Yahoo Tuning Groups Ultimate Backup tuning Interesting tetrachordal Mohajira Near-MOS, and towards a systematic exploration of near-MOS's in general?

I was playing around more with the "semitonal" structures that I
talked about in this post:
/tuning/topicId_96260.html#96260

By taking 1:2:3:4 and replacing the 3:4 with 9:10:11:12, you get
6:9:10:11:12. If this still sounds like it refers to 1, then keep
doubling the 6 down a few octaves until it doesn't. Now, if you take
that 9:10:11:12 to be a tetrachord and just double it down so that
another copy of it starts where the "6" is, you arrive at
18:20:22:24:27:30:33:36, or in Scala format:

!
Tetrachordal semitonal scale
7
!
10/9
11/9
4/3
3/2
5/3
11/6
2/1

So the first obvious thing to do is start tempering away. It seems
pretty obvious to get rid of 121/120 and 81/80 here, and once you go
that far, 176/175 is sure to follow. This reimagines the following
scale as

!
Tetrachordal Mohajira Near-MOS in 31-tet
7
!
193.54839
348.38710
503.22581
696.77419
890.32258
1045.16129
2/1

This is a beautiful near-MOS of mohajira, sort of a neutral diatonic
scale if you will, and I really like the sound of it.

There are more temperaments than I can keep track of these days, and I
have so far not delved into their near-MOS's at all. There are no
doubt a lot more beautiful scales like these that make sense when
analyzed as near-MOS's of some temperament we know (Paul's
pentachordal scales are among them). I also had like a 3-hour jam
session on my 31-tet guitar today and realized that, while the Graham
complexity of 11 in meantone is pretty high, this isn't as relevant if
you just keep modulating between meantone near-MOS's that have 11/8 in
them. AND, in fact, this is what we do in jazz all the time - switch
between lydian dominant here, to the altered scale there, to ionian
here, to lydian aug #2 there, etc. These are all modes of varioua
meantone near-MOS's.

In fact, I use near-MOS's more than I use MOS's. What have I been missing?

But, from what I know, near-MOS's are, in general, poorly understood.
So my question is - what about them is so poorly understood exactly?
Does the difficulty lie in indexing them and categorizing them, or is
there some property that we're not sure if they have or don't have?

And so we're on the same page, by "near-MOS," I'm talking about a
scale from some temperament whose periodicity block shares the unison
vectors for that temperament, but looks more like a jigsaw puzzle
piece than a parallelogram.

-Mike

🔗Michael <djtrancendance@...>

MikeB>"
!
Tetrachordal semitonal scale
7
!
10/9
11/9
4/3
3/2
5/3
11/6
2/1"

Isn't this merely a mode of Ptolemy's Homalon scale (which I happen to like a lot, btw)?

---------------
>"!
Tetrachordal Mohajira Near-MOS in 31-tet
7
!

193.54839 1.1179326948
348.38710 1.2222222222
503.22581 1.337154960
696.77419 1.494849248
890.32258 1.6721064
1045.16129 1.828718904
2/1"

...which looks almost exactly like the "Arab" mode of my Dimension scale a couple of cents off, if that. Add an interval around 6/5 in place of the one around 11/9 and you get the Dimension "Hybrid" scale. Add a 9/5 to the whole thing and you get the 9-note Dimension-1 tuning, complete with a 7-tone scale which uses both the 6/5 and 9/5 in place of the 11/6 and 11/9 to get a mode of, yes, mean-tone. Which goes as a piece of my greater puzzle that Mohajira, Meantone, and Ptolemy's Homalon scale system can all be tied into one greater system with very strong accuracy at all three within 9 notes...IF you allow for irregular temperament.
----------------------------------------------------

>"but looks more like a jigsaw puzzle piece than a parallelogram."

Sound to me like you are optimizing away from a pure MOS in order to make certain dyads more accurate via irregular temperament drawing on a combination between Ptolemy's Homalon scales, Mohajira, and Meantone scales...IE the same thing I've been working on for ages.

On the bright side maybe (finally) I have someone somewhat on board with my ideas... :-D Maybe you can put this all into more convincing terms than I have.

🔗Mike Battaglia <battaglia01@...>

On Tue, Feb 15, 2011 at 9:33 PM, Michael <djtrancendance@...> wrote:
>
> Isn't this merely a mode of Ptolemy's Homalon scale (which I happen to like a lot, btw)?

If the Homalon scale is this, then yes, it's the same thing:

/tuning/topicId_85623.html#85790

> ---------------
> >"!
> Tetrachordal Mohajira Near-MOS in 31-tet
> 7
> !
>
> 193.54839 1.1179326948
> 348.38710 1.2222222222
> 503.22581 1.337154960
> 696.77419 1.494849248
> 890.32258 1.6721064
> 1045.16129 1.828718904
> 2/1"

> ...which looks almost exactly like the "Arab" mode of my Dimension scale a couple of cents off, if that. Add an interval around 6/5 in place of the one around 11/9 and you get the Dimension "Hybrid" scale.

Post these scales and let's see.

> Add a 9/5 to the whole thing and you get the 9-note Dimension-1 tuning, complete with a 7-tone scale which uses both the 6/5 and 9/5 in place of the 11/6 and 11/9 to get a mode of, yes, mean-tone.

How can you add a 9/5 to a 7-note scale to obtain a 9-note scale?

> Which goes as a piece of my greater puzzle that Mohajira, Meantone, and Ptolemy's Homalon scale system can all be tied into one greater system with very strong accuracy at all three within 9 notes...IF you allow for irregular temperament.

I haven't ever taken a strong look at your Dimension scales, but
perhaps they make the most sense if they're viewed as Mohajira
well-temperaments. As for how they're related, mohajira and meantone
are already related in that they both temper out 81/80, and mohajira
is just one possible 11-limit extension of meantone. Ptolemy's Homalon
scale system is related to this because it seems natural to eliminate
81/80, and I'm sure you can see why that is, and 243/242, which is the
difference between two 11/9 neutral thirds and 3/2. This also means
that 121/120 vanishes, since 243/242 / 81/80 = 121/120, which means
that 11/10 and 12/11 are equated.

There are no doubt tons of other ways to temper this scale as well,
but the "overarching system" that you describe is mohajira, which
appears to be the structure that you've conceptually latched onto,
which is itself a part of the "overarching system" of meantone.

Read the xenharmonic wiki more :)

> >"but looks more like a jigsaw puzzle piece than a parallelogram."
>
> Sound to me like you are optimizing away from a pure MOS in order to make certain dyads more accurate via irregular temperament drawing on a combination between Ptolemy's Homalon scales, Mohajira, and Meantone scales...IE the same thing I've been working on for ages.

No, it has nothing to do with dyadic accuracy or irregular
temperaments. "Near-MOS" doesn't mean that it's an MOS that's
irregularly tempered, it means that it's a scale that is not an MOS.
However, it's almost an MOS, and has some of the properties that MOS
scales do, but specifically it doesn't have the one in which all of
the interval classes work out to have two specific interval sizes.

An example of a near-MOS scale is the 12-tet ascending melodic minor
scale. Some of the intervals here have two step sizes (like the
seconds), but some have three (like the fifths). Take a look at it:
- 81/80 still vanishes, since 9/8 and 10/9 are equated
- 128/125 still vanishes, since the diminished fourth that now exists
in this scale is the same as the major third, as popularly exploited
on the 7th mode of this scale
- 25/24 still serves as a chromatic vector

So far as the 5-limit is concerned, the only tuning that eliminates
both 81/80 and 128/125 is 12-tet (if you do the tempering evenly). If
you're going to make 25/24 the chromatic vector, then you will end up
splitting the lattice into 7-note blocks. The thing about the melodic
minor scale is that these blocks, while still remaining 7 notes long,
will be uneven - they'll look more like a block with a chunk of the
corner ripped off and pasted onto the other side, like a jigsaw puzzle
piece or something.

> On the bright side maybe (finally) I have someone somewhat on board with my ideas... :-D Maybe you can put this all into more convincing terms than I have.

Post your dimension scale up and we'll see how close to mohajira it
is. But like I said, this doesn't really have anything to do with
well-temperaments.

-Mike

🔗genewardsmith <genewardsmith@...>

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

> Tetrachordal Mohajira Near-MOS in 31-tet

This is listed here

http://xenharmonic.wikispaces.com/Strictly+proper+7-note+31edo+scales

as "Sikah; Neutral Diatonic Hypolydian" under "Mohajira type".

> There are more temperaments than I can keep track of these days, and I
> have so far not delved into their near-MOS's at all. There are no
> doubt a lot more beautiful scales like these that make sense when
> analyzed as near-MOS's of some temperament we know (Paul's
> pentachordal scales are among them).

Looking at the surveys of proper scales in various edos is certainly place to start.

I also had like a 3-hour jam
> session on my 31-tet guitar today and realized that, while the Graham
> complexity of 11 in meantone is pretty high, this isn't as relevant if
> you just keep modulating between meantone near-MOS's that have 11/8 in
> them.

Similar remarks apply to other temperaments where the 11 might seem too complex, such as myna. Or even where something else might seem too complex, such as orwell or miracle.

> In fact, I use near-MOS's more than I use MOS's. What have I been missing?

I dunno, but you could start to look at all these non-MOS regularly tempered scales I keep spewing forth and tell me what you find interesting or not.

> But, from what I know, near-MOS's are, in general, poorly understood.
> So my question is - what about them is so poorly understood exactly?

There are a lot of them, and you need to ask what you want from them to go about finding optimal examples.

🔗Michael <djtrancendance@...>

MikeB>"How can you add a 9/5 to a 7-note scale to obtain a 9-note scale?"

Before I mentioned a note around 6/5 in addition to the 9/5. Adding these 2 notes (tempered) to your 7 tempered ones apparently gives a 9 tone irregularly tempered scale very close to Dimension (again, I believe within a couple of cents). The cool thing is, if it's true...you managed this, apparently, without a computer program to optimize the tempering.

>"but perhaps they make the most sense if they're viewed as Mohajira well-temperaments"

Indeed. Like I told Igs, I think Dimension is "somewhere in the middle of Mohajira and standard Meantone"

>". "Near-MOS" doesn't mean that it's an MOS that's irregularly tempered, it means that it's a scale
that is not an MOS. However, it's almost an MOS, and has some of the properties that MOS scales do"

In that case, it looks like we used different approaches to end up with something very similar.

>"Post your dimension scale up and we'll see how close to mohajira it is. But like I said, this doesn't really have anything to do with well-temperaments."
Huh? Sounds like you are directly contradicting what you said above...

Anyhow, here is my Dimension EC tuning system (the whole 12 tones)

! E:\DIMENSION EC.scl
!
Dimension EC Scale
12
!
119.558
196.1985
315.6413
352.7508
505.7750
620.4284
701.9550
822.85912
891.9594
1011.52634
1047.1581
2/1

...and here is your scale vs. the closest seven tones in Dimension EC to it...

Your system - Mine
> 193.54839 - 196.1985

> 348.38710 - 352.7508

> 503.22581 - 505.7750

> 696.77419 - 701.9550

> 890.32258 - 891.9594

> 1045.16129 - 1047.1581

Seems like my system is between 2-4 cents off yours depending on the note, but definitely in the same ballpark.

🔗Mike Battaglia <battaglia01@...>

On Wed, Feb 16, 2011 at 7:46 AM, genewardsmith
<genewardsmith@...> wrote:
>
> This is listed here
>
> http://xenharmonic.wikispaces.com/Strictly+proper+7-note+31edo+scales
>
> as "Sikah; Neutral Diatonic Hypolydian" under "Mohajira type".

There you go. I figured this scale would have turned up plenty of times before.

> > There are more temperaments than I can keep track of these days, and I
> > have so far not delved into their near-MOS's at all. There are no
> > doubt a lot more beautiful scales like these that make sense when
> > analyzed as near-MOS's of some temperament we know (Paul's
> > pentachordal scales are among them).
>
> Looking at the surveys of proper scales in various edos is certainly place to start.

Do you feel that propriety is really of cognitive importance? We could
start there, but it would make me happy if we could systematically
index all of the near-MOS's of a scale, just as we index the MOS's,
and just search all of them, period.

I guess the near-MOS's of a scale are just the MOS's, but where one or
more of the notes is transposed by the chromatic vector. Maybe a good
way to index them would be to start by the number of notes transposed.

Many of the most useful, at least for meantone, seem to be where it's
only one note that's transposed (the meantone melodic minor, harmonic
minor, and harmonic major scales are examples of these). There are
also scales like C D E# F G A B C which might be probably less
harmonically useful than C D Eb F G A B C, for instance.

I admit that I haven't explored the near-MOS's of other temperaments,
so I'm not sure if this is just something that applies to meantone or
if it's a general truism. This will probably all make more sense when
I've finished my self-study in linear algebra.

> Similar remarks apply to other temperaments where the 11 might seem too complex, such as myna. Or even where something else might seem too complex, such as orwell or miracle.

Miracle is the first thing that comes to mind here. This is how people
have been using miracle, right? Using the decimal MOS as a cognitive
base, and then altering different notes chromatically for the sake of
harmony? If so, then that's jazz harmony right there in a nutshell,
except instead of talking about altering different notes chromatically
for the sake of harmony, we talk more about "modes."

> > In fact, I use near-MOS's more than I use MOS's. What have I been missing?
>
> I dunno, but you could start to look at all these non-MOS regularly tempered scales I keep spewing forth and tell me what you find interesting or not.

Have you spewed forth any that are of roughly diatonic or chromatic size?

> > But, from what I know, near-MOS's are, in general, poorly understood.
> > So my question is - what about them is so poorly understood exactly?
>
> There are a lot of them, and you need to ask what you want from them to go about finding optimal examples.

I'm not sure. The MOS's seem to align into magical music-making
possibilities for no reason at all. I thought maybe some near-MOS's
would align the same way. What I really want is to consider average
entropy per chord in the scale, but we're a ways off from that.

-Mike

🔗genewardsmith <genewardsmith@...>

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

> Do you feel that propriety is really of cognitive importance? We could
> start there, but it would make me happy if we could systematically
> index all of the near-MOS's of a scale, just as we index the MOS's,
> and just search all of them, period.

I think propriety makes sense to look at in the small scale range, such as the famous 5-10 note range. I think Carl has nominated other things as more important, so let's see if he chips in.

> I guess the near-MOS's of a scale are just the MOS's, but where one or
> more of the notes is transposed by the chromatic vector.

What I've called MODMOS on this list.

> > Similar remarks apply to other temperaments where the 11 might seem too complex, such as myna. Or even where something else might seem too complex, such as orwell or miracle.
>
> Miracle is the first thing that comes to mind here. This is how people
> have been using miracle, right? Using the decimal MOS as a cognitive
> base, and then altering different notes chromatically for the sake of
> harmony?

That's not how I've been using it, but I don't know about anyone else.

> > I dunno, but you could start to look at all these non-MOS regularly tempered scales I keep spewing forth and tell me what you find interesting or not.
>
> Have you spewed forth any that are of roughly diatonic or chromatic size?

Everything on the list of 7-note proper 31edo scales is of diatonic size. All of these 12 note hobbits I've been cranking out are of chromatic size. You might check here:

http://xenharmonic.wikispaces.com/Gallery+of+12-tone+Tempered+Scales

🔗Carl Lumma <carl@...>

Mike & Gene wrote:

> > Do you feel that propriety is really of cognitive importance?
> > We could start there, but it would make me happy if we could
> > systematically index all of the near-MOS's of a scale, just
> > as we index the MOS's, and just search all of them, period.
>
> I think propriety makes sense to look at in the small scale
> range, such as the famous 5-10 note range. I think Carl has
> nominated other things as more important, so let's see if he
> chips in.

In the 5-10 note range, scale evenness is definitely audible.
If it's audible it can be important. Rothenberg propriety is
one of many ways to measure it. Whether it's really better
than any other way is a question for experiment. But it's at
least plausible that it's among the better ways, and it's
fairly admissive as these things go, so it's probably the best
starting point. Lumma impropriety is a related concept I've
been known to advance.

Mean variety is also going to be correlated to evenness, but
I suspect it has some importance of its own, strictly from a
melodic standpoint. From a harmonic standpoint, we know scales
with at most 2 kinds of generic interval contain tunings of
rank 2 temperaments.

Scale size is important within the 5-10 note range, but maybe
more important for scales that are pretty even. That's an
interesting prediction that can be tested: do melodies in 5-ET
and 6-ET sound more different than in a pair of 5- and 6-tone
improper scales?

Finally, there are octave equivalence and omnitetrachordality.
I think they're audible melodically. Harmonic subdivision may
be too - we've talked about that recently.

Harmonically, you get into things like, Is there a generic
interval that maps to the same concordance in most modes?
This makes it possible to quickly set up a fundamental in every
mode, and quickly identify its corresponding generic interval
(e.g. fifth). Paul talks about this in his first paper I think.
Omnitetrachordality will tend to give it to you. So will MOS
where the generator is a concordance. A lot of these things
overlap.

One thing I think is original to me - or at least I came up
with it independently - is my "diatonic property". This is
where a given generic interval is concordant in most modes,
but via more than one concordance. That make it possible to
harmonize a line with a fixed generic interval (e.g. third)
without having the lines fuse, like on an organ. I think it
explains why parallel fifths are forbidden in classic voice
leading. A read several explanations of that rule but I've
never seen this pretty obvious one.

I talk about a bunch of this stuff at

http://lumma.org/music/theory/gd/gd3-spec.txt
and
http://lumma.org/music/theory/gd/gd3-results.xls
and
http://lumma.org/music/theory/gd/gd3-scales.zip

What was the question again? Er, let me know if this helps,

-Carl

🔗Mike Battaglia <battaglia01@...>

On Wed, Feb 16, 2011 at 7:55 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > Do you feel that propriety is really of cognitive importance? We could
> > start there, but it would make me happy if we could systematically
> > index all of the near-MOS's of a scale, just as we index the MOS's,
> > and just search all of them, period.
>
> I think propriety makes sense to look at in the small scale range, such as the famous 5-10 note range. I think Carl has nominated other things as more important, so let's see if he chips in.
//
> What I've called MODMOS on this list.

Wait, what's near-MOS then? That's what I thought was near-MOS.
Pretend I used "MODMOS" instead of "near-MOS" in all of the previous
replies and perhaps my questions will make more sense.

What about transposition by other vectors? Like in 31-tet, something
like C D E F^ G A B C, where C-F^ is 11/8. Is that a MODMOS? Perhaps
MODMOS's make the most sense if defined with respect to a certain
vector of alteration, which might be 25/24 or something else. I really
don't know anything about it or what work has been done so far.

As for narrowing it down, it makes sense to only look at proper
scales, but then you'd miss something like C Db E F G Ab B C. For
meantone, the four most widely-used near-MOS's do happen to be proper
for any sensible tuning of the generator.

Then again, maybe that scale is best analyzed as being something
outside of meantone, since I don't see how the concept of 81/80
emerges in that little 7-note block at all. Does anyone see it?
Perhaps that's a good way to bound MODMOS's: if you modulate the
periodicity block so much that the unison vectors aren't even involved
anymore, it's no longer a MODMOS of a certain temperament.

> > > I dunno, but you could start to look at all these non-MOS regularly tempered scales I keep spewing forth and tell me what you find interesting or not.
> >
> > Have you spewed forth any that are of roughly diatonic or chromatic size?
>
> Everything on the list of 7-note proper 31edo scales is of diatonic size. All of these 12 note hobbits I've been cranking out are of chromatic size. You might check here:
>
> http://xenharmonic.wikispaces.com/Gallery+of+12-tone+Tempered+Scales

I'll check it out, but what I'm really after is a way to rigorously
and formally describe the MOD/near/whateverMOS's of a scale, so that I
can punch numbers into MATLAB and have it spit out beautiful music.
Well, not quite, but you know what I mean.

-Mike

🔗Mike Battaglia <battaglia01@...>

On Wed, Feb 16, 2011 at 9:21 AM, Michael <djtrancendance@...> wrote:
>
> MikeB>"How can you add a 9/5 to a 7-note scale to obtain a 9-note scale?"
>
> Before I mentioned a note around 6/5 in addition to the 9/5. Adding these 2 notes (tempered) to your 7 tempered ones apparently gives a 9 tone irregularly tempered scale very close to Dimension (again, I believe within a couple of cents). The cool thing is, if it's true...you managed this, apparently, without a computer program to optimize the tempering.

What do you mean? I did use a computer program to optimize the
tempering. The POTE generator for mohajira is pretty much identical to
the neutral third of 31-tet, which is why I used it.

> >"but perhaps they make the most sense if they're viewed as Mohajira well-temperaments"
>
> Indeed. Like I told Igs, I think Dimension is "somewhere in the middle of Mohajira and standard Meantone"

Mohajira is just an 11-limit extension of meantone. I don't know how
you can be in the middle.

> >". "Near-MOS" doesn't mean that it's an MOS that's irregularly tempered, it means that it's a scale
> that is not an MOS. However, it's almost an MOS, and has some of the properties that MOS scales do"
>
> In that case, it looks like we used different approaches to end up with something very similar.

What was your approach?

> >"Post your dimension scale up and we'll see how close to mohajira it is. But like I said, this doesn't really have anything to do with well-temperaments."
> Huh? Sounds like you are directly contradicting what you said above...

No. Near-MOS's or MODMOS's or whatever they're called have more to do
with "modal harmony," in the colloquial sense, than optimizing a
tuning around a particular key.

> Anyhow, here is my Dimension EC tuning system (the whole 12 tones)
//snip snip
> Seems like my system is between 2-4 cents off yours depending on the note, but definitely in the same ballpark.

It's a very interesting scale, but tempered a bit unevenly. I wish
you'd eliminate the difference between (11/9)^2 and 3/2 and get it
overwith.

-Mike

🔗Mike Battaglia <battaglia01@...>

That was a very thorough reply.

On Wed, Feb 16, 2011 at 8:50 PM, Carl Lumma <carl@...> wrote:
>
> In the 5-10 note range, scale evenness is definitely audible.
> If it's audible it can be important. Rothenberg propriety is
> one of many ways to measure it. Whether it's really better
> than any other way is a question for experiment. But it's at
> least plausible that it's among the better ways, and it's
> fairly admissive as these things go, so it's probably the best
> starting point. Lumma impropriety is a related concept I've
> been known to advance.

Tonalsoft says it like this:

"For improper scales, Lumma's impropriety factor is defined as the
portion of the spectrum which is more than singly covered. For scales
which are proper or strictly proper, there are no overlapping
intervals and the impropriety is therefore always zero."

The implications of this aren't immediately apparent to me. What are
you getting at here...?

It would be nice to pick an approach that doesn't throw magic[7] out
the window too. I'm not sure that dicot[7], which is the proper
version, is more intelligible. Maybe in a certain way it is.

> Mean variety is also going to be correlated to evenness, but
> I suspect it has some importance of its own, strictly from a
> melodic standpoint. From a harmonic standpoint, we know scales
> with at most 2 kinds of generic interval contain tunings of
> rank 2 temperaments.

Tonalsoft has nothing on "mean variety." Is mean variety just what it
sounds like, the average variety of size per interval class? AKA, to
be an MOS, the mean variety of a scale has to be less than 2?

> Scale size is important within the 5-10 note range, but maybe
> more important for scales that are pretty even. That's an
> interesting prediction that can be tested: do melodies in 5-ET
> and 6-ET sound more different than in a pair of 5- and 6-tone
> improper scales?

How about magic[7] vs 7-tet? We could take some of Graham's magic
compositions and see how they sound.

> Finally, there are octave equivalence and omnitetrachordality.
> I think they're audible melodically. Harmonic subdivision may
> be too - we've talked about that recently.

Omnitetrachordality is interesting. I'm not sure I fully understand it
though. Paul explains it here:

/tuning/topicId_28692.html#28696

Looks like an error here, since I don't see how F lydian falls into
two identical 4/3 spans. F-G-A-B isn't 4/3 at all.

> Harmonically, you get into things like, Is there a generic
> interval that maps to the same concordance in most modes?
> This makes it possible to quickly set up a fundamental in every
> mode, and quickly identify its corresponding generic interval
> (e.g. fifth). Paul talks about this in his first paper I think.
> Omnitetrachordality will tend to give it to you. So will MOS
> where the generator is a concordance. A lot of these things
> overlap.

I don't understand this one at all, you're miles ahead of me here.

> One thing I think is original to me - or at least I came up
> with it independently - is my "diatonic property". This is
> where a given generic interval is concordant in most modes,
> but via more than one concordance. That make it possible to
> harmonize a line with a fixed generic interval (e.g. third)
> without having the lines fuse, like on an organ. I think it
> explains why parallel fifths are forbidden in classic voice
> leading. A read several explanations of that rule but I've
> never seen this pretty obvious one.

That is very interesting. I think what's also important, and I've
never heard this discussed, is that a lot of the triads/tetrads/etc be
rooted (or quasi-rooted, like with 10:12:15) concordances. This means
that, no matter where you land, at least you're on somewhat stable
ground. Machine[11] has this property, and outside of that and pajara
and meantone I haven't seen a lot of others. I'm not sure it's really
a "diatonic" property think that might be even more important than
MOS.

I've also been throwing around the idea of having the diatonicity of a
scale relate to something like avg. concordance/chord. I posted this
somewhere before, but I'll post it again. No matter what chord you hit
in the meantone pentatonic scale, it's sure to be decently concordant,
no matter how many notes, no matter what the notes are. Things are
different with the meantone diatonic scale, where you have to be a bit
more careful: "most" chords work, but lots of them are now discordant,
and that's a good thing for tonality. For meantone chromatic, it's a
lot different: most chords are dissonant, but some of them are super
consonant.

So there are two observations here -
- Average concordance is going down
- Maximum concordance is going up

So in general the standard deviation here is getting smaller. This
would ideally be done with HE, but as a practical consideration could
probably be done with Tenney Height as well. Finding a way to quickly
compute the lowest tempered-equivalent Tenney height of every single
chord in a scale is something I don't know how to do. How to weight
the contribution of triads vs tetrads is also something I don't know.
Whether or not it's necessary to do this for every single chord, or
just for the scale as a whole, is also something I don't know.

> I talk about a bunch of this stuff at
>
> http://lumma.org/music/theory/gd/gd3-spec.txt
> and
> http://lumma.org/music/theory/gd/gd3-results.xls
> and
> http://lumma.org/music/theory/gd/gd3-scales.zip

Thanks, I'll read through this. Man, I have a lot of stuff to read
through these days...

-Mike

🔗Carl Lumma <carl@...>

Mike wrote:

> Tonalsoft says it like this:
> "For improper scales, Lumma's impropriety factor is defined as
> the portion of the spectrum which is more than singly covered.
> For scales which are proper or strictly proper, there are no
> overlapping intervals and the impropriety is therefore always
> zero."
> The implications of this aren't immediately apparent to me.
> What are you getting at here...?
> It would be nice to pick an approach that doesn't throw magic[7]
> out the window too.

Rothenberg never used propriety this way. He only used
stability. The Rothenberg stability of a proper scale is 1.
For improper scales, he counts the number of overlaps.
Lumma impropriety is always zero for a proper scale. For an
improper scale, I measure the portion of the octave covered by
overlaps. Lumma stability is the portion not covered at all.
In the link I provided, I use s/(1+i) to combine the two. You
can try them yourself in Scala. In 41-ET, Magic[7] has
i = 0.512195, which is a blood bath.

> I'm not sure that dicot[7], which is the proper version,
> is more intelligible. Maybe in a certain way it is.

Way. Magic[7] sounds more like a 6-tone scale!

> Tonalsoft has nothing on "mean variety." Is mean variety just
> what it sounds like, the average variety of size per interval
> class? AKA, to be an MOS, the mean variety of a scale has to
> be less than 2?

Yes.

> Omnitetrachordality is interesting. I'm not sure I fully
> understand it though.

I measure it by the mean distance the tones of the scale move
when the scale is transposed by 3:2 (assuming octave equivalence).
So the diatonic scale, you get F -> F# or 100 cents / 7.
I test all pairings to get the minimum mean distance. I don't
know if Paul would endorse this formulation, but I posted the
results and he never objected. It's related to the "voice
leading distance" from my Progression Strength spec.

> > Harmonically, you get into things like, Is there a generic
> > interval that maps to the same concordance in most modes?
> > This makes it possible to quickly set up a fundamental in every
> > mode, and quickly identify its corresponding generic interval
> > (e.g. fifth). Paul talks about this in his first paper I think.
> > Omnitetrachordality will tend to give it to you. So will MOS
> > where the generator is a concordance. A lot of these things
> > overlap.
>
> I don't understand this one at all, you're miles ahead of me here.

It just says that there's a 3:2 or other strong concordance
in most modes and that it's always the same generic interval
when it appears. Like the 3:2 is always a fifth in the
diatonic scale and you get 6/7. Read Paul's 22-ET paper
for more.

> > One thing I think is original to me - or at least I came up
> > with it independently - is my "diatonic property". This is
> > where a given generic interval is concordant in most modes,
> > but via more than one concordance. That make it possible to
> > harmonize a line with a fixed generic interval (e.g. third)
> > without having the lines fuse, like on an organ. I think it
> > explains why parallel fifths are forbidden in classic voice
> > leading. -A- [I've] read several explanations of that rule
> > but I've never seen this pretty obvious one.
>
> That is very interesting. I think what's also important, and
> I've never heard this discussed, is that a lot of the
> triads/tetrads/etc be rooted (or quasi-rooted, like with
> 10:12:15) concordances. This means that, no matter where you
> land, at least you're on somewhat stable ground. Machine[11]
> has this property, and outside of that and pajara and meantone
> I haven't seen a lot of others. I'm not sure it's really a
> "diatonic" property think that might be even more important
> than MOS.

It sounds like you're describing the previous property (above).
A 3:2 is enough to get a root and other intervals can work too.
MOS will give it to you if the generator is concordant enough.
The diatonic property is almost the opposite.

> I've also been throwing around the idea of having the
> diatonicity of a scale relate to something like avg.
> concordance/chord. I posted this somewhere before, but I'll
> post it again. No matter what chord you hit in the meantone
> pentatonic scale, it's sure to be decently concordant, no
> matter how many notes, no matter what the notes are.

If this were the case, harmonic series segments would be
diatonic. But they're usually not considered to be.

-Carl

🔗Mike Battaglia <battaglia01@...>

On Wed, Feb 16, 2011 at 11:15 PM, Mike Battaglia <battaglia01@...> wrote:
> In the 5-10 note range, scale evenness is definitely audible.
> If it's audible it can be important. Rothenberg propriety is
> one of many ways to measure it. Whether it's really better
> than any other way is a question for experiment.

A useful data point here -

After thinking about this heavily, and after a lengthy discussion with
Paul about this (I can't say whether or not he agrees) - I have always
had some kind of issue with the notion of propriety being directly
cognitively relevant. Specifically my problem with it is that I feel
that it's used sometimes as an explanation for why the diatonic scale
generally sounds "stable" as a cognitive percept.

The real reason I've had a problem with this is that, aside from that
it does seem to have some application to the ease of transposition of
melodies, I'm not sure how important that is to my fundamental
perception of music. In fact, the whole concept of there being some
kind of "diatonic hearing" I have always viewed as completely
antithetical to the way that I perceive music, and I'm always very
vocal about that. This is because I'm not used to centering music, or
centering chord progressions, or centering melodies, around some kind
of central diatonic scale to begin with. Often I'll jump from scale to
scale throughout a piece of music, springboarding from one to the
other as much as possible. Usually it's like, every chord will have
its own scale, and often they'll be very different from one another. I
guess you could say that there's some kind of separate "diatonic
hearing" going on for every single chord, but the way that I've heard
the concept used just doesn't sync up for me.

But I just realized - I haven't defeated Rothenberg at all. I've just
moved the prediction away from "diatonic" hearing to "chromatic"
hearing. Every prediction I've ever heard about "diatonic" hearing,
which I've always hated, actually sums me up pretty much in a nutshell
if you just replace it with "chromatic" hearing. Once I realized this,
the world cycled promptly through a series of colors and I heard a
gong go off somewhere in the distance.

The concept of using the chromatic scale as a "measuring stick," and
the prediction that my categorical perception is almost completely
defined by this, are all true. In fact, this concept almost completely
dominates my entire perception of music. My AP is even somehow
partially based off of this.

The reason is probably that I've trained myself to internalize how all
of these scales in 12-tet relate to one another, and how they relate
to different transpositions of one another, and how they relate to the
octatonic scale, and etc. Like I'm aware of how to turn melodic minor,
by a few alterations, into the octatonic scale, and then I'm also
aware of how those alterations fit into meantone harmony, so I can
springboard off of the octatonic scale as though it were a dom7 chord
with some extensions. I have a little whole cognitive world based
around this concept, but the "way" I actually do this is by using
12-tet as a measuring stick, just like Rothenberg predicts.

Maybe people who tend to play more common practice music think more
often in terms of the diatonic scale and slight alterations to it, and
I've just lost the ability to hear things that way now. I definitely
can't hear the pentatonic scale that way anymore.

So I think that propriety may actually be of paramount importance when
setting up a "base" chromatic structure to perform mental
manipulations on. I don't have much of a problem moving to the
meantone[12] MOS, although it usually takes a second for me to map out
where the diatonic vs chromatic half steps are. I might have a problem
moving to a 12-note MOS if it's ridiculously improper, in terms of
using this scale as a mental measuring stick. In fact, I think that
even MOS matters here, because if I had four or five different
"fundamental" interval sizes that I thought in instead of just one
12-tet half step, or 2 meantone half steps - that would be complete
insanity.

So maybe the way to go is to find proper "chromatic"-sized MOS's, and
then look at "diatonic"-sized subsets of those scales. If one can
learn to "think" in the proper chromatic structure, then I feel like
you have a winner.

This is an experiment that I would like to see done, and seems very
related to my fundamental perception of music, probably more so than
HE or anything like that. That is all.

-Mike

PS: An example of what I mean by this is this Keith Jarrett rendition
of Autumn Leaves: http://www.youtube.com/watch?v=io1o1Hwpo8Y&t=0m47s
He's barely flirting with the diatonic scale, if that. The scale he's
playing completely changes like every 2 seconds on average.
Furthermore a lot of the chords he's using take advantage of the
128/125 unison vector - if you're playing the octatonic scale or the
7th mode of melodic minor over a dom7 chord, we've left the realm of
just simply altering the diatonic scale fashion in such a way that you
get a proper scale.

Or if you want to really get out there, then all of the stuff that
Jaco does in his string arrangement of Herbie's "Speak Like a Child" -
http://www.youtube.com/watch?v=u3dKJATAJmA&t=2m17s. This is a near-MOS
near-orgy. At one point he uses Bm9/maj7, which in the context it's in
implies B melodic minor #4, to resolve to Bb dorian. Feel free to
analyze why that one works, I still have no idea.

This is a completely different paradigm than something like common
practice music, where maybe you'd do something like augment the second
to resolve it leading-tone style to a major third, but in general
don't do stuff like this.

🔗Mike Battaglia <battaglia01@...>

The last email I sent here was pretty long so I'll keep this one shorter.

On Thu, Feb 17, 2011 at 12:50 AM, Carl Lumma <carl@...> wrote:
>
> Rothenberg never used propriety this way. He only used
> stability. The Rothenberg stability of a proper scale is 1.
> For improper scales, he counts the number of overlaps.
> Lumma impropriety is always zero for a proper scale. For an
> improper scale, I measure the portion of the octave covered by
> overlaps. Lumma stability is the portion not covered at all.
> In the link I provided, I use s/(1+i) to combine the two. You
> can try them yourself in Scala. In 41-ET, Magic[7] has
> i = 0.512195, which is a blood bath.

So the application of my last email to this was, that perhaps if there
were a larger proper scale that Magic[7] were seen as a subset of, it
would be easier to cognize. But how does this apply to augmented[6]?
Augmented[6] is proper, I believe, but it's almost the same as
Magic[7], just with some shifting around and a note added in really.

> > I'm not sure that dicot[7], which is the proper version,
> > is more intelligible. Maybe in a certain way it is.
>
> Way. Magic[7] sounds more like a 6-tone scale!

Yeah. Yeah, it does. Why does it sound more like a 6-tone scale? It
sounds like an extension of the augmented scale. Because we're used to
that from 12-tet?
> > Omnitetrachordality is interesting. I'm not sure I fully
> > understand it though.
>
> I measure it by the mean distance the tones of the scale move
> when the scale is transposed by 3:2 (assuming octave equivalence).
> So the diatonic scale, you get F -> F# or 100 cents / 7.
> I test all pairings to get the minimum mean distance. I don't
> know if Paul would endorse this formulation, but I posted the
> results and he never objected. It's related to the "voice
> leading distance" from my Progression Strength spec.

So what makes it omnitetrachordal? If the distance is zero? Paul was
saying the diatonic scale IS omnitetrachordal, and I don't see how.

> > I don't understand this one at all, you're miles ahead of me here.
>
> It just says that there's a 3:2 or other strong concordance
> in most modes and that it's always the same generic interval
> when it appears. Like the 3:2 is always a fifth in the
> diatonic scale and you get 6/7. Read Paul's 22-ET paper
> for more.

You mean 5\7? But yeah, this is the same thing I mentioned. This is
like The Property for scales I wish we were measuring. Every scale we
find like this that has tons of rooted chords other than 4:5:6 in it
is a goldmine in my view. Machine is good but doesn't have strong
3/2's, but it's still usable. If you're in 22, it's definitely usable,
but you really at that point have to give up the notion that tonality
has to do with scales.

> It sounds like you're describing the previous property (above).
> A 3:2 is enough to get a root and other intervals can work too.
> MOS will give it to you if the generator is concordant enough.
> The diatonic property is almost the opposite.

I see that Gene talked about some potential theorems for when
omnitetrachordality is present. Did we ever get those...?

> > I've also been throwing around the idea of having the
> > diatonicity of a scale relate to something like avg.
> > concordance/chord. I posted this somewhere before, but I'll
> > post it again. No matter what chord you hit in the meantone
> > pentatonic scale, it's sure to be decently concordant, no
> > matter how many notes, no matter what the notes are.
>
> If this were the case, harmonic series segments would be
> diatonic. But they're usually not considered to be.

There are three classes of scale that I've been looking at -
chromatic, diatonic, and "pentatonic." By "pentatonic" I mean a scale
that's pretty much concordant everywhere you turn, and which usually
means it has less notes. I put the last one in quotes because
obviously a scale doesn't have to have just 5 notes to fit that
criteria, and there should probably be a better name for scales like
that.

These scales tend to be nice for melodies, and sometimes for soloing,
for obvious reasons. I think that if you work it out, most harmonic
series chords would be concordant, and the avg concordance per chord
would tend to be closer to the pentatonic scale than the diatonic
scale.

I also think that Paul's SPM scales will be somewhere between meantone
diatonic and meantone chromatic, and that blackwood[10] will be closer
to meantone diatonic than meantone chromatic despite being closer to
12 than 7, and that most really useful scales will fall somewhere
between the cracks.

-Mike

🔗Carl Lumma <carl@...>

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

> perhaps if there were a larger proper scale that Magic[7] were
> seen as a subset of, it would be easier to cognize.

I doubt it. Anything can be "cognized" with enough exposure.
Why does having a scale within a scale help?

> > > I'm not sure that dicot[7], which is the proper version,
> > > is more intelligible. Maybe in a certain way it is.
> >
> > Way. Magic[7] sounds more like a 6-tone scale!
>
> Yeah. Yeah, it does. Why does it sound more like a 6-tone scale?

Because two of the tones are a lot closer together than
the others.

> > I measure it by the mean distance the tones of the scale move
> > when the scale is transposed by 3:2 (assuming octave
> > equivalence). So the diatonic scale, you get F -> F# or
> > 100 cents / 7. I test all pairings to get the minimum mean
> > distance. I don't know if Paul would endorse this formulation,
> > but I posted the results and he never objected. It's related
> > to the "voice leading distance" from my Progression
> > Strength spec.
>
> So what makes it omnitetrachordal? If the distance is zero?

Again, just as with propriety, I don't think of it as a
binary condition. I don't know how Paul thinks of it.

> Paul was saying the diatonic scale IS omnitetrachordal, and
> I don't see how.

100/7 isn't much.

> > It just says that there's a 3:2 or other strong concordance
> > in most modes and that it's always the same generic interval
> > when it appears. Like the 3:2 is always a fifth in the
> > diatonic scale and you get 6/7. Read Paul's 22-ET paper
> > for more.
>
> You mean 5\7?

No, 6 out of 7 modes.

> I also think that Paul's SPM scales

What's SPM?

> blackwood[10] will be closer to meantone diatonic than
> meantone chromatic despite

blackwood[10] is a model diatonic citizen, as are the usual
pentatonic and diatonic scales in 12-ET. Since it sounds weird
to say the diatonic scale is a diatonic scale, we have the
term "gd" (for Generalized Diatonic). Hence, the URLs I
posted. So I should say, blackwood[10] and meantone[5] and
meantone[7] are all model gd citizens. Harmonic series
segments, not so much.

> being closer to 12 than 7, and that most really useful
> scales will fall somewhere between the cracks.

From my point of view it seems like you are desperately
trying to shove everything into some kind of relationship with
the scales you already know.

-Carl

🔗Kalle Aho <kalleaho@...>

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

> Omnitetrachordality is interesting. I'm not sure I fully understand it
> though. Paul explains it here:
>
> /tuning/topicId_28692.html#28696
>
> Looks like an error here, since I don't see how F lydian falls into
> two identical 4/3 spans. F-G-A-B isn't 4/3 at all.

I don't think those ~4/3 spans need to start from the lowest note. For
omnitetrachordality you just have to have two identical ~4/3 spans
~4/3 or ~3/2 apart within every octave span (and the notes of the
leftover interval must be adjacent.)

> That is very interesting. I think what's also important, and I've
> never heard this discussed, is that a lot of the triads/tetrads/etc be
> rooted (or quasi-rooted, like with 10:12:15) concordances. This means
> that, no matter where you land, at least you're on somewhat stable
> ground. Machine[11] has this property, and outside of that and pajara
> and meantone I haven't seen a lot of others. I'm not sure it's really
> a "diatonic" property think that might be even more important than
> MOS.

What counts as rooted or quasi-rooted? Is a 3:5:7 chord rooted if the
scale repeats at the tritave? What about 1/1:7/5:7/3?

/tuning/topicId_62588.html#62588

Kalle

🔗Mike Battaglia <battaglia01@...>

On Thu, Feb 17, 2011 at 3:42 AM, Carl Lumma <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > perhaps if there were a larger proper scale that Magic[7] were
> > seen as a subset of, it would be easier to cognize.
>
> I doubt it. Anything can be "cognized" with enough exposure.
> Why does having a scale within a scale help?

Because you then have a proper scale to compare it to.

> > I also think that Paul's SPM scales
>
> What's SPM?

Standard pentachordal major.

> > blackwood[10] will be closer to meantone diatonic than
> > meantone chromatic despite
>
> blackwood[10] is a model diatonic citizen, as are the usual
> pentatonic and diatonic scales in 12-ET. Since it sounds weird
> to say the diatonic scale is a diatonic scale, we have the
> term "gd" (for Generalized Diatonic). Hence, the URLs I
> posted. So I should say, blackwood[10] and meantone[5] and
> meantone[7] are all model gd citizens. Harmonic series
> segments, not so much.
>
> > being closer to 12 than 7, and that most really useful
> > scales will fall somewhere between the cracks.
>
> From my point of view it seems like you are desperately
> trying to shove everything into some kind of relationship with
> the scales you already know.

I'm not sure why you say that, but if the first random diatonic
property I throw out there is just me trying to shove everything into
the relationship with the scales I already know, then the same applies
to all of these other random diatonic properties we're discussing as
well.

-Mike

🔗Mike Battaglia <battaglia01@...>

On Thu, Feb 17, 2011 at 11:56 AM, Kalle Aho <kalleaho@...> wrote:
>
> > That is very interesting. I think what's also important, and I've
> > never heard this discussed, is that a lot of the triads/tetrads/etc be
> > rooted (or quasi-rooted, like with 10:12:15) concordances. This means
> > that, no matter where you land, at least you're on somewhat stable
> > ground. Machine[11] has this property, and outside of that and pajara
> > and meantone I haven't seen a lot of others. I'm not sure it's really
> > a "diatonic" property think that might be even more important than
> > MOS.
>
> What counts as rooted or quasi-rooted? Is a 3:5:7 chord rooted if the
> scale repeats at the tritave? What about 1/1:7/5:7/3?
>
> /tuning/topicId_62588.html#62588

I say that a chord is n-rooted if it refers to a note that is
n-equivalent of one of the notes. I don't think that tritave
equivalence is something that can really be internalized like people
think that it can, but if you believe otherwise, then you could say
that 3:5:7 is 3-rooted, sure.

10:12:15 is quasi-rooted because it usually sounds like it points to
5, even though the GCD here is 1. As for 1/1 7/5 7/3, I'm not sure how
that would line up. If you feel that it's quasi-rooted you can feel
free to build scales around it, I really haven't explored tritave
equivalence much...

-Mike

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

On Thu, Feb 17, 2011 at 3:01 PM, Carl Lumma <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > > > perhaps if there were a larger proper scale that Magic[7] were
> > > > seen as a subset of, it would be easier to cognize.
> > >
> > > I doubt it. Anything can be "cognized" with enough exposure.
> > > Why does having a scale within a scale help?
> >
> > Because you then have a proper scale to compare it to.
>
> If the larger scale is proper that can certainly help.
> But then you're really using the larger scale, aren't you?

And what I'm saying is, since you seem to have skipped over my first
email on this, that that's how I hear music. Even with the diatonic
scale. I don't hear diatonically, I hear chromatically. Obviously if
I'm playing a diatonic scale, those notes are emphasized, but I don't
use the diatonic scale as a "measuring stick" in the way that
Rothenberg describes it. I am however, at all times using the 12-tet
chromatic scale as the measuring stick, which is something I didn't
realize before. If this differs from how others do it, it's probably
because of how I had to learn to constantly relate scales in my jazz
training.

So all of that has led to me cognizing things "chromatically" almost
at all times and almost never purely "diatonically." I can sort of
remember a time in which I perhaps heard that way, but I'm not sure.
When I play a pentatonic scale I tend to think more diatonically,
perhaps.

As to how this applies to magic[7] - when I'm working with an improper
scale in 12-tet, I'm always aware of how it fits against the backdrop
of 12-tet and how it's related to other "nearby" scales. I don't get
confused when I hear something like C Eb F F# G Bb C, because I always
know that C-Eb is 3\12 and the F-G is 2\12, whether or not one of them
is "a second" or "a third" in that scale. And I'm also always aware
that C-Eb is 6/5 and F-G is 9/8. That sort of thing. Point is, if I
didn't have 12-tet as a reference, I might be up against some shaky
waters there. So maybe this applies to other improper scales as well -
they might become much easier to cognize if viewed as subsets of a
proper scale. At the very least, that would fit more in line with how
I am conditioned to cognize scales. That's all I am saying, no more,
no less.

-Mike

PS: Even MOS seems to become of paramount cognitive importance if you
apply it to a chromatic "universe" set. At that point it just becomes
a matter of learning more universe sets that lend themselves to easy
mental grasping. Or perhaps it's a matter of finding out what makes
for easy grasping right now, and then just making sure to hit the
sweet spot of novelty between boredom and mass confusion. Maybe all of
this is really "set theory done right" or something.

🔗Chris Vaisvil <chrisvaisvil@...>

🔗Carl Lumma <carl@...>

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

> > If the larger scale is proper that can certainly help.
> > But then you're really using the larger scale, aren't you?
>
> And what I'm saying is, since you seem to have skipped over my
> first email on this,

I take it you studied all the materials I linked to in my
original before sending it?

> that that's how I hear music. Even with the
> diatonic scale. I don't hear diatonically, I hear chromatically.
> Obviously if I'm playing a diatonic scale, those notes are
> emphasized, but I don't use the diatonic scale as a "measuring
> stick" in the way that Rothenberg describes it.

Couple things:

* Just because you can listen chromatically, why does this mean
you can't also listen diatonically? And how do you know you
don't? What about happy birthday in Amin... is the melody
recognizable to you? Try it in 7-ET. Try it in the Hungarian
major and minor.

* Even if you do listen exclusively chromatically in 12/diatonic
music, does this mean you must also listen this way in other
scales and systems?

-Carl

🔗Mike Battaglia <battaglia01@...>

On Thu, Feb 17, 2011 at 10:58 PM, Carl Lumma <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > > If the larger scale is proper that can certainly help.
> > > But then you're really using the larger scale, aren't you?
> >
> > And what I'm saying is, since you seem to have skipped over my
> > first email on this,
>
> I take it you studied all the materials I linked to in my
> original before sending it?

Sure did, and if it addressed anything about jazz musicians thinking
chromatically instead of diatonically I missed it.

> > that that's how I hear music. Even with the
> > diatonic scale. I don't hear diatonically, I hear chromatically.
> > Obviously if I'm playing a diatonic scale, those notes are
> > emphasized, but I don't use the diatonic scale as a "measuring
> > stick" in the way that Rothenberg describes it.
>
> Couple things:
>
> * Just because you can listen chromatically, why does this mean
> you can't also listen diatonically?

Maybe I can, but it's not as accurate as applying predictions like
these to "chromatic" hearing.

> And how do you know you don't?

That's generally unfalsifiable.

> What about happy birthday in Amin... is the melody
> recognizable to you? Try it in 7-ET. Try it in the Hungarian
> major and minor.

It's recognizable to me in every one of those, even the Hungarian
major and minor ones. Hungarian minor was the weirdest. Pentatonic
melodies are also recognizable to me in improper pentatonic scales as
well.

> * Even if you do listen exclusively chromatically in 12/diatonic
> music, does this mean you must also listen this way in other
> scales and systems?

I certainly hope you don't think I'm saying that.

-Mike

🔗Mike Battaglia <battaglia01@...>

🔗Carl Lumma <carl@...>

🔗Michael <djtrancendance@...>

>"What I really want is to consider average entropy per chord in the scale"
I believe Scala can already find all the chords in a scale of size >= x. Why not ask for a feature that plugs your preferred entropy formula to all those chords and takes an average?

--- On Thu, 2/17/11, Chris Vaisvil <chrisvaisvil@...> wrote:

From: Chris Vaisvil <chrisvaisvil@...>
Subject: Re: [tuning] Re: Interesting tetrachordal Mohajira Near-MOS, and towards a systematic exploration of near-MOS's in general?
To: tuning@yahoogroups.com
Date: Thursday, February 17, 2011, 7:46 PM

Is the objective of "average entropy per chord in the scale" to provide a means to shift through large numbers of alternative tunings/ scale subsets for some desired property?

Chris

On Wed, Feb 16, 2011 at 7:42 PM, Mike Battaglia <battaglia01@...> wrote:

I'm not sure. The MOS's seem to align into magical music-making

possibilities for no reason at all. I thought maybe some near-MOS's

would align the same way. What I really want is to consider average

entropy per chord in the scale, but we're a ways off from that.

-Mike

🔗Mike Battaglia <battaglia01@...>

On Fri, Feb 18, 2011 at 3:02 AM, Carl Lumma <carl@...> wrote:
>
> It seems you are saying it's not equally recognizable in
> all of them. For me it is most recognizable in the natural
> minor, then 7-ET, followed by the Hungarian minor, and
> weirdest is the Hungarian major. That's consistent with
> Rothenberg.

I admitted that Rothenberg's stuff has some application to melody. I
think it also applies to melodies that are in the pentatonic scale.
This video is pretty striking:
http://www.youtube.com/watch?v=DBJ7mBxi8LM

I always thought that stuff like that was interesting on some level,
but it never seemed worthwhile to me to elevate it to being a
fundamental driving force in music cognition. I'm more aware of how
the "augmented second" in the harmonic minor scale is 3\12 than how it
is "a second" of the scale, and augmented seconds and minor thirds are
the same as far as 12-tet chromatic hearing is concerned because
they're both 3\12.

I guess I'm aware of that the two notes separated by an augmented
second lie "adjacent" to one another in that scale in some sense,
which means that they are separated by a "second," which validates
your point but I am conditioned to trigger the first mode of awareness
far more. When you're used to the diminished fourth in the 7th mode of
melodic minor acting like a major third over dominant seventh chords,
you start to think more about how both of them are 4\12 and that's
what matters.

But even besides this debate, I have to concede your point because I
haven't really defeated Rothenberg at all, I've just deferred all of
the predictions to my personal sense of chromatic hearing instead of
diatonic hearing. And those predictions there work stunningly well, so
much that when applied there they do become some kind of fundamental
driving force in my cognition of music. So while we all have some kind
of distaste for academia's viewpoint that 12-equal consists of the
Ultimate Universe Set from which all music springeth forth, I do think
that does make for "a" good universe set to use to cognize music. And
my hypothesis is that universe sets that fit the following features
will be The Most Good For Musical Cognition:

1) Sets that are proper
2) Sets that are MOS (or equal)

These would be things that I'd like to test. I can't be the first to
mix these two concepts together, is there more research on this I can
read about?

-Mike

🔗Mike Battaglia <battaglia01@...>

🔗Carl Lumma <carl@...>

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

> I always thought that stuff like that was interesting on some
> level, but it never seemed worthwhile to me to elevate it to
> being a fundamental driving force in music cognition. I'm more
> aware of how the "augmented second" in the harmonic minor scale
> is 3\12 than how it is "a second" of the scale,

I suspect you represent a small minority of (expert) listeners
in this.

> and augmented seconds and minor thirds are the same as far as
> 12-tet chromatic hearing is concerned because they're both 3\12.

One of Paul Erlich's favorite examples is how 4\12 is a
consonance as a third and a dissonance as a diminished fourth.
At least I think that's the example he used.

> When you're used to the diminished fourth in the 7th mode of
> melodic minor acting like a major third over dominant seventh
> chords, you start to think more about how both of them are
> 4\12 and that's what matters.

...So much for that. :)

> But even besides this debate, I have to concede your point
> because I haven't really defeated Rothenberg at all, I've just
> deferred all of the predictions to my personal sense of
> chromatic hearing instead of diatonic hearing. And those
> predictions there work stunningly well, so much that when
> applied there they do become some kind of fundamental driving
> force in my cognition of music.

Just the fact that conventional music theory, without regard
for intonation at all, has stuck with the diatonic degree
names, even after 100+ years of enharmonics, might mean
something.

Probably Krumhansl or somebody has done some experiments
along these lines...

> So while we all have some kind of distaste for academia's
> viewpoint that 12-equal consists of the Ultimate Universe Set
> from which all music springeth forth, I do think that does
> make for "a" good universe set to use to cognize music. And
> my hypothesis is that universe sets that fit the following
> features will be The Most Good For Musical Cognition:
> 1) Sets that are proper
> 2) Sets that are MOS (or equal)
> These would be things that I'd like to test. I can't be the
> first to mix these two concepts together, is there more
> research on this I can read about?

Not sure what you're referring to. One of the main points of
MOS is that it generalizes Yasser's observation. Any highly
regular scale will produce, through its transpositions, a
chromatic universe not much bigger than itself, and learning
to hear that universe is something that experts in the system
will do, and that certainly might add to the subtly of their
enjoyment. Or something.

-Carl

🔗Mike Battaglia <battaglia01@...>

On Fri, Feb 18, 2011 at 6:56 PM, Carl Lumma <carl@...> wrote:
>
> > I always thought that stuff like that was interesting on some
> > level, but it never seemed worthwhile to me to elevate it to
> > being a fundamental driving force in music cognition. I'm more
> > aware of how the "augmented second" in the harmonic minor scale
> > is 3\12 than how it is "a second" of the scale,
>
> I suspect you represent a small minority of (expert) listeners
> in this.

This is tripping me out.

> One of Paul Erlich's favorite examples is how 4\12 is a
> consonance as a third and a dissonance as a diminished fourth.
> At least I think that's the example he used.
//snip
> ...So much for that. :)

Then Paul Erlich's favorite example has about 100 years of music
against it. Wikipedia's page on the altered scale (7th mode of melodic
minor) sucks, but they mention something about it on the humorously
titled "jazz scale" page:

http://en.wikipedia.org/wiki/Jazz_scale#Altered_dominant_scale

Let's just say that academia's analysis of "jazz theory" is about as
good as its analysis of microtonal theory. I could put together some
musical examples of how the 7th mode of melodic minor can function
over a V7 chord if you'd like, since I'm not finding any good YouTube
videos on it. It's a pretty stereotypical jazz sound.

If you've never seen any of this in the academic music theory
literature before, then now you know why I'd lost all respect for
academia's take on music theory long before I joined this list. This
list only served to make the contrast between academia and real life
all the more apparent.

Aside from that, this pattern shows up all over the near-MOS's of
meantone, especially between the harmonic minor and harmonic major
ones. Take the following two scales, for instance (view fixed width):

C D E F G# A B C (third mode of harmonic minor)
C D E F G Ab B C (first mode of harmonic major)

They're almost the same thing. And if you just smush the two together,
you get this:

C D E F G G# A B C

This is also humorously referred to in the literature as "the bebop
scale." It might just sound to you like a diatonic scale with a
chromatic note between G and A. Here's a mode of that scale which
probably does not sound like that:

C C# D# E F# G# A B C, which is a synthesis of

C D# E F# G# A B C (lydian augmented #2, sixth mode of harmonic major)
C C# D# Fb Gb Ab Bbb C (altered bb7, seventh mode of harmonic minor)

If you think those two 7-note scales sound completely different then
you're hearing music almost completely differently than I am.

The above could also be viewed as a near-MOS of diminished[8] and
pajara[8], if anyone's interested. Or it's like lydian aug, but you
split the natural 2 into a b2 and a #2.

> > But even besides this debate, I have to concede your point
> > because I haven't really defeated Rothenberg at all, I've just
> > deferred all of the predictions to my personal sense of
> > chromatic hearing instead of diatonic hearing. And those
> > predictions there work stunningly well, so much that when
> > applied there they do become some kind of fundamental driving
> > force in my cognition of music.
>
> Just the fact that conventional music theory, without regard
> for intonation at all, has stuck with the diatonic degree
> names, even after 100+ years of enharmonics, might mean
> something.

It means that it's easier to cram a system of extended harmony that
utilizes 128/125 as a unison vector into an existing notation system
rather than invent a completely new one, especially when you need to
hire working musicians to play this music. There is no impetus to
invent a new system of notation for the octatonic scale, when that
scale is generally being used most often over diminished and dominant
7 chords. There may be mass confusion, however.

So to avoid mass confusion, the "standard" way to spell out extended
harmonies in jazz is to refer to the b9, #9, #11, b7, and b13.
Sometimes you'll see b5 and #5 too, in certain cases. But nobody will
ever spell the major third in an altered chord out as a diminished
fourth, ever. The altered scale consists of a root, a b9, a #9, a
major third, a b5 or a #11 depending on which makes for an easier to
read score in context, a b13, and a b7. The octatonic scale also
consists of a b9, a #9, a major third, a #4, a 5, a natural 6, a b7,
and the octave.

So far as "convention" is concerned, this is the messy solution we're
stuck with, it's how I was taught, it's how working jazz musicians
tend to read with perhaps a few minor regional variations.

> Not sure what you're referring to. One of the main points of
> MOS is that it generalizes Yasser's observation. Any highly
> regular scale will produce, through its transpositions, a
> chromatic universe not much bigger than itself, and learning
> to hear that universe is something that experts in the system
> will do, and that certainly might add to the subtly of their
> enjoyment. Or something.

I think there's more to it than that - being able to conceptualize a
larger universe implies more puns that can be used for musical effect,
or at least can make them more apparent. If you can conceptualize the
12-tet universe, then the dim4/maj3 pun leads to the ability to use
the altered and octatonic scales over dominant 7 chords (the latter
being one of my favorite musical techniques in the world). To be
honest, I'm pretty sure you could use some of those same techniques
even if your universe was 12 notes of meantone, because if you think
those two sizes of semitone are close enough to be used for "similar"
musical effect in different instances, because they're both similarly
sized discordant intervals, then you're already very roughly thinking
in terms of a 128/125 pun existing.

It also makes it easier to figure out how the near-MOS's of a certain
scale work, or at least it does for meantone and I don't see why it
wouldn't for something like porcupine.

-Mike

🔗Mike Battaglia <battaglia01@...>

On Fri, Feb 18, 2011 at 8:19 PM, Mike Battaglia <battaglia01@...> wrote:
>> Not sure what you're referring to. One of the main points of
>> MOS is that it generalizes Yasser's observation. Any highly
>> regular scale will produce, through its transpositions, a
>> chromatic universe not much bigger than itself, and learning
>> to hear that universe is something that experts in the system
>> will do, and that certainly might add to the subtly of their
>> enjoyment. Or something.

A few last addenda here -

- This all begs the question of whether or not one can have an
"open-ended" universe, meaning something that just goes on forever.
This is probably how they (probably) used to think of meantone,
although rumor is it that Mozart's dad advocated for something like
55-ET as a universe set (correct me if I'm wrong).

- Theoretically, I don't see why mental structures like these couldn't
be possible, but it would probably work out to be some kind of
"layered cognition" scheme. Using meantone as an example, I think the
diatonic scale notes would be cognized most firmly, a background
awareness of the chromatic scale would exist, a dimmer awareness of a
19-note hyperchromatic scale would exist, an even dimmer awareness of
a 31-note pattern would exist, and so on. Or perhaps the 31-note
pattern wouldn't be fleshed out fully, but there'd be some indirect
awareness of it as a "discovering of what lies beyond" as you continue
down the spiral of fifths. Maybe you'd hit a mental wall at 19 or
something, and assuming that that represents a common mental wall to
hit, maybe you'd like 19-equal.

Lastly, you said this a little while ago:
- Even if you do listen exclusively chromatically in 12/diatonic
music, does this mean you must also listen this way in other
scales and systems?

Obviously not. However, I think that you can mentally split a major
third into 4 roughly equal parts any time you want, whether or not the
tuning system "supports" it or not. To do so probably means you're
aware of potential accordance of how every one of those new notes
could fit into the current chord or a related chord. Whether or not
this system contains a better approximation to 9/8, or distinguishes
between 10/9 or 9/8, isn't going to stop your brain from screaming at
you "here's a possibility!" if you're trying to improvise. This is
obviously not the only musically useful possibility that could exist.

My brain keeps screaming at me these days to split a minor third into
two equal parts, but the tuning system I'm playing in doesn't support
it. That doesn't stop my brain from screaming it at me though.

-Mike

🔗Carl Lumma <carl@...>

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

> > One of Paul Erlich's favorite examples is how 4\12 is a
> > consonance as a third and a dissonance as a diminished fourth.
> > At least I think that's the example he used.
>
> Then Paul Erlich's favorite example has about 100 years of music
> against it. Wikipedia's page on the altered scale (7th mode of
> melodic minor) sucks, but they mention something about it on the
> humorously titled "jazz scale" page:
> http://en.wikipedia.org/wiki/Jazz_scale#Altered_dominant_scale

It doesn't matter if there's a style of music in which the
dim 4th isn't a dissonance, only that there is a style in
which it is. Major 3rds are dissonances in medieval music.

> Let's just say that academia's analysis of "jazz theory" is about
> as good as its analysis of microtonal theory. I could put together
> some musical examples of how the 7th mode of melodic minor can
> function over a V7 chord if you'd like, since I'm not finding any
> good YouTube videos on it. It's a pretty stereotypical jazz sound.

I don't know what you mean. The wikipedia link you provided
discussed the function over the V7 chord, and I didn't spot any
huge problems that you seem to be eluding to. Music theory
content of all stripes is bad on wikipedia FWIW.

> C D# E F# G# A B C
> C C# D# Fb Gb Ab Bbb C
>
> If you think those two 7-note scales sound completely different
> then you're hearing music almost completely differently than
> I am.

Hard to say.

From the archives, Paul says,
"George Secor posted examples here
/tuning/topicId_48499.html#49594?var=0&l=1
showing how the diminished fourth, diminished sixth, and
diminished seventh sound like dissonances, while the major
third, perfect fifth, and major sixth sound like consonances,
despite the fact that the only way of distinguishing the first
set of intervals from the second (since 12-equal was used)
is by relating them to the prevailing diatonic context."

> So to avoid mass confusion, the "standard" way to spell out
> extended harmonies in jazz is to refer to the b9, #9, #11, b7,
> and b13. Sometimes you'll see b5 and #5 too, in certain cases.
> But nobody will ever spell the major third in an altered chord
> out as a diminished fourth, ever.

You seem to be saying that jazz theory is a chromatic theory,
which is fine by me.

> > Any highly
> > regular scale will produce, through its transpositions, a
> > chromatic universe not much bigger than itself, and learning
> > to hear that universe is something that experts in the system
> > will do, and that certainly might add to the subtly of their
> > enjoyment
>
> I think there's more to it than that - being able to
> conceptualize a larger universe implies more puns that can be
> used for musical effect,

Howso?

> the dim4/maj3 pun leads to the ability to use the altered
> and octatonic scales over dominant 7 chords (the latter
> being one of my favorite musical techniques in the world).

You must be using a different definition of "pun" than I'm
expecting.

> if you think those two sizes of semitone are close enough to
> be used for "similar" musical effect in different instances,
> because they're both similarly sized discordant intervals,
> then you're already very roughly thinking in terms of a
> 128/125 pun existing.

Puns as I think of them have nought to do with 'discordant
intervals of about the same size'.

-Carl

🔗Mike Battaglia <battaglia01@...>

On Sat, Feb 19, 2011 at 12:20 AM, Carl Lumma <carl@...> wrote:
>
> It doesn't matter if there's a style of music in which the
> dim 4th isn't a dissonance, only that there is a style in
> which it is. Major 3rds are dissonances in medieval music.

It is possible to use 4/12 as a dissonant interval. I'm not sure that
the potential dissonance of that interval is related to diatonic
hearing. I'm not sure exactly how or why diatonic hearing would be
related to dissonance anyway, or what exactly from a strictly melodic
standpoint would make the concept of a diminished fourth somehow be
dissonant to begin with. All of the examples that I can think of in
which a diminished fourth sounds dissonant can be explained more
simply by harmonic means.

> > Let's just say that academia's analysis of "jazz theory" is about
> > as good as its analysis of microtonal theory. I could put together
> > some musical examples of how the 7th mode of melodic minor can
> > function over a V7 chord if you'd like, since I'm not finding any
> > good YouTube videos on it. It's a pretty stereotypical jazz sound.
>
> I don't know what you mean. The wikipedia link you provided
> discussed the function over the V7 chord, and I didn't spot any
> huge problems that you seem to be eluding to. Music theory
> content of all stripes is bad on wikipedia FWIW.

There's no major third in this scale, only a diminished fourth. This
supposed huge shift in sound between 4\12 because it's now a
diminished fourth doesn't happen.

> From the archives, Paul says,
> "George Secor posted examples here
> /tuning/topicId_48499.html#49594?var=0&l=1
> showing how the diminished fourth, diminished sixth, and
> diminished seventh sound like dissonances, while the major
> third, perfect fifth, and major sixth sound like consonances,
> despite the fact that the only way of distinguishing the first
> set of intervals from the second (since 12-equal was used)
> is by relating them to the prevailing diatonic context."

Or by some basic concept of priming and harmonic entropy. The last
second here was more effective than the first one.

Here's an example of my own: play the following chord in the left hand:

C F# Bb E

Then, in the right hand, play the altered scale: C Db Eb Fb Gb Bb Ab C

Then resolve the whole thing to F minor. It sounds like some kind of
Danny Elfman V-I or something. Now, to make that E/Fb sound much
darker, play the following chord in the left hand:

C F# Bb Eb

Then in the right hand, also play the altered scale: C Db Eb Fb Gb Bb Ab C

> > So to avoid mass confusion, the "standard" way to spell out
> > extended harmonies in jazz is to refer to the b9, #9, #11, b7,
> > and b13. Sometimes you'll see b5 and #5 too, in certain cases.
> > But nobody will ever spell the major third in an altered chord
> > out as a diminished fourth, ever.
>
> You seem to be saying that jazz theory is a chromatic theory,
> which is fine by me.

You asked why we've been sticking with diatonic note-naming
conventions for hundreds of years despite that people have been using
128/125 based puns for so long. I pointed out all of the irritating
enharmonic conventions that we had to learn which resulted from people
trying to cram expanded harmony into the diatonic naming structure.

But that's just one group of people. In contrast, the classical folks,
who may not play as much of this kind of music, don't have this
problem and perhaps think diatonically more than the rest of us. The
songwriters and electronic musicians out there may not even read music
at all to begin with, and as far as I know people who don't read music
tend to spell things out enharmonically in strange ways that would
cause my AP teacher to fail them in high school.

> > I think there's more to it than that - being able to
> > conceptualize a larger universe implies more puns that can be
> > used for musical effect,
>
> Howso?
//
> You must be using a different definition of "pun" than I'm
> expecting.
//
> Puns as I think of them have nought to do with 'discordant
> intervals of about the same size'.

I just meant novel musical possibilities that emerge from tempering
out some comma. Specifically I meant about the type of possibility
that equates one note with another and pretends they were never
different to begin with. Sometimes this takes the form of a long chord
progression in which you end back where you started although you
wouldn't in JI. Sometimes there are things that you don't even realize
won't work in JI until you try, like Dm7 Fmaj/G Cmaj, which requires
81/80 to vanish to actually work as 5-limit harmony. I've just been
calling them all "puns."

25/24 and 16/15 are discordant intervals of about the same size. If
you temper 128/125, does not a "pun" exist between those two notes
now?

-Mike

🔗Carl Lumma <carl@...>

Hi Mike,

> It is possible to use 4/12 as a dissonant interval. I'm not sure
> that the potential dissonance of that interval is related to
> diatonic hearing. I'm not sure exactly how or why diatonic
> hearing would be related to dissonance anyway, or what exactly
> from a strictly melodic standpoint would make the concept of a
> diminished fourth somehow be dissonant to begin with.

The idea is, we learn associations between actual intervals
and scalar intervals...

> All of the examples that I can think of in which a diminished
> fourth sounds dissonant can be explained more simply by
> harmonic means.

...I'm not saying it doesn't reference harmony, just that this
harmony is not present but instead is signaled through the
scalar intervals. Compare George's first and last examples:

C.B..B.B.C
G.Ab.G.F.Eb

and

F.Eb.Eb.Eb.D
B.C..B..C..B

In the first, Ab:B is 6:5 but dissonant, moving to
G:B = 5:4 = consonant. In the second, C:Eb = 6:5 = consonant,
moving to B:Eb = 5:4 = dissonant. Obviously this is not
based on the chromatic intervals involved.

> Here's an example of my own: play the following chord in the
> left hand: C F# Bb E
> Then, in the right hand, play the altered scale:
> C Db Eb Fb Gb Bb Ab C
> Then resolve the whole thing to F minor. It sounds like some
> kind of Danny Elfman V-I or something. Now, to make that E/Fb
> sound much darker, play the following chord in the left hand:
> C F# Bb Eb
> Then in the right hand, also play the altered
> scale: C Db Eb Fb Gb Bb Ab C

Hm, don't really hear much of a difference in this one.

> 25/24 and 16/15 are discordant intervals of about the same size.
> If you temper 128/125, does not a "pun" exist between those two
> notes now?

A pun exists only when two intervals are conflated through
the mapping of concordances.

-Carl

🔗Mike Battaglia <battaglia01@...>

On Sat, Feb 19, 2011 at 8:34 PM, Carl Lumma <carl@...> wrote:
>
> Hi Mike,
>
> > It is possible to use 4/12 as a dissonant interval. I'm not sure
> > that the potential dissonance of that interval is related to
> > diatonic hearing. I'm not sure exactly how or why diatonic
> > hearing would be related to dissonance anyway, or what exactly
> > from a strictly melodic standpoint would make the concept of a
> > diminished fourth somehow be dissonant to begin with.
>
> The idea is, we learn associations between actual intervals
> and scalar intervals...

I don't understand. Are you saying that we hear diminished fourths as
dissonant because we hear them as severely mistuned 4/3's or
something, whereas major thirds we hear as only slightly mistuned
5/4's?

> > All of the examples that I can think of in which a diminished
> > fourth sounds dissonant can be explained more simply by
> > harmonic means.
>
> ...I'm not saying it doesn't reference harmony, just that this
> harmony is not present but instead is signaled through the
> scalar intervals. Compare George's first and last examples:
>
> C.B..B.B.C
> G.Ab.G.F.Eb
>
> and
>
> F.Eb.Eb.Eb.D
> B.C..B..C..B
>
> In the first, Ab:B is 6:5 but dissonant, moving to
> G:B = 5:4 = consonant. In the second, C:Eb = 6:5 = consonant,
> moving to B:Eb = 5:4 = dissonant. Obviously this is not
> based on the chromatic intervals involved.

I'm not sure I understand your meaning. Try this: hold a C down in the
bass. Then, an octave up, arpeggiate a JI 8->9->10->9->8, so that the
8 is an octave above the C and the whole thing fleshes out an
arpeggiated 4:8:9:10 chord. Then, to compare, try
16->17->19->20->19->17->16, so that what we were calling "8" before we
now call 16, so that the whole thing fleshes out an arpeggiated
8:16:17:19:20 chord. Then, to compare with something more xenharmonic,
try 12->13->14->15->14->13->12, so that the whole thing fleshes out an
arpeggiated 6:12:13:14:15 chord. The latter two make the 5/4 sound
more dissonant than the first one. Is this close to what you are
talking about?

Here's another one. Try the following chord progression, which is
related to George Secor's example but uses chords:

Cm Fm Cm Abm Cm

The Abm here sounds much more dissonant than the other minor chords.
It would also not, in diatonic terminology be a minor chord at all, as
you'd spell it out Ab B Eb, making it an aug2 chord. But this can also
be explained by priming, because the following chord progression:

10/4 ||: Cmaj Dbmaj7 Ebmaj6 (C Bb C C,) :||

Contains mostly major chords, but the Dbmaj sounds much more dissonant
than the other major chords as well, again due to a mixture of
harmonic entropy and priming.

I'm not sure what you meant by "this harmony is not present but
instead is signaled through the scalar intervals," so maybe this isn't
what you were getting at.

> > Then in the right hand, also play the altered
> > scale: C Db Eb Fb Gb Bb Ab C
>
> Hm, don't really hear much of a difference in this one.

I'll have to come up with a MIDI file for it, I'm not sure I really
communicated it well the way I wrote it.

> > 25/24 and 16/15 are discordant intervals of about the same size.
> > If you temper 128/125, does not a "pun" exist between those two
> > notes now?
>
> A pun exists only when two intervals are conflated through
> the mapping of concordances.

I don't understand. If you're tempering out 128/125, then the way
you're mapping the prime concordances 2, 3, and 5 is such that 25/24
and 16/15 are conflated.

-Mike

🔗Carl Lumma <carl@...>

Mike wrote:
> > The idea is, we learn associations between actual intervals
> > and scalar intervals...
>
> I don't understand. Are you saying that we hear diminished
> fourths as dissonant because we hear them as severely mistuned
> 4/3's or something, whereas major thirds we hear as only
> slightly mistuned 5/4's?

No...

> > ...I'm not saying it doesn't reference harmony, just that this
> > harmony is not present but instead is signaled through the
> > scalar intervals. Compare George's first and last examples:
> >
> > C.B..B.B.C
> > G.Ab.G.F.Eb
> > and
> > F.Eb.Eb.Eb.D
> > B.C..B..C..B
> >
> > In the first, Ab:B is 6:5 but dissonant, moving to
> > G:B = 5:4 = consonant. In the second, C:Eb = 6:5 = consonant,
> > moving to B:Eb = 5:4 = dissonant. Obviously this is not
> > based on the chromatic intervals involved.
>
> I'm not sure I understand your meaning.

Do you agree with the given consonance/dissonance assessment?

> Here's another one. Try the following chord progression,
> which is related to George Secor's example but uses chords:
> Cm Fm Cm Abm Cm
> The Abm here sounds much more dissonant than the other minor
> chords. It would also not, in diatonic terminology be a minor
> chord at all, as you'd spell it out Ab B Eb, making it an
> aug2 chord.
> But this can also be explained by priming,

I think it's due to the fact that it reminds us that it's
part of the dim7 in the scale - same as George's example.

> I'm not sure what you meant by "this harmony is not present
> but instead is signaled through the scalar intervals," so
> maybe this isn't what you were getting at.

How else would George's example work?

> Try this: hold a C down in the bass. Then, an octave up,
> arpeggiate a JI 8->9->10->9->8, so that the 8 is an octave
> above the C and the whole thing fleshes out an arpeggiated
> 4:8:9:10 chord. Then, to compare,
> try 16->17->19->20->19->17->16, so that what we were
> calling "8" before we now call 16, so that the whole thing
> fleshes out an arpeggiated 8:16:17:19:20 chord. Then, to
> compare with something more xenharmonic, try
> 12->13->14->15->14->13->12, so that the whole thing fleshes
> out an arpeggiated 6:12:13:14:15 chord. The latter two make
> the 5/4 sound more dissonant than the first one. Is this close
> to what you are talking about?

Not at all. There's no particular scale referenced here.
And I the 5:2 sounds the same to me in the first two
examples. And it's a 5:3 in the last example, which yeah,
is more discordant than 5:2.

> because the following chord progression:
> 10/4 ||: Cmaj Dbmaj7 Ebmaj6 (C Bb C C,) :||
> Contains mostly major chords, but the Dbmaj sounds much more
> dissonant than the other major chords as well, again due to a
> mixture of harmonic entropy and priming.

I don't see how either harmonic entropy or priming come
into play. Nor do I hear the Dbmaj7 as more dissonant (only
very slightly due to, I think, absolute pitch effects).

> > > Then in the right hand, also play the altered
> > > scale: C Db Eb Fb Gb Bb Ab C
> >
> > Hm, don't really hear much of a difference in this one.
>
> I'll have to come up with a MIDI file for it, I'm not sure I
> really communicated it well the way I wrote it.

Ok, but I'm pretty sure I know what you meant.

> > > 25/24 and 16/15 are discordant intervals of about the same
> > > size. If you temper 128/125, does not a "pun" exist between
> > > those two notes now?
> >
> > A pun exists only when two intervals are conflated through
> > the mapping of concordances.
>
> I don't understand. If you're tempering out 128/125, then the
> way you're mapping the prime concordances 2, 3, and 5 is such
> that 25/24 and 16/15 are conflated.

Yes, but only if you play them in context. When you mentioned
that they're discordant and about the same size, I imagined
you meant juxtaposing them as harmonic intervals or something.
Sorry if I misunderstood.

-Carl

🔗Mike Battaglia <battaglia01@...>

On Sun, Feb 20, 2011 at 7:01 PM, Carl Lumma <carl@...> wrote:
>
> Mike wrote:
> > > The idea is, we learn associations between actual intervals
> > > and scalar intervals...
> >
> > I don't understand. Are you saying that we hear diminished
> > fourths as dissonant because we hear them as severely mistuned
> > 4/3's or something, whereas major thirds we hear as only
> > slightly mistuned 5/4's?
>
> No...

I think I'm lost.

> > > F.Eb.Eb.Eb.D
> > > B.C..B..C..B
> Do you agree with the given consonance/dissonance assessment?

I do agree with it. I can also flip my brain around to hear that B-Eb as
being Cb-Eb, such that the second example could also end like this:

F.Eb.Eb.F..Gb
B.C..Cb.Cb.Bb

In this sense, the 5/4 is more consonant, and it's also spelled like a
proper major third. However, although this correlation exists, I'm not
seeing a causative relationship, and I also know examples where it doesn't
hold.

I also think that they sound dissonant in the same sense that in ||: Cmaj |
Gm7 | Cmaj | Bbm7 :||, the Bbm7 sounds more dissonant than the Gm7. Or, in
my mind, the example you gave and this one are the same thing, except
George's example used dyads and mine uses chords.

> > Here's another one. Try the following chord progression,
> > which is related to George Secor's example but uses chords:
> > Cm Fm Cm Abm Cm
> > The Abm here sounds much more dissonant than the other minor
> > chords. It would also not, in diatonic terminology be a minor
> > chord at all, as you'd spell it out Ab B Eb, making it an
> > aug2 chord.
> > But this can also be explained by priming,
>
> I think it's due to the fact that it reminds us that it's
> part of the dim7 in the scale - same as George's example.

I think I agree, but that's what I meant by priming. All of this "reminding
us" business is what I've been referring to as priming. And the reason that
dim7 chords are dissonant is because their entropy is high.

But while I have you on the same page about the dissonance of the Abm being
greater than the dissonance of the other chords, then here's one more chord
example which is related to that:

||: Cmaj | Gm | Cmaj | Dm :||
vs
||: Cmaj | Gm | Cmaj | Fm :||
vs
||: Cmaj | Gm | Cmaj | Abm :||

I think the Fm is more dissonant than the Dm. However, I think that the Abm
is more dissonant than both. Do you agree?

> > I'm not sure what you meant by "this harmony is not present
> > but instead is signaled through the scalar intervals," so
> > maybe this isn't what you were getting at.
>
> How else would George's example work?

If you play C-E-G-E-C, arpeggiating the notes, it's more consonant sounding
than if you play C-Eb-G-Eb-C. This is pretty easily explained by a
combination of priming and HE - two "virtual" chords are being fleshed out
here, and we already know that HE explains why major chords sound less
dissonant than minor chords. I don't see any reason why this wouldn't extend
to chord progressions and scales just as you'd expect, with the whole thing
fleshing out some kind of background structure in your mind (which is
usually a scale). I think that the discordance of that structure is what
leads to different modes, chord progressions, or countermelodies as in
George's example sounding consonant or dissonant in different cases.

It's all very predictable: chord progressions from phrygian tend to sound
darker than chord progressions from aeolian, which tend to sound darker than
chord progressions from mixolydian. Chord progressions from mixolydian b6
(Radiohead) tend to sound darker than chord progression from mixolydian.
Critical band effects wouldn't matter here unless you're playing all of the
notes at the same time.

To pick some nits, I think all of this is being performed on a virtual
harmonic structure in which the volume of each note is a function of the
last time you heard it. This assumes that HE can be extended in a
well-behaved way to chords in which the volume of each note varies. I hope
so, because if you're playing 20:24:25:30, and as you lower the volume of
24, the discordance of this chord for all intents and purposes will start to
approach that of 4:5:6.

> > Try this: hold a C down in the bass. Then, an octave up,
> > arpeggiate a JI 8->9->10->9->8, so that the 8 is an octave
> > above the C and the whole thing fleshes out an arpeggiated
> > 4:8:9:10 chord. Then, to compare,
> > try 16->17->19->20->19->17->16, so that what we were
> > calling "8" before we now call 16, so that the whole thing
> > fleshes out an arpeggiated 8:16:17:19:20 chord. Then, to
> > compare with something more xenharmonic, try
> > 12->13->14->15->14->13->12, so that the whole thing fleshes
> > out an arpeggiated 6:12:13:14:15 chord. The latter two make
> > the 5/4 sound more dissonant than the first one. Is this close
> > to what you are talking about?
>
> Not at all. There's no particular scale referenced here.
> And I the 5:2 sounds the same to me in the first two
> examples. And it's a 5:3 in the last example, which yeah,
> is more discordant than 5:2.

In the last example, it's a 12:15 on top, which is a 5:4, and the outer dyad
is 6:15, is a 5:2...

> > because the following chord progression:
> > 10/4 ||: Cmaj Dbmaj7 Ebmaj6 (C Bb C C,) :||
> > Contains mostly major chords, but the Dbmaj sounds much more
> > dissonant than the other major chords as well, again due to a
> > mixture of harmonic entropy and priming.
>
> I don't see how either harmonic entropy or priming come
> into play. Nor do I hear the Dbmaj7 as more dissonant (only
> very slightly due to, I think, absolute pitch effects).

I don't know what you mean by absolute pitch effects here. I hear the Dbmaj7
as much darker than the other chords.

In general, I think you'll agree that that chord progression is darker than,
say, ||: Cmaj | Fmaj | Gm | Fmaj :||, despite that the Gm is a minor chord.
Compare "Everything in its Right Place" and "Louie Louie" - which one is
darker?

-Mike

🔗Carl Lumma <carl@...>

Mike wrote:

> > I think it's due to the fact that it reminds us that it's
> > part of the dim7 in the scale - same as George's example.
>
> I think I agree, but that's what I meant by priming. All of
> this "reminding us" business is what I've been referring to as
> priming.

That's not really the meaning of the term
http://en.wikipedia.org/wiki/Priming_%28psychology%29
but the point is in *how* it reminds us -- obviously via
the scalar intervals used.

> here's one more chord example which is related to that:
> ||: Cmaj | Gm | Cmaj | Dm :||
> vs
> ||: Cmaj | Gm | Cmaj | Fm :||
> vs
> ||: Cmaj | Gm | Cmaj | Abm :||
> I think the Fm is more dissonant than the Dm. However, I think
> that the Abm is more dissonant than both. Do you agree?

I do. And I get the same effect just from C | Dm vs
C | Fm vs C | Abm, even when C is voiced in root position,
Fm in 2nd inversion, and Abm in 1st inversion. It may be
because the first progression is consistent with a CM scale,
the second with an F melodic min scale, and the third not
really with any scale I know well and therefore represents
a modulation (or perhaps it suggests the B-D-F-Ab dim7 in
the C harmonic minor).

-Carl

🔗Mike Battaglia <battaglia01@...>

Sorry, I missed this reply...

One thing before I reply, which was back to this example:

F.Eb.Eb.Eb.D
B.C..B..C..B

The substitution here would reimagine the B-Eb as part of a B altered
scale, which could then resolve to E minor. So try this:

F.Eb.Eb.Eb.E
B.C..B..C..B

If you're having trouble seeing the harmonic context of this, the
following bass notes will help frame it properly:

F.Eb.Eb.Eb.E
B.C..B..C..B
B.B..B..B..E

Now you have a diminished fourth sounding consonant.

My thoughts - once you flip into this way of hearing it, it's kind of
jarring to suddenly take that scale and reframe it as part of C minor
again. Once you do that, it's kind of jarring to flip it around and
hear it as part of an extended harmonic structure resolving to E
minor.

The difference is that as part of C minor, as you pointed out - some
part of the color of this scale fragment is likely derived from the
nearby diminished 7 chord. For there to be a diminished 7 chord at
all, you'd have to be in C harmonic minor (which is what my brain
seems to gravitate to) anyways. This means you'd end up with the 7th
mode of harmonic minor, which is altered bb7, not the normal altered
scale. Something about the presence of that Ab really changes things
around.

On Sun, Feb 20, 2011 at 11:02 PM, Carl Lumma <carl@...> wrote:
>
> > > I think it's due to the fact that it reminds us that it's
> > > part of the dim7 in the scale - same as George's example.
> >
> > I think I agree, but that's what I meant by priming. All of
> > this "reminding us" business is what I've been referring to as
> > priming.
>
> That's not really the meaning of the term
> http://en.wikipedia.org/wiki/Priming_%28psychology%29
> but the point is in *how* it reminds us -- obviously via
> the scalar intervals used.

I meant priming in the sense that if you play an Eb, and then 10
seconds later you play a C-G dyad, it'll sound vaguely minor.
Furthermore, it even sounds "minor" in the abstract sense in that it
sounds "sad," or higher in entropy, or lower in tonalness, or
whatever. I've heard "priming" used to describe that effect. So for
this to happen, and assuming that we're still in agreement that all of
this "sadness" stuff has something to do with chords being lower in
tonalness, that means periodicity processing must even be active on
"memories" of notes that aren't even being played right now.

So I think that this doesn't just apply to obvious cases like hitting
an Eb and then a C-G later, but also more subtly to scales. If I play
D minor, and then Cmaj7, the whole thing will imply a 7-note structure
which has its own entropy and hence feeling. In this case it's the
ionian mode. And as far as modal harmony is concerned, there is a
reason that Phrygian sounds darker than Aeolian, and that's probably
it.

So if, when you say that scalar intervals can "remind" you of things,
you mean specifically that memories of scale-appropriate notes are
pulled up from long-term memory due to a lifetime of conditioning, and
those virtual notes are then processed with the VF mechanism due to
some kind of abstract LTP/classical conditioning version of "priming,"
then yes, I agree. Otherwise I'm not sure I understand.

> > here's one more chord example which is related to that:
> > ||: Cmaj | Gm | Cmaj | Dm :||
> > vs
> > ||: Cmaj | Gm | Cmaj | Fm :||
> > vs
> > ||: Cmaj | Gm | Cmaj | Abm :||
> > I think the Fm is more dissonant than the Dm. However, I think
> > that the Abm is more dissonant than both. Do you agree?
>
> I do. And I get the same effect just from C | Dm vs
> C | Fm vs C | Abm, even when C is voiced in root position,
> Fm in 2nd inversion, and Abm in 1st inversion. It may be
> because the first progression is consistent with a CM scale,
> the second with an F melodic min scale, and the third not
> really with any scale I know well and therefore represents
> a modulation (or perhaps it suggests the B-D-F-Ab dim7 in
> the C harmonic minor).

OK, so C | Dm vs C | Fm. Your scalar analysis is what I was getting
at, although I'd frame the Cmaj | Fm one as being a part of C
mixolydian b6, since I hear the C as the root.

The point I'm making here, even aside from the Abm example, is that C
| Fm is more dissonant than C | Dm. Both of these examples are easily
cognized into some stereotypically western scale structure, so the
dissonance of Fm can't derive from that. There has to be a reason for
this, and the way I see it, Cmixob6 is just more dissonant than
Cmajor. Furthermore, I think that as the "flavor" of C minor derives
from its entropy, I think that the flavor of Cmixob6 also derives from
its entropy, and I think that Cmixob6 is probably just higher in
entropy than C major. Do you agree?

-Mike

🔗Carl Lumma <carl@...>

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

> > I do. And I get the same effect just from C | Dm vs
> > C | Fm vs C | Abm, even when C is voiced in root position,
> > Fm in 2nd inversion, and Abm in 1st inversion. It may be
> > because the first progression is consistent with a CM scale,
> > the second with an F melodic min scale, and the third not
> > really with any scale I know well and therefore represents
> > a modulation (or perhaps it suggests the B-D-F-Ab dim7 in
> > the C harmonic minor).
[snip]
> The point I'm making here, even aside from the Abm example,
> is that C | Fm is more dissonant than C | Dm. Both of these
> examples are easily cognized into some stereotypically
> western scale structure, so the dissonance of Fm can't
> derive from that.

But that's exactly where I was saying it derived from!

> There has to be a reason for
> this, and the way I see it, Cmixob6 is just more dissonant than
> Cmajor. Furthermore, I think that as the "flavor" of C minor
> derive from its entropy, I think that the flavor of Cmixob6 also
> derives from its entropy, and I think that Cmixob6 is probably
> just higher in entropy than C major. Do you agree?

No. Most of what you wrote sounds like gibberish to me.
Don't mind me though. My brain's not in a tuning way
of late.

-Carl

🔗Mike Battaglia <battaglia01@...>

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

On Fri, Feb 25, 2011 at 11:18 PM, Carl Lumma <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > > Read what I originally wrote. A major scale is less 'dissonant'
> > > than a minor one.
> >
> > OK, then that's what I was also saying, and I claimed that this
> > was due to the heptadic entropy of the scale as well as the
> > entropy of its subsets. You said you didn't agree with it.
>
> Yes, I strongly disagree it has anything to do with heptadic
> entropy (N.B. Steve has solved the terminology problem offlist,
> with 2HE, 3HE, etc.) I do think it has to do with subsets,
> namely, the chords used in typical progressions for the scale.

So how do you explain Cmaj -> Fm vs Cmaj -> Dm? The entropy of Fm and
Dm are the same, because they're both just minor chords. The only
thing that could possibly differentiate the feeling produced by the
two are the way in which they relate to the previous chord, and once
you do that you've already moved past the entropy of each chord
individually.

> In the case of the harmonic minor, the scale is covered by the
> root minor triad and dim7 and the typical progression -- at least
> the one George's example invokes -- just alternates between
> the two. The diatonic scale has a richer vocabulary, with six
> triads to draw on and several typical ways of stringing them
> together. -Carl

I can see this for certain types of music, but I think it has to do
with the type of music you're used to playing. I'm a Debussy-ite,
which means I tend to think almost exclusively in modes as sonic
entities within themselves. I will try to "imply" a mode with a dense
chord, or two chords, or one chord with a tiny counterline in there.
However, to someone who's used to treating the diatonic scale as more
of a rough guideline to play triads within, the 3HE of the subsets
will be more important than the 7HE of the scale.

I think that 7HE will always be somewhat relevant as the full scale
will always be somewhere in the background of your mind.

-Mike

🔗Carl Lumma <carl@...>

Mike wrote:

> > Yes, I strongly disagree it has anything to do with heptadic
> > entropy (N.B. Steve has solved the terminology problem offlist,
> > with 2HE, 3HE, etc.) I do think it has to do with subsets,
> > namely, the chords used in typical progressions for the scale.
>
> So how do you explain Cmaj -> Fm vs Cmaj -> Dm? The entropy of
> Fm and Dm are the same, because they're both just minor chords.

I feel like I'm taking crazy pills. Did I not just reiterate
/tuning/topicId_96322.html#96518
my original answer
/tuning/topicId_96322.html#96423?var=1&l=1
?

> The only thing that could possibly differentiate the feeling
> produced by the two are the way in which they relate to the
> previous chord, and once you do that you've already moved past
> the entropy of each chord individually.

? Did I say that *only* the entropy of the subsets mattered?
The things that matter (that I can think of just now) are the
chords themselves, the progression between them (see my
Progression Strength document), the voice leading between them
(same document), and other chords and progressions associated
in the listener's memory (what we're talking about here).

> > In the case of the harmonic minor, the scale is covered by the
> > root minor triad and dim7 and the typical progression -- at least
> > the one George's example invokes -- just alternates between
> > the two. The diatonic scale has a richer vocabulary, with six
> > triads to draw on and several typical ways of stringing them
> > together. -Carl
>
> I can see this for certain types of music, but I think it has to
> do with the type of music you're used to playing. I'm a Debussy-
> ite, which means I tend to think almost exclusively in modes as
> sonic entities within themselves. I will try to "imply" a mode
> with a dense chord, or two chords, or one chord with a tiny
> counterline in there.

That's great but I fail to see the relevance. You already said
you hear the distinction in George's example. That's all that
matters. It's a constructive proof that scalar intervals are
important. Even to a perfect-pitch-having, jazz-trained,
Debussy-ite.

-Carl

🔗Mike Battaglia <battaglia01@...>

On Sat, Feb 26, 2011 at 2:07 AM, Carl Lumma <carl@...> wrote:
>
> Mike wrote:
>
> > > Yes, I strongly disagree it has anything to do with heptadic
> > > entropy (N.B. Steve has solved the terminology problem offlist,
> > > with 2HE, 3HE, etc.) I do think it has to do with subsets,
> > > namely, the chords used in typical progressions for the scale.
> >
> > So how do you explain Cmaj -> Fm vs Cmaj -> Dm? The entropy of
> > Fm and Dm are the same, because they're both just minor chords.
>
> I feel like I'm taking crazy pills. Did I not just reiterate
> /tuning/topicId_96322.html#96518
> my original answer
> /tuning/topicId_96322.html#96423?var=1&l=1
> ?

You said that chord progressions taken from a melodic minor scale will
sound more dissonant than those taken from a major scale. I said that
due to priming, this could be modeled well by some kind of 7HE
calculation, or more specifically 8HE since one of those notes will be
emphasized and doubled down in the bass. You strongly disagree with
this, but I don't know why, or how specifically you propose it should
work for something like Cmaj -> Fm.

> > The only thing that could possibly differentiate the feeling
> > produced by the two are the way in which they relate to the
> > previous chord, and once you do that you've already moved past
> > the entropy of each chord individually.
>
> ? Did I say that *only* the entropy of the subsets mattered?
> The things that matter (that I can think of just now) are the
> chords themselves, the progression between them (see my
> Progression Strength document), the voice leading between them
> (same document), and other chords and progressions associated
> in the listener's memory (what we're talking about here).

1) Arpeggiating C-E-G leads to a very consonant sound
2) Arpeggiating C-Eb-G leads to a less consonant sound
3) Arpeggiating C-D-E-F-G-A-B-C leads to a very consonant sound
4) Arpeggiating C-Db-Eb-F-Gb-Ab-Bb-C leads to a less consonant sound

You seem to be saying that 3HE matters in the first two examples, but
that 7HE doesn't matter in the last two. Why?

> You already said you hear the distinction in George's example. That's all that
> matters. It's a constructive proof that scalar intervals are important.

You posted an example in which a ~5/4 sounds consonant in one context
and dissonant in another. You postulated that the dissonance in the
second context stems from it being a diminished fourth, whereas in the
first it's a major third. I came up with a counterexample in which a
diminished fourth sounds consonant, which to me proves that all of
this has nothing at all to do whether the ~5/4 subtends three vs four
scale steps. I also posted the 4:8:9:10 vs 8:16:17:19:20 vs
6:12:13:14:15 example, which is what I think that it does have to do
with. Now you say that none of that matters because in one example, a
major third sounded consonant and a diminished fourth sounded
dissonant, therefore correlation equals causation. Now I feel like I'm
the one taking crazy pills.

And I still don't understand why exactly a diminished fourth is
supposed to be dissonant, or how dissonance could possibly emerge from
anything except for periodicity processing. When I asked this, you
responded with the following two statements

> The idea is, we learn associations between actual intervals and scalar intervals...

and

> > All of the examples that I can think of in which a diminished
> > fourth sounds dissonant can be explained more simply by
> > harmonic means. (me)
>
> ...I'm not saying it doesn't reference harmony, just that this
> harmony is not present but instead is signaled through the
> scalar intervals. (you)

What does this mean? Harmony being signaled through the scalar
intervals? Associations between actual intervals and scalar intervals?
What are we associating to a diminished fourth, 32/25? Seriously man,
I'm completely lost here.

-Mike

🔗Carl Lumma <carl@...>

Mike wrote:

> > I feel like I'm taking crazy pills. Did I not just reiterate
> > /tuning/topicId_96322.html#96518
> > my original answer
> > /tuning/topicId_96322.html#96423?var=1&l=1
> > ?
>
> You said that chord progressions taken from a melodic minor
> scale will sound more dissonant than those taken from a major
> scale. I said that due to priming, this could be modeled well
> by some kind of 7HE calculation, or more specifically 8HE since
> one of those notes will be emphasized and doubled down in the
> bass. You strongly disagree with this, but I don't know why,

Perhaps it's because 7HE and priming have next to nothing to
do with the things I've been writing about.

> or how specifically you propose it should
> work for something like Cmaj -> Fm.

You understand this progression implies the melodic minor?
The root of which is Fmin? And that C -> Dmin implies a major
scale, the root of which is C?

> > > The only thing that could possibly differentiate the feeling
> > > produced by the two are the way in which they relate to the
> > > previous chord, and once you do that you've already moved
> > > past the entropy of each chord individually.
> >
> > ? Did I say that *only* the entropy of the subsets mattered?
> > The things that matter (that I can think of just now) are the
> > chords themselves, the progression between them (see my
> > Progression Strength document), the voice leading between them
> > (same document), and other chords and progressions associated
> > in the listener's memory (what we're talking about here).
>
> 1) Arpeggiating C-E-G leads to a very consonant sound
> 2) Arpeggiating C-Eb-G leads to a less consonant sound
> 3) Arpeggiating C-D-E-F-G-A-B-C leads to a very consonant sound
> 4) Arpeggiating C-Db-Eb-F-Gb-Ab-Bb-C leads to a less consonant
> sound
> You seem to be saying that 3HE matters in the first two
> examples, but that 7HE doesn't matter in the last two. Why?

It's not clear to me HE matters in any of them. Meanwhile,
have you noticed a tendency, when I make a direct statement,
to respond by introducing a new exercise or example which is
unrelated to my statement?

> or how dissonance could possibly emerge from
> anything except for periodicity processing.

???

I think you mean discordance, but even so, there's more to
discordance than just "periodicity processing".

> When I asked this, you
> responded with the following two statements
>
> > The idea is, we learn associations between actual intervals
> > and scalar intervals...
> and
> > ...I'm not saying it doesn't reference harmony, just that
> > this harmony is not present but instead is signaled through
> > the scalar intervals. (you)
>
> What does this mean? Harmony being signaled through the scalar
> intervals? Associations between actual intervals and scalar
> intervals? What are we associating to a diminished fourth,
> 32/25? Seriously man, I'm completely lost here.

Here are the examples again

C_B__B_B_C
G_Ab_G_F_Eb

and

F_Eb_Eb_Eb_D
B_C__B__C__B

The pattern in the first is C D C D C and in the second,
D C D C D where C = consonant and D = dissonant.

Now think of the Rothenberg paradigm: when we hear the first
dyad in the first example, we try to figure out where it fits
in one of the scales we know. (All this should work just as
well with the dyads arpeggiated by the way.) We hear a 4:3,
which we know is a 4th, unless we're dealing with the
(relatively rare) Hungarian major where one 3rd fits the bill.
Next both notes move inward, which means we are hearing a 2nd.
It is not a 1:1, so the first dyad can not have been a 3rd and
so that mode of the Hungarian major is out. It's a 6:5, and
there is no 4th = 4:3 that can move inward to a 2nd = 6:5 in
the Hungarian major scale. Of the principal scales used in
tonal music, only the harmonic minor and Hungarian minor can
do it. And the Hungarian minor isn't very principal (nor is
it proper). It does have two modes that work almost to the
end of the example, and they both have a dim triad interleaved
with the root minor chord. But at latest, you know it's the
harmonic minor by the time you get to the end. And you know
the odd measures are about the dim7. The same kind of thing
applies to the second example.

-Carl

🔗Mike Battaglia <battaglia01@...>

On Sat, Feb 26, 2011 at 5:05 AM, Carl Lumma <carl@...> wrote:
>
> > or how specifically you propose it should
> > work for something like Cmaj -> Fm.
>
> You understand this progression implies the melodic minor?
> The root of which is Fmin? And that C -> Dmin implies a major
> scale, the root of which is C?

No. I understand that Cmaj -> Fm implies C mixolydian b6, or the
"hindu scale," or whatever you want to call it; C D E F G Ab Bb C, the
root of which is C. Or perhaps it implies C harmonic major, the root
of which is C.

> > 1) Arpeggiating C-E-G leads to a very consonant sound
> > 2) Arpeggiating C-Eb-G leads to a less consonant sound
> > 3) Arpeggiating C-D-E-F-G-A-B-C leads to a very consonant sound
> > 4) Arpeggiating C-Db-Eb-F-Gb-Ab-Bb-C leads to a less consonant
> > sound
> > You seem to be saying that 3HE matters in the first two
> > examples, but that 7HE doesn't matter in the last two. Why?
>
> It's not clear to me HE matters in any of them.

What explanation do you propose for why C-E-G, when arpeggiated,
sounds more consonant than C-Eb-G? What explanation do you propose for
why C-G, when played together after an Eb has been played

> Meanwhile,
> have you noticed a tendency, when I make a direct statement,
> to respond by introducing a new exercise or example which is
> unrelated to my statement?

I've been begging you to make a "direct statement" since this
conversation started. The examples I posted are me trying to interpret
statements like "that this harmony is not present but instead is
signaled through the scalar intervals" the best I can. The examples I
posted are also me advancing a counter-idea when I feel that something
you've said doesn't adequately explain my perception.

> Here are the examples again
>
> C_B__B_B_C
> G_Ab_G_F_Eb
>
> and
>
> F_Eb_Eb_Eb_D
> B_C__B__C__B
>
> The pattern in the first is C D C D C and in the second,
> D C D C D where C = consonant and D = dissonant.

I'm not sure in what sense you'd call the B-D dyad at the end of the
second example "dissonant," but okay.

> Now think of the Rothenberg paradigm: when we hear the first
> dyad in the first example, we try to figure out where it fits
> in one of the scales we know. (All this should work just as
> well with the dyads arpeggiated by the way.) We hear a 4:3,
> which we know is a 4th, unless we're dealing with the
> (relatively rare) Hungarian major where one 3rd fits the bill.

If Hungarian major is C Db E F G Ab B C, I don't see where any of the
thirds are 4/3...

> Next both notes move inward, which means we are hearing a 2nd.
> It is not a 1:1, so the first dyad can not have been a 3rd and
> so that mode of the Hungarian major is out. It's a 6:5, and
> there is no 4th = 4:3 that can move inward to a 2nd = 6:5 in
> the Hungarian major scale. Of the principal scales used in
> tonal music, only the harmonic minor and Hungarian minor can
> do it. And the Hungarian minor isn't very principal (nor is
> it proper). It does have two modes that work almost to the
> end of the example, and they both have a dim triad interleaved
> with the root minor chord. But at latest, you know it's the
> harmonic minor by the time you get to the end. And you know
> the odd measures are about the dim7. The same kind of thing
> applies to the second example.

I'm not sure I'm following this, since I'm not seeing a 4/3 as a third
in either Hungarian major or Hungarian minor. But assuming that the
above analysis applies in some sense to some scale set that you can
narrow down to harmonic minor via scalar logic, I still don't
understand why exactly this explains why the diminished fourth in the
second example sounds dissonant. Are you saying that the diminished
fourth is somehow conceptualized as being a part of the diminished 7
chord, with some kind of extension on it?

-Mike

🔗Carl Lumma <carl@...>

Mike wrote:

>> > work for something like Cmaj -> Fm.
>>
>> You understand this progression implies the melodic minor?
>> The root of which is Fmin? And that C -> Dmin implies a major
>> scale, the root of which is C?
>
> No. I understand that Cmaj -> Fm implies C mixolydian b6,

That is not a tonal mode.

>>> 1) Arpeggiating C-E-G leads to a very consonant sound
>>> 2) Arpeggiating C-Eb-G leads to a less consonant sound
>>> 3) Arpeggiating C-D-E-F-G-A-B-C leads to a very consonant
>>> sound
>>> 4) Arpeggiating C-Db-Eb-F-Gb-Ab-Bb-C leads to a less
>>> consonant sound
>>> You seem to be saying that 3HE matters in the first two
>>> examples, but that 7HE doesn't matter in the last two. Why?
>>
>> It's not clear to me HE matters in any of them.
>
> What explanation do you propose

Why do I have to propose one?

>> Here are the examples again
>>
>> C_B__B_B_C
>> G_Ab_G_F_Eb
>>
>> and
>>
>> F_Eb_Eb_Eb_D
>> B_C__B__C__B
>>
>> The pattern in the first is C D C D C and in the second,
>> D C D C D where C = consonant and D = dissonant.
>
> I'm not sure in what sense you'd call the B-D dyad at the end of the
> second example "dissonant," but okay.
>
>> Now think of the Rothenberg paradigm: when we hear the first
>> dyad in the first example, we try to figure out where it fits
>> in one of the scales we know. (All this should work just as
>> well with the dyads arpeggiated by the way.) We hear a 4:3,
>> which we know is a 4th, unless we're dealing with the
>> (relatively rare) Hungarian major where one 3rd fits the bill.
>
> If Hungarian major is C Db E F G Ab B C, I don't see where any
> of the thirds are 4/3...

________2nds 3rds 4ths 5ths 6ths 7ths 8ths
0.0_____100.0 400.0 600.0 700.0 900.0 1000.0 1200.0
100.0___300.0 500.0 600.0 800.0 900.0 1100.0 1200.0
400.0___200.0 300.0 500.0 600.0 800.0 900.0 1200.0
600.0___100.0 300.0 400.0 600.0 700.0 1000.0 1200.0
700.0___200.0 300.0 500.0 600.0 900.0 1100.0 1200.0
900.0___100.0 300.0 400.0 700.0 900.0 1000.0 1200.0
1000.0__200.0 300.0 600.0 800.0 900.0 1100.0 1200.0

>> Next both notes move inward, which means we are hearing a 2nd.
>> It is not a 1:1, so the first dyad can not have been a 3rd and
>> so that mode of the Hungarian major is out. It's a 6:5, and
>> there is no 4th = 4:3 that can move inward to a 2nd = 6:5 in
>> the Hungarian major scale. Of the principal scales used in
>> tonal music, only the harmonic minor and Hungarian minor can
>> do it. And the Hungarian minor isn't very principal (nor is
>> it proper). It does have two modes that work almost to the
>> end of the example, and they both have a dim triad interleaved
>> with the root minor chord. But at latest, you know it's the
>> harmonic minor by the time you get to the end. And you know
>> the odd measures are about the dim7. The same kind of thing
>> applies to the second example.
>
> assuming that the above analysis applies in some sense to some
> scale set that you can narrow down to harmonic minor via scalar
> logic, I still don't understand why exactly this explains why
> the diminished fourth in the second example sounds dissonant.
> Are you saying that the diminished fourth is somehow
> conceptualized as being a part of the diminished 7 chord,

That is what I've said. Several times.

-Carl

🔗Mike Battaglia <battaglia01@...>

On Sat, Feb 26, 2011 at 1:59 PM, Carl Lumma <carl@...> wrote:
>
> Mike wrote:
>
> >> > work for something like Cmaj -> Fm.
> >>
> >> You understand this progression implies the melodic minor?
> >> The root of which is Fmin? And that C -> Dmin implies a major
> >> scale, the root of which is C?
> >
> > No. I understand that Cmaj -> Fm implies C mixolydian b6,
>
> That is not a tonal mode.

Are you sure?

Even if you buy into this whole tritone hypothesis thing, there's a
tritone lying adjacent to the root.

http://www.youtube.com/watch?v=2Lnltl3YoqQ
http://www.youtube.com/watch?v=8FU-8-noAy0
http://www.youtube.com/watch?v=KgE29oRPhrI
http://www.youtube.com/watch?v=d1tQFX_9ct0

> >> It's not clear to me HE matters in any of them.
> >
> > What explanation do you propose
>
> Why do I have to propose one?

You don't, so now we're gridlocked. And priming is what you, yourself,
have used to explain why C-G sounds minor after Eb has previously been
played. And, offlist, you said that minorness came from chords that
are low in tonalness, which are high in entropy. And arpeggiating
C-Eb-G sounds low in tonalness to me.

> > If Hungarian major is C Db E F G Ab B C, I don't see where any
> > of the thirds are 4/3...
>
> ________2nds 3rds 4ths 5ths 6ths 7ths 8ths
> 0.0_____100.0 400.0 600.0 700.0 900.0 1000.0 1200.0
> 100.0___300.0 500.0 600.0 800.0 900.0 1100.0 1200.0
> 400.0___200.0 300.0 500.0 600.0 800.0 900.0 1200.0
> 600.0___100.0 300.0 400.0 600.0 700.0 1000.0 1200.0
> 700.0___200.0 300.0 500.0 600.0 900.0 1100.0 1200.0
> 900.0___100.0 300.0 400.0 700.0 900.0 1000.0 1200.0
> 1000.0__200.0 300.0 600.0 800.0 900.0 1100.0 1200.0

I see. That isn't the scale I thought you meant by Hungarian Major.
Any time I hear the above scale, my brain immediately turns it into
the octatonic scale, which the above scale is a 7-note subset of.

> > assuming that the above analysis applies in some sense to some
> > scale set that you can narrow down to harmonic minor via scalar
> > logic, I still don't understand why exactly this explains why
> > the diminished fourth in the second example sounds dissonant.
> > Are you saying that the diminished fourth is somehow
> > conceptualized as being a part of the diminished 7 chord,
>
> That is what I've said. Several times.

And diminished 7 chords are dissonant because they are really high in entropy.

-Mike

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

On Sat, Feb 26, 2011 at 5:26 PM, Carl Lumma <carl@...> wrote:
>
> Mike wrote:
>
> > > >> It's not clear to me HE matters in any of them.
> > > >
> > > > What explanation do you propose
> > >
> > > Why do I have to propose one?
> >
> > You don't, so now we're gridlocked.
>
> We're not gridlocked because your ability to come up with
> examples I can't explain doesn't mean anything.

These are just my reservations with your previous explanation. I
thought that you might perhaps have a way to explain those as well, so
I threw them out there. Barring that, I found your ideas interesting
and sought to extend them in a way that explains these
counterexamples.

> > And, offlist, you said that minorness came from chords that
> > are low in tonalness, which are high in entropy.
>
> What I said both on- and offlist is that the 'sadness'
> of 10:12:15 (and approximations thereof) is due to its
> *combination* of both low tonalness and low roughness.

You also said that low tonalness was the same thing as high entropy.
But now you're saying that the sadness of an arpeggiated C-Eb-G vs the
happiness of an arpeggiated C-E-G doesn't stem from HE. Roughness is a
side issue here, as I'd hope you agree that there is definitely no
roughness if you're not playing the notes at the same time!

> > And diminished 7 chords are dissonant because they are really
> > high in entropy.
>
> They are discordant for that reason, yes.

OK, but you're not actually playing the chord. The discordance, in
this case, is coming from you simply imagining that chord, how it fits
into the current notes that are being played, coming to an awareness
of the entire harmonic structure as some kind of "virtual chord" that
you're just imagining, and then assessing how discordant it is. Is
this what you're saying? Because now we're back to HE and priming
again. Maybe we're talking about classical conditioning rather than
priming.

I suppose the difference between this and priming is that priming has
to do with short-term memory, and this has to do with long term
memory, but I still don't see why that should make a difference.

-Mike

🔗Carl Lumma <carl@...>

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

> Roughness is a side issue here,

Why would you say this when I just finished pointing out that
it's critical to the explanation of sadness that you brought up?

> as I'd hope you agree that there is definitely no
> roughness if you're not playing the notes at the same time!

There's no HE either!

> > > And diminished 7 chords are dissonant because they are really
> > > high in entropy.
> >
> > They are discordant for that reason, yes.
>
> OK, but you're not actually playing the chord. The discordance,
> in this case,

dissonance

> is coming from you simply imagining that chord,
> how it fits into the current notes that are being played,
> coming to an awareness of the entire harmonic structure as some
> kind of "virtual chord" that you're just imagining, and then
> assessing how discordant it is.

No. I said it possibly comes from remembering music previously
heard.

> Is this what you're saying? Because now we're back to HE and
> priming again. Maybe we're talking about classical conditioning
> rather than priming.

I don't think priming ever came into the discussion. I sent
you the definition of priming for this reason. I don't see how
classical conditioning is involved either. What about "memory"?

http://www.youtube.com/watch?v=hpjwotips7E

> I suppose the difference between this and priming is that
> priming has to do with short-term memory, and this has to do
> with long term memory, but I still don't see why that should
> make a difference.

You don't see a reason? Well why didn't you say so! There
isn't one then. Not possible. No way, no how. :P

-Carl

🔗Mike Battaglia <battaglia01@...>

On Sat, Feb 26, 2011 at 6:32 PM, Carl Lumma <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > Roughness is a side issue here,
>
> Why would you say this when I just finished pointing out that
> it's critical to the explanation of sadness that you brought up?

Because roughness takes place in the cochlea, and in my examples we're
never playing any of the notes at the same time.

> > as I'd hope you agree that there is definitely no
> > roughness if you're not playing the notes at the same time!
>
> There's no HE either!

HE is something that takes place in the brain. If you play C-G and you
imagine an Eb, it sounds less tonal than if you imagine an E. You
don't need priming to trigger the effect. We spoke about this offlist
and you said you had no problem believing any of this because memories
can weakly reactivate relevant neural pathways or something like that.
Likewise, I believe that remembering, or even just imagining these
notes can influence the way that periodicity processing works. Play a
bare E-Bb dyad, and then imagine that as part of different chords, and
the tonalness of the E-Bb will subtly change.

In fact, let's get even simpler with it: a long time, when we were
talking about periodicity buzz, you posted an example where 1/1 was in
the left ear and 7/4 was in the right ear, and showed us that although
this gets rid of buzz, the general "quality" of the interval is the
same as ever. You used this to "prove" that the periodicity mechanism
was still at work. I'm now doing the same thing with priming, but if
you think that perceptually just checking the quality of the sounds
you hear is a bad way to test these things, then it also invalidates
examples like the one you posted.

> > is coming from you simply imagining that chord,
> > how it fits into the current notes that are being played,
> > coming to an awareness of the entire harmonic structure as some
> > kind of "virtual chord" that you're just imagining, and then
> > assessing how discordant it is.
>
> No. I said it possibly comes from remembering music previously
> heard.

What does remembering music previously heard mean if not remembering
individual chords and such?

> > Is this what you're saying? Because now we're back to HE and
> > priming again. Maybe we're talking about classical conditioning
> > rather than priming.
>
> I don't think priming ever came into the discussion. I sent
> you the definition of priming for this reason. I don't see how
> classical conditioning is involved either. What about "memory"?
>
> http://www.youtube.com/watch?v=hpjwotips7E

I don't have 15 minutes to watch this now, but ok, we'll call it
memory. I'll respond to this when I get a second to watch later on.

> > I suppose the difference between this and priming is that
> > priming has to do with short-term memory, and this has to do
> > with long term memory, but I still don't see why that should
> > make a difference.
>
> You don't see a reason? Well why didn't you say so! There
> isn't one then. Not possible. No way, no how. :P

I never said that there's no possible way it could make a difference,
but if you think that priming can influence HE, but this can't, I'd at
least like to know why.

-Mike