MMM Psychoacoustics offshoot

On Mon, Sep 13, 2010 at 3:41 AM, Carl Lumma <carl@...> wrote:

> 7-ET is actually a very good 5-limit temperament.

For the 3-limit I could see this, but why do you say for the 5-limit? The
thirds are both right at a local max of HE...

> It may be. JI is only the concordance reality (and even then only
> mostly -- you know about "magic" chords). Puns may be audible as
> departures from JI when they involve a single chord change, but I'm
> not so sure about longer comma pumps.

I hate that question, and can drive myself nuts trying to answer it, because
it gets absurdly philosophical.

At one point, I spent a few days playing and trying to "think" exclusively
in 5-limit JI. After a few days, I started trying to throw some obvious
comma pumps in, and figure out the best way to voice them in 5-limit JI. I
voiced them so that there ends up with a wolf on one chord unless you're in
meantone.

Cmaj -> Am -> Fmaj -> G, for example, works. But make that Fmaj an Fmaj6, or
even better, Dm/F, and you have a perfectly normal diatonic chord
progression that suddenly poses a problem in 5-limit JI. But in this case, I
found that the Dm/F ends up working well as 16:20:27, which in this
situation sounds bright and unresolved and great. After getting used to this
sound, I went back to meantone in which that 20:27 becomes a very, very
resonant 4:3, which threw me for a loop entirely. Hence I had, to myself at
least, "identified" the characteristic sound of the syntonic pun.

And in truth, I did get it, or at least I have it figured out in a way that
makes sense to me. But the issue of the placebo effect aside, how could I
ever know if this is because I had just formed a new map, or if the map was
always there in the form of JI and I had to rediscover it? And then it gets
philosophically absurd when you start to get into "Is there a difference? Is
it just semantics here?" etc.

So tuning theory makes for some good zen koans. We should start a secret
society, but instead of teaching the meaning of life through compass and
square imagery, we can use scales and psychoacoustics.

-Mike

On Mon, Sep 13, 2010 at 4:08 AM, Carl Lumma <carl@...> wrote:
>
> What do you make of the 7-limit otonal/utonal tetrads... especially
> the inversions of the latter, which sound a bit like different
> chords...? Do they have a major/minor quality? Maybe reply offlist
> or on tuning.
The 7-limit otonal tetrad sounds like a dominant 7 chord, the utonal tetrad
sounds like a m6 chord, and the utonal tetrad in 1/4:1/5:1/6:1/7 inversion
sounds like a half diminished 7 chord. Most interesting to me here is the
parallel between the utonal tetrad in the "m6" inversion, and a subminor 6
chord 6:7:9:10, can sound so similar. But in the second case, unless you're
playing a 3 and a 1.5 in the bass, the 1 fundamental can become so loud that
it just starts sounding like effectively a fifth note, so the whole thing
starts to sound like a dom9 chord with the upper partials being emphasized.

> >For the minor triad I'm even less sure that 10:12:15 serves an
> >archetypical function. I did a test on this the other day and heard
> >the 10:12:15 as having a fundamental of "5", and the 6:7:9 as having a
> >fundamental of "1" (or maybe it was 2 or 4, either way it was
> >definitely a chroma a fourth off from the other one).
>
> Were 10: and 6: the same pitch or...? For me, the lowest note
> in both chords can clearly be the fundamental, due to the outside
> fifth (2:3). Unless, in the case of 6:7:9, I'm primed with
> 4:6:7:9 (or similar) beforehand.
No, they were different. I did the test differently this time, using an idea
I had to get past any type of "mapping bias": I made a MIDI file of the
melody to Yankee Doodle in C major. I sent it through a 3-op virtual analog
synth. I set the 3 oscillators to 4:5:6, set about 2 octaves above middle C.
As you'd expect, it played in C major.

I then set them to 10:12:15, and they played in the key of C an octave up,
and the timbre sounded like it had an extra bell-like inharmonic component
to it. So at that point I realized why everyone came to the realization that
the C-G dyad is what's emphasized, and the Eb is thrown away. But, if I
tried, I could "refocus" on another fundamental appearing all the way down
at Ab somewhere, I wasn't sure if this was 2 or 1. I didn't really look for
Eb although I probably should have. This might have also been due to the
presence of some kind of nonlinear distortion too.

I then set it to 6:7:9, and Yankee Doodle played in F, which was pretty
awesome at the time. I was going to test 16:19:24 and answer The Ultimate
Question Of Minorness, and then SONAR crashed and I lost everything, and I
gave up. I'll do it again though.

One interesting thing, though, was at one point I heard a messed up
distorted F popping out of it, and I realized I was perceiving 10:12:15 as a
detuned 6:7:9. It was really fragile and lasted for only a short while, and
then went back to being C again.

> 4:5:6 seems to have a wider field of attraction than either 6:7:9
> or 10:12:15.
I did consider that as an explanation - that I'm just hearing the supermajor
triad as a detuned 4:5:6. I also considered that this might "bias" me to
hearing the minor triad as a 10:12:15, since the 4:5 would become the top of
a 10:12:15.

I'm still open to that interpretation, but I have a few reasons that I'm not
sure if that's what it is:

1) Where does it stop? Would that mean that all musical perception DOES
directly derive from JI, if you have intervals influencing the perception of
intervals influencing the perception of intervals and so on? Occam's Razor
says no, but it's still possible.

2) Especially after playing with mavila[5], I think that when we hear a 5/4,
a number of things happen that we all lump together under the "major third"
umbrella. Part of it has to do with cultural/diatonic stuff, and another
part of it has to do with how it is rooted and concordant, and we just lump
them together in with the "major third" name.

3) After playing with mavila[5] I got to separate some of these things a
bit, and end up in the aural situation where the first major third quality
was assigned to 6/5, and the last was not. This happened mainly when playing
stacked-fifth (or even better, octave-reduced stack fifth stuff), which
"flipped my brain" to hear that 6/5 as very much a major third. Is this
because I'm "hearing" 81/64, which I also call a "major third?" Or cultural
diatonic stuff that has nothing to do with JI? I wish I knew... :)

4) If you play a 6/5 minor third, say C-Eb, note how easy it is to imagine
the root as C; that is, imagine it as being part of a Cm triad instead of
Abmaj. Of course, the fundamental being produced is still going to be Ab and
noticeably so, but in a musical context it is very easy to just ignore that
Ab as extra "noise" and imagine the root as C.

When I play a 14:18:21 triad, with a timbre with a weaker 5th partial, it
sounds unsettlingly unrooted compared to 4:5:6. I find that I can get used
to it, but it just takes on a different "flavor" than the major triad - it
still has the "function" of a major triad in diatonic harmony, but is
nowhere near as resonant and rooted. It's almost like a minor triad in that
I feel like the direct super-resonance of 4:5:6 is gone, and you just have
the resonance of the perfect fifth with this foreign interval in between,
which for some inexplicable reason made me hear it as almost sad. I actually
got a full-blown synesthetic experience out of it - it was still "major,"
but reminded me of the feeling of being "chilly," as if it was the end of
summer and turning to autumn, and so on.

The above are really just my subjective experiences. Perhaps the sensible
thing to be done is to do another listening test with 14:18:21, and see what
comes out. (I also want to do one in which different triads are put in front
of 10:12:15, and see if you can "prime" it so that different fundamentals
pop out each time from the same chord.)

-Mike

Mike:

> > 7-ET is actually a very good 5-limit temperament.
>
> For the 3-limit I could see this, but why do you say for the
> 5-limit? The thirds are both right at a local max of HE...

It has lower 5-limit TOP damage than any other ET < 12.

> > What do you make of the 7-limit otonal/utonal tetrads...
> > especially the inversions of the latter, which sound a bit
> > like different chords...? Do they have a major/minor quality?
> > Maybe reply offlist or on tuning.
>
> The 7-limit otonal tetrad sounds like a dominant 7 chord, the
> utonal tetrad sounds like a m6 chord, and the utonal tetrad in
> 1/4:1/5:1/6:1/7 inversion sounds like a half diminished 7 chord.

Right. And there are two other inversions...

> Most interesting to me here is the parallel between the utonal
> tetrad in the "m6" inversion, and a subminor 6 chord 6:7:9:10,
> can sound so similar. But in the second case, unless you're
> playing a 3 and a 1.5 in the bass, the 1 fundamental can become
> so loud that it just starts sounding like effectively a fifth
> note, so the whole thing starts to sound like a dom9 chord with
> the upper partials being emphasized.

I was more asking about its major/minor quality. I think all
these inversions, despite sounding like different 12-ET
chords, share a kind of minor quality. Just a subjective
observation.

> > 4:5:6 seems to have a wider field of attraction than either
> > 6:7:9 or 10:12:15.
>
> I did consider that as an explanation - that I'm just hearing
> the supermajor triad as a detuned 4:5:6.

9:7 reminds me of the case we were just talking about with the
720-cent fifth, which was far away from 3:2 but still in 3:2's
field of attraction -- and that's partly why it sounds so bad.
Same with 9:7. Still in 5:4's basin of attraction. Unlike
720 cents, it can be beatless. Still sounds bad on its own,
though it sounds fantastic in 4:5:7:9. So clearly the
psychoacoustic identity (in terms of JI) of intervals and
chords is important.

-Carl

Carl>"Same with 9:7. Still in 5:4's basin of attraction. Unlike
720 cents, it can be beatless. Still sounds bad on its own,
though it sounds fantastic in 4:5:7:9. So clearly the
psychoacoustic identity (in terms of JI) of intervals and
chords is important."

Let me get this right...
A) Harmonic Entropy sets the guidelines for "basis of attraction" (I haven't
heard yet of another theory that does so far)
B) 9/7 is supposedly a bad dyad because the brain tries to make it out as a 5/4
and concludes it's a lousy 5/4 rather than it's own identity.

Off the top of my head...I'll agree 5/4 seems to have a large field of
attraction. But you know...9/7 isn't all that far from 4/3 either (which also,
if I have it right, has an equally large field of attraction). Makes me wonder
if part of the problem is those two dyads fighting for "control" of the 9/7.

The amusing thing is how 4:5:7:9 works so well. Completely subjective...but
I wonder if the brain sees it as an extension to 4:5:6:7. Something weird
happens with the minor second in a C E F A chord in 12TET as well that makes
even that terribly dissonant semi-tone sound great in context. I wonder if a
common pattern/theoty exists between all of these with explains the whole
dyad=bad but dyad in chord=good pattern...

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> I wonder if a common pattern/theoty exists between all of these with explains the whole
> dyad=bad but dyad in chord=good pattern...
>

Well, the tolerance for roughness in chords seems to be a lot larger than in dyads, and it goes up the more notes you have in a chord. I suspect that this is because too many unique notes (i.e. not octave-doublings) sort of "overload" the perceptive faculties of most listeners, and when you get much more complex than triads, you're already pushing the limit. I mean, changing one note in a triad creates a world of difference, but changing one note in a pentad or a hexad and you're lucky if the change is noticeable unless it's a huge change! The overall effect of having a bad dyad in a chord can be "drowned out" by other good dyads, and the "roughness" added by that bad dyad may actually be pleasant (since modern humans don't seem to mind a bit of roughness, especially as a contrast to purity).

-Igs

Igs>"I mean, changing one note in a triad creates a world of difference, but
changing one note in a pentad or a hexad and you're lucky if the change is
noticeable unless it's a huge change!"
Exactly! On one hand, I'd say with 5 or more unique/"non-octave-doubled"
notes in a chord making a change barely matters in 12TET...but I have noticed
through composing in other, "more tall chord capable" temperaments that it
doesn't matter all that much there either.

>"The overall effect of having a bad dyad in a chord can be "drowned out" by
>other good dyads, and the "roughness" added by that bad dyad may actually be
>pleasant"
Right, otherwise, at least as I hear it...the chord would begin to feel
"empty" and perhaps somewhat non-dramatic in emotional content.

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

> Same with 9:7. Still in 5:4's basin of attraction.

No it's not. A 9/7 diad can even sound rooted on the higher tone.
> Unlike
> 720 cents, it can be beatless. Still sounds bad on its own,

No it doesn't. It's often not to my taste, and to my ears tends to do what all the simple 7th-partial intervals do, which is want to drive everything into some kind of simple relation with 7 (fights against 5 so to speak, for example, perhaps this is a key element of blues). But
a chalmeau type instrument playing a 9/7 is really pretty, even as
a naked diad.

> it sounds fantastic in 4:5:7:9.

I agree there.

>So clearly the
> psychoacoustic identity (in terms of JI) of intervals and
> chords is important.

And I certainly agree with this.

Oh, I should add that I sometimes find a kind of "minor" quality to a 9:7. 5/4 my butt.

--- In tuning@yahoogroups.com, "cameron" <misterbobro@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
>
>
> > Same with 9:7. Still in 5:4's basin of attraction.
>
> No it's not. A 9/7 diad can even sound rooted on the higher tone.
> > Unlike
> > 720 cents, it can be beatless. Still sounds bad on its own,
>
> No it doesn't. It's often not to my taste, and to my ears tends to do what all the simple 7th-partial intervals do, which is want to drive everything into some kind of simple relation with 7 (fights against 5 so to speak, for example, perhaps this is a key element of blues). But
> a chalmeau type instrument playing a 9/7 is really pretty, even as
> a naked diad.
>
>
> > it sounds fantastic in 4:5:7:9.
>
> I agree there.
>
> >So clearly the
> > psychoacoustic identity (in terms of JI) of intervals and
> > chords is important.
>
> And I certainly agree with this.
>

On Mon, Sep 13, 2010 at 5:50 AM, Carl Lumma <carl@...> wrote:
>
> Mike:
>
> > > 7-ET is actually a very good 5-limit temperament.
> >
> > For the 3-limit I could see this, but why do you say for the
> > 5-limit? The thirds are both right at a local max of HE...
>
> It has lower 5-limit TOP damage than any other ET < 12.

I always knew I liked it for a reason :)

TOP damage is synonymous with TOP error?

> > The 7-limit otonal tetrad sounds like a dominant 7 chord, the
> > utonal tetrad sounds like a m6 chord, and the utonal tetrad in
> > 1/4:1/5:1/6:1/7 inversion sounds like a half diminished 7 chord.
>
> Right. And there are two other inversions...

OK, let's call the "m6" variant root position. So first inversion is
something like C E F# A, and sounds like it could either be a m6 chord
in first inversion or the upper partials to a D9. Second inversion is
something like C D F Ab, and sounds like it could either be a m6 chord
in second inversion or the upper partials to a Bb9. Third inversion is
something like C Eb Gb Bb and sounds like a half-dim7 chord. At least
that was my impression of all of them.

Doing this experiment with the subminor equivalent of this chord, or
6:7:9:10, yielded pretty much the same results but sounded much more
resonant and concordant, as you'd probably expect. The louder
fundamental, however, biased me to hear everything as upper partials
to dom9 chords.

> 9:7 reminds me of the case we were just talking about with the
> 720-cent fifth, which was far away from 3:2 but still in 3:2's
> field of attraction -- and that's partly why it sounds so bad.

Right, but a few things come to mind with that:

1) The #1 thing that makes 720 cents to me sound so bad is the beating
between the partials of the two notes. If you play it with a pure
tone, or pick a clever timbre to hide this (like use a triangle wave
so there's no 2 to beat against the 3), it sounds much, much better.
2) Even if you use sine waves, it sounds really sharp, but I think
part of this may be due to me starting to hear it move into "minor
6th" territory. Cultural biases make this hard to pinpoint. All I know
is, while I typed this entire message I had a triangle-ish recorder
patch playing 3\5, and now that it's been like 5 minutes with that
drone I hear it as a decent fifth.
3) However, even assuming that this is entirely an issue of
periodicity, I used to think the same about the 686 7-tet fifth. And
after hearing knowsur's album, I think you could probably use 720
cents to sound harmonically pleasant as well, if you're deft enough at
constructing the proper musical context for it as knowsur did.

> Same with 9:7. Still in 5:4's basin of attraction. Unlike
> 720 cents, it can be beatless. Still sounds bad on its own,
> though it sounds fantastic in 4:5:7:9. So clearly the
> psychoacoustic identity (in terms of JI) of intervals and
> chords is important.

The points I raised with #1 and #2 apply here. But to get some more
useful data, I ran the timbral listening test again, with a just
supermajor triad as the timbre, with the 3 oscillators tuned to sines.
And instead of Yankee Doodle, I did a Mozart piece in C.

What is interesting, as a precursor to this, is that I ran the minor
triad first. The minor triad is set up to be a masterpiece of priming.
If we're talking C Eb G, you can make yourself hear the fundamental as
C (the obvious choice), as Ab (start with the C Eb and gradually bring
up the volume of the G, focusing on the Ab the whole time), as Eb
(start with Eb and G, and bring up the C gradually; I found this one
harder than Ab for some reason), and even as an Ab an octave below the
other Ab, which indicates placement of the full 10:12:15 triad (I
think this one might have been due to speaker distortion though). At
one point, I got an isolated C-Eb dyad to sound like 5:4 (i.e. a C was
popping out in a lower octave), then I heard the fundamental as Ab and
now it's hard to snap back. Sometimes you can hear more than one
fundamental at once. The whole tonal mass, if you focus on it, if a
complex polytonal object where different fundamental come in and out
of existence, sometimes more than one existing simultaneously, and
with the 3:2 dyad on the outside being the strongest. Keep in mind
that the notes themselves are also fundamentals.

So I set out to see how 14:18:21 fares. Right away, I heard the piece
play in C 2 octaves down, thus indicating that it was being heard as
4:5:6, but the presence of some crazy extraneous bell-like overtone
was also present. I then tried for just 7:9 and it was still in C. I
then tried just the 18:21 (which is a 7:6), and should have heard it
in A, but instead the whole thing was completely ambiguous and I only
could hear "hints" of it being in A, which popped out at random, and I
wasn't sure quite what I was hearing at first. Putting 6:7:8 in made
the "A" pop out, though. I was surprised that 7:6 was such a weak
concordance. 7:9 was completely impossible, and was heard as 5:4.

However, there were moments when I heard the supermajor triad in the
same way I heard the minor one: with the octave above popping out, and
hearing just a random inharmonic tone in the middle. So that is also
in line with my earlier perception of the supermajor triad: usually,
it just sounds like an out of tune major triad, but there are brief
moments where it sounds different, similar to the minor chord in that
it's a sonority that doesn't sound "fully rooted," which is probably
what gave me the synesthetic reaction I had. Moments where my musical
perception was like that were rare, as were moments where my timbral
perception was like that also rare.

Thus ends my situation report, and now I really feel like I know nothing.

-Mike

On Tue, Sep 14, 2010 at 12:59 AM, cameron <misterbobro@...> wrote:
>
> Oh, I should add that I sometimes find a kind of "minor" quality to a 9:7. 5/4 my butt.

As you have expressed that you are synesthetic, you will note that in
my earlier post I had a similar reaction - it's a less rooted triad
with a note in the middle that isn't 5/4, just like minor. However, it
is also true that most of the time we can both hear it as just being a
detuned major chord too, if we try.

Well, the timbral listening test I just did is in agreement with it.
Most of the time, the fundamental pops out as if it were 4:5:6, and
sometimes the fundamental pops out only as if it were a 2:3 on the
outside (e.g. an octave up), and there's this random garbage tone that
pops up. However, unlike minor, I could never get to hear the 7:9 as a
fundamental on its own (this was done entirely with sines), and could
only barely get to hear the 6:7 as a fundamental on its own. But,
rarely, I could.

Which is in agreement with my earlier thoughts - the supermajor triad
takes on a polytonal de-rooted gestalt a la minor "sometimes." But
it's more rare than with 10:12:15, and it also can sound like 4:5:6
too.

-Mike

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

> TOP damage is synonymous with TOP error?

Ya.

> Doing this experiment with the subminor equivalent of this chord, or
> 6:7:9:10, yielded pretty much the same results but sounded much more
> resonant and concordant, as you'd probably expect. The louder
> fundamental, however, biased me to hear everything as upper partials
> to dom9 chords.

So do they sound minor or not?

> 1) The #1 thing that makes 720 cents to me sound so bad is the
> beating between the partials of the two notes.

Yeah, but not so with 9/7. And try 21/16 with sines.

> then I heard the fundamental as Ab and [snip]

You're doing analytical listening, which is fine, but don't
miss the forest for the trees.

-Carl

On Tue, Sep 14, 2010 at 1:54 AM, Carl Lumma <carl@...> wrote:
>
> > Doing this experiment with the subminor equivalent of this chord, or
> > 6:7:9:10, yielded pretty much the same results but sounded much more
> > resonant and concordant, as you'd probably expect. The louder
> > fundamental, however, biased me to hear everything as upper partials
> > to dom9 chords.
>
> So do they sound minor or not?

The subminor equivalent? Yes, it sounds minor, although perhaps if I
was the proud owner of a map in which those two were distinguished,
maybe it wouldn't. As you can see, I am clearly having trouble
distinguishing musical meaning from psychoacoustics at this point.

> > 1) The #1 thing that makes 720 cents to me sound so bad is the
> > beating between the partials of the two notes.
>
> Yeah, but not so with 9/7. And try 21/16 with sines.

Well, after 7/6 failing so miserably, I didn't expect it to sound like
anything but an irritatingly flat 4/3, and it did.

> > then I heard the fundamental as Ab and [snip]
>
> You're doing analytical listening, which is fine, but don't
> miss the forest for the trees.

Right, I'm basically giving up, haha. I get that you're trying to
guide me to the answer with the Socratic method (or maybe you're just
throwing ideas out there). But I really am unable to see the forest
here. Every time I come up with a forest, there's a new forest I've
missed :)

What is your view of the "big picture" then - do you think how all the
pieces interact has been figured out? Musical meaning clearly derives
from the map to a huge extent, but perhaps psychoacoustic identity
plays into it as well. Where does one draw the line? Perhaps it's that
psychoacoustic identity plays a role in how we construct maps?

Why does the fact that subminor with superpyth and minor with meantone
both have different fundamentals not matter in that they're both
called "minor," but the fact that supermajor and major don't have
different fundamentals does matter...?

I feel like I'm coming into this years after all of the revelations
were made, and I missed some important initial discussions somewhere
down the line.

-Mike

On Tue, Sep 14, 2010 at 2:34 AM, Mike Battaglia <battaglia01@...> wrote:
>
> Why does the fact that subminor with superpyth and minor with meantone
> both have different fundamentals not matter in that they're both
> called "minor," but the fact that supermajor and major don't have
> different fundamentals does matter...?

To reframe this, an alternative formulation of this question is - if
our psychoauditory system were set up to be more precise in that we
could hear 9/7 as its own sonority without any necessary priming,
would supermajor chords in superpyth sound like a different "kind" of
chord? Or, is it just that they would sound more concordant, and hence
more stable, while still sounding like a type of major chord for
mapping reasons?

The invariance of minor/subminor intonational differences with
diatonic makes me think the latter, but that would then go against
your statement that psychoacoustic identity matters in how we perceive
major/minor.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > So do they sound minor or not?
>
> The subminor equivalent?

No, the inversions of the utonal tetrad. Have you been
reading anything I've written?

> > > 1) The #1 thing that makes 720 cents to me sound so bad is the
> > > beating between the partials of the two notes.
> >
> > Yeah, but not so with 9/7. And try 21/16 with sines.
>
> Well, after 7/6 failing so miserably, I didn't expect it to
> sound like anything but an irritatingly flat 4/3, and it did.

Forget what it sounds like - does it sound discordant?

-Carl

On Tue, Sep 14, 2010 at 2:40 AM, Carl Lumma <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > > So do they sound minor or not?
> >
> > The subminor equivalent?
>
> No, the inversions of the utonal tetrad. Have you been
> reading anything I've written?

I said that I can either hear them as minor 6 triads in inversion or
part of a rootless dom9 voicing with the root a fifth down. I can flip
my perception around as I want and it's completely variable and
influenced by priming. Other than that I don't know what definition of
minorness to give to it.

> > > > 1) The #1 thing that makes 720 cents to me sound so bad is the
> > > > beating between the partials of the two notes.
> > >
> > > Yeah, but not so with 9/7. And try 21/16 with sines.
> >
> > Well, after 7/6 failing so miserably, I didn't expect it to
> > sound like anything but an irritatingly flat 4/3, and it did.
>
> Forget what it sounds like - does it sound discordant?

It still sounds concordant, I guess. If I play it with sines, it just
sounds like a pseudo-fourth. If I leave it on for a second and go to
4/3, the 4/3 sounds sharp. If I start with the 4/3 first, the 21/16
sounds flat. If I start with nothing, the 21/16 sounds flat. If I try
to imagine a diatonic structure with 21/16 as "a fourth," the whole
thing becomes unpleasant to think about.

-Mike

I wrote:
>
> It still sounds concordant, I guess. If I play it with sines, it just
> sounds like a pseudo-fourth. If I leave it on for a second and go to
> 4/3, the 4/3 sounds sharp. If I start with the 4/3 first, the 21/16
> sounds flat. If I start with nothing, the 21/16 sounds flat. If I try
> to imagine a diatonic structure with 21/16 as "a fourth," the whole
> thing becomes unpleasant to think about.

To clarify this, the timbral example makes it sound somewhat
bell-like, so if that's what discordance means then yes.

-Mike

Here, in order to lend some concreteness to what I'm saying, I came up
with an audio example. I was playing around with different types of
minor scales, and started messing around with tuning the minor thirds
a bit flatter than subminor.

So here's a listening test, it's very short. I made a score - read
this while you listen please, and follow along:

http://www.mikebattagliamusic.com/music/subsubminor.pdf

Here's the listening example:
http://www.mikebattagliamusic.com/music/belowsubminor.mp3

It just plays the minor scale to set up the map, then a i-iv-v-iv-i
progression, then the chord progression in question. Although the
minor/subminor/whatever thirds sound uncomfortably flat, they still
sound like minor thirds, right?

-Mike

One more, another 16 bar example. I did a supermajor example this
time. Same thing, I set up the scale, did a I-IV-V, and then do some
stuff with lydian #2.

Score: http://www.mikebattagliamusic.com/music/supermajor.mp3

Listening example:
http://www.mikebattagliamusic.com/music/supermajorchromatic.pdf

Again, does everything sound right, despite that the supermajor triads
are uncomfortably sharp? :)

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Tue, Sep 14, 2010 at 12:59 AM, cameron <misterbobro@...> wrote:
> >
> > Oh, I should add that I sometimes find a kind of "minor" quality to a 9:7. 5/4 my butt.
>
> As you have expressed that you are synesthetic, you will note that in
> my earlier post I had a similar reaction - it's a less rooted triad
> with a note in the middle that isn't 5/4, just like minor. However, it
> is also true that most of the time we can both hear it as just being a
> detuned major chord too, if we try.

But in a detuned major chord, I would want to tune the third down, or the "root" up. 9/7, to me, wants to expand outward, strongly. But I think that what you might really mean is "mi", according to the idea of a diatonic map. And there, yes I agree, it can sound like "mi". Anything from about 350-450 cents can sound like "mi", in context. 9/7 can also function as "fa", if the diatonic tetrachord is all shrunk down some.

But, I suspect that what we hear in the case of 9/7 sounding like "mi" is really hearing it as the "mi" of the dominant, ie. it's "ti", and there's an implied dominant 7th chord feeling to 9/7, probably helped out by the coincidence, and therefore amplification, at the seventh partial of the "root". Mi of the dominant, Ti, resolving upward, and often well sharped in practice, with instruments of flexible pitch. This is very cultural of course, but we don't know the extent of the psychoacoustic basis of that cultural thing.

You just can't equate "mi" with "5/4", and then hear 9/7 as "mi" and therefore equate it with 5/4, that's bogus. In some musics the equation of "mi" with 5/4 is made, that's fine because it's a specific artistic choice. Declaring this as universal is bunk.

-Cameron
>
> Well, the timbral listening test I just did is in agreement with it.
> Most of the time, the fundamental pops out as if it were 4:5:6, and
> sometimes the fundamental pops out only as if it were a 2:3 on the
> outside (e.g. an octave up), and there's this random garbage tone that
> pops up. However, unlike minor, I could never get to hear the 7:9 as a
> fundamental on its own (this was done entirely with sines), and could
> only barely get to hear the 6:7 as a fundamental on its own. But,
> rarely, I could.
>
> Which is in agreement with my earlier thoughts - the supermajor triad
> takes on a polytonal de-rooted gestalt a la minor "sometimes." But
> it's more rare than with 10:12:15, and it also can sound like 4:5:6
> too.
>
> -Mike
>

Isn't that I in measure four kind of reminiscent of a I7 to you? I suspect so, for you've taken it to IV, that is, you've got, in the sound of it, a little bit of ambiguity between I-IV-V-IV-I and V7-I-II-I-V7. Cf. what I said about mi/ti in the previous post.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> One more, another 16 bar example. I did a supermajor example this
> time. Same thing, I set up the scale, did a I-IV-V, and then do some
> stuff with lydian #2.
>
> Score: http://www.mikebattagliamusic.com/music/supermajor.mp3
>
> Listening example:
> http://www.mikebattagliamusic.com/music/supermajorchromatic.pdf
>
> Again, does everything sound right, despite that the supermajor triads
> are uncomfortably sharp? :)
>
> -Mike
>

I would have guessed something like fourths chords with diminished fourths. Like, 450 cents + 500 cents, or stacked 21/16s or something. Looking at the score I can imagine it as out of tune m3 chords, but that feels kind of forced. Perhaps I'm assuming that with minor chords the roots would be more obvious to me, while this sounds like funky inversions I'd have to poke at some to really get a root progression going.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> Here, in order to lend some concreteness to what I'm saying, I came up
> with an audio example. I was playing around with different types of
> minor scales, and started messing around with tuning the minor thirds
> a bit flatter than subminor.
>
> So here's a listening test, it's very short. I made a score - read
> this while you listen please, and follow along:
>
> http://www.mikebattagliamusic.com/music/subsubminor.pdf
>
> Here's the listening example:
> http://www.mikebattagliamusic.com/music/belowsubminor.mp3
>
> It just plays the minor scale to set up the map, then a i-iv-v-iv-i
> progression, then the chord progression in question. Although the
> minor/subminor/whatever thirds sound uncomfortably flat, they still
> sound like minor thirds, right?
>
> -Mike
>

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

> It just plays the minor scale to set up the map, then a i-iv-v-iv-i
> progression, then the chord progression in question. Although the
> minor/subminor/whatever thirds sound uncomfortably flat, they still
> sound like minor thirds, right?

No, they do not. This is an excellent example of why I object to the orgy of subjectivity which has been ongoing here lately: what sounds in a certain way to A may not sound in the same way to B. But thanks for providing an example, which is something I wish people would do more often. A midi file would suffice.

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

> Again, does everything sound right, despite that the supermajor triads
> are uncomfortably sharp? :)

"Sounds right"? What does that even mean? Does the following "sound right"?

http://www.archive.org/details/NightOnPorcupineMountain

What about this, does this "sound right"?

http://www.archive.org/details/Pacem

If there is a recognizable similarity between a Mad Science retuning and the original, that doesn't prove they are the same thing, only that there is a relationship. It's not the same as saying that a diatonic piece in 19et sounds "the same" in some sense as the same piece in 12et, despite the very audible difference in tuning; a line has been crossed in one case which is not crossed in the other.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> It just plays the minor scale to set up the map, then a i-iv-v-iv-i
> progression, then the chord progression in question. Although the
> minor/subminor/whatever thirds sound uncomfortably flat, they still
> sound like minor thirds, right?
>
> -Mike
>

That's a big negative. I'm hearing 2nds. Large 2nds, yes...but most definitely 2nds. As in "sus2" chords.

On Tue, Sep 14, 2010 at 9:21 AM, cameron <misterbobro@...> wrote:
>
> I would have guessed something like fourths chords with diminished
fourths. Like, 450 cents + 500 cents, or stacked 21/16s or something.
Looking at the score I can imagine it as out of tune m3 chords, but that
feels kind of forced. Perhaps I'm assuming that with minor chords the roots
would be more obvious to me, while this sounds like funky inversions I'd
have to poke at some to really get a root progression going.

It is kind of forced, and I'm saying to force it :)

But the question is, do you hear the melody as G-C-D-Eb-D-C after the
i-iv-v-iv-i progression?

-Mike

On Tue, Sep 14, 2010 at 7:09 AM, cameron <misterbobro@...> wrote:
>
> You just can't equate "mi" with "5/4", and then hear 9/7 as "mi" and therefore equate it with 5/4, that's bogus. In some musics the equation of "mi" with 5/4 is made, that's fine because it's a specific artistic choice. Declaring this as universal is bunk.

I agree. I simply asked if you heard it as sounding like what I wrote
on the score.

In fact, I really agree, because that's the whole point of this
example: The C-D#, or the augmented second interval, or "ri" or
however you want to call it, is tuned 5/4. However, despite this, it
still sounds like "ri" in this case, and not "mi." I didn't want to
give it away because I wanted everyone else's subjective impression
first. But that's the point :)

-Mike

Hi Mike, Carl...just wanted to jump in a bit upstream here, as I missed a lot of this discussion when it was current.

Carl wrote:
> > So do they sound minor or not?

Mike replied:
> The subminor equivalent? Yes, it sounds minor, although perhaps if I
> was the proud owner of a map in which those two were distinguished,
> maybe it wouldn't. As you can see, I am clearly having trouble
> distinguishing musical meaning from psychoacoustics at this point.

Describing intervals as "major" and "minor" is, I think, a red herring. And perhaps a false dichotomy. The terms themselves basically mean nothing more than "wide" and "narrow" or "large" and "small". So of course, when you play diatonic music where there are two types of third, one's going to big and the other small, and these sizes will be relative to each other; thus asking if a chord sounds "major" or "minor" is simply asking "does this chord sound like it has a relatively-small or relatively-large third in it?"

I don't think this is *really* what you guys are trying to figure out. You're using "major" and "minor" to refer to the musico-semantic *content* typically associated with major and minor chords, effectively trying to ask "can two chords with different JI templates carry the same musico-semantic content?" Or, in other words, "is it possible to associate multiple audibly-distinct psychoacoustic phenomena with the same perceptual gestalt?"

To this, all I can say is: doing "deep listening" on a single dyad, I am perfectly capable of extracting (or perhaps projecting) any number of meanings from (or onto) ANY one dyad. I can hear a 4/3 as anything I want, it seems, regardless of whether it's played with sines, with saws, with squares, on a piano, on a guitar, in a choir...I can get it to sound like a 5/4, a 3/2, a 7/4, a 21/16, a 15/11, a 9/8...you name it! But what I really mean is that I can get it to cause the same change in cognitive state associated with any of those other intervals. This is because music, just like words, loses its semantic definitiveness under close scrutiny. Doing "deep listening" is the musical equivalent of repeating a single word over and over again. If you've never done that, try it: say "door" over and over again to yourself and pay attention to how the word's meaning changes. Its meaning sort of unravels, or is eclipsed by the phonetic qualities (or something).

My point is thus: listening to different chords over and over again under close scrutiny reveals nothing about their musico-semantic content. If you really want to know how if 7/6 really differs from 6/5, or if 9/7 really differs from 5/4, concoct a few diatonic-esque scales where the two thirds are ONLY 7/6 and 6/5, or ONLY 5/4 and 9/7. Then see if you can tell the difference when playing chord progressions. HINT: you may need to go non-octave to get these scales to work. Perhaps this will reveal that 5/4 can sound "minor", or that 6/5 can sound "major"? Either way, comparing superpyth with meantone won't help, because in any given instance, you're not comparing 7/6 and 6/5 relative to each other, or 9/7 and 5/4 relative to each other; you're comparing 7/6 relative to 9/7, and 6/5 relative to 5/4. You have to put the ratios you're comparing together in the same scale.

-Igs

On Tue, Sep 14, 2010 at 11:05 AM, genewardsmith <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > It just plays the minor scale to set up the map, then a i-iv-v-iv-i
> > progression, then the chord progression in question. Although the
> > minor/subminor/whatever thirds sound uncomfortably flat, they still
> > sound like minor thirds, right?
>
> No, they do not. This is an excellent example of why I object to the orgy
of subjectivity which has been ongoing here lately: what sounds in a certain
way to A may not sound in the same way to B. But thanks for providing an
example, which is something I wish people would do more often. A midi file
would suffice.

After the i-iv-v-iv-i, does the melody sound like G-C-D-Eb-D-C to you?

On Tue, Sep 14, 2010 at 11:18 AM, genewardsmith <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > Again, does everything sound right, despite that the supermajor triads
> > are uncomfortably sharp? :)
>
> "Sounds right"? What does that even mean? Does the following "sound
right"?
It means that the listening example sounds like a mistuned version of what
I wrote down on the score. Does it? Or does it sound like something
completely different?

> If there is a recognizable similarity between a Mad Science retuning and
the original, that doesn't prove they are the same thing, only that there is
a relationship. It's not the same as saying that a diatonic piece in 19et
sounds "the same" in some sense as the same piece in 12et, despite the very
audible difference in tuning; a line has been crossed in one case which is
not crossed in the other.

If you want to get away from the "orgy of subjectivity," and you aim to be
fair, then there's no point making statements like that. This is hardly a
Mad Science tuning; I replaced the major triads with supermajor triads to
see if diatonic melodies (in this case with chromatic alterations) were
still recognizable. To me, they are, and they do sound like mistunings of
"the same thing" a la 12-tet and 19-tet. Do they to you? If they don't
sound that way, then that is your subjective impression, as is my impression
subjective as well.

The difference here is that the scale is improper, so the C-D# sounds
ambiguous. After enough priming, it to me still sounds like C-D#, and not
anything else.

-Mike

On Tue, Sep 14, 2010 at 12:56 PM, cityoftheasleep <igliashon@...>
wrote:
>
> That's a big negative. I'm hearing 2nds. Large 2nds, yes...but most
definitely 2nds. As in "sus2" chords.

Does the melody still sound like G-C-D-Eb-D-C to you after the i-iv-v? Or
does it sound like G-C-D-mistuned D-D-C?

Most importantly, CAN you get yourself to hear it that way if you want?

I would like to hear your thoughts on the other example, since I feel it was
more effective at accomplishing what I was going for.

> I don't think this is *really* what you guys are trying to figure out.
You're using "major" and "minor" to refer to the musico-semantic *content*
typically associated with major and minor chords, effectively trying to ask
"can two chords with different JI templates carry the same musico-semantic
content?" Or, in other words, "is it possible to associate multiple
audibly-distinct psychoacoustic phenomena with the same perceptual gestalt?"

Right. And I think that the answer is yes, although I'm not sure that Carl
would disagree. But I think it's possible to hear 5/4 with a "minor gestalt"
and 6/5 with a "major gestalt."

> To this, all I can say is: doing "deep listening" on a single dyad, I am
perfectly capable of extracting (or perhaps projecting) any number of
meanings from (or onto) ANY one dyad. I can hear a 4/3 as anything I want,
it seems, regardless of whether it's played with sines, with saws, with
squares, on a piano, on a guitar, in a choir...I can get it to sound like a
5/4, a 3/2, a 7/4, a 21/16, a 15/11, a 9/8...you name it! But what I really
mean is that I can get it to cause the same change in cognitive state
associated with any of those other intervals. This is because music, just
like words, loses its semantic definitiveness under close scrutiny. Doing
"deep listening" is the musical equivalent of repeating a single word over
and over again. If you've never done that, try it: say "door" over and over
again to yourself and pay attention to how the word's meaning changes. Its
meaning sort of unravels, or is eclipsed by the phonetic qualities (or
something).

Glad to see we are in such close agreement. I think that the debate here is
really how much the qualitative nature of the "cognitive state" shift you're
talking about comes directly from psychoacoustics and how much comes from
psychology. That means, when you hear 4/3 as a 5/4 or a 3/2 or what not, are
you actually changing how you perceive the fundamental of that dyad? Or is
something else going on?

Can you listen to that supermajor example? :)

> My point is thus: listening to different chords over and over again under
close scrutiny reveals nothing about their musico-semantic content. If you
really want to know how if 7/6 really differs from 6/5, or if 9/7 really
differs from 5/4, concoct a few diatonic-esque scales where the two thirds
are ONLY 7/6 and 6/5, or ONLY 5/4 and 9/7.

Yes, you are saying to construct a scale in which they serve different
functions. And if you create a scale where they serve the same function, or
compare a just major scale with a just supermajor one, or meantone with
superpyth, they will sound "the same." It is certainly possible to create a
map in which 7/6 and 6/5 are distinguished and then draw a difference in
musical quality between them by referring to that map. You could probably
create a pseudo-map in which they're distinguished by just playing 6/5 and
7/6 over and over. But that is not the same as saying that sonic quality
derives only from the fundamental, as you can also create a map in which
they are interchangeable (i.e. superpyth aeolian vs meantone), and so will
they sound "the same."

> Then see if you can tell the difference when playing chord progressions.
HINT: you may need to go non-octave to get these scales to work. Perhaps
this will reveal that 5/4 can sound "minor", or that 6/5 can sound "major"?

Listen to the supermajor example :)

-Mike

MikeB>"Listening example:
http://www.mikebattagliamusic.com/music/supermajor.mp3
Again, does everything sound right, despite that the supermajor triads
are uncomfortably sharp? :)"

Hate to say it...but my ears are whining at me after about 20 seconds. It
sounds just plain disorganized to me from that point on. But, to be honest, the
9/7 to me sounds easily different than 5/4 right off the bat in the whole
"Do-Re-Mi" example at the beginning. It almost sounds like a very low
fourth...almost neutral in feel between the third and fourth. If you went back
and played Do-Re-FA note-by-note in one example and Do-Re-Mi in the next...I
think you'd be surprised how much they sound alike without, as in your example,
the Fa following the Mi. Which seems to just say that, when you play the scale
in ascending order, the brain tries to give it sounds akin to diatonic
notes...but if you make gaps in that order...I'm betting you'll hear your mind
string them together differently. Heck...I've seen the same thing happen with
7TET vs. diatonic under 12TET.

To it's credit it doesn't sound bad in the triads...but as soon as the more
complex parts take over it becomes blatantly obvious something different than
major feel is going on: kind of like the skew elaborates on itself. From
composition I get the feeling this is what generally happens with such "neurral"
interval that are right in-between two very strong ones: they shift color a lot
depending on what surrounds them...and when the colors quickly alternate, the
ears/brain gets confused.

Yes this is "subjective", no I don't have some massive survey to back it up
(hey, neither do you for your observations)...but all I can say is try the
example "tests" I describe and see what you think...I'm interested to see how
many people do/don't agree with the results of my tests when actually listening
to the sounds from the "counter-proof" tests I described.

Igs wrote:

> Describing intervals as "major" and "minor" is, I think, a red
> herring. And perhaps a false dichotomy. The terms themselves
> basically mean nothing more than "wide" and "narrow"

Most people feel that minor chords and keys sound 'sad'
whereas major ones sound 'happy'. That's an extremely
widely reported effect, much like the nearly universal
agreement that red is more 'active' than blue. Why Mike
doesn't experience such qualities and feels compelled to
wax on with irrelevant comparisons when asked about them
is certainly an interesting question.

-Carl

On Tue, Sep 14, 2010 at 2:57 PM, Carl Lumma <carl@...> wrote:
>
> Igs wrote:
>
> > Describing intervals as "major" and "minor" is, I think, a red
> > herring. And perhaps a false dichotomy. The terms themselves
> > basically mean nothing more than "wide" and "narrow"
>
> Most people feel that minor chords and keys sound 'sad'
> whereas major ones sound 'happy'. That's an extremely
> widely reported effect, much like the nearly universal
> agreement that red is more 'active' than blue. Why Mike
> doesn't experience such qualities and feels compelled to
> wax on with irrelevant comparisons when asked about them
> is certainly an interesting question.

Thanks for the unnecessary hostility and the elaborate strawman. I
don't ever remember saying that I didn't think major chords sounded
happy and that minor chords don't sound sad. What I said was that I
don't think those qualities have anything to do with psychoacoustics,
and emerge entirely from the diatonic and chromatic map that we all
have.

Listen to the second example, please.

-Mike

I wrote:
> What I said was that I
> don't think those qualities have anything to do with psychoacoustics,
> and emerge entirely from the diatonic and chromatic map that we all
> have.

To clarify, where I think that psychoacoustics fits into this is that
there are optimal ways of tuning things so that they are pleasant to
listen to. Supermajor triads are unpleasant because they're relatively
discordant, so they don't function well as stable sonorities. The same
doesn't hold for minor vs subminor triads.

-Mike

Hi Mike,

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

> Does the melody still sound like G-C-D-Eb-D-C to you after the i-iv-v? Or
> does it sound like G-C-D-mistuned D-D-C?
>
> Most importantly, CAN you get yourself to hear it that way if you want?

It sounds like the latter, and after listening to it several times in a row, I have no idea what I'm hearing anymore, so sure, it kinda sounds like the former. ;->

> I would like to hear your thoughts on the other example, since I feel it was
> more effective at accomplishing what I was going for.

Yes, the supermajor version sounds pretty normal to me. Rough, but normal. Now try a version of it where you use 21/16 instead of 9/7, and a version where you use 4/3, and let's see what happens!

I said:
>> Or, in other words, "is it possible to associate multiple
>> audibly-distinct psychoacoustic phenomena with the same perceptual gestalt?"

You said:
> Right. And I think that the answer is yes, although I'm not sure that Carl
> would disagree. But I think it's possible to hear 5/4 with a "minor gestalt"
> and 6/5 with a "major gestalt."

Have you tried it yet? I'm inclined to think the answer is yes, too, but I think we need some experimentation.

> Glad to see we are in such close agreement. I think that the debate here is
> really how much the qualitative nature of the "cognitive state" shift you're
> talking about comes directly from psychoacoustics and how much comes from
> psychology. That means, when you hear 4/3 as a 5/4 or a 3/2 or what not, are
> you actually changing how you perceive the fundamental of that dyad? Or is
> something else going on?

I guess this all presumes that I'm capable of perceiving the "fundamental" of the dyad. I've never been convinced that I'm capable of this. I can occasionally do it for triads, but generally-speaking, I'm never quite certain. It took one of my music-major friends a lot of work to convince me that A-C-F is the same chord as F-A-C. I was convinced that the former was clearly some kind of A chord, and that in general the "lowest note" was always the fundamental. Of course, I suppose if I called it "A-C-E#", I could have won the argument, but this was before I knew that "enharmonic equivalence" didn't just mean "musical synonym".

But I digress. If I play a drone, say "A", and then play various notes above it--say a 6/5, a 5/4, a 9/7, a 4/3, and a 3/2, I really don't know how to hear different "fundamentals" as the dyad changes. I hear "A" as the root, usually because, being a drone, I'm primed to think of it as the root. It's the same reason that "modes" are a legitimate way of thinking about music. Just because C Major and F Lydian share the same notes, it doesn't mean that C is always the tonic--we can tonicize any note in the scale, really. If this didn't work, then we could never resolve to F with the Lydian scale.

I guess where I'm going with this is that the psychoacoustic "fundamental" is a much weaker phenomenon than you think. I mean, I might hear a shift in the difference tones between 6:7:9 and 10:12:15, but I swear I don't hear either of them as having a "missing fundamental" that the difference tones fill in or whatever. If you build them both on "A", I hear them both as having "A" as the root.

> Can you listen to that supermajor example? :)

So, what exactly are you trying to demonstrate with this example? That a 9/7 does substitute for 5/4 with no alteration of musico-semantic content? It does feel a little different. But I'm pretty sure if you subbed 4/3 for 9/7, it wouldn't be like "oh my god it's a completely different WORLD!!!!". Sus4 chords have always felt like just "exaggerated major" chords to me.

> Yes, you are saying to construct a scale in which they serve different
> functions. And if you create a scale where they serve the same function, or
> compare a just major scale with a just supermajor one, or meantone with
> superpyth, they will sound "the same." It is certainly possible to create a
> map in which 7/6 and 6/5 are distinguished and then draw a difference in
> musical quality between them by referring to that map. You could probably
> create a pseudo-map in which they're distinguished by just playing 6/5 and
> 7/6 over and over. But that is not the same as saying that sonic quality
> derives only from the fundamental, as you can also create a map in which
> they are interchangeable (i.e. superpyth aeolian vs meantone), and so will
> they sound "the same."

Well, I still think you need to try my suggestion--WILL they sound distinct if the map distinguishes them? What if we concoct a map based on 5:6:7 triads and their utonal inversions (30:35:42), i.e. a hypothetical tonality where 5:7 takes the place of 2:3, 5:6 takes over for 4:5, and 6:7 takes over for 5:6? Such a map will clearly distinguish 5:6 from 6:7, but will we hear 5:6:7 as any more "major" than 30:35:42?

Hmm...I think I can more or less do this in 18-EDO, maybe *I* should try it? 18-EDO is, I believe, the lowest EDO that distinguishes 6/5 and 7/6, and its error is no worse than 12-tET in this regard.

Although, I think contrasting major and supermajor might be more illuminating...but I don't know what kind of scale you could use to do it. Using 4:5 and 7:9 to make chords leads to 28:35:45 and 28:36:45--not exactly a huge difference, and it'd be tough to say which one is otonal and which one is utonal, since they're so close in the harmonic series! In fact, I'd be surprised if I could tell the difference between them.

-Igs

P.S. did you read my reply at MMM?

On Tue, Sep 14, 2010 at 3:05 PM, cityoftheasleep
<igliashon@...> wrote:
>
> > I would like to hear your thoughts on the other example, since I feel it was
> > more effective at accomplishing what I was going for.
>
> Yes, the supermajor version sounds pretty normal to me. Rough, but normal. Now try a version of it where you use 21/16 instead of 9/7, and a version where you use 4/3, and let's see what happens!
//
> So, what exactly are you trying to demonstrate with this example? That a 9/7 does substitute for 5/4 with no alteration of musico-semantic content? It does feel a little different. But I'm pretty sure if you subbed 4/3 for 9/7, it wouldn't be like "oh my god it's a completely different WORLD!!!!". Sus4 chords have always felt like just "exaggerated major" chords to me.

The 9/7 substituting for 5/4 comparison is really a red herring;
there's another "feature" I've hidden in this which was really more my point:

The augmented second is tuned as 5/4. C-D#, that is, is 5/4, which
substitutes for 7/6 in 31-tet, and they both have the same meaning
here. It is a bit more "unstable" here because the scale is improper,
and hence the augmented second is a semitone larger than the minor
third, but I tried to finesse that away by choosing the melody
carefully.

First I play a huge cluster chord with the D#-E-F#-E-D#-E-B melody on
top; then I remove the cluster chord and play only the parallel
sixths. The third time around it's just bare dyads, e.g.
D#-E-F#-E-D#-E-B with a C on the bottom. The C-D# dyad is 5/4, and the
C-E dyad is 9/7, and yet the 5/4 still functions as an augmented
second in this case, and even has a bit of a minor vibe to it,
although the impropriety creates a bit of an unstable gestalt here. I
then did the whole thing over C-G-C so as to create a 2:3:4:5 sonority
when the D# is played, and it STILL resolves to E, although now it
sounds even more unstable still.

Either way I'll respond to the rest of your message later, I have to
take a break from here for a bit.

-Mike

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Igs wrote:
>
> > Describing intervals as "major" and "minor" is, I think, a red
> > herring. And perhaps a false dichotomy. The terms themselves
> > basically mean nothing more than "wide" and "narrow"

> Most people feel that minor chords and keys sound 'sad'
> whereas major ones sound 'happy'. That's an extremely
> widely reported effect, much like the nearly universal
> agreement that red is more 'active' than blue.

And yet, red is a lower-frequency, and thus lower-energy light than blue. Perhaps red is considered more active because of the universally-known things we associate with it: blood, fire, inflamed skin, the inside of a mouth, the sky at sunrise (time to begin activity) and sunset (time to prepare for the dangers of the coming darkness). Blue, OTOH, gets associated with the sky during calm weather and a body of water reflecting said sky--typically low-threat experiences. But I digress.

Yes, the familiar 4:5:6 and 10:12:15 triads of diatonic music are typically associated with "happy and sad" feelings. And yet, the V chord in a minor scale, typically played as a major, is a really sad-sounding chord. Devastating, even, if done right. And it remains to be seen if it's possible to force 4:5 into a "minor" feeling if the only third it has to contrast with is 7:9. I'm posing the question of whether the semantic content of major and minor chords comes from their contrast with each other, as opposed to their harmonic series identities.

Carl, can you suggest a scale that would enable us to treat 4:5 as a "minor" and 7:9 as a "major"?

-Igs

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
> If you really want to know how if 7/6 really differs from 6/5, or if 9/7 really differs from 5/4, concoct a few diatonic-esque scales where the two thirds are ONLY 7/6 and 6/5, or ONLY 5/4 and 9/7. Then see if you can tell the difference when playing chord progressions.

There are a bunch of "tritriad" scales in the Scala directory. Here's one:

! tritriad3d.scl
!
From 1/1 7/6 5/3, a variant of the 3.5.7 triad
7
!
7/6
6/5
25/18
7/5
5/3
35/18
2/1

If this is tempered in starling, it mutates into a six note scale. Replacing 25/18 by 4/3 and tempering would make sense, unless you want to avoid the sheer evil of a major triad.

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

> After the i-iv-v-iv-i, does the melody sound like G-C-D-Eb-D-C to you?

No.

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

> Supermajor triads are unpleasant because they're relatively
> discordant, so they don't function well as stable sonorities. The same
> doesn't hold for minor vs subminor triads.

I don't think they are unpleasant, though my on experiments with using them in place of major thirds suggests they aren't very good major thirds. And I would certainly not call them boring or irritating, which was my personal subjective reaction to certain 12et chords and intervals. They have a certain steely, bell-like quality which is actually quite nice for what it is, if you aren't trying to make it into a major third.

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

> What I said was that I don't think those qualities have anything
> to do with psychoacoustics, and emerge entirely from the diatonic
> and chromatic map that we all have.

I disagree.

> Listen to the second example, please.

Why?

-Carl

On Tue, Sep 14, 2010 at 3:19 PM, cityoftheasleep
<igliashon@...> wrote:
>
> Yes, the familiar 4:5:6 and 10:12:15 triads of diatonic music are typically associated with "happy and sad" feelings. And yet, the V chord in a minor scale, typically played as a major, is a really sad-sounding chord. Devastating, even, if done right.

Because it's a major chord with a different mapping behind it. Gadzooks

> And it remains to be seen if it's possible to force 4:5 into a "minor" feeling if the only third it has to contrast with is 7:9. I'm posing the question of whether the semantic content of major and minor chords comes from their contrast with each other, as opposed to their harmonic series identities.

That was the entire point of my second example, and now I'm going to
make a third.

-Mike

On Tue, Sep 14, 2010 at 3:57 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > After the i-iv-v-iv-i, does the melody sound like G-C-D-Eb-D-C to you?
>
> No.
//
> I don't think they are unpleasant, though my on experiments with using them in place of major thirds suggests they aren't very good major thirds. And I would certainly not call them boring or irritating, which was my personal subjective reaction to certain 12et chords and intervals. They have a certain steely, bell-like quality which is actually quite nice for what it is, if you aren't trying to make it into a major third.

Alright, I'll stop playing games and get to what I was getting at: I
like supermajor triads too. And the second example, which I think was
more successful in what I was trying to do, if you can get yourself to
hear 14:18:21 as a pseudo-diatonic "major" triad, then 5/4 can play
the role of the augmented second, and takes on a sort of "minor" vibe
to it. And then 9/7 takes on the quality of a major third, although it
is considerably more discordant and in this specific case fairly
irritating.

At least that's how I hear it, and seems to be how Igs is hearing it,
so I was curious how many other people hear it the same way.

-Mike

On Tue, Sep 14, 2010 at 4:11 PM, Carl Lumma <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > What I said was that I don't think those qualities have anything
> > to do with psychoacoustics, and emerge entirely from the diatonic
> > and chromatic map that we all have.
>
> I disagree.

OK.

> > Listen to the second example, please.
>
> Why?

You know what, on second thought, just don't worry about it.

-Mike

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

> That was the entire point of my second example, and now I'm going to
> make a third.

Neat, but I'm not sure I caught it. Can you make one a little more obvious?

Though, I'll say that playing around on my 16-EDO guitar using the 375-cent and 450-cent intervals as "6/5" and "5/4" to make a 750-cent "3/2", I clearly hear the 375 as sounding minor in comparison to the 450. CLEARLY. So yes, my ears seem to be in agreement with you! But I encourage more people to try it.

And please, give a listen to my 5:6 vs 6:7 example. There's a case that seems to show the opposite of the major vs. supermajor example!

-Igs

Heh, one listen-through. I could be wildly wrong, including whether there are 8 or 9 chords. I think there were 9, that's why I'm laughing--I'm not sure.

The chords bleed into each other, so that colors the effect.

They sound to me like 3-note chords.

They didn't sound "pure", like dead-on 7/6 or 6/5 isolated over a drone--easiest way to distinguish.

1)OT, so 7/6?

2) not OT, so 6/5?

3) not

4) not

5) OT

6) OT

7) not

8) not

9) OT

how'd I do?

(There's nothing riding on this--I've got no dog in this fight.)

caleb

On Sep 14, 2010, at 4:32 PM, cityoftheasleep wrote:

> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > That was the entire point of my second example, and now I'm going to
> > make a third.
>
> Neat, but I'm not sure I caught it. Can you make one a little more obvious?
>
> Though, I'll say that playing around on my 16-EDO guitar using the 375-cent and 450-cent intervals as "6/5" and "5/4" to make a 750-cent "3/2", I clearly hear the 375 as sounding minor in comparison to the 450. CLEARLY. So yes, my ears seem to be in agreement with you! But I encourage more people to try it.
>
> And please, give a listen to my 5:6 vs 6:7 example. There's a case that seems to show the opposite of the major vs. supermajor example!
>
> -Igs
>
>

On Tue, Sep 14, 2010 at 4:32 PM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > That was the entire point of my second example, and now I'm going to
> > make a third.
>
> Neat, but I'm not sure I caught it. Can you make one a little more obvious?

Check my reply to your last post, I wrote out where it occurs in
detail. Also, you mentioned that you haven't had common practice
training; it just occured to me that perhaps you don't read music?

The melody is D#-E-F#-E-D#-E-B, played over C. C-E is tuned 9/7, and
C-D# is tuned 5/4. I could also have written it Eb-E-F#-E-Eb-E-B, and
"decided" that it was going to be called C-Eb in this case, since I'm
not dealing with a linear temperament at this point. I then change the
chord underneath it to highlight the C-E as 5/4, throwing in a C-G-C
under it at the end, thus making it 2:3:4:5. At least to my ears, this
confuses my brain, because the C-G-C-D# is very concordant, but the
9/7 also sounds like a major third, and resolution upwards hence makes
"sense" in a different kind of way, and so on. A lot of this confusion
comes from, I think, the fact that the scale is improper; the
augmented second C-D# is over a semitone higher than the minor third
C-Eb, but I tried to avoid the ambiguity as best I can.

Hence how concordance and mappings work, I think: concordance creates
little islands of consonance within the larger framework of the map,
but it doesn't really matter too much what the exact concordance is.
Changing the exact concordance is like sort of changing the "shade" of
an underlying color, but not the color itself.

> Though, I'll say that playing around on my 16-EDO guitar using the 375-cent and 450-cent intervals as "6/5" and "5/4" to make a 750-cent "3/2", I clearly hear the 375 as sounding minor in comparison to the 450. CLEARLY. So yes, my ears seem to be in agreement with you! But I encourage more people to try it.

Right.

> And please, give a listen to my 5:6 vs 6:7 example. There's a case that seems to show the opposite of the major vs. supermajor example!

I'll give it a go. I'll respond to your other messages offlist, since
there are a lot of them and I have a lot to say.

-Mike

second listen

2 7/6's

2 6/5's

2 7/6's

2 6/5's

back to square 1

-c

On Sep 14, 2010, at 4:49 PM, caleb morgan wrote:

> Heh, one listen-through. I could be wildly wrong, including whether there are 8 or 9 chords. I think there were 9, that's why I'm laughing--I'm not sure.
>
>
> The chords bleed into each other, so that colors the effect.
>
> They sound to me like 3-note chords.
>
> They didn't sound "pure", like dead-on 7/6 or 6/5 isolated over a drone--easiest way to distinguish.
>
> 1)OT, so 7/6?
>
> 2) not OT, so 6/5?
>
> 3) not
>
> 4) not
>
> 5) OT
>
> 6) OT
>
> 7) not
>
> 8) not
>
> 9) OT
>
>
> how'd I do?
>
> (There's nothing riding on this--I've got no dog in this fight.)
>
> caleb
>
>
> On Sep 14, 2010, at 4:32 PM, cityoftheasleep wrote:
>
>>
>> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>>
>> > That was the entire point of my second example, and now I'm going to
>> > make a third.
>>
>> Neat, but I'm not sure I caught it. Can you make one a little more obvious?
>>
>> Though, I'll say that playing around on my 16-EDO guitar using the 375-cent and 450-cent intervals as "6/5" and "5/4" to make a 750-cent "3/2", I clearly hear the 375 as sounding minor in comparison to the 450. CLEARLY. So yes, my ears seem to be in agreement with you! But I encourage more people to try it.
>>
>> And please, give a listen to my 5:6 vs 6:7 example. There's a case that seems to show the opposite of the major vs. supermajor example!
>>
>> -Igs
>>
>
>
>

Igs wrote:

> > Most people feel that minor chords and keys sound 'sad'
> > whereas major ones sound 'happy'. That's an extremely
> > widely reported effect, much like the nearly universal
> > agreement that red is more 'active' than blue.
>
> And yet, red is a lower-frequency, and thus lower-energy
> light than blue.

Correct.

> Perhaps red is considered more active because of the
> universally-known things we associate with it: blood, fire,
> inflamed skin, the inside of a mouth, the sky at
> sunrise (time to begin activity) and sunset (time to
> prepare for the dangers of the coming darkness).

Aren't toxic frogs and sexy bird feathers more often red?
Our eyes are more sensitive in the 600-700nm range than
the 400-500nm range:
http://en.wikipedia.org/wiki/File:Eyesensitivity.png

> And it remains to be seen if it's possible
> to force 4:5 into a "minor" feeling if the only third it has
> to contrast with is 7:9.

Not a chance.

> Carl, can you suggest a scale that would enable us to treat
> 4:5 as a "minor" and 7:9 as a "major"?

This came up in connection with mavila, when Mike wrote:

>>I wonder if someone who was raised on mavila would hear
>>the pieces I hear as being in major as being in minor,
>>and so on.

My answer to that is, heck no. Here's a scl file with
mavila[7] mapped to the white notes:

!
mavila[7] in 30-ET for C Major keyboard mapping.
12
!
100.0 ! C#
160.0
300.0 ! Eb
320.0
520.0
600.0 ! F#
680.0
800.0 ! Ab
840.0
950.0 ! Bb
1000.0
2/1
!

-Carl

Mike wrote:

>> And yet, the V chord in a minor scale, typically played as a
>> major, is a really sad-sounding chord. Devastating, even, if
>> done right.
>
> Because it's a major chord with a different mapping behind it.
> Gadzooks

Yes. But the mapping has the quality it does because of the
bare quality of its tonic triad. -Carl

Mike wrote:

> > Why?
>
> You know what, on second thought, just don't worry about it.

I did listen of course. The googles did nothing. -C.

Carl:
> Most people feel that minor chords and keys sound 'sad'
> whereas major ones sound 'happy'.

My perception on that is the same.

However on another level, I have heard minor chords as more
relaxed in, say, a piece with a sad feel than a major chord...and
that, indeed, if what Mike is talking about is tension of
major vs. minor (that they can be swapped in function and gestalt
across tunings)...I agree with him. That is...if a tuning has a
more "minor" feel, the minor chord sounds more relaxed to me...and
if a tuning has a more "major" feel the major chord sounds more
relaxed. I experience this when I compose electronica
(particularly Trance and D&B) where anything that doesn't sound
dark sounds undisciplined/corny/out-of-place and more tense (both
in terms of use of minor chord and scales).

The Indonesians hear slendro as sad and pelog as happy.
Pretty much the opposite of us.
It seem more attention is put on how others hear while forgetting ones own.
what good are universals if they don't sound good to you.

/^_,',',',_ //^ /Kraig Grady_ ^_,',',',_
Mesotonal Music from:
_'''''''_ ^North/Western Hemisphere:
North American Embassy of Anaphoria Island <http://anaphoria.com/>

_'''''''_ ^South/Eastern Hemisphere:
Austronesian Outpost of Anaphoria <http://anaphoriasouth.blogspot.com/>

',',',',',',',',',',',',',',',',',',',',',',',',',',',',',

a momentary antenna as i turn to water
this evaporates - an island once again

On 15/09/10 4:57 AM, Carl Lumma wrote:
>
> Igs wrote:
>
> > Describing intervals as "major" and "minor" is, I think, a red
> > herring. And perhaps a false dichotomy. The terms themselves
> > basically mean nothing more than "wide" and "narrow"
>
> Most people feel that minor chords and keys sound 'sad'
> whereas major ones sound 'happy'. That's an extremely
> widely reported effect, much like the nearly universal
> agreement that red is more 'active' than blue. Why Mike
> doesn't experience such qualities and feels compelled to
> wax on with irrelevant comparisons when asked about them
> is certainly an interesting question.
>
> -Carl
>
>

On Tue, Sep 14, 2010 at 5:23 PM, Carl Lumma <carl@...> wrote:
>
> Mike wrote:
>
> >> And yet, the V chord in a minor scale, typically played as a
> >> major, is a really sad-sounding chord. Devastating, even, if
> >> done right.
> >
> > Because it's a major chord with a different mapping behind it.
> > Gadzooks
>
> Yes. But the mapping has the quality it does because of the
> bare quality of its tonic triad. -Carl

If you play this scale as phrygian dominant, e.g. C Db E F G Ab Bb C - which
is a way that it's prominently used in middle eastern cultures - the I chord
becomes C-E-G. This doesn't sound "happy" as much as "mystical" or
something. Here's an example I found:
http://www.youtube.com/watch?v=bucvq1V6MjA

So the musical identity of any one chord is almost completely determined by
the rest of the notes in the scale. What I am finding is that this concept
goes even further when we're dealing with extremely tempered scales, or
stuff that gets completely away from diatonic.

I am, admittedly, very surprised to see all of the disagreement here, since
I basically went to Paul with the "psychoacoustic identity" theory, and he
set me straight with this new paradigm (which I feel is simpler and more
accurate), and I had just assumed this is how everyone saw it. Clearly I
didn't realize that there was such a diversity of opinion on the lists,
given that everyone is in agreement on 99% of it. Has this been a
long-standing source of disagreement here?

On Tue, Sep 14, 2010 at 5:24 PM, Carl Lumma <carl@...> wrote:
>
> Mike wrote:
>
> > > Why?
> >
> > You know what, on second thought, just don't worry about it.
>
> I did listen of course. The googles did nothing. -C.

Er, what do you mean? As per your own statements, supermajor chords sound
like detuned major chords because 9/7 is still in 5/4's sphere of influence.
And from a periodicity standpoint, as per my timbre test, you are absolutely
right. So I constructed a musical supermajor example, and to me it sounds
like a very discordant Lydian #2 scale.

You have no doubt read the "punchline" by now since I've typed it over and
over. The point wasn't that 9/7 can just be a crappy major third, but that
if you get used to 9/7 being the crappy major third, then 5/4 can be the
crappy augmented second. Although it's very weird for the C-D# to be tuned
as a concordant interval and move to C-E which is tuned as a discordant
interval, it still works. It isn't ideal from an intonational standpoint but
it doesn't destroy the entire sonority. What does very nearly destroy the
entire sonority is that the scale is extremely improper, but I tried to be
clever about handling that.

And how did you hear it?

-Mike

Hi Kraig,

> The Indonesians hear slendro as sad and pelog as happy.
> Pretty much the opposite of us.

Not of me -- I definitely hear pelog as happy. I haven't
had as much exposure to slendro to say, other than it's not
as happy as pelog.

-Carl

Hi Carl,

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> > And it remains to be seen if it's possible
> > to force 4:5 into a "minor" feeling if the only third it has
> > to contrast with is 7:9.
>
> Not a chance.

Okay, well, I haven't tried this with 7:9 yet, but on my 16-EDO guitar I've been playing around with approximate 10:13:16 chords, i.e. 0-450-825 (I miss-counted the 825 as a 750-cent interval in a previous post), and I can definitely say that in comparison, a 0-375-825 chord sounds pretty gosh-darn minor. But I guess this is comparing an approximate 16/13 to an approximate 10/13, even though 375 cents is really closer to 5/4 than it is to 16/13.

But let me try playing some 22-EDO (I'll have to use a keyboard since I sold my 22-EDO guitar), we'll see if I can get a 1-5/4-8/5 triad to sound minor compared to a 1-9/7-8/5 triad.

> > Carl, can you suggest a scale that would enable us to treat
> > 4:5 as a "minor" and 7:9 as a "major"?
>
> This came up in connection with mavila, when Mike wrote:
>
> >>I wonder if someone who was raised on mavila would hear
> >>the pieces I hear as being in major as being in minor,
> >>and so on.
>
> My answer to that is, heck no. Here's a scl file with
> mavila[7] mapped to the white notes:

I think Mike was referring to 7-EDO with that comment, i.e. that he hears some 7-EDO pieces as more "major", and he wonders if someone used to Mavila would hear those same pieces as more "minor".

I don't think that would be the case, either, but for the reason that Mavila isn't really all that different from the Diatonic, from a chordal perspective. You still have 3 minor and 3 major chords, they're still connected by a chain of "fifths", it's just that the VII chord is augmented instead of diminished. I play in Mavila all the damn time and I have to say that chord progressions like I-III-VI-IV-II-V don't sound bizarre at all, they sound totally diatonic and normal (if you ignore the beating fifth). It's only when you move by the neutral 2nd that changes start to sound weird, like in a I-V-IV-II-III or something. But even then, it's not that pronounced. And you can play Mavila modally, too, and tonicize the major VI chord just as easily as you can tonicize the minor VI chord in a Major scale.

-Igs

Mike wrote:

> I am, admittedly, very surprised to see all of the disagreement
> here, since I basically went to Paul with the "psychoacoustic
> identity" theory, and he set me straight with this new paradigm
> (which I feel is simpler and more accurate), and I had just
> assumed this is how everyone saw it. Clearly I didn't realize
> that there was such a diversity of opinion on the lists, given
> that everyone is in agreement on 99% of it. Has this been a
> long-standing source of disagreement here?

Actually this came up in 2000 (about whether the minor quality
of the minor scale comes from the scale or its tonic triad) and
Paul agreed I was right. Here's the message:

/tuning/topicId_10208.html#10219

-Carl

Igs:

> I play in Mavila all the damn time and I have to say that
> chord progressions like I-III-VI-IV-II-V don't sound bizarre
> at all, they sound totally diatonic and normal

Sure, but do minor triads start to sound happy and major
ones sad? Of course not! -C.

Mike wrote:

> > Yes. But the mapping has the quality it does because of the
> > bare quality of its tonic triad. -Carl
>
> If you play this scale as phrygian dominant,
> e.g. C Db E F G Ab Bb C - which is a way that it's prominently
> used in middle eastern cultures - the I chord becomes C-E-G.
> This doesn't sound "happy" as much as "mystical" or something.

It sounds minor, because usually they hang out almost exclusively
on the V or the III, where there are minor thirds. Maqam music
is non-diatonic. The whole point is to travel far away from the
tonic, and only touch on it briefly at the ends of extended
phrases.

> Here's an example I found:
> http://www.youtube.com/watch?v=bucvq1V6MjA

Yeah, as usual, the 'tonic' triad is avoided at all costs.
When you do hear it, it sounds happy as ever.

> > > > Why?
> > >
> > > You know what, on second thought, just don't worry about it.
> >
> > I did listen of course. The googles did nothing. -C.
>
> Er, what do you mean?

What am I supposed to be listening for?

> You have no doubt read the "punchline" by now since I've typed
> it over and over. The point wasn't that 9/7 can just be a crappy
> major third, but that if you get used to 9/7 being the crappy
> major third, then 5/4 can be the crappy augmented second.
> Although it's very weird for the C-D# to be tuned as a
> concordant interval and move to C-E which is tuned as a
> discordant interval, it still works.

So you're saying is that a 5/4 can behave like a 2nd if
it is, in fact, a 2nd. That should hardly be surprising.
What's the URL again?

-Carl

On Tue, Sep 14, 2010 at 6:48 PM, Carl Lumma <carl@...> wrote:
>
> > Here's an example I found:
> > http://www.youtube.com/watch?v=bucvq1V6MjA
>
> Yeah, as usual, the 'tonic' triad is avoided at all costs.
> When you do hear it, it sounds happy as ever.

It sounds "like major," but I wouldn't say it sounds happy.

> > Er, what do you mean?
>
> What am I supposed to be listening for?

Just to see if what you hear and the score match up.

> So you're saying is that a 5/4 can behave like a 2nd if
> it is, in fact, a 2nd. That should hardly be surprising.
> What's the URL again?

That's not what I'm saying. Before I tell you what I'm saying, I'd rather
you just listen to it.
http://www.mikebattagliamusic.com/music/supermajor.mp3

-Mike

Mike wrote:

> That's not what I'm saying. Before I tell you what I'm saying,
> I'd rather you just listen to it.
> http://www.mikebattagliamusic.com/music/supermajor.mp3

Ok, I listened again for the first time. Now where's the beef?

-Carl

On Tue, Sep 14, 2010 at 7:01 PM, Carl Lumma <carl@...> wrote:
>
> Mike wrote:
>
> > That's not what I'm saying. Before I tell you what I'm saying,
> > I'd rather you just listen to it.
> > http://www.mikebattagliamusic.com/music/supermajor.mp3
>
> Ok, I listened again for the first time. Now where's the beef?

So you would say that it matches up to the score all the way through,
although it sounds "detuned"?
http://www.mikebattagliamusic.com/music/supermajorchromatic.pdf

-Mike

As mentioned in that thread, my theory says that all ASSes
should sound minor. That's all the chords in the table at
the bottom of this page:

http://x31eq.com/ass.htm

-Carl

I wrote:

> Actually this came up in 2000 (about whether the minor quality
> of the minor scale comes from the scale or its tonic triad) and
> Paul agreed I was right. Here's the message:
>
> /tuning/topicId_10208.html#10219

On Tue, Sep 14, 2010 at 6:21 PM, Carl Lumma <carl@...> wrote:
>
> Actually this came up in 2000 (about whether the minor quality
> of the minor scale comes from the scale or its tonic triad) and
> Paul agreed I was right. Here's the message:
>
> /tuning/topicId_10208.html#10219

As you know I think the tritone explanation is a bit simplistic, but we need
not go into that now for fear of destroying the inboxes of the list.
Needless to say, I disagree; I think that perhaps some of it comes from the
psychoacoustic quality of the minor triad (at this point I think it's
doubtful), but most of it comes from placing it mentally in a diatonic
setting, and people have trouble distinguishing the two. I think that the
fact that mavila[7] and meantone[7] aren't indistinguishable comes from the
fact that they have two completely different rank order matrices, and that
mavila[5] and meantone[5] are a bit more similar.

Have you listened to the mavila->neutral example yet? I'm really interested
to hear your thoughts on that one.

-Mike

Mike:

> > > http://www.mikebattagliamusic.com/music/supermajor.mp3
> >
> > Ok, I listened again for the first time. Now where's the beef?
>
> So you would say that it matches up to the score all the way through,
> although it sounds "detuned"?
> http://www.mikebattagliamusic.com/music/supermajorchromatic.pdf

I don't know. The detuning is pretty severe compared to what
I expect looking at the score. -Carl

Mike wrote:

> Have you listened to the mavila->neutral example yet? I'm really
> interested to hear your thoughts on that one.

I've listened to everything you've posted, most of it more
than once. None of it seems to have anything to do with
anything. Here's one for instance:

> /tuning/files/MikeBattaglia
> /flatdiatonic.mid
>
> It should sound like this:
>
> C-Eb-G
> C-D-Eb-F-G
> C-D-Eb-F-G (sustained)
> C-G-D-A-E (octave equivalent, sustained)

-Carl

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

> Sure, but do minor triads start to sound happy and major
> ones sad? Of course not! -C.
>

Yeah, that was kind of my point! ;->

-Igs

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

> Have you listened to the mavila->neutral example yet? I'm really interested
> to hear your thoughts on that one.
>
> -Mike
>

I couldn't figure out what it was that was supposed to sound like a major third.

Yes, besides both terms are well established and essential for all tonal and extended tonal music, functional harmony etc. That means few hundred years of development of Western music and its theory. There's no reason to stop using such basic terms for the music which they describe well and belong to. We don't need to analyze Mozart's music from the point of view of 72 EDO for example. Major/minor is enough good.

It can be used even for atonal music, but of course it's not necessary, we can use just numbers to describe size of intervals. Chords have often different structure than triadic, there's no place for "major" and "minor".

Most of microtonal music needs (and uses) a new terminology, where "major" and "minor" is not necessary and maybe even should be avoided.

Daniel Forro

On 15 Sep 2010, at 3:57 AM, Carl Lumma wrote:

> Igs wrote:
>
>> Describing intervals as "major" and "minor" is, I think, a red
>> herring. And perhaps a false dichotomy. The terms themselves
>> basically mean nothing more than "wide" and "narrow"
>
> Most people feel that minor chords and keys sound 'sad'
> whereas major ones sound 'happy'. That's an extremely
> widely reported effect, much like the nearly universal
> agreement that red is more 'active' than blue. Why Mike
> doesn't experience such qualities and feels compelled to
> wax on with irrelevant comparisons when asked about them
> is certainly an interesting question.
>
> -Carl

On Tue, Sep 14, 2010 at 7:19 PM, Carl Lumma <carl@...> wrote:
>
> As mentioned in that thread, my theory says that all ASSes
> should sound minor. That's all the chords in the table at
> the bottom of this page:
>
> http://x31eq.com/ass.htm

3:5:19:15 sounds major to me right off the bat. It's a maj6 chord in some
goofy spread out voicing.

> I don't know. The detuning is pretty severe compared to what
> I expect looking at the score. -Carl

If that's the case, which it isn't for me, then I suppose for you supermajor
chords really do end up sounding like different sonorities.

On Tue, Sep 14, 2010 at 7:28 PM, Carl Lumma <carl@...> wrote:
>
> Mike wrote:
>
> > Have you listened to the mavila->neutral example yet? I'm really
> > interested to hear your thoughts on that one.
>
> I've listened to everything you've posted, most of it more
> than once. None of it seems to have anything to do with
> anything. Here's one for instance:

I'm asking if the neutral C-D-E-G-A at the end sounds colored with the major
sonority or not to you. To me, it does. I'm sure you can figure out the
purpose of posting auditory examples in a discussion over the fundamental
nature of musical perception. If not, then like I said, just don't worry
about it.

-Mike

On Tue, Sep 14, 2010 at 7:52 PM, genewardsmith <genewardsmith@...>
wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > Have you listened to the mavila->neutral example yet? I'm really
interested
> > to hear your thoughts on that one.
> >
> > -Mike
> >
>
> I couldn't figure out what it was that was supposed to sound like a major
third.

The last bit, the C-G-D-A-E. It all sounded minor to you?

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> The last bit, the C-G-D-A-E. It all sounded minor to you?

It just sounded terrible. I think the pitch bends were
screwing up with the sustain. I tried two players. -Carl

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Tue, Sep 14, 2010 at 7:19 PM, Carl Lumma <carl@...> wrote:
> >
> > As mentioned in that thread, my theory says that all ASSes
> > should sound minor. That's all the chords in the table at
> > the bottom of this page:
> >
> > http://x31eq.com/ass.htm
>
> 3:5:19:15 sounds major to me right off the bat. It's a maj6
> chord in some goofy spread out voicing.

Do you mean 3:5:9:15? That's not a voicing, it's just
odd numbers. You should try all inversions. I will too
(later tonight).

> I'm sure you can figure out the
> purpose of posting auditory examples in a discussion over the
> fundamental nature of musical perception. If not, then like
> I said, just don't worry about it.

No, I just think your examples suck. You still haven't said
what we're supposed to be listening for and why, and even if
you did, they sound so funky I don't think I'd hear it.

-Carl

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

> The last bit, the C-G-D-A-E. It all sounded minor to you?

IIRC it started out in the key of dismal and mutated to slightly weird. Interesting stuff, really.

On Tue, Sep 14, 2010 at 11:57 PM, Carl Lumma <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > The last bit, the C-G-D-A-E. It all sounded minor to you?
>
> It just sounded terrible. I think the pitch bends were
> screwing up with the sustain. I tried two players. -Carl

There is supposed to be sustain. I uploaded it again though, in mp3
form, here: http://www.mikebattagliamusic.com/music/flatdiatonic.mp3

It is, again, supposed to be a very detuned version of:

C-Eb-G
C-D-Eb-F-G
C-D-Eb-F-G (sustained)
C-G-D-A-E (sustained, cluster chord, pentatonic scale played
simultaneously in one octave, with a slight major sonority to it)

Your job is to tell me if that's how you hear it. And if not at first,
if you can play with your perception to hear it that way, especially
the last chord.

On Wed, Sep 15, 2010 at 12:01 AM, Carl Lumma <carl@...> wrote:
>
> > 3:5:19:15 sounds major to me right off the bat. It's a maj6
> > chord in some goofy spread out voicing.
>
> Do you mean 3:5:9:15?

Yes.

> That's not a voicing, it's just
> odd numbers.

...Uh? Are you telling me that I can make it octave equivalent? Right
now 3:5:9:15 sounds like a maj6 chord in a goofy spread out voicing.

> You should try all inversions. I will too
> (later tonight).

OK, keeping it spread out, these are my impressions:

3:5:9:15 - this is a maj6 chord in a goofy spread out voicing.
5:9:15:24 - this is a m7 chord in a goofy spread out voicing.
9:15:24:40 - this is a maj6 chord in third inversion, in a goofy
spread out voicing
15:24:40:72 - this is a m7 chord in a voicing that is spread out, and goofy

> No, I just think your examples suck. You still haven't said
> what we're supposed to be listening for

I have told you over, and over, and over again what you're supposed to
be listening for. I have typed it really quite a few times now. At
this point I don't know what you want. I actually took the time not
only to make the examples, but to make a score for each one, and
asking you to confirm or deny if you hear the examples as written in
the score.

This is absurd: I spent all of that time writing a score, rendering
mp3's and uploading pdf's and so on, telling you exactly what to
listen for, and you're trying to frame it like these are just random
unmusical examples that I'm throwing out of left field? What the hell
are you trying to do? Get a rise out of me?

> and why

Because in each instance, I have hidden various intervals in ways that
you wouldn't expect, making them sound much different than you're used
to. However, the scales are all improper, which means that they're
unstable, and so the perception is such that it can "flip flop"
between the regular diatonic meaning for that interval and the altered
one. I didn't tell you which is which because I don't want to
introduce any bias into the equation. So I simply asked if you heard
it like it's written in the score.

The question is whether the flip flopping comes from scale
impropriety, or from the fundamental reverting to some more "basic"
"meaning.' An example in which JI intervals are being substituted with
other ones and there is no impropriety would basically answer this
question - if the chords in the scale sound unrecognizably different,
then it comes down to periodicity stuff, if they sound the same, then
it comes down to mapping. At the very least, a scale which is only
"slightly" improper, or where the impropriety is hidden in intervals
that aren't often played, or where the impropriety is such that
cognitively it's still "mostly proper," would suffice.

I know of one such scale in which this is the case, and it's the
superpyth aeolian vs the meantone aeolian example, and it behaves as I
would expect.

> and even if you did, they sound so funky I don't think I'd hear it.

I got in a discussion with my friends a while ago about high-energy
physics. I told them that if you had a nuclear bomb, and you put it in
a giant thermodynamically sealed box that was impervious to
destruction, put it on a giant scale, and then detonated the bomb, the
weight of the box wouldn't go down. I then said that if you opened up
a windowpane in the box that simply allows light to leave, the weight
of the box would go down.

They thought that it was a "silly example," because it was just
completely impractical and unrealistic. I said that if we're going to
be talking about theoretical physics at all, then we're going to be
dealing with "impractical" examples that push the limits of reality,
and to criticize my example on that grounds is absurd.

If we're going to be dealing with the fundamentals of musical
perception, we're going to be dealing with examples that push the
limits of musical perception, so to criticize them on the grounds that
they're "unmusical" or "unpleasant" is likewise absurd. They're
supposed to sound like distorted diatonic melodies, because to figure
out how this works, the approach I'm taking is to distort them until
something breaks, and find out where and how.

-Mike

Mike wrote:

> There is supposed to be sustain. I uploaded it again though,
> in mp3 form, here:
> http://www.mikebattagliamusic.com/music/flatdiatonic.mp3

Yes I know. Often gives bad results with MIDI pitchbend retuning.
This is somewhat better.

> It is, again, supposed to be a very detuned version of:
> C-Eb-G
> C-D-Eb-F-G
> C-D-Eb-F-G (sustained)
> C-G-D-A-E (sustained, cluster chord, pentatonic scale played
> simultaneously in one octave, with a slight major sonority to it)
> Your job is to tell me if that's how you hear it.

How I hear it how? It sounds very much as you describe it!

> > That's not a voicing, it's just
> > odd numbers.
>
> ...Uh? Are you telling me that I can make it octave equivalent?

These are odd-limit beasts, so yes. Graham says so on the page.

> Right now 3:5:9:15 sounds like a maj6 chord in a goofy spread
> out voicing.
>
> > You should try all inversions. I will too (later tonight).
>
> OK, keeping it spread out, these are my impressions:
>
> 3:5:9:15 - this is a maj6 chord in a goofy spread out voicing.

10:12:15:18 is the usual voicing (1/1 6/5 3/2 9/5) - a min7
chord. The M6 voicing is the next inversion (1/1 5/4 3/2 5/3).
Then comes 1/1 6/5 4/3 8/5, and finally 1/1 10/9 4/3 5/3.
Conveniently all these can be played with the scale

!
10:12:15:18 ASS scale
12
!
100.0 ! C#
10/9
6/5
5/4
4/3
600.0 ! F#
3/2
8/5
5/3
9/5
1100.0 ! B
2/1
!

C Eb G Bb: sounds minor
C E G A: sounds minor
C Eb F Ab: sounds minor, perhaps more so than the others
C D F A: sounds minor, perhaps less so than the others

There you have it.

-Carl

MikeB>"if the chords in the scale sound unrecognizably different, then it comes
down to periodicity stuff"
So, in other words, your example really leans more toward scales where there
is a lot of temperament and context determines in which direction IE toward
which of two possible JI intervals each chord is tempered?

Also, do I have it right that you are saying there may be a diatonic map
which pushes you in which direction the brain (in the case of being in-between
two JI intervals) interprets the interval as? If I also have it right...this
would be different from Harmonic Entropy in that simpler ratios wouldn't be the
ones with most "gravity"...and instead diatonic ones would be (and, perhaps,
things like the root tone changing could swap the base tone of the chord and
turn a minor dyad to be interpreted as major one in order to better fit the new
root tone assuming a diatonic "scale" (within the new chord) starting from the
new root tone of that new chord)?

On Wed, Sep 15, 2010 at 3:03 AM, Carl Lumma <carl@...> wrote:
>
> > It is, again, supposed to be a very detuned version of:
> > C-Eb-G
> > C-D-Eb-F-G
> > C-D-Eb-F-G (sustained)
> > C-G-D-A-E (sustained, cluster chord, pentatonic scale played
> > simultaneously in one octave, with a slight major sonority to it)
> > Your job is to tell me if that's how you hear it.
>
> How I hear it how? It sounds very much as you describe it!

I know it does :)

Want to guess how the Eb is tuned, and how the E is tuned?

> > Right now 3:5:9:15 sounds like a maj6 chord in a goofy spread
> > out voicing.
> >
> > > You should try all inversions. I will too (later tonight).
> >
> > OK, keeping it spread out, these are my impressions:
> >
> > 3:5:9:15 - this is a maj6 chord in a goofy spread out voicing.
>
> 10:12:15:18 is the usual voicing (1/1 6/5 3/2 9/5) - a min7
> chord. The M6 voicing is the next inversion (1/1 5/4 3/2 5/3).
> Then comes 1/1 6/5 4/3 8/5, and finally 1/1 10/9 4/3 5/3.
> Conveniently all these can be played with the scale

I will check this out. Is this a CPS?

> C Eb G Bb: sounds minor
> C E G A: sounds minor
> C Eb F Ab: sounds minor, perhaps more so than the others
> C D F A: sounds minor, perhaps less so than the others
>
> There you have it.

When you say you hear C E G A as minor, you mean that you hear it as an Am7
chord, fundamentally, in first inversion? I definitely do not hear C E G A
as anything but a major 6 chord if I'm unprimed, but I can "imagine" it as a
m7 chord in inversion very easily. C D F A is the most naturally ambiguous
one for me, as I can hear it as Dm/C (I'm imagining D dorian chord
progressions in my head as I write this), or Fmaj6/C (I'm imagining a
plagal cadence resolving to C as I write this).

But like I said, I can imagine this chord two ways very easily. I can also
imagine C-Eb-G-Bb as Abmaj9, or Fsus9. Part of what I had to learn at school
was to "reframe" chords like that (my teacher calls it developing "the bass
player in your head"). The ones I wrote above were my unprimed impressions,
which are a bit arbitrary really as the slightest shred of context can
destroy them.

-Mike

On Wed, Sep 15, 2010 at 1:44 AM, Michael <djtrancendance@...> wrote:
>
> MikeB>"if the chords in the scale sound unrecognizably different, then it comes down to periodicity stuff"
>    So, in other words, your example really leans more toward scales where there is a lot of temperament and context determines in which direction IE toward which of two possible JI intervals each chord is tempered?
//
>    Also, do I have it right that you are saying there may be a diatonic map which pushes you in which direction the brain (in the case of being in-between two JI intervals) interprets the interval as?   If I also have it right...this would be different from Harmonic Entropy in that simpler ratios wouldn't be the ones with most "gravity"...and instead diatonic ones would be (and, perhaps, things like the root tone changing could swap the base tone of the chord and turn a minor dyad to be interpreted as major one in order to better fit the new root tone assuming a diatonic "scale" (within the new chord) starting from the new root tone of that new chord)?

Right, so this is a clever question, and one that it is good that you
ask. If you've listened to my examples so far, then you've heard
instances in which 5/4 functions as an aug2 (which would be 75/64 if
JI was what mattered). In 12-tet, this interval is approximately 6/5.
In 31-tet, it's 7/6. Makes no difference. And I'm not talking about
like an aug2 as just a randomly altered chromatic interval, I'm
talking about C-E-B-D#, which is a maj7#9 chord, and it has a certain
"quality" to it, and that is the "quality" of the aug2 interval.

And if you listened to the recent mavila example, then you heard 6/5
take on a very "flat major" quality.

So what you're really asking is - when I'm hearing 5/4 as an aug2, is
my brain placing 5/4 as 75/64? When I hear 6/5 as major, is my brain
placing 6/5 as 5/4? When I hear subminor chords function just as well
as minor chords in a tempered aeolian scale, is my brain placing 7/6
as 6/5?

Or is something else going on?

That's what you're asking, I think. And it's a good question, and one
I don't have the answer for.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> I know it does :)
> Want to guess how the Eb is tuned, and how the E is tuned?

Not really.

> > 10:12:15:18 is the usual voicing (1/1 6/5 3/2 9/5) - a min7
> > chord. The M6 voicing is the next inversion (1/1 5/4 3/2 5/3).
> > Then comes 1/1 6/5 4/3 8/5, and finally 1/1 10/9 4/3 5/3.
> > Conveniently all these can be played with the scale
>
> I will check this out. Is this a CPS?

Most things are. But it's not a principle CPS.

> > C Eb G Bb: sounds minor
> > C E G A: sounds minor
> > C Eb F Ab: sounds minor, perhaps more so than the others
> > C D F A: sounds minor, perhaps less so than the others
> >
> > There you have it.
>
> When you say you hear C E G A as minor, you mean that you hear
> it as an Am7 chord, fundamentally, in first inversion?

No, I mean I hear it as a chord of low tonalness and low
roughness.

-Carl

On Wed, Sep 15, 2010 at 4:08 AM, Carl Lumma <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > I know it does :)
> > Want to guess how the Eb is tuned, and how the E is tuned?
>
> Not really.

Why, I thought you'd never ask! The Eb is tuned as a bit flat of 7/6,
and the E is tuned as a 6/5. So when you said that you heard the
mavila[5] pentatonic scale as a really flat major, you were hearing
6/5 as a really flat major.

(There you go, Igs.)

> > When you say you hear C E G A as minor, you mean that you hear
> > it as an Am7 chord, fundamentally, in first inversion?
>
> No, I mean I hear it as a chord of low tonalness and low
> roughness.

...How was I ever going to know that that was your definition of "minor"?

Is 6:7:9 "minor"?

-Mike

Mike wrote;

> Why, I thought you'd never ask! The Eb is tuned as a bit flat
> of 7/6, and the E is tuned as a 6/5. So when you said that you
> heard the mavila[5] pentatonic scale as a really flat major,
> you were hearing 6/5 as a really flat major.

When did I say that?

> > No, I mean I hear it as a chord of low tonalness and low
> > roughness.
>
> ...How was I ever going to know that that was your definition
> of "minor"?

By reading the thread from ten years ago you seemed to
have read.

> Is 6:7:9 "minor"?

Only to the extent the 6 is established as the root.

-Carl

On Wed, Sep 15, 2010 at 4:27 AM, Carl Lumma <carl@...> wrote:
>
> Mike wrote;
>
> > Why, I thought you'd never ask! The Eb is tuned as a bit flat
> > of 7/6, and the E is tuned as a 6/5. So when you said that you
> > heard the mavila[5] pentatonic scale as a really flat major,
> > you were hearing 6/5 as a really flat major.
>
> When did I say that?

Two replies ago. I gave a description of the scale as starting out in
minor and then moving into a really flat pentatonic major at the end,
and you said that's exactly how you hear it. And I'm saying, that's
how I hear it too, and all of that despite the "major third" being
6/5.

> > ...How was I ever going to know that that was your definition
> > of "minor"?
>
> By reading the thread from ten years ago you seemed to
> have read.

I couldn't actually read it, because it was split up. The link you
sent me to seemed to have Paul replying to things that you'd said, but
those posts didn't come up in the thread.

> > Is 6:7:9 "minor"?
>
> Only to the extent the 6 is established as the root.

Alright, so that there are no more miscommunications, what is your
theory? So to you majorness refers to any triad that points to a
single fundamental, and minorness refers to any triad that points to
multiple fundamentals simultaneously, is concordant, and doesn't beat?
And somehow those become happiness and sadness in complex,
Rorshach-like fashion?

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Tue, Sep 14, 2010 at 11:57 PM, Carl Lumma <carl@...> wrote:
> >
> > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> > >
> > > The last bit, the C-G-D-A-E. It all sounded minor to you?
> >
> > It just sounded terrible. I think the pitch bends were
> > screwing up with the sustain. I tried two players. -Carl
>
> There is supposed to be sustain. I uploaded it again though, in mp3
> form, here: http://www.mikebattagliamusic.com/music/flatdiatonic.mp3
>
> It is, again, supposed to be a very detuned version of:
>
> C-Eb-G
> C-D-Eb-F-G
> C-D-Eb-F-G (sustained)
> C-G-D-A-E (sustained, cluster chord, pentatonic scale played
> simultaneously in one octave, with a slight major sonority to it)
>
> Your job is to tell me if that's how you hear it. And if not at first,
> if you can play with your perception to hear it that way, especially
> the last chord.

I think I get it. The first chord doesn't sound all that much like C-Eb-G, but by the time you get to the last chord, that sounds semi major.

Mike wrote:
> Two replies ago. I gave a description of the scale as starting
> out in minor and then moving into a really flat pentatonic major
> at the end, and you said that's exactly how you hear it.

I said, after being browbeaten into issuing a statement on
something I had particular insight about, that it was "pretty
much" as you described. You should draw no conclusions from
this because I was basically just humoring you.

> I couldn't actually read it, because it was split up. The
> link you sent me to seemed to have Paul replying to things
> that you'd said, but those posts didn't come up in the thread.

The thread viewer at the bottom doesn't work on old posts.
You have to flip through the archives message by message.

> > > Is 6:7:9 "minor"?
> >
> > Only to the extent the 6 is established as the root.
>
> Alright, so that there are no more miscommunications, what
> is your theory?

My theory is that chords which have low tonalness, but which
are not obscured by roughness or beating, have a recognizable
quality, and that this quality is a large part of the quality
of the conventional minor triad in Western music.
In the case of 6:7:9, it sounds major if we can hear some
octave doubling of 1. If not, then it sounds minor, because
there is no 7/6-9/7 pattern above 1 in the harmonic series.
In Igs' example, it is easy to hear that the 5:6:7 triads
sound a lot like 4:5:6:7 chords, which are strongly major.
The utonal versions do not sound this way.

> And somehow those become happiness and sadness in complex,
> Rorshach-like fashion?

I can't say that all utonal and ASS chords sound sad, but
many of them seem to. What's not really debatable is that
10:12:15 triads do, and that this is a perceptual trait
that is quite common and seemingly not limited to any one
culture.

-Carl

On Wed, Sep 15, 2010 at 5:09 AM, Carl Lumma <carl@...> wrote:
>
> Mike wrote:
> > Two replies ago. I gave a description of the scale as starting
> > out in minor and then moving into a really flat pentatonic major
> > at the end, and you said that's exactly how you hear it.
>
> I said, after being browbeaten into issuing a statement on
> something I had particular insight about, that it was "pretty
> much" as you described. You should draw no conclusions from
> this because I was basically just humoring you.

Then what is the purpose of this conversation? Is it that you're just
having fun baiting me? Up until this point I have taken your
statements in good faith.

If you have never experienced the phenomenon of major thirds sometimes
sounding like minor thirds and vice versa in mavila[5], then I don't
know what to tell you. If your theory is dependent on the fact that
this cannot happen, then it doesn't describe the music in my world, or
the world of most people that I've talked to who have played around
with mavila pentatonic scales.

> In Igs' example, it is easy to hear that the 5:6:7 triads
> sound a lot like 4:5:6:7 chords, which are strongly major.
> The utonal versions do not sound this way.

I heard no clear difference between Igs' triads, I had to listen
pretty much over and over and over until I got the fundamental to pop
out. They both sounded "diminished."

> I can't say that all utonal and ASS chords sound sad, but
> many of them seem to.

I'll have to check out the other ASS chords. Major 6 chords do not
sound sad to me. If I imagine them as minor 7 chords in inversion,
they start to sound sad. I think that is significant.

-Mike

On Wed, Sep 15, 2010 at 4:27 AM, Carl Lumma <carl@...> wrote:
>
> > Is 6:7:9 "minor"?
>
> Only to the extent the 6 is established as the root.
>
> -Carl

Also, I just thought about something else. How about a bare 6:5 dyad?
A bare 7:6? Or how about something like G#-F#-b#, a m7 chord without
the 5? I would be hardpressed to believe that G# will ever pop up as
the fundamental to that specific grouping of notes, but to me they
still capture the "essence" of "minorness" from a musical standpoint
more than just polytonal un-rough chords do.

By the way, it occurred to me that if I did an advanced search for
"harmonic entropy continuing" in the title, I'd get the whole thread.
So I just did manage to read it, and I found it an interesting read.
It left me with quite a few thoughts though:

1) The sound of a minor triad still to me sounds to be minor, even
outside of the context of a diatonic scale; I agree.

2) This could also be because of some inherent psychoacoustic
implication of the minor triad, or because we start to immediately
imagine it as part of a diatonic scale, or at least start to imagine a
"significant subset" of the diatonic scale sufficient enough to
impress upon us the quality of minorness.

3) Initially, Occam's razor suggests the former. The fact that a bare
minor third still sounds minor, whether it's anywhere between 7/6 to
somewhere less than a neutral third, however, confounds that. It can
even sound rooted if you want it to, especially if we're in 12-tet.

4) For the former to be true in light of the above, this would mean
that the reason a bare minor third sounds "minor" is because we
subconsciously "imagine" other notes there (perhaps the fifth), thus
priming the auditory system to hear the shadow of full minor triad.
The rootedness is still not explainable as far as I can see - if you
assume it's because we're viewing the minor third as 19/16, then you
don't have a "low tonalness" triad anymore.

5) This is the same assumption as just that we're conditioned to hear
how a minor third could fit in with other diatonic notes and that
minorness arises from that, so Occam's razor no longer suggests the
former. If it is so that we can spontaneously imagine the fifth and
have that weighted into the periodicity calculation, then there is no
reason that we couldn't spontaneously imagine other "key notes" of the
diatonic scale as well.

6) The point of the mavila example was not whether the last chord
seems major at first sight, but whether you CAN make it sound like a
"really flat major" if you try. If you can't, mess around with
mavila[5] (NOT mavila[7]) for a while and I guarantee you will find
yourself in the situation more than once where major thirds sound
minor and minor thirds sound major. It is transient, but it happens. I
will assume that you have experienced this phenomenon at some point.

7) To perceive a minor third as sounding like a "flat major third", or
to perceive a major third as sounding like a "sharp minor third," or a
"sharp augmented second" (which has a sonority all its own, it's not
just an altered second) means that one of two things are happening
that require an equal amount of assumptions: one is that you are
actually managing to squeeze the wrong fundamental out of a dyad due
to insane amounts of priming, which leads to the different meaning.
The other is that you are managing to push an interval into a mental
mapping position in which it usually doesn't go, which leads to the
different meaning.

8) The distinction between the two might be illusory. That is, musical
quality might derive from cognitive or subconscious procedures taking
place on the map, or it might derive from subconscious projections
onto various psychoacoustic percepts. Or, it might be that the map
itself is a way of biasing the auditory system towards certain ways of
perceiving intervals. For example, in a minor triad, the two most
concordant intervals are the perfect fifth and the major third;
perhaps this is what the auditory system hears as "important" and
hence figures out that 6/5 is what's left over, even if you make the
minor triads 6:7:9. Hence the sound of "minor" would really be "6/5."

Or perhaps a sort of "de-priming" can occur for melodic motion by
discordant interval (such as a half step); that is, perhaps the brain
perceives a motion of 70 cents as so unlikely to fit into a larger
harmonic context that the following note is perceived as a
fundamentally "different" voice. This would have a clear evolutionary
advantage. And hence perhaps a "mapping" really is a way of biasing
the auditory system to behave in a certain way.

9) Or, perhaps it's something different.

-Mike

On Wed, Sep 15, 2010 at 5:06 AM, genewardsmith
<genewardsmith@...> wrote:
>
> > Your job is to tell me if that's how you hear it. And if not at first,
> > if you can play with your perception to hear it that way, especially
> > the last chord.
>
> I think I get it. The first chord doesn't sound all that much like C-Eb-G, but by the time you get to the last chord, that sounds semi major.

It sounded like it to me, but either way, the point is, the last chord
sounds semi-major. Although I said it was a "neutral third," it's
really just 4 cents sharp of minor, so it's pretty much 6/5. The point
is, if you managed to listen to this enough to experience the chord
popping into "very flat major" category, then you're experiencing 6/5
as a very flat major. Whether this means you're experiencing 6/5 as a
very flat 5/4, or something else entirely, isn't for me to say, but I
don't see much reason to believe the first one.

-Mike

I don't get it- the last chord sounds like an ill-advised Dorian, clustered.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > On Tue, Sep 14, 2010 at 11:57 PM, Carl Lumma <carl@> wrote:
> > >
> > > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> > > >
> > > > The last bit, the C-G-D-A-E. It all sounded minor to you?
> > >
> > > It just sounded terrible. I think the pitch bends were
> > > screwing up with the sustain. I tried two players. -Carl
> >
> > There is supposed to be sustain. I uploaded it again though, in mp3
> > form, here: http://www.mikebattagliamusic.com/music/flatdiatonic.mp3
> >
> > It is, again, supposed to be a very detuned version of:
> >
> > C-Eb-G
> > C-D-Eb-F-G
> > C-D-Eb-F-G (sustained)
> > C-G-D-A-E (sustained, cluster chord, pentatonic scale played
> > simultaneously in one octave, with a slight major sonority to it)
> >
> > Your job is to tell me if that's how you hear it. And if not at first,
> > if you can play with your perception to hear it that way, especially
> > the last chord.
>
> I think I get it. The first chord doesn't sound all that much like C-Eb-G, but by the time you get to the last chord, that sounds semi major.
>

I think you have a lot of interesting ideas, Mike. But the only way I can even half-imagine how to test them is if we miraculously got access to a large number of people from cultures where diatonic music is unheard. Whatever quality we assign to "major" and "minor" thirds--or triads--that we can say is "characteristic" of those intervals/chords, the only way to know if it comes from cultural bias (i.e. our diatonic maps) is to see if those qualities are assigned to the same intervals by people without our maps.

However, my guess about why different intervals can share the same "musical quality" for us is that it's the same thing that happens when people try to understand an unfamiliar language. Have you ever seen that old flash video "Hyakugojyuuichi"? It's a music video for a song with Japanese lyrics, except that the Japanese has been "interpreted" as being heavily-accented English in the sub-titles, giving English lyrics that are completely absurd but sound reasonably like the Japanese words in the song.

Simply put, our brains love patterns and will do anything to fit sensory input into some established pattern. If the incoming sensory information can even REMOTELY fit a familiar pattern, our brains will "jam it in there". Psychologists have long known that this desire to fit sensory input into familiar patterns can actually cause forms of blindness--so-called "change blindness." For instance, a STOP sign where the P is replaced with an F can actually go totally unnoticed. Of course, there is a threshold for change-blindness; replace the P with a Q, or the T with an N (or something) and people will notice immediately. But F is close enough to P that the mind can ignore the difference.

What you have been noticing--that neutral intervals "flip-flop", that major thirds can sound minor if we're primed to accept "supermajor thirds" as major thirds, that superpyth and meantone scales can function equally-well for diatonic music--all this points strongly to your brain doing its best to cram unfamiliar intervals into a familiar template. What exactly the "nature" of this template is, I'm not sure, and I don't know if it can be successfully investigated by any of us since we're not (to my knowledge) psychologists. But of course, one of the reasons that what you've noticed about all these intervals may not be agreed upon by everyone on this list could be because they have different "templates". I mean, Carl and Gene have been at this for a long time, so maybe they've developed a greater sense of pitch discrimination than young whipper-snappers like you and I.

The really question, to me anyway, is whether we can ascribe qualities of "majorness" or "minorness" to any triad, or just those that are "close enough" to something familiar (and how close is "close enough"?). Why is this the "real question" to me? Because the limits of what can be perceived as major/minor are the limits of possible tonal bases (basises?) for musical systems. I have some hypotheses, but nothing fleshed out yet.

-Igs

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Wed, Sep 15, 2010 at 4:27 AM, Carl Lumma <carl@...> wrote:
> >
> > > Is 6:7:9 "minor"?
> >
> > Only to the extent the 6 is established as the root.
> >
> > -Carl
>
> Also, I just thought about something else. How about a bare 6:5 dyad?
> A bare 7:6? Or how about something like G#-F#-b#, a m7 chord without
> the 5? I would be hardpressed to believe that G# will ever pop up as
> the fundamental to that specific grouping of notes, but to me they
> still capture the "essence" of "minorness" from a musical standpoint
> more than just polytonal un-rough chords do.
>
> By the way, it occurred to me that if I did an advanced search for
> "harmonic entropy continuing" in the title, I'd get the whole thread.
> So I just did manage to read it, and I found it an interesting read.
> It left me with quite a few thoughts though:
>
> 1) The sound of a minor triad still to me sounds to be minor, even
> outside of the context of a diatonic scale; I agree.
>
> 2) This could also be because of some inherent psychoacoustic
> implication of the minor triad, or because we start to immediately
> imagine it as part of a diatonic scale, or at least start to imagine a
> "significant subset" of the diatonic scale sufficient enough to
> impress upon us the quality of minorness.
>
> 3) Initially, Occam's razor suggests the former. The fact that a bare
> minor third still sounds minor, whether it's anywhere between 7/6 to
> somewhere less than a neutral third, however, confounds that. It can
> even sound rooted if you want it to, especially if we're in 12-tet.
>
> 4) For the former to be true in light of the above, this would mean
> that the reason a bare minor third sounds "minor" is because we
> subconsciously "imagine" other notes there (perhaps the fifth), thus
> priming the auditory system to hear the shadow of full minor triad.
> The rootedness is still not explainable as far as I can see - if you
> assume it's because we're viewing the minor third as 19/16, then you
> don't have a "low tonalness" triad anymore.
>
> 5) This is the same assumption as just that we're conditioned to hear
> how a minor third could fit in with other diatonic notes and that
> minorness arises from that, so Occam's razor no longer suggests the
> former. If it is so that we can spontaneously imagine the fifth and
> have that weighted into the periodicity calculation, then there is no
> reason that we couldn't spontaneously imagine other "key notes" of the
> diatonic scale as well.
>
> 6) The point of the mavila example was not whether the last chord
> seems major at first sight, but whether you CAN make it sound like a
> "really flat major" if you try. If you can't, mess around with
> mavila[5] (NOT mavila[7]) for a while and I guarantee you will find
> yourself in the situation more than once where major thirds sound
> minor and minor thirds sound major. It is transient, but it happens. I
> will assume that you have experienced this phenomenon at some point.
>
> 7) To perceive a minor third as sounding like a "flat major third", or
> to perceive a major third as sounding like a "sharp minor third," or a
> "sharp augmented second" (which has a sonority all its own, it's not
> just an altered second) means that one of two things are happening
> that require an equal amount of assumptions: one is that you are
> actually managing to squeeze the wrong fundamental out of a dyad due
> to insane amounts of priming, which leads to the different meaning.
> The other is that you are managing to push an interval into a mental
> mapping position in which it usually doesn't go, which leads to the
> different meaning.
>
> 8) The distinction between the two might be illusory. That is, musical
> quality might derive from cognitive or subconscious procedures taking
> place on the map, or it might derive from subconscious projections
> onto various psychoacoustic percepts. Or, it might be that the map
> itself is a way of biasing the auditory system towards certain ways of
> perceiving intervals. For example, in a minor triad, the two most
> concordant intervals are the perfect fifth and the major third;
> perhaps this is what the auditory system hears as "important" and
> hence figures out that 6/5 is what's left over, even if you make the
> minor triads 6:7:9. Hence the sound of "minor" would really be "6/5."
>
> Or perhaps a sort of "de-priming" can occur for melodic motion by
> discordant interval (such as a half step); that is, perhaps the brain
> perceives a motion of 70 cents as so unlikely to fit into a larger
> harmonic context that the following note is perceived as a
> fundamentally "different" voice. This would have a clear evolutionary
> advantage. And hence perhaps a "mapping" really is a way of biasing
> the auditory system to behave in a certain way.
>
> 9) Or, perhaps it's something different.
>
> -Mike
>

Mike wrote:
> > I said, after being browbeaten into issuing a statement on
> > something I had particular insight about, that it was "pretty
> > much" as you described. You should draw no conclusions from
> > this because I was basically just humoring you.
>
> Then what is the purpose of this conversation? Is it that
> you're just having fun baiting me? Up until this point I have
> taken your statements in good faith.

So have I, but then you started putting words in my mouth.

In order to reach a conclusion with these sorts of things,
you need to ask a question that people can answer and you
need to be able to tell which way they answered it. That's
pretty basic but I guess I have to spell it out.

> They both sounded "diminished."

Let me just tell you what I think's going on here and
maybe it'll save us a lot of trouble. Far from emancipating
the structure of music, you are in fact doing the opposite --
interpreting xenharmonic chords and scales in terms of
Western common practice. It's something you're doing that's
interfering with your understanding of xenharmonic music,
not something everyone else is doing that governs their
understanding of it. I base this on your comments when
listening to stuff... you are always using 12-ET pitch
classes, common practice chord names, etc. to describe
what you hear. Probably this is because your ear is better
trained for conventional music than most others here, and/or
you have less experience listening to xenharmonic stuff.

-Carl

Me> So, in other words, your example really leans more toward scales where
there is a lot of temperament and context determines in which direction IE
toward which of two possible JI intervals each chord is tempered?
....as an example....
MikeB>"When I hear 6/5 as major, is my brain placing 6/5 as 5/4?
When I hear subminor chords function just as well
as minor chords in a tempered aeolian scale, is my brain placing 7/6
as 6/5? Or is something else going on?"

Exactly! That was my point...

>"That's what you're asking, I think. And it's a good question, and one I don't
>have the answer for."
Thanks and, hey...I'll start really thinking about how this one might be
solved as well....
On the side, I generally stick the near-exact JI (within 8 cents of) types
of scales because I haven't heard of or found a way either to "guarantee how
temperament is guided". When I do though...that should be fun: I could
potentially get a whole lot more emotional flexibility per interval and do so
without sacrificing much of (if at all) the sense of stability of near-exact
intervals.

On Wed, Sep 15, 2010 at 11:42 AM, cityoftheasleep
<igliashon@...> wrote:
>
> I think you have a lot of interesting ideas, Mike. But the only way I can even half-imagine how to test them is if we miraculously got access to a large number of people from cultures where diatonic music is unheard. Whatever quality we assign to "major" and "minor" thirds--or triads--that we can say is "characteristic" of those intervals/chords, the only way to know if it comes from cultural bias (i.e. our diatonic maps) is to see if those qualities are assigned to the same intervals by people without our maps.

I was in an acoustics class a while ago - the teacher played 400, 500,
and 600 Hz together to show how the brain hears it as a 100 Hz tone.
And it did, and the context was such that it was extremely difficult
for me to even hear the three notes individually. And when I did, no
musical context popped up at all; they didn't sound like a major
chord, just three overtones I was picking out of a note.

> Simply put, our brains love patterns and will do anything to fit sensory input into some established pattern. If the incoming sensory information can even REMOTELY fit a familiar pattern, our brains will "jam it in there". Psychologists have long known that this desire to fit sensory input into familiar patterns can actually cause forms of blindness--so-called "change blindness." For instance, a STOP sign where the P is replaced with an F can actually go totally unnoticed. Of course, there is a threshold for change-blindness; replace the P with a Q, or the T with an N (or something) and people will notice immediately. But F is close enough to P that the mind can ignore the difference.

Yes.

> What you have been noticing--that neutral intervals "flip-flop", that major thirds can sound minor if we're primed to accept "supermajor thirds" as major thirds, that superpyth and meantone scales can function equally-well for diatonic music--all this points strongly to your brain doing its best to cram unfamiliar intervals into a familiar template. What exactly the "nature" of this template is, I'm not sure, and I don't know if it can be successfully investigated by any of us since we're not (to my knowledge) psychologists.

I don't either. Like I said, Paul's the guy turning me onto this new
wavelength of thought, and I'm not sure he really has it figured out
either. I wish he'd just join back the lists for the rest of this
conversation.

> But of course, one of the reasons that what you've noticed about all these intervals may not be agreed upon by everyone on this list could be because they have different "templates".

That's what I'm saying!

> I mean, Carl and Gene have been at this for a long time, so maybe they've developed a greater sense of pitch discrimination than young whipper-snappers like you and I.

Yes!

> The really question, to me anyway, is whether we can ascribe qualities of "majorness" or "minorness" to any triad, or just those that are "close enough" to something familiar (and how close is "close enough"?). Why is this the "real question" to me? Because the limits of what can be perceived as major/minor are the limits of possible tonal bases (basises?) for musical systems. I have some hypotheses, but nothing fleshed out yet.

Igs: did you listen to the mavila example?

-Mike

Mike wrote:

> > > Is 6:7:9 "minor"?
> >
> > Only to the extent the 6 is established as the root.
>
> Also, I just thought about something else. How about a bare 6:5
> dyad? A bare 7:6?

I don't think they really sound minor on their own.

> Or how about something like G#-F#-b#, a m7 chord without
> the 5?

What chord are you referring to, exactly? i.e. what
tuning what voicing and what is "b#"?

> 1) The sound of a minor triad still to me sounds to be minor,
> even outside of the context of a diatonic scale; I agree.

Whew!

> 2) This could also be because of some inherent psychoacoustic
> implication of the minor triad, or because we start to immediately
> imagine it as part of a diatonic scale, or at least start to
> imagine a "significant subset" of the diatonic scale sufficient
> enough to impress upon us the quality of minorness.
> 3) Initially, Occam's razor suggests the former.

Of course it does. I can also remember hearing it as sad
and discussing this with my grandmother in one of my first
piano lessons when I was 4, before I really had much of a
handle on the diatonic scale. Of course you can argue about
exposure in the womb and so on, but let's face it: most music
hangs out on arpeggios and pentatonics -- especially most
popular music -- and most adults couldn't sing simple
diatonic patterns if their life depended on it.

Also you could synthesize it as a timbre so the attacks are
perfectly simultaneous. Also you could synthesize a series
with progressively staggered attacks and see if that makes a
difference. Also it's plainly obvious the quality flows from
the chord to the scale, since 1. the minor scale is a mode of
the major scale, so the rank-order matrices are essentially
the same and 2. the mavila[7] experiment produces results, in
both me and Igs and anyone who will ever try it, that are
consistent only with the former hypothesis.

> The fact that a bare
> minor third still sounds minor, whether it's anywhere between
> 7/6 to somewhere less than a neutral third, however, confounds
> that.

Even if I agreed with that I don't see how it would
confound anything. The only potentially 'rooted' interval
in this size range is 19:16 and it almost certainly
approximates 6:5. But even if it didn't, it's at least as
easy for me to claim it reminds people of a minor triad
vs. reminding them of the minor scale.

> The rootedness is still not explainable as far as I can see -
> if you assume it's because we're viewing the minor third as
> 19/16, then you don't have a "low tonalness" triad anymore.

I don't understand. 16:19:24 may or may not have a life
of its own -- I doubt it, but I should listen to it again
and see what it does to 2010 Carl. Even if it did, it
would have very low tonalness compared to something like
4:5:6.

> 5) This is the same assumption as just that we're conditioned
> to hear how a minor third could fit in with other diatonic
> notes and that minorness arises from that, so Occam's razor no
> longer suggests the former.

Don't you think it's simpler if something reminds people
of 1 additional note vs. 5 additional notes?

> 6) The point of the mavila example was not whether the last
> chord seems major at first sight, but whether you CAN make it
> sound like a "really flat major" if you try.

You can make anything seem any way with categorical perception.
I played a 7/8-scale piano keyboard for a day and when I got
home the keys on my piano looked like giant canoes. So what?

> If you can't, mess around with mavila[5] (NOT mavila[7]) for
> a while and I guarantee you will find yourself in the
> situation more than once where major thirds sound minor
> and minor thirds sound major.

Can you phrase this in a way where I'll have a chance of
knowing if it's happened or not? Like, "Mess around with
mavila[5] and I guarantee you'll temporarily experience
hearing a mavila-approximate 10:12:15 triad sound happy",
or...?

-Carl

On Wed, Sep 15, 2010 at 2:07 PM, Carl Lumma <carl@...> wrote:
>
> > Then what is the purpose of this conversation? Is it that
> > you're just having fun baiting me? Up until this point I have
> > taken your statements in good faith.
>
> So have I, but then you started putting words in my mouth.
>
> In order to reach a conclusion with these sorts of things,
> you need to ask a question that people can answer and you
> need to be able to tell which way they answered it. That's
> pretty basic but I guess I have to spell it out.

I thought I was doing that. You said there's no way anyone would ever
hear 6/5 as sounding "major." I came up with a musical example in
mavila that I thought sounds major at the end despite the 6/5 being
there, and I wanted you to tell me if you heard majorness it. I didn't
want to tell you the tuning because the perception is quite fragile,
and I thought if you knew to expect it being tuned to 6/5, it would
introduce bias into the experiment. It is, of course, quite easy to
hear it as being minor as well, which isn't the point; the point is
that it can be heard as a very flat major too. This flexibility of
perception makes the example particularly susceptible to bias.

After first attacking the example as unmusical and saying it was
irrelevant, you proceeded to say you listened to it and didn't answer
the question of whether you heard it the way I described. After asking
for you to listen again and reiterating how I heard it, you said that
you heard it pretty much the same way. I then used it to illustrate my
point that 6/5 can be heard as major given the right context and
distorting of the diatonic (or in this case pentatonic) map.

So where exactly did our communication go wrong? Perhaps you missed my
initial message in which I described what I was asking for you to
listen to? Apparently not, since you quoted it.

> > They both sounded "diminished."
>
> Let me just tell you what I think's going on here and
> maybe it'll save us a lot of trouble. Far from emancipating
> the structure of music, you are in fact doing the opposite --
> interpreting xenharmonic chords and scales in terms of
> Western common practice.

I tried to use the terminology that you were using from the original
thread. You said that major chords sound happy and minor chords sound
sad, and that this was because major chords are otonal and minor
chords are less tonal and not rough. You used the ASS's to illustrate
your point that the perception of sadness comes right out of the "less
tonal and not rough" quality, and hence that otonality leads to
happiness, and stable chords of low tonalness and low roughness lead
to sadness. At least that's what I took you to mean.

When I listened to Igs' example, I didn't hear "happy, happy, sad,
sad, happy, happy, sad, sad." I heard "really sad and ambiguous,
really sad and ambiguous, really sad and ambiguous" - which is what
diminishedness sounds like to me. After enough listens I finally heard
a weak fundamental popping out for some of them, and a different
fundamental popping out for the others.

Perhaps if I listen enough to it, I will hear it as "happy, happy,
sad, sad." But why does that not mean that happiness and sadness have
something to do with internal cognitive templates, and I haven't
developed the ones for this example yet?

> It's something you're doing that's
> interfering with your understanding of xenharmonic music,
> not something everyone else is doing that governs their
> understanding of it. I base this on your comments when
> listening to stuff... you are always using 12-ET pitch
> classes, common practice chord names, etc. to describe
> what you hear. Probably this is because your ear is better
> trained for conventional music than most others here, and/or
> you have less experience listening to xenharmonic stuff.

Let's not forget that the way you and I perceive music is, also, very
different. I have AP, which leads to an entirely different level of
cognitive processing than most people have, and biases things in
different ways.

I think that once I hear a piece of music that sets up a cohesive
cognitive structure for xenharmonic music, I will instantly hear
different shades of happiness and sadness in a way I don't now.
Knowsur's album was one of the first to really nail that, and I heard
neutral triads as musically consonant for the first time, and it was a
pivotal moment in my understanding of music. In other words, the
perception of harmonies can be affected by learning, which seemed to
be something you were disagreeing with before.

-Mike

Mike wrote:
> You said there's no way anyone would ever
> hear 6/5 as sounding "major."

Bzzz.

> I came up with a musical example in
> mavila that I thought sounds major at the end

Bzzz.

> Let's not forget that the way you and I perceive music is,
> also, very different. I have AP,

Yes, that's what I was alluding to. Your AP is screwing
you up. You're not the first. However, there were some
folks who claimed to turn their AP into "microtonal AP"...
I don't have the link just now.

> In other words, the
> perception of harmonies can be affected by learning,
> which seemed to be something you were disagreeing with before.

Perception of color can be affected by learning too, in
very important ways. But no amount of learning is going
to make blue look green and vice versa - those are hard
wired (I hate that phrase, but oh well).

-Carl

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

> I thought I was doing that. You said there's no way anyone would ever
> hear 6/5 as sounding "major." I came up with a musical example in
> mavila that I thought sounds major at the end despite the 6/5 being
> there, and I wanted you to tell me if you heard majorness it.

I heard "semi-majorness" in it. It had a sort of subdued happy major quality, and it sounded "in tune", but it didn't really sound exactly major. But I note that different people had different reactions.

Carl wrote:
> > Or how about something like G#-F#-b#, a m7 chord without
> > the 5?
>
> What chord are you referring to, exactly? i.e. what
> tuning what voicing and what is "b#"?

Sorry, I screwed up. That should be just b natural. I mean G#-F#-b, as
in G#m7 without the 5. Let's say it's voiced as 10:18:24. To me, that
still sounds like minor, in the common practice sense.

As for you saying you don't think that a bare minor 3rd doesn't sound
like minor to you, play the following little cadence:

C-Eb -> D-F -> C-Eb -> B-D -> C-Eb

That is, Eb-F-Eb-D-Eb with a minor third under each one. Don't ever
play G. If that doesn't sound like minor to you, I'll post a video
clip of myself wearing a wig singing lady gaga tunes. Retempered to
porcupine. Maybe.

> > 1) The sound of a minor triad still to me sounds to be minor,
> > even outside of the context of a diatonic scale; I agree.
>
> Whew!

Haha, well I hope you don't think I was ever saying otherwise!

> > 2) This could also be because of some inherent psychoacoustic
> > implication of the minor triad, or because we start to immediately
> > imagine it as part of a diatonic scale, or at least start to
> > imagine a "significant subset" of the diatonic scale sufficient
> > enough to impress upon us the quality of minorness.
> > 3) Initially, Occam's razor suggests the former.
>
> Of course it does. I can also remember hearing it as sad
> and discussing this with my grandmother in one of my first
> piano lessons when I was 4, before I really had much of a
> handle on the diatonic scale. Of course you can argue about
> exposure in the womb and so on, but let's face it: most music
> hangs out on arpeggios and pentatonics -- especially most
> popular music -- and most adults couldn't sing simple
> diatonic patterns if their life depended on it.

It's good that you started playing when you were really young - I also
started playing when I was young, somewhere around 2. (Ironically, I
was also taught by my grandmother.) And my perspective is that I think
I would have had to have lived in an isolation chamber away from all
music and then hear a minor chord for the first time to really
determine if it comes from psychoacoustics and sounds sad. I don't
think it has to do with exposure in the womb, but exposure out of the
womb in early life to music. Listening to a few pieces in minor is
probably sufficient for you to associate the feeling with the bare
minor triad for the rest of your life, especially at an early age...
People today can barely sing diatonically at all, but they still
understand something about the template intuitively. I don't really
think that the "full diatonic scale" is necessary for it to sound the
way it does, but rather just perhaps a very small subset. I think it
has something to do with leading tones and falling tones, more on that
later (sort of a generalization of the tritone hypothesis that makes
sense to me).

But by itself, a minor chord is just a sort of sound-object, so I
don't know why it would be sad... The "mapping-as-auditory-biasing"
hypothesis I outlined at the end of my last email would explain this.

> 2. the mavila[7] experiment produces results, in
> both me and Igs and anyone who will ever try it, that are
> consistent only with the former hypothesis.

It produces the same result with me, but it is consistent with the
latter hypothesis as well: when I hear a ssLsssL scale, it sounds like
a shifting mix of aeolian and phrygian as I go up the scale. Keep in
mind that "aeolian" and "phrygian" are words that to me represent two
very distinct musical feelings, as do the words "major" and "minor" to
you. It has just occurred to me that perhaps there is a huge
disconnect in communication here because of how we're perceiving these
words.

But I also hear the same shades of meaning in 7-tet, where it's all
the same. So the first hypothesis would explain this by saying that
different diatonic maps are being applied.

Damn, I wish Paul would just join the list back for this conversation.
I gave him the same exact argument and he responded as I just did. You
have good points too, however.

> Even if I agreed with that I don't see how it would
> confound anything. The only potentially 'rooted' interval
> in this size range is 19:16 and it almost certainly
> approximates 6:5. But even if it didn't, it's at least as
> easy for me to claim it reminds people of a minor triad
> vs. reminding them of the minor scale.

Does C-D-Eb, played simultaneously in 12-tet, sound like minor to you?

> I don't understand. 16:19:24 may or may not have a life
> of its own -- I doubt it, but I should listen to it again
> and see what it does to 2010 Carl. Even if it did, it
> would have very low tonalness compared to something like
> 4:5:6.

I really do understand what you're getting at, and if you're right, it
would probably be the most brilliant insight into the workings of
music ever. Minor songs would sound sad because you have a tonal
heirarchy emphasizing a sonority that sounds ambiguous; auditory scene
analysis stuff would reveal this sound-object that is unknown and
hence may be a threat, hence sadness. Major songs would sound happy
because the tonal heirarchy would emphasize a sonority that sounds
rooted and resolved; the whole structure can be understood better, and
hence represents not a threat, happiness. The blues would be explained
as African Americans, while stuck in a hellish world of misery, having
figured out that the typical "happy/sad" divide of major and minor can
be resolved if minor is played on top of major, thus envisioning the
minor third as 16:19 (C-E-Bb-C-Eb-G, for example, might work best if
tuned this way), hence the minor third starts to become otonal and
rooted and "major" by your earlier definition.

It is elegant and intuitive, and correlates brilliantly with lots of
things, and could probably lead one to become quite euphorically manic
if followed for a long time. However, after the supermajor example I
played for you - when 5/4 clearly takes the role of 75/64 (which is a
color in and of itself in my world, or at least aug2 chords are, a la
C-E-B-D#. They aren't just altered large seconds) - I can't see that
as being the case anymore. Perhaps it still is in a way that I am
missing.

The blues can be also explained as an alternate tonal set that happens
to be a mode of Paul's standard pentachordal major.

> > 5) This is the same assumption as just that we're conditioned
> > to hear how a minor third could fit in with other diatonic
> > notes and that minorness arises from that, so Occam's razor no
> > longer suggests the former.
>
> Don't you think it's simpler if something reminds people
> of 1 additional note vs. 5 additional notes?

I don't think that all 5 additional notes need to be imagined for the
minor triad to take on its familiar "minor" role. It might be only
one. It might, in fact, be just that the three notes in the minor
triad make up their own little mini-map, which is then cognized. My
point is that I think meaning comes from a subconscious cognizing of
the mini-map, rather than inherently from the VF's produced. I think
this is because you can push a 5/4 into crazy situations where it has
a completely different meaning produced, and because you manage to
cognize it in a totally different way, despite the same VF's being
produced. I think there is simply just another level of music left to
explore (semiology literature, anyone? Anyone know any good books?).
But the more that I talk about this the more I start to think what we
are saying overlaps somewhat...

> > 6) The point of the mavila example was not whether the last
> > chord seems major at first sight, but whether you CAN make it
> > sound like a "really flat major" if you try.
>
> You can make anything seem any way with categorical perception.
> I played a 7/8-scale piano keyboard for a day and when I got
> home the keys on my piano looked like giant canoes. So what?

How do you explain this then? In the supermajor example I posted, the
melody is still recognizable, and 5/4 takes on the extremely
bittersweet, sad characteristic that the D# takes in C-E-B-D#. Even at
the end, when I play C-G-C under the melody, the C-G-C-D# (which is a
2:3:4:5 and clearly has a fundamental of 1) STILL has the color of
that bittersweet chord I posted above (although one can flip it
around). Hence if we're defining major and minor as colors, then this
is another color I know from my vast experiments with expanded
diatonic harmony, and I got 2:3:4:5 to sound like it. That is...
significant!

> > If you can't, mess around with mavila[5] (NOT mavila[7]) for
> > a while and I guarantee you will find yourself in the
> > situation more than once where major thirds sound minor
> > and minor thirds sound major.
>
> Can you phrase this in a way where I'll have a chance of
> knowing if it's happened or not? Like, "Mess around with
> mavila[5] and I guarantee you'll temporarily experience
> hearing a mavila-approximate 10:12:15 triad sound happy",
> or...?

When you listen to a neutral triad, you can either hear it as a very
flat major triad, or a very sharp minor triad. When you mess around
with mavila[5], you will sometimes hear times when that minor third
sounds like a very, very, very flat major third, and vice versa. That
is, it takes on the quality of "major," but just sounds flat as hell.
And after enough exposure to mavila, I don't hear it as sounding "flat
as hell" anymore; that is, while it never sounds like 5/4, it doesn't
sound irritatingly "wrong," just different.

So the question is, is this because you're perceiving 6/5 as a very
flat 5/4? Or because you start to cognize the 6/5 in the same way that
you cognize 5/4? I believe that the latter is the case, because there
are certain "cues" that make this trick work. One is to play with the
pentatonic scale by transposing a fifth up it. Go C-G -> D-A -> E-C ->
G-D -> A-E and so on. That E-C will still be minor if you focus on it,
but starts to pick up some of the "majorness" of the major pentatonic
one. Stacking fifths like C-G-D-A-E can sometimes get the E to sound
pseudo-"major" ish, especially if it's all in one octave, and preceded
by a subminor triad. 23-equal or 30-equal I find are good tuning for
these.

-Mike

A quick afterthought: the more I think about it, the more I realize
that the mapping-as-auditory-system-priming hypothesis makes sense. I
also think that rather than having "different maps", they are
basically all going to approach one huge super-map. This is what has
been seen culturally with 12-tet, where the octatonic scale is used
over dom7 chords, and people switch from different diatonic maps to
the blues to the octatonic scale to the whole tone scale to the
augmented scale and back again, seeing how they all interrelate.
Whether this super-map approaches JI or not is, I think, an
interesting question. It seems to be approaching some form of
"universal temperament" in which anything can be tempered.

-Mike

On Wed, Sep 15, 2010 at 3:57 PM, Mike Battaglia <battaglia01@...> wrote:
> Carl wrote:
>> > Or how about something like G#-F#-b#, a m7 chord without
>> > the 5?
>>
>> What chord are you referring to, exactly? i.e. what
>> tuning what voicing and what is "b#"?

Hi Mike,

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

Igs said:
> > But of course, one of the reasons that what you've noticed about all these intervals
> > may not be agreed upon by everyone on this list could be because they have different > > "templates".

Mike said:

> That's what I'm saying!

Right, and therein lies the rub: even among those of us trained in and accustomed to diatonic music, there's variation in the templates. For some of us, IOW, the change-blindness might not be there. So how do we know if our templates have enough in common to support generalizations?

> > The real question, to me anyway, is whether we can ascribe qualities of "majorness"
> > or "minorness" to any triad, or just those that are "close enough" to something familiar
> > (and how close is "close enough"?). Why is this the "real question" to me? Because the
> > limits of what can be perceived as major/minor are the limits of possible tonal bases
> > (basises?) for musical systems. I have some hypotheses, but nothing fleshed out yet.
>
> Igs: did you listen to the mavila example?

Yes. Didn't fool me.

I did, however, mis-phrase the above sentence. I should have said, "The real question to me is whether we can ascribe qualities of majorness and minorness to any *pair* of otonal-utonal related triads." Another good question is whether majorness and minorness can be ascribed to a pair of triads that are NOT otonal-utonal related. Also, what is the relationship between otonality and majorness, as well as "larger interval first" and majorness? Consider the following three examples:

4:5:6 vs. 10:12:15: 4:5:6 is lower in the series, thus the "otonal" member of the pair. It also has a larger interval--5/4--first.

6:7:9 vs. 14:18:21: 6:7:9 is lower in the series, thus the "otonal" member of the pair, yet it has a smaller interval--7/6--first. It tends to sound "minor" in comparison to its utonal partner.

16:18:21 vs. 48:56:63: 16:18:21 is lower in the series, thus the "otonal" member of the pair, and it also has a smaller interval--9/8--first. To my ears, however, it tends to sound "major" in comparison.

Now, we can probably all agree that otonal chords make better tonic chords, generally-speaking. But 6:7:9 certainly has a different emotional quality to my diatonic-accustomed ears than the 4:5:6 does.

It is interesting that in comparing 5:6 and 6:7, I can hear the 5:6 as somewhat "major", and comparing 7:9 to 4:5, I can hear the 4:5 as somewhat "minor" (listening example forthcoming). But comparing 6:7 and 8:9, I still hear the 6:7 as "minor". And comparing 3:4 and 7:9, I cannot hear the 7:9 as "minor" (listening examples for these forthcoming as well). Thus, the "major-minor relativity" for my ears only seems to hold when both intervals are in the range of what can be called "thirds".

-Igs

I, for one, would welcome such a video.

-c

On Sep 15, 2010, at 3:57 PM, Mike Battaglia wrote:

>
> ... I'll post a video
> clip of myself wearing a wig singing lady gaga tunes. Retempered to
> porcupine. Maybe.
>
>
>

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

> When you listen to a neutral triad, you can either hear it as a very
> flat major triad, or a very sharp minor triad.

?????! Why not just hear it like billions of other people hear middle thirds, and hear it as a middle-third triad?

On Wed, Sep 15, 2010 at 4:06 PM, cityoftheasleep
<igliashon@...> wrote:
>
> > That's what I'm saying!
>
> Right, and therein lies the rub: even among those of us trained in and accustomed to diatonic music, there's variation in the templates. For some of us, IOW, the change-blindness might not be there. So how do we know if our templates have enough in common to support generalizations?

They don't. And I'm not trying to make generalizations, and sorry if I
came off that way. But the point that I'm making is - I think musical
meaning emerges from the templates, whatever they are. They emerge
from the cognization of some kind of template. They do not emerge from
the fundamental. That is, at least, my theory, although now that the
discussion between me and Carl is getting more interesting, perhaps I
will change my mind about that.

But you said that sus4 chords to you sounded like exaggerated major
chords, as did supermajor chords. That indicates to me that you're
fitting them to some kind of major template. They definitely do not
sound like major chords to me; I can imagine different things that I
"can do" with them than what I can do with major. This is part of the
"meaning" of the sus4 chord in my world.

My recent enlightenment, I think, is this: there is no scale. The
scale is an abstraction that doesn't exist. It exists for convenience.
When you hear the "meaning" of a chord, part of what you are hearing
is that it can move around in pitch space, which does not necessarily
have to correlate to JI and is not limited to any scale.

So if I knew a musical system in which a supermajor chord "did
something different" than a major chord, I would stop trying to cram
it into the major chord template and it would suddenly stop sounding
so dissonant. And this is where I think psychoacoustics DOES play into
it: we want discordant sonorities to resolve to concordant ones. The
exact type of concordance, though, I think isn't important.

Carl's theory seems to be that there are only two types of concordance
that we distinguish between: that of the fully tonal sonority (major)
and that of the half-tonal but not rough sonority (minor). It's an
interesting theory, and one that I am open to. I'm not entirely sure I
believe it, since minor thirds in isolation still sound minor to me,
even if they're 7/6. But I am open to it.

> > > The real question, to me anyway, is whether we can ascribe qualities of "majorness"
> > > or "minorness" to any triad, or just those that are "close enough" to something familiar
> > > (and how close is "close enough"?). Why is this the "real question" to me? Because the
> > > limits of what can be perceived as major/minor are the limits of possible tonal bases
> > > (basises?) for musical systems. I have some hypotheses, but nothing fleshed out yet.
> >
> > Igs: did you listen to the mavila example?
>
> Yes. Didn't fool me.

The point isn't whether or not it fooled you - it isn't supposed to
"fool" you. The point is whether or not you CAN get the last sonority
to sound like a flat "major" by playing around with your perception of
it. So far, the tally is that most people can get it to sound sort of
"major," but in a weird way that is kind of "wrong." After playing
with this chord for the last month, I can easily flip my perception of
it around to major, and it no longer sounds "wrong" to me, just
"different." That is, I have managed to get the minor third into the
major third position in my internal template - or have I?

Let's assume that this happens to you at some point (it's much easier
with mavila[5], which still follows the same intervallic pattern as
meantone[5]; mavila[7] is where it diverges). When this happens, the
fundamental question is:

1) Is this minor third taking on some imprint of the "major" sonority
because I'm perceiving 6/5 as 5/4, and the major sonority comes
directly from the JI relationship we're perceiving it as?
2) Or, is this minor third taking on some imprint of the "major"
sonority because I'm cramming the minor third into the "major third"
position in some cognitive map I have, and the major sonority comes
directly from that map?

This is, I think, the disagreement that Carl and I are having.

> I did, however, mis-phrase the above sentence. I should have said, "The real question to me is whether we can ascribe qualities of majorness and minorness to any *pair* of otonal-utonal related triads." Another good question is whether majorness and minorness can be ascribed to a pair of triads that are NOT otonal-utonal related.

C-Eb-G-B-D is mostly otonal, but sounds minor to me. I don't think
Carl is saying that minorness is coming from utonality though. I think
he's saying it comes from polytonality, in a sense. Polytonality
without roughness or discordance. It's an interesting theory and takes
advantage of the fact that "rooted" intervals have a fundamental that
is octave-equivalent to the lower note in the dyad, and octave
equivalence takes on special significance in the mammalian brain. I'm
still on the fence with it.

> 4:5:6 vs. 10:12:15: 4:5:6 is lower in the series, thus the "otonal" member of the pair. It also has a larger interval--5/4--first.
>
> 6:7:9 vs. 14:18:21: 6:7:9 is lower in the series, thus the "otonal" member of the pair, yet it has a smaller interval--7/6--first. It tends to sound "minor" in comparison to its utonal partner.

I think there are different qualities to the "minor" chord that we all
know and love, and you are picking one of them and defining all of
minorness as being related to that. I'll come up with another
listening example and we'll see how it goes. I predict that if you
play a chord like C Eb G B D Fv Av - where Fv and Av are 11/4 and 13/4
respectively - that it will still sound "minor" in another more
fundamental way, despite being almost entirely otonal.

-Mike

On Wed, Sep 15, 2010 at 4:25 PM, cameron <misterbobro@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > When you listen to a neutral triad, you can either hear it as a very
> > flat major triad, or a very sharp minor triad.
>
> ?????! Why not just hear it like billions of other people hear middle thirds, and hear it as a middle-third triad?

You can do that too. That's why I'm such a fan of knowsur's album,
since it was the first time I heard a "middle-third triad" as sounding
like a concordant sonority in its own right. I just meant that if you
were trying to cram it into one of those perceptions, you could do it
equally.

Perhaps you are more experienced with neutral triads and hear them as
a third type of sonority; I am building that type of map now, but the
perception of it is fragile right now, and is still intertwined with
its sounding somewhat "ambiguous" to me.

-Mike

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

>
> Perhaps you are more experienced with neutral triads and hear them as
> a third type of sonority; I am building that type of map now, but the
> perception of it is fragile right now, and is still intertwined with
> its sounding somewhat "ambiguous" to me.

Ambiguous is cool, it's a lot like real life.

On Wed, Sep 15, 2010 at 3:57 PM, Mike Battaglia <battaglia01@...> wrote:
>>
>> Don't you think it's simpler if something reminds people
>> of 1 additional note vs. 5 additional notes?
>
> I don't think that all 5 additional notes need to be imagined for the
> minor triad to take on its familiar "minor" role. It might be only
> one. It might, in fact, be just that the three notes in the minor
> triad make up their own little mini-map, which is then cognized.

I am going to defeat my own point here that any additional notes need
to be imagined. If you play a minor triad as part of a
C-D-Eb-F#-G-A-B-C scale (melodic minor #4), vs a C-Db-Eb-F-G-Ab-Bb-C
scale (phrygian), they both sound "minor" despite the fact that every
single other note in the scale is different.

But I'm still not convinced that no cognitive layer lies between
psychoacoustics and the end result, and that meaning arises from that
cognitive layer.

I had a thought about this recently: there is no "scale" in reality as
far as harmony is concerned. That is, the scale is a useful
abstraction, but it doesn't really exist. It's just an arbitrary way
to emphasize different notes in an infinitude of pitch space, which
doesn't necessarily mean JI. Even within a single scale, there are
going to be "avoid notes" that you don't want to sustain over a
particular chord. There are simply different levels of "organizational
relatedness" that arise in some way that I don't fully understand
(perhaps having to do with psychoacoustics, perhaps due to unrelated
cognitive factors), and we as humans group them into discrete
categories - chord tones, nonchord tones that are consonant, avoid
notes that are consonant on some chords but not others, and notes that
are "out of the scale." When you start investigating other tonal
structures like the blues, these distinctions break down and are drawn
differently (the difference between "avoid note" and "chromatic note"
becomes quite blurry). (melodically it's different)

So when we talk about the meaning that a chord has, part of what we're
talking about is what it "can do" in pitch space independent of any
scale; how it could resolve, how it relates to other hypothetical
notes, etc. This is almost certainly learned, and I think a huge part
of where the "meaning" of a chord comes from; it is almost entirely
cognitive. Whether it is actually entirely psychoacoustic boils down
to the hypothesis earlier that mappings are ways of biasing and
priming the auditory system to do stuff, which I'm not sure how we
could determine in advance.

-Mike

On Wed, Sep 15, 2010 at 4:43 PM, cameron <misterbobro@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> >
> > Perhaps you are more experienced with neutral triads and hear them as
> > a third type of sonority; I am building that type of map now, but the
> > perception of it is fragile right now, and is still intertwined with
> > its sounding somewhat "ambiguous" to me.
>
> Ambiguous is cool, it's a lot like real life.

It's like a white overcast sky.

-Mike

Mike wrote:

> Sorry, I screwed up. That should be just b natural.
> I mean G#-F#-b, as in G#m7 without the 5. Let's say it's
> voiced as 10:18:24. To me, that still sounds like minor,
> in the common practice sense.

Tuned 10:18:24, or in 12-ET? Please try to be specific.
Also, why are you using a lower case b? Also, why G#
for a root... isn't it easier in C? Sorry for all the
questions, I mean them sincerely.

Going forward, perhaps I should use different terms too...
otonal/utonal would still cause confusion. I will therefore
say "tonal" and "nontonal". I should also stress that this
distinction should only account for a PART of what goes
into major and minor in everyday music.

> As for you saying you don't think that a bare minor 3rd
> doesn't sound like minor to you, play the following
> little cadence:

No cadences! C'mon, geez. I can make you think you're
wearing a hat with a cadence.

> It's good that you started playing when you were really
> young - I also started playing when I was young, somewhere
> around 2. (Ironically, I was also taught by my grandmother.)

My grandmother taught piano her whole life. Very talented
too, for a local teacher in a Philadelphia suburb. Alas, I
only took with her for a year and didn't return to the
instrument until I was 16.

> But by itself, a minor chord is just a sort of sound-object,
> so I don't know why it would be sad...

But it is. Go figure.

There's a common belief, due mainly to liberal ideology and
rampant in the social sciences, that everything is cultural
and nothing innate. What nonsense.

> > 2. the mavila[7] experiment produces results, in
> > both me and Igs and anyone who will ever try it, that are
> > consistent only with the former hypothesis.
>
> It produces the same result with me, but it is consistent with
> the latter hypothesis as well: when I hear a ssLsssL scale, it
> sounds like a shifting mix of aeolian and phrygian as I go up
> the scale.

I have no such perception.

> Does C-D-Eb, played simultaneously in 12-tet, sound like
> minor to you?

It sounds discordant.

> I really do understand what you're getting at, and if you're
> right, it would probably be the most brilliant insight into the
> workings of music ever.

It should be obvious that it's right, but I hardly think it's
such a great insight! In fact I think it's so pedestrian that
I hardly ever mention it.

> Minor songs would sound sad because you have a tonal
> heirarchy emphasizing a sonority that sounds ambiguous;

Not that you were saying otherwise, but just to point it out,
there may be MANY reasons a song sounds sad.

> The blues would be explained

Yes, the blues! Something to think about when I'm not late
for a convention. The minor pentatonic... a mode of the
pentatonic with a minor chord at the bottom... just like the
case with the major and minor diatonic modes.

> However, after the supermajor example I
> played for you - when 5/4 clearly takes the role of 75/64 (which
> is a color in and of itself in my world,

75/64 has no identity in terms of tunable-by-ear ratios,
and questionable identity any other way. But for someone
with high-functioning AP, I'm sure every interval has its
own color.

> > > 6) The point of the mavila example was not whether the last
> > > chord seems major at first sight, but whether you CAN make it
> > > sound like a "really flat major" if you try.
> >
> > You can make anything seem any way with categorical perception.
> > I played a 7/8-scale piano keyboard for a day and when I got
> > home the keys on my piano looked like giant canoes. So what?
>
> How do you explain this then? In the supermajor example I posted,
> the melody is still recognizable, and 5/4 takes on the extremely
> bittersweet, sad characteristic that the D# takes in C-E-B-D#.

That's the kind of thing I wish you'd pointed out when I had
the example and score on my desktop. Too late now. Honestly,
I don't think I can keep up with this level of tuning list
involvement.

> > Can you phrase this in a way where I'll have a chance of
> > knowing if it's happened or not? Like, "Mess around with
> > mavila[5] and I guarantee you'll temporarily experience
> > hearing a mavila-approximate 10:12:15 triad sound happy",
> > or...?
>
> When you listen to a neutral triad, you can either hear it
> as a very flat major triad, or a very sharp minor triad.

I suppose it depends on the context, but generally I'm more
like Cameron in that I tend to hear it as a neutral triad.

> So the question is, is this because you're perceiving 6/5
> as a very flat 5/4?

Boy, I'm lost. Maybe your latest listening test post
will help.

-Carl

On Wed, Sep 15, 2010 at 7:47 PM, Carl Lumma <carl@...> wrote:
>
> Tuned 10:18:24, or in 12-ET? Please try to be specific.
> Also, why are you using a lower case b? Also, why G#
> for a root... isn't it easier in C? Sorry for all the
> questions, I mean them sincerely.

Haha, sorry, I just imagined it in G# when I wrote it. Could have been
in C. As for the tuning, either 12-tet or JI will do.

Let's do it this way: put it 10:12:18, in JI. C-Eb-Bb. I hear that as
C minor 7, without the 5th - not Ebmaj6 without the third, or Ebm6
without the third (since there's no third, it could be either major or
minor).

> Going forward, perhaps I should use different terms too...
> otonal/utonal would still cause confusion. I will therefore
> say "tonal" and "nontonal". I should also stress that this
> distinction should only account for a PART of what goes
> into major and minor in everyday music.

I agree, but I don't think the nontonal part is what is fundamental
about minor - note the latest listening example I posted. I will say
that there does seem to be a peculiar effect that happens when you
have a harmonic series with "one" note detuned, but in a concordant
way. Another example is a maj7 chord, which is even happier than
major, so much that it's almost sad. I'm not sure if this is a
correlation or the cause.

> No cadences! C'mon, geez. I can make you think you're
> wearing a hat with a cadence.

Haha, alright.

> My grandmother taught piano her whole life. Very talented
> too, for a local teacher in a Philadelphia suburb. Alas, I
> only took with her for a year and didn't return to the
> instrument until I was 16.

Haha, mine too! My grandmother was the south Philly neighborhood piano
teacher. Didn't realize there was that parallel.

> > But by itself, a minor chord is just a sort of sound-object,
> > so I don't know why it would be sad...
>
> But it is. Go figure.
>
> There's a common belief, due mainly to liberal ideology and
> rampant in the social sciences, that everything is cultural
> and nothing innate. What nonsense.

Well, I'm certainly very far from "liberal." I do think that there is
something innate going on here. I just think that it lies above the
psychoacoustic layer.

> > It produces the same result with me, but it is consistent with
> > the latter hypothesis as well: when I hear a ssLsssL scale, it
> > sounds like a shifting mix of aeolian and phrygian as I go up
> > the scale.
>
> I have no such perception.

What was your perception? Sounded like that to me, and Paul expressed
a similar perception. If we're in ssLsssL mavila, and I play a i chord
and move it up diatonically, I hear the following chord qualities:

im -> bIImaj -> IIImaj -> ivm -> vm -> VImaj -> VIIaug -> im

Which starts out in phrygian, and morphs into some kind of aeolian
with a #4 at the end. And if I go back down, I can hear it
differently, with that VIIaug sounding almost like major if played
quick enough, etc. So my perception of this scale seems to be entirely
due to diatonic template stuff, although the more I mess with it the
more the templates seem to merge into one mavila template which is
ambiguous and includes both.

> > Does C-D-Eb, played simultaneously in 12-tet, sound like
> > minor to you?
>
> It sounds discordant.

But does it sound sad like minor, or happy like major? How about
C-Eb-D, with the D up an octave? How about that vs C-D-E and C-E-D?

> It should be obvious that it's right, but I hardly think it's
> such a great insight! In fact I think it's so pedestrian that
> I hardly ever mention it.

But for the mapping thing does matter as well. I am basically going
with your theory and the mapping theory in parallel at this point,
since they both seem to make decent predictions and require roughly
equal amounts of assumptions, and have times when they both break down
(for my perception). I expect somewhere down the road I will discover
some way to tie them in together - the mapping as auditory biasing
would be one way of doing that, but there could be others. And that
would be quite the insight to make, I think, and probably be the holy
grail of music theory.

> > The blues would be explained
>
> Yes, the blues! Something to think about when I'm not late
> for a convention. The minor pentatonic... a mode of the
> pentatonic with a minor chord at the bottom... just like the
> case with the major and minor diatonic modes.

Right. As I said in my addendum, I don't think that the full diatonic
scale is what gives the minor chord its sound, since C dorian #4 and C
phrygian have different notes in every position besides the minor
triad, and it still sounds minor.

What I wrote about "there is no scale" and mini-maps fitting into an
infinitude of larger maps I think applies here.

> 75/64 has no identity in terms of tunable-by-ear ratios,
> and questionable identity any other way. But for someone
> with high-functioning AP, I'm sure every interval has its
> own color.

It isn't as much the 75/64, it's just that when you play C-E-B-D#,
which is a very bittersweet sound, the D# would be "ideally" tuned
75/64. If the theory that chord qualities derive from psychoacoustics,
then I would imagine the bittersweetness of this chord derives from
that the 75/64 is "what we're hearing" (or 75/32 in this case).

> > How do you explain this then? In the supermajor example I posted,
> > the melody is still recognizable, and 5/4 takes on the extremely
> > bittersweet, sad characteristic that the D# takes in C-E-B-D#.
>
> That's the kind of thing I wish you'd pointed out when I had
> the example and score on my desktop. Too late now.

Perhaps I should just come up with a 12-tet example and then the supermajor one.

> Honestly, I don't think I can keep up with this level of tuning list
> involvement.

Haha, me neither. I'm going back to Haiti in a few days for 3 weeks. I
think I need some time to organize all of these new ideas, there are a
lot of new thoughts here.

> > When you listen to a neutral triad, you can either hear it
> > as a very flat major triad, or a very sharp minor triad.
>
> I suppose it depends on the context, but generally I'm more
> like Cameron in that I tend to hear it as a neutral triad.

But you can "flip" the chord around to hear it as a flat major or a
sharp minor, right?

-Mike

Mike Battaglia wrote:
> On Tue, Sep 14, 2010 at 3:57 PM, genewardsmith
> <genewardsmith@...> wrote:
>> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>>
>>> After the i-iv-v-iv-i, does the melody sound like G-C-D-Eb-D-C to you?
>> No.
> //
>> I don't think they are unpleasant, though my on experiments with using them in place of major thirds suggests they aren't very good major thirds. And I would certainly not call them boring or irritating, which was my personal subjective reaction to certain 12et chords and intervals. They have a certain steely, bell-like quality which is actually quite nice for what it is, if you aren't trying to make it into a major third.
> > Alright, I'll stop playing games and get to what I was getting at: I
> like supermajor triads too. And the second example, which I think was
> more successful in what I was trying to do, if you can get yourself to
> hear 14:18:21 as a pseudo-diatonic "major" triad, then 5/4 can play
> the role of the augmented second, and takes on a sort of "minor" vibe
> to it. And then 9/7 takes on the quality of a major third, although it
> is considerably more discordant and in this specific case fairly
> irritating.
> > At least that's how I hear it, and seems to be how Igs is hearing it,
> so I was curious how many other people hear it the same way.
> > -Mike

In the "supermajorchromatic" example, the "D#" notes in the melody sound more and more like E as the example goes on (even as I'm following the music and see them written as "D#"), which then makes me interpret the preceding and following "E" notes as F and the "F#" notes as some variety of G.

On Wed, Sep 15, 2010 at 11:12 PM, Herman Miller <hmiller@...> wrote:
>
> In the "supermajorchromatic" example, the "D#" notes in the melody sound
> more and more like E as the example goes on (even as I'm following the
> music and see them written as "D#"), which then makes me interpret the
> preceding and following "E" notes as F and the "F#" notes as some
> variety of G.

Right. I deliberately set it up to break the D# perception down as
time went on - or rather set it up so as to challenge that perception.

I really should have been more clear, since we're dealing with an
issue of categorical perception. The name of the game is to see if you
can, through some tremendous force of willpower (not so tremendous for
me, but I've played this example over and over for the last day now),
still get that D# to sound like E all the way through the end. It is
clearly possible for you to hear it as "E", but the question is if you
can still maintain the D# mapping of that note.

If you can, the question thus becomes: what are you doing? Are you
hearing the E as 75/64? I can still keep my brain in D# mode all the
way through the end, even when the C-G-C-D# dyad ends up being
2:3:4:5. Does it mean that I'm hearing the harmonic structure as a
2:3:4:(75/64)?

Or does it have nothing to do with harmonic structure, and everything
to do with something else..?

And for the record, I think that the reason this scale "flips" back
and forth so much is that it's improper - the augmented second is 5/4,
more than a semitone larger than the minor third of ~7/6. If you had a
scale in which you could test whether different JI ratios "function"
the same way without having to distort it so much as to introduce an
obvious impropriety, the "harmonic structure = identity" hypothesis
would say that different JI ratios wouldn't substitute for each other
(since they'd all produce different "identities," as different as
major and minor). The "scale structure = identity" hypothesis would
say that different JI ratios would substitute for each other.

There is such a scale, and it's superpyth aeolian vs meantone aeolian,
and the 7/6's function for the 6/5's just fine. But after a lengthy
conversation with Carl on just this, I have come to the conclusion
that both hypotheses are slightly simplified, and that there is
something else at work.

The basic question is, does musical meaning (e.g. "happiness" for
major, "sadness" for minor) come from psychoacoustics, or does it come
from a cognitive layer that has to do with tonal organization? Or if
both, how do they interact? This musical example is supposed to be a
zen koan providing insight into the answers to those questions. Once
you manage to get the 5/4 to sound like D# all the way through, the
meditation can begin: how did you do that, what exactly did you do,
and what does it mean?

-Mike

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

> The basic question is, does musical meaning (e.g. "happiness" for
> major, "sadness" for minor) come from psychoacoustics, or does it come
> from a cognitive layer that has to do with tonal organization? Or if
> both, how do they interact? This musical example is supposed to be a
> zen koan providing insight into the answers to those questions. Once
> you manage to get the 5/4 to sound like D# all the way through, the
> meditation can begin: how did you do that, what exactly did you do,
> and what does it mean?

Oh man, you are sending me in a time-warp back to my "Modern Philosophy" class. What is "reality"? Are we going to be Rationalists about this? Empiricists? Phenomenologists? Or perhaps Existentialists (though that's getting a little more "post-modern")?

Really, if you want to be Zen about it, ask yourself whether a single note is major or minor. That's where the answer lies.

I'm serious, by the way. Just make sure you listen to a sound where the subharmonics are audible, too.

-Igs

On Thu, Sep 16, 2010 at 12:26 AM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > The basic question is, does musical meaning (e.g. "happiness" for
> > major, "sadness" for minor) come from psychoacoustics, or does it come
> > from a cognitive layer that has to do with tonal organization? Or if
> > both, how do they interact? This musical example is supposed to be a
> > zen koan providing insight into the answers to those questions. Once
> > you manage to get the 5/4 to sound like D# all the way through, the
> > meditation can begin: how did you do that, what exactly did you do,
> > and what does it mean?
>
> Oh man, you are sending me in a time-warp back to my "Modern Philosophy" class. What is "reality"? Are we going to be Rationalists about this? Empiricists? Phenomenologists? Or perhaps Existentialists (though that's getting a little more "post-modern")?
>
> Really, if you want to be Zen about it, ask yourself whether a single note is major or minor. That's where the answer lies.
>
> I'm serious, by the way. Just make sure you listen to a sound where the subharmonics are audible, too.
>
> -Igs

Haha, I can't tell if you really are serious. If you are, then
imagining whether a single note is major or minor begs the question -
is it that you're "imagining" different psychoacoustic periodic
relationships, or "imagining" different cognitive maps for the note?

-Mike

More zen: is silence major or minor?

Daniel Forro

On 16 Sep 2010, at 1:26 PM, cityoftheasleep wrote:
>
> Really, if you want to be Zen about it, ask yourself whether a > single note is major or minor. That's where the answer lies.
>

--- In tuning@yahoogroups.com, Daniel Forró <dan.for@...> wrote:
>
> More zen: is silence major or minor?

Ha! Minor. Definitely minor. ;->

-Igs

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> Haha, I can't tell if you really are serious. If you are, then
> imagining whether a single note is major or minor begs the question -
> is it that you're "imagining" different psychoacoustic periodic
> relationships, or "imagining" different cognitive maps for the note?

What if you're not imagining anything? What if *everything* is always there, all the time, but you are only shifting your focus?

That, if anything, is what the harmonic and subharmonic series have taught me. It's not that we're projecting something onto the sound, it's that we're carving away from it.

Even more enlightening are inharmonic series'. I have a friend who is a Sikh, and he teaches meditation classes. His favorite teaching aid is...a gigantic gong. But he plays it softly, spreading out different resonances, some of which I swear produce the same effect as those "binaural beats". Through that gong, I have realized that sound really is...EVERYTHING. I'm not spiritual or religious, but when my friend says "the gong is God", I have to agree.

-Igs

On Thu, Sep 16, 2010 at 1:30 AM, cityoftheasleep
<igliashon@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> > Haha, I can't tell if you really are serious. If you are, then
> > imagining whether a single note is major or minor begs the question -
> > is it that you're "imagining" different psychoacoustic periodic
> > relationships, or "imagining" different cognitive maps for the note?
>
> What if you're not imagining anything? What if *everything* is always there, all the time, but you are only shifting your focus?
>
> That, if anything, is what the harmonic and subharmonic series have taught me. It's not that we're projecting something onto the sound, it's that we're carving away from it.
>
> Even more enlightening are inharmonic series'. I have a friend who is a Sikh, and he teaches meditation classes. His favorite teaching aid is...a gigantic gong. But he plays it softly, spreading out different resonances, some of which I swear produce the same effect as those "binaural beats". Through that gong, I have realized that sound really is...EVERYTHING. I'm not spiritual or religious, but when my friend says "the gong is God", I have to agree.

Ha!

Well, I have to agree with your premise, but it doesn't settle the
debate. The truth is, if I play a 12-tet C-Eb-G, and you can shift
your perception of that chord into that of being "major," you're
better at tripping yourself out than I am.

But let's assume you get so good with this map warping stuff that you
can do that. The fundamental question is - where do musical feelings
arise from?

1) From the mental map?
2) From psychoacoustics?

That is, do minor chords sound "sad" because of an inherent
psychoacoustic implication, or do they sound sad because of our mental
map for them and understanding of how they'd fit into a diatonic
context?

Understanding that perception is flexible is one part, but it doesn't
answer the question of what you're flexing.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> Haha, I can't tell if you really are serious. If you are, then
> imagining whether a single note is major or minor begs the question -
> is it that you're "imagining" different psychoacoustic periodic
> relationships, or "imagining" different cognitive maps for the note?

What if you're not imagining anything? What if *everything* is always there, all the time, but you are only shifting your focus?

That, if anything, is what the harmonic and subharmonic series have taught me. It's not that we're projecting something onto the sound, it's that we're carving away from it.

Even more enlightening are inharmonic series'. I have a friend who is a Sikh, and he teaches meditation classes. His favorite teaching aid is...a gigantic gong. But he plays it softly, spreading out different resonances, some of which I swear produce the same effect as those "binaural beats". Through that gong, I have realized that sound really is...EVERYTHING. I'm not spiritual or religious, but when my friend says "the gong is God", I have to agree.

-Igs

Carl wrote:
> I don't understand. 16:19:24 may or may not have a life
> of its own -- I doubt it, but I should listen to it again
> and see what it does to 2010 Carl. Even if it did, it
> would have very low tonalness compared to something like
> 4:5:6.

Also, a quick note as I'm messing around with scala - I have no idea
if 16:19:24 has a life of its own, but 16:18:19:24 does, and
16:18:19:22:24 does even more still. Or 16:18:19:21:24, pick whichever
you like. I just played this in an upper register and a single note
popped out an octave below, clear as day. So it is "tonal," but still
sounds minor to me.

I have to tell you this is a fascinating concept, though, and there
are lots of moments where it really does work. I'm still struggling to
figure out what it all means. 9:11:13 and its utonal variant are good
examples, although those to me sound like really flat major and minor
chords anyway. 8:9:11:12 and its utonal variant are also good
examples, although if I'm going to go with that 1/(8:9:11:12) is "sad"
(which to me it is), I'm going to have to go with that the otonal mass
I posted earlier with 5/4 replaced with 6/5 also sounds "sad," which
to me it does.

7:9:11 is another good one, although now I can't figure out if it's
the placebo effect due to bias. If I listen hard, I can hear the
difference, but now I really want otonal triads to sound happy and
utonal or polytonal or nontonal with low roughness ones to sound sad
because it would be a cool theory, and hence I can't be impartial
anymore. Either way there is something interesting at work here...
I've never paid close attention to the utonal version of things like
7:9:11 before.

-Mike

Mike wrote:

> Let's do it this way: put it 10:12:18, in JI. C-Eb-Bb.

I know you were trying to be helpful, but to me, 10:12:18 and
C-Eb-Bb are fundamentally different things.

> I hear that as C minor 7, without the 5th

Ok me too. Isn't that because there's a 'C' on the bottom?

> I agree, but I don't think the nontonal part is what is
> fundamental about minor - note the latest listening example
> I posted.

I noted it but it seemed to back up the tonalness interpretation.

> Another example is a maj7 chord, which is even happier than
> major,

Huh, I think a major triad is happier than a Maj7 chord.

> Haha, mine too! My grandmother was the south Philly
> neighborhood piano teacher. Didn't realize there was that
> parallel.

Well, this was Lansdale. You might recognize it as a SEPTA
stop. Wow, did I get that right, SEPTA? OMG, flashback.

> Well, I'm certainly very far from "liberal."

Didn't mean to imply otherwise.

> > > It produces the same result with me, but it is consistent with
> > > the latter hypothesis as well: when I hear a ssLsssL scale, it
> > > sounds like a shifting mix of aeolian and phrygian as I go up
> > > the scale.
> >
> > I have no such perception.
>
> What was your perception?

It didn't really remind me of anything from a piano.
Let me play it some more and get back to you.

> im -> bIImaj -> IIImaj -> ivm -> vm -> VImaj -> VIIaug -> im
>
> Which starts out in phrygian, and morphs into some kind of aeolian
> with a #4 at the end.

Ok, I'm getting back to you. I hear what you're saying,
but I wouldn't have thought to describe it that way.

I found that the mode

160.0 360.0 520.0 680.0 880.0 1040.0 2/1

sounds the most stable to me, and in fact reminds me a
lot of the ionian mode of the diatonic scale.

> > > Does C-D-Eb, played simultaneously in 12-tet, sound like
> > > minor to you?
> >
> > It sounds discordant.
>
> But does it sound sad like minor, or happy like major?

Discordance overrides all of that.

> How about C-Eb-D, with the D up an octave?

Sounds minor.

> > It should be obvious that it's right, but I hardly think it's
> > such a great insight! In fact I think it's so pedestrian that
> > I hardly ever mention it.
>
> But for the mapping thing does matter as well.

I agree. But I think "mapping" has been getting a bit loose
lately. I basically subscribe to the Rothenberg approach.

> > 75/64 has no identity in terms of tunable-by-ear ratios,
> > and questionable identity any other way. But for someone
> > with high-functioning AP, I'm sure every interval has its
> > own color.
>
> It isn't as much the 75/64, it's just that when you play
> C-E-B-D#, which is a very bittersweet sound, the D# would be
> "ideally" tuned 75/64.

(grumbling noises) Stop analyzing xenharmonic with 12-ET!

> > I suppose it depends on the context, but generally I'm more
> > like Cameron in that I tend to hear it as a neutral triad.
>
> But you can "flip" the chord around to hear it as a flat major
> or a sharp minor, right?

Not listening to it cold. With an appropriate cadence, yes,
I'm sure.

-Carl

Mike wrote:

> I have to tell you this is a fascinating concept, though,
> and there are lots of moments where it really does work.

I'm a bit perplexed because, even if 16:18:19:21:24 were
extremely 'major' that wouldn't be evidence against my idea.
I'm not sure why you think it would be.

> I'm still struggling to figure out what it all means.

By the way, I haven't reviewed Genesis lately, but I think
Partch basically had the same idea. At least, he equated
minor with utonal. And as far as chords that have as little
tonalness and roughness as possible, they should be champions.

The problem differentiating it from the cultural hypothesis
is that the 5-limit triads are the champs among all utonal
chords. Because, as we have discussed at length, the low
tonalness rapidly becomes discordance as utonal chords are
extended. With their outer 3:2 strongly establishing the 10
as the root, I don't think you're gonna beat 10:12:15 for
nontonalness/minorness.

Maybe we should have a listen to the 3-limit: 3:4:6 v 2:3:4.
What do you think?

I find the 9-limit is about the endpoint for utonal
concordance. What do you make of 1/1-9/7-3/2-9/5-9/4 v
4:5:6:7:9 ? It helps to fiddle with the relative volumes
of the notes in the utonal chord, and the relative volumes
don't matter in the otonal chord, so you can find what
works best for the utonal one and then just match it
somehow (say, top to bottom) in the otonal one.

> I've never paid close attention to the utonal version of
> things like 7:9:11 before.

Me either. 1/1-9/7-11/7 vs 1/1-11/9-11/7... Wow,
really strong happy/sad feel here!

Excellent correspondence Mike; thanks.

-Carl

On Thu, Sep 16, 2010 at 5:13 PM, Carl Lumma <carl@...> wrote:

> I know you were trying to be helpful, but to me, 10:12:18 and
> C-Eb-Bb are fundamentally different things.

How so?

> > I hear that as C minor 7, without the 5th
>
> Ok me too. Isn't that because there's a 'C' on the bottom?

Intuitively, yes. But you were saying that you didn't hear 6/5 as
minor by itself, so I added a 3/2 on top of the 6... There is nothing
psychoacoustically implying the C as the root in the VF of that chord.

> > I agree, but I don't think the nontonal part is what is
> > fundamental about minor - note the latest listening example
> > I posted.
>
> I noted it but it seemed to back up the tonalness interpretation.

To me it sounds both minor and tonal. I'm really amazed at how our
perception diverges...

> > Another example is a maj7 chord, which is even happier than
> > major,
>
> Huh, I think a major triad is happier than a Maj7 chord.

I suppose this is where the "happy/sad" distinction breaks down,
really. To me a maj7 chord is happier than a maj chord, but so happy
that it's almost sad. Maj9 chords are even more so, and Maj9#11 chords
even even more so to the point where they're almost cathartic (these
chords are just stacked alternating major and minor thirds).

> > Haha, mine too! My grandmother was the south Philly
> > neighborhood piano teacher. Didn't realize there was that
> > parallel.
>
> Well, this was Lansdale. You might recognize it as a SEPTA
> stop. Wow, did I get that right, SEPTA? OMG, flashback.

Haha, damn! Yeah, SEPTA. What an awful public transit system.

> Ok, I'm getting back to you. I hear what you're saying,
> but I wouldn't have thought to describe it that way.
>
> I found that the mode
>
> 160.0 360.0 520.0 680.0 880.0 1040.0 2/1
>
> sounds the most stable to me, and in fact reminds me a
> lot of the ionian mode of the diatonic scale.

Me too, although if I focus on the second last chord, it turns into a
viim, instead of a vii diminished, which makes it sound sort of lydian
by the end. The second chord is two "major thirds," but the sum of
them is 720 cents, which to me still sounds like a fifth, and I can
still hear it as minor. If I play it faster without focusing it just
sounds like ionian.

But the fact that the chord qualities can just morph like that
indicates to me that categorical perception is most important in
determining musical meaning, although perhaps the original
"categories" derive from psychoacoustics (maybe). I think there may be
an entire middle layer of cognitive stuff in between psychoacoustics
and the end result which is where the "meaning" takes place, and where
the peculiar ambiguous character of 10:12:15 gets transformed into
"sadness." Hence why I want to study it so much.

I keep talking about the literature on semiology but really can't find
anything good yet. I know there's been some good research on it, they
talk about the creation of musical cognitive "icons" and "signs" and
"sound-objects" and stuff.

> > But does it sound sad like minor, or happy like major?
>
> Discordance overrides all of that.

Wow. Again, I'm amazed to hear how my perception differs from yours
here... It just sounds like obnoxious useless beating noise to you...?
Seriously, when I play C-D-Eb, I hear a clustered voicing that sounds
unmistakably "minor," with sadness arising and all of that.

This is really a quite astonishing observation for me, as I use
voicings like that when I play all the time, and now I wonder it
sounds like to everyone else... I'll use voicings like G-E-F-G-A-E for
Gsus13 all the time, played at the same time, and I wonder if everyone
else hears it as noise.

> > But for the mapping thing does matter as well.
>
> I agree. But I think "mapping" has been getting a bit loose
> lately. I basically subscribe to the Rothenberg approach.

Paul seems to think that categorical perception means "12-tet." Based
on my experience with things like 27-equal, where I can get a diatonic
G# to sound like a G# if I play C-E-G -> E-G#-B (both in terms of the
AP pitch "chroma" and its diatonic function) - despite that that G# is
way closer to A - I think Rothenberg is more close to how it works.

But in light of what we've just discussed, I think it might be even
simpler and deeper than that. When you see a hammer, you're not just
aware of what it feels and looks like, but also what it "can do." This
forms part of the meaning for that hammer. I would expect a similar
process works with chords. So when you hear a chord, part of the
feeling that emerges comes from an awareness of what a chord "could
do" or how it "could function" in any musical setting that you have
learned so far (or ones that logically follow from those). I just
listened to Igs' 16-tet clip, and I heard a lot of really bright stuff
that sounded really familiar. He avoided the fifth and just played
dom9 chords without it.

My brain, of course, would have no idea that he was in 16-tet if you
just played that clip in isolation, because the concept of 16-tet is
just an abstraction that doesn't really exist. I might also be in
16000-tet, where some kind of meantone fifth still exists alongside
the mavila one.

(If I say the word "shit," it still has a meaning whether I use it in
a sentence or not; I would expect something similar happens with
chords.)

> > It isn't as much the 75/64, it's just that when you play
> > C-E-B-D#, which is a very bittersweet sound, the D# would be
> > "ideally" tuned 75/64.
>
> (grumbling noises) Stop analyzing xenharmonic with 12-ET!

It isn't 12-ET; it's meantone. It's a major third on top of a fifth on
top of a major third.

> > But you can "flip" the chord around to hear it as a flat major
> > or a sharp minor, right?
>
> Not listening to it cold. With an appropriate cadence, yes,
> I'm sure.

Then there is some radical divergence in perception here between us,
and this is starting to become really quite shocking for me. And I
sincerely mean that, because I sort of assumed how I heard stuff was
how everyone heard it, minus the synesthetic "chroma" AP part.

-Mike

On Thu, Sep 16, 2010 at 5:18 PM, Carl Lumma <carl@...> wrote:
>
> Mike wrote:
>
> > I have to tell you this is a fascinating concept, though,
> > and there are lots of moments where it really does work.
>
> I'm a bit perplexed because, even if 16:18:19:21:24 were
> extremely 'major' that wouldn't be evidence against my idea.
> I'm not sure why you think it would be.

I'm saying that it sounds tonal and minor. In my perception, tonalness
and minorness aren't mutually exclusive. I have heard minor chords
that sound tonal and they still sound "minor." That is, you have
defined minorness as the absence of tonalness; if we're going to go
with a purely psychoacoustic definition, I would think it's more like
the presence of polytonalness that matters. 16:18:19:21:24 to me
sounds both minor and resonant; a resonant way to voice minor. But
what I'm saying is - this is reality to me. The definition you gave
may well sum it up for you, but it doesn't for me. I swear! :)

I'm about to post another message with an interesting correlation that
I have observed about major/minor... You will find this interesting, I
think. It is going to be long, but I ask that you read it, because I
feel I may have hit upon something... you no doubt will have insights
to add.

> By the way, I haven't reviewed Genesis lately, but I think
> Partch basically had the same idea. At least, he equated
> minor with utonal. And as far as chords that have as little
> tonalness and roughness as possible, they should be champions.

Indeed, but I do hear that 15-limit otonal sonority with the 5/4
switched out with 6/5 as "minor."

> Maybe we should have a listen to the 3-limit: 3:4:6 v 2:3:4.
> What do you think?

Sounds sadder if the C-G-C is flattened to C-F#-C rather than C-F-C,
which is consistent with my "divergence from the harmonic series"
pattern. Make the F# about 1 step of 17-tet away from G. C-G#-C is
also sadder. Make the G# about 1 step of 17-tet sharp of G.

> I find the 9-limit is about the endpoint for utonal
> concordance. What do you make of 1/1-9/7-3/2-9/5-9/4 v
> 4:5:6:7:9 ?

I think that it sounds sadder if you put a fifth above the 9/7, which
is consistent with the hypothesis I'm about to post.

> > I've never paid close attention to the utonal version of
> > things like 7:9:11 before.
>
> Me either. 1/1-9/7-11/7 vs 1/1-11/9-11/7... Wow,
> really strong happy/sad feel here!
>
> Excellent correspondence Mike; thanks.

Likewise, I have a lot to think about for the next three weeks in Haiti...

-Mike

Mike wrote:

> > I know you were trying to be helpful, but to me, 10:12:18
> > and C-Eb-Bb are fundamentally different things.
>
> How so?

Depending on who I'm talking to and the prior context,
C-Eb-Bb is either a chord in 12-ET, or in some unspecified
tuning of meantone, or in some unspecified scale in the most
general case. 10:12:18 aka 5:6:9 refers to a particular
chord in just intonation.

> > > I hear that as C minor 7, without the 5th
> >
> > Ok me too. Isn't that because there's a 'C' on the bottom?
>
> Intuitively, yes. But you were saying that you didn't hear 6/5 as
> minor by itself, so I added a 3/2 on top of the 6... There is
> nothing psychoacoustically implying the C as the root in the
> VF of that chord.

The bottom note is important. If a chord doesn't have a
strong VF other than the lowest note, then the lowest note
is gonna be it.

> > Huh, I think a major triad is happier than a Maj7 chord.
>
> I suppose this is where the "happy/sad" distinction breaks down,
> really. To me a maj7 chord is happier than a maj chord, but so
> happy that it's almost sad. Maj9 chords are even more so, and
> Maj9#11 chords even even more so to the point where they're
> almost cathartic (these chords are just stacked alternating
> major and minor thirds).

To me, anything built on a Maj7 tetrad sounds a lot like a
Maj7 tetrad... but I'm not that experienced with extended jazz
chords. The Maj7 tetrad sounds resigned, introspective, or
peaceful to me (just words coming off the top of my head).
Interestingly, 4:5:6:9 (or its approximations in 12-ET) has a
completely different sound. It's bold, decisive, optimistic.

> But the fact that the chord qualities can just morph like that
> indicates to me that categorical perception is most important
> in determining musical meaning, although perhaps the original
> "categories" derive from psychoacoustics (maybe).

There's a ton of stuff going on; I don't think anyone really
has a clue. I prefer to study what's easy to study, and that
turned out to be sufficient to create a theory of intonation.
The stuff you're talking about is more what you'd need for a
theory of composition.

> I keep talking about the literature on semiology but really
> can't find anything good yet.

And you won't. You'll find that sitting around cafes talking
about something called "semiology" produces just the kind of
results you'd expect.

> I'll use voicings like G-E-F-G-A-E for Gsus13 all the time,

That's not the same kind of thing as C-D-Eb.

> So when you hear a chord, part of the feeling that emerges
> comes from an awareness of what a chord "could do" or how it
> "could function" in any musical setting that you have learned
> so far

I can hear chords that way, but I can also turn that off
and hear them as blots of sound if I want.

> (If I say the word "shit," it still has a meaning whether I
> use it in a sentence or not; I would expect something similar
> happens with chords.)

How do you know you're not hearing a Greek word that
sounds like "shit" but means something else?

> > > It isn't as much the 75/64, it's just that when you play
> > > C-E-B-D#, which is a very bittersweet sound, the D# would be
> > > "ideally" tuned 75/64.
> >
> > (grumbling noises) Stop analyzing xenharmonic with 12-ET!
>
> It isn't 12-ET; it's meantone. It's a major third on top of
> a fifth on top of a major third.

Ok, stop analyzing xenharmonic music with meantone.

-Carl

Mike wrote:

> > I'm a bit perplexed because, even if 16:18:19:21:24 were
> > extremely 'major' that wouldn't be evidence against my idea.
> > I'm not sure why you think it would be.
>
> I'm saying that it sounds tonal and minor. In my perception,
> tonalness and minorness aren't mutually exclusive.

Right, I think I said a lot of things contribute to
"minor", I'm only trying to explain part of it, and that's
why I switched terms.

> > Maybe we should have a listen to the 3-limit: 3:4:6 v 2:3:4.
> > What do you think?
>
> Sounds sadder if the C-G-C is flattened to C-F#-C rather than
> C-F-C,

You didn't answer the question!

-Carl

On Fri, Sep 17, 2010 at 3:34 AM, Carl Lumma <carl@...> wrote:
>
> > > Maybe we should have a listen to the 3-limit: 3:4:6 v 2:3:4.
> > > What do you think?
> >
> > Sounds sadder if the C-G-C is flattened to C-F#-C rather than
> > C-F-C,
>
> You didn't answer the question!
>
> -Carl

Carl: I don't think either of them are sad... But I think I just
gained a bit of insight into why that is. This comes after a long,
long meditation on our recent conversation. Something about your
nontonalness insight struck me as profound, and I wanted to figure out
what. I noted that there are a LOT of "patterns" that emerge with the
minor chord, and one of them has to be "it." The utonality one is sort
of close sometimes, but isn't quite it. Yours is much, much closer,
although as you noted sometimes breaks down, and I think still
reflects a brilliant insight that I wanted to fully understand. So I
did a lot of ruminating and this is what I came to. This is very long,
so you will probably want to read this in parts, but it is my complete
train of thought, and I feel I should say it.

Dissonance can be PAINFUL. Think fingernails on a chalkboard painful.
Think my listening examples that you hated painful. It can be so
painful that we'd rather listen to silence than listen to it. That is
to say, we don't like it. I don't know how psychoacoustics can lead to
happiness and sadness, but I do know that it can lead to displeasure,
and that displeasure can lead to sadness. So strike one for liberal
cultural relativism.

Let's make some predictions. The most dissonant interval that I can
think of is slightly flatter than a semitone, preferably 1\17. It's so
dissonant that it functions as a "depriming" interval that makes us
hear the next note as a definitive movement away from the last one and
hence works great for melody. I believe it's near the global maximum
of harmonic entropy too. Let's look at what happens if we take the
harmonic series and detune different notes by something near this
interval, which I will refer to as the "depriming interval." There may
be other ways to do this, but this is the first one I tried.

To do this, let's pick a tuning system where something decently close
to this depriming interval exists. I think 12 notes per octave should
do, no doubt much to your chagrin. So I'm going to make some 12-tet
predictions, because it works there too and even explains chords I've
been using all my life, and makes this theory easy to communicate to
you. I will end with a few xenharmonic predictions and leave the rest
for you to have fun and see what you can find. Maybe there's a way to
extend this further. I think there is a pattern here that you will no
doubt see and understand intuitively and from a psychoacoustic
standpoint, and perhaps be able to extend.

Please play the following chords, and keep in mind exactly what
they're approximating. Play a C an octave below all of these. You will
also note, if you ever do this in JI, that when a combination of
intervals is detuned so as to push the whole thing into another
"concordant" sonority, the illusion is completely destroyed, as you
predicted.

C-E -> happy. make sure you keep the octave below this.
C-Eb -> sad. to avoid yourself as hearing Ab as the root, play C an
octave below, as I said.
C-F -> happy, because you end up with an otonal sonority despite the C
in the bass, as you predicted. It's just too concordant. Go to C-E+ or
some kind of slightly sharp supermajor third and it'll get painful and
slightly sad, or disturbingly manic perhaps. Note that people often
hear supermajor triads as having a bit of sadness to them.

C-Eb-G -> detune the E, and get C-Eb-G -- sad.
C-Eb-Gb -> detune the G and the E, and get C-Eb-Gb - more sad, so sad
that it's hopeless.
C-E+-G -> make the E sharp, but not as sharp as F. Find some middle
ground of discordance. Supermajor perhaps. Sad. This can't be done in
12-tet.
C-E-F# -> make the G flat to C-E-F#. Needs to be done in JI for the
full effect, but works decently well in 12-tet. Sounds like lydian.
Kind of sad, but in a different way than minor. Works better if the F#
is flat - try 16:20:23.
C-E-G# -> make the G sharp to C-E-G#. Really needs to be in JI to get
the full effect - try 16:20:25.8. Pretty painful. Detuning the fifth
seems to be more painful than detuning the third (this is going to be
a theme and I'm sure you can see why)

Let's go to 4 notes. I'm going to call it C-E-G-Bb, I don't want to
hear any complaining.

C-Eb-G-Bb -> detune the E, get C-Eb-G-Bb - not quite as sad as C-Eb-G,
the Bb stabilizes it a bit.
C-Eb-G-B -> detune two notes, predicting more dissonance and pain.
Change the E and the Bb, so go to C-Eb-G-B. Holy $#&#, this is sad,
even more so than C minor. If you detune the B so that it goes to A,
it's also equally sad, and happens to be sort of near with the 7-limit
utonality. If you make the A a little sharper than the 12-tet one it's
sadder. Find some maximum of harmonic entropy.
C-E-Gb-B -> detune three notes. You get C-Eb-Gb-B, which is even
sadder, hopeless, sinister, etc. Or C-Eb-Gb-A.
C-E-F#-Bb and C-E-G#-Bb -> these are sort of like the other discordant
examples, but less dissonant. Stabilized. Not sad, but curious. Note
how the meaning changes as you get in between consonance and
dissonance. This works better in JI.
C-E-G-A/C-E-G-B -> detune the Bb, get C-E-G-A or C-E-G-B. Both of
these are "happy" like major, but also a bit sad (as you yourself
described). Make the A sharp and it's even more sad. This effect is
intensified if you go into JI and make the B a little bit sharp.
C-E+-G-B+ -> for heightened sadness, make the major thirds both 9/7's
or slightly sharper. More sad.

I'll spare you the full set, but I'll bring you to a few more notable ones:
Start with C-E-G-Bb-D - Make the B sharp, and you go to C-E-G-B-D.
Sad. Make the D sharp, and go to C-E-G-B-D#. Really sad, bittersweet.
This is the chord I took advantage of in my supermajor example, where
I got that D# to be intoned as 5/2 above C. Again correlating with the
notion that if you place notes a depriming interval away from the
harmonic series, it sounds more dissonant, more painful, and sadder.
Detune the G to F# - you get C-E-F#-B-D#. Even more so, but starts to
sound concordant in a way because the F#-B-D# forms a major triad.
This mixture of biting dissonance and concordance is going to come in
handy in forming a definition of what "minor" is.

Start with 4:5:6:7:9:11 and detune to 12-tet C-Eb-G-A-D-F# (or B-D-F#)
- this is an approximate 4:5:6:7:9:11 in which the 5 is flattened by a
depriming interval, the 7 is flattened by a priming interval, the 9 is
left alone, and the 11 is sharpened by a priming interval. This is
sad. The sadness can again be enhanced by going to anti-JI and
detuning things. The F# isn't quite sharp enough, and if you make it
sharper, it's, as predicted, more dissonant, and more painful, and
hence more poignant. Same with the A.

C-Eb-G-B-D-F#-A -- This is the same chord with a B in the 7/4 position
and an A on top approximating an anti-13/8. I can intuitively tell
that if I make the A sharper, it'll be more biting and dissonant, and
so it is.

This also predicts new xenharmonic chords, which is why I seem to be
having a psychotic break from reality:

Start with C-E-G-Bb-D. Detune one note and you get C-Eb-G-Bb-D - a bit
sadder. Detune one more and you get C-Eb-G-B-D - sadder still. Detune
that last D to C-Eb-G-B-D#. Well, it's "almost" sadder, but not quite,
because in 12-tet Eb and D# are the same thing. Go to 19-tet and it
works -really- well. This successful prediction is what encouraged me
to continue this train of thought.

Another xenharmonic prediction that I just came up with while typing
this that works: Go to scala, and go to the chord creator, and put the
"decimal" feature on. Try this chord:
1/1 - 19/16 - 3/2 - 12/7 - 8.8/4 - 8/3 - 12.9/4

Note that I'm creating a combination of divergent notes from the
series, and convergent notes with the series, which I think is
essential to defining the "minor" sound. It's in between pain and
pleasure and in between consonance and dissonance. And in fact, if you
screw around with this enough, you will see sinister evilness morph
into despair morph into sadness morph into being not happy but being
chilled out morph into being nostalgic morph into being"cool" morph
into being "earthy" morph into being "mystical". Try something like
this back in 12-tet: C-E-G becoming C-Eb-G, sad. C-E-G-Bb becoming
C-E-G-B, happy yet sad, wistful, nostalgic. C-E-G-Bb-D becoming
C-E-G-Bb-Eb, hendrix chord, "cool." C-E-G-Bb-D-F# is itself a detuned
4:5:6:7:9:11, and sounds "mystical." These sounds are representative
of different ways in which consonance and dissonance, and the feelings
they produce are representative of different ways in which pleasure
and pain interact.

There were a few other chords that we couldn't do in 12-tet. Try
different ways of making the 5 and 6 in 4:5:6 sharper, but note that
if you go too far with it, you'll end up getting to 3:4:5, which
destroys the painfulness as it starts being tonal (or concordant), as
your prediction states. One is a major sixth chord with a sixth that's
a bit sharper. Try 1/1 - 5/4 - 3/2 - 12/6. This to me is a very
interesting sonority that isn't quite sad, somewhere on a lower level
than sad. Make 5/4 become 14/11 and it becomes a bit sadder. Make the
3/2 become something like 49/32 and you have yourself a
semi-consonant, somewhat painful but not too much, very colorful
tetrad. 1/1 - 5/4 - 3/2 - 15/8 too - detune the 15/8 even more to
27/14 and you have something more painful, but still kind of painless
and rooted with the 4:5:6. Make the 5/4 become 9/7 and it pops to
life. Make the 5/4 become 13/10 and it becomes more sad, but make the
15/8 become 39/20. Seemed like it was going to become less sad, but
the 39/30 is close enough to 2/1 that it starts to sound concordant,
and hence doesn't freak you out and stimulate your heartbeat, or sound
like nails on a chalkboard, or resemble the call of an ancient
predator, or whatever lead this feature of the auditory system to
evolve.

Note one last thing: I have left open the question of how to tune
these things. Do we want them to beat like hell and be maximally
discordant, or make them maximally concordant? And my answer is -
whatever you want. If you like the sound of there being no roughness,
tune them concordantly. If you want your minor triads to sound rooted,
go with 16:19:24. If you want them to sound simpler and have the
thirds be 5/4, go with 10:12:15. If you want them to be LESS biting,
go a bit further away from the priming interval. 6:7:9 is more serene
(and almost rooted), as are neutral triads. If you want them to be
more biting as far as my ears go, make the minor third a bit sharp,
maybe around 333 cents.

A few random odds and ends: this is an abstraction of the "major is
happy, minor is sad, diminished is depressingly" sad concept. Note how
often this aligns with utonal chords, which might be decent for tuning
these sonorities if you want to avoid beating. Minorness is a mixture
of tones that are divergent from the series, as well as tones that are
convergent with the series, thus in between pleasure and pain, a
mixture of both. I hypothesize that if we work out the math and come
up with the "most discordant sound," it will BE the nails on a
chalkboard sound. I have read that this response evolved because it
resembles the call of an ancient predator. Hence any psychoacoustic
feature can be used to make music.

The structure of scales, modes, and tonality becomes very, very
interesting when looked at from this perspective. We have studied
consonance so far, henceforth I want to delve into dissonance.

I only hope that you hear this the same way I do. One last prediction:
these two chords should be somewhat roughly equivalent in "sadness"
from a 12-tet standpoint:

C-Eb-G
C-E-G-B-D-F#

-Mike

On Fri, Sep 17, 2010 at 5:24 AM, Mike Battaglia <battaglia01@...> wrote:
>
> A few random odds and ends: this is an abstraction of the "major is
> happy, minor is sad, diminished is depressingly" sad concept. Note how
> often this aligns with utonal chords, which might be decent for tuning
> these sonorities if you want to avoid beating. Minorness is a mixture
> of tones that are divergent from the series, as well as tones that are
> convergent with the series, thus in between pleasure and pain, a
> mixture of both. I hypothesize that if we work out the math and come
> up with the "most discordant sound," it will BE the nails on a
> chalkboard sound. I have read that this response evolved because it
> resembles the call of an ancient predator. Hence any psychoacoustic
> feature can be used to make music.
>
> The structure of scales, modes, and tonality becomes very, very
> interesting when looked at from this perspective. We have studied
> consonance so far, henceforth I want to delve into dissonance.

A few last addenda: this depriming concept is just the first thing
that I'd tried. But it might just boil down, in the end, to harmonic
entropy. Minorness is somewhere between fingernails on a chalk board
screech and a w-limit harmonic series - perhaps this boils down
entirely to concordance. If we had harmonic entropy in a way that
wasn't tied down to any limit of notes, perhaps it would reveal that
C-Eb-G and C-E-G-B-D-F# are of roughly equal discordance.

That being said, I invite criticism of the above ideas, and you should
know to separate my speculation on the psychoacoustic basis for this
phenomenon from the phenomenon itself. Feel free to add to it, extend
it, etc. The pattern does seem to be valid though, at least for me.

-Mike

On Fri, Sep 17, 2010 at 6:09 AM, Mike Battaglia <battaglia01@...> wrote:
>
> That being said, I invite criticism of the above ideas, and you should
> know to separate my speculation on the psychoacoustic basis for this
> phenomenon from the phenomenon itself. Feel free to add to it, extend
> it, etc. The pattern does seem to be valid though, at least for me.
>
> -Mike

One last thing: I didn't investigate this for chunks of harmonic
series in which the root isn't a multiple of 2. Carl and I both
noticed that 7:9:11's utonal inversion is "sad" as opposed to happy.
Let's get that 9 moved down by a depriming interval, or generally find
the most discordant place to put it, and see if we can't squeeze some
real pain out of it.

I just hope that you all hear these chords the same way that I did,
and that there's a clear increase in sadness and despair from C-Eb-G
to C-Eb-G-B to C-Eb-G-B-D-F#. Note that I skipped altering D, because
to sharpen it to D# in 12-tet is to just make it an octave above Eb,
which is pretty concordant. If you flip back and forth between
C-Eb-G-B-D-F# and C-Eb-G-B-Eb-F#, you might feel that there is another
level of sadness that might be reached if you hit a note between them.
Go to 31-tet and play D#, and it works as predicted.

-Mike

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Mike wrote:
>
> > > I know you were trying to be helpful, but to me, 10:12:18
> > > and C-Eb-Bb are fundamentally different things.
> >
> > How so?
>
> Depending on who I'm talking to and the prior context,
> C-Eb-Bb is either a chord in 12-ET, or in some unspecified
> tuning of meantone, or in some unspecified scale in the most
> general case. 10:12:18 aka 5:6:9 refers to a particular
> chord in just intonation.

Same here I'm afraid, except that my default assumption is meantone. I don't normally think in terms of 12et; it's too ambiguous.

On Fri, Sep 17, 2010 at 8:27 AM, genewardsmith
<genewardsmith@...> wrote:
>
> Same here I'm afraid, except that my default assumption is meantone. I don't normally think in terms of 12et; it's too ambiguous.

Gene, I don't know if you read the massive tome that I just wrote, but
the cliffnotes are that I think discordant intervals are important,
because they cause pain, and a mixture of pain and concordance is
"minor" to varying degrees. Do you think it would be possible to
formulate an approach to regular mapping that includes "painful"
intervals as basis vectors in addition to harmonic ones?

I'm thinking along the lines of that something along the lines of
60-70 cents is some kind of "maximally discordant interval", hence why
it's so great for melody. If you flatten or sharpen the 6 in 4:6 by
this amount, it sounds unstable and discordant and painful. If you
keep the 4:6 the same and make it 4:5:6, and flatten the 5 by this
amount, it's not so painful, just "sad." If you sharpen it by about
this amount, you get supermajor, which is disturbingly manic and a bit
sad. The idea is that the higher up the overtone series you do this,
the less effective the "pain" is, and if you do it to more than one
interval, you make things even more painful, and hence more sad.
Flatten the 5 in 4:5:6:7 by this amount and also flatten or sharpen
the 7, and you get something even more despairing and sad than minor.
You will find a predictable and consistent pattern for this all up and
down the series, unless you flatten or sharpen things in a way that it
starts to form another chunk of the series. You might need to temper
things by less than 65 cents as overtones get closer together; use
your ear and find what's most discordant.

So perhaps it would be a worthwhile venture for us to explore linear
temperaments that contain lots of discordant notes in addition to lots
of consonant notes, which might be useful for generating some kind of
new type of tonal system in addition to the new ones we already have.
If you temper out the difference between a 5/4 lowered by this
interval and 6/5, we already have our first regular temperament with
this expanded JI/anti-JI pitch space. Perhaps we could call it "minor
temperament" or something.

Any thoughts? I think it might be a decent idea, and has some
psychoacoustic basis to it. Probably why I also liked Michael's PHI
scale so much back in the day. Either way, we should have linear
temperaments that generate an equal amount of pain and pleasure!

-Mike

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

> I'm thinking along the lines of that something along the lines of
> 60-70 cents is some kind of "maximally discordant interval", hence why
> it's so great for melody.

> Any thoughts?

Temperaments where 28/27 (63 cents) or 25/24 (70.7 cents) are of low complexity come to mind. Something tempering out 225/224 would identify the two, come to that. Magic is one possibility, with a complexity of 3. Valentine is a little fatter than what you want, but with a complexity of 1; sycamore has this also. There's also squares, sentinel, shrutar, vishnu, liese and roman.

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

> I'm thinking along the lines of that something along the lines of
> 60-70 cents is some kind of "maximally discordant interval", hence why
> it's so great for melody.

I don't understand the "hence" part of this: why would maximally discordant interval be great for melody?

Kalle

On Fri, Sep 17, 2010 at 10:16 AM, genewardsmith
<genewardsmith@...t> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > I'm thinking along the lines of that something along the lines of
> > 60-70 cents is some kind of "maximally discordant interval", hence why
> > it's so great for melody.
>
> > Any thoughts?
>
> Temperaments where 28/27 (63 cents) or 25/24 (70.7 cents) are of low complexity come to mind. Something tempering out 225/224 would identify the two, come to that. Magic is one possibility, with a complexity of 3. Valentine is a little fatter than what you want, but with a complexity of 1; sycamore has this also. There's also squares, sentinel, shrutar, vishnu, liese and roman.

I'll check that out. I was thinking, as well, it might be interesting
if something like 28/27 were used as a basis vector - and if you used
7-limit JI plus that interval, what would happen. If you could find a
way to temper it with some other interval in such a way that it has
low complexity, but not too low, it might lead to some interesting
things.

-Mike

On Fri, Sep 17, 2010 at 2:23 PM, Kalle Aho <kalleaho@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > I'm thinking along the lines of that something along the lines of
> > 60-70 cents is some kind of "maximally discordant interval", hence why
> > it's so great for melody.
>
> I don't understand the "hence" part of this: why would maximally discordant interval be great for melody?
>
> Kalle

Well, let's note that 1\17 IS great for melody, first off. And let's
note that its semitone is around near that maximum of HE. And it's
also the noble mediant between 15/8 and 2/1, or so I hear.

That being said, I think it's that's because the brain hears it as so
discordant that movement by that interval couldn't possibly be
harmonically related to the first note. It's not some kind of unison,
and it's not 16/15, it's in this maximally discordant space between
the two. It's a "depriming" signal.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Fri, Sep 17, 2010 at 2:23 PM, Kalle Aho <kalleaho@...> wrote:
> >
> > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > > I'm thinking along the lines of that something along the lines of
> > > 60-70 cents is some kind of "maximally discordant interval", hence why
> > > it's so great for melody.
> >
> > I don't understand the "hence" part of this: why would maximally discordant interval be great for melody?
> >
> > Kalle
>
> Well, let's note that 1\17 IS great for melody, first off. And let's
> note that its semitone is around near that maximum of HE. And it's
> also the noble mediant between 15/8 and 2/1, or so I hear.
>
> That being said, I think it's that's because the brain hears it as so
> discordant that movement by that interval couldn't possibly be
> harmonically related to the first note. It's not some kind of unison,
> and it's not 16/15, it's in this maximally discordant space between
> the two. It's a "depriming" signal.

Okay, why is it good for melody if the notes couldn't be harmonically
related? Is it then bad if a melody is based on arpeggiated chords?
And are the other local maxima of HE also great for melody?

Kalle

This is sort of tangential... but then again not.

This morning I sat down at the keyboard and started banging at 13ET, and it
sounded bad and confused, at first.

After some 15 minutes or so I started to hear the chords in a badly out of
tune 12 edo context - a little further it no longer sounded out of tune but
took on a logic of its own.

That was a rather interesting experience.

And a further aside - Carl I tried miracle 9 - meh
I tried Miracle 12 and found a nice progression but it sounded so 12 edo I'm
not sure it was any different.

G sus in 1 st inversion, G first inversion, B minor, F# 1st inversion, rinse
and repeat.

Tuning is below

Chris

|
0: 1/1 C unison, perfect prime
1: 83.872 cents C// Db/
2: 200.587 cents
3: 317.303 cents D// Eb/
4: 350.147 cents D#\ E\\
5: 466.862 cents
6: 583.578 cents F// Gb/
7: 700.294 cents G
8: 817.009 cents
9: 849.853 cents G#\ A\\
10: 966.569 cents A/ Bb
11: 1083.284 cents
12: 1200.000 cents C

> Okay, why is it good for melody if the notes couldn't be harmonically
> related? Is it then bad if a melody is based on arpeggiated chords?
> And are the other local maxima of HE also great for melody?
>
> Kalle
>
>
>

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> After some 15 minutes or so I started to hear the chords in a
> badly out of tune 12 edo context - a little further it no longer
> sounded out of tune but took on a logic of its own.

For 13, this is an interesting scale:

!
Single-chain MOS of 5:4's in 13-ET.
10
!
184.615 !....2
276.923 !....3
369.231 !....4
553.846 !....6
646.154 !....7
738.462 !....8
923.077 !...10
1015.385 !..11
1107.692 !..12
2/1 !.......13
!
! Scale is proper.

There are many others.

> And a further aside - Carl I tried miracle 9

miracle[10]? The MOS or Gene's scale?

> 0: 1/1 C unison, perfect prime
> 1: 83.872 cents C// Db/
> 2: 200.587 cents
> 3: 317.303 cents D// Eb/
> 4: 350.147 cents D#\ E\\
> 5: 466.862 cents
> 6: 583.578 cents F// Gb/
> 7: 700.294 cents G
> 8: 817.009 cents
> 9: 849.853 cents G#\ A\\
> 10: 966.569 cents A/ Bb
> 11: 1083.284 cents
> 12: 1200.000 cents C

Hm, interesting. It's definitely to do with miracle,
but it doesn't look like miracle[12]. Where'd you get it?

-Carl

On Sat, Sep 18, 2010 at 3:21 PM, Kalle Aho <kalleaho@...> wrote:
>
> Okay, why is it good for melody if the notes couldn't be harmonically
> related? Is it then bad if a melody is based on arpeggiated chords?
> And are the other local maxima of HE also great for melody?
>
> Kalle

I don't think that it's bad if a melody is based on arpeggiated
chords. I just notice that if you're trying to move by leading tone,
e.g. B->C, it sounds better if you get that interval into the area of
maximum discordance. V-I sounds less "effective" in JI if there's
something like a B-C resolution, and much better if you sharpen the B,
and lots of people have noticed that it works best if that B is at
about 70 cents.

Like I said, it's just a half-assed theory, but the pattern is not.
Check out the listening example I just posted.

-Mike

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

> !
> Single-chain MOS of 5:4's in 13-ET.
> 10
> !
> 184.615 !....2
> 276.923 !....3
> 369.231 !....4
> 553.846 !....6
> 646.154 !....7
> 738.462 !....8
> 923.077 !...10
> 1015.385 !..11
> 1107.692 !..12
> 2/1 !.......13
> !
> ! Scale is proper.

I like it better in 58et:

! 10-13-58.scl
Single chain pseudo-MOS of major and neutral thirds in 58et
10
!
186.20690
289.65517
393.10345
537.93103
641.37931
744.82759
931.03448
1034.48276
1096.55172
1200.00000
!
! Scale is improper.

Gene wrote:

> I like it better in 58et:

The point of using 13 is that, IIRC, it is the strictly
proper point for the 5:4 in this scale. -Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Gene wrote:
>
> > I like it better in 58et:
>
> The point of using 13 is that, IIRC, it is the strictly
> proper point for the 5:4 in this scale. -Carl

It's the borderline between proper and strictly proper, but why is that "the point"? I missed something, evidently.

I like the idea of either (5/4)^6 (11/9)^3 (7/6) or (5/4)^5 (11/9)^4 (7/6) cycles, but 58 doesn't seem like the way to go with that idea. Garibaldi would work for the first type, but there's the question of how to best order the circle.

Gene wrote:

> It's the borderline between proper and strictly proper, but
> why is that "the point"? I missed something, evidently.

See here:

/tuning/topicId_840.html#7125

-Carl

Hi Carl,

Here are the 2 miracle tunings I used today:

! mir9.scl
Mir9
9
!
116.7156
233.4312
350.1468
499.7064
616.4220
733.1376
933.7248
1050.4403
1200.0000

and

! mir12.scl
Mir12
12
!
83.8715
200.5871
317.3027
350.1468
466.8624
583.5780
700.2936
817.0092
849.8532
966.5688
1083.2844
1200.0000

I have recordings of these but I'm not sure they are worth sharing.

I'll take a look at that 13 ET scale probably later tonight. I copied it.
Got some things to take care of.

Chris

On Sat, Sep 18, 2010 at 3:59 PM, Carl Lumma <carl@...> wrote:

>
>
> --- In tuning@yahoogroups.com <tuning%40yahoogroups.com>, Chris Vaisvil
> <chrisvaisvil@...> wrote:
> >
> > After some 15 minutes or so I started to hear the chords in a
> > badly out of tune 12 edo context - a little further it no longer
> > sounded out of tune but took on a logic of its own.
>
> For 13, this is an interesting scale:
>
> !
> Single-chain MOS of 5:4's in 13-ET.
> 10
> !
> 184.615 !....2
> 276.923 !....3
> 369.231 !....4
> 553.846 !....6
> 646.154 !....7
> 738.462 !....8
> 923.077 !...10
> 1015.385 !..11
> 1107.692 !..12
> 2/1 !.......13
> !
> ! Scale is proper.
>
> There are many others.
>
>
> > And a further aside - Carl I tried miracle 9
>
> miracle[10]? The MOS or Gene's scale?
>
>
> > 0: 1/1 C unison, perfect prime
> > 1: 83.872 cents C// Db/
> > 2: 200.587 cents
> > 3: 317.303 cents D// Eb/
> > 4: 350.147 cents D#\ E\\
> > 5: 466.862 cents
> > 6: 583.578 cents F// Gb/
> > 7: 700.294 cents G
> > 8: 817.009 cents
> > 9: 849.853 cents G#\ A\\
> > 10: 966.569 cents A/ Bb
> > 11: 1083.284 cents
> > 12: 1200.000 cents C
>
> Hm, interesting. It's definitely to do with miracle,
> but it doesn't look like miracle[12]. Where'd you get it?
>
> -Carl
>
>
>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Sat, Sep 18, 2010 at 3:21 PM, Kalle Aho <kalleaho@...> wrote:
> >
> > Okay, why is it good for melody if the notes couldn't be harmonically
> > related? Is it then bad if a melody is based on arpeggiated chords?
> > And are the other local maxima of HE also great for melody?
> >
> > Kalle
>
> I don't think that it's bad if a melody is based on arpeggiated
> chords. I just notice that if you're trying to move by leading tone,
> e.g. B->C, it sounds better if you get that interval into the area of
> maximum discordance. V-I sounds less "effective" in JI if there's
> something like a B-C resolution, and much better if you sharpen the B,
> and lots of people have noticed that it works best if that B is at
> about 70 cents.

Right, I'm just trying to understand why this (optimal leading tone
interval =~ max HE) isn't just a coincidence.

If I remember correctly Paul Erlich thinks that in pentatonic and
decatonic scales it's the more rare *large* steps that function as
leading tone-like sign posts. Would it then make sense melodically
to tune them close to the local HE maximum?

Kalle

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

> Carl: I don't think either of them are sad... But I think I just
> gained a bit of insight into why that is. This comes after a long,
> long meditation on our recent conversation. Something about your
> nontonalness insight struck me as profound, and I wanted to figure
> out what. I noted that there are a LOT of "patterns" that emerge
> with the minor chord, and one of them has to be "it." The utonality
> one is sort of close sometimes, but isn't quite it. Yours is much,
> much closer, although as you noted sometimes breaks down, and I
> think still reflects a brilliant insight that I wanted to fully
> understand. So I did a lot of ruminating and this is what I came
> to. This is very long,

Yes, it was.

The general approach is interesting, though I don't always
agree with your descriptions of the examples... though I would
appreciate a more test-based approach (preferably blinded).
I also find the use of 12-ET notation obnoxious. 12-ET should
never be used for pyschoacoustics experiments.

-Carl

Mike wrote:

> perhaps this boils down entirely to concordance.

I agree completely, accept to exclude roughness.
Because it interferes with our ability to discern
individual notes in a chord. And also because
roughness is not sad. C-E-G is not sadder than
4:5:6, though it is rougher. 0-75.0-125.0 cents
isn't sad at all, it's just a mess.

-Carl

On Sun, Sep 19, 2010 at 10:16 AM, Kalle Aho <kalleaho@...> wrote:
>
> Right, I'm just trying to understand why this (optimal leading tone
> interval =~ max HE) isn't just a coincidence.

It could be a coincidence, but I don't think so. I think not because
that interval simply represents, for dyadic entropy, the interval that
is in the cone of maximum confusion with the unison and another
interval. It might just boil down to a "feature" of tetradic entropy
that we haven't considered though, since we haven't calculated it (in
the process of changing it).

There is a big difference between 5:6:7 and 1.25:2.5:5:6:7, though.
Unless, that is, you hear the root of the 5:6:7 as "5" anyway.

There are a few options, which I think are interconnected:
1) The brain is trying to place concordant relationships in any way
possible, and one of the options is always to decide that the sonority
is two unrelated notes.
2) If you take 4:5:6 and push the 5 TOO far, you'll get another
sonority, like 6:7:9 if you go too flat, or 10:13:15 if you go too
far.
3) If you push it less far, you get something like 10:12:15 or
14:18:21, which are both more dissonant.
4) There will be a bunch of nearby intervals in which if you push the
sonority too far, you'll get something like 6:7:9 or 10:13:15, which
are both less painful than 10:12:15 and 14:11:21.
5) The lower dyad in these triads differ by 4:5 by things like 15/14,
26/25, etc.
6) 60 cents is maximally distinct, and yet maximally a part of, ALL of
these semitone-quartertone sized intervals, hence functions well as a
decent "rule of thumb" to find a maximally discordant interval near
5/4 in either direction. Note that if you sharpen 5/4 by 60 cents
though, you get 10:13:15, which isn't as discordant as 14:18:21. So
it's just a rule of thumb, and you have to use your ears to find the
most discordant possible sonority.

Hence the theory is, minorness is a watered down version of
ultra-discordance. Dyadic entropy is not triadic entropy, and it's
definitely not tetradic entropy. 5:4 and 6:5 are concordant dyads, but
so what? How does that apply to the brain trying to fit 5:10:12:15?

> If I remember correctly Paul Erlich thinks that in pentatonic and
> decatonic scales it's the more rare *large* steps that function as
> leading tone-like sign posts. Would it then make sense melodically
> to tune them close to the local HE maximum?

That's what people have noticed with 17-tet; its melodic properties
are almost unbeatable. Also what Darreg noticed when he said that if
you sharpen the leading tone in 31-tet by a diesis (how does one
pronounce diesis exactly?), it resolves better.

I have talked to Paul about this; I think his "rare interval" theory
is a decent one, but I'm not entirely sure it covers the matter 100%
to my satisfaction. I think a number of things go into the
construction of some kind of tonality, them being

1) Having maximally discordant tones lying adjacent to the tonic,
"leading" and "falling" tones
2) Having a wide range of other harmonic chords to "move" to, with
different roots, so that the tonic isn't the only concordant sonority
to hang out on. Without this, there's no root movement.
3) Other than that, I view the scale as a tonal abstraction serving
these properties; a conceptual tool for simplification that doesn't
really exist -except- for melodic purposes, a la Rothenberg.

Strong version (not the same as Paul's strong version):
4) The two dissonant intervals should form another dissonant interval
- that can resolve inward or outward to a harmonic sonority,
preferably the tonic.

So from that perspective, some "tonal" 7-note scales of western music,
if we're in the 5-limit, would be:

1) Ionian (C-F-B to C-E-C, or make it G-F-B to C-E-C. But the F-B to
E-C is what's important)
2) Harmonic Major (C-F-B -> C-E-C, C-Ab-B -> C-G-C, C-F-Ab-B ->
C-E-G-C. Don't tune the Ab and B to harmonic intervals, but rather to
areas of maximum discordance. Ab might be best a bit flat, B a bit
sharp.)
3) Aeolian (C-D-Ab resolves to C-Eb-G)
4) Harmonic Minor (C-D-Ab-B -> C-Eb-G-C).

I got these by starting with the notes C F G C, and then filling in
either E or Eb. If we relax the strong version, a ton of other systems
can be used as tonal systems, although you have to learn to be more
creative:

5) Descending Melodic Major (C D E F G Ab Bb C).
6) Lydian
7) Phrygian
8) A million others

People have been exploiting Phrygian's harmonic properties in common
practice music for a while under the guise of the Neapolitan sixth
chord.

This is just my train of thought, anyway.

-Mike

On Mon, Sep 20, 2010 at 4:32 AM, Carl Lumma <carl@...> wrote:
>
> Yes, it was.
>
> The general approach is interesting, though I don't always
> agree with your descriptions of the examples... though I would
> appreciate a more test-based approach (preferably blinded).

This is an earlier description of the theory, actually... this is the
first thing I wrote. After some more thoughts and the parallel
conversation I'm having with Igs it's evolving, slowly. I think it
just has to do with discordance now.

As for tests, I posted a listening test here in a parallel thread -
feel free to listen to it first and then get my subjective take on it
after. It may take a few listens before the quality of it really pops
out - some of my 12-tet friends have noticed that 7:9:11 and its
utonal inverse don't sound "happy vs sad" but rather "augmented vs
augmented." I don't expect this will be quite as much of a problem
with you :)

> I also find the use of 12-ET notation obnoxious. 12-ET should
> never be used for pyschoacoustics experiments.

I used 12-ET very much on purpose, though. To highlight a few things

1) 12-ET -is- a detuned series of overtones, and it seems worthwhile
to look at temperaments that way. 13-ET really pops to life if you
view its super-sharp 3/2 as 2:3#, hence being an interval with a
certain amount of "pain." Pain is an abstract perceptual quality that
I'm defining of which the fingernails on a chalkboard sound is an
ultimate example, and which I believe minor is a small version of.
2) So intervals that are detuned JI ratios are no longer a liability
but an asset, from this perspective, and 12-TET is chock full of them
:)
3) Some of the predictions that this perspective makes generates
chords in 12-TET that I've been using for literally years. It
generates, in particular, the major -> minor -> diminished sequence of
increasing negativity, and the minor -> minor/maj7 -> minor9/maj7#11
sequence of increasing negativity, and the fact that lydian can
sometimes sound "sad" as can minor. The fact that it predicted that
minor9/maj7#11 could become more harsh by sharpening the 9 (which
isn't possible in 12-tet without just doubling the minor third) made
me realize there was something going on here...

Which should be intuitive, because if you take the overtone series and
keep making it more and more discordant, it's going to sound crappier
and crappier. What I didn't expect was that if you pretend you don't
know anything about "minor," and try to slowly increase the
discordance, minor is one chord in a huge series. And there are chords
equivalent in pain to minor that you can make by keeping the major
third major and detuning a combination of other overtones, above.

-Mike

Mike:

> I used 12-ET very much on purpose, though. To highlight a few
> things
>
> 1) 12-ET -is- a detuned series of overtones,

Oh please.

> 3) Some of the predictions that this perspective makes generates
> chords in 12-TET that I've been using for literally years. It
> generates, in particular, the major -> minor -> diminished
> sequence of increasing negativity,

Nothing that requires 12. Also those years of experience
are a hindrance for this, if anything.

-Carl

On Mon, Sep 20, 2010 at 4:43 AM, Carl Lumma <carl@...> wrote:
>
> Mike wrote:
>
> > perhaps this boils down entirely to concordance.
>
> I agree completely, accept to exclude roughness.

> Because it interferes with our ability to discern
> individual notes in a chord. And also because
> roughness is not sad.

This is something, though, that I think is listener dependent and can
change with practice. You hear C-D-Eb as a bunch of noise, I hear it
as 1-2-b3 and could distinguish it from other similar noisy sonorities
in a double blind test, I guarantee you, 100% of the time. Come up
with a suitable test, give me long, lengthy, depriming breaks, and
I'll pass it. In fact, play all of the notes from C-F except for one,
and I'll tell you which is missing :)

Although it is tempting to attribute this ability to my having AP, I
think it's more an adaptation that can occur in how we handle
roughness. At one point I had it trained so I could get the missing
note in an octave (assuming you actually hit the other notes on the
piano at the same volume, which nobody ever does). I didn't keep up
with it, because it wasn't really too musically useful, and I thought
it was kind of a dumb party trick (that goes against every virtue of
modesty I know too). So I dunno how sharp with it I'd be today.

That being said, if you want to get rid of roughness, you are more
than welcome to - just find the JI interval near the maximally
discordant one, and I'm trying to figure out how to extend regular
mapping to define two additional operators - b and #. So you could
temper the difference between 4:5b and 5:6 if you wanted to, and call
it something like "minor temperament." Which would also be useful in
generating linear temperaments with as many "minor" sonorities as
"major" ones.

> C-E-G is not sadder than
> 4:5:6, though it is rougher.

I do hear it as slightly sadder - note the difference between Cmaj9#11
chords in 12-tet, and those in JI (stack 5/4's on top of 6/5's here).

-Mike

On Mon, Sep 20, 2010 at 5:14 AM, Carl Lumma <carl@...> wrote:
>
> Mike:
>
> > I used 12-ET very much on purpose, though. To highlight a few
> > things
> >
> > 1) 12-ET -is- a detuned series of overtones,
>
> Oh please.
//
> Nothing that requires 12. Also those years of experience
> are a hindrance for this, if anything.

It just seemed natural for me to analyze, after this huge train of
thought, common practice music with the new perspective. Or "jazz,"
since that's what I'm used to. That's all. Perhaps it was imprudent of
me to communicate that first, and I should have started with more
xenharmonic stuff. I posted a xenharmonic listening example a little
bit ago once I saw how negative the reaction was to 12. Starts off
with 7:8:9:10:11 and then its "minor" counterpart, which I was
unsuccessful at eliminating roughness for.

And assuming you see my point there, which you seem to be in agreement
on - and we're saying that detuning overtones is an asset in creating
musical feeling - then there's no reason to apply the same perspective
to 12. I see it as an interesting way to reevaluate temperaments.
Detuned sonorites become "minor" assets, rather than unusable
liabilities. Start playing with 13-tet and treat the sharp fifth as a
pain-evoking "minor" fifth, and there's lots of cool stuff... Chords
like 0 6 8 11 15 18, for instance.

Not to worry, because I'll be throwing out some xenharmonic sound
examples soon enough. :) Perhaps from Haiti.

-Mike

Mike wrote:

> You hear C-D-Eb as a bunch of noise, I hear it
> as 1-2-b3 and could distinguish it from other similar noisy
> sonorities in a double blind test, I guarantee you, 100% of
> the time.

I know, I've tested APers before, and probably ones with
better AP than you, buster.

> Come up with a suitable test,

Actually that's what you need to be doing, if you want to
advance your ideas.

> That being said, if you want to get rid of roughness, you are
> more than welcome to

I did, with utonal chords.

> I'm trying to figure out how to extend regular
> mapping to define two additional operators - b and #.

Way too soon for that.

> > C-E-G is not sadder than
> > 4:5:6, though it is rougher.
>
> I do hear it as slightly sadder

Not me.

> - note the difference between
> Cmaj9#11 chords in 12-tet, and those in JI (stack 5/4's on top
> of 6/5's here).

That's not remotely the same kind of comparison as
C-E-G vs 4:5:6.

-Carl

On Mon, Sep 20, 2010 at 5:25 AM, Carl Lumma <carl@...> wrote:
>
> Mike wrote:
>
> > You hear C-D-Eb as a bunch of noise, I hear it
> > as 1-2-b3 and could distinguish it from other similar noisy
> > sonorities in a double blind test, I guarantee you, 100% of
> > the time.
>
> I know, I've tested APers before, and probably ones with
> better AP than you, buster.

What miraculous feats can they accomplish that I must train myself to do?

> > Come up with a suitable test,
>
> Actually that's what you need to be doing, if you want to
> advance your ideas.

That's a bit premature at this stage, but something I'm in the process of doing.

> > - note the difference between
> > Cmaj9#11 chords in 12-tet, and those in JI (stack 5/4's on top
> > of 6/5's here).
>
> That's not remotely the same kind of comparison as
> C-E-G vs 4:5:6.

Yes it is. It just enhances the effect. Both have the 5, 7, and 11
further from just, and the emotion increases predictably.

-Mike

Mike wrote:

> It just seemed natural for me to analyze,

There's no excuse for using 12-ET as the basis of a
pyschoacoustics investigation, ever, period. -Carl

Mike wrote:

>> I know, I've tested APers before, and probably ones with
>> better AP than you, buster.
>
> What miraculous feats can they accomplish that I must train
> myself to do?

Tell me which notes I miss as I mash my forearm on the piano?

>But the first set starts at 0:00, the second at 0:07, the third
>at 0:20, and the last at 0:45.

I thought the original text went on to say there's like 8 more
chords or something. Sorry if I'm reading crossways at this AM.

> > That's not remotely the same kind of comparison as
> > C-E-G vs 4:5:6.
>
> Yes it is. It just enhances the effect. Both have the 5, 7,
> and 11 further from just, and the emotion increases
> predictably.

No, it's not. Stacking 5/4s and 6/5s in JI like you suggested
does not necessarily lead to chords that 12-ET approximates.
C-E-G does approximate 4:5:6.

> Yes, but after all of the reading I just did, it seems they
> actually take the opposite role. Or at least that's what
> this new paper says. The outer hair cells form a "ratchet"
> mechanism, as I understand it that acts as a damper for this
> basilar membrane feedback mechanism.

I thought they were saying the motion of the outer hair cells
increased the displacement of the membrane... more later I'm
sure (and may I suggest, offlist).

-Carl

On Mon, Sep 20, 2010 at 5:57 AM, Carl Lumma <carl@...> wrote:
>
> Mike wrote:
>
> >> I know, I've tested APers before, and probably ones with
> >> better AP than you, buster.
> >
> > What miraculous feats can they accomplish that I must train
> > myself to do?
>
> Tell me which notes I miss as I mash my forearm on the piano?

Haha, that's interesting. I don't know if I could pull that off. The
more notes you miss, the more I could pull it off, and the less
coherently they're timed together, the more I could pull it off. If
your friends can get like your forearm smashing every note in 2 and a
half octaves minus one hit simultaneously, and they can tell you the
one missing note, I'm going to have to concede defeat, haha.

But either way, the idea is that I remembered you saying that
roughness is the failure of the cochlea to resolve what was going on,
hence C-D-Eb is just unusable, and my point is that if you can pick
the notes out, it just sounds "minor." At least it does to me. So
resolving critical band roughness has to be some kind of cognitive
process that can be altered by learning.

> > Yes it is. It just enhances the effect. Both have the 5, 7,
> > and 11 further from just, and the emotion increases
> > predictably.
>
> No, it's not. Stacking 5/4s and 6/5s in JI like you suggested
> does not necessarily lead to chords that 12-ET approximates.
> C-E-G does approximate 4:5:6.

I'm not sure why you say that or what you mean. If I do the Yankee
doodle timbre test, and I use 0-400-700 as the timbre, are you saying
I won't hear -2400 cents pop out? That's the only way to tell if
something "approximates" a JI ratio that I can think of that
completely bypasses categorical perception.

In lieu of that, what I'm more curious to hear about, rather than my
terminology failings, are if my predictions are having the described
effect. Does the 12-tet C-E-G-B-D-F# sound more painful/sad/discordant
than

> I thought they were saying the motion of the outer hair cells
> increased the displacement of the membrane... more later I'm
> sure (and may I suggest, offlist).

Maybe. That's not the impression I got, but it's 6 AM here. We can
continue a side discussion offlist if you'd like, but it'll be slower
for the next few days.

> Nearby being the key. If we have voronoi cells on a 2-D plot
> of triads ala Erlich, we might say that as we move from a JI
> chord a:b:c (a*b*c < T) to its cell boundary, discordance
> should go up, and we are depriming it. Cross the boundary,
> and we are now repriming a neighboring chord.

I think that this is really a feature of tetradic entropy, though. As
you mentioned, 6:7:9 can be either otonal or "minor" depending on
whether 6 or 1 is heard as the root. The same applies to 10:12:15 as
well. A way to turn this perceptual and mental distinction into
something real, I think, would be to consider the difference in
discordance between 4:6:7:9 and 3:6:7:9, or between 8:10:12:15 and
5:10:12:15. The latter, in each case, forces the lowest note in each
triad to be heard as the root (although you can "sort of" hear the 1
still in 3:6:7:9), but it is of lower complexity/Tenney height.

So here's your unbiased listening test - do you hear 4:6:7:9 or
3:6:7:9 as more discordant? How about 8:10:12:15 and 5:10:12:15?

Actually, something I just thought of: how does triadic entropy (or
voronoi cells) compare something like 2:4:5 and 5:10:12?

> Incidentally, David Finnamore made sound files based on such
> maneuvers. See
>
> /tuning/files/Finnamore/
>
> I have the program notes to these files if anybody's
> interested.

Yes please. Would appreciate. What were these made in, CSound?

-Mike

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

> There's no excuse for using 12-ET as the basis of a
> pyschoacoustics investigation, ever, period. -Carl
>

This should be on the front page here.

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

> 3) Some of the predictions that this perspective makes generates
> chords in 12-TET that I've been using for literally years. It
> generates, in particular, the major -> minor -> diminished sequence of
> increasing negativity, and the minor -> minor/maj7 -> minor9/maj7#11
> sequence of increasing negativity, and the fact that lydian can
> sometimes sound "sad" as can minor.

You keep speculating and proposing and discussng, and perhaps as a consequence I don't know what your theory *is* or how it can possibly make any predictions. Could you lay it out concisely?

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

> And assuming you see my point there, which you seem to be in agreement
> on - and we're saying that detuning overtones is an asset in creating
> musical feeling -

Any kind of harmony can evoke musical feeling of some kind or another. All of us have always known this. What's your point?

> Detuned sonorites become "minor" assets, rather than unusable
> liabilities. Start playing with 13-tet and treat the sharp fifth as a
> pain-evoking "minor" fifth, and there's lots of cool stuff... Chords
> like 0 6 8 11 15 18, for instance.

I don't even know what this means. Instead of treating the 8/13 octave interval as 738.5 cents, or an approximate 23/15, or anything else of that sort I treat as if someone was stabbing a pencil in my ear while I was listening to a fifth? How do I turn that into a compositional technique?

> Not to worry, because I'll be throwing out some xenharmonic sound
> examples soon enough. :) Perhaps from Haiti.

Examples of what, trying to show what?

Mike wrote:

> > No, it's not. Stacking 5/4s and 6/5s in JI like you suggested
> > does not necessarily lead to chords that 12-ET approximates.
> > C-E-G does approximate 4:5:6.
>
> I'm not sure why you say that or what you mean. If I do the
> Yankee doodle timbre test, and I use 0-400-700 as the timbre,
> are you saying I won't hear -2400 cents pop out?

Huh?

What I mean is that C-E-G-B-D-F# does NOT necessarily
approximate 1/1_5/4_3/2_15/8_9/4_45/8. In fact the latter
may be a poor approximation of the former, if you believe
in magic chords. Or the F# may be approximating 11, etc.

The example I gave; C-E-G, is a clear approximation of
4:5:6. No categorical perception involved.

> In lieu of that, what I'm more curious to hear about, rather
> than my terminology failings, are if my predictions are having
> the described effect.

So far I haven't seen any predictions!

> > Nearby being the key. If we have voronoi cells on a 2-D plot
> > of triads ala Erlich, we might say that as we move from a JI
> > chord a:b:c (a*b*c < T) to its cell boundary, discordance
> > should go up, and we are depriming it. Cross the boundary,
> > and we are now repriming a neighboring chord.
>
> I think that this is really a feature of tetradic entropy,
> though.

Finnamore did both triadic and tetradic walks...

> A way to turn this perceptual and mental distinction into
> something real, I think, would be to consider the difference
> in discordance between 4:6:7:9 and 3:6:7:9,

I did suggest that. There isn't much difference in
discordance. Technically the latter should be slightly more
concordant, but because of rootedness the former is generally
heard as more concordant.

> So here's your unbiased listening test - do you hear ...
> 8:10:12:15 [or] 5:10:12:15 [as more discordant]?

> Actually, something I just thought of: how does triadic
> entropy (or voronoi cells) compare something like 2:4:5 and
> 5:10:12?

The area of the cells is roughly proportional to the inverse
of the Tenney height.

> > Incidentally, David Finnamore made sound files based on such
> > maneuvers. See
> > /tuning/files/Finnamore/
> > I have the program notes to these files if anybody's
> > interested.
>
> Yes please. Would appreciate. What were these made in, CSound?

I forget. Notes are now in my folder here.

-Carl

genewardsmith <genewardsmith@...> wrote:
> You keep speculating and proposing and discussng, and perhaps as a consequence I don't know what your theory *is* or how it can possibly make any predictions. Could you lay it out concisely?

Yes. Here's the simplest form of it, with as few assumptions made as possible.

1) Extreme discordance can be painful to listen to.
2) By creating an overtone series and detuning the notes in it,
discordance can be created in controlled fashion.
3) By creating discordance, "pain" can be produced.
4) By creating concordance, "pain" can be abetted.
5) By creating a sonority in which pain is only partially present,
musical feelings like "sadness" can be created, which I propose are
just lesser amounts of nails-on-a-chalkboard pain in small doses.
6) If you detune a note enough so as to hit another concordant
sonority which creates a strong and perceptible different "root,"
perhaps simultaneously existing with the first one, the effect will be
destroyed.
7) I predict that as long as 2 and 4 have the perception of being the
root, there will be a "field of discordance" around each interval in
which there approaches a point of maximum discordance, and slowly
resolves into more concordance as it gets further from this point and
starts to approach other concordant dyads.
8) I predict that putting a higher overtone at its point of maximum
discordance with the rest of the sonority will have less of an effect
than a lower overtone, since it is less significant from a
psychoacoustic standpoint.
9) I predict that putting a combination of overtones at their points
of maximum discordance will have more of an effect than just detuning
a single one.
10) I predict that the addition of non-detuned overtones at the points
of maximum -con-cordance will "undo" some of the pain caused by the
detuning of other overtones.
11) Since I claim that minorness is a watered down version of
discordance, or a combination of concordance and discordance, I
predict that putting an overtone at an intermediate point of
discordance can have a musical effect similar to minorness - a slight
amount of pain. So can putting it at a maximum point of discordance
and adding enough concordant overtones. Hence equivalent amounts of
pain can be created from different sounds.
13) At this point the above process is best approached from a
listening perspective to "find" the points of maximum discordance
nearby by ear, until we have n-adic harmonic entropy to do it for us.
This does not diminish the claim that minorness is a watered down
version of extreme discordance, and a proof of concept can still be
drawn nonetheless.
14) I claim that, due to cultural reasons, it may be more pleasant to
find JI intervals that are nearby to the altered discordant ones to
avoid roughness.

Here is a fully-laid-out example.

Let's start with something like 2:4:5:6:7:9:11:13. The 2 is there to
force the perception of the chroma that 2 and 4 share as being the
"root." We will start with just 2:4:5:6, then detune a note. Then
we'll add another concordant overtone, and detune it further to see
what happens.

From 2:4:5:6 - detune 5 to about 333 cents. This becomes more painful
and hence starts to sound minor. I will refer to this as 2:4:5-:6 from
here on out to save having to type so much. You can find equivalent
amounts of sadness and painfulness if you sharpen 5 instead, but for
the purposes of this example we're going to go the minor route.
From 2:4:5-:6:7 - A bit less painful - may start to sound "major"
again. Sharpen the 7 to somewhere around 15/8 or 27/14 and it should
become more painful, or flatten it to somewhere around 12/7 - use your
ears and find the most painful spot. Note that this corresponds
roughly to the utonal tetrad, which is often heard as minor. We'll go
with the sharpened route to continue the example. From this point on,
know that you could alter the note either way to find some sweet spot
of discordance, but I'm just going to arbitrarily pick one and keep
going to keep this shorter.
From 2:4:5-:6:7+:9 - May very, very slightly stabilize the chord, but
in a much less perceptible way. Adding 9:11:13 may stabilize it more.
Now sharpen the 9 to about 9.2/4, or maybe sharper. You should hear
the "discordance" increase slightly, but in a way that is starting to
resemble musical "dissonance." Find the most discordant spot if you
want and be sure to pay attention to intermediate spots.
From 2:4:5-:6:7+:9+:11 - sharpen the 11 to something like 1830-1858
cents and watch the pain increase. Let's say 1858 cents.
From 2:4:5-:6:7+:9+:11+:13 - sharpen the 13 to something like 2131 cents.
From 2:4:5-:6:7+:9+:11+:13- - Now let's go back and alter the 6. Make
the 4:6 about something like 650 cents, or 750 cents if you want to go
sharper. Watch the pain change. It may increase slightly, but will be
a detriment as we resolve things back in because it lessens the
rootedness of what's going on as the 2:4:6 is destroyed. If you put a
1 underneath this, so that the 6 isn't as important to establishing
the root, there is a clearer increase in pain as 6 is changed, and/or
if you add 3 to the sonority. Let's say that you add both. Note also
that if you detune 5 and sharpen 6, the 5-:6+ might approach 3:4, and
so 2:5-:6+ approaches a relative 5:6:8. Let's say you flatten the 6 in
this case to keep it simpler, although you can find similarly
discordant sonorities in the "up" direction. Get 4:6- to be like 650
cents.

Ending point: 1:2:3:4:5-:6-:7+:9+:11+:13+

At this point you should have an extremely discordant "ultra-minor"
sonority, and have seen a progression in which minor increases into
ear shrapnel. There are a million progressions you could make of which
"minor" is a part, but to my ears, this is a particularly useful one.
Whether you want to treat it as an abstraction of "minor" or not is up
to you, but it seems more useful than the otonal/utonal concept, which
stops working for a while. Note that the utonal cases which DO work
generally happen to line up with this pattern. Note that if you do
hear 1/1-6/5-3/2-12/7 as a "more minor version" of minor, then you may
also hear 1/1-6/5-3/2-15/8 (or 27/14) as an also "more minor version"
of minor, or at least I do. This perspective predicts both of them.

Hold your horses! Let's bring things back in, SLOWLY, and see what happens.

From 1:2:3:4:5-:6-:7+:9+:11+:13+ to 1:2:3:4:5-:6+:7+:9+:11:13 - bring
the 11 and 13 back to just. Note what is happening to the sound, and
the musical feeling that is being produced.
From 1:2:3:4:5-:6-:7+:9:11:13 to 1:2:3:4:5-:6-:7:9:11:13 - bring the 7
and 9 back to just. Note that this is starting to sound almost major,
as if the 333 cent "minor third" is starting to flip into major third
territory. Until I have n-adic entropy calculated, this is something
that you will have to note by ear. n-adic entropy will predict this.
Or, at least, it will have to, if it's going to match up with
real-life discordance.
From 1:2:3:4:5-:6-:7:9:11:13 to 1:2:3:4:5--:6-:7:9:11:13 - detune the
333 cents to 6/5 or perhaps even as low as 19/16. Find the sound in
which it's "most out," and the pain increases again. Note that the
pain increasing in this case has a particular musical effect - you may
hear it as flipping from major to minor as the pain increases. Note
how the other notes are biasing the perception of the detuned 4:5.
Let's say you bring it to 19/16.
From 2:4:5--:6-:7:9:11:13 to 2:4:5--:6:7:9:11:13 - bring the 6- back
up to 6. Note the decrease in pain and/or depressingness.
From 2:4:5--:6:7:9:11:13 to 2:4:5:6:7:9:11:13 - resolve the 5-- to 5.
Pain gone, happy intense OHHHHHMMMM otonality. If this is still
painful, decrease the volume of successive overtones to approximate a
1/N rolloff or a 1/N^2 rolloff.

Hopefully that leaves nothing up to question. One last thing: If you
start with 4:5:6, and you detune a combination of 7, 9, and 11, and
13, you can :get a sonority that is equal in "pain" or sadness to
minor. Perhaps 4:5:6: 7.65 :9: 11.55 : 13.6, or find nearby JI ratios
if you can't stand the roughness. Something like 0-417-730-1133 too,
perhaps.

> Any kind of harmony can evoke musical feeling of some kind or another. All of us have always known this. What's your point?

Whoo, I can practically feel the contempt beaming at me through space.
The point is that mixtures of concordance and discordance can lead to
"musical feeling of some kind or another," with mixtures of more
concordance leading to "some kind," and mixtures of more discordance
leading to "another."

> > Detuned sonorites become "minor" assets, rather than unusable
> > liabilities. Start playing with 13-tet and treat the sharp fifth as a
> > pain-evoking "minor" fifth, and there's lots of cool stuff... Chords
> > like 0 6 8 11 15 18, for instance.
>
> I don't even know what this means. Instead of treating the 8/13 octave interval as 738.5 cents, or an approximate 23/15, or anything else of that sort I treat as if someone was stabbing a pencil in my ear while I was listening to a fifth? How do I turn that into a compositional technique?

You treat it as a semi-augmented fifth which is slightly "painful" and
add concordant overtones on top of it to stabilize it and transform it
away from being so painful that it's a pencil being stabbed into your
ear and into a level of painfulness comparable to "minorness." One
interval which is available in 13-tet for doing this is ~11/8. Try
working in JI first - take this detuned fifth and then adding a just
7/4, 9/8, 11/8, or whatever intervals you like until you hear the
sound transform into something more palatable. Note the precise
feeling created.

Then see what options are available to do similar things in 13-tet.
Notes that are "slightly out" in 13-tet might slightly stabilize it,
or make it more painful, depending on how out they are and how complex
the base JI interval is.

-Mike

On Mon, Sep 20, 2010 at 7:16 PM, Carl Lumma <carl@...> wrote:
>
> Huh?
>
> What I mean is that C-E-G-B-D-F# does NOT necessarily
> approximate 1/1_5/4_3/2_15/8_9/4_45/8. In fact the latter
> may be a poor approximation of the former, if you believe
> in magic chords. Or the F# may be approximating 11, etc.
>
> The example I gave; C-E-G, is a clear approximation of
> 4:5:6. No categorical perception involved.

Oh, I'm sorry. I thought you said, at 5 in the morning, that C-E-G
does -not- approximate 4:5:6.

The point I'm making is that C-E-G-B-D-F# does NOT approximate 1/1 5/4
3/2 15/8 9/4 45/8. I'm saying that both of them are perceived as
divergent from 4:5:6:7:9:11, but not divergent enough to cause a new
rooted or tonal sonority to develop; hence discordance, hence pain,
hence "sadness." C-E-G-B-D-F# is more divergent than 1/1 5/4 3/2 15/8
9/4 45/8, and hence should be slightly more painful. 1/1 9/7 3/2 27/14
9/4 81/28 should be even more so. And I personally hear a very
significant transformation from rooted and slightly sad to more sad,
longing, to even more sad and slightly painful, and beyond as I take
1/1 - xx - 3/2 - xx - 9/4 - xx, start the xx's at 5/4, 15/8, and 45/16
respectively, and start to sharpen them.

> > A way to turn this perceptual and mental distinction into
> > something real, I think, would be to consider the difference
> > in discordance between 4:6:7:9 and 3:6:7:9,
>
> I did suggest that. There isn't much difference in
> discordance. Technically the latter should be slightly more
> concordant, but because of rootedness the former is generally
> heard as more concordant.

Correct. Except I think that it's not so much rootedness specifically,
but that you have to generalize HE for dyads to triads to tetrads in
such a way that the concordance of different subtriads and such is
taken into account. That being said, 3:6:7:9 is heard as matching
1:2:xx:3. When you increase the xx slowly, you will eventually reach
2:4:5:6. As you approach 2:4:5:6, you will pass through a region where
it's "almost" 2:4:5:6, and yet it's not. It's on the border between
distorted and harmonic, and inharmonic, so to speak.

So from a perceptual standpoint, this is the region of maximum
discordance for tetradic entropy - it's right between placing it and
giving up. And this causes perceptual pain for reasons I can only
speculate about. So do this for 4:5:6, and detune the 5 to something
like 11/9, or wherever you hear it as more discordant and painful.
Then add 7, 9, and 11, and maybe 13, and see if it lessens the pain a
bit. And then detune the overtones and cause more pain, etc. And then
bring the 11/9 back into 5/4, or out a bit further to 6/5, to the
point where it starts to "give up" more and perceive it as two
separate sounds and maybe only try to place it "a little bit," and the
pain will abet slightly. Find something that you enjoy, and then find
JI ratios nearby so that there's no roughness, and you will have a
whole new variety of interesting and xenharmonic sounds to play with,
of which the utonal sonorities are very close to a subset of (but of
which there may be better "minor" options for higher limits).

So what I'm saying is, if you really hate my theory and think I'm
totally off my rocker, at least just play around a bit with this and
have some fun, and you will hopefully see the pattern. Start with 1/1
- 6/5 - 3/2 - 12/7, which is the 7-limit utonality. It sounds sad.
Increase the top one to 7/4, and it's less so, although the roughness
might bum you out, so go to something like 9/5. Then if you alter this
7th in the other way - make it sharper - I hear the 15/8 as being even
"more minor" than the 7-limit utonality."

Either way I'm really becoming frustrated discussing it. Perhaps it
would be best if I just develop these ideas further offlist, bring
them back to the list when I have a listening test, and we can go into
it then.

-Mike

Mike wrote:

> Correct. Except I think that it's not so much rootedness
> specifically, but that you have to generalize HE for dyads to
> triads to tetrads in such a way that the concordance of
> different subtriads and such is taken into account.

I also suggested that.

> So from a perceptual standpoint, this is the region of maximum
> discordance for tetradic entropy

We don't know that.

> So what I'm saying is, if you really hate my theory and think
> I'm totally off my rocker,

I can't figure it out, is all. Can you come up with a way
to quantify it?

> and you will hopefully see the pattern

I don't do that on the stock market either.

> Either way I'm really becoming frustrated discussing it.

You're writing too much, too fast. I think it has potential,
but you've got to find a way to quantify it, then maybe we
can test it.

-Carl

MikeB>"5) By creating a sonority in which pain is only partially present,
musical feelings like "sadness" can be created, which I propose are just lesser
amounts of nails-on-a-chalkboard pain in small doses."
How does this not simply equate to, for example, a hypothesis that all
lower-limit chords are major and all fairly high odd limit chords (those not
close to lower limit chords either) are minor?

>"6) If you detune a note enough so as to hit another concordant sonority which
>creates a strong and perceptible different "root," perhaps simultaneously
>existing with the first one, the effect will be destroyed."
So what is this "de-tuning limit" perceived to be near (7 cents, 13 cents,
different per each interval...)...or are tests you run going to determine it?

>"11) Since I claim that minorness is a watered down version of discordance, or a
>combination of concordance and discordance, I predict that putting an overtone
>at an intermediate point of discordance can have a musical effect similar to
>minorness - a slight amount of pain."
So your statement of minorness is calculated from discordance of matching
between all overtones (both in position and perhaps also amplitude) and not just
between root tones, in other words?

_,_._,___

On Mon, Sep 20, 2010 at 9:42 PM, Carl Lumma <carl@...> wrote:
>
> > So from a perceptual standpoint, this is the region of maximum
> > discordance for tetradic entropy
>
> We don't know that.

We do know that in reality, since if you do an actual listening test,
you can find a point in which the sound is maximally discordant if you
try. If tetradic entropy as formulated naively by just giving each
tetrad a complexity of something like geomean(a*b*c*d) and assigning
the incoming tetrad a generalized gaussian 4-dimensional probability
curve, the point may not line up with this. If you generalize dyadic
entropy to the four dimensional case another way, it may. Whichever
way -does- line up with this is going to be the most effective way to
generalize it, as by definition, it's going to pass the most listening
tests.

> > So what I'm saying is, if you really hate my theory and think
> > I'm totally off my rocker,
>
> I can't figure it out, is all. Can you come up with a way
> to quantify it?

Harmonic entropy first represents a dyad as "matching" partially a set
of basis dyads. The entropy equation comes entirely out of that. I am
then going to investigate the representation of the set of all dyads
"matching" an incoming dyad as the set of orthogonal (or
non-orthogonal with an orthogonal subset, I haven't decided yet) basis
functions for a theoretical vector space. Then I'm going to try and
turn this into a mathematical transform, which is how the Fourier
transform already does things. The way HE does things is more similar
to the Laplace transform from that perspective than the Fourier
transform, so I'm going to see what happens if I generalize the
Laplace transform in order to incorporate a signal with harmonics.
Given that HE has been so successful in predicting discordance from a
purely information theory standpoint, I would expect that this
approach will be at least equally successful. It may be that somewhere
between the Laplace transform and the HE way of doing things lies the
answer.

From this perspective, the distinction is that the Laplace transform
uses basis functions which are exponentially damped sine waves (you
can think of the Laplace transform as being a way to represent a
signal in terms of basic components of damped harmonic motion rather
than simple harmonic motion), and the HE fundamental calculation uses
something more like sinc-damped sine waves. This is because each one
is treated as having a "reach" in either direction that is total for
its domain and then stops. This is equivalent to its domain being a
rect function in the frequency domain with an amplitude of 1 and a
width of sqrt(n*d) (actually in this "dyadic" domain that I hope to
generalize in a more organic way), which is a sinc function in the
time domain.

You will note that the characteristics of a sinc function and e^(-at)
are very similar in terms of how they taper off over time. I would
expect that the differences would be very small. The main distinction
is that the use of the Laplace transform will give each dyad a domain
that looks something like a Gaussian taper rather than a concrete
"domain," which I think makes more sense anyway. I don't think the
entropy curve is going to see much of a difference; it may just
increase slightly since everything will match slightly more dyads.

And then I'm going to find the paper here
(http://ieeexplore.ieee.org/Xplore/login.jsp?url=http%3A%2F%2Fieeexplore.ieee.org%2Fiel5%2F7486%2F20359%2F00940605.pdf%3Farnumber%3D940605&authDecision=-203)
and see if I can steal a trick from their book and get the whole thing
down to nlogn time, as they did with the FFT.

So that's how I'm going to quantify it. I'm going to see how accurate
this is for n-adic entropy, and once I get it perfectly accurate, I'm
going to then see if there is a correlation between musical "sadness"
and entropic discordance.

> > and you will hopefully see the pattern
>
> I don't do that on the stock market either.
//
> You're writing too much, too fast.
//
> you've got to find a way to quantify it, then maybe we can test it.

Given that this recent outburst of excitement is a continuation of
something I've been working on for over a year, all of that is pretty
insulting. I do admire your willingness not to buy into something
until it's proven, however.

-Mike

[replying offlist] -C.