Yahoo Tuning Groups Ultimate Backup tuning Question on Consistency

On Fri, Jan 6, 2012 at 2:57 PM, cityoftheasleep <igliashon@...> wrote:
>
> Is 24-ET consistent on the 2.3.5.11.13.17.19.31.37.43.57.59 subgroup? How about 17-ET on 2.3.7.11.13.23.25.41.59.61? Is there a quick way to check that?
>
> If so, then 24-ET would allow 16:17:18:19:20:22:24:25:26:27:30:31:33:37:39:43:45:51:57:55:59 chords, which is f*$^%ing insane--you could play 7/8 of all the notes in the tuning simultaneously and it would approximate a chunk of the harmonic series (pretty accurately, too)! Not that I'd probably ever use a 21-note chord, but that allows for an awful lot of subgroup possibilities. In 17, you have the 2.3.7.11.13.23.25.41.59.61 subgroup (assuming it's consistent), meaning 16:18:21:22:23:24:25:26:27:28:33:39:41:49:59:61--16/17ths of the tuning could be played simultaneously and approximate a chunk of the harmonic series (though not quite as accurately) as 24, I think...).
>
> Is there any benefit to thinking about ETs in this way, do you think?

Why does consistency matter in this case? Just pick the best val and
roll with it.

Any EDO is going to sync up with a whole ton of harmonics down the
road, far outside of the realm of what most people are considering
now. If you're going to really going to look at things like the
61-limit, you can keep going on forever and find an infinite number of
harmonics that get arbitrarily close to notes in 24-EDO. But, the only
way you're ever going to get something like 59/45 to output that
actual VF is to use it in the context of some giant 21-note chord like
you mentioned. So you can't just cop out and play random dyads and be
like "yay, 61-limit harmony!"

Keenan actually found a list of vals, with octave stretch, which are
consistent with their own TOP tuning in the -infinite- limit, so you
might want to look at some of those.

OK, so what do you do with this? Algorithmically, you could generate a
subgroup containing all of the harmonics that are deemed to "appear"
in some EDO, like 24-EDO, up to infinity. Then, you can generate a
huge, infinitely large, single chord, containing the 24-EDO tempered
version of those harmonics, making them drop off in volume as
successive harmonics increase in complexity, and also perhaps in
error. This would lead to the most concordant sound possible in
24-EDO. This would be rather difficult to play in real life, however,
because it would require an infinite amount of fingers and an infinite
amount of control over the volume over each note.

In general though, one can take from this the rule of thumb that if
you ever want to make use of really complex harmonics, and have them
actually generate the VF that you're analyzing them as generating, you
need to play really large chords. So you could just play huge frickin
chords all the time, chords which have like 16 notes or so. You might
still want to consider dropping the amplitude on the higher or more
inaccurate notes, and using a really mellow timbre.

As to how much error can be tolerated for really complex harmonics in
the context of a gigantic chord - I have no idea, poke around and
figure it out. I almost wish Gene would just go nuts one day and write
31-limit music just to see what'd happen.

If you put all of the pieces together, picking a suitable tuning and
avoiding error and so on, this would lead to a very interesting and
exotic style of music that's very different from what we're used to
now. Chords will effectively sound entirely like timbres, and chord
progressions would sound like timbres which end up getting broken into
little pieces and shifted around in parallax relative to one another,
forming new timbres - "timbre progressions," perhaps. You probably
won't be able to pick out individual notes anymore. Which is
interesting, because right now we consider a "note" to be basically a
chunk of the harmonic series, so the basic unit of music-making might
not be a "note" in this style, but rather a larger chunk of the
harmonic series; a "piece of timbre," so to speak, which is combined
with other timbral pieces to form larger timbres (which is what we're
doing now with "notes" and "chords"). I have no idea what would mean
for scales or for melody.

-Mike

🔗gbreed@...

You can't be infinite limit consistent with approximations. Any finite error will pile up to exceed a half step eventually

Graham

------Original message------
From: Mike Battaglia <battaglia01@...>
To: <tuning@yahoogroups.com>
Date: Friday, January 6, 2012 4:27:44 PM GMT-0500
Subject: Re: [tuning] Question on Consistency

Why does consistency matter in this case? Just pick the best val and
roll with it.

Keenan actually found a list of vals, with octave stretch, which are
consistent with their own TOP tuning in the -infinite- limit, so you
might want to look at some of those.

-Mike

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🔗Mike Battaglia <battaglia01@...>

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

🔗Carl Lumma <carl@...>

It's remarkable that a half-dozen of the smartest people
I've ever known spent 4+ years doing it wrong.

The hangup was thinking that things like "24-tone equal
temperament" were atomic. It didn't occur to us that
there are MANY different rank 1 TEMPERAMENTS compatible
with the TUNING you get dividing the octave 24 times.

So the hangup was ultimately caused by a failure to
distinguish TUNINGS and TEMPERAMENTS. This abstraction
is probably Gene's greatest contribution to the whole
thing. And it's why I so vigorously defend separate
definitions every time the definitions thread comes up.
People argue that definitions be "friendly" to whatever
they learned growing up in band class or something. No!
Definitions influence thinking and they are important!

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> IOW, inconsistency wasn't something wrong with certain
> temperaments, it was something wrong with the way we
> were measuring error!
>
> It's a great example of how scientific progress occurs...
> the kind of realizations it takes, and how obvious they
> seem in retrospect. -Carl
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
> >
> > The whole point of "consistency" is that naive error
> > calculations didn't always reflect regular mapping.
> > So you were meant to ignore temperaments where that
> > happened. Gene came along and said it was better to
> > measure error in a way that DID enforce regular mapping.
> > Then you could consider all temperaments and compare
> > them. If there was a moment when RMP officially exited
> > the womb, that would be it. -Carl
>

🔗Mike Battaglia <battaglia01@...>

On Fri, Jan 6, 2012 at 5:26 PM, Carl Lumma <carl@...> wrote:
>
> It's remarkable that a half-dozen of the smartest people
> I've ever known spent 4+ years doing it wrong.
>
> The hangup was thinking that things like "24-tone equal
> temperament" were atomic. It didn't occur to us that
> there are MANY different rank 1 TEMPERAMENTS compatible
> with the TUNING you get dividing the octave 24 times.
>
> So the hangup was ultimately caused by a failure to
> distinguish TUNINGS and TEMPERAMENTS. This abstraction
> is probably Gene's greatest contribution to the whole
> thing. And it's why I so vigorously defend separate
> definitions every time the definitions thread comes up.
> People argue that definitions be "friendly" to whatever
> they learned growing up in band class or something. No!
> Definitions influence thinking and they are important!

Thanks for explaining this. I have a few comments:

1) OK, but this is precisely why I don't like the name "24-ET." People
sometimes talk about "the difference between 24-EDO and 24-ET." I
totally understand what you're saying, but what exactly is 24-ET? The
7-limit patent val? The 7-limit val with lowest error? If we find a
better error function than TE next year, will it all change?

2) For the record, I think that some aspects of what you said -
missing the forest for the trees - apply to the way some people treat
the relationship between ratios and categories. That's why I'm so
fascinated with them. It took me a month of playing 11-limit harmony
in 22-EDO for the sound of intervals like 11/8 or 9/7 by itself to
completely change. It took me another month of playing in 16-EDO for
the sound of the 675 cent fifths to change. This is what I keep saying
was Ron's insight in exploring 16-EDO (who turned him onto that
tuning, anyway?). In retrospect the notion that out of the infinitude
of EDOs (or even temperaments) out there, that only a tiny fraction
are "musically useful" because of "psychoacoustics," was such a
terrible limitation that I can't believe I ever thought that was the
case. It limited the type of training that I was willing to engage in,
and hence limited the results I got from such training, which finally
circularly reinforced my limited psychoacoustic ideas that this is
"just the way things are."

3) I've since come around that things work more easily if 14-EDO is a
"tuning system" which implements the 7p "temperament," but then I wish
that we had a linear algebra-based approach to looking at untempered
"tuning systems." Maybe we could get what you called "scale theory"
out of the dark ages then.

4) Since the theme of this last month has been to heap praise on
Keenan Pepper, I think it's worth noting that he's the first person in
recent memory to stop arguing over names and definitions, just use
whatever people want, and continue to pursue the goal of applying
mathematics to music theory. And that spirit has permeated almost
every discussion on tuning-math since then, and I hope it continues.

-Mike

🔗genewardsmith <genewardsmith@...>

🔗gbreed@...

Yes, if you can get the words to do enough work for you then you can prove anything.
Consistency means there's a mapping such that no interval has an error greater than half a scale step. You can generalize that to get error times complexity badness. No need for patent vals.
The old definition of consistency still works fine. Nothing about the regular mapping paradigm abolishes odd limits.

Graham

------Original message------
From: Carl Lumma <carl@...>
To: <tuning@yahoogroups.com>
Date: Friday, January 6, 2012 10:00:23 PM GMT-0000
Subject: Re: [tuning] Question on Consistency

The question of consistency is, in its most general form,
whether the patent val is the optimal one. For TOP damage,
Dr Pepper did indeed find that there are certain octave
sizes that have this property in the infinity-limit. Well,
he didn't prove it, but I busted my dual-core trying to
find a counterexample and couldn't.

The more specific definition of "consistency" is outdated
now that we RMP, in which everything is consistent according
to this older definition.

-Carl

--- In tuning@yahoogroups.com, "gbreed@..." <gbreed@...> wrote:
>
> You can't be infinite limit consistent with approximations.
> Any finite error will pile up to exceed a half step eventually
>

------------------------------------

🔗Mike Battaglia <battaglia01@...>

Gene,

With all due respect, I wish you'd stop making these inferences into
what I'm saying, beyond what I actually say, and then respond with
these colorful admonishments of how bad what I'm saying is. I
understand there's no malice on your part but from my perspective I
just keep fending off strawman after strawman, never feeling as though
I manage to successfully transmit any information in these
conversations. Especially because I don't really have any solid ideas,
nor a theory: I have nothing but a series of observations that I enjoy
talking about with likeminded people, and I'm openly admitting that I
don't know what the big picture is, which is partly why I'd like to
talk about it.

But any time I even mention something that might matter other than
ratios, you seem to extrapolate from it a more extreme stance than I
am actually taking, take it out of context and then demolish it. And
it makes communication difficult if you assume that I am saying
something far stupider than I actually am any time I say anything. In
this case, the response you wrote doesn't seem to be related to what I
said, so I can only assume you've misunderstood and will start over.

I'm stating that a group of us have discovered that if you spend some
time with 675 cent fifths, you get used to them, especially if you use
timbres that are a bit less harsh. They will never sound as pure and
open as just 3/2's, but they no longer sound actively "bad," and hence
can be used as vehicles for music making that don't invalidate the
usefulness of an entire tuning like 16-EDO. What part of this do you
take objection to? Is it that you think I'm just lying and full of
shit? Are you claiming that some aspect of some theory somewhere
proves that this isn't possible? Is it that you don't care if this is
possible because you already know what you like and you're sticking to
it? What?

On Fri, Jan 6, 2012 at 7:05 PM, genewardsmith
<genewardsmith@sbcglobal.net> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> > In retrospect the notion that out of the infinitude
> > of EDOs (or even temperaments) out there, that only a tiny fraction
> > are "musically useful" because of "psychoacoustics," was such a
> > terrible limitation that I can't believe I ever thought that was the
> > case.
>
> You speak of this as a strange, new idea when in fact it is extremely common--in fact, in good measure, the whole microtonal thing has been a reaction against this dogma. Which raises the question--if you think psychoacoustics can and should be ignored because it all comes down to what we are used to hearing, why do you talk about it, and how did you end up on this list?

🔗genewardsmith <genewardsmith@...>

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

On Fri, Jan 6, 2012 at 8:20 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > I'm stating that a group of us have discovered that if you spend some
> > time with 675 cent fifths, you get used to them
>
> Another group of us has discovered that if you spend your whole life with 400 cent major thirds, you never grow to think they are quite as good as a 386 cent third.

OK, I can accept that. I also said, right below this, that they will
never sound as pure and open as JI 3/2's. It's just that they stop
being actively "bad"

The correct way to synthesize this sort of observation is that
individual tolerance to tuning error varies. So since that's the case,
I don't understand why you sometimes say things like "675 cents is
just not a good fifth any way you slice it," or say things about how
we're all just playing 16-EDO because we care about shredding and
being cool and so on. Those are these sweeping generalizations of the
sort that you accuse me of making.

> especially if you use
> > timbres that are a bit less harsh. They will never sound as pure and
> > open as just 3/2's, but they no longer sound actively "bad," and hence
> > can be used as vehicles for music making that don't invalidate the
> > usefulness of an entire tuning like 16-EDO. What part of this do you
> > take objection to?
>
> I don't LIKE 675 cent fifths, and since all you are telling me is that with enough effort I can learn not to dislike them as much, why should I bother to try?

I'm not quite saying that. You've said this before: that you know what
you like, and that's your right. That's why, when I wrote what I did
above, I deliberately said that there is a group of us who have
learned that we did come to like it. Therefore the statement "675 cent
fifths sound BAD because of psychoacoustics" is not absolutely true,
but only for some people.

> Is it that you think I'm just lying and full of
> > shit?
>
> I think you have no basis for claiming if I just listened to 675 fifths for a year, I'd grow to like it. That's what they told me about margarine when I was small. Yum, those trans fats! You just need to get used to them.
>
> It's all theory, Mike. And as I pointed out, not a new one.

The basis I have for claiming that you, specifically, will come to
like it, is flimsy. But the basis for saying that an arbitrary person
will never come to like it is nonexistent, and has evidence against
it.

-Mike

🔗Carl Lumma <carl@...>

Mike wrote:

> 1) OK, but this is precisely why I don't like the
> name "24-ET." People sometimes talk about "the difference
> between 24-EDO and 24-ET." I totally understand what you're
> saying, but what exactly is 24-ET? The 7-limit patent val?
> The 7-limit val with lowest error? If we find a better
> error function than TE next year, will it all change?

I don't think the folks who coined and promote "EDO" do it
to make this important abstraction. They do it because they
don't want a temperament OR a tuning of one, but rather just
an 'anything goes' bunch of notes. At any rate I hardly
think it's an improvement on "ET". "ED2" might be an
improvement and I've been considering switching to it.

> 2) For the record, I think that some aspects of what you
> said - missing the forest for the trees - apply to the way
> some people treat the relationship between ratios
> and categories.

To whom are you referring!?

> that only a tiny fraction are "musically useful" because of
> "psychoacoustics," was such a terrible limitation that I can't
> believe I ever thought that was the case.

I can't believe it either, since none of the theory here
uses such an assumption, and in case there was any doubt,
I admonished you against it from the time you first joined
the list, and about a dozen times since.

It's a bit like saying meat isn't the only important food.
Of course meat isn't the only important food, but it IS an
important food. It remains important even if you're a
vegetarian. It's especially important if you're vegan.
To say meat isn't an important food is to definitely join
the ranks of nihilism. And from this day on I will quote
the Big Lebowski whenever you or Igs make some remark about
how 13 sounds just as concordant as 31.

My idea of a "major third" is a gestalt or categorical
notion I learned through a lifetime of experience with
diatonic music. It wraps up memories of that music, cliches
of that music, emotions I've had hearing and performing it.
Contained in it are even motor memories of how to execute a
major third with my vocal chords, with my lips when playing
the trumpet, with my hands on a keyboard, etc.

With enough training I can learn new categories based on
other scales, other music, other experiences and emotions
and so on. If the new categories happen to fall on
discordances, I can get accustomed to them and learn to
appreciate them.

What I cannot do is make 21:16 sound more concordant than
3:2. I can like 21:16 better than buttered toast, but next
to 3:2 it will always sound discordant.

The fact that 3:2 is more concordant may itself be due to
training -- a very special kind that takes place in the womb
and as an infant, when my mother's voice was the most
important thing in the universe and connections in my brain
were being pruned at a rate I'll never achieve again.

If I go live in a cave and listen to nothing but 21:16 for
weeks on end, with a synth whose timbre emphasizes 21:16,
my brain may recruit some of the neurons that had been doing
3:2 and maybe I could flip it around. But I doubt it. When
I switched to Dvorak I forgot QWERTY (which I first learned
at age 14). But people who go to China and speak nothing but
Chinese don't forget their native language (first learned at
age 0).

And that's assuming it's learned. It's possible that 3:2
is just a lot easier to entrain a network of oscillators to
than 21:16. It may may be a physical limitation of neurons
and their networks to 'perform' such ratios.

-Carl

🔗Herman Miller <hmiller@...>

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

On Fri, Jan 6, 2012 at 9:39 PM, Carl Lumma <carl@...> wrote:
>
> Mike wrote:
>
> > 1) OK, but this is precisely why I don't like the
> > name "24-ET." People sometimes talk about "the difference
> > between 24-EDO and 24-ET." I totally understand what you're
> > saying, but what exactly is 24-ET? The 7-limit patent val?
> > The 7-limit val with lowest error? If we find a better
> > error function than TE next year, will it all change?
>
> I don't think the folks who coined and promote "EDO" do it
> to make this important abstraction. They do it because they
> don't want a temperament OR a tuning of one, but rather just
> an 'anything goes' bunch of notes. At any rate I hardly
> think it's an improvement on "ET". "ED2" might be an
> improvement and I've been considering switching to it.

I remember Igs said he was going to start using it because then we can
say that 13-EDO has 2/1-oct period, and 13-EDT has 3/1-oct period,
whereas 13-ET is ambiguous. Then I heard ED2 and ED3 used as
alternatives. I thought that was a good idea so I started using it.

Then I remember hearing someone, like Paul, talk about the difference
between 24-EDO and 24-ET, and not to get them confused, and that was
the first time I heard of that. And I've heard people here and there
make the same sort of distinction. And I think it's a bad one unless
ET specifically means "the patent val of whatever division you just
wrote with 2/1 as period."

> > 2) For the record, I think that some aspects of what you
> > said - missing the forest for the trees - apply to the way
> > some people treat the relationship between ratios
> > and categories.
>
> To whom are you referring!?

I wasn't talking about you, just a general vibe in the community.

> It's a bit like saying meat isn't the only important food.
> Of course meat isn't the only important food, but it IS an
> important food. It remains important even if you're a
> vegetarian. It's especially important if you're vegan.
> To say meat isn't an important food is to definitely join
> the ranks of nihilism. And from this day on I will quote
> the Big Lebowski whenever you or Igs make some remark about
> how 13 sounds just as concordant as 31.

I don't think I ever said that. I said that 13 can stop sounding like
crap if you get used to it. And, I also happen to think that it can
sound just as "pleasant" as 31 in the right circumstances, because
there's more to musical pleasantness than playing accurate otonal
chords.

If you doubt the power of very, very sharp fifths to sound very, very
beautiful, bright, and -not- dissonant under the right circumstances,
I totally disagree in every way possible. But to the extent that the
word "concordant" means "activates the missing fundamental
phenomenon," and after our recent conversation on Facebook I'm no
longer sure that it does to you, I'll obviously never make the claim
that 13 does that as well as 31.

> My idea of a "major third" is a gestalt or categorical
> notion I learned through a lifetime of experience with
> diatonic music. It wraps up memories of that music, cliches
> of that music, emotions I've had hearing and performing it.
> Contained in it are even motor memories of how to execute a
> major third with my vocal chords, with my lips when playing
> the trumpet, with my hands on a keyboard, etc.

This is true to the point that when I went to Paul's place up on
Boston, and I played his Ensoniq keyboard, I was like "wow, this
tuning is great, what is it?" And he was like "12 notes of mavila." I
noticed at that point that the major fingerings I was playing were
actually producing minor chords, and then my brain rewired itself and
they stopped sounding "happy" and major and started sounding "sad" and
minor. I found that to be significant.

> With enough training I can learn new categories based on
> other scales, other music, other experiences and emotions
> and so on. If the new categories happen to fall on
> discordances, I can get accustomed to them and learn to
> appreciate them.
>
> What I cannot do is make 21:16 sound more concordant than
> 3:2. I can like 21:16 better than buttered toast, but next
> to 3:2 it will always sound discordant.

Paul on Facebook said that the word "discordance" basically means
"dissonance apart from any musical context." I'm going to roll with
that definition for now.

Consider the Bach retuning I posted in 75-EDO. Go listen to that, and
tell me if you still can make out tritone resolutions and so on. I
definitely can, at least as long as I can make the scale structure
out. I hear major as happy, minor as sad, tritones as resolving, etc.
In this case, the major thirds in the above example are rather close
to 21/16, and the diminished fourths are rather close to 3/2, and in
the context of the posted example the major thirds are consonant and
the diminished fourths are dissonant.

One way to explain this is that I'm just remembering the sound of 3/2
for the generator, and remembering the sound of 7/5 or some unresolved
crap for the tritone, and projecting that onto the 75-EDO map. That's
one hypothesis, but I don't think it's conclusively proven, and I'm
not sold on it. There could be something else at work that has to do
with the melodic structure which we don't understand. There could be
another item of data that goes into the "major third" bucket, other
than 5/4-ness, that could cause a pleasant sensation when major thirds
are played. Any such thing that could possibly exist, the discovery of
which would surely revolutionize our little corner of science, would
be completely missed by assuming the truth of that assumption and not
considering if music is possibly a bit stranger than we think.

So now, the question is: assume a listener is a native 75-EDO
listener, and we play a 3/2. They then categorize it as an augmented
fourth, and it sounds like a dissonant tritone which happens to
generate a strong VF. Then we play a 21/16, which they categorize as a
major third, and it sounds like a consonant major third which happens
to not generate a strong VF. To them, this is something they're
hearing as an isolated dyad apart from any fragment of music, so it
reasonably fits into the definition of "concordance" above. And it may
be that "discordance"

> If I go live in a cave and listen to nothing but 21:16 for
> weeks on end, with a synth whose timbre emphasizes 21:16,
> my brain may recruit some of the neurons that had been doing
> 3:2 and maybe I could flip it around. But I doubt it. When
> I switched to Dvorak I forgot QWERTY (which I first learned
> at age 14). But people who go to China and speak nothing but
> Chinese don't forget their native language (first learned at
> age 0).

What I know is that in the context of that 75-EDO Bach composition,
21/16 is consonant and 3/2 is dissonant. Again, you might argue it's
because I'm "remembering" 5/4 and 3/2, but how do we know? That would
imply some kind of "imprinting" hypothesis whereby categories are
associated with ratios. I've wrote about that possibility on here
before, but I have my reservations about it.

-Mike

🔗Mike Battaglia <battaglia01@...>

🔗cityoftheasleep <igliashon@...>

🔗Mike Battaglia <battaglia01@...>

On Sat, Jan 7, 2012 at 12:55 AM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> > And from this day on I will quote
> > the Big Lebowski whenever you or Igs make some remark about
> > how 13 sounds just as concordant as 31.
>
> 8:11:13:17:21 chords in 13 are more concordant than the same tuned in 31. To me, concordance is the texture of partials of multiple tones "locking in". If I can hear a "locking in", I call something concordant. It's quite difficult for me to evaluate degrees of concordance, because I either hear it or I don't (I think).

For clarity's sake to Carl, this is not quite the same thing I'm
talking about. Igs is using the word concordance differently than I
am. So be sure to keep my statements separate from Igs' statements in
your reply. We should perhaps make sure we're all agreed on a common
definition of what concordance actually means.

I don't think that 8:11:13:17:21 chords in 13-EDO are more concordant
than 4:5:6 chords in 31-EDO. I also don't think that 13-EDO's fifths
are as concordant as 31-EDO's.

But I think they're just as beautiful as 31-EDO's fifths. They're
beautiful in a different way, for whatever reason, perhaps partly
psychoacoustic and partly learned and partly something else. And, I
think that this beauty can be used to treat them on a higher, more
abstract level as a "consonant" interval. This is in opposition to the
way that justly-intoned 7/5's, which are more concordant, can be
snapped into a mental frame of reference where they're somehow
dissonant.

But I don't claim that 738 cent fifths are "concordant" in a
psychoacoustic sense, nor do I claim that they need to be to be
"consonant" in a musical sense.

-Mike

🔗Mike Battaglia <battaglia01@...>

🔗cityoftheasleep <igliashon@...>

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

> For clarity's sake to Carl, this is not quite the same thing I'm
> talking about. Igs is using the word concordance differently than I
> am. So be sure to keep my statements separate from Igs' statements in
> your reply. We should perhaps make sure we're all agreed on a common
> definition of what concordance actually means.

That would be a great idea. What's problematic about my description of it, to you?

> I don't think that 8:11:13:17:21 chords in 13-EDO are more concordant
> than 4:5:6 chords in 31-EDO. I also don't think that 13-EDO's fifths
> are as concordant as 31-EDO's.

Neither do I! Obviously I wouldn't use 13-ED2 for the same things that 31-ED2 is good for. Or at least, I *hope* that's obvious?

> But I think they're just as beautiful as 31-EDO's fifths.

That's like comparing a Picasso (or perhaps a Pollock) to a Monet!

But in any case, look at what happens to 31-ED2 if you play in the 13-note MOS generated by the ~21/16...31 can actually be used to sound basically just like 13, so it's definitely capable of the same kind of "nihilism".

> But I don't claim that 738 cent fifths are "concordant" in a
> psychoacoustic sense, nor do I claim that they need to be to be
> "consonant" in a musical sense.

I don't claim that either, though if you play them a couple octaves up then it gets pretty hard to hear any discordance. Also if you're in 26-ED2 and you play an approximate 16:28:49, you can get 1938 cents to sound surprisingly smooth.

But one thing I've always said is that beating is relaxing. Ever play with a set of tibetan prayer bells? Or do a gong meditation? You hear all sorts of partials clashing with each other, and it induces a trance-like state in most people, including myself. I can get a very similar effect from 13-ED2, and that's the direction I've been going with it lately. It's a very different kind of relaxing than you get with meantone.

-Igs

🔗Mike Battaglia <battaglia01@...>

On Sat, Jan 7, 2012 at 10:52 AM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > For clarity's sake to Carl, this is not quite the same thing I'm
> > talking about. Igs is using the word concordance differently than I
> > am. So be sure to keep my statements separate from Igs' statements in
> > your reply. We should perhaps make sure we're all agreed on a common
> > definition of what concordance actually means.
>
> That would be a great idea. What's problematic about my description of it, to you?

Your definition referred to partials "locking in," which I assume
means chords sharing common partials and so on. My definition doesn't
refer to partials at all, and in that regard even chords made of sine
waves can be concordant.

There are two definitions of concordance I've seen thrown around with
endless variations

1) The end result "pleasantness" of a sound apart from its musical context
2) The extent to which a sound can clearly activate a single virtual fundamental

My problem with assuming the first one naively is that we don't know
what, exactly, we're measuring. We're measuring things like VF
strength and lack of beating, for sure, but we might also be measuring
OCD automatic categorization effects that might happen when you hear
an interval. For example, I used to prefer 1000 cents to 7/4 because I
knew (on a preconscious level) I couldn't split it into two "perfect
fourths," nor could I do all of the other things that I was used to
doing in 12-EDO. So although I could hear 7/4 as more concordant, I
also heard it as "wrong" at the time. And even aside from this obvious
and intuitive example, there might be a host of deeper patterns of
learned behavior which influence our perception of the consonance and
dissonance of an interval without us knowing it, literally in a manner
completely independent of the concordance of that interval. If you
managed to hear the usual diatonic structure in my 75-EDO Bach
retuning example, and managed to hear tritones resolving and all that,
then you know what I'm talking about, even if you don't know you know
it.

#2 gets around that problem, but is it what we want? Are we also
looking to measure beating and periodicity buzz and stuff as well? Is
it too limiting, and is there just a bigger picture that we're trying
to measure which is some weighted average of the overall effect of
accurate, simple ratios on the auditory sense?

I don't care what definition we pick, but are we all talking about the
same thing?

> > But I think they're just as beautiful as 31-EDO's fifths.
>
> That's like comparing a Picasso (or perhaps a Pollock) to a Monet!

Sure, what's wrong with that? Except I hear the 13-EDO fifths as being
akin to Monet; they're like an impressionist watercolor, and use broad
strokes of shades of color to create a certain mood or ambiance. On
the other hand, the 31-EDO fifths are more like a Michaelangelo
painting, with lots of details and everything perfectly defined, etc.

> > But I don't claim that 738 cent fifths are "concordant" in a
> > psychoacoustic sense, nor do I claim that they need to be to be
> > "consonant" in a musical sense.
>
> I don't claim that either, though if you play them a couple octaves up then it gets pretty hard to hear any discordance. Also if you're in 26-ED2 and you play an approximate 16:28:49, you can get 1938 cents to sound surprisingly smooth.
>
> But one thing I've always said is that beating is relaxing. Ever play with a set of tibetan prayer bells? Or do a gong meditation? You hear all sorts of partials clashing with each other, and it induces a trance-like state in most people, including myself. I can get a very similar effect from 13-ED2, and that's the direction I've been going with it lately. It's a very different kind of relaxing than you get with meantone.

All of these things are true, but for me it's just that I like the
sound of a really sharp fifth. It's a different sort of interval; it
just sets a mood or atmosphere and that's it. This is in contrast to
the usual fifth, which doesn't seem to add any sort of emotional
character, but rather "strengthens" the sound of whatever chord you
use it in - so much that omitting the fifth is rather common in common
practice music. I'm not sure if I'm talking about "3/2" or "fifth"
here.

-Mike

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

🔗cityoftheasleep <igliashon@...>

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

> Your definition referred to partials "locking in," which I assume
> means chords sharing common partials and so on. My definition doesn't
> refer to partials at all, and in that regard even chords made of sine
> waves can be concordant.

I rarely hear chords made up of sine waves as concordant or discordant, unless there are critical band effects happening. Harmonic and inharmonic, sure. But if chords made up of sines can be discordant, then that means timbres can be discordant, which seems confused. There are harsh, unpleasant timbres out there to be sure--but calling them discordant seems a misuse of the word.

> There are two definitions of concordance I've seen thrown around with
> endless variations
>
> 1) The end result "pleasantness" of a sound apart from its musical context

That's the one I like.

> 2) The extent to which a sound can clearly activate a single virtual fundamental

That one I would prefer to call "harmonicity" or something.

> My problem with assuming the first one naively is that we don't know
> what, exactly, we're measuring. We're measuring things like VF
> strength and lack of beating, for sure, but we might also be measuring
> OCD automatic categorization effects that might happen when you hear
> an interval.

That's not really a problem as long as A) we have a large-enough sample size to control for individual idiosyncrasies and B) we find a model that fits the data and successfully predicts further results. The "lack of beating" model we know to be problematic because there are Setharesian spectrally-matched chords that sound discordant but don't beat. I suspect this is because the timbre of these chords is innately unpleasant, and people are confusing the unpleasantness of the timbre with the discordance of the chords. But that's just me.

> For example, I used to prefer 1000 cents to 7/4 because I
> knew (on a preconscious level) I couldn't split it into two "perfect
> fourths," nor could I do all of the other things that I was used to
> doing in 12-EDO. So although I could hear 7/4 as more concordant, I
> also heard it as "wrong" at the time.

But you still heard it as more concordant--so it seems even in that naive state, you were able to separate your OCD categorization from your perception of concordance.

> And even aside from this obvious
> and intuitive example, there might be a host of deeper patterns of
> learned behavior which influence our perception of the consonance and
> dissonance of an interval without us knowing it, literally in a manner
> completely independent of the concordance of that interval.

It's a good thing we're not talking about consonance and dissonance (yet)!

> #2 gets around that problem, but is it what we want? Are we also
> looking to measure beating and periodicity buzz and stuff as well? Is
> it too limiting, and is there just a bigger picture that we're trying
> to measure which is some weighted average of the overall effect of
> accurate, simple ratios on the auditory sense?

#2 is something I don't want to bring into concordance/discordance. For while Paul is fond of mentioning the difference between utonal and otonal chords, there is a similarity that is also important to note. I'd say utonal chords are concordant but inharmonic. What do you think of that?

> I don't care what definition we pick, but are we all talking about the
> same thing?

Depends. Can we all agree with what I wrote above?

> > That's like comparing a Picasso (or perhaps a Pollock) to a Monet!
>
> Sure, what's wrong with that?

Clearly, you did not go to art school ;->. It's a whole different kind of beauty, and it's inappropriate to compare the two because of this difference. Someone who likes the beauty of a Monet or a Michaelangelo may not like the beauty of a Pollock or Picasso.

-Igs

🔗Mike Battaglia <battaglia01@...>

On Sat, Jan 7, 2012 at 12:33 PM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > Your definition referred to partials "locking in," which I assume
> > means chords sharing common partials and so on. My definition doesn't
> > refer to partials at all, and in that regard even chords made of sine
> > waves can be concordant.
>
> I rarely hear chords made up of sine waves as concordant or discordant, unless there are critical band effects happening. Harmonic and inharmonic, sure. But if chords made up of sines can be discordant, then that means timbres can be discordant, which seems confused. There are harsh, unpleasant timbres out there to be sure--but calling them discordant seems a misuse of the word.

You seem to have some notion in your head about what concordant or
discordant means, but I don't know what it is. Concordant is a term
that we're trying to define, so for me to propose a definition and for
you to then say that you don't hear that definition as being
"concordant" means you have some other idea of what concordant means.
What is it?

The way I define concordance seems to be what you're calling "harmonicity."

> > My problem with assuming the first one naively is that we don't know
> > what, exactly, we're measuring. We're measuring things like VF
> > strength and lack of beating, for sure, but we might also be measuring
> > OCD automatic categorization effects that might happen when you hear
> > an interval.
>
> That's not really a problem as long as A) we have a large-enough sample size to control for individual idiosyncrasies and B) we find a model that fits the data and successfully predicts further results.

We would need a large enough sample size to control for culture-wide
idiosyncrasies. We don't have that.

Assuming that we do find that, any study measuring preferences like
that still wouldn't prove anything fundamental about psychoacoustics
or about music cognition, or invalidate that learned factors beyond
the prenatal ones that Carl mentioned factor into the end pleasantness
of a sound even across cultures. It would only be an epidemiological
study that gives a statistical average of the sounds that people tend
to like circa 2011. It says nothing about why those results are the
way they are, whether they'd change if a significantly new form of
music was invented, the potential for them to change longitudinally
with training, etc, unless you actually measure that.

Also, how useful you'd find the information from this study would
depend on your personal goals and compositional style. I personally
don't care at all what the preferences of a Reasonable Person with 2.6
kids are, because I'm a trained musician who already appreciates music
significantly above the norm and I joined this list to dig further
into that. I care more about pushing the limits of my own perception,
and finding ways to take people along with me, than about figuring out
what people already like and leaving it at that.

> > For example, I used to prefer 1000 cents to 7/4 because I
> > knew (on a preconscious level) I couldn't split it into two "perfect
> > fourths," nor could I do all of the other things that I was used to
> > doing in 12-EDO. So although I could hear 7/4 as more concordant, I
> > also heard it as "wrong" at the time.
>
> But you still heard it as more concordant--so it seems even in that naive state, you were able to separate your OCD categorization from your perception of concordance.

I heard it as what I called "concordant" from my second definition,
and what you called "harmonic" in your definition. I could hear the
periodicity buzz and all that, but it still sounded "wrong."

> > And even aside from this obvious
> > and intuitive example, there might be a host of deeper patterns of
> > learned behavior which influence our perception of the consonance and
> > dissonance of an interval without us knowing it, literally in a manner
> > completely independent of the concordance of that interval.
>
> It's a good thing we're not talking about consonance and dissonance (yet)!

We may be, without realizing it, when we talk about "pleasantness
absent an explicit musical context."

> #2 is something I don't want to bring into concordance/discordance. For while Paul is fond of mentioning the difference between utonal and otonal chords, there is a similarity that is also important to note. I'd say utonal chords are concordant but inharmonic. What do you think of that?

I don't care what we call it. If we're going to call concordance
something like overall pleasantness, though, we then need a term for
the things that are really are concretely and psychoacoustically
measurable.

> > I don't care what definition we pick, but are we all talking about the
> > same thing?
>
> Depends. Can we all agree with what I wrote above?

What is concordance - the end pleasantness produced by a dyad for an
arbitrary listener, even if that incorporates learned factors for that
listener? And the thing that has to do with VFs and beating is
"harmonicity?"

> > > That's like comparing a Picasso (or perhaps a Pollock) to a Monet!
> >
> > Sure, what's wrong with that?
>
> Clearly, you did not go to art school ;->. It's a whole different kind of beauty, and it's inappropriate to compare the two because of this difference. Someone who likes the beauty of a Monet or a Michaelangelo may not like the beauty of a Pollock or Picasso.

I think they're both beautiful in different ways and I don't mind
saying that. Gene may disagree.

-Mike

🔗cityoftheasleep <igliashon@...>

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

> You seem to have some notion in your head about what concordant or
> discordant means, but I don't know what it is.

Harmonies can be concordant or discordant (whatever those terms mean), while timbres can be harmonic or inharmonic. There seems to be some thorniness here, because you're talking about playing chords with sine waves, but there's also this thing called "additive synthesis" which makes timbres by playing a bunch of simultaneous sine waves. So it seems either we have to say that a single note can be the same thing as a harmony, or that you can't make a chord out of sine waves. If this is indeed the dichotomy we're facing and there's not a 3rd option, I'd recommend the latter option.

> Concordant is a term
> that we're trying to define, so for me to propose a definition and for
> you to then say that you don't hear that definition as being
> "concordant" means you have some other idea of what concordant means.
> What is it?

All I know is that it's a property shared by all harmonies judged to be pleasant outside of any musical context, all other factors being equal.

> The way I define concordance seems to be what you're calling "harmonicity."

That's clearly problematic for one of us. What term would you use for what I'm defining as concordance?

> We would need a large enough sample size to control for culture-wide
> idiosyncrasies. We don't have that.

No, we wouldn't, unless we were trying to extend our claims outside of our own culture. To my knowledge, we're not.

> Assuming that we do find that, any study measuring preferences like
> that still wouldn't prove anything fundamental about psychoacoustics
> or about music cognition, or invalidate that learned factors beyond
> the prenatal ones that Carl mentioned factor into the end pleasantness
> of a sound even across cultures. It would only be an epidemiological
> study that gives a statistical average of the sounds that people tend
> to like circa 2011. It says nothing about why those results are the
> way they are, whether they'd change if a significantly new form of
> music was invented, the potential for them to change longitudinally
> with training, etc, unless you actually measure that.

That's why we build models and test their ability to make successful predictions. We're *never* going to be able to *prove* ANYTHING in this realm. All we can do is sample, model, test, refine, repeat, gradually improving our models. Or just give up on it all together and get by on luck and intuition.

> Also, how useful you'd find the information from this study would
> depend on your personal goals and compositional style. I personally
> don't care at all what the preferences of a Reasonable Person with 2.6
> kids are, because I'm a trained musician who already appreciates music
> significantly above the norm and I joined this list to dig further
> into that. I care more about pushing the limits of my own perception,
> and finding ways to take people along with me, than about figuring out
> what people already like and leaving it at that.

Either you do care about people's preferences, or you don't care about taking people along with you.

> I heard it as what I called "concordant" from my second definition,
> and what you called "harmonic" in your definition. I could hear the
> periodicity buzz and all that, but it still sounded "wrong."

You mean you heard it as producing an obvious VF in a way that 1000 cents doesn't, and didn't notice anything about partials beating in sync or timbral fusion or anything like that?
Your second definition only accounts for the VF phenomenon, not any other sensory components.

> > It's a good thing we're not talking about consonance and dissonance (yet)!
>
> We may be, without realizing it, when we talk about "pleasantness
> absent an explicit musical context."

How, if we define consonance and dissonance as being musical-context-dependent?

> I don't care what we call it. If we're going to call concordance
> something like overall pleasantness, though, we then need a term for
> the things that are really are concretely and psychoacoustically
> measurable.

How is a subjective experience concretely measurable?

> What is concordance - the end pleasantness produced by a dyad for an
> arbitrary listener, even if that incorporates learned factors for that
> listener?

Sure.

> And the thing that has to do with VFs and beating is
> "harmonicity?"

Whoa whoa whoa, you never said anything about beating before. VFs-->harmonicity; beating-->concordance.

> I think they're both beautiful in different ways and I don't mind
> saying that. Gene may disagree.

The difference in the ways in which they are beautiful disallows the comparison. It's like saying this bowl of cereal tastes better than this cup of tea is warm.

-Igs

🔗Mario Pizarro <piagui@...>

Igliashon,
Mike,

I think that the progression of musical cells detects the consonant ratios.

Mario

January, 7
<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
----- Original Message ----- From: "cityoftheasleep" <igliashon@...>
To: <tuning@yahoogroups.com>
Sent: Saturday, January 07, 2012 12:33 PM
Subject: [tuning] Re: Question on Consistency

> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
>> Your definition referred to partials "locking in," which I assume
>> means chords sharing common partials and so on. My definition doesn't
>> refer to partials at all, and in that regard even chords made of sine
>> waves can be concordant.
>
> I rarely hear chords made up of sine waves as concordant or discordant, > unless there are critical band effects happening. Harmonic and > inharmonic, sure. But if chords made up of sines can be discordant, then > that means timbres can be discordant, which seems confused. There are > harsh, unpleasant timbres out there to be sure--but calling them > discordant seems a misuse of the word.
>
>> There are two definitions of concordance I've seen thrown around with
>> endless variations
>>
>> 1) The end result "pleasantness" of a sound apart from its musical >> context
>
> That's the one I like.
>
>> 2) The extent to which a sound can clearly activate a single virtual >> fundamental
>
> That one I would prefer to call "harmonicity" or something.
>
>> My problem with assuming the first one naively is that we don't know
>> what, exactly, we're measuring. We're measuring things like VF
>> strength and lack of beating, for sure, but we might also be measuring
>> OCD automatic categorization effects that might happen when you hear
>> an interval.
>
> That's not really a problem as long as A) we have a large-enough sample > size to control for individual idiosyncrasies and B) we find a model that > fits the data and successfully predicts further results. The "lack of > beating" model we know to be problematic because there are Setharesian > spectrally-matched chords that sound discordant but don't beat. I suspect > this is because the timbre of these chords is innately unpleasant, and > people are confusing the unpleasantness of the timbre with the discordance > of the chords. But that's just me.
>
>> For example, I used to prefer 1000 cents to 7/4 because I
>> knew (on a preconscious level) I couldn't split it into two "perfect
>> fourths," nor could I do all of the other things that I was used to
>> doing in 12-EDO. So although I could hear 7/4 as more concordant, I
>> also heard it as "wrong" at the time.
>
> But you still heard it as more concordant--so it seems even in that naive > state, you were able to separate your OCD categorization from your > perception of concordance.
>
>> And even aside from this obvious
>> and intuitive example, there might be a host of deeper patterns of
>> learned behavior which influence our perception of the consonance and
>> dissonance of an interval without us knowing it, literally in a manner
>> completely independent of the concordance of that interval.
>
> It's a good thing we're not talking about consonance and dissonance (yet)!
>
>> #2 gets around that problem, but is it what we want? Are we also
>> looking to measure beating and periodicity buzz and stuff as well? Is
>> it too limiting, and is there just a bigger picture that we're trying
>> to measure which is some weighted average of the overall effect of
>> accurate, simple ratios on the auditory sense?
>
> #2 is something I don't want to bring into concordance/discordance. For > while Paul is fond of mentioning the difference between utonal and otonal > chords, there is a similarity that is also important to note. I'd say > utonal chords are concordant but inharmonic. What do you think of that?
>
>> I don't care what definition we pick, but are we all talking about the
>> same thing?
>
> Depends. Can we all agree with what I wrote above?
>
>> > That's like comparing a Picasso (or perhaps a Pollock) to a Monet!
>>
>> Sure, what's wrong with that?
>
> Clearly, you did not go to art school ;->. It's a whole different kind of > beauty, and it's inappropriate to compare the two because of this > difference. Someone who likes the beauty of a Monet or a Michaelangelo > may not like the beauty of a Pollock or Picasso.
>
> -Igs
>
>
>
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