Yahoo Tuning Groups Ultimate Backup tuning Functional Harmony -- Meaning and Mechanism

There's been a lot of discussion recently about functional
harmony, tonal music, etc. But what do these terms mean?

They are terms from conventional music theory, so I thought
a bit about what they mean in conventional theory. And it
seems to me that functional harmony is the ability to make
chord changes within a single "key".

A functional progression is a series of chords, each with
its own root pitch, that somehow also gives the impression
of an unchanging global root pitch called the "tonic".
(I say much the same thing in this post from October:
/tuning/topicId_93833.html#93929 )

The term functional __harmony__ in fact implies a melody,
which is harmonized with a functional chord progression.
"Tonal music", then, will be music with functional harmony.
So it's

functional progression -> functional harmony -> tonal music

~ Part 2: Mechanism ~

Harmonic entropy tells us that some chords inherently sound
more rooted than others. But it's not clear that any chord
is absolutely excluded from having a root.

But OK, we at least have some idea what a chord root is.
The more mysterious thing is the global tonic. What causes
a chord progression to have one? I don't know.

If I have a chord progression where the intersection of
chords' pitch classes contains only one element, that's an
obvious candidate. Any progression of three or more chords
from a tonality diamond will have this property. But the
intersection of I-IV-V-I is empty.

A composer can use repetition to emphasize a pitch class.
But the great Romantic sonatas are known for not doing
this, and in fact for maintaining key centers despite
protracted "excursions", repeating notes other than the
tonic, avoiding the tonic, etc.

Maybe it's more of a melodic thing. If we know the scale
being used, we can assign scale degrees to pitches we hear
by recognizing melodic intervals. There are two basic
ways to recognize them: by absolute size or relative size.
Absolute size is like, "I know that's 700 cents". If you
can recognize by absolute size you can always find your
place in any scale you know. If you can only recognize by
relative size, the scale must be Rothenberg-proper.

Let's assume that one way or the other you can map scale
degrees to the pitches you're hearing. But which pitch is
degree #1? This is the same as asking what mode the music
is in, and the same as knowing which pitch is the tonic.

If society just arbitrarily picks a standard -- one mode
that is the only possible tonic mode -- that would do it.
Of course it's necessary that the modes of the scale be
different! 6-ET won't work. Here's a matrix showing its
modes as rows, with intervals in relative sizes:

1 2 3 4 5 6
1 2 3 4 5 6
1 2 3 4 5 6
1 2 3 4 5 6
1 2 3 4 5 6
1 2 3 4 5 6

This is also called the ROM (rank-order matrix) for 6-ET.
Since every mode is the same, there's no way to find the
one you agreed on! So tonal music in this scale would be
impossible if the 'melodic origin' hypothesis is right.
Here's the ROM for the diatonic scale in 12-ET:

2 4 5 7 9 11 12
2 3 5 7 9 10 12
1 3 5 7 8 10 12
2 4 6 7 9 11 12
2 4 5 7 9 10 12
2 3 5 7 8 10 12
1 3 5 6 8 10 12

Here every mode is different, so you're in business.
Though Rothenberg pointed out they're still very similar.
There are many pairs that different in only 1 or 2 spots.
So it's possible for a given stretch of music to be
tonally ambiguous. For example, what mode is 1-3-8-3-10?
Rothenberg thought this is what allowed Romantic sonatas
to play those tricks.

Of course classical tonality had two modes in the flop --
ionian and aeolian. Composition was used to signal which
mode was intended. Starting chord was probably the big
one. If it started on a major chord, it was ionian.
Minor chord, aeolian. For whatever reason(s), a variety
of scale substitutions were possible in minor pieces.
The root of the starting chord was still to be the tonic.

Is any of this melodic stuff even necessary then? Why not
simply, "The root of the first chord"?

I have no idea. And I'm sure there are other possible
explanations I haven't considered. To the extent jazz is
tonal, it seems any mode is acceptable, so perhaps there
are compositional signals there. Maybe Mike and other jazz
experts can weigh in on how that works. Is it just the
starting chord? Do chromatic notes in the extended chords
provide signals?

Well this is pretty long, so I'll stop here.

-Carl

🔗Mike Battaglia <battaglia01@...>

On Fri, Apr 29, 2011 at 4:04 PM, Carl Lumma <carl@...> wrote:
>
> If I have a chord progression where the intersection of
> chords' pitch classes contains only one element, that's an
> obvious candidate. Any progression of three or more chords
> from a tonality diamond will have this property. But the
> intersection of I-IV-V-I is empty.

What do you mean? The intersection of Cmaj -> Fmaj -> Gmaj is C.

> A composer can use repetition to emphasize a pitch class.
> But the great Romantic sonatas are known for not doing
> this, and in fact for maintaining key centers despite
> protracted "excursions", repeating notes other than the
> tonic, avoiding the tonic, etc.

If this is what you want, then I'd have thought you'd be happy with
the functional excerpt I posted, where I basically modulate out into
porcupine-space for a bit with some secondary dominants, and then
ultimately land on the IV chord where I then move back home. I
certainly wouldn't say it's not functional. Likewise, I wouldn't say
that Cmaj -> C#dim -> D7 -> G7b9 -> Cmaj in meantone isn't functional.
But I wouldn't say that it doesn't stick to the Ionian mode.

I think that it doesn't satisfy you because you're not just looking
for functional harmony, which is based on the concept of there being
such a thing as a "resolution." The evolved version of a "resolution"
is a sense of "key," but furthermore, I don't think you're just
looking for that either. I think you're looking for a harmonization of
"tonality" and "modality," which is what the diatonic scale does. The
diatonic scale provides all kinds of resolutions and key centers, but
also gives a sense of "mode," e.g. gives the impression that certain
chord qualities "belong" over certain roots, and that the chords that
are set up this way are mainstays to the diatonic scale.

That means that when you're in major, you're predominantly using the
IV chord, not the iv chord. And you're using the ii and iii chords,
not the II and III chords. You might use those other chords sometimes,
but they mainly serve as points of departure to spice up the blandness
of vanilla diatonic harmony. If you use secondary dominants like V7/ii
and V7/iii, they'll generally resolve to ii and iii, not II and III.
So you get the sense of ii and iii being these old friends of the
diatonic scale, and the whole thing becomes sensible in a way. This is
why I say that Dorian has a certain sound, that Phrygian has a certain
sound, and why I keep linking to all of these 90s rock groups as
examples of these sounds - because if you're in Dorian, one of the
mainstays is the IV7 chord, and if you're in Phrygian, one of the
mainstays is the bII chord. This creates the "sound" of that mode.
These sounds were never explored in common practice music, but they
have been pretty deeply explored in the last century.

So my chord progressions with porcupine lacked the feeling of there
being some novel, original, xenharmonic porcupine "sound." They
weren't an attempt to make one, just an attempt to modulate around the
lattice and see if I could make the whole thing sound predictable, but
avoid 81/80 pumps. Petr's examples, on the other hand, stick more
closely to porcupine[8], but sometimes I wish there were V-I's in
certain cases where he uses v-I's. He doesn't want to do that because
he's trying to limit the size of the chain of generators as much as
possible (which means that chromatically altering intervals is an
unattractive option). A middle path here is to stick to porcupine[8]
and alter things sometimes to increase the strength of the
resolutions, which is what we historically did with the minor scale.
We didn't "learn to hear v-i as a strong resolution," we just changed
it.

> Here every mode is different, so you're in business.
> Though Rothenberg pointed out they're still very similar.
> There are many pairs that different in only 1 or 2 spots.
> So it's possible for a given stretch of music to be
> tonally ambiguous. For example, what mode is 1-3-8-3-10?
> Rothenberg thought this is what allowed Romantic sonatas
> to play those tricks.

What does 1-3-8-3-10 signify? Why does 3 appear twice?

> Of course classical tonality had two modes in the flop --
> ionian and aeolian. Composition was used to signal which
> mode was intended. Starting chord was probably the big
> one. If it started on a major chord, it was ionian.
> Minor chord, aeolian. For whatever reason(s), a variety
> of scale substitutions were possible in minor pieces.
> The root of the starting chord was still to be the tonic.

I don't know why you always say aeolian here, when V-i completely
dominates v-i in terms of the frequency of use in minor. I'd say that
harmonic minor is more common than aeolian. Or really, what I'd say is
that minor is a certain concept, and that the concept lends itself in
meantone to three parallel minor scales, which we've picked for the
sake of keeping things Rothenberg proper and sized at 7 notes. If we
were in dicot, those three would be tempered to one scale, so you
wouldn't need parallel natural/melodic/harmonic minor scales.
Likewise, in porcupine, if you're trying to play in something similar
to common practice "major," you'd end up needing parallel
natural/melodic/harmonic major scales, which I laid out in one of my
previous posts. However, in meantone, or mavila, you only need one.

-Mike

🔗Mike Battaglia <battaglia01@...>

On Fri, Apr 29, 2011 at 4:04 PM, Carl Lumma <carl@...> wrote:
>
> I have no idea. And I'm sure there are other possible
> explanations I haven't considered. To the extent jazz is
> tonal, it seems any mode is acceptable, so perhaps there
> are compositional signals there. Maybe Mike and other jazz
> experts can weigh in on how that works. Is it just the
> starting chord? Do chromatic notes in the extended chords
> provide signals?

Sorry, missed this. If, say, you want to create a tonicized Dorian,
just use chords that happen to be mainstays of Dorian instead of
mainstays of Aeolian. This means that instead of going to the bVI, go
to the IV or the IV7 chord. But the point is that doing so doesn't
mean that you have to limit yourself to only the notes in Dorian -
they certainly didn't with Aeolian. If you ever do want a strong
resolution back to the I chord, feel free to temporarily raise the 7
so you can play a proper V7 chord. Or you can cheat and use something
like Gmaj6/A as a V chord which resolves to Dm9. The end result is you
still get the feeling of being in D minor, but you come to understand
that the Gmaj is a mainstay of the scale you're at, so that when you
move to Gm (which would be Aeolian) it sounds like a modulation.

Maybe some history would be useful. There are a lot of different
styles of extended 20th century harmony, but in terms of the
Gershwin->Cole Porter->Standards->Bebop axis, which is where most of
this started, chromatic signaling is a huge part of it. The basic unit
of chromatic signaling in jazz is the "2-5" progression, which you'd
more formally notate as iim7->V7 (-> Imaj7). So you play ii-V and it
causes you to expect a I. If you want to imply minor, you'd go iim7b5
-> V7b9 -> i. So in that sense, you can still think of it as just
using borrowed progressions from major and harmonic minor, which is
how the whole thing started. This is kind of what I was trying to do
with the porcupine examples, just use ii-V's all over the place so
that I can follow it mentally, but have the whole thing end up
differently than it would in meantone. Except instead of ii-V's, I
just used secondary dominants to make it sound more common practice-y.
There's also ivm7->bVII7->Imaj7, i.e. Fm7 -> Bb9 -> Cmaj7, which you
could say is loosely based around ascending melodic major. This is
also how Giant Steps works - ii-V-I's moving up in major thirds. Then
they'd just add higher-limit extensions over whatever they wanted, but
since the basic root of it is still built on meantone comma pumps and
ii-V-I's (or just V-I's), the whole thing still sounds like it makes
sense, which is what I was trying to get at with my higher-limit
porcupine example.

So effective is this trick that bebop musicians ran it completely into
the ground. People started to get really tired of it, and expanded on
the approach with the whole "modal jazz" thing. Bill Evans really
helped to make this happen by influencing Miles' playing on Kind of
Blue, and Evans is known for his use of introducing impressionistic
harmony. At first, they mainly used drones, which didn't do much in
the way of functional harmony, but was a good way to get everyone to
familiarize themselves with having different mainstay chords for the
tonic they're in. Then they started to move around more
(http://www.youtube.com/watch?v=NrP7KI6--2c), so that suddenly you
start to hear things where instead of there being chord progressions,
there are "mode progressions," different mainstay modes and ones that
are further out, which might be just another way of saying we started
to get familiar with really extended harmony. They were already kind
of doing this with bebop by reharmonizing every chord they played, but
it really took off here. Wayne Shorter, Herbie Hancock, etc, all did
lots of great work here (http://www.youtube.com/watch?v=fvRkGglLe-U).

This is when everything forks off, and I can't give you as clear a
picture. Certain aspects of this movement jumped over into pop music,
so that we started seeing more extended harmonies everywhere, where
I'd have to say that R&B and neo-soul ended up dominating that
concept. Progressive rock folks got down on it too, and it stopped
being about "jazz." Electronic musicians and hip hop artists, who
generally have to repeat the same musical fragment for 5 minutes in a
row, had to make sure their loops were as interesting as possible, so
they'd use modes all the time. Metal groups would use Phrygian and
Locrian a lot. Meanwhile, in jazz, the whole thing kept continuing,
reaching a peak with albums like In a Silent Way, where things resolve
for reasons that I can't explain, and I think they stumbled on
something completely different. Then things got kind of crappy during
the fusion era (still plenty of modal writing though), and we're now
seeing a resurgence of lots of interesting ideas.

So that should give you some context in how to look at this stuff.
There are lots, and lots, and lots of harmonic concepts to be derived
from the modal exploration. What you're looking for is someone who
modulates out for a while and then comes back in an emphatically
"Dorian" sound, and you're not going to find that, because while jazz
and pop musicians were doing all of this, the classical world was
stuck in a perpetual serialist loop. Steve Reich brought a lot of the
sound back, although not in a way that resolves. At one point I wanted
to write a series of fugues in every mode, but never did, since I
decided microtonal music was more interesting. So for now, you're
going to be limited to proof chord progressions that repeat every two
bars when you try to find examples of much of it. But it does prove
that harmony is bigger than major and minor.

-Mike

🔗Carl Lumma <carl@...>

--- Mike Battaglia <battaglia01@...> wrote:

> > If I have a chord progression where the intersection of
> > chords' pitch classes contains only one element, that's an
> > obvious candidate. Any progression of three or more chords
> > from a tonality diamond will have this property. But the
> > intersection of I-IV-V-I is empty.
>
> What do you mean? The intersection of Cmaj -> Fmaj -> Gmaj
> is C.

Where's the C in Gmaj?

> > A composer can use repetition to emphasize a pitch class.
> > But the great Romantic sonatas are known for not doing
> > this, and in fact for maintaining key centers despite
> > protracted "excursions", repeating notes other than the
> > tonic, avoiding the tonic, etc.
>
> If this is what you want, then I'd have thought you'd be
> happy with the functional excerpt I posted, where I basically
> modulate out into porcupine-space for a bit with some
> secondary dominants, and then ultimately land on the IV
> chord where I then move back home. I certainly wouldn't
> say it's not functional.

I didn't say I wanted it, I gave it as a counterexample to
the notion that repetition is necessary for functionality.
I liked your example quite much and don't yet have an
opinion whether it's functional.

> I think that it doesn't satisfy you because you're not just
> looking for functional harmony,

I'm not looking for anything. Just chatting about the
idea of functional harmony.

> > Here every mode is different, so you're in business.
> > Though Rothenberg pointed out they're still very similar.
> > There are many pairs that different in only 1 or 2 spots.
> > So it's possible for a given stretch of music to be
> > tonally ambiguous. For example, what mode is 1-3-8-3-10?
> > Rothenberg thought this is what allowed Romantic sonatas
> > to play those tricks.
>
> What does 1-3-8-3-10 signify? Why does 3 appear twice?

It's a melody fragment in the diatonic scale. In the key
of C, it could be either

E F G C G D or B C D G D A

-Carl

🔗Mike Battaglia <battaglia01@...>

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> Harmonic entropy tells us that some chords inherently sound
> more rooted than others. But it's not clear that any chord
> is absolutely excluded from having a root.

This is one of the reasons where I think looking at things in terms of ratios gets confusing. Take the triads 4:5:6, 6:7:9, 10:12:15, and 14:18:21, where the lowest note of each chord is the same pitch (say an "A" of 440 Hz). They all are said to "point" to a different 1/1, but in actual practice, they all sound like "A" chords. I mean, if you play E-G-B in a superpyth temperament, you're not going to "hear it" as "A9(no root, no 3)" or whatever.

> But OK, we at least have some idea what a chord root is.
> The more mysterious thing is the global tonic. What causes
> a chord progression to have one? I don't know.

I think you're making a mistake in thinking that there is a "global tonic" that is constantly in the background of every chord functional progression. The fact that modulations are possible at all suggests to me that you can depart from any point in an unresolved chord progression and find a path that will let you resolve to any consonant triad. Some chords may require a more circuitous route than others to make you feel them as a tonic, but the point is that until the chord progression is "finished", the tonic is undefined. I mean, you can go hog-wild with all sorts of borrowed chords and secondary dominants and what-have-you, but as long as you come back to a strong resolution like a V-I or V7-I or V-i or something, whatever chord that resolution drops you onto is more likely than not going to feel like a "tonic". Tritone subs are good too, like F7-Emaj...heck, it might all come down to the leading-tone, for all I know. That would explain why V-i is stronger than v-i.

I feel this all the time in Blackwood[10]. According to Rothenbergian ideas, there shouldn't be a tonal center, but really, there are at least 5 "potential" tonal centers (maybe 10, haven't done much work with minor resolutions yet). Why? Because every major triad can extend to both a major 7th AND a dominant 7th, and also has another major triad a fifth above it and a fifth below it. So you can do a V7-I resolution to any major triad, and guess what? It works every time, especially with appropriate tension-building set-up. Moreover, it doesn't matter at all what chord you start the piece on, since there are natural progressions in Blackwood[10] that almost feel like modulations.

On the other hand, 7-EDO doesn't feel atonal to me, either, and I concur with Mike that I hear some crazy auditory illusions when playing "normal" progressions like I-vi-ii-V-I in 7-EDO, such that I hear majors and minors where there are only neutrals, and still get a sense of the I being the tonic, despite the lack of a leading-tone.

I hate to say this, but I think even 6-EDO can be tonal and functional. Maybe not to as large an extent as the larger EDOs, but noodling around in it right now I keep finding little motifs that lead me to a note that feels "resolved".

Thus, my hypothesis about "tonality" and "functionality" is that they are not inherent properties of scales (although there may be scales that are inherently atonal), but are sensations created by specific types of chordal or melodic motion. It's not the whole chord progression that creates the sense of tonality, but the resolution at the end. That's my best guess at what makes Mike's porcupine example work, what makes jazz work, what makes my own microtonal music work. But even if I'm right about this, there's still a lot of unanswered questions.

-Igs

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

I'm glad I was lazy in responding to Igs' last email, because it looks
like we're on the same page after all:

On Fri, Apr 29, 2011 at 7:32 PM, cityoftheasleep
<igliashon@...> wrote:
>
> > But OK, we at least have some idea what a chord root is.
> > The more mysterious thing is the global tonic. What causes
> > a chord progression to have one? I don't know.
>
> I think you're making a mistake in thinking that there is a "global tonic" that is constantly in the background of every chord functional progression.

I agree, I think it's more like if you ever do come back to the tonic,
it just sounds familiar. You don't need your childhood home to be in
the background of your life constantly to feel refreshed when you go
back to it. Familiarity is the concept. The entire concept is based
around a clever manipulation of long-term memory to somehow create
pleasure.

> The fact that modulations are possible at all suggests to me that you can depart from any point in an unresolved chord progression and find a path that will let you resolve to any consonant triad. Some chords may require a more circuitous route than others to make you feel them as a tonic, but the point is that until the chord progression is "finished", the tonic is undefined.

Agreed, although many people have played around with the shared
expectations of their audience to imply a tonic based on what folks
have learned. Such movements tend to be transient and get superceded
by periods of harmonic expansion. I also think this is why folks seem
to differ in their perception of ||: Gm7 -> C7 :||, which to me sounds
like a stereotypical Carlos Santana progression in G dorian, but to
many seems to imply Fmaj is coming up.

> I mean, you can go hog-wild with all sorts of borrowed chords and secondary dominants and what-have-you, but as long as you come back to a strong resolution like a V-I or V7-I or V-i or something, whatever chord that resolution drops you onto is more likely than not going to feel like a "tonic". Tritone subs are good too, like F7-Emaj...heck, it might all come down to the leading-tone, for all I know. That would explain why V-i is stronger than v-i.

I thought it was the leading tone as well, but see my last post about
using sines and awkward voice leading - still sounds stronger.

> On the other hand, 7-EDO doesn't feel atonal to me, either, and I concur with Mike that I hear some crazy auditory illusions when playing "normal" progressions like I-vi-ii-V-I in 7-EDO, such that I hear majors and minors where there are only neutrals, and still get a sense of the I being the tonic, despite the lack of a leading-tone.

I think Knowsur gave a good clue as to how this works:

http://soundcloud.com/knowsur/haneru

Do you hear this as predominantly being "minor?" I'm not talking about
dorian vs aeolian vs etc, I'm asking if the tonic triad to you sounds
like it's major or minor. I hear it as being minor.

In 7-tet notation, the melody that comes in on the bell-like
instrument is B E D G C, G F C B, E, G

Note that B-E-G is a dicot-tempered 3:4:5, which when you put it over
C becomes a Cm7 chord, and that's exactly how I hear it. Furthermore,
he keeps playing this figure, constantly reinforcing this perception.
So the big picture to me is that

1) B-E-G clues you into 3:4:5
2) Harmonic Entropy leaves the scene and learned factors come into it
3) HE sends the "3:4:5" cue on down the line, and we have some kind of
learned system of logic to figure out what 3:4:5 means in this
context, with the bass note going on, etc.
4) Whatever those cues are somehow end up cluing us into hearing it as minor
5) We can argue about what percentage of the cues are psychoacoustic,
and what percentage are based in learning, but that's beside the point

> Thus, my hypothesis about "tonality" and "functionality" is that they are not inherent properties of scales (although there may be scales that are inherently atonal), but are sensations created by specific types of chordal or melodic motion. It's not the whole chord progression that creates the sense of tonality, but the resolution at the end. That's my best guess at what makes Mike's porcupine example work, what makes jazz work, what makes my own microtonal music work. But even if I'm right about this, there's still a lot of unanswered questions.

A lot of it has to do with comma pumps, which enable you to leave the
tonic in one direction and come back to it from another. All of
western music makes use of this. For example:

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

Merry Christmas. The chords are

Emaj -> Amaj -> F#maj -> Bmaj -> G#maj -> C#m -> Amaj Bmaj -> Emaj

OK, so the first thing that happens is that this chord progression
takes us straight into hyperspace, building a huge sense of tension as
you eventually get to that C#m. Then, finally, it goes C#m -> Amaj
Bmaj -> Emaj, resolving the tension and bringing us back home! Yes!

Sounds good, doesn't it? Well guess what? It only works because 81/80
vanishes. The whole thing makes no sense in JI, and you end up 81/80
down from the root. So the entire building of tension -> climax ->
coming back to the tonic via a different route only works because of
the comma pump. In fact, the entire concept IS a comma pump. How the
hell are you going to ever come back to the tonic via a different
route than you departed if we're in JI, where nothing is tempered
together?

If what people want from tonality is a sense of departure and return,
or expectation and fulfillment, they really want comma pumps. This is
what Petr seems to have figured out, but I don't know why it's not
being screamed on here like a basic tenet of regular mapping theory.
It pretty much explains all of common practice music. Thus ends my
report.

OK, one last footnote before my report really ends: what about father,
where the generators themselves are tempered together? I don't know.
As we've seen, there are these cognitive cues that clue you into
hearing tempered intervals one way vs the other. I'd say that the
concept of starting with a protoharmonic JI lattice, which you then
temper to create comma pumps, all takes place after these cues have
kicked in. So if you're playing a just 16/11, but for some reason you
were cued into hearing it as a 3/2, then as far as you're concerned,
it IS a tempered 3/2, and you should treat it that way accordingly on
the lattice. So in father, if you're treating it as a 5-limit
temperament, I'd still say there are 3 axes - 5/4, 3/2, and 2/1 - but
that it takes some trickery to get you to actually hear things as
moving vs the 5/4 axis vs the 4/3 axis. What this trickery is, I don't
know. I assign the job of figuring that out to you.

-Mike

🔗Carl Lumma <carl@...>

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Igs wrote:
>
> > I think you're making a mistake in thinking that there is a
> > "global tonic" that is constantly in the background of every
> > chord functional progression.
>
> Er, I didn't say there had to be one for each piece, or anything
> of the kind.

You said:

> The more mysterious thing is the global tonic. What causes
> a chord progression to have one? I don't know.

I didn't say anything about a "piece". If what I said wasn't clear, I'll rephrase it: I don't think functional chord progressions have a "global tonic". Put it this way: the tonic of a chord progression is indeterminate until the progression reaches a point of resolution and is "finished"; an unfinished chord progression always has the potential to modulate and thus change the tonal center. You can't definitively give the key of a chord progression until its finished, and I think it's a mistake to retroactively apply the final tonic to the whole progression as if the suggestion of that tonic was always somehow present in the progression.

> I can go V-I all day long, I don't think that necessarily
> produces tonal music. What did you make of Petr's
> Among Other Things example?

Haven't heard that example, I must have missed the post where it was linked to. But in any case you very definitely *can* make tonal music with just a V-I, or even better a V-i. One of my old friends in Santa Cruz, a gifted pianist (among his many other talents), could do more with those two chords than a lot of musicians can do with twelve. I didn't even realize so many of his songs were just two chords over and over again until I tried to figure them out on guitar. Granted, it was his melodies that made it work, but in any case V-I over and over on its own may get boring, but it's tonal. Or, hey..."Take a Walk on the Wild Side", it's just IV-I over and over again.

Why the idea of tonality seems so confusing is maybe because it's possible to go so far out over the course of a progression and yet still have a single tonic chord feel like "home", and you're trying to look at all those "middle" chords for some kind of pattern (or patterns) that explains why the tonic can still feel like "home" at the end of the progression. But I don't think those middle chords have anything at all to do with creating or maintaing the sense of tonic, except insofar as they build tension and prepare you for the resolution. The resolution is the only part of the progression that really "cements" the feeling of the tonal center, so if we can come to understand how and why different resolutions work, that should be enough. Not that that's at all going to be easy...

-Igs

🔗Graham Breed <gbreed@...>

On 30 April 2011 08:21, cityoftheasleep <igliashon@...> wrote:

> I didn't say anything about a "piece". If what I said wasn't clear, I'll rephrase it: I don't think functional chord progressions have a "global tonic". Put it this way: the tonic of a chord progression is indeterminate until the progression reaches a point of resolution and is "finished"; an unfinished chord progression always has the potential to modulate and thus change the tonal center. You can't definitively give the key of a chord progression until its finished, and I think it's a mistake to retroactively apply the final tonic to the whole progression as if the suggestion of that tonic was always somehow present in the progression.

I think Carl's right, in that there's a sense of sense of key center.
The tonic isn't indeterminate until the resolution. The listener
expects it to resolve a certain way. Experiments have verified this
-- you can halt a progression and ask people how they expect it to
finish, or play two chords and ask which is correct. Most people
agree in a very clear way that agrees with music theory.

Yes, it's possible to surprise the listener by resolving in a
different way to what they expect, but to do that you're playing with
a very real expectation. It's like the punchline to a joke. It
wouldn't work if it wasn't a surprise.

There's a book by Krumhansl that covered the scientific understanding
of all this. It isn't a simple business. There are some innate
components to it, but it's also about learned scales and harmonic
patterns. Most of the time there is a sense of key. In a modulation,
you have to make the key ambiguous, and then clarify it in a different
way to how you started.

I remember a good example from rec.music.theory. Unfortunately, I
don't remember the details, like the name of the song. But, it's a
famous song, by a mainstream band, and the tonic is never stated in
the chorus (I think) until the resolution. Still, it's clear what the
key is. So the sense of key isn't only about remembering the first
chord, or one chord or note being repeated more than others.

Graham

🔗Carl Lumma <carl@...>

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:

> I didn't say anything about a "piece". If what I said wasn't
> clear, I'll rephrase it: I don't think functional chord
> progressions have a "global tonic".

Ok, sorry I misunderstood.

> Put it this way: the tonic of a chord progression is
> indeterminate until the progression reaches a point of
> resolution and is "finished"; an unfinished chord progression
> always has the potential to modulate and thus change the
> tonal center.

If this is true, how could it be possible to finish a
progression on the 'wrong' chord (even if the last two
chords are major chords separated by a 3:2)? Because
it is possible.

> You can't definitively give the key of a chord progression
> until its finished,

It certainly flies in the face of what they taught me in
school. I mean, they don't teach you to start at the last
chord, label it "I" and work backward.

> > I can go V-I all day long, I don't think that necessarily
> > produces tonal music. What did you make of Petr's
> > Among Other Things example?
>
> Haven't heard that example, I must have missed the post
> where it was linked to. But in any case you very definitely
> *can* make tonal music with just a V-I, or even better a V-i.

I can make it without those too.

-Carl

🔗Carl Lumma <carl@...>

Igs wrote:

> > Haven't heard that example, I must have missed the post
> > where it was linked to.

Sorry, it's here:
/tuning/topicId_98428.html#98707
(he's talking about the 2nd link)

Igs also wrote:

> I feel this all the time in Blackwood[10]. According to
> Rothenbergian ideas, there shouldn't be a tonal center, but
> really, there are at least 5 "potential" tonal centers
> (maybe 10, haven't done much work with minor resolutions yet).
[snip]
> you can do a V7-I resolution to any major triad, and guess
> what? It works every time,

You may be right. In my original, I do express doubt
about the melodic origin hypothesis.

> On the other hand, 7-EDO doesn't feel atonal to me, either,
> and I concur with Mike that I hear some crazy auditory
> illusions when playing "normal" progressions like
> I-vi-ii-V-I in 7-EDO, such that I hear majors and minors
> where there are only neutrals, and still get a sense of
> the I being the tonic, despite the lack of a leading-tone.

I can hear 7-ET this way too. It may be a case of 7-ET
supporting the diatonic mapping - h[7] as I think Gene used
to call it - which we already know.

6-ET is one I have some practice with. I'm not going to
say functional progressions are impossible, but the scale
certainly does seem more suited to floaty type stuff than
the diatonic scale, even if we're just talking melody.
Ditto the octatonic scale (which, like blackwood[10], has
two types of modes). But the octatonic scale and
blackwood[10] can sound Petr-functional with chord
progressions that suit.

-Carl

🔗Carl Lumma <carl@...>

Mike wrote:

> Sorry, missed this. If, say, you want to create a tonicized
> Dorian, just use chords that happen to be mainstays of Dorian
> instead of mainstays of Aeolian. This means that instead of
> going to the bVI, go to the IV or the IV7 chord. But the
> point is that doing so doesn't mean that you have to limit
> yourself to only the notes in Dorian - they certainly didn't
> with Aeolian. If you ever do want a strong resolution back to
> the I chord, feel free to temporarily raise the 7 so you can
> play a proper V7 chord.

OK thanks. It seems like you're agreeing here than the
'chords of the mode' are important. I have no problems with
substitutions. If the basic skeleton is coming from the mode,
something like the 'melodic origin hypothesis' might be
at work.

> Or you can cheat and use something
> like Gmaj6/A as a V chord which resolves to Dm9. The end result
> is you still get the feeling of being in D minor, but you come
> to understand that the Gmaj is a mainstay of the scale you're
> at, so that when you move to Gm (which would be Aeolian) it
> sounds like a modulation.

Hey, have I been misunderstanding you all along? It seems
you're saying Gmin signals D aeolian because Bb isn't
in D dorian.

> in terms of the Gershwin->Cole Porter->Standards->Bebop axis,
> chromatic signaling is a huge part of it. The basic unit of
> chromatic signaling in jazz is the "2-5" progression, which
> you'd more formally notate as iim7->V7 (-> Imaj7). So you
> play ii-V and it causes you to expect a I. If you want to
> imply minor, you'd go iim7b5 -> V7b9 -> i.
> So in that sense, you can still think of it as just using
> borrowed progressions from major and harmonic minor,
> which is how the whole thing started.

Thanks! I wish I'd paid better attention to my jazz teacher.
I learned to read fake book (a bit) but not really the theory
behind it.

It still seems here like this is consistent with the kind of
thing I've been chatting about.

> There's also ivm7->bVII7->Imaj7, i.e. Fm7 -> Bb9 -> Cmaj7,
> which you could say is loosely based around ascending melodic
> major. This is also how Giant Steps works - ii-V-I's moving
> up in major thirds. Then they'd just add higher-limit
> extensions over whatever they wanted, but since the basic
> root of it is still built on meantone comma pumps and ii-V-I's
> (or just V-I's), the whole thing still sounds like it makes
> sense, which is what I was trying to get at with my
> higher-limit porcupine example.

The 'extensions' version is by far my favorite. I'm not
sure what to make of that. I guess I've always said I expect
higher-limit extensions of diatonic harmony to be a hugely
fertile direction. Jules Siegel is the example I've always
thought of (if you remember "Calliope"). And George Secor.

> People started to get really tired of it, and expanded on
> the approach with the whole "modal jazz" thing. Bill Evans
> really helped to make this happen by influencing Miles'
> playing on Kind of Blue, and Evans is known for his use of
> introducing impressionistic harmony. At first, they mainly
> used drones, which didn't do much in the way of functional
> harmony, but was a good way to get everyone to familiarize
> themselves with having different mainstay chords for the
> tonic they're in.

Hm! Bebop is my favorite jazz. I never took much to
Kind of Blue. Maybe I'm detecting a pattern!

> Then they started to move around more
> (http://www.youtube.com/watch?v=NrP7KI6--2c), so that
> suddenly you start to hear things where instead of there
> being chord progressions, there are "mode progressions,"
> different mainstay modes and ones that are further out,
> which might be just another way of saying we started
> to get familiar with really extended harmony. They were
> already kind of doing this with bebop by reharmonizing
> every chord they played, but it really took off here.

Wow, I enjoyed Freddie Hubbard in high school for the
trumpet playing. But I think this is the first time I'm
listening to the chords! Pretty nice, and definitely
modal I would say.

> Wayne Shorter, Herbie Hancock, etc, all did lots of
> great work here (http://www.youtube.com/watch?v=fvRkGglLe-U).

My jazz teacher in college made me get Speak No Evil.
I never liked it much and I must say it's not doing a whole
lot for me right now either.

> This is when everything forks off, and I can't give you as
> clear a picture. Certain aspects of this movement jumped
> over into pop music,

I always think of Miles and Herbie that way, actually.
I like Miles' electric stuff much better than Kind of Blue,
but still not as much as bebop.

> What you're looking for is someone who modulates out for a
> while and then comes back in an emphatically "Dorian" sound,
> and you're not going to find that, because while jazz and pop
> musicians were doing all of this, the classical world was
> stuck in a perpetual serialist loop. Steve Reich brought a
> lot of the sound back, although not in a way that resolves.

Wait, why won't I find something that goes way out and comes
back to end on Dorian? Do you mean because pop musicians
don't write long things, and classical musicians normally
would but were screwing with atonal serialism?

> At one point I wanted to write a series of fugues in every
> mode, but never did, since I decided microtonal music was
> more interesting.

Have you heard Shostakovich's 24 preludes and fugues? They
often have flip abruptly back and forth between modal and
tonal, often with the same themes. A perfect laboratory for
this stuff in fact!

My favorite by far is #17 in Abmaj, which I consider among
the best fugues ever written. It's in 4 voices, 5/4 time,
and harmonizes the theme with itself in augmentation.
I tried to learn to play it, made it through the first
three entrances and got slaughtered. It may not be the best
modal/tonal flipping example in the set though.

-Carl

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

On Sat, Apr 30, 2011 at 3:33 AM, Carl Lumma <carl@...> wrote:
>
> Mike wrote:
>
> > Sorry, missed this. If, say, you want to create a tonicized
> > Dorian, just use chords that happen to be mainstays of Dorian
> > instead of mainstays of Aeolian. This means that instead of
> > going to the bVI, go to the IV or the IV7 chord. But the
> > point is that doing so doesn't mean that you have to limit
> > yourself to only the notes in Dorian - they certainly didn't
> > with Aeolian. If you ever do want a strong resolution back to
> > the I chord, feel free to temporarily raise the 7 so you can
> > play a proper V7 chord.
>
> OK thanks. It seems like you're agreeing here than the
> 'chords of the mode' are important. I have no problems with
> substitutions. If the basic skeleton is coming from the mode,
> something like the 'melodic origin hypothesis' might be
> at work.

"Important" how? They're important for imparting a strong sense of
"modality" to what's going on, but I don't think they're important to
functional harmony. I think that Cmaj -> A7b13 -> D7#11 -> G13b9 ->
Cmaj is very functional indeed, although you'd play a different scale
over every one of those chords (C ionian -> A altered -> D lydian
dominant -> G diminished[8] -> Cmaj).

> > Or you can cheat and use something
> > like Gmaj6/A as a V chord which resolves to Dm9. The end result
> > is you still get the feeling of being in D minor, but you come
> > to understand that the Gmaj is a mainstay of the scale you're
> > at, so that when you move to Gm (which would be Aeolian) it
> > sounds like a modulation.
>
> Hey, have I been misunderstanding you all along? It seems
> you're saying Gmin signals D aeolian because Bb isn't
> in D dorian.

That's what I'm saying, yes. And if you're in D Aeolian, and you start
playing B, it signals Dorian. What did you think I was saying?

> > So you play ii-V and it causes you to expect a I. If you want to
> > imply minor, you'd go iim7b5 -> V7b9 -> i.
> > So in that sense, you can still think of it as just using
> > borrowed progressions from major and harmonic minor,
> > which is how the whole thing started.
>
> It still seems here like this is consistent with the kind of
> thing I've been chatting about.

It is. Although I should mention that ii-V's don't always have to
imply I, but they certainly imply a mode of some sort. I think it has
more to do with Rothenberg minimal sets than anything. As an example

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

The form to this is AABA, it's rhythm changes. It's in Bb. The B
section chord are Bm7 | E7 | Bbm7 | Eb7 | Am7 D7 | Abm7 Db7 | Gm7 C7 |
F#m7 B7 (-> Bbmaj). So you have a bunch of ii-V's that go down
chromatically, and then the last one resolves via tritone sub to
Bbmaj.

> The 'extensions' version is by far my favorite. I'm not
> sure what to make of that. I guess I've always said I expect
> higher-limit extensions of diatonic harmony to be a hugely
> fertile direction. Jules Siegel is the example I've always
> thought of (if you remember "Calliope"). And George Secor.

Right, but in the extensions version, I'm placing the higher-limit
extensions on a porcupine shell, not a diatonic shell. So instead of
leaving the tonic and returning by way of ii-V-I, which usually means
you're making use of an 81/80 pun in there somewhere, I have the whole
thing leaving the tonic by 10/9 and returning by IV -> V -> I, with a
diminished chord and a I6/4 thrown in there somewhere. You can follow
it mentally because the chord progression atoms are all things like
Cmaj -> Amaj -> Dmaj -> Bmaj -> Emaj -> C#maj -> F#maj, except you end
up at F instead of F#. The atomic chord progressions are all familiar,
even though how they line up lands you at an unfamiliar place. You can
even follow it if I place higher-limit stuff everywhere, because after
the 8 sets of examples preceding, you should have enough of a
porcupine template built up to follow the whole thing - kind of like
what happens when you play Cmaj -> A7b9 -> D7#11 -> G13b9 -> C9#11 in
meantone. You understand the 81/80-pun logic enough to follow the
progression no matter what chord qualities you put over the roots.

> Hm! Bebop is my favorite jazz. I never took much to
> Kind of Blue. Maybe I'm detecting a pattern!

Kind of Blue isn't as blatant with the modal stuff as everyone likes
to claim it is, but it was a start.

> Wow, I enjoyed Freddie Hubbard in high school for the
> trumpet playing. But I think this is the first time I'm
> listening to the chords! Pretty nice, and definitely
> modal I would say.
//snip
> My jazz teacher in college made me get Speak No Evil.
> I never liked it much and I must say it's not doing a whole
> lot for me right now either.

The seminal genre here to look for is "post bop," where this approach
really took off.

Check out
http://www.youtube.com/watch?v=P1jOIAos3nk

Maybe you'll like these better, which mix the functional and modal approaches:

http://www.youtube.com/watch?v=lTNLWi-xAkE
http://www.youtube.com/watch?v=pz9IFn1tnnk
http://www.reverbnation.com/play_now/song_884437

All of these are modal, and yet oddly comprehensible in a "functional"
sense, which is the direction that this approach continues to evolve
in. Anyway, Debussy is the o.g. who made it all start

http://www.youtube.com/watch?v=GZHL1E4ILHo

> > This is when everything forks off, and I can't give you as
> > clear a picture. Certain aspects of this movement jumped
> > over into pop music,
>
> I always think of Miles and Herbie that way, actually.
> I like Miles' electric stuff much better than Kind of Blue,
> but still not as much as bebop.

The "It's About That Time" section of In a Silent Way, which if you
haven't noticed I post every chance I can get, is in my opinion one of
the landmark pieces of music of the entire 20th century. But there was
still some modal stuff going on in bebop -

http://www.youtube.com/watch?v=KX_iUXGk0js

Although most of this piece is functional, the first few chords are
Ebmaj7 | % | Ebm7 | Ab7 - which is first Eb ionian, then Eb dorian -
and then Fm7 | % | Abm7 | Cb7 - which is F dorian and then Ab dorian.

> Wait, why won't I find something that goes way out and comes
> back to end on Dorian? Do you mean because pop musicians
> don't write long things, and classical musicians normally
> would but were screwing with atonal serialism?

Right.

> My favorite by far is #17 in Abmaj, which I consider among
> the best fugues ever written. It's in 4 voices, 5/4 time,
> and harmonizes the theme with itself in augmentation.
> I tried to learn to play it, made it through the first
> three entrances and got slaughtered. It may not be the best
> modal/tonal flipping example in the set though.

Never heard it! I'll have to check it out.

-Mike

🔗Mike Battaglia <battaglia01@...>

I wrote:
>> Wait, why won't I find something that goes way out and comes
>> back to end on Dorian? Do you mean because pop musicians
>> don't write long things, and classical musicians normally
>> would but were screwing with atonal serialism?
>
> Right.

One notable exception to this, and one of my favorite choral works
ever, is Sibelius' "Joululaulu":

http://www.passionato.com/preview/WN28a4583e52877/

Most of this is in D Dorian - the melody of the first phrase is D E F
G A B C A, for example. The chords he uses are almost entirely from
Dorian. I think he was clearly thinking of the piece that way, which
is evident in the way he handles certain small details.

For example, sometimes he throws the V7 in there, so he has to move
out of Dorian for a bit. But the the ii chord he decides to precede it
with is iim7, as opposed to iim7b5 - he really wants to keep that B
involved. When people are writing in Aeolian, and they want to throw
the V chord in, they move from Aeolian to harmonic minor - i.e. they
keep the b6 involved. He instead decides to move from Dorian ->
melodic minor, because he wants to keep the nat6 involved. The result
is to my ears a very clear functionalization of Dorian mode.

At the end of the third phrase, you finally a Bb in the form of C7 ->
Bb, which should sound like a modulation of some kind (to Aeolian).
For the fourth and final phrase, he stays in Aeolian, going to the bVI
chord, and then finally ending with the Picardy third on Dmaj. My top
secret, patent pending mode-finding-algorithm suggests D E F# G A Bb
(C/C#) D as the mode for that Dmaj, with the C/C# in parentheses
because I didn't hear a clear signal and my ears are telling me to
avoid playing type of C at all - just make it hexatonic. Octatonic
might work too - D E F# G A Bb C C# D, if propriety's your thing.

It's a great concept, and I wish I had more examples of it. The
Shostakovich fugue you linked me to is pretty awesome, although I'm
not hearing much in the way of exotic modal harmony in it. I do hear
some unexpected movements and resolutions though, although it sounds
to me like it's always in ionian or aeolian/harmonic minor, but
modulating to unexpected keys. Every so often I'll hear a hint of
Phrygian or something, which is cool.

-Mike

🔗genewardsmith <genewardsmith@...>

🔗cityoftheasleep <igliashon@...>

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

> If this is true, how could it be possible to finish a
> progression on the 'wrong' chord (even if the last two
> chords are major chords separated by a 3:2)? Because
> it is possible.

Well, you have to set the V up, too. I didn't mean to imply that a resolution is as simple as just throwing a V-I in after any ol' chord. If that were true, chain-of-fifths progressions would confuse the hell out of us. Do you think it's possible to finish on a wrong chord if the last three chords are major chords following root movements of 4/3-3/2-1/1?

> > You can't definitively give the key of a chord progression
> > until its finished,
>
> It certainly flies in the face of what they taught me in
> school. I mean, they don't teach you to start at the last
> chord, label it "I" and work backward.

If you already have the last chord, it doesn't matter whether you look at the end or the beginning, because the progression is finished regardless. The point I was trying to make is if you start at the beginning and you don't know where it ends, you don't know if a modulation is coming or not. There are a million different ways a progression can go from any point that's not part of a resolution. If you're three chords into a progression, let's say you've had Cmaj, Fmaj, Dmin. You might think, "okay, it could go Gmaj, Cmaj, and then end, making C the tonic." But does it have to do that? No, there are plenty of functional ways it could get into another key. And what if these aren't the first three chords, but somewhere in the middle of a progression? What if the first chord is a Bb major or something?

The point is for the idea of a "global tonic" of a progression to exist, it'd have to be obvious at every point (or else it wouldn't be "global"). Therefore, you should be able to take any slice of the progression and be able to discern the tonic from it, which is obviously impossible. The only way to determine a global tonic is to analyze a chord progression "after the fact" or on paper (although most composers of classical functional music give you the key in the notation).

> I can make it without those too.

I'm sorry if I've given the impression that I think V-I is the only thing that will do. Of course there are other types of resolutions! But I think it is of obvious importance that while you *can* make tonal music with just a V-I over and over again, you can't do it with just any ol' pair of chords over and over again. I think if we want to figure out anything about how tonality works, we should start with the minimal conditions and build out from there. Also examples of what *doesn't* work might actually be more helpful than examples of what does.

-Igs

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
> I think Carl's right, in that there's a sense of sense of key center.
> The tonic isn't indeterminate until the resolution. The listener
> expects it to resolve a certain way. Experiments have verified this
> -- you can halt a progression and ask people how they expect it to
> finish, or play two chords and ask which is correct. Most people
> agree in a very clear way that agrees with music theory.

Okay, let me back up a bit. I am not saying there is no such thing as a "global tonic". I am saying that global tonics may be absent, and yet a chord progression can still sound functional, which means that global tonics are not an essential feature of functional harmony. Which you actually seem to agree with, because you say:

> In a modulation, you have to make the key ambiguous, and then clarify it in a different
> way to how you started.

The fact that you *can* make the key ambiguous, and then "clarify it" means you are (at least temporarily) destroying the sense of global tonic, and then creating another sense of tonic, meaning that the progression itself *does not have* a global tonic but only two "local" tonics and an area of ambiguity. This completely agrees with what I am saying. In a progression where there is a sense of global tonic, all that means is that the chords all stay close to home. The "global" tonic is actually a local tonic that never gets departed from.

> I remember a good example from rec.music.theory. Unfortunately, I
> don't remember the details, like the name of the song. But, it's a
> famous song, by a mainstream band, and the tonic is never stated in
> the chorus (I think) until the resolution. Still, it's clear what the
> key is. So the sense of key isn't only about remembering the first
> chord, or one chord or note being repeated more than others.

Couldn't agree more.

-Igs

🔗Carl Lumma <carl@...>

🔗cityoftheasleep <igliashon@...>

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

> Let me clarify what I meant by these terms. By "global" I
> didn't mean for an entire piece. I just meant one level
> above chord roots. The bottom line is that in order to be
> functional, the chords in a progression have to relate to
> each other somehow.

What do you mean, "relate"? Any chord can relate to any other chord, so you must mean something else. And if you're using the term "global tonic", I think what you must really mean is that all chords in the progression must relate back to a single chord, and what you are wondering is why some relationships sound...I dunno, "obvious"? "Natural"?...while others don't.

Can you maybe demonstrate a progression that is not functional?

> If you can give them names (such as "V")
> that's a good sign such a relation exists. It's clear that
> major triads whose roots are related by an approximate 3:2
> have a certain sound for psychoacoustic reasons. But that
> alone doesn't justify calling them "V" and "I".

In Blackwood[10], all major chords are "potentially" both I and V (or I and VII if you prefer decatonic numeration). So I agree that something else has to explain how it is that certain progressions can "collapse" the chords into sounding like definitely one or definitely the other. I sure do wish people who were actually classically trained would take a shot at writing in Blackwood[10], really get in deep with it and see if they can explain what's going on.

> If you take the Animaniacs theme for instance, it does not
> end on the I it started with. But the progression is still
> functional.

So what's the "global tonic" in that progression?

-Igs

🔗Carl Lumma <carl@...>

--- Mike Battaglia <battaglia01@...> wrote:

> > OK thanks. It seems like you're agreeing here than the
> > 'chords of the mode' are important. I have no problems with
> > substitutions. If the basic skeleton is coming from the mode,
> > something like the 'melodic origin hypothesis' might be
> > at work.
>
> "Important" how? They're important for imparting a strong sense
> of "modality" to what's going on, but I don't think they're
> important to functional harmony. I think that
> Cmaj -> A7b13 -> D7#11 -> G13b9 -> Cmaj
> is very functional indeed, although you'd play a different
> scale over every one of those chords
> (C ionian -> A altered -> D lydian dominant ->
> G diminished[8] -> Cmaj).

G13 eh? I like that chord.

Seriously though, I improve with progressions like
I-VI-II-V-I all the time. Because long ago I concluded
that common tones are all that really matter to me.
Even though the 3rd is altered in the VI and II chords,
the added b7 keeps a common dyad in the C maj scale
in both cases...

> > Hey, have I been misunderstanding you all along? It seems
> > you're saying Gmin signals D aeolian because Bb isn't
> > in D dorian.
>
> That's what I'm saying, yes. And if you're in D Aeolian, and
> you start playing B, it signals Dorian. What did you think
> I was saying?

The above is consistent with the Rothenberg-type explanation
I posted. I guess I assumed you were arguing against that...

> I think it has more to do with Rothenberg minimal sets than
> anything.

...guess not!

> http://www.youtube.com/watch?v=pz9IFn1tnnk

Wow, this is amazing for a number of reasons. Make that
incredibly amazing.

> http://www.reverbnation.com/play_now/song_884437

Love it! I think I've heard of Aaron Parks before.
Also this is a neat site, in that it lets you browse
around without interrupting playback.

> Anyway, Debussy is the o.g. who made it all start
> http://www.youtube.com/watch?v=GZHL1E4ILHo

My jazz teacher said the same thing. I was nonplussed
because I never cared much for Debussy! There is something
interesting going on in this one though, e.g. 1:06-1:35 and
again toward the end. It's reminiscent of the finale
from Firebird.

-Carl

🔗Carl Lumma <carl@...>

Igs wrote:

> I sure do wish people who were actually classically trained
> would take a shot at writing in Blackwood[10], really get in
> deep with it and see if they can explain what's going on.

Blackwood himself doesn't qualify?

>> If you take the Animaniacs theme for instance, it does not
>> end on the I it started with. But the progression is still
>> functional.
>
> So what's the "global tonic" in that progression?

There are two - one before the transposition and one after.

> Can you maybe demonstrate a progression that is not functional?

Good question. To start, I'd say strictly parallel harmony
like this must be non-functional
http://upload.wikimedia.org/wikipedia/commons/4/4a/Le_Tombeau_de_Couperin_triadic_planing.mid

Gene's Vaughan Williams suggestion seems to have been a really
good one. I'm not familiar with V.W. at all and I'm still
listening. This performance on YouTube is really excellent!
http://www.youtube.com/watch?v=27C4xXrUn4Q
http://www.youtube.com/watch?v=QW4nXjO0T_Y

I'll add Mike's Freddie Hubbard link to the list. It might
be more toward the functional side than the above but it
still is pretty disconnected I'd say
http://www.youtube.com/watch?v=NrP7KI6--2c

The first thing that came to my mind when you asked:
http://www.amazon.com/gp/recsradio/radio/B00000J7U8/
let's say "Modus III" especially.
(They made a sequel which I bought about 6 months ago but
still haven't listened to
http://www.amazon.com/Extempore-II-Orlando-Consort/dp/B00007FP8I
)

Or go straight for authentic
http://www.youtube.com/watch?v=UHzPcPHmNJQ

Maybe someone with better ears than me can put all this
together.

-Carl

🔗Mike Battaglia <battaglia01@...>

On Sat, Apr 30, 2011 at 8:46 PM, Carl Lumma <carl@...> wrote:
>
> > "Important" how? They're important for imparting a strong sense
> > of "modality" to what's going on, but I don't think they're
> > important to functional harmony. I think that
> > Cmaj -> A7b13 -> D7#11 -> G13b9 -> Cmaj
> > is very functional indeed, although you'd play a different
> > scale over every one of those chords
> > (C ionian -> A altered -> D lydian dominant ->
> > G diminished[8] -> Cmaj).
>
> G13 eh? I like that chord.
>
> Seriously though, I improve with progressions like
> I-VI-II-V-I all the time. Because long ago I concluded
> that common tones are all that really matter to me.
> Even though the 3rd is altered in the VI and II chords,
> the added b7 keeps a common dyad in the C maj scale
> in both cases...

So why don't you hear the porcupine excerpt I wrote as functional
then? That's basically what I did there.

I'd say that common dyads are definitely important. If you play it
right, you can make it so that your melody is in C maj, where all of
the chords you play under it aren't, which is a neat and pretty common
effect. But I'd also say that the Ebm7 in Cmaj7 -> Ebm7 -> Dm7 ->
G13b9 -> is pretty functional. I'd also say that out of all of the
scales that you could play over Ebm7, Dorian will probably sound the
most natural, as it retains most of the common tones of the previous
chord (Cmaj7). In fact, sharping the 7 so that you have a min/maj7
chord would make it sound even more natural. And if you also flat the
5 so that you end up with a diminished maj7 chord, that'd sound even
more natural, and you'd end up playing diminished[8] over that one.

> > That's what I'm saying, yes. And if you're in D Aeolian, and
> > you start playing B, it signals Dorian. What did you think
> > I was saying?
>
> The above is consistent with the Rothenberg-type explanation
> I posted. I guess I assumed you were arguing against that...
>
> > I think it has more to do with Rothenberg minimal sets than
> > anything.
>
> ...guess not!

I think that Rothenberg does a better job of explaining modality than
tonality. If you can keep 7 notes in your mind simultaneously, then
it's easy to see how they relate to one another. The simultaneous
awareness of how all of these notes form chords, and how all of these
notes and chords relate to the tonic, is what the "mode" of the
current chord you're in is. This is what I was referring to earlier
when I spoke about different chords being mainstays of different
modes.=

The gist of it is - when you move to a new chord, find the mode that
fits all of the notes of this new chord while changing as few notes as
possible from the old one. That's about it. And, I note a "natural"
behavior that's emerged out of extended harmony is - should you ever
find yourself at something like C D# E F# G A Bb C, which is improper,
99 times out of 100 people will stick the Db in there and turn it into
diminished[8]. So propriety certainly has something to do with it.

So if you're playing a novel chord that requires a modulation, you
will naturally end up gravitating to the one that has as many common
tones as the last one - unless you deliberately want to modulate more
than that. Lastly, if the resulting scale is improper, you'll probably
find a proper closure for it, and probably the least dissonant note
will sound the most natural. Then you'll continue to emphasize those
notes in your mind by playing them as the melody. However, there's
certainly nothing stopping you from leaving that mode, and doing so
clearly doesn't destroy the functionality of the harmony. And learning
to think in something like Pajara[10] generally just ends up with
there being more "avoid notes" within the scale, so the result doesn't
sound all that different. Whether or not you have a learned melodic
imprint that has lots of avoid notes, or a learned melodic imprint
that doesn't but treats the other notes as "chromatic," doesn't seem
to affect the actual sound much.

> > Anyway, Debussy is the o.g. who made it all start
> > http://www.youtube.com/watch?v=GZHL1E4ILHo
>
> My jazz teacher said the same thing. I was nonplussed
> because I never cared much for Debussy!

!@#(*&^!(@*&(!@#*&(@@(*@@@@@@@@@@#^!&^#!*&yc(ibuyciuyc(*7HCC@#()$*&)#(@*&v)($#:;;;;;LLL;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

;

> There is something
> interesting going on in this one though, e.g. 1:06-1:35 and
> again toward the end. It's reminiscent of the finale
> from Firebird.

Right after that part is probably the most overtly modal. This
recording does it better:

http://www.youtube.com/watch?v=QH2ZsZ0rwxI&t=1m46s

The walkdown in the left hand lands you at Cb melodic minor #4, which
is a mode of harmonic major. That was the first time I'd ever heard
that mode before. A good voicing is - B D E# F# G# A# E#'. So every
one of these modes has their own sound. Except I don't think it
derives from the scalar structure of the modes themselves, because
there's all kinds of ridiculous sounds to be found as soon as you get
out of strictly "modal" thinking, because what you're really exploring
is extended and tempered 5-limit harmony.

-Mike

🔗Mike Battaglia <battaglia01@...>

On Sat, Apr 30, 2011 at 9:20 PM, Carl Lumma <carl@...> wrote:
>
> OMG, apparently there's a name for this
>
> http://en.wikipedia.org/wiki/Constant_structure
>
> I wonder if Erv named his concept after it?!?!

This just looks like parallel harmony - that's one trick you can use,
but check out this piece:

http://www.youtube.com/watch?v=xqKTIwhB4pI

Omar Hakim wrote this, and apparently at the time the chords were
pretty ordinary. So Wayne Shorter and Joe Zawinul took it apart and
reharmonized it, and the above is the result. This is definitely
modal, but it's functional. Not a lot of use of parallel harmony
either.

The point that I'm making when I say it's "functional" is that
although Dm7 -> Amaj7 doesn't actually fit into any proper 7-note
scale, it still causes a certain musical effect, and over time you can
learn to predict what this effect will be in advance and use it in
part of a larger progression to make "functional" music - music that
enables people to predict in some sense what will happen next, or
comprehend what did just happen.

You can learn to figure out in advance what Cm7 -> Gbmaj7 will do -
it'll cause a huge color shift and it's also a borrowed chord from C
locrian, so the color shift will tend to lead to a very "dark" mood.
Then you know that Gbmaj7 can resolve to Fm7, so you can create Cm7 ->
Gbmaj7 -> Fm7. And then you might decide to get back to Cm7 by the
same resolution, so you'll go Cm7 -> Gbmaj7 -> Fm7 -> Dbmaj7. You'll
figure out that Fm7 -> Dbmaj7 will cause less of a color shift than
Cm7 -> Gbmaj7 because of all the common tones. The fact that you've
now become familiar with this means you're doing something very
similar to what common practice composers were doing with I, IV, V,
and diminished chords, and ii, and iii, and so on, except with new
chords and resolutions. So it's very functional indeed. Instead of
using the subdominant IV chord or perhaps the vi chord as a point of
repose, there are now tons of new points of repose all over the place,
many of which involve modulating from mode to mode.

Over time you start to get the picture that the modes themselves have
nothing to do with it, but that meantone tempered 5-limit harmony has
something to do with it, and the modes simply facilitate an analysis
of what's going on. There are plenty of chords that don't even fit
into a mode that I know of, although most of this turns out to be more
experimental and less developed territory. (Even much of the Rite of
Spring can be analyzed using modes).

-Mike

PS: another thing I forgot - here's another modal passage from the
Rite of Spring:

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

🔗Mike Battaglia <battaglia01@...>

🔗Carl Lumma <carl@...>

--- Mike Battaglia <battaglia01@...> wrote:

> So why don't you hear the porcupine excerpt I wrote as
> functional then? That's basically what I did there.

I didn't say it wasn't functional! I said I don't how to tell
if a piece of xenharmonic music is functional. As you can see
from the present thread, I'm still working on telling in 12-ET.
In fact I'd love your input on my answer to Igs' question, and
on the Shosty preludes & fugues.

Also note, I refused to call Petr's example functional.

> But I'd also say that the Ebm7 in Cmaj7 -> Ebm7 -> Dm7 ->
> G13b9 -> is pretty functional.

Hm. Seems like it's a 'passing chord'.

> > My jazz teacher said the same thing. I was nonplussed
> > because I never cared much for Debussy!
>
> !@#(*&^!(@*&(!@#*&(@@(*@@@@@@@@@@#^!&^#!*&yc(ibuyciuyc(*7HCC@#
> ()$*&)#(@*&v)($#:;;;;;LLL;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

I know, I consider it a personal weakness.

It's odd. I bought a bunch of recordings and tried several
times over the years to like them, but never could. One of
them was even based on rolls recorded by the great man himself.
But one time Paul Bailey played a Debussy thing on my piano
after he tuned it, and it was pretty cool. And the thing you
just linked me to is neat. So maybe I'm just not listening
to the right stuff. But I've always put him in the same bucket
as Chopin - dopey French songs arranged with too many arpeggios.

> > There is something
> > interesting going on in this one though, e.g. 1:06-1:35 and
> > again toward the end. It's reminiscent of the finale
> > from Firebird.
>
> Right after that part is probably the most overtly modal.

Sounds like something that wanted to be a filter sweep. :)

-Carl

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

On Sun, May 1, 2011 at 2:40 AM, Carl Lumma <carl@...> wrote:
>
> --- Mike Battaglia <battaglia01@...> wrote:
>
> > So why don't you hear the porcupine excerpt I wrote as
> > functional then? That's basically what I did there.
>
> I didn't say it wasn't functional! I said I don't how to tell
> if a piece of xenharmonic music is functional. As you can see
> from the present thread, I'm still working on telling in 12-ET.

The whole concept of functional vs modal is a bit shaky. I don't think
you can really draw a clear line between the two. How can you? The
further we delve into modal harmony, the more we just end up
discovering novel and exotic forms of "functional" harmony, to the
point where the two overlap and you can't tell the difference. You can
use all kinds of modal substitutions and still not destroy the sense
of key that you're in. Furthermore, you can create the sense of a song
being in the key of say D, while still having it be predominantly in,
say Dorian, which has its own sound and is different sounding from
Aeolian. The Sibelius piece I linked you to reflects in my view what
would have happened if we had started writing music with Dorian
instead of Aeolian mode - we'd just have two minor scales, and they'd
be Dorian and melodic minor. The tonal heirarchy of the piece is
definitely still centered around D. So I think the whole concept is
antiquated and outdated.

But, for the purpose of this example, I went with the notion that
functional means there exist things like chords "resolving." So,
rather than to prove a point about that you can still create and
discover new and exotic resolutions by working within other modal
systems, I decided that I'd just stick with IV, and V, and I, and some
diminished chords and stuff, just to create clear expectations and
resolve them. I avoided 81/80 like the plague, and when possible
treated it like 25/24 (which it is in porcupine). Lastly, I wanted the
whole thing to land you at a chord you don't expect, and then exploit
that for further "functional" harmony, e.g. in this case you keep
moving up in whole steps but somehow end at the fourth. I wanted it to
not work in meantone and only to work in porcupine, and I also
deliberately wanted to NOT stick to to the smallest chain of porcupine
generators possible to make a point. And so that's what I made. The
end result is that each individual chord progression between two
adjacent chords is easily followable, because it's something you've
heard a million times before, but that the whole thing only works in
porcupine.

I felt like folks in real life got what I was going for more so than
the folks on the list. My friends suddenly seemed to "get it." They
described hearing some kind of internal logic in it, although they
were confused at the big picture of what was going on. They seemed to
hear it as some kind of auditory equivalent of the Penrose stairs. One
of my friends who's a virtuosic sax player figured out during the AXiS
improv that the reason the progression worked was because the minor
thirds were sharp. Before this, they were into "I dunno, microtonal
music is cool, but kind of scary sounding, I just need to listen to it
more to get used to it I guess." So I won't claim that this is some
kind of monumental compositional achievement - in fact I'd certainly
say it wasn't - but I'm happy that my simple experiment seemed to go
well and suggest a direction for me to plow in further. I can utilize
all of these exotic modal resolutions I've been trying to work out my
whole life, and when chained together they'll simply line up
differently when chained together in porcupine than in meantone. And
that's even besides any concept of exploring new territory with
higher-limit harmony.

Now on the list, one criticism was that I was still stuck in meantone
thinking by utilizing V-I resolutions. I think that this is a
self-limiting wolf in sheep's clothing. The idea was also proposed
that I'm not really exploring porcupine[8] unless I learn to hear
porcupine[8] as tonal, but I disagree that the actual porcupine tonal
structure at large depends on that particular MOS. And I certainly
disagree with the notion seems to be that chromatically altering
things is cheating, because we want to limit the amount of porcupine
generators, when I don't see how the group-theory based notion of a
"generator" has anything to do with musical cognition at all. If
getting people to hear something like v-I in porcupine as strong as
V-I hinges on limiting their exposure to V-I, I think that might be a
sign that we're headed in the wrong direction. And, besides, if you
disagree, I'll win by force - I'll bombard everyone's ears with V-I in
porcupine until they hear v-i as weak by comparison. Let's call that a
xen koan.

> In fact I'd love your input on my answer to Igs' question, and
> on the Shosty preludes & fugues.

Which question? As for the fugue you sent me, I liked it a lot, and I
heard it as pretty clearly functional, without that much modality
involved, although there were hints of it.

Here's another winner: http://www.youtube.com/watch?v=K1f8HjIkU3M

> Also note, I refused to call Petr's example functional.
>
> > But I'd also say that the Ebm7 in Cmaj7 -> Ebm7 -> Dm7 ->
> > G13b9 -> is pretty functional.
>
> Hm. Seems like it's a 'passing chord'.

It is, but when the Ebm7 resolves downward to Dm7, that's a pretty
strong resolution. Feel free to make it ||: Cmaj | Ebm7 Ab7 | Dm7 |
G13b9 :|| as well.

Or try this chord progression: ||: Dbmaj9 | C7#9 | Fm7 A7/E | Ebm9 D7#9#11 :||

That's from Just the Two of Us. Note the Fm7 -> A7/E -> Ebm9
resolution, and how smoothly the A7/E resolves to Ebm9. Make sure the
melody over those three chords is Ab -> A -> Bb on top. That's also a
"passing

If you happened to be in some scale that contained all of those
chords, Ebm7 would still be a passing chord. It's kind of like Cmaj ->
G7/D -> Cmaj/E - the G7/D is a passing chord between the two Cmaj
chords. In fact, there are plenty of times when, if you're harmonizing
a melody, you'd just throw a spurious passing chord like that in just
because it sounds better. But it doesn't change anything

> It's odd. I bought a bunch of recordings and tried several
> times over the years to like them, but never could. One of
> them was even based on rolls recorded by the great man himself.
> But one time Paul Bailey played a Debussy thing on my piano
> after he tuned it, and it was pretty cool. And the thing you
> just linked me to is neat. So maybe I'm just not listening
> to the right stuff.

I'd check Gieseking's recordings out. Reflections in the Water is a
good start. Feuilles Mortes is darker and more out there. Clair de
Lune is something you've probably already heard. Gardens in the Rain
is what I just sent. Arabesque is played out. Check out Hommage a
Rameau for a good deep cut.

> But I've always put him in the same bucket
> as Chopin - dopey French songs arranged with too many arpeggios.

http://marrettcounseling.com/images/anger%202.jpg

> > > There is something
> > > interesting going on in this one though, e.g. 1:06-1:35 and
> > > again toward the end. It's reminiscent of the finale
> > > from Firebird.
> >
> > Right after that part is probably the most overtly modal.
>
> Sounds like something that wanted to be a filter sweep. :)

Haha, what do you mean?

-Mike

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

On Tue, May 3, 2011 at 4:47 PM, Carl Lumma <carl@...> wrote:
>
> > > In fact I'd love your input on my answer to Igs' question, and
> > > on the Shosty preludes & fugues.
> >
> > Which question? As for the fugue you sent me, I liked it a lot,
> > and I heard it as pretty clearly functional, without that much
> > modality involved, although there were hints of it.
>
> Which fugue did I send?

The #17 fugue in Ab.

> I tried to answer his question here:
> /tuning/topicId_98715.html#98790

The phrase "functional harmony" is defined here pretty well:

http://en.wikipedia.org/wiki/Diatonic_function#Functional_harmony

Although much of this is rooted in common practice thinking, and the
article has a clear 12-equal or general diatonic bias to it, the
takehome point is - if a chord has a well-defined "function" that it
fulfills in relation to the tonic, then that chord is functional as
far as the tonic is actually established as the key of the piece. A
function could be: setting up expectation, fulfilling that
expectation, being a point of repose, moving away from the tonic along
xyz direction, moving away from the tonic along zyx direction, being a
substitute for the tonic, other things we haven't discovered. There is
a clear subjective component to it.

History has seen a clear trend in that we have continued to break away
from the diatonic scale in our exploration of functional harmony. We
continually laser in on novel "extended harmonies" and work them in as
part of tonal harmony. It started simply enough with secondary
dominants, which later on turned into throwing dominant 7s over the I
chord and playing the diminished scale over V7 chords. We started
seeing the altered scale used over dominant 7's as well. People
discovered the blues, which could perhaps be thought of as an
alternate system of functional harmony. People started exploring modal
harmony, initially as a way to get away from common-practice
functionality, and ended up also discovering more functional harmony.
For example:

http://www.youtube.com/watch?v=SDgxnjgVFi4

The intro is in B dorian, and he then moves to B aeolian for the chord
progressions in the verse. Why did he randomly go to dorian in the
intro? Because the songwriters knew what dorian would sound like
there, and they wanted the feeling of being able to go Bm7 ->
G#m7b5/B, etc. They wanted the dorian "sound." Maybe the "sound" that
they were getting at was the 7-limit utonality, who knows - either way
they knew what they wanted and went there accordingly, so it was
"functional."

So where do you draw the line? Well, one of the common functions that
we utilize in chord progressions is that of creating and then
fulfilling expectations. To that extent, many people dismiss lots of
pieces as being non-functional, because they don't have clear ii-V-I's
or whatever. These people would still say that ||: Cmaj | Fmaj :|| is
functional, although there's no V-I in there either. So there's no
clear definition there, and frankly I wouldn't trust academic music
theorists to even try to broach the subject.

The whole thing is also very subjective. If for whatever reason
someone doesn't hear I-IV-ii-V-I as setting up and then resolving an
expectation, then for that person the progression is certainly not
functional. Or if you hear a piece and for the first verse you can't
figure out what the tonic is, but then it becomes clear in the chorus,
the functionality of everything you just heard will suddenly
completely change on the second listen. For example, the first time
you listen to this, you won't hear much functionality in it

http://www.youtube.com/watch?v=fnoN3qEYJS4

But after spending some time with it, you'll start to hear snippets of
really extended functional harmony in it. The Gm7b5 -> C7b9 ->
Bmaj7#11 (third, fourth and fifth chords of the piece) is a tritone
sub landing on B major (lydian), for example.

-Mike

🔗Carl Lumma <carl@...>

--- Mike Battaglia <battaglia01@...> wrote:

>>> Which question? As for the fugue you sent me, I liked it a lot,
>>> and I heard it as pretty clearly functional, without that much
>>> modality involved, although there were hints of it.
>>
>> Which fugue did I send?
>
> The #17 fugue in Ab.

Ok, that one. Well, the theme itself flips between Ab lydian
and Ab ionian, doesn't it? And the first episode, while in
Ab ionian, uses IV and iii chords to evoke Db lydian and
C phrygian, no?

> if a chord has a well-defined "function" that it fulfills in
> relation to the tonic, then that chord is functional as far as
> the tonic is actually established as the key of the piece. A
> function could be: setting up expectation, fulfilling that
> expectation, being a point of repose, moving away from the tonic
> along xyz direction, moving away from the tonic along zyx
> direction, being a substitute for the tonic, other things we
> haven't discovered.

I agree completely.

> People started exploring modal harmony, initially as a way
> to get away from common-practice functionality, and ended up
> also discovering more functional harmony.
> For example: http://www.youtube.com/watch?v=SDgxnjgVFi4
> The intro is in B dorian, and he then moves to B aeolian for
> the chord progressions in the verse. Why did he randomly go to
> dorian in the intro? Because the songwriters knew what dorian
> would sound like there, and they wanted the feeling of being
> able to go Bm7 -> G#m7b5/B, etc. They wanted the dorian "sound"
> Maybe the "sound" that they were getting at was the 7-limit
> utonality, who knows - either way they knew what they wanted
> and went there accordingly, so it was "functional."

I guess the distinction is, whether the name of the mode is
heard as a tonic, with chords relating to it. Versus just
floating around with no tonic. If that makes any sense.
What did you think of the examples I gave Igs?

> For example, the first time
> you listen to this, you won't hear much functionality in it
> http://www.youtube.com/watch?v=fnoN3qEYJS4
> But after spending some time with it, you'll start to hear
> snippets of really extended functional harmony in it.
> The Gm7b5 -> C7b9 -> Bmaj7#11 (third, fourth and fifth chords
> of the piece) is a tritone sub landing on B major (lydian),
> for example.

You're right, I didn't hear that as functional.

-Carl

🔗Mike Battaglia <battaglia01@...>

On Thu, May 5, 2011 at 3:07 AM, Carl Lumma <carl@...> wrote:
>
> Ok, that one. Well, the theme itself flips between Ab lydian
> and Ab ionian, doesn't it? And the first episode, while in
> Ab ionian, uses IV and iii chords to evoke Db lydian and
> C phrygian, no?

I heard it mainly as being composed of lots of secondary dominants and
temporary retonicizations of the V chord, rather than the tonic
actually being I lydian. When it moves to C phrygian, it stays there
long enough for me to start to hear phrygian as the tonic The net
gestalt is different than if lydian and phrygian were being used over
the I chord.

> > if a chord has a well-defined "function" that it fulfills in
> > relation to the tonic, then that chord is functional as far as
> > the tonic is actually established as the key of the piece. A
> > function could be: setting up expectation, fulfilling that
> > expectation, being a point of repose, moving away from the tonic
> > along xyz direction, moving away from the tonic along zyx
> > direction, being a substitute for the tonic, other things we
> > haven't discovered.
>
> I agree completely.

So, if we're looking at things from this angle, then you also have the
fact that certain "modal" pieces sound like they consist of constantly
wandering tonics with no relationship to one another (what "Nefertiti"
might sound like), whereas other ones sound like they just have really
awesome and hip chords that still function in novel and exotic ways in
relationship to the tonic. The dichotomy is "modal harmony as
consonant vs atonal harmony" as opposed to "modal harmony as
post-common practice 'extended' functional harmony." So although we've
been talking about "functional" vs "nonfunctional" harmony, it's
probably better for us to talk about describing tonal vs atonal
harmony. Note that "atonal" in this sense is not the same thing as
serialist, but functions in a capacity similar to what people like to
do with the eikosany.

We need to talk more about modality. Modality is - which chord are you
playing now, and what are the chords that are most closely in the
"vicinity" of this chord? If you're playing C minor, is it F minor
(aeolian) or F major (dorian) that's most closely related at the
moment? Let's say it's F major - what about G minor (dorian) vs G
major (melodic minor)? These determine which mode you'd be using. So
modes encapsulate not only the actual, but suggest a heirarchical
representation of the potential and an accompanying set of
probabilities.

So what happens then if your tonic is C major, your potential set most
strongly contains G major and F major, you stick mainly to
permutations of those notes to constantly reinforce that "mode," and
you also try at every juncture to, within this structure, maximize the
expectation/resolution functions?

> > Maybe the "sound" that they were getting at was the 7-limit
> > utonality, who knows - either way they knew what they wanted
> > and went there accordingly, so it was "functional."
>
> I guess the distinction is, whether the name of the mode is
> heard as a tonic, with chords relating to it. Versus just
> floating around with no tonic. If that makes any sense.

I wrote the above before I read this, so I think that's the same thing
I'm saying. Or basically, what I'm getting at, is that the following
video game elevator music snippet is both tonal and modal:

http://www.youtube.com/watch?v=GHyYRlhgg2E

The chords for the first section are Amaj7 | Cmaj7/D | Amaj | Dmaj7.
That Cmaj7/D, which would just be called "Dsus" in jazz circles, is
not at all a part of A major, but it serves a very well defined
function anyway - it takes you away from the tonic towards the
subdominant, and it also fulfills the function of providing a strong
modal contrast with the tonic (it's borrowed from the parallel A
Dorian). If you're a 14 year old kid, it also implies the tripping you
out function, but that may apply more if you just got Mega Man 8 for
Christmas than if you've never played the game and are just discussing
tuning on the internet.

Then, at the end, it goes Gmaj7 | Fmaj7 | Gmaj7 | Fmaj7. However, over
the Fmaj7, they still play an F# in the melody, but it sounds really
natural. This is another very salient point.

> What did you think of the examples I gave Igs?

You mention parallel harmony as being strictly non-functional. I'd say
that nothing is strictly non-functional, and that functionality is
subjective. I spent a good part of middle and high school trying to
burn as many extended functional relationships into my head as
possible. Not even parallel harmony means that it'll be nonfunctional
- I IV V is all parallel, for an obvious example. For a less obvious
example that fits into some kind of middle ground, check out some more
Mega Man

http://www.youtube.com/watch?v=l88-qEhws8I

Almost every chord in this is a major 7 chord, and they're all
parallel. Furthermore, you can hear the tonic drifting, but the whole
thing is connected in a certain way that Nefertiti is not. The tonics
themselves are related, whereas those of Nefertiti weren't. And
furthermore, the tonics move slowly enough, with enough pivot chords,
that you can follow the whole thing.

> > The Gm7b5 -> C7b9 -> Bmaj7#11 (third, fourth and fifth chords
> > of the piece) is a tritone sub landing on B major (lydian),
> > for example.
>
> You're right, I didn't hear that as functional.

If you spend some time with it, you'll find ways to functionalize it.
Then you throw some passing chords to ease the transition from each
chord to the next, along the lines of whatever functional
relationships you worked out, and suddenly you're a substitute chord
progression master. Since 12-tet is a heavily tempered system, there
will be zillions of ways to work stuff like that out. And people will
ask you questions about harmony, and you can tell them "Nah bro I
don't think in terms of theory man, you just have to feel it" and all
that. And also people will like it because it'll make more sense,
except for the ones who liked when it made no sense.

-Mike

🔗Carl Lumma <carl@...>

--- Mike Battaglia <battaglia01@...> wrote:

> So, if we're looking at things from this angle, then you also
> have the fact that certain "modal" pieces sound like they
> consist of constantly wandering tonics with no relationship
> to one another (what "Nefertiti" might sound like),

Sorry- did you link to a piece called Nefertiti? I searched
the archives and only found this message.

> whereas other ones sound like they just have really awesome
> and hip chords that still function in novel and exotic ways in
> relationship to the tonic.

Yes.

> The dichotomy is "modal harmony as consonant vs atonal harmony"

I try to avoid "atonal" since it's used so many different ways
and tends to confuse folks.

> > I guess the distinction is, whether the name of the mode is
> > heard as a tonic, with chords relating to it. Versus just
> > floating around with no tonic. If that makes any sense.
>
> I wrote the above before I read this, so I think that's the
> same thing I'm saying. Or basically, what I'm getting at, is
> that the following video game elevator music snippet is both
> tonal and modal:
> http://www.youtube.com/watch?v=GHyYRlhgg2E
> The chords for the first section are
> Amaj7 | Cmaj7/D | Amaj | Dmaj7. That Cmaj7/D, which would
> just be called "Dsus" in jazz circles, is not at all a part
> of A major, but it serves a very well defined function anyway -
> it takes you away from the tonic towards the subdominant,
> and it also fulfills the function of providing a strong modal
> contrast with the tonic (it's borrowed from the parallel
> A Dorian).
> Then, at the end, it goes Gmaj7 | Fmaj7 | Gmaj7 | Fmaj7.
> However, over the Fmaj7, they still play an F# in the melody,
> but it sounds really natural. This is another very salient point.

Yes, I think we're agreed that it's possible to be functional
in modes other than the ionian and aeolian. If we go back to
my original /tuning/topicId_98715.html#98715
it says, "Of course classical tonality had two modes in the
flop... Composition was used to signal which mode was intended."
So if composition can signal one out of 2, it presumably can
signal one out of seven.

> > What did you think of the examples I gave Igs?
>
> You mention parallel harmony as being strictly non-functional.
> I'd say that nothing is strictly non-functional, and that
> functionality is subjective. I spent a good part of middle
> and high school trying to burn as many extended functional
> relationships into my head as possible. Not even parallel
> harmony means that it'll be nonfunctional - I IV V is all
> parallel, for an obvious example.

That's true.

> > > The Gm7b5 -> C7b9 -> Bmaj7#11 (third, fourth and fifth chords
> > > of the piece) is a tritone sub landing on B major (lydian),
> > > for example.
> >
> > You're right, I didn't hear that as functional.
>
> If you spend some time with it, you'll find ways to
> functionalize it.

Yes, you're right. -Carl

🔗cityoftheasleep <igliashon@...>

Does anyone have a progression that is *not* functional/tonal in some way?

-Igs

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- Mike Battaglia <battaglia01@> wrote:
>
> > So, if we're looking at things from this angle, then you also
> > have the fact that certain "modal" pieces sound like they
> > consist of constantly wandering tonics with no relationship
> > to one another (what "Nefertiti" might sound like),
>
> Sorry- did you link to a piece called Nefertiti? I searched
> the archives and only found this message.
>
> > whereas other ones sound like they just have really awesome
> > and hip chords that still function in novel and exotic ways in
> > relationship to the tonic.
>
> Yes.
>
> > The dichotomy is "modal harmony as consonant vs atonal harmony"
>
> I try to avoid "atonal" since it's used so many different ways
> and tends to confuse folks.
>
> > > I guess the distinction is, whether the name of the mode is
> > > heard as a tonic, with chords relating to it. Versus just
> > > floating around with no tonic. If that makes any sense.
> >
> > I wrote the above before I read this, so I think that's the
> > same thing I'm saying. Or basically, what I'm getting at, is
> > that the following video game elevator music snippet is both
> > tonal and modal:
> > http://www.youtube.com/watch?v=GHyYRlhgg2E
> > The chords for the first section are
> > Amaj7 | Cmaj7/D | Amaj | Dmaj7. That Cmaj7/D, which would
> > just be called "Dsus" in jazz circles, is not at all a part
> > of A major, but it serves a very well defined function anyway -
> > it takes you away from the tonic towards the subdominant,
> > and it also fulfills the function of providing a strong modal
> > contrast with the tonic (it's borrowed from the parallel
> > A Dorian).
> > Then, at the end, it goes Gmaj7 | Fmaj7 | Gmaj7 | Fmaj7.
> > However, over the Fmaj7, they still play an F# in the melody,
> > but it sounds really natural. This is another very salient point.
>
> Yes, I think we're agreed that it's possible to be functional
> in modes other than the ionian and aeolian. If we go back to
> my original /tuning/topicId_98715.html#98715
> it says, "Of course classical tonality had two modes in the
> flop... Composition was used to signal which mode was intended."
> So if composition can signal one out of 2, it presumably can
> signal one out of seven.
>
> > > What did you think of the examples I gave Igs?
> >
> > You mention parallel harmony as being strictly non-functional.
> > I'd say that nothing is strictly non-functional, and that
> > functionality is subjective. I spent a good part of middle
> > and high school trying to burn as many extended functional
> > relationships into my head as possible. Not even parallel
> > harmony means that it'll be nonfunctional - I IV V is all
> > parallel, for an obvious example.
>
> That's true.
>
> > > > The Gm7b5 -> C7b9 -> Bmaj7#11 (third, fourth and fifth chords
> > > > of the piece) is a tritone sub landing on B major (lydian),
> > > > for example.
> > >
> > > You're right, I didn't hear that as functional.
> >
> > If you spend some time with it, you'll find ways to
> > functionalize it.
>
> Yes, you're right. -Carl
>

🔗Carl Lumma <carl@...>

🔗cityoftheasleep <igliashon@...>

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> Igs wrote:
>
> > I sure do wish people who were actually classically trained
> > would take a shot at writing in Blackwood[10], really get in
> > deep with it and see if they can explain what's going on.
>
> Blackwood himself doesn't qualify?

I haven't read his book...have you?

> There are two - one before the transposition and one after.

But it's technically "one" progression, right?

> Good question. To start, I'd say strictly parallel harmony
> like this must be non-functional
>
>http://upload.wikimedia.org/wikipedia/commons/4/4a/Le_Tombeau_de_Couperin_triadi > c_planing.mid

This actually sounds functional, just failing to actually arrive at the tonic. Adding one or two more chords to the end of this (retaining the strict parallel harmony, even) I think it could sound as functional as anything.

> Gene's Vaughan Williams suggestion seems to have been a really
> good one. I'm not familiar with V.W. at all and I'm still
> listening. This performance on YouTube is really excellent!
> http://www.youtube.com/watch?v=27C4xXrUn4Q
> http://www.youtube.com/watch?v=QW4nXjO0T_Y

Now *this* is interesting, because it is definitely "non-functional" but also pretty strictly diatonic. It's completely fascinating to me that he is able to keep a feeling of suspense going the whole time but just hanging out with really consonant diatonic harmonies.

> I'll add Mike's Freddie Hubbard link to the list. It might
> be more toward the functional side than the above but it
> still is pretty disconnected I'd say
> http://www.youtube.com/watch?v=NrP7KI6--2c

I think this is functional, or at least as functional as most jazz. A few listens would probably really cement it in.

> The first thing that came to my mind when you asked:
> http://www.amazon.com/gp/recsradio/radio/B00000J7U8/
> let's say "Modus III" especially.
> (They made a sequel which I bought about 6 months ago but
> still haven't listened to
> http://www.amazon.com/Extempore-II-Orlando-Consort/dp/B00007FP8I
> )
>
> Or go straight for authentic
> http://www.youtube.com/watch?v=UHzPcPHmNJQ

Like the other pieces (save for the Freddie), I hear this stuff as "functional harmony that avoids resolution". Meaning that I hear lots of points that could lead to a resolution that go in another direction instead. This stuff also sounds very strictly tonal (though full of false relations, unless my ears deceive me).

In any case, I think these Orlando Consort examples, as well as the Vaughan Williams, pretty solidly demonstrate that the diatonic scale does not inescapably lead to functionality and/or tonality.

But here's another log for the fire: I realized today that when I try to play something "modal", I instinctively use certain rhythmic and structural devices to tonicize pretty much any note I want. What I do is alternate between two notes or two chords, the first one being fairly arbitrary and the second one being the desired tonic. The first one gets a short duration and the second one gets a longer hold, sort of "1..2.....", and then I repeat a few times, slowing the tempo and lengthening the hold on the 2 a little each time. I repeat at least three times, and one the final time play the 2nd chord/note an octave lower. By the end of it, it doesn't even matter what key I was in before hand or how awkward the 1&2 were when first introduced, that short repetition sort of just pounds it home.

This is all making me suspect that the study of tuning has little to teach us about the workings of tonality. Or at least that no scale/tuning is guaranteed to be tonal or atonal.

-Igs

🔗Carl Lumma <carl@...>

Igs wrote:

> > > I sure do wish people who were actually classically trained
> > > would take a shot at writing in Blackwood[10], really get in
> > > deep with it and see if they can explain what's going on.
> >
> > Blackwood himself doesn't qualify?
>
> I haven't read his book... have you?

Most of it. The 15-tone etude is in blackwood[10]. It's
also one of my all-time favorite pieces of microtonal music.

The book describes how he found scales to use for the etudes.
He basically looked for approximations to major and minor
triads and approximate classical cadences involving them.
Not an extended JI or regular mapping or MOS approach at all.
But he did manage to find blackwood[10], probably because
it's analogous to the octatonic scale in 12-ET (Blackwood
was a student of Messiaen).

> > Good question. To start, I'd say strictly parallel harmony
> > like this must be non-functional
>
> This actually sounds functional, [snip]

Mike also pointed out that I-IV-V-I is parallel. So
much for that idea.

> > Gene's Vaughan Williams suggestion seems to have been a really
> > good one. I'm not familiar with V.W. at all and I'm still
> > listening. This performance on YouTube is really excellent!
> > http://www.youtube.com/watch?v=27C4xXrUn4Q
> > http://www.youtube.com/watch?v=QW4nXjO0T_Y
>
> Now *this* is interesting, because it is definitely
> "non-functional" but also pretty strictly diatonic. It's
> completely fascinating to me that he is able to keep a feeling
> of suspense going the whole time but just hanging out with
> really consonant diatonic harmonies.

Yeah, me too.

> > I'll add Mike's Freddie Hubbard link to the list. It might
> > be more toward the functional side than the above but it
> > still is pretty disconnected I'd say
> > http://www.youtube.com/watch?v=NrP7KI6--2c
>
> I think this is functional, or at least as functional as
> most jazz. A few listens would probably really cement
> it in.

I can hear stuff going on. But it's definitely more
floaty than a Mozart sonata no matter how many times I
listen.

> > Or go straight for authentic
> > http://www.youtube.com/watch?v=UHzPcPHmNJQ
>
> Like the other pieces (save for the Freddie), I hear this
> stuff as "functional harmony that avoids resolution".
> Meaning that I hear lots of points that could lead to a
> resolution that go in another direction instead.

Yes, that's it. I wonder why...

> In any case, I think these Orlando Consort examples, as well
> as the Vaughan Williams, pretty solidly demonstrate that the
> diatonic scale does not inescapably lead to functionality
> and/or tonality.
> But here's another log for the fire: I realized today that
> when I try to play something "modal", I instinctively use
> certain rhythmic and structural devices to tonicize pretty
> much any note I want. What I do is alternate between two
> notes or two chords, the first one being fairly arbitrary
> and the second one being the desired tonic. The first one
> gets a short duration and the second one gets a longer hold,
> sort of "1..2.....", and then I repeat a few times, slowing
> the tempo and lengthening the hold on the 2 a little
> each time. I repeat at least three times, and one the final
> time play the 2nd chord/note an octave lower. By the end of
> it, it doesn't even matter what key I was in before hand or
> how awkward the 1&2 were when first introduced, that short
> repetition sort of just pounds it home.
> This is all making me suspect that the study of tuning has
> little to teach us about the workings of tonality. Or at
> least that no scale/tuning is guaranteed to be tonal or atonal.

It looks like Mike and I reached a similar conclusion in the
other thread ("compositional signals").

I actually think the last link I gave
http://www.youtube.com/watch?v=UHzPcPHmNJQ
is the most critical example. I should give the score a look.
I still can't help but wonder if it's the clearest example
because perfect 4ths and 5ths occur in more modes of the
diatonic scale than triads or extended chords. And hey- maybe
jazz can tonicize all the modes because the extended chords
narrow it down faster! Hm.

-Carl

🔗Valentine, Bob <bob.valentine@...>

Igs : But here's another log for the fire: I realized today that when I try to play something "modal", I instinctively use certain rhythmic and structural devices to tonicize pretty much any note I want. <snip>
This is all making me suspect that the study of tuning has little to teach us about the workings of tonality. Or at least that no scale/tuning is guaranteed to be tonal or atonal.

Thank you. Strong beat / weak beat, dynamics and how the melody resolves should not be ignored.

For two 'modal vamps' that demonstrate this

Dorian ||: Dm G :|| ala Carlos Santana
Mixolydian ||: G Dm :|| ala Broadway

Harmony is a reduction of polyphony. For the past few hundred years we sort of let that reduction take over a lot of ways of thinking. I've been listening to a lot of "pre functional" classical music
and a very common cadence, as we would write it now, is

Bm C (C probably has no third in it)

The melodic resolution are all very nice

B-->C
F#-->G
D-->C

Then they started twiddling with the lead voice

B-->A-->C
F#-->G
D-->C

And that same lead voice a few hundred years later, after 'tonal' music started became 'melodic minor'.

V-->I is not universal, even in the West!

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🔗Mike Battaglia <battaglia01@...>

On Thu, May 5, 2011 at 4:04 PM, Carl Lumma <carl@...> wrote:
>
> --- Mike Battaglia <battaglia01@...> wrote:
>
> > So, if we're looking at things from this angle, then you also
> > have the fact that certain "modal" pieces sound like they
> > consist of constantly wandering tonics with no relationship
> > to one another (what "Nefertiti" might sound like),
>
> Sorry- did you link to a piece called Nefertiti? I searched
> the archives and only found this message.

Nefertiti is this one:

http://www.youtube.com/watch?v=fnoN3qEYJS4

> > Then, at the end, it goes Gmaj7 | Fmaj7 | Gmaj7 | Fmaj7.
> > However, over the Fmaj7, they still play an F# in the melody,
> > but it sounds really natural. This is another very salient point.
>
> Yes, I think we're agreed that it's possible to be functional
> in modes other than the ionian and aeolian. If we go back to
> my original /tuning/topicId_98715.html#98715
> it says, "Of course classical tonality had two modes in the
> flop... Composition was used to signal which mode was intended."
> So if composition can signal one out of 2, it presumably can
> signal one out of seven.

What mode does the chord D F B E A D F# signal? Imagine those notes
are in ascending order, so it's like a minor third, a tritone, some
fourths, and a major third on top all stacked vertically.

What mode does the chord C E G B D F# A C# signal?

What mode does Gb D Bb C F A E signal?

How about D A F# B E A# signal?

How about C E Bb Eb Gb Ab Eb F?

What mode does the progression F#maj7/D -> F#maj7b5/D -> Gm7 signal?
Sounds like D altered -> Dorian, but the C# in that first chord
doesn't fit into altered.

-Mike

🔗Carl Lumma <carl@...>

--- Mike Battaglia <battaglia01@...> wrote:

> Nefertiti is this one:
> http://www.youtube.com/watch?v=fnoN3qEYJS4

Ah, thanks.

I'm thinking the Machaut is the critical example for me
right now, so I'm going to try to analyze it when I get
a chance.

> > Yes, I think we're agreed that it's possible to be functional
> > in modes other than the ionian and aeolian. If we go back to
> > my original /tuning/topicId_98715.html#98715
> > it says, "Of course classical tonality had two modes in the
> > flop... Composition was used to signal which mode was intended."
> > So if composition can signal one out of 2, it presumably can
> > signal one out of seven.
>
> What mode does the chord D F B E A D F# signal?
> What mode does the chord C E G B D F# A C# signal?
> What mode does Gb D Bb C F A E signal?
> How about D A F# B E A# signal?
> How about C E Bb Eb Gb Ab Eb F?

I dunno, I guess I need to write a function to handle this
volume of inquiry. I guess we could also ask, what mode
does C E G signal? Or G B D signal? etc. Those don't
signal any mode, but put triads together in a progression
and pretty soon they do (or key if you prefer). With larger
chords, perhaps some notes are allowed to be outside the
key and instead common tones between chords are used for
signaling (like the C > A7b13 > D7#11 > G13b9 > C example
we saw earlier, which has common dyads in C major). I admit
it's a speculative idea I can't take the time to test at
the moment.

> What mode does the progression
> F#maj7/D -> F#maj7b5/D -> Gm7 signal?
> Sounds like D altered -> Dorian, but the C# in that first
> chord doesn't fit into altered.

If I understand slash notation (I don't really) I believe
that'll look like this

E -o--- E ----- F
C# ---- C -x
A# -o-- A# -o-- Bb
F# -o-- F# ---- G
D -o--- D -o--- D

Common tones across the whole progression are: D, A#/Bb
Common tones between adjacent chords are: D, F#, A#/Bb, E

That doesn't exactly point to D dorian. Then again, it's
a really short progression.

-Carl

🔗David Bowen <dmb0317@...>

🔗Mike Battaglia <battaglia01@...>

On Mon, May 9, 2011 at 2:09 PM, Carl Lumma <carl@...> wrote:
>
> > What mode does the chord D F B E A D F# signal?
> > What mode does the chord C E G B D F# A C# signal?
> > What mode does Gb D Bb C F A E signal?
> > How about D A F# B E A# signal?
> > How about C E Bb Eb Gb Ab Eb F?
>
> I dunno, I guess I need to write a function to handle this
> volume of inquiry. I guess we could also ask, what mode
> does C E G signal? Or G B D signal? etc. Those don't
> signal any mode, but put triads together in a progression
> and pretty soon they do (or key if you prefer).

I guess the Socratic method doesn't work if you don't lead into it
properly. Yes, you're right, when you play C E G and then G B D, it's
ambiguous as to whether or not you're playing Ionian or Lydian. You
can play a 6-note hexachord if you'd like, or pick either Ionian or
Lydian to intentionally flesh it out more in one of those directions.

But look at the original chord, D F B E A D F#. Which F is in the
mode, F or F#? How about C E G B D F# A C#? If you look at the bottom
of that chord, it's C lydian, but the top makes it look like C#
locrian. Gb D Bb C F A E on bottom looks like it's going to be lydian
augmented #2, but the E on top is a #6. D A F# B E A# has both a 5 and
a #5 in it. The point is that all of these don't fit into any mode.

Let's go back to D F B E A D F#. There are two ways to handle this
problem in practice: one is to pick a different mode to play over the
bottom half of the chord than the upper half. For the bottom half,
there's no G or C specified, so we'll make a creative decision to pick
G and C natural. Then for the bottom half, you could play D dorian,
and over the top, you'd end up playing D mixolydian. I've heard the
term "modal field" thrown around to describe this before, but can't
see much about it on Google.

A second option might be to find some kind of scale that encompasses
the whole thing. You could smush all of the notes together to get D E
F F# G A B C D, but this is improper. Since the choice of G was left
open, you could change it to G#. In 12-tet this gives you D E F F# G#
A B C D, which is a proper MODMOS of diminished[8]. You could play
that over everything.

There's also probably an augmented[9] MODMOS that would work as well.
In general, you can find ways to construct scales around whatever
harmonies you'd like, and there's often more than one way to do it.

> With larger
> chords, perhaps some notes are allowed to be outside the
> key and instead common tones between chords are used for
> signaling (like the C > A7b13 > D7#11 > G13b9 > C example
> we saw earlier, which has common dyads in C major). I admit
> it's a speculative idea I can't take the time to test at
> the moment.

How about Cmaj9 -> Eb9 -> Abmaj7 -> Db9#11 -> Cmaj9?

> > What mode does the progression
> > F#maj7/D -> F#maj7b5/D -> Gm7 signal?
> > Sounds like D altered -> Dorian, but the C# in that first
> > chord doesn't fit into altered.
>
> If I understand slash notation (I don't really) I believe
> that'll look like this
>
> E -o--- E ----- F
> C# ---- C -x
> A# -o-- A# -o-- Bb
> F# -o-- F# ---- G
> D -o--- D -o--- D

The E in the first two chords should be F#. There is an augmented[9]
MODMOS that fits over this chord (D Eb F F# G# A Bb C C# D), but it
would probably sound more natural to just play a different scale over
the bottom than the top of the chord. Throw a D# in there as well to
even further confuse things.

> Common tones across the whole progression are: D, A#/Bb
> Common tones between adjacent chords are: D, F#, A#/Bb, E
>
> That doesn't exactly point to D dorian. Then again, it's
> a really short progression.

I'd play D altered over the first one, but at the top of the scale,
rather than going back to D, I'd go to C#. Then I'd do the same thing
over the second scale. Then I'd go to either G dorian or aeolian at
the end. I was basically taking it from

A-C-Eb-G-B-D -> D-Gb-Bb-C-F -> G-E-Bb-D-F#

You'd play locrian#2 over the first one, D altered over the second
one, and G melodic minor over the last one. This is the cliche and
standard ii-V-i that we were taught to play to go to minor chords
(more elegant ways of doing this exist). I took the second chord,
which is rooted in D altered, and threw a C# into it. Sooner or later
you start to feel like there's no point in thinking about chords
signalling modes to begin with, and that it rather works where you can
play one of any number of modes around any chord. Sometimes there are
chords that no commonly used mode will fit.

-Mike

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

🔗Carl Lumma <carl@...>

--- Mike Battaglia <battaglia01@...> wrote:

> > Yes, and I've been using the 'progression common tones'
> > approach for that. That is, actually, the speculative idea
> > I was referring to.
>
> I'm not sure I really understand the idea.

Oh, idea is, you allow some chord tones to be 'just for color'
but insist that the common tones across the progression signal
the underlying mode. Or something like that. Well, it seemed
to work in the C > A7b13 > D7#11 > G13b9 > C example and I
managed to get D phrygian for F#maj7/D -> F#maj7b5/D -> Gm7
once David corrected my mistake (would D phrygian work if you
had to pick a single diatonic mode to use with it?)

> I can tell you for a fact
> that common tones have a lot to do with what mode you'd likely
> find the most natural sounding over a chord. // I wouldn't
> claim that D F B E A D F# "signals" the diminished/augmented
> MODMOS's I laid out in that email, but I would claim that those
> scales might be decent choices to play over the chord, although
> I like the modal field approach more.

Ok, it's just that it's got to signal something if it's going
to be functional - some way of relating the chords to one
another. That doesn't have to be a scale but it seems like
it could usually be. Maybe it's as simple as the list of
chord roots, I dunno.

Also, I wrote:
> Thanks! I don't understand modes or extended chords
> (beyond 7th chords) at all - at least not in a way I can
> access when composing or jamming.

I don't mean to express false modesty, I do wish I understood
them better (the kind of understanding you can only get
through much practice). I composed the piece just by trying
things by ear. -Carl

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

On Tue, May 10, 2011 at 1:58 AM, Carl Lumma <carl@...> wrote:
>
> Oh, idea is, you allow some chord tones to be 'just for color'
> but insist that the common tones across the progression signal
> the underlying mode. Or something like that. Well, it seemed
> to work in the C > A7b13 > D7#11 > G13b9 > C example and I
> managed to get D phrygian for F#maj7/D -> F#maj7b5/D -> Gm7
> once David corrected my mistake (would D phrygian work if you
> had to pick a single diatonic mode to use with it?)

I would think of it more as G aeolian, since the whole thing is
basically an evolved V7->I, but yeah, that's what I'd play over the
end. I think you might get better results if you just draw 7 blank
spaces, _ _ _ _ _ _ _, and then fill in the blanks with the first
chord. If the first chord leaves a few diatonic positions ambiguous,
I'd leave it blank. Then, for the next chord, fill in the remaining
blanks. If one of the notes in this chord clashes with the note you
have written, then change it, and change as few notes as possible. The
mode you end up with at every step of this process will be the most
natural sounding mode to play during each step. The mode that's being
signaled is always transient.

If you end up with the unfortunately improper C D# E F# G A Bb C, do
yourself a favor and throw C# in there to turn it into diminished[8].
One last note - people like to use the altered scale like this

C Db Eb Fb Gb Ab Bb C

Although it's technically Fb, you're better off treating the scale like

C Db D# E F# G#/Ab Bb C

Meaning you treat it like there are two seconds, a b2 and a #2 (or a
b9 and a #9). It gets even messier when you use the diminished scale
over dominant 7 chords. This is basically the beginning of the whole
system breaking down and revealing that what we're doing is trying to
fit proper scales to the underlying harmony, not the other way around.
But it still works well enough.

> > I can tell you for a fact
> > that common tones have a lot to do with what mode you'd likely
> > find the most natural sounding over a chord. // I wouldn't
> > claim that D F B E A D F# "signals" the diminished/augmented
> > MODMOS's I laid out in that email, but I would claim that those
> > scales might be decent choices to play over the chord, although
> > I like the modal field approach more.
>
> Ok, it's just that it's got to signal something if it's going
> to be functional - some way of relating the chords to one
> another. That doesn't have to be a scale but it seems like
> it could usually be. Maybe it's as simple as the list of
> chord roots, I dunno.

I tend to think of it as some kind of, uh, musico-spatial reasoning
that we end up building. Melodic motion is pretty floaty, so we have
to learn how to make sense of it all. We end up with a set of learned
behaviors that cue us into piecing what's going on differently in
different contexts. Hence when you listen to Knowsur's album in
14-tet, you hear "majorness" and "minorness" in it. For example,
although this could theoretically be in any mode at all, I predict
you'll probably hear it as being very loosely in Mixolydian - meaning
you'll hear the base sonority as being "Major" over "minor" (if you
had to pick one) and having a b7 instead of a #7:

http://www.youtube.com/watch?v=m9NlHaWllwU

I also predict you'll hear this being very loosely centered around
minor, either perhaps Aeolian or a bastardized Aeolian with a neutral
sixth:

http://soundcloud.com/knowsur/haneru

I hear a few pretty sweet porcupine-ish or mohajira-ish moments in
this as well, but on the whole I'd say I hear it as minor over major.

As a last note, I was showing Mark Nowitzky my functional porcupine
example yesterday. The melody goes something like
G-Av-Av-Bb-Bb-C-C-D-E-C-D-B-C, where G-Av-Bb-C is 3 equal divisions of
the 4/3. Mark claimed he heard the melody as G-A-A-B-B-C-C, where the
B is a major third above the root. He heard two whole steps in a row,
so his brain clued the result into major third mode - never mind that
these are actually 10/9 whole steps and two of them land you at 6/5.
Then the C was a clear 4/3 away from where I started, so he heard C.
These are the kind of signaling cues I'm talking about, and I think
some evolved version of this concept applies to chord progressions as
well.

> Also, I wrote:
> > Thanks! I don't understand modes or extended chords
> > (beyond 7th chords) at all - at least not in a way I can
> > access when composing or jamming.
>
> I don't mean to express false modesty, I do wish I understood
> them better (the kind of understanding you can only get
> through much practice). I composed the piece just by trying
> things by ear. -Carl

I'm not sure where you're at, so I might as well just give you the
full run down from the beginning. The modes form a spectrum of colors,
of which major and minor are just two points on a spectrum. Arrange
the modes out from "brightest" to "darkest" (generators up to
generators down)

Lydian
Ionian
Mixolydian
Dorian
Aeolian
Phrygian
Locrian

For each of those modes, a good exercise is to figure out what the
tonic is, and then figure out where the similar quality chords are

Lydian - I, II, V
Ionian - I, IV, V
Mixolydian - I, bVII, IV
Dorian - i, ii, v
Aeolian - i, iv, v
Phrygian - i, bvii, iv
Locrian - im7omit5, biii, v, bvii

Your task: screw around with these chord progressions for a while. So
let's say you're starting with Mixolydian. You must first immediately
rip off the Who by playing Cmaj -> Bbmaj -> Fmaj for a little bit.
Once you get comfortable with that progression, your next task is to
explore using borrowed chords to create a modal shift. So let's try
borrowing a chord from Dorian and throwing it in the cycle

||: Cmaj | Ebmaj | Bbmaj | Fmaj :||

Now it changes colors repeatedly through the cycle. Or, is it that
you're really signaling the scale C D Eb E F G A Bb C, and this "color
shift" is just an ordinary chord progression change within that scale?
The answer: both.

There's lots more, but maybe that'll help you get some ideas. A few
guidelines: if you just borrow chords at random from other random
modes, the whole thing might sound disconnected. For example, Cmaj ->
Gbmaj is like borrowing a chord from Locrian, but it'll probably just
sound like some kind of vaguely diaschismic or perhaps just
disconnected mush. To avoid this, you might want to try only borrowing
chords from one or two modes in either direction on the above chart,
expanding more as your ear starts to branch out and hear these new and
often very abstract relationships. And for some reason I like
borrowing chords from darker modes more than brighter modes, but maybe
that's just me. So for example, the C-Gb root movement works better in
the context of ||: Cm7 | Gbmaj7#11 | Fm7 | Bb13 :||, where you're
moving from Aeolian to Locrian. If you think

Phew.

-Mike

🔗Carl Lumma <carl@...>

--- Mike Battaglia <battaglia01@...> wrote:

> Hence when you listen to Knowsur's album in
> 14-tet, you hear "majorness" and "minorness" in it. For example,
> although this could theoretically be in any mode at all, I
> predict you'll probably hear it as being very loosely in
> Mixolydian - meaning you'll hear the base sonority as being
> "Major" over "minor" (if you had to pick one) and having
> a b7 instead of a #7:
> http://www.youtube.com/watch?v=m9NlHaWllwU

Alas, my mixolydian perception isn't well developed enough
to categorically perceive things as being mixolydian. :(
This track sounds pretty neutral to me.

> I also predict you'll hear this being very loosely centered
> around minor, either perhaps Aeolian or a bastardized Aeolian
> with a neutral sixth:
> http://soundcloud.com/knowsur/haneru

This sounds completely neutral to me. It sounds a bit more
'modal' or floaty than the last one. Maybe that's related.
Maybe also that I've spent a fair amount of time fooling
around with neutral scales over the years.

> I'm not sure where you're at, so I might as well just give you
> the full run down from the beginning. The modes form a spectrum
> of colors, of which major and minor are just two points on a
> spectrum. Arrange the modes out from "brightest" to "darkest"
> (generators up to generators down)
> Lydian
> Ionian
> Mixolydian
> Dorian
> Aeolian
> Phrygian
> Locrian

Thanks, I'll try listening to them in this order later.

> Lydian - I, II, V
> Ionian - I, IV, V
> Mixolydian - I, bVII, IV
> Dorian - i, ii, v
> Aeolian - i, iv, v
> Phrygian - i, bvii, iv
> Locrian - im7omit5, biii, v, bvii
>
> Your task: screw around with these chord progressions for
> a while.

OK!

> ||: Cmaj | Ebmaj | Bbmaj | Fmaj :||
> Now it changes colors repeatedly through the cycle. Or, is it
> that you're really signaling the scale C D Eb E F G A Bb C,
> and this "color shift" is just an ordinary chord progression
> change within that scale? The answer: both.

That's a nice progression of a kind I fool with a lot.
I'm not sure I hear a color shift in it though. Oh, with
the right voicing, the F sounds like the I, so that when
it repeats there's a jump when C becomes the new I. Is
that what you mean? I love that sort of thing.

-Carl

🔗Mike Battaglia <battaglia01@...>

On Wed, May 11, 2011 at 6:23 PM, Carl Lumma <carl@...> wrote:
>
> > I also predict you'll hear this being very loosely centered
> > around minor, either perhaps Aeolian or a bastardized Aeolian
> > with a neutral sixth:
> > http://soundcloud.com/knowsur/haneru
>
> This sounds completely neutral to me. It sounds a bit more
> 'modal' or floaty than the last one. Maybe that's related.
> Maybe also that I've spent a fair amount of time fooling
> around with neutral scales over the years.

So if you had to pick this track as being either major or minor, you'd
say neither?

> > I'm not sure where you're at, so I might as well just give you
> > the full run down from the beginning. The modes form a spectrum
> > of colors, of which major and minor are just two points on a
> > spectrum. Arrange the modes out from "brightest" to "darkest"
> > (generators up to generators down)
> > Lydian
> > Ionian
> > Mixolydian
> > Dorian
> > Aeolian
> > Phrygian
> > Locrian
>
> Thanks, I'll try listening to them in this order later.

Do it with all modes in parallel, e.g. all starting on C. None of this
"starting on the different keys of the C major scale" crap. Generators
up vs generators down is what you want.

> > ||: Cmaj | Ebmaj | Bbmaj | Fmaj :||
> > Now it changes colors repeatedly through the cycle. Or, is it
> > that you're really signaling the scale C D Eb E F G A Bb C,
> > and this "color shift" is just an ordinary chord progression
> > change within that scale? The answer: both.
>
> That's a nice progression of a kind I fool with a lot.
> I'm not sure I hear a color shift in it though. Oh, with
> the right voicing, the F sounds like the I, so that when
> it repeats there's a jump when C becomes the new I. Is
> that what you mean? I love that sort of thing.

That isn't really what I was getting at. Let's reframe it so that
you're in F. So now the progression is

||: Fmaj | Cmaj | Ebmaj | Bbmaj :||

Or I V bVII IV. Now, before playing that progression, just play I IV V
a bunch of times, so you stick mostly to F ionian. Then after getting
the sound of F ionian in your head, start doing the progression above,
e.g. throw the Ebmaj in there. To my ears at least, the Eb causes a
pretty strong color shift.

-Mike

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

🔗Chris Vaisvil <chrisvaisvil@...>

🔗genewardsmith <genewardsmith@...>

🔗cityoftheasleep <igliashon@...>

I really like the 14-EDO etude, but I wouldn't say it sounds "major" OR "neutral". To me it feels "suspended" for the most part. Like, I can't even tell what interval the main melody is harmonized with--is it a 3rd or a 4th? I'll agree it's definitely not minor, but it sounds really really NOT major. I'm listening to it as I type this...man, this might actually be my favorite etude! He does some really brilliant stuff in the middle section, throwing in some pseudo-diminished chords and really jacking up the tension, and then playing that off the odd tropical suspended brightness of the 7-EDO scale. It sounds really smooth, compelling, and even natural to me, much like the 23-EDO etude. But very definitely not fit into my associations with "major". Sure, it's probably more "major" than "minor", but only in the sense that I find a sus2 or sus4 more "major" or "minor" (so it's an artificial dichotomy, in my ears).

-Igs

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Tue, May 17, 2011 at 4:31 AM, Carl Lumma <carl@...> wrote:
> >
> > --- Mike Battaglia <battaglia01@> wrote:
> >
> > > > Neutral seems to be a gestalt I recognize, so I'd say neutral.
> > >
> > > Alright, how about Blackwood's 14-equal? That's definitely
> > > neutral, but to me it also sounds major. It does not
> > > sound minor.
> >
> > It sounds more major to me than neutral. Like really out
> > of tune major. I've never liked it.
>
> I really like it too. Anyway, I think that that's significant, and I
> wouldn't imagine there's a person on this list who hears that piece as
> major. In fact, I bet that if you went and sat at a piano, the closest
> match to the melody at 0:03 would sound like C#-B-A-F#-E-C#-E-E,
> although it could theoretically be anything, and I predict that every
> single person on this list will hear it the same way. Now to see how
> that might vary by region.
>
> -Mike
>

🔗Mike Battaglia <battaglia01@...>

On Tue, May 17, 2011 at 2:05 PM, cityoftheasleep
<igliashon@...> wrote:
>
> I really like the 14-EDO etude, but I wouldn't say it sounds "major" OR "neutral". To me it feels "suspended" for the most part. Like, I can't even tell what interval the main melody is harmonized with--is it a 3rd or a 4th?

Igs, THIS is what I was talking about when I posted the link to the
Frere Jacques study. What you're saying is that you are having trouble
finding the "roots" for the dyads in this piece of music, as does it
seem like you're having difficult figuring out what the individual
pitches are, which is the same thing as finding the root for each
pitch in isolation. Since this process can be so difficult, we can
acquire a set of rules to aid us in doing it, and these rules can be
improved or increased with musical training. Likewise, the learned
memory of the melody for "Frere Jacques" can provide a listener with a
set of rules to predict and follow the roots that should come next,
which dramatically alters how VF estimation occurs.

Furthermore, there really is no "correct" way to do this, who's to say
that it's not suspended as you said? Just because Carl and Gene and I
heard it as neutral-ish major, who's to say that that's "right" and
that the interpretation of it as suspended is "wrong?" That was the
point of the study, to demonstrate that a set of learned rules like
this actually completely dominates VF perception.

For the record, it's both, thirds and fourths in alternation; he's
arpeggiating a 7-equal pentatonic scale.

One last question, what about this knowsur piece?

http://soundcloud.com/knowsur/haneru/

Give it a listen, then afterwards go to rot13.com and type this in:
Guvf vf zbfgyl zvabe, jvgu fbzr "arhgeny" ryrzragf guebja va, ohg gur
gbavp vf trarenyyl zvabe, zber fcrpvsvpnyyl n zvabe 7 pubeq.

See if you agree.

> I'll agree it's definitely not minor, but it sounds really really NOT major. I'm listening to it as I type this...man, this might actually be my favorite etude! He does some really brilliant stuff in the middle section, throwing in some pseudo-diminished chords and really jacking up the tension, and then playing that off the odd tropical suspended brightness of the 7-EDO scale. It sounds really smooth, compelling, and even natural to me, much like the 23-EDO etude. But very definitely not fit into my associations with "major". Sure, it's probably more "major" than "minor", but only in the sense that I find a sus2 or sus4 more "major" or "minor" (so it's an artificial dichotomy, in my ears).

It's a pretty damn sweet etude. I think the 13-equal is my favorite
right now though, I feel like I'm underwater.

-Mike