Yahoo Tuning Groups Ultimate Backup tuning "Fields of Attraction" and Temperament

I've tried bringing this up before, but I don't think I succeeded in articulating myself properly. But in light of recent discussions about "fields of attraction", I'd like to bring it up again.

If you buy that intervals have fields of attraction based on simple ratios, does this mean that certain temperaments are "unhearable"? Consider, for example, Dicot temperament. In tempering out 25/24, we equate 6/5 with 5/4, and also two 6/5s (or two 5/4s) with 3/2. However, right between 5/4 and 6/5, there is 11/9. If the Dicot generator is right in the middle of 6/5 and 5/4, then it's obviously in the territory of 11/9. Doesn't that mean that we are going to hear the interval "as" neither 6/5 nor 5/4, but "as" 11/9? And that we are going to thus hear Dicot as a temperament where two 11/9s equal 3/2, or in other words a 2.3.11 temperament where 243/242 vanishes? Perceptually-speaking, the two temperaments should be more or less identical (TOP dicot is <1206.410, 350.456], TOP 2.3.11 243/242 is <1200.064, 350.544]). I've always thought that this implies that only one of these two temperaments is musically "real", as I don't really understand how anyone could differentiate between the two of them compositionally or as a listener. I believe this is why Paul Erlich uses the term "exo-temperament" to describe temperaments like Dicot and Father.

But in any case, it seems that given the existence of "fields of attraction" (or "fields of interaction" to keep the 'Wad from crying havoc), for any set of temperaments whose generators are all sufficiently similar in tuning, there should be only one temperament mapping in the set that correctly describes the perception of music made in tunings derived from those temperaments. Or, given some non-Just tuning, there should be only one temperament that describes correctly how that tuning will be heard.

The only exception to this I can think of is for tunings that locate a sufficient quantity of their notes between all plausible fields of attraction, in which case multiple temperament mappings will stand a chance of being accurate descriptors of perception. However, I suspect these to be comparatively rare, and it seems like it might be worthwhile to weed out temperaments that will be "heard as" other temperaments, since they just make matters confusing (for instance, who can tell me how I could musically differentiate whether a tuning based on generators <1200, 260] is Beep or Superpelog? Seems like 27/25 and 135/128 are very different commas, yet throw 49/48 into the mix and suddenly you get two identical-looking tunings).

-Igs

🔗Ryan Avella <domeofatonement@...>

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
> If you buy that intervals have fields of attraction based on simple ratios, does this mean that certain temperaments are "unhearable"? Consider, for example, Dicot temperament. In tempering out 25/24, we equate 6/5 with 5/4, and also two 6/5s (or two 5/4s) with 3/2. However, right between 5/4 and 6/5, there is 11/9. If the Dicot generator is right in the middle of 6/5 and 5/4, then it's obviously in the territory of 11/9. Doesn't that mean that we are going to hear the interval "as" neither 6/5 nor 5/4, but "as" 11/9? And that we are going to thus hear Dicot as a temperament where two 11/9s equal 3/2, or in other words a 2.3.11 temperament where 243/242 vanishes? Perceptually-speaking, the two temperaments should be more or less identical (TOP dicot is <1206.410, 350.456], TOP 2.3.11 243/242 is <1200.064, 350.544]). I've always thought that this implies that only one of these two temperaments is musically "real", as I don't really understand how anyone could differentiate between the two of them compositionally or as a listener. I believe this is why Paul Erlich uses the term "exo-temperament" to describe temperaments like Dicot and Father.

I do not doubt such fields of attraction do exist, but they would be based on entirely subjective or arbitrary thresholds. For example, some people hear 417 cents as a type of 5/4, but I hear it as 14/11.

It is also really dependent on how we play those intervals as well. Consider playing 350 cents as a melodic interval, a brief harmonic interval, and elongated over a deep drone. In the first example, we are more likely to hear 5/4 or 6/5. In the second example, there is a better chance we will realize it is beating too much to be major or minor, but we might discard it as an unintentional mistuning. With the last example, we will very likely hear it as a neutral third.

Mavila is another good example besides Father and Dicot. I don't hear the fourths in Mavila as 4/3, but as 15/11. It therefore makes more sense for me to use the more-accurate 11-limit Mabila mapping when I play around in anti-diatonic scales.

Ryan

🔗Mike Battaglia <battaglia01@...>

On Fri, Jan 27, 2012 at 3:03 PM, cityoftheasleep
<igliashon@...> wrote:
>
> If you buy that intervals have fields of attraction based on simple ratios, does this mean that certain temperaments are "unhearable"?

It only means this if you define "unhearable" in a very limited sense
as an outcome for the experiments on which you based your operational
definition of "field of attraction."

> Consider, for example, Dicot temperament. In tempering out 25/24, we equate 6/5 with 5/4, and also two 6/5s (or two 5/4s) with 3/2. However, right between 5/4 and 6/5, there is 11/9. If the Dicot generator is right in the middle of 6/5 and 5/4, then it's obviously in the territory of 11/9. Doesn't that mean that we are going to hear the interval "as" neither 6/5 nor 5/4, but "as" 11/9? And that we are going to thus hear Dicot as a temperament where two 11/9s equal 3/2, or in other words a 2.3.11 temperament where 243/242 vanishes? Perceptually-speaking, the two temperaments should be more or less identical (TOP dicot is <1206.410, 350.456], TOP 2.3.11 243/242 is <1200.064, 350.544]).

No, because in the lab experiments you talk about, 11/9 doesn't have
its own "field of attraction" at all, I believe.

> I've always thought that this implies that only one of these two temperaments is musically "real", as I don't really understand how anyone could differentiate between the two of them compositionally or as a listener.
//snip
> But in any case, it seems that given the existence of "fields of attraction" (or "fields of interaction" to keep the 'Wad from crying havoc), for any set of temperaments whose generators are all sufficiently similar in tuning, there should be only one temperament mapping in the set that correctly describes the perception of music made in tunings derived from those temperaments.
//snip
> The only exception to this I can think of is for tunings that locate a sufficient quantity of their notes between all plausible fields of attraction, in which case multiple temperament mappings will stand a chance of being accurate descriptors of perception.

OK, now it seems like you're making further assumptions about "fields
of attraction" which I don't agree with at all. What you said above
about "musical realness," "the perception of music," "compositional
differentiation," "accurate descriptors of perception" are not things
which follow from your limited definition of "unhearable." This "heard
as" thing so far has been given a very limited behavioral,
non-psychoacoustic definition based on the somewhat musically sterile
results of hypothetical lab experiments performed only with dyads.
Once you start talking about these experiments determining "musical
realness," especially in a "compositional" sense, you need to make
certain assumptions about how these (very limited) experiments with
dyads apply to the big picture of music cognition that don't make
sense to me at all.

An actual piece of music includes a number of phenomena which are
perceptually relevant and sometimes poorly understood: tonal centers,
the perception of a background mode or scale, chords that are quickly
"implied" by snippets of arpeggiation and other things, etc. On the
other hand, the experiments on which your definition is based involve
giving people a set of dyads in isolation and telling them to retune
them until they feel they're maximally "in tune." This would seem to
place a harsh limit of the applicability of these experiments to the
bigger picture of music cognition in its broadest sense, and to make
broad generalizations about overall musical perception from them would
seem to paint an absurdly oversimplified picture of a musical
composition.

These dyads aren't placed in any musically relevant temporal setting
at all, nor placed in a setting where any of these other, poorly
understood phenomena occur. They don't even test chords, for example.
11/9 might not have a "field of attraction" under your definition at
all, but how do we apply that to 8:9:10:11:12? And beyond obvious
things like chords, these dyads weren't placed in any musically
relevant temporal setting at all, nor placed in a setting where any of
these other, poorly understood phenomena occur, etc.

Lastly, even in the ultra-limited sense of "heard as," there might be
tunings other than POTE that let you "hear things" in a dicot-tempered
sense. Check out the 13p val, for example: with pure octaves, the
dicot-tempered major chord is 0-369-730. 369 cents is probably enough
for someone under strict laboratory conditions to retune to 5/4, and
730 is probably enough for someone under strict laboratory conditions
to retune to 3/2. So that would appear to be a dicot-tempered 4:5:6,
with steps of 5/4-5/4 on the inside, and 3/2 on the outside.

-Mike

🔗Mike Battaglia <battaglia01@...>

On Fri, Jan 27, 2012 at 7:52 PM, Ryan Avella <domeofatonement@...> wrote:
>
> --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
> > If you buy that intervals have fields of attraction based on simple ratios, does this mean that certain temperaments are "unhearable"? Consider, for example, Dicot temperament. In tempering out 25/24, we equate 6/5 with 5/4, and also two 6/5s (or two 5/4s) with 3/2. However, right between 5/4 and 6/5, there is 11/9. If the Dicot generator is right in the middle of 6/5 and 5/4, then it's obviously in the territory of 11/9. Doesn't that mean that we are going to hear the interval "as" neither 6/5 nor 5/4, but "as" 11/9? And that we are going to thus hear Dicot as a temperament where two 11/9s equal 3/2, or in other words a 2.3.11 temperament where 243/242 vanishes? Perceptually-speaking, the two temperaments should be more or less identical (TOP dicot is <1206.410, 350.456], TOP 2.3.11 243/242 is <1200.064, 350.544]). I've always thought that this implies that only one of these two temperaments is musically "real", as I don't really understand how anyone could differentiate between the two of them compositionally or as a listener. I believe this is why Paul Erlich uses the term "exo-temperament" to describe temperaments like Dicot and Father.
>
> I do not doubt such fields of attraction do exist, but they would be based on entirely subjective or arbitrary thresholds. For example, some people hear 417 cents as a type of 5/4, but I hear it as 14/11.

Ryan, Igs is using a very limited definition of "heard as" that's a
bit different than what you might intuitively think. He's using it to
refer to the results of "free-retuning experiments" where you give
listeners a knob controlling the width of an interval, and you tune it
to something random, and tell them to retune this interval until they
feel it's maximally "in tune." It's still not clear how these
experiments really relate to something larger like a musical
composition which has things like chords, tonal centers, temporal
context, etc, nor how adaptation due to consistent bombardment with
high-entropy music might change things (I definitely hear 11/8 much
differently than when I started out, for instance).

I'm still a little bit surprised at the results of these experiments,
frankly. I should take a look at these Benade papers and see if they
really make sense. For instance, say I took a bunch of "unmusical"
listeners with no musical training and gave them a knob initially set
to a tritone of some kind, and told them to retune it until it's
maximally in tune. I'd actually be quite surprised if they honed in on
7/5 or something. Given the experimental conditions, I'd expect them
to make more dramatic changes in the sound and stop at something like
3/2 or 4/3. But maybe not.

> It is also really dependent on how we play those intervals as well. Consider playing 350 cents as a melodic interval, a brief harmonic interval, and elongated over a deep drone. In the first example, we are more likely to hear 5/4 or 6/5. In the second example, there is a better chance we will realize it is beating too much to be major or minor, but we might discard it as an unintentional mistuning. With the last example, we will very likely hear it as a neutral third.
>
> Mavila is another good example besides Father and Dicot. I don't hear the fourths in Mavila as 4/3, but as 15/11. It therefore makes more sense for me to use the more-accurate 11-limit Mabila mapping when I play around in anti-diatonic scales.

Yeah, I think in these cases you're referring more to just labels
you'd apply to the interval spectrum, which can get almost as fine as
you want. It also seems like you're talking about interval
recognition, where the beating for 350 cents would "clue you in" to
that it's not the typical "major" third so you'd call it "neutral"
instead. I also think there are things other than 5/4 you might call
"major" too. But Igs is talking entirely about this experiment.

In what sense do you hear the fourths in Mavila as 15/11?

-Mike

🔗cityoftheasleep <igliashon@...>

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

> It only means this if you define "unhearable" in a very limited sense
> as an outcome for the experiments on which you based your operational
> definition of "field of attraction."

This hypothetical is mostly for Carl, as he's the one who's positing fields of attraction most strongly. It seems to me like if you buy the idea of fields of attraction, you've got to buy everything else I said, and I want to see if there's a way around it.

> No, because in the lab experiments you talk about, 11/9 doesn't have
> its own "field of attraction" at all, I believe.

I'm going more off our various HE curves as modeling intervals that could be said to have fields of attraction. Of course under some s values, 11/9 will not appear as a local minimum. Under others it will.

> OK, now it seems like you're making further assumptions about "fields
> of attraction" which I don't agree with at all. What you said above
> about "musical realness," "the perception of music," "compositional
> differentiation," "accurate descriptors of perception" are not things
> which follow from your limited definition of "unhearable." This "heard
> as" thing so far has been given a very limited behavioral,
> non-psychoacoustic definition based on the somewhat musically sterile
> results of hypothetical lab experiments performed only with dyads.
> Once you start talking about these experiments determining "musical
> realness," especially in a "compositional" sense, you need to make
> certain assumptions about how these (very limited) experiments with
> dyads apply to the big picture of music cognition that don't make
> sense to me at all.

I'm not limiting myself just to the experiments Carl cited. What about observations of adaptive JI in free-pitched ensemble settings? What about the idea of "in-tuneness" being related to beatlessness?

I think you're reading too much into the whole "heard as" thing; we study temperament, which is based on representing JI. Not all temperaments represent JI well, and if you imagine trying to adaptively intonate a temperament without losing the character of that temperament, that poses real challenges for temperaments like Bug, Dicot, and Father. If you don't like my "heard as" terminology, consider this: how would you tune Dicot in adaptive JI? What do you do, from an adaptive JI perspective, when a single tempered interval represents multiple consonances? And if there's no way to tune a temperament in adaptive JI consistently or without losing the character of the temperament, does that not mean said temperament isn't "real" in some sense?

> Lastly, even in the ultra-limited sense of "heard as," there might be
> tunings other than POTE that let you "hear things" in a dicot-tempered
> sense. Check out the 13p val, for example: with pure octaves, the
> dicot-tempered major chord is 0-369-730. 369 cents is probably enough
> for someone under strict laboratory conditions to retune to 5/4, and
> 730 is probably enough for someone under strict laboratory conditions
> to retune to 3/2. So that would appear to be a dicot-tempered 4:5:6,
> with steps of 5/4-5/4 on the inside, and 3/2 on the outside.

I've thought of this before, too. Consider Dicot in 18-ED2, with triads 0-333.33-666.67; it's like your example, but for 6/5 instead of 5/4. What about Bug, though? Is there any tuning of Bug you can think of where the generator legitimately sounds like a 6/5, but the 4/3 still sounds like a 4/3?

-Igs

🔗Mike Battaglia <battaglia01@...>

On Fri, Jan 27, 2012 at 10:31 PM, cityoftheasleep
<igliashon@...> wrote:
> It seems to me like if you buy the idea of fields of attraction, you've got to buy everything else I said, and I want to see if there's a way around it.

The other things you said don't follow from the assumptions you've
made, nor from your stated definition of how I should interpret your
statements about hearing an interval as another interval. You'd have
to make additional assumptions, such as the non-effect of temporal
context, tonal center, modality, the futility of training, timbre,
harmonic context, scalar context, and a million other things in order
to believe that these experiments predict something like "musical
realness." You'd have to prove that those other things aren't a factor
at all. There's no serious music cognition researcher that I know of
who'd be willing to make such assumptions, because they lead to an
overly simplistic view of music cognition.

> > No, because in the lab experiments you talk about, 11/9 doesn't have
> > its own "field of attraction" at all, I believe.
>
> I'm going more off our various HE curves as modeling intervals that could be said to have fields of attraction. Of course under some s values, 11/9 will not appear as a local minimum. Under others it will.

It's not clear to me exactly how you view the HE curve as predicting
field of attraction. There are a few ways I can think of doing it. For
example, if you work out the probability distribution for an arbitrary
point on the curve, the point which tends to have the highest
probability is not, as a general rule, the nearest local minimum. But
if your hypothesis is that someone will attempt to retune an interval
so that the harmonic entropy drops, even if the dominant interval
shifts, then that would imply that the minima are terminal points for
these "fields of attraction." But if that's what you're after, then
the minima change depending on your "s" value, so for some s the
nearest minimum to 11/9 is 5/4, and for other s the nearest minimum
might be 11/9 itself.

> I'm not limiting myself just to the experiments Carl cited. What about observations of adaptive JI in free-pitched ensemble settings? What about the idea of "in-tuneness" being related to beatlessness?
>
> I think you're reading too much into the whole "heard as" thing; we study temperament, which is based on representing JI.

No, it's that I'm not reading into it enough, apparently. I make no
inferences into the whole "heard as" thing beyond what was said. We
seem to have very different viewpoints about how things work, so for
communication's sake I'm making no further assumptions beyond what
you've actually said.

You mentioned beatlessness. Well, I started off with a different
approach: first I deliberately attempted to get someone to make a
concrete statement about psychoacoustics, fields of attraction, "what
people like," and was unsuccessful. At one point, I attempted to
define "fields of attraction" purely interms of psychoacoustic
phenomena like beatlessness or virtual pitch clarity, but I was told
that that's definitively not the correct interpretation of the
concept. Instead, I was told to make no psychoacoustic assumptions at
all, but to simply reduce everything to the way that people behave in
certain, very limited experiments. And that's how I've been
interpreting your statements ever since.

Your post here now seems to be making a larger statement about the
applicability of these experiments to music cognition, which is
precisely the thing that nobody wanted to do before. So now, if you're
making further assumptions now, particularly things that have to do
with psychoacoustics, it would be helpful if you could state
explicitly what they are.

> Not all temperaments represent JI well, and if you imagine trying to adaptively intonate a temperament without losing the character of that temperament, that poses real challenges for temperaments like Bug, Dicot, and Father. If you don't like my "heard as" terminology, consider this: how would you tune Dicot in adaptive JI? What do you do, from an adaptive JI perspective, when a single tempered interval represents multiple consonances? And if there's no way to tune a temperament in adaptive JI consistently or without losing the character of the temperament, does that not mean said temperament isn't "real" in some sense?

I don't know what you mean by the "character" of a temperament. Part
of the character of mavila is that everything is flat, which I think
makes it sound nice and relaxing and chilled out. If I adaptively
retune mavila, as Kalle did with a mavila comma pump today on XA, it
doesn't sound flat anymore, so that this aspect of the sound has
changed. To answer your question, I don't think that the adaptive
mavila comma pump "isn't mavila," nor do I think that mavila major
chords don't have anything to do with 4:5:6, and I don't know of any
sense I can think of in which mavila isn't real.

This would also imply that dominant temperament isn't real, because
the tempered minor third represents multiple consonances: 6/5 or 7/6.
I don't agree with that either.

> > Lastly, even in the ultra-limited sense of "heard as," there might be
> > tunings other than POTE that let you "hear things" in a dicot-tempered
> > sense. Check out the 13p val, for example: with pure octaves, the
> > dicot-tempered major chord is 0-369-730. 369 cents is probably enough
> > for someone under strict laboratory conditions to retune to 5/4, and
> > 730 is probably enough for someone under strict laboratory conditions
> > to retune to 3/2. So that would appear to be a dicot-tempered 4:5:6,
> > with steps of 5/4-5/4 on the inside, and 3/2 on the outside.
>
> I've thought of this before, too. Consider Dicot in 18-ED2, with triads 0-333.33-666.67; it's like your example, but for 6/5 instead of 5/4. What about Bug, though? Is there any tuning of Bug you can think of where the generator legitimately sounds like a 6/5, but the 4/3 still sounds like a 4/3?

I don't know what you mean by "sounds like" a 6/5 here. To my f'd up
evil AP ears, minor thirds in Bug sound like minor thirds, and 4:5:6's
in something like 9-EDO still sort of "sound like" 4:5:6.

If your question is specifically to find a tuning for Bug in which the
tempered 6/5 dyad, by itself, would be freely retuned to 6/5 by the
majority of listeners, and the 4/3 dyad would also be freely retuned
as 4/3 by the majority of listeners, then I doubt it. But that still
says nothing about those dyads when used in larger chords.

The average listener might retune 11/9 to something else, but that
doesn't mean that 11/9 isn't "real" for them. There's still
4:5:6:7:9:11 chords.

-Mike

🔗lobawad <lobawad@...>

🔗Mike Battaglia <battaglia01@...>

🔗lobawad <lobawad@...>

🔗Mike Battaglia <battaglia01@...>

🔗cityoftheasleep <igliashon@...>

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

> The other things you said don't follow from the assumptions you've
> made, nor from your stated definition of how I should interpret your
> statements about hearing an interval as another interval. You'd have
> to make additional assumptions, such as the non-effect of temporal
> context, tonal center, modality, the futility of training, timbre,
> harmonic context, scalar context, and a million other things in order
> to believe that these experiments predict something like "musical
> realness." You'd have to prove that those other things aren't a factor
> at all. There's no serious music cognition researcher that I know of
> who'd be willing to make such assumptions, because they lead to an
> overly simplistic view of music cognition.

Now, wait just a cotton-pickin' minute. I'm not talking about nebulous concepts like "major 3rd" here. I'm talking about the ability of tempered intervals to represent rational ones. Are you suggesting that things like "temporal context, tonal center, modality, the futility of training, timbre, harmonic context, scalar context" etc. might have the power to make a 6/5 sound like a 4/3?

Let me ask you: when we say a tempered interval represents a Just one, what do you think we mean?

> But
> if your hypothesis is that someone will attempt to retune an interval
> so that the harmonic entropy drops, even if the dominant interval
> shifts, then that would imply that the minima are terminal points for
> these "fields of attraction." But if that's what you're after, then
> the minima change depending on your "s" value, so for some s the
> nearest minimum to 11/9 is 5/4, and for other s the nearest minimum
> might be 11/9 itself.

Did I not just say exactly that?!

> Your post here now seems to be making a larger statement about the
> applicability of these experiments to music cognition, which is
> precisely the thing that nobody wanted to do before. So now, if you're
> making further assumptions now, particularly things that have to do
> with psychoacoustics, it would be helpful if you could state
> explicitly what they are.

I don't think I'm making any more assumptions than anyone else who believes that "temperament" is a meaningful concept. Temperament is entirely based on the idea that you can take JI, mistune it by some amount, and still achieve a similar effect with the resulting intervals. When we create temperament mappings, we are making an explicit list of which Just intervals our tempered intervals should be "heard as"--or, "adaptively intoned as" (same difference).

> I don't know what you mean by the "character" of a temperament.

It can be understood purely quantitatively. I can't give you a hard cut-off, but if you have to substantially re-tune the intervals in the adaptation, you're probably losing the character of the temperament.

> Part
> of the character of mavila is that everything is flat, which I think
> makes it sound nice and relaxing and chilled out. If I adaptively
> retune mavila, as Kalle did with a mavila comma pump today on XA, it
> doesn't sound flat anymore, so that this aspect of the sound has
> changed. To answer your question, I don't think that the adaptive
> mavila comma pump "isn't mavila," nor do I think that mavila major
> chords don't have anything to do with 4:5:6, and I don't know of any
> sense I can think of in which mavila isn't real.

Mavila's an inaccurate temperament, but it doesn't map intervals across fields of attraction.

> This would also imply that dominant temperament isn't real, because
> the tempered minor third represents multiple consonances: 6/5 or 7/6.
> I don't agree with that either.

In some temperaments, there are musical circumstances where one interval can sound like two separate consonances--in a dominant-tempered 4:5:6:7 chord, for instance, or a semaphore-tempered 6:7:8:9. If you wanted to tune dominant temperament adaptively, you'd tune 1/1-5/4-3/2-9/5 chords to 4:5:6:7, every time, no ambiguity. That's how the temperament works. I might even guess that most people confronted with 1/1-5/4-3/2-9/5 would say that 4:5:6:7 sounds like a smoother version of the same chord, suggesting that even if they're not *playing* in dominant temperament, they're still *hearing* in it.

But if you take the abstraction further, it gets thorny--what about minor triads? Those would be problematic, from an adaptive standpoint, because dominant temperament equates 10:12:15 with 6:7:9. How would you figure out which one to choose?

> I don't know what you mean by "sounds like" a 6/5 here. To my f'd up
> evil AP ears, minor thirds in Bug sound like minor thirds, and 4:5:6's
> in something like 9-EDO still sort of "sound like" 4:5:6.

If someone played you a minor triad in Bug temperament, and asked you to tweak it so it sounds in tune, would you tune it to 10:12:15, or 6:7:9? The Bug minor 3rd is flat of a 6/5 by a huge amount, and flat of a 7/6 by much less. I would say that unequivocally suggests that a minor triad in Bug should be adaptively intoned as a 6:7:9. But if that's the case, then this isn't Bug temperament, it's 2.3.7 semiphore. But then, if those wonky Bug major triads still sound like 4:5:6, and the minors sound like 6:7:9, well holy crap 36/35 just added itself to our comma list. So we started from the abstraction of tempering out 27/25, but that perceptually "implies" 49/48 and 36/35, meaning that Bug does not exist as an independent entity and "just is" Beep...or rather, that Bug exists only as an abstraction and can't be realized in music.

Consider the following temperaments:
http://x31eq.com/cgi-bin/rt.cgi?ets=1&limit=3&key=1_1
http://x31eq.com/cgi-bin/rt.cgi?ets=1b_1c&limit=5
http://x31eq.com/cgi-bin/rt.cgi?ets=2c_1c&limit=5

They are all "real" in the abstract sense, and they all can produce tunings. But is there any way at all that you can make music in them, such that the sounds you hear will sound like they are representing what the temperament mapping says they are representing? If not, does that not mean that these temperaments are not "real" in the same sense that meantone is real?

This goes back to a conversation I had with Paul once. I wanted to argue that 690 cents is not a meantone generator, because four of them gets you to 16/13 (360 cents) while eleven of them gets you to 5/4 (390 cents), and I thought it was ludicrous to ignore the better mapping for 5/4. But Paul insisted, rightly so I think, that if I was playing major and minor triads in a 7-note MOS from the 690-cent generator, it would still be meantone because those 0-360-690 and 0-330-690 triads would still sound like they're representing 5-limit triads. He then suggested that if, on the other hand, I used a bunch of 8:12:13 chords to pump the 1053/1024 comma, I could legitimately claim it wasn't meantone. This blew my mind and I was kind of angry about it for a while and didn't want to believe it.

But the more I thought about it, the more sense it made. Temperament is not tuning, and just because a tuning is derived from some temperament, doesn't mean it actually *is* that temperament. A tuning can represent multiple things, no matter how it's derived, and it's only in music that those representations are "called forth". Temperaments are abstractions that can only be instantiated in tunings, and tunings are abstractions that are only instantiated in music.

-Igs

🔗Mike Battaglia <battaglia01@...>

On Sat, Jan 28, 2012 at 12:06 PM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > The other things you said don't follow from the assumptions you've
> > made, nor from your stated definition of how I should interpret your
> > statements about hearing an interval as another interval. You'd have
> > to make additional assumptions, such as the non-effect of temporal
> > context, tonal center, modality, the futility of training, timbre,
> > harmonic context, scalar context, and a million other things in order
> > to believe that these experiments predict something like "musical
> > realness." You'd have to prove that those other things aren't a factor
> > at all. There's no serious music cognition researcher that I know of
> > who'd be willing to make such assumptions, because they lead to an
> > overly simplistic view of music cognition.
>
> Now, wait just a cotton-pickin' minute. I'm not talking about nebulous concepts like "major 3rd" here. I'm talking about the ability of tempered intervals to represent rational ones. Are you suggesting that things like "temporal context, tonal center, modality, the futility of training, timbre, harmonic context, scalar context" etc. might have the power to make a 6/5 sound like a 4/3?

No, of course not. I said nothing about major thirds or categorical
perception either. But they obviously do have the power to make a 13/9
sound like a 13/9.

> Let me ask you: when we say a tempered interval represents a Just one, what do you think we mean?

Igs, I'll tell you what: I found this Benade book online for free, and
I'm going to write a post explaining it with a link so you can read it
yourself. It's not anywhere as long, or complicated, or drawn out as
you might think - it's like 2-3 pages long and pretty much in layman's
terms. If, after you read that, you still want me to respond to this,
let me know and I'll come back here and finish this post. At this
point, there's nothing more worthwhile in this conversation than
discussing the relevant literature directly.

-Mike