outside the realm of 12-TET.

One thing I've always said of JI is that while I believe the idea that Just intervals are a fiction in general outside of very carefully-controlled listening environments, the JI paradigm allows for the construction of unique musical systems that seem to prove not only useful to some musicians but also productive of some very fine music. Some of my favorite microtonal music is (at least nominally) in JI. So while I don't buy the theoretical "justification" of JI (that these are "pure" intervals and are superior to tempered ones), I can't deny that the paradigm has served as an effective guide to many people.

I guess this a realization I've been failing to apply to the regular mapping paradigm, but which seems to be implicitly understood by the progenitors of the paradigm. Namely, we should not be concerning ourselves with strict delineations; multiple interpretations are always possible and the validity of an interpretation is determined by its usefulness. Since we can't know what every musician everywhere will find useful or not, there's no point in trying to settle ambiguities.

I guess in this sense I'm conceding to John L. Moriarty, insofar as agreeing that if thinking of 13-EDO as a Father temperament or 11-EDO as a Hanson temperament gives someone a conceptual foot-hold in those tunings that they otherwise can't figure out, more power to them. Hell, for all my blathering about 13-EDO really being "Uncle", I tend to treat it as "A-Team", the 2.9.21 subgroup that I guess I discovered.

Maybe all the talk of psychoacoustics and what not has been clouding my mind, pushing me toward thinking there is always going to be "one psychoacoustically-correct interpretation" of every tuning, and that we need to figure out what those interpretations are and enforce them on everyone. But even if there *is* only "one true psychoacoustic interpretation" of everything, that doesn't really matter so long as there are other interpretations that continue to prove useful despite their falsity/inaccuracy. IOW *per*ception is less important than *con*ception, perhaps. So I guess I just need to shift my focus to understanding ways of *conceptually* organizing pitch, rather than ways of *perceptually* organizing it.

-Igs

🔗Mike Battaglia <battaglia01@...>

On Thu, Jun 9, 2011 at 3:18 PM, cityoftheasleep <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > But where do these nuances of interpretation stop being "the RTP" and
> > just start being someone's interpretation of the larger picture of
> > music cognition? If anything, the RTP doesn't associate with any of
> > them, but rather allows for the expression of all of these viewpoints;
> > it is a branch of pure mathematics that has nothing to do with
> > psychoacoustics.
>
> Yep. The paradigm is indeed not at all concerned with psychoacoustics. It is apparently a messy and contentious process to try to anchor the paradigm into something more related to musical cognition. I suppose you could say it's really this attempt at anchoring I'm giving up on; I've been meditating a lot in the last few days about the "point" of any paradigm of alternative tuning systems. It seems to me that the purpose of any paradigm is just to help guide musicians through the infinite possibilities available outside the realm of 12-TET.

Right. An ideal paradigm would provide some kind of insight into why
things sound the way they do, without making judgment calls as to what
sounds "good" or "bad."

> One thing I've always said of JI is that while I believe the idea that Just intervals are a fiction in general outside of very carefully-controlled listening environments, the JI paradigm allows for the construction of unique musical systems that seem to prove not only useful to some musicians but also productive of some very fine music. Some of my favorite microtonal music is (at least nominally) in JI. So while I don't buy the theoretical "justification" of JI (that these are "pure" intervals and are superior to tempered ones), I can't deny that the paradigm has served as an effective guide to many people.

So has HE, which has served as an effective guide at least for me. HE
represents any interval as the -superposition- of a whole set of just
intervals, and give you a set of probabilities for how likely you're
going to hear something as that interval. That has also served as an
effective guide, and FWIW I find it a bit more useful than thinking in
raw JI. But I think we've squeezed all the juice out of both of these
models, which are both obviously very oversimplified.

For instance, you've described 520 cent fourths before as sounding
like "drunken, wobbly fourths," which is a useful idea to communicate
under some musical circumstances. However, you didn't describe them as
sounding like "strong, resonant 27/20's." Here's one instance in which
the HE paradigm wins out over the JI one. However, HE doesn't take
into account how 520 cent fourths are going to sound if you grew up in
the Mavila village your whole life - will they still sound wobbly?
What will purely tuned 4/3's start to sound like to you? Will they
sound "wrong?" etc.

A paradigm oversteps its bounds when it starts making calls about
what's going to sound "good" or "bad," as in the interpretation of the
HE curve where a purely tuned 4/3 is supposed to sound "good" and a
520 cent mavila fourth is supposed to sound "bad."

> I guess in this sense I'm conceding to John L. Moriarty, insofar as agreeing that if thinking of 13-EDO as a Father temperament or 11-EDO as a Hanson temperament gives someone a conceptual foot-hold in those tunings that they otherwise can't figure out, more power to them. Hell, for all my blathering about 13-EDO really being "Uncle", I tend to treat it as "A-Team", the 2.9.21 subgroup that I guess I discovered.

It wasn't even about that. 11-EDO isn't really a fantastic Hanson
temperament. It's just that we need to give these scales names, and
there's no reason to not just let the most notorious temperament name
that fits that MOS get the trophy, and then be more specific if need
be. Musicians have been prizing convention over rigor for quite a
while anyway.

> Maybe all the talk of psychoacoustics and what not has been clouding my mind, pushing me toward thinking there is always going to be "one psychoacoustically-correct interpretation" of every tuning, and that we need to figure out what those interpretations are and enforce them on everyone. But even if there *is* only "one true psychoacoustic interpretation" of everything, that doesn't really matter so long as there are other interpretations that continue to prove useful despite their falsity/inaccuracy. IOW *per*ception is less important than *con*ception, perhaps. So I guess I just need to shift my focus to understanding ways of *conceptually* organizing pitch, rather than ways of *perceptually* organizing it.

Don't be surprised when concept influences percept.

-Mike

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> Right. An ideal paradigm would provide some kind of insight into why
> things sound the way they do, without making judgment calls as to what
> sounds "good" or "bad."

I wouldn't even go that far, personally. I don't feel the need to explain sounds, or even necessarily to describe them. It's the structural relationships that I am concerned with. For me, I always start with specific tunings as given, then try to find chords I like, then try to find ways to relate the chords together that I like. If I were starting w/JI, it would be different--I'd have the chords worked out beforehand and would then be looking for some way to structure them together into a scale. Or maybe I'd just pick an overtone series and try to analyze the harmonic relationships contained therein. But anyway all of these paradigms go back to ways of trying to answer the question "if I'm not going to use 12-TET, what can I use instead and how can I make it sound good?"

> So has HE, which has served as an effective guide at least for me. HE
> represents any interval as the -superposition- of a whole set of just
> intervals, and give you a set of probabilities for how likely you're
> going to hear something as that interval. That has also served as an
> effective guide, and FWIW I find it a bit more useful than thinking in
> raw JI. But I think we've squeezed all the juice out of both of these
> models, which are both obviously very oversimplified.

Whatever works for you. For me, what I'm "really" hearing something "as" is not important. But treating an interval conceptually as 9/7 vs 13/10 vs 41/32 vs 14/11 leads to different ways of relating it to other pitches in the scale. This to me is more important than what the interval really "is" perceptually. YMMV.

> For instance, you've described 520 cent fourths before as sounding
> like "drunken, wobbly fourths," which is a useful idea to communicate
> under some musical circumstances. However, you didn't describe them as
> sounding like "strong, resonant 27/20's." Here's one instance in which
> the HE paradigm wins out over the JI one. However, HE doesn't take
> into account how 520 cent fourths are going to sound if you grew up in
> the Mavila village your whole life - will they still sound wobbly?
> What will purely tuned 4/3's start to sound like to you? Will they
> sound "wrong?" etc.

Who knows? Let's fly to Africa and find out!

> A paradigm oversteps its bounds when it starts making calls about
> what's going to sound "good" or "bad," as in the interpretation of the
> HE curve where a purely tuned 4/3 is supposed to sound "good" and a
> 520 cent mavila fourth is supposed to sound "bad."

What I don't like about HE is that it doesn't really dictate any structures (although Keenan Pepper's look at the HE of various MOS scales was rather illuminating, if predictable), and from the curve it is not obvious (or at all apparent, really) exactly which various rational intervals are superimposed at any given point. What do you see HE as being good for, aside from doing exactly what you don't want it to (telling us what is supposed to sound "good" or "bad")?

> It wasn't even about that. 11-EDO isn't really a fantastic Hanson
> temperament. It's just that we need to give these scales names, and
> there's no reason to not just let the most notorious temperament name
> that fits that MOS get the trophy, and then be more specific if need
> be. Musicians have been prizing convention over rigor for quite a
> while anyway.

Yep. I am officially giving up on trying to enforce rigor. You can quote me on that, and please do if you catch me back-sliding ;->. Personally I'm sticking with the #L#s system.

> Don't be surprised when concept influences percept.

Sure, yeah, whatever. Percept can sort itself out on its own time, as far as I'm concerned.

-Igs

🔗Herman Miller <hmiller@...>

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
>
> > But where do these nuances of interpretation stop being "the RTP" and
> > just start being someone's interpretation of the larger picture of
> > music cognition? If anything, the RTP doesn't associate with any of
> > them, but rather allows for the expression of all of these viewpoints;
> > it is a branch of pure mathematics that has nothing to do with
> > psychoacoustics.
>
> Yep. The paradigm is indeed not at all concerned with psychoacoustics.

How wrong can you get? Helmholtz practically founded the thing.
Without the key insight that the chords of common practice music
Approximate just intonation, there can be no RTP. In any case, RTP
Is in no way a branch of pure math. -Carl

It is apparently a messy and contentious process to try to anchor the paradigm into something more related to musical cognition. I suppose you could say it's really this attempt at anchoring I'm giving up on; I've been meditating a lot in the last few days about the "point" of any paradigm of alternative tuning systems. It seems to me that the purpose of any paradigm is just to help guide musicians through the infinite possibilities available outside the realm of 12-TET.
>
> One thing I've always said of JI is that while I believe the idea that Just intervals are a fiction in general outside of very carefully-controlled listening environments, the JI paradigm allows for the construction of unique musical systems that seem to prove not only useful to some musicians but also productive of some very fine music. Some of my favorite microtonal music is (at least nominally) in JI. So while I don't buy the theoretical "justification" of JI (that these are "pure" intervals and are superior to tempered ones), I can't deny that the paradigm has served as an effective guide to many people.
>
> I guess this a realization I've been failing to apply to the regular mapping paradigm, but which seems to be implicitly understood by the progenitors of the paradigm. Namely, we should not be concerning ourselves with strict delineations; multiple interpretations are always possible and the validity of an interpretation is determined by its usefulness. Since we can't know what every musician everywhere will find useful or not, there's no point in trying to settle ambiguities.
>
> I guess in this sense I'm conceding to John L. Moriarty, insofar as agreeing that if thinking of 13-EDO as a Father temperament or 11-EDO as a Hanson temperament gives someone a conceptual foot-hold in those tunings that they otherwise can't figure out, more power to them. Hell, for all my blathering about 13-EDO really being "Uncle", I tend to treat it as "A-Team", the 2.9.21 subgroup that I guess I discovered.
>
> Maybe all the talk of psychoacoustics and what not has been clouding my mind, pushing me toward thinking there is always going to be "one psychoacoustically-correct interpretation" of every tuning, and that we need to figure out what those interpretations are and enforce them on everyone. But even if there *is* only "one true psychoacoustic interpretation" of everything, that doesn't really matter so long as there are other interpretations that continue to prove useful despite their falsity/inaccuracy. IOW *per*ception is less important than *con*ception, perhaps. So I guess I just need to shift my focus to understanding ways of *conceptually* organizing pitch, rather than ways of *perceptually* organizing it.
>
> -Igs
>

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:

> How wrong can you get? Helmholtz practically founded the thing.
> Without the key insight that the chords of common practice music
> Approximate just intonation, there can be no RTP. In any case, RTP
> Is in no way a branch of pure math. -Carl

Interestingly, the question "How wrong can you get?" is the question specifically not answered by the paradigm, which is what led me to make that statement. The operations involved in going from untempered prime-space to tempered space are pure math, and there are no explicitly-defined constraints defining which tempering operations are permitted. You can use the paradigm to arrive at all sorts of absurd temperaments:
http://x31eq.com/cgi-bin/rt.cgi?ets=1bdddddeefffffffgggg_1bdddeefffffgggg&limit=17

http://x31eq.com/cgi-bin/rt.cgi?ets=1bccdddeefffgggghhhh_1bccdddeefgggghhhh&limit=19

http://x31eq.com/cgi-bin/rt.cgi?ets=1bccccdddeeeeee_1bccdddeeee&limit=11
(just to name a few of my favorites)

You are also not mathematically bound to interpret a tuning according to any particular temperament, although psychoacoustics suggest otherwise. Nothing inherent in the mathematical operations of the paradigm prevents me from applying a meantone mapping to 3-EDO. The equations don't fail if the error gets too high. It is only our idea of "good sense" and a desire to reach temperaments which are psychoacoustically valid that prevents us from doing that, but the paradigm itself is just a set of mathematical tools that can be used for any ends. That the paradigm arose as a formal mathematical way of arriving at temperaments which are for the most part low in error does not mean that such considerations are formally incorporated in the paradigm. If it did, there would be some irrefutable way to settle the boundary issues, or to settle which temperament is the "one true psychoacoustically-valid" interpretation of any given tuning. Rather, these questions are only to be answered by appeal to factors not incorporated into the operations of the paradigm itself.

-Igs

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

🔗genewardsmith <genewardsmith@...>

🔗Carl Lumma <carl@...>

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> Error is most definitely formally and in all other ways incorporated
> to RMP, which does much better than stop you from coming up with
> absurd temperaments- it tells you precisely how absurd
> they are.

That's missing the point. There's a whole lot more to approximation, psychoacoustics, and music cognition than simple error, as evidenced by the recent debacle over which mapping is the most perceptually/psychoacoustically "valid" for something like 13-EDO. Nothing in the paradigm tells you that if you sharp your 3/2 by 15 cents, it's going to turn your 9/8 into an 8/7, or if you sharp it by 7 cents, it's going to turn your 81/64 into a 9/7 instead of a 5/4. Nothing in the paradigm tells you that under some circumstances, a higher-error mapping might actually be more accurate at describing the perception of a tuning than a lower-error mapping. Nor does the paradigm tell you that with some timbres, a "high-error" temperament may actually sound better than a lower one. All the paradigm gives you is a mapping and a minimal error, and it's up to you to figure out what it all means. It's so open-ended that it's perfectly fine for some people to go around saying that 22-EDO is a Meantone temperament, 11-EDO is a Hanson temperament, 13-EDO is an Orwell temperament, and 7-EDO is pretty much every temperament that generates a 7-note MOS.

The reason I say that psychoacoustics is not integrated into the paradigm is because the paradigm allows for the existence of temperaments which cannot exist perceptually. Those absurd temperaments I linked to in the last post don't exist in reality. There are no circumstances under which they could be heard as what the mapping tells us they are. If psychoacoustics were integrated into the paradigm, there would be a parameter that would tell us when a certain mapping is not valid. If you believe, for instance, that anything tuned as a 7/6 will sound like a 7/6, a mapping that maps 6/5 to an interval around 260 cents would be psychoacoustically invalid. If you believe that it's not that simple and that sometimes something tuned like a 7/6 can actually sound like a 6/5, then an integration of psychoacoustics would mean that something would tell you when your mapping of 6/5 to 260 cents is valid and when it isn't. As it stands, this is not the case. Everyone acknowledges that this is not the case, and everyone acknowledges that we all ought to exercise our best judgment when determining what is actually going on temperamentally in music. Nothing in the paradigm itself prohibits the use of absurd mappings, so we have to use something outside the paradigm--i.e. our good sense, our knowledge of psychoacoustics, etc.--to make our judgments.

Duh.

-Igs