More about superpyth[7] vs meantone[7], a high level account, tonalness, "Concordance Tables"

Uh, back to my original post, which is what I was going to write about
before this whole Pompei thing completely derailed me. Things line up
differently than meantone and in a particularly interesting way.

Let's assume we're in 27-tet for this, because I think that that's
pretty good for superpyth, yes? Go to scala and type mode/equal 5 5 1
5 5 5 1 to load up superpyth ionian.

I think it's proven that every triad class in a MOS comes in three
specific triad sizes assuming the period is the octave. If not, that's
how it seems to be for most MOS's. For meantone, if you look at the
1-3-5 triad class, this scale has the nice property that these three
types of triads are very different in concordance from one another.
Three very obviously perceptually distinct categories of tonalness
emerge from this. This is also part of why I think the scale is so
easy to cognize.

These three categories are generally referred to as "major," "minor,"
and "diminished." The first is very tonal, the middle is semitonal,
and the latter is almost completely non-tonal. The diminished chord is
ONLY non-tonal insofar as it doesn't sound like 5:6:7, which it
doesn't if you double the root in the bass... Bummer.

(In fact, it's such a bummer that diminished chords actually compel
you to wish, on some level, that this harsh, unpleasant sound would go
away. This is part of why it's so nice when it resolves to a
concordant sound. This is probably because the brain doesn't like the
spectrum being flooded with lots of random, uncorrelated periodicity
information while it's trying to figure out what's going on. There are
chords that are even more discordant that will probably have people in
the room asking you to wear headphones, which means their brain is
like "beep boop beep organism take action to remove stimulus." I also
think that the same process happens in attenuated form with minor
chords, and this is... anyway)

So let's see how things are laid out for meantone - a review. Here's
something called a concordance table, which is a generalized version
of those diatonic triad quality charts:

Meantone Diatonic 1-3-5 Triad Class Concordance Table

Degree - Notes - Class - Oddly appropriate emoticon
I - C E G - major - :)
ii - D F A - minor - :|
iii - E G B - minor - :|
IV - F A C - major - :)
V - G B D - major - :)
vi - A C E - minor - :|
viiº - B D F - dim. - >:O

I didn't put 4:5:6 and 10:12:15 in there because I don't think that
10:12:15 or 1/(4:5:6) has anything to do with why minor chords sound
minor. Instead, "minor" refers to a perceptual category in which a
chord is lower in tonalness than an otonality, but not so low that you
want to get rid of it. Someday I'll replace the "oddly appropriate
emoticon" with a measure of harmonic entropy for each of these chords.

OK, the point: in superpyth, everything works out differently. There
are still three interval classes, and we can still call them major,
minor, and diminished, although that might mess people up. The "major"
chord is something like D-A-C, which is 4:6:7, and the "minor" chord
is something like C-G-B, which is 14:21:27. B-F-A is the "diminished"
chord, and who knows what it is. We'll use that terminology.

(Note: what's more consonant - C-G-B in 22-tet, or C-Eb-G in meantone?)

Superpyth Diatonic 1-5-7 Triad Class Concordance Table

Degree - Notes - Class - Oddly appropriate emoticon
i - C G B - minor - :]
II - D A C - major - 8-)!
III - E B D - major - 8-)!
iv - F C E - minor - :]
V - G D F - major - 8-)!
VI - A E G - major - :8-)!
viiº - B F A - dim. - >:O

Wow, that's a lot different! So you have four major chords in this
layout, two minor chords, and one diminished chord. However, you might
notice that the III chord still kind of sounds darker than the other
ones. Let's try the 1-5-7-9 tetrad class table, the "major" chord of
which is 4:6:7:9, and see how that looks. We'll call the classes
"major," "minor," "more minor," and "diminished."

Superpyth Diatonic 1-5-7-9 Tetrad Class Concordance Table

Degree - Notes - Class - Oddly appropriate emoticon
i - C G B D - minor - :}
II - D A C E - major - :)!
III - E B D F - more m.- :|
iv - F C E G - minor - :}
V - G D F A - major - :)!
VI - A E G B - major - :)!
viiº - B F A C - dim. - >:O

I rated the E B D F as more minor sounding than C G B D, because
that's how it sounds to me. Feel free to lay things out your own way
if you see differently. But I think that this is why you're going to
hear E-B-D-E as having more "background dissonance" in that scale than
G-D-F-G, because you'll probably play the F at some point. If you
really avoid it you can probably force the perception of E-B-D-E to
major, just like if you're in meantone C ionian you can force the
perception of B-b-d to minor instead of diminished if you just never
play that F.

In closing, I think that just like folks a thousand years ago couldn't
hear the major third as anything but dissonant - I think that there
are other tonal structures multiplexed into the diatonic scale that we
could be using that we haven't explored. Perhaps if we start playing
around with 4:6:7 chords in superpyth, we can take advantage of new
sounds hidden in the diatonic scale that we aren't properly imagining
right now. At least, that's just my hope.

And I think it'd be worthwhile to find more scales that have
perceptually similar categories too.

-Mike

On Sun, Mar 6, 2011 at 2:10 AM, Mike Battaglia <battaglia01@...> wrote:
>
> In closing, I think that just like folks a thousand years ago couldn't
> hear the major third as anything but dissonant - I think that there
> are other tonal structures multiplexed into the diatonic scale that we
> could be using that we haven't explored. Perhaps if we start playing
> around with 4:6:7 chords in superpyth, we can take advantage of new
> sounds hidden in the diatonic scale that we aren't properly imagining
> right now. At least, that's just my hope.

Also, a quick note to add to this - the four major chords are separate
from one another by fifth. So you have, if we're in C ionian

G 4:6:7
D 4:6:7
A 4:6:7
E 4:6:7

(we really need a generalization of major. Should we just say that a
piece is in the key of C 4:6:7 major?)

Of these, D and A have major IV and V chords. E works if you don't
mind the V chord being half-diminshed, which is kind of a jazzier
sound, since us jazz guys like lots of extensions on our V chords. And
if you're in 22-tet the tritone is actually 11/8, which is nice.

If you're into the tritone hypothesis, A is the tonal "major" system
here and C is the tonal "minor" one. So superpyth aeolian is the
winner. If you're like me and think tonality isn't about scale
structure, then most of these will do as tonal structures of different
feeling and strength.

It's also noteworthy that the subminor third functions in some sense
as an "avoid" note over these 4:6:7 chords in that it forces the
perception of the chord as minor. If you don't mind that, play it. If
you don't like that, be careful of it. Perhaps one thing to do is to
throw some extra 5/4's in where needed to counter that perception, but
to use the superpyth scale as a bare skeleton to start out with. And
then you're doing something similar to all of this modal jazz modern
harmony I keep talking about.

-Mike

On Sun, Mar 6, 2011 at 2:10 AM, Mike Battaglia <battaglia01@...> wrote:
>
> In closing, I think that just like folks a thousand years ago couldn't
> hear the major third as anything but dissonant - I think that there
> are other tonal structures multiplexed into the diatonic scale that we
> could be using that we haven't explored.

Addendum: Ravel got there first. Check out

http://www.youtube.com/watch?v=7vq6hAQJaRA

This video has two pieces stuck back to back; the first one is the one
of interest. It's about 3 minutes long, so give it a listen. The part
I'm referring to specifically is 1:51, where he resolves from Ebm7 ->
Bb9omit3. You'll recognize the part I'm talking about because the
whole thing brings you into some kind of mystical 7-limit trancelike
state.

At this point, the melody sticks to Eb pentatonic minor, which
combined with the below chord puts you in Bb aeolian. The strings
modulate beautifully around within it, so it doesn't strictly stick to
Bb aeolian, but that's the gist. Ravel harmonizes it, however, by
playing a dominant-tempered version of 4:7:9:12, which snaps you back
into "otonal" mode. The effect is completely sublime and chilling and
completely transforms the feel of aeolian mode into something entirely
different. It wouldn't sound "right" if you threw a major third in at
the bottom, turning the chord into 4:5:7:9:12, but it also wouldn't
sound right if you threw the minor third in either. Anything would
completely destroy the feeling of that chord.

So there you go. Lots of hidden higher-limit possibilities hidden in
the diatonic scale after all.

-Mike

On Sat, Apr 23, 2011 at 4:31 AM, Mike Battaglia <battaglia01@...> wrote:
>
> Addendum: Ravel got there first. Check out
>
> http://www.youtube.com/watch?v=7vq6hAQJaRA
>
> This video has two pieces stuck back to back; the first one is the one
> of interest. It's about 3 minutes long, so give it a listen. The part
> I'm referring to specifically is 1:51, where he resolves from Ebm7 ->
> Bb9omit3. You'll recognize the part I'm talking about because the
> whole thing brings you into some kind of mystical 7-limit trancelike
> state.

You know, instead of me just posting into the void all the time, would
it be better if I just threw stuff like this up onto the wiki? Is
there a superpyth page that I can add my above analysis to? I'm not
sure exactly where it should go.

-Mike

Mike wrote:

> You know, instead of me just posting into the void all the time,
> would it be better if I just threw stuff like this up onto
> the wiki? Is there a superpyth page that I can add my above
> analysis to? I'm not sure exactly where it should go.

I would suggest a blog. There are unusually few microtonal
bloggers - Prent, Carlo, and Graham are the only I can
think of. -Carl

On Sat, Apr 23, 2011 at 5:49 PM, Carl Lumma <carl@...> wrote:
>
> Mike wrote:
>
> > You know, instead of me just posting into the void all the time,
> > would it be better if I just threw stuff like this up onto
> > the wiki? Is there a superpyth page that I can add my above
> > analysis to? I'm not sure exactly where it should go.
>
> I would suggest a blog. There are unusually few microtonal
> bloggers - Prent, Carlo, and Graham are the only I can
> think of. -Carl

You've suggested this before, and it's a good idea. I bought
xenaesthetic.com a little while ago, so maybe now's a good time for
it. But I wish I had a way to take my ideas and constructively
organize them into useful information for everyone to read later. The
blog format can be cool, but might be a bit unintelligible to
newcomers.

-Mike

Me too

www.chrisvaisvil.com

-----Original Message-----
From: "Carl Lumma" <carl@...>
Sender: tuning@yahoogroups.com
Date: Sat, 23 Apr 2011 21:49:36
To: <tuning@yahoogroups.com>
Reply-To: tuning@yahoogroups.com
Subject: [tuning] Re: More about superpyth[7] vs meantone[7], a high level account, tonalness, "Concordance Tables"

Mike wrote:

> You know, instead of me just posting into the void all the time,
> would it be better if I just threw stuff like this up onto
> the wiki? Is there a superpyth page that I can add my above
> analysis to? I'm not sure exactly where it should go.

I would suggest a blog. There are unusually few microtonal
bloggers - Prent, Carlo, and Graham are the only I can
think of. -Carl

> You've suggested this before, and it's a good idea. I bought
> xenaesthetic.com a little while ago, so maybe now's a good time for
> it. But I wish I had a way to take my ideas and constructively
> organize them into useful information for everyone to read later. The
> blog format can be cool, but might be a bit unintelligible to
> newcomers.
>
> -Mike

I like the domain. Blogs are an accepted way of building up a useful archive of information from daily inspiration - perfect for you. They aren't as approachable as a book, but people who read blogs have learned skills for approaching them, and several blogs I read have been turned into books by their authors. -Carl

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

> But I wish I had a way to take my ideas and constructively
> organize them into useful information for everyone to read later. The
> blog format can be cool, but might be a bit unintelligible to
> newcomers.

The Wiki format is good for that. Wiki wiki!