Yahoo Tuning Groups Ultimate Backup tuning V

On Tue, May 3, 2011 at 11:55 AM, Kalle Aho <kalleaho@...> wrote:
>
> > Hm. I guess it's true that when you take away the leading tone, the
> > strength of the resolution changes, but Gmaj -> Cm just has a
> > different sound and feeling to it than Gm -> Cm.
>
> Sure, they sound different but with those voicings and sine waves
> they are just two different chord changes. I don't hear them as
> resolutions. On the other hand, G D Bb G -> C G E C sounds more like
> a resolution probably because minor chord is more tense than major
> even with sine waves.

I guess it really does work pretty well. Maybe part of the resolution
is that the leading tone is so satisfying, combined with the 3/2 root
movement in the bass, that we just like it a lot and hope it happens
again and again.

> I used to think that instead of (IV-)V-I the true authentic cadence
> was V7-I. I'm not so sure about that anymore but I think that there
> can be V-I progressions as harmonizations of melodies without them
> necessarily being cadential while V7-I is probably always cadential
> (even when I already half-anticipate some obscure example from you
> where this is not the case :)).

What do you mean by cadential?

> I have no idea if the plain V-I was ever used cadentially before
> that. [AFAIK the cadences used to be progressions from imperfect
> (thirds and sixths) to perfect (unisons, fifths and octaves)
> consonances.] Certainly after that, yes, but I speculate that the use
> of dominant seventh chords conditioned people to hear also the plain
> V-I as cadential.

That's very possible, although I note that I hear it as resolving even
if it's played on an acoustic guitar with power chords. But it seems
to depend on what I hear as the "key" - e.g. Gmaj -> Cmaj sounds like
it's resolving if the key is C, but not if the key is G. Then it just
sounds like I - IV.

> A similar phenomenon is the use of dominant seventh
> chords without the proper voice leading. But then again, I tend to
> view the history of music as a series of creative
> misunderstandings. :)

I think the history of music can give us some strong clues as to what
matters and doesn't matter, but we should also keep in mind that
people tended to just search for and discover order in the tools that
they had available at the time. When those tools didn't provide
exploration for further order, they tended to abandon them. So while
we discovered lots of order in the diatonic scale, when the time came
to move onto extended harmony, we left it behind. That's the only
point I was making - that although people overstructured everything
around the diatonic scale at the time, they were mistaken to place
cognitive importance on it as the source of all functional harmony. So
perhaps that's what you mean by "creative misunderstandings."

> Returning to my natural minor cadence I'd say that it has qualities
> similar to authentic cadence even if the root movement is from
> subdominant to tonic.

I guess the contracting tritone makes it sound kind of similar, but
the root movement being from subdominant to tonic overwhelms all else
in my mind. If you make it go D B F A -> C C E A it starts to sound
more and more like it's in some kind of middle ground.

-Mike

🔗Kalle Aho <kalleaho@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Tue, May 3, 2011 at 11:55 AM, Kalle Aho <kalleaho@...> wrote:
> >
> > > Hm. I guess it's true that when you take away the leading tone, the
> > > strength of the resolution changes, but Gmaj -> Cm just has a
> > > different sound and feeling to it than Gm -> Cm.
> >
> > Sure, they sound different but with those voicings and sine waves
> > they are just two different chord changes. I don't hear them as
> > resolutions. On the other hand, G D Bb G -> C G E C sounds more like
> > a resolution probably because minor chord is more tense than major
> > even with sine waves.
>
> I guess it really does work pretty well. Maybe part of the resolution
> is that the leading tone is so satisfying, combined with the 3/2 root
> movement in the bass, that we just like it a lot and hope it happens
> again and again.

There is 3/2 root movement in IV-I too and a semitonal motion from
the subdominant's root to the third of the tonic. Apparently leading
to the root of the tonic is more satisfying. But what's the secret of
leading tones? Is it simply the pitch proximity? Some say that it is
rather the rarity of semitones in the diatonic scale that makes them
work as signposts. This would be good news for scales where the large
step is the rare one. But this is already outside your paradigm
because you don't allow the context of scales to determine functional
relationships. But this might explain why Emaj-Cmaj doesn't sound
like a strong resolution even though there is a leading tone to the
tonic.

> > I used to think that instead of (IV-)V-I the true authentic cadence
> > was V7-I. I'm not so sure about that anymore but I think that there
> > can be V-I progressions as harmonizations of melodies without them
> > necessarily being cadential while V7-I is probably always cadential
> > (even when I already half-anticipate some obscure example from you
> > where this is not the case :)).
>
> What do you mean by cadential?

Concluding a phrase, section or piece. Also establishing the key.

> > I have no idea if the plain V-I was ever used cadentially before
> > that. [AFAIK the cadences used to be progressions from imperfect
> > (thirds and sixths) to perfect (unisons, fifths and octaves)
> > consonances.] Certainly after that, yes, but I speculate that the use
> > of dominant seventh chords conditioned people to hear also the plain
> > V-I as cadential.
>
> That's very possible, although I note that I hear it as resolving even
> if it's played on an acoustic guitar with power chords. But it seems
> to depend on what I hear as the "key" - e.g. Gmaj -> Cmaj sounds like
> it's resolving if the key is C, but not if the key is G. Then it just
> sounds like I - IV.

What about a single bass voice?

> > A similar phenomenon is the use of dominant seventh
> > chords without the proper voice leading. But then again, I tend to
> > view the history of music as a series of creative
> > misunderstandings. :)
>
> I think the history of music can give us some strong clues as to what
> matters and doesn't matter, but we should also keep in mind that
> people tended to just search for and discover order in the tools that
> they had available at the time. When those tools didn't provide
> exploration for further order, they tended to abandon them. So while
> we discovered lots of order in the diatonic scale, when the time came
> to move onto extended harmony, we left it behind. That's the only
> point I was making - that although people overstructured everything
> around the diatonic scale at the time, they were mistaken to place
> cognitive importance on it as the source of all functional harmony. So
> perhaps that's what you mean by "creative misunderstandings."

Not really. I mean things like starting to hear certain verticalities
in counterpoint as independent entities i.e. chords, then later making
these chords and their progressions central to music even to the
point of disregarding good voice leading (e.g. strumming). Then there
is what happened to rhythm in popular music: there used to be songs
that you could sing without rhythmic accompaniment (also you could
hear the accompanying chords in your mind's ear) and it would make
perfect sense to the listeners who could even dance to the mere
melody. For contemporary pop we need some kind of karaoke background
because without that the melodies sound like unrelated fragments most
of the time. I view some of these as heresies and others as great
developments. :)

> > Returning to my natural minor cadence I'd say that it has qualities
> > similar to authentic cadence even if the root movement is from
> > subdominant to tonic.
>
> I guess the contracting tritone makes it sound kind of similar, but
> the root movement being from subdominant to tonic overwhelms all else
> in my mind. If you make it go D B F A -> C C E A it starts to sound
> more and more like it's in some kind of middle ground.

I'm waiting what you say about that single bass voice.

Kalle

🔗Mike Battaglia <battaglia01@...>

🔗Kalle Aho <kalleaho@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Thu, May 5, 2011 at 11:13 AM, Kalle Aho <kalleaho@...> wrote:
> >
> > There is 3/2 root movement in IV-I too and a semitonal motion from
> > the subdominant's root to the third of the tonic. Apparently leading
> > to the root of the tonic is more satisfying. But what's the secret of
> > leading tones? Is it simply the pitch proximity? Some say that it is
> > rather the rarity of semitones in the diatonic scale that makes them
> > work as signposts.
>
> Who says this, and why?

Browne, Richmond (1981). "Tonal Implications of the Diatonic Set", In
Theory Only 5, nos. 1 and 2: 3-21

and Paul Erlich quoting him "rare intervals aid position finding" in
his 22-tone paper. Haven't read the Browne paper so I don't know why
exactly they say this.

> I think the two effects are just different -
> rare intervals can have one effect, and leading tones that have
> minimal spectral overlap can have another effect. In the case of the
> diatonic scale, the two overlap. But when you have D F A C -> Db F Ab
> B -> C E G C, that Db-C resolves really well, even though we aren't
> sticking to a single diatonic scale there.

I think it's once again the resolving tritone that makes this a nice
resolution. Of course the Db-C adds to the voice leading. But note
that this tritone substitution sounds noticeably less strong than V7-
I. So this example doesn't really refute the effect of scale
structure. It may even support it, F and B are still members of the
scale.

> But check out the sLssLss mode of mavila[7], which has major chords
> at I, IV, and V - V still resolves to one really nicely. Check out
> some mavila comma pumps in this scale - let's call the notes
> C D E F G A B C for sLssLss.

I hear them resolving only weakly at best.

> > But this is already outside your paradigm
> > because you don't allow the context of scales to determine functional
> > relationships. But this might explain why Emaj-Cmaj doesn't sound
> > like a strong resolution even though there is a leading tone to the
> > tonic.
>
> It doesn't explain why Db7 -> Cmaj does sound like a strong resolution, however.

Maybe it does, see above.

> > > That's very possible, although I note that I hear it as resolving even
> > > if it's played on an acoustic guitar with power chords. But it seems
> > > to depend on what I hear as the "key" - e.g. Gmaj -> Cmaj sounds like
> > > it's resolving if the key is C, but not if the key is G. Then it just
> > > sounds like I - IV.
> >
> > What about a single bass voice?
>
> Sure, the same applies for a single bass voice.

Then I think the reason is conditioning. Or can you think of a
psychoacoustic reason why a descending fifth should sound like a
resolution and an ascending fifth shouldn't (when you hear the center
note as the key center)?

Kalle

🔗Mike Battaglia <battaglia01@...>

On Wed, May 11, 2011 at 8:47 AM, Kalle Aho <kalleaho@...> wrote:
>
> > Who says this, and why?
>
> Browne, Richmond (1981). "Tonal Implications of the Diatonic Set", In
> Theory Only 5, nos. 1 and 2: 3-21
>
> and Paul Erlich quoting him "rare intervals aid position finding" in
> his 22-tone paper. Haven't read the Browne paper so I don't know why
> exactly they say this.

Yes, I'm aware that some people say this, but I don't see any reason
for it. I haven't read the Browne paper either, so maybe there's
something there. But in general, I'm tired of unfalsifiable,
self-limiting notions like these. What I do know is

1) If you also want to find things that we like, naturally, but that
"different from what we're accustomed to," and
2) If you tend to automatically overattribute every single thing that
we like to "conditioning," and
3) If your goal is to find things that we naturally like that we
aren't conditioned to like, well then

the resulting set of musical possibilities is the null set. Now, I'm
not saying that you specifically are doing this, but I am saying that
I've seen these ideas pop up from time to time, and I disagree with
them. At that point I might as well make any chord progression at all
and just claim that you can hear it as "functional" after another
20-30 years of listening, and who's to say I'm wrong? It's
unfalsifiable. I'm not saying that learning doesn't matter, but I'm
saying that we have no idea how most of the process works, and for us
to overassume that everything is learned leads to this.

Hey, here's a vaguely related question, what do you hear as more
"comprehensible?" Keemun[7] in 15-equal, or Augmented[9] in 12-equal?
Because for me, and for most of my naive 12-tet friends, it seems to
be Keemun[7], which sounds like an awesomely otonal version of the
diminished scale. Augmented[9] sounds like a jumbled mess of random
half and whole steps. You never know what's a whole step and what's
just two half steps in augmented[9]. Now, some people claim that I
just have to learn to wrap my head around augmented[9]. Yeah, well, it
didn't take me this long to wrap my head around diminished[8] when I
first learned it, and I picked up on Keemun[7] and Triforce[9]
instantly. Sometimes there are deeper elements at work than just
learning.

> I think it's once again the resolving tritone that makes this a nice
> resolution. Of course the Db-C adds to the voice leading. But note
> that this tritone substitution sounds noticeably less strong than V7-
> I. So this example doesn't really refute the effect of scale
> structure. It may even support it, F and B are still members of the
> scale.

It doesn't sound less strong to me at all, if anything it sounds even
stronger. Tritone subs can really strengthen resolutions when thrown
in at the right time.

> > But check out the sLssLss mode of mavila[7], which has major chords
> > at I, IV, and V - V still resolves to one really nicely. Check out
> > some mavila comma pumps in this scale - let's call the notes
> > C D E F G A B C for sLssLss.
>
> I hear them resolving only weakly at best.

Well, if you spend some more time with them, maybe you'll hear them
resolving more strongly. But who says chords have to come from scales
to begin with? What about the blues?

Modulation in what sense?

> > Sure, the same applies for a single bass voice.
>
> Then I think the reason is conditioning. Or can you think of a
> psychoacoustic reason why a descending fifth should sound like a
> resolution and an ascending fifth shouldn't (when you hear the center
> note as the key center)?

What's the "center" note in this case? There's only a lower and an upper note.

And even if it is conditioning, so what? That still doesn't imply that
one can be conditioned in any way at all. There are probably limits on
what we can be conditioned to hear.

-Mike

🔗Kalle Aho <kalleaho@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Wed, May 11, 2011 at 8:47 AM, Kalle Aho <kalleaho@...> wrote:
> >
> > > Who says this, and why?
> >
> > Browne, Richmond (1981). "Tonal Implications of the Diatonic Set", In
> > Theory Only 5, nos. 1 and 2: 3-21
> >
> > and Paul Erlich quoting him "rare intervals aid position finding" in
> > his 22-tone paper. Haven't read the Browne paper so I don't know why
> > exactly they say this.
>
> Yes, I'm aware that some people say this, but I don't see any reason
> for it. I haven't read the Browne paper either, so maybe there's
> something there. But in general, I'm tired of unfalsifiable,
> self-limiting notions like these.

How is it self-limiting? It is also pretty obviously true when the
rare steps are different enough from the other steps. That doesn't
mean all music absolutely must use this as a cue for cognition.

> What I do know is
>
> 1) If you also want to find things that we like, naturally, but that
> "different from what we're accustomed to," and
> 2) If you tend to automatically overattribute every single thing that
> we like to "conditioning," and
> 3) If your goal is to find things that we naturally like that we
> aren't conditioned to like, well then
>
> the resulting set of musical possibilities is the null set. Now, I'm
> not saying that you specifically are doing this, but I am saying that
> I've seen these ideas pop up from time to time, and I disagree with
> them. At that point I might as well make any chord progression at all
> and just claim that you can hear it as "functional" after another
> 20-30 years of listening, and who's to say I'm wrong? It's
> unfalsifiable. I'm not saying that learning doesn't matter, but I'm
> saying that we have no idea how most of the process works, and for us
> to overassume that everything is learned leads to this.
>
> Hey, here's a vaguely related question, what do you hear as more
> "comprehensible?" Keemun[7] in 15-equal, or Augmented[9] in 12-equal?
> Because for me, and for most of my naive 12-tet friends, it seems to
> be Keemun[7], which sounds like an awesomely otonal version of the
> diminished scale. Augmented[9] sounds like a jumbled mess of random
> half and whole steps. You never know what's a whole step and what's
> just two half steps in augmented[9]. Now, some people claim that I
> just have to learn to wrap my head around augmented[9]. Yeah, well, it
> didn't take me this long to wrap my head around diminished[8] when I
> first learned it, and I picked up on Keemun[7] and Triforce[9]
> instantly. Sometimes there are deeper elements at work than just
> learning.

To whom you are addressing this "rant"? Because I'm not the guy. :)

> > I think it's once again the resolving tritone that makes this a nice
> > resolution. Of course the Db-C adds to the voice leading. But note
> > that this tritone substitution sounds noticeably less strong than V7-
> > I. So this example doesn't really refute the effect of scale
> > structure. It may even support it, F and B are still members of the
> > scale.
>
> It doesn't sound less strong to me at all, if anything it sounds even
> stronger.

OK.

> Tritone subs can really strengthen resolutions when thrown in at the
> right time.

Sure, they are cool.

> > > But check out the sLssLss mode of mavila[7], which has major chords
> > > at I, IV, and V - V still resolves to one really nicely. Check out
> > > some mavila comma pumps in this scale - let's call the notes
> > > C D E F G A B C for sLssLss.
> >
> > I hear them resolving only weakly at best.
>
> Well, if you spend some more time with them, maybe you'll hear them
> resolving more strongly.

I heard C D A C -> C E G C as pretty strong though. It's interesting
as the D-A is a sharp fifth, all others are flat. In TOP Mavila it's
coincidentally relatively well tuned too.

> But who says chords have to come from scales to begin with?
> What about the blues?

They don't have to. But when they do, the scale structure can have
some influence on how the harmony is heard. That's all.

When I play it so that the first Cmaj and the last are voiced in
different inversions, I hear as if the key has changed. Surely it is
the comma pump playing tricks on me!

> > > Sure, the same applies for a single bass voice.
> >
> > Then I think the reason is conditioning. Or can you think of a
> > psychoacoustic reason why a descending fifth should sound like a
> > resolution and an ascending fifth shouldn't (when you hear the center
> > note as the key center)?
>
> What's the "center" note in this case? There's only a lower and an
> upper note.

I meant like if the center is C then the fifth ascends from F and
descends from G.

> And even if it is conditioning, so what? That still doesn't imply that
> one can be conditioned in any way at all. There are probably limits on
> what we can be conditioned to hear.

I agree and hearing an ascending root movement by fifth with
appropriate chords as strongly cadential is in my opinion well within
those limits.

Kalle

🔗Mike Battaglia <battaglia01@...>

On Thu, May 12, 2011 at 10:03 AM, Kalle Aho <kalleaho@...> wrote:
> >
> > Yes, I'm aware that some people say this, but I don't see any reason
> > for it. I haven't read the Browne paper either, so maybe there's
> > something there. But in general, I'm tired of unfalsifiable,
> > self-limiting notions like these.
>
> How is it self-limiting? It is also pretty obviously true when the
> rare steps are different enough from the other steps. That doesn't
> mean all music absolutely must use this as a cue for cognition.

I have not seen sufficient evidence for this "tritone hypothesis," nor
have I seen any evidence for this "rare interval" hypothesis, and so I
don't understand why people believe it. One example of a system that's
based around all of this is Pajara, which for me is a test case for
all of this theory.

I'll just leave it at that Pajara, which is based on this thinking,
doesn't work for me. The "rare intervals" in Pajara that are supposed
to act as "signposts" don't signal things as they're supposed to in my
perception. The response I usually get when I say this is that I've
spent 20 years learning the diatonic scale, and so I just need to keep
waiting and training myself and I'll eventually learn Pajara too.
-That- is what is self-limiting and unfalsfiable. You see, no matter
how long I take, there's always the chance that tomorrow I might hear
it differently! The same apparently applies to augmented[9] - although
it sounds like an incoherent mess, I can supposedly learn to hear it
as coherent if I just keep training myself. In the meantime, it turns
out that I can latch onto Keemun[7] almost instantly, so what happened
to learning? There must be some reason Keemun just snapped into place,
but Pajara didn't, or why Porcupine[7] sometimes sounds awkward, but
Keemun[7] doesn't sound like a screwed up diminished[8], which I have
plenty of experience with.

So this is why I say that ideas like that can be self-limiting. At one
point, wasn't it the case that everyone was all into learning to hear
different JI inflections as different musical phenomena, and then all
of you guys realized that people were just running into a wall by not
accepting their limitations? Then HE came about as a way to model
these limitations. I feel like the theory could use a similar update
now with stuff like this. It can't all just be about learning. Or, if
it can, then I wish I knew we had more insight into what that sort of
learning might entail, and something that took into account the last
century and a half worth of extremely harmonically complex music.

> To whom you are addressing this "rant"? Because I'm not the guy. :)

I'm just a ramblin fool I guess.

> > Well, if you spend some more time with them, maybe you'll hear them
> > resolving more strongly.
>
> I heard C D A C -> C E G C as pretty strong though. It's interesting
> as the D-A is a sharp fifth, all others are flat. In TOP Mavila it's
> coincidentally relatively well tuned too.

In 25-equal or 9-equal you might hear it as even stronger.

> > But who says chords have to come from scales to begin with?
> > What about the blues?
>
> They don't have to. But when they do, the scale structure can have
> some influence on how the harmony is heard. That's all.

How so?

> > Modulation in what sense?
>
> When I play it so that the first Cmaj and the last are voiced in
> different inversions, I hear as if the key has changed. Surely it is
> the comma pump playing tricks on me!

I think that it's a learned series of cues to pre-search for different
virtual pitches that's playing tricks on you. I think that this
learned series of cues could maybe come from scalar structure, or from
anything. I also think that much of the literature on this subject
ignores the last century and a half worth of music, because we're
dealing with an inbred crowd of academics that haven't kept up with
modern musical developments.

Whatever it is we've learned has its basis in some very simple
fundamental concept that has been "scaled upward" to create the
musical universe we inhabit today, but I don't quite understand what
that concept is. I think that the end result is that we end up
constructing a little musical "space" in our head, and mavila
completely destroys that space. I also think that, since we're very
sapient creatures, we are well aware of how this space and virtual
pitch perception interact, and don't really treat them as two
completely separate things.

> > > > Sure, the same applies for a single bass voice.
> > >
> > > Then I think the reason is conditioning. Or can you think of a
> > > psychoacoustic reason why a descending fifth should sound like a
> > > resolution and an ascending fifth shouldn't (when you hear the center
> > > note as the key center)?
> >
> > What's the "center" note in this case? There's only a lower and an
> > upper note.
>
> I meant like if the center is C then the fifth ascends from F and
> descends from G.

F-C sounds like a resolution to me, it's a plagal resolution.

> > And even if it is conditioning, so what? That still doesn't imply that
> > one can be conditioned in any way at all. There are probably limits on
> > what we can be conditioned to hear.
>
> I agree and hearing an ascending root movement by fifth with
> appropriate chords as strongly cadential is in my opinion well within
> those limits.

Clearly it is, because that's how we hear it. However, learning to
hear any rare interval in any scale at all as signaling the tonic may
be outside of those limits.

-Mike

🔗Kalle Aho <kalleaho@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Thu, May 12, 2011 at 10:03 AM, Kalle Aho <kalleaho@...> wrote:
> > >
> > > Yes, I'm aware that some people say this, but I don't see any reason
> > > for it. I haven't read the Browne paper either, so maybe there's
> > > something there. But in general, I'm tired of unfalsifiable,
> > > self-limiting notions like these.
> >
> > How is it self-limiting? It is also pretty obviously true when the
> > rare steps are different enough from the other steps. That doesn't
> > mean all music absolutely must use this as a cue for cognition.
>
> I have not seen sufficient evidence for this "tritone hypothesis," nor
> have I seen any evidence for this "rare interval" hypothesis, and so I
> don't understand why people believe it. One example of a system that's
> based around all of this is Pajara, which for me is a test case for
> all of this theory.

If the hypothesis is just that rare intervals aid position finding
then I think it is pretty innocuous. But maybe you are talking about
establishing the tonic? What exactly is "tritone hypothesis" anyway?

> I'll just leave it at that Pajara, which is based on this thinking,
> doesn't work for me. The "rare intervals" in Pajara that are supposed
> to act as "signposts" don't signal things as they're supposed to in my
> perception.

I think the following progression signals the tonic just fine:

http://soundcloud.com/kalleaho/a-progression-in-standard

> > > But who says chords have to come from scales to begin with?
> > > What about the blues?
> >
> > They don't have to. But when they do, the scale structure can have
> > some influence on how the harmony is heard. That's all.
>
> How so?

If you think about a typical intelligible melody it's not just a
succession of sounds, it's actually heard as a movement through pitch
space where there are specific locations i.e. scale degrees that have
different attractive tendencies.

Now if the music has chords connected through proper voice leading the
tones making up the chords produce petite melodies. The attractive
tendencies of scale degrees will surely then influence the way the
harmony is heard. But I'm not simply reducing harmony to melodic
lines: a change of harmony also changes the attractive tendencies of
different scale degrees.

> > > > > Sure, the same applies for a single bass voice.
> > > >
> > > > Then I think the reason is conditioning. Or can you think of a
> > > > psychoacoustic reason why a descending fifth should sound like a
> > > > resolution and an ascending fifth shouldn't (when you hear the center
> > > > note as the key center)?
> > >
> > > What's the "center" note in this case? There's only a lower and an
> > > upper note.
> >
> > I meant like if the center is C then the fifth ascends from F and
> > descends from G.
>
> F-C sounds like a resolution to me, it's a plagal resolution.

OK. But plagal is supposed to be weaker than authentic. So let me
ask: can you think of a psychoacoustic reason why a fifth descending
to the tonic should sound like a stronger resolution than a fifth
ascending to the tonic?

Kalle

🔗Mike Battaglia <battaglia01@...>

On Sun, May 15, 2011 at 6:55 PM, Kalle Aho <kalleaho@...> wrote:
> >
> > I have not seen sufficient evidence for this "tritone hypothesis," nor
> > have I seen any evidence for this "rare interval" hypothesis, and so I
> > don't understand why people believe it. One example of a system that's
> > based around all of this is Pajara, which for me is a test case for
> > all of this theory.
>
> If the hypothesis is just that rare intervals aid position finding
> then I think it is pretty innocuous. But maybe you are talking about
> establishing the tonic? What exactly is "tritone hypothesis" anyway?

The tritone hypothesis, which I've usually seen mentioned at the same
time as the rare interval hypothesis, is that the one "rare" size of
fifth is the diminished fifth, and it lies adjacent to the Aeolian and
Ionian modes. This supposedly explains why Aeolian and Ionian took
precedence over the other modes for tonal harmony. Except that

1) Aeolian never took precedence for tonal harmony
2) Harmonic minor has more to do with tonal minor harmony than
Aeolian, and in general V7-I and V7-i are what took precedence for
tonal harmony, even if that meant using more than one scale (like the
three minor scales)
3) I have never seen any evidence put out there to support this idea
4) Being as this list usually strongly discourages finding
numerological patterns in scales (like the "Deep scale" property), I'm
surprised that people sometimes cite this as if it has explanatory
power

So when you talked about the "rare interval" thing I assumed you were
talking about that. Perhaps I misunderstood.

As for rare intervals aiding position finding in a scale, the concept
of which you call innocuous - yes, I agree, that's innocuous enough,
but that's not what I thought you were saying. I thought you said that
leading tones "resolved" because they were the rare intervals in the
major scale. So then I have to ask, if you're playing C harmonic
minor, the Ab-B is now the "rare interval." Are we now to believe that
Ab-B is going to resolve to Cm/maj7 more strongly than B-C will
resolve to Cm, because Ab-B is twice as rare as B-C in the scale? Or
how about Melodic minor #4 - C D Eb F# G A B C - am I to believe that
the F#-Eb resolution will now be stronger than the F#-G or the B-C?

> > I'll just leave it at that Pajara, which is based on this thinking,
> > doesn't work for me. The "rare intervals" in Pajara that are supposed
> > to act as "signposts" don't signal things as they're supposed to in my
> > perception.
>
> I think the following progression signals the tonic just fine:
>
> http://soundcloud.com/kalleaho/a-progression-in-standard

It sounds cool, but I'm a little bit lost. What is the tonic? It ends
on what sounds like the 22-equal equivalent of B D# F G#, so does that
mean the tonic is supposed to be G#m6? Which is of course
exceptionally hip because it's the 7-limit utonality.

But no, to me this doesn't signal a tonic, whereas the porcupine
functional excerpt I made did. But whatever you did was cool, perhaps
I just have to learn to hear the logic in it.

> > How so?
>
> If you think about a typical intelligible melody it's not just a
> succession of sounds, it's actually heard as a movement through pitch
> space where there are specific locations i.e. scale degrees that have
> different attractive tendencies.

Right.

> Now if the music has chords connected through proper voice leading the
> tones making up the chords produce petite melodies.

You mean via the counterpoint?

> The attractive tendencies of scale degrees will surely then influence the way the
> harmony is heard. But I'm not simply reducing harmony to melodic
> lines: a change of harmony also changes the attractive tendencies of
> different scale degrees.

What do you mean exactly by "attractive tendencies?"

> > F-C sounds like a resolution to me, it's a plagal resolution.
>
> OK. But plagal is supposed to be weaker than authentic. So let me
> ask: can you think of a psychoacoustic reason why a fifth descending
> to the tonic should sound like a stronger resolution than a fifth
> ascending to the tonic?

We're discussing something that blends psychoacoustics and learning
together, so I don't know where one ends and the other begins. I think
it might have to do with comma pumps - I note that Gmaj -> Cmaj only
sounds strong if the Cmaj is established as the tonic. If you're in G
mixolydian, Fmaj -> Cmaj -> Gmaj sounds like it's resolving to Gmaj,
and you can flip your brain around to hear it either way. However, I
note that a surefire way to get yourself to hear it as C major is Dm7
-> Gmaj -> Cmaj, which is interesting because now you've blended the
subdominant and the dominant together with this tempered D, so you can
run around in a tempered circle. G7 -> C does the same thing, but
smushed into one chord.

Furthermore, just to throw out some shameless wild speculation that I
can't support at all, G7 is almost certainly related to some kind of
perception of 4:5:6:7, so perhaps that's another level of comma
pumping on top of it. This would mean that C is an otonal interval on
top of F which is an otonal interval on top of G which is an otonal
interval on top of C. But that's more speculative.

I had some interesting examples worked out in mavila, but then my
computer crashed and I lost them all. I remember they were vaguely
built around the comma pump Cmaj-Gmaj-Dmaj-Fm, where the F#-A from the
Dmaj and the F-Ab from the Fm are actually the same thing. The whole
thing fits into a single mavila[7] and is the anti-diatonic
counterpart of Cm-Gm-Dm-Fmaj. I'll come up with some examples soon.

-Mike

🔗Mike Battaglia <battaglia01@...>

🔗Kalle Aho <kalleaho@...>

Sorry for the delay in answering, my excuse is that my wife delivered
a baby boy wednesday morning. :)

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Sun, May 15, 2011 at 6:55 PM, Kalle Aho <kalleaho@...> wrote:
> > >
> > > I have not seen sufficient evidence for this "tritone hypothesis," nor
> > > have I seen any evidence for this "rare interval" hypothesis, and so I
> > > don't understand why people believe it. One example of a system that's
> > > based around all of this is Pajara, which for me is a test case for
> > > all of this theory.
> >
> > If the hypothesis is just that rare intervals aid position finding
> > then I think it is pretty innocuous. But maybe you are talking about
> > establishing the tonic? What exactly is "tritone hypothesis" anyway?
>
> The tritone hypothesis, which I've usually seen mentioned at the same
> time as the rare interval hypothesis, is that the one "rare" size of
> fifth is the diminished fifth, and it lies adjacent to the Aeolian and
> Ionian modes. This supposedly explains why Aeolian and Ionian took
> precedence over the other modes for tonal harmony. Except that
>
> 1) Aeolian never took precedence for tonal harmony

Yeah, this has bothered me too. This was also the whole point I
started this thread. I think that the natural minor cadence D B F A -
A C E A could have been adopted but history progressed differently.
The semitonal motion to the "tonic" note in cadences has been a
feature of the Western musical tradition since the 13th century.

> 2) Harmonic minor has more to do with tonal minor harmony than
> Aeolian, and in general V7-I and V7-i are what took precedence for
> tonal harmony, even if that meant using more than one scale (like the
> three minor scales)
> 3) I have never seen any evidence put out there to support this idea
> 4) Being as this list usually strongly discourages finding
> numerological patterns in scales (like the "Deep scale" property), I'm
> surprised that people sometimes cite this as if it has explanatory
> power
>
> So when you talked about the "rare interval" thing I assumed you were
> talking about that. Perhaps I misunderstood.
>
> As for rare intervals aiding position finding in a scale, the concept
> of which you call innocuous - yes, I agree, that's innocuous enough,
> but that's not what I thought you were saying. I thought you said that
> leading tones "resolved" because they were the rare intervals in the
> major scale.

I mentioned it in the context of wondering why leading tones work the
way they do, if it is simply the pitch proximity and/or some other
reason.

> So then I have to ask, if you're playing C harmonic
> minor, the Ab-B is now the "rare interval." Are we now to believe that
> Ab-B is going to resolve to Cm/maj7 more strongly than B-C will
> resolve to Cm, because Ab-B is twice as rare as B-C in the scale? Or
> how about Melodic minor #4 - C D Eb F# G A B C - am I to believe that
> the F#-Eb resolution will now be stronger than the F#-G or the B-C?

The augmented second is a rare interval but it's not a characteristic
dissonance in Paul's sense because seconds are not consonances. The
characteristic dissonance idea is not quite the same as the rare
interval hypothesis as far as I know.

> > > I'll just leave it at that Pajara, which is based on this thinking,
> > > doesn't work for me. The "rare intervals" in Pajara that are supposed
> > > to act as "signposts" don't signal things as they're supposed to in my
> > > perception.
> >
> > I think the following progression signals the tonic just fine:
> >
> > http://soundcloud.com/kalleaho/a-progression-in-standard
>
> It sounds cool, but I'm a little bit lost. What is the tonic? It ends
> on what sounds like the 22-equal equivalent of B D# F G#, so does that
> mean the tonic is supposed to be G#m6? Which is of course
> exceptionally hip because it's the 7-limit utonality.

Yes.

> But no, to me this doesn't signal a tonic, whereas the porcupine
> functional excerpt I made did. But whatever you did was cool, perhaps
> I just have to learn to hear the logic in it.

Actually the first half of the progression ends in a bass movement
from "subdominant" (the scale degree) to tonic and the latter half
ends in a bass movement from "dominant" to tonic. I thought you said
that these mere bass movements sound plagal and authentic to you, so
why not in this case?

The progression simply visits all the 7-limit tetrads of the scale
(and some intermediate chords too) and the penultimate chord contains
the characteristic dissonance that resolves in contrary motion
(that's the Erlich-y part of the progression). (It also contains ~9:7
which is also a characteristic dissonance in Paul's theory, that
resolves in oblique motion.) Perhaps that chord should have been held
longer to really hear the characteristic dissonance(s).

I hear the pentachordal minor tonic as the tonic and I hear two
cadences in this progression.

I'm pretty sure other modes of pentachordal (and probably
symmetrical) decatonic can be tonicized in some way too but are the
pentachordal major and minor really the most tonal as Paul's theories
suggest? I don't know.

> > > How so?
> >
> > If you think about a typical intelligible melody it's not just a
> > succession of sounds, it's actually heard as a movement through pitch
> > space where there are specific locations i.e. scale degrees that have
> > different attractive tendencies.
>
> Right.
>
> > Now if the music has chords connected through proper voice leading the
> > tones making up the chords produce petite melodies.
>
> You mean via the counterpoint?

Not necessarily full blown counterpoint but good voice leading so
that you can hear voices moving in pitch space, not just successive
members of chords frozen in time. There is also a concept of interval
that changes i.e. interval between voices that is also relevant here.
You couldn't hear dissonances resolving to consonances without it.

> > The attractive tendencies of scale degrees will surely then influence the way the
> > harmony is heard. But I'm not simply reducing harmony to melodic
> > lines: a change of harmony also changes the attractive tendencies of
> > different scale degrees.
>
> What do you mean exactly by "attractive tendencies?"

I don't have an exact definition but how for example the chord tones
sound more like points of repose and the root note more than others.
Or the tendency of voices moving stepwise and through leading tones,
that sort of thing. Play c-d-e-f-g-a-b and stop there, kind of
annoying?

> > > F-C sounds like a resolution to me, it's a plagal resolution.
> >
> > OK. But plagal is supposed to be weaker than authentic. So let me
> > ask: can you think of a psychoacoustic reason why a fifth descending
> > to the tonic should sound like a stronger resolution than a fifth
> > ascending to the tonic?
>
> We're discussing something that blends psychoacoustics and learning
> together, so I don't know where one ends and the other begins. I think
> it might have to do with comma pumps - I note that Gmaj -> Cmaj only
> sounds strong if the Cmaj is established as the tonic. If you're in G
> mixolydian, Fmaj -> Cmaj -> Gmaj sounds like it's resolving to Gmaj,
> and you can flip your brain around to hear it either way. However, I
> note that a surefire way to get yourself to hear it as C major is Dm7
> -> Gmaj -> Cmaj, which is interesting because now you've blended the
> subdominant and the dominant together with this tempered D, so you can
> run around in a tempered circle. G7 -> C does the same thing, but
> smushed into one chord.

I may be too tired but I don't see how this answers my question. I
meant just the bass line in the above question.

Quoting our conversation:

> Furthermore, just to throw out some shameless wild speculation that I
> can't support at all, G7 is almost certainly related to some kind of
> perception of 4:5:6:7, so perhaps that's another level of comma
> pumping on top of it. This would mean that C is an otonal interval on
> top of F which is an otonal interval on top of G which is an otonal
> interval on top of C. But that's more speculative.

What's an otonal interval? I thought that only chords can be otonal.
But perhaps dominant seventh is a roughly tuned ~4:5:6:7. It can be
extended too. Maybe this is why Emaj-Cmaj doesn't sound cadential
i.e. there must be a higher level of tension in the penultimate
chord. Note that this applies to early music dyadic cadences as well.

Kalle

🔗Mike Battaglia <battaglia01@...>

On Sat, May 21, 2011 at 10:48 AM, Kalle Aho <kalleaho@...> wrote:
>
> Sorry for the delay in answering, my excuse is that my wife delivered
> a baby boy wednesday morning. :)

Hey, congratulations! Welcome to Earth Kalle Jr! You know, Kalle, he
could be "The One."

> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > The tritone hypothesis, which I've usually seen mentioned at the same
> > time as the rare interval hypothesis, is that the one "rare" size of
> > fifth is the diminished fifth, and it lies adjacent to the Aeolian and
> > Ionian modes. This supposedly explains why Aeolian and Ionian took
> > precedence over the other modes for tonal harmony. Except that
> >
> > 1) Aeolian never took precedence for tonal harmony
>
> Yeah, this has bothered me too. This was also the whole point I
> started this thread. I think that the natural minor cadence D B F A -
> A C E A could have been adopted but history progressed differently.
> The semitonal motion to the "tonic" note in cadences has been a
> feature of the Western musical tradition since the 13th century.

I think that D-B-F-A -> A-C-E-A is decently strong, and honestly I've
heard that resolution used quite a few times, although it's a bit more
modern. But even if history had gone that route, it still wouldn't
change the fact that V-i is still strong, perhaps even stronger,
therefore "strength" isn't strictly caused by scale structure.

It may be caused by various abstract things that scales can have, such
as leading tones, contracting tritones, and comma pumps, but these
things don't have to be in a scale for tonality to work - you can
change the scale over and over and over and still have tonality. If
there so happens to be a scale that includes a lot of these, great. If
not, we'll use parallel scales to get the features we want, as we did
with the minor scale.

But like I said in my followup message to you, I might have to concede
part of my point, as mavila is blowing my mind. Try the comma pump
Cmaj -> Em -> Bm -> Fmaj -> Cmaj, where B-F is still 4/3. Or try it
backwards - Cmaj -> Em -> Bm -> Fmaj -> Cmaj. You see how that Bm -
Fmaj is the equivalent of meantone iv-I? However, it doesn't sound
like dark romantic harmony, but oddly "diatonic" in some sense. Play
the whole progression really quickly, you'll see what I mean.

> > As for rare intervals aiding position finding in a scale, the concept
> > of which you call innocuous - yes, I agree, that's innocuous enough,
> > but that's not what I thought you were saying. I thought you said that
> > leading tones "resolved" because they were the rare intervals in the
> > major scale.
>
> I mentioned it in the context of wondering why leading tones work the
> way they do, if it is simply the pitch proximity and/or some other
> reason.

Once I finish getting this working

/tuning/topicId_99227.html#99227

We'll know for sure. :)

PS - any suggestions for what piece to try? Something with lots of
meantone comma pumps would be good.

> > So then I have to ask, if you're playing C harmonic
> > minor, the Ab-B is now the "rare interval." Are we now to believe that
> > Ab-B is going to resolve to Cm/maj7 more strongly than B-C will
> > resolve to Cm, because Ab-B is twice as rare as B-C in the scale? Or
> > how about Melodic minor #4 - C D Eb F# G A B C - am I to believe that
> > the F#-Eb resolution will now be stronger than the F#-G or the B-C?
>
> The augmented second is a rare interval but it's not a characteristic
> dissonance in Paul's sense because seconds are not consonances. The
> characteristic dissonance idea is not quite the same as the rare
> interval hypothesis as far as I know.

What do you mean? If seconds aren't consonances, then they're
dissonances, right? And if there's only one of them, wouldn't that be
a "characteristic" dissonance? What if we tuned it in 17-equal, where
the augmented seconds were ~11/9?

> > But no, to me this doesn't signal a tonic, whereas the porcupine
> > functional excerpt I made did. But whatever you did was cool, perhaps
> > I just have to learn to hear the logic in it.
>
> Actually the first half of the progression ends in a bass movement
> from "subdominant" (the scale degree) to tonic and the latter half
> ends in a bass movement from "dominant" to tonic. I thought you said
> that these mere bass movements sound plagal and authentic to you, so
> why not in this case?

Holy bass, Batman! I didn't realize there was bass before. I just put
my headphones on instead of my crappy computer speakers and this is a
whole new pump. But yes, now they sound like you described, and I
don't think you need the Pajara scale to do it. In fact, you could
hear this whole thing as just chromatic heptatonic harmony. In fact,
if you want, I'll come up with a musical example that uses a different
scale over every note and still sounds tonicified, if you want.

In fact, now that I've heard it with the bass, I can "remember" what
it sounds like after the bass, so now it sounds tonal. Therein lies a
clue :)

> The progression simply visits all the 7-limit tetrads of the scale
> (and some intermediate chords too) and the penultimate chord contains
> the characteristic dissonance that resolves in contrary motion
> (that's the Erlich-y part of the progression). (It also contains ~9:7
> which is also a characteristic dissonance in Paul's theory, that
> resolves in oblique motion.) Perhaps that chord should have been held
> longer to really hear the characteristic dissonance(s).

With the bass it sounds a lot different. If you changed the melody on
the last chord from F#-G# to G-G#, e.g. sharp the top note on the
penultimate chord, I predict it'll make the whole thing stronger.

> I'm pretty sure other modes of pentachordal (and probably
> symmetrical) decatonic can be tonicized in some way too but are the
> pentachordal major and minor really the most tonal as Paul's theories
> suggest? I don't know.

I just can't get into scales anymore. Haha, I'm sorry. I think it's
just too limiting of a paradigm. If they had stuck to the diatonic
scale when working out minor harmony, music today would absolutely
suck. I wish we could all focus on our efforts on finding whatever
these tonal "features" are directly without trying to find them in
scales. If we get lucky and there's one scale that has them, great. If
not, then we can always use parallel scales like they did with minor.
Why not?

Dorian mode can be tonicized by just throwing the V chord in there
sometimes, and using melodic minor instead of harmonic minor. Is it
cheating? If so, I am a dirty cheater! But did you hear the Sibelius
example I posted? He does the same thing, and I think the result is
beautiful. To my ears, that's what music would have sounded like if
we'd gone with Dorian instead of Aeolian harmony - instead of having
natural, harmonic, melodic minor, we'd just have dorian and melodic
minor. Instead of using bVI we'd be using IV more. I really like the
sound.

> > > Now if the music has chords connected through proper voice leading the
> > > tones making up the chords produce petite melodies.
> >
> > You mean via the counterpoint?
>
> Not necessarily full blown counterpoint but good voice leading so
> that you can hear voices moving in pitch space, not just successive
> members of chords frozen in time. There is also a concept of interval
> that changes i.e. interval between voices that is also relevant here.
> You couldn't hear dissonances resolving to consonances without it.

What do you mean interval between voices? But yes, I think I agree.
Voice leading sounds good even if the scale doesn't have it.

> I don't have an exact definition but how for example the chord tones
> sound more like points of repose and the root note more than others.
> Or the tendency of voices moving stepwise and through leading tones,
> that sort of thing. Play c-d-e-f-g-a-b and stop there, kind of
> annoying?

Are these attractive tendencies caused by scale structure or just
learning in general?

> I may be too tired but I don't see how this answers my question. I
> meant just the bass line in the above question.

OK, I think that it has to do with learning, but I am not sure exactly
what we've learned.

> > Furthermore, just to throw out some shameless wild speculation that I
> > can't support at all, G7 is almost certainly related to some kind of
> > perception of 4:5:6:7, so perhaps that's another level of comma
> > pumping on top of it. This would mean that C is an otonal interval on
> > top of F which is an otonal interval on top of G which is an otonal
> > interval on top of C. But that's more speculative.
>
> What's an otonal interval? I thought that only chords can be otonal.
> But perhaps dominant seventh is a roughly tuned ~4:5:6:7. It can be
> extended too. Maybe this is why Emaj-Cmaj doesn't sound cadential
> i.e. there must be a higher level of tension in the penultimate
> chord. Note that this applies to early music dyadic cadences as well.

I meant "rooted" interval, I guess. How about E7-Cmaj, where the 7 is
tuned 7/4? That sounds pretty sweet to me.

-Mike

🔗Carl Lumma <carl@...>

🔗Kalle Aho <kalleaho@...>

🔗genewardsmith <genewardsmith@...>

🔗Kalle Aho <kalleaho@...>

🔗genewardsmith <genewardsmith@...>

🔗chrisvaisvil@...

🔗Carl Lumma <carl@...>

🔗Chris Vaisvil <chrisvaisvil@...>

🔗Daniel Nielsen <nielsed@...>

🔗Kalle Aho <kalleaho@...>

Mike, I hope you don't mind me heavily trimming our discussion. I've
tried to answer the most important points.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > > So then I have to ask, if you're playing C harmonic
> > > minor, the Ab-B is now the "rare interval." Are we now to believe that
> > > Ab-B is going to resolve to Cm/maj7 more strongly than B-C will
> > > resolve to Cm, because Ab-B is twice as rare as B-C in the scale? Or
> > > how about Melodic minor #4 - C D Eb F# G A B C - am I to believe that
> > > the F#-Eb resolution will now be stronger than the F#-G or the B-C?
> >
> > The augmented second is a rare interval but it's not a characteristic
> > dissonance in Paul's sense because seconds are not consonances. The
> > characteristic dissonance idea is not quite the same as the rare
> > interval hypothesis as far as I know.
>
> What do you mean? If seconds aren't consonances, then they're
> dissonances, right? And if there's only one of them, wouldn't that be
> a "characteristic" dissonance? What if we tuned it in 17-equal, where
> the augmented seconds were ~11/9?

A characteristic dissonance is a dissonance that is produced from the
same number of steps that otherwise produces consonances. Diminished
fifth is one because the number of steps it spans otherwise produces
perfect fifths. So Ab-B is not a characteristic dissonance because
seconds are dissonances.

> > The progression simply visits all the 7-limit tetrads of the scale
> > (and some intermediate chords too) and the penultimate chord contains
> > the characteristic dissonance that resolves in contrary motion
> > (that's the Erlich-y part of the progression). (It also contains ~9:7
> > which is also a characteristic dissonance in Paul's theory, that
> > resolves in oblique motion.) Perhaps that chord should have been held
> > longer to really hear the characteristic dissonance(s).
>
> With the bass it sounds a lot different. If you changed the melody on
> the last chord from F#-G# to G-G#, e.g. sharp the top note on the
> penultimate chord, I predict it'll make the whole thing stronger.

If the top note is sharpened by the chroma L-s the penultimate chord
becomes an ~7:8:9:10 and to my ears the resolution doesn't sound
stronger.

> > I'm pretty sure other modes of pentachordal (and probably
> > symmetrical) decatonic can be tonicized in some way too but are the
> > pentachordal major and minor really the most tonal as Paul's theories
> > suggest? I don't know.
>
> I just can't get into scales anymore. Haha, I'm sorry. I think it's
> just too limiting of a paradigm. If they had stuck to the diatonic
> scale when working out minor harmony, music today would absolutely
> suck.

Because?

> I wish we could all focus on our efforts on finding whatever
> these tonal "features" are directly without trying to find them in
> scales. If we get lucky and there's one scale that has them, great. If
> not, then we can always use parallel scales like they did with minor.
> Why not?

I don't really know what this non-scale approach would be like. How
are the tonal features found "directly"?

Also, I don't think of minor as three parallel "scales" (even if that
concept makes some sense melodically). For me a minor key has seven
degrees some of which are mutable. The same applies to a degree
(or two :D) in major too. You could even think that the key doesn't
really have to be major or minor but can have a mutable third degree
as well. But there is this "sevenness" that I think Western listeners
hear. Melodic movement by chromatic semitone sounds instantly like
going outside the basic seven degrees while typical use of the minor
doesn't.

> Dorian mode can be tonicized by just throwing the V chord in there
> sometimes, and using melodic minor instead of harmonic minor. Is it
> cheating? If so, I am a dirty cheater! But did you hear the Sibelius
> example I posted? He does the same thing, and I think the result is
> beautiful. To my ears, that's what music would have sounded like if
> we'd gone with Dorian instead of Aeolian harmony - instead of having
> natural, harmonic, melodic minor, we'd just have dorian and melodic
> minor. Instead of using bVI we'd be using IV more. I really like the
> sound.

Do you think that the music is in a minor key? Why say it's in dorian?
My answer is that the alteration of degrees happens only in special
situations like cadences.

Kalle

🔗Mike Battaglia <battaglia01@...>

Kalle - my opinions have changed a bit, see my Father example for more
of my thinking now.

Kalle wrote:
> > With the bass it sounds a lot different. If you changed the melody on
> > the last chord from F#-G# to G-G#, e.g. sharp the top note on the
> > penultimate chord, I predict it'll make the whole thing stronger.
>
> If the top note is sharpened by the chroma L-s the penultimate chord
> becomes an ~7:8:9:10 and to my ears the resolution doesn't sound
> stronger.

Can you post an example? And does sharpening the top note by L-s turn
the melodic motion in the top voice for the last two chords into 2\22?
Because if not I say to hell with the chroma!

> > > I'm pretty sure other modes of pentachordal (and probably
> > > symmetrical) decatonic can be tonicized in some way too but are the
> > > pentachordal major and minor really the most tonal as Paul's theories
> > > suggest? I don't know.
> >
> > I just can't get into scales anymore. Haha, I'm sorry. I think it's
> > just too limiting of a paradigm. If they had stuck to the diatonic
> > scale when working out minor harmony, music today would absolutely
> > suck.
>
> Because?

Because they'd have to be on crack to ignore something as obvious as
V-i. Arbitrary limitations and preconceptions have never served
anyone.

> > I wish we could all focus on our efforts on finding whatever
> > these tonal "features" are directly without trying to find them in
> > scales. If we get lucky and there's one scale that has them, great. If
> > not, then we can always use parallel scales like they did with minor.
> > Why not?
>
> I don't really know what this non-scale approach would be like. How
> are the tonal features found "directly"?

Kalle, all I'm saying is that when they started to mess around with
modern, cliche, "tonal" harmony, they opted to DITCH the aeolian scale
and start using things like V-i. They left the scale because V-i
improved the "tonalness" of the harmony. Hence, this is a "tonal
feature" that they "directly" found and that lies outside of the
scalar structure of aeolian mode.

For melody, rather than using aeolian and forcing the harmony into
that, they opted instead to use a rotating cast of heptatonic scales
for harmony, and let the melody be as it will. If you have some kind
of reservation to this objection, I'd love to hear why, and why the
answer couldn't just be that perhaps there's more to tonality than
Paul laid in the Pajara paper.

I am more than willing to admit that scale structure may play a role
in this, and my recent experiments with Father suggests that it may.
But it may simply have more to do with "leading tones" than some sort
of holographic tonalness scale property. The fact that 17-equal seems
to be universally recognized as having excellent melodic properties,
and 19-equal as well if you sharp the leading tone by 1\19, suggests
that there is some kind of psychoacoustic component to what makes
leading tones work. Leading tones can exist outside of a scale.

The fact that you can sort of hear inflections of majorness and
minorness in 7-equal is noteworthy as well, not sure how that relates
to anything.

> Also, I don't think of minor as three parallel "scales" (even if that
> concept makes some sense melodically). For me a minor key has seven
> degrees some of which are mutable.

OK, that's what I was trying to say, but the way you put it is more
elegant. They generally make the choice of heptatonic scale conform to
the harmony, changing the 6th and 7th degrees as appropriate.

> Melodic movement by chromatic semitone sounds instantly like
> going outside the basic seven degrees while typical use of the minor
> doesn't.

What do you mean "typical use of the minor?"

> > Dorian mode can be tonicized by just throwing the V chord in there
> > sometimes, and using melodic minor instead of harmonic minor. Is it
> > cheating? If so, I am a dirty cheater! But did you hear the Sibelius
> > example I posted? He does the same thing, and I think the result is
> > beautiful. To my ears, that's what music would have sounded like if
> > we'd gone with Dorian instead of Aeolian harmony - instead of having
> > natural, harmonic, melodic minor, we'd just have dorian and melodic
> > minor. Instead of using bVI we'd be using IV more. I really like the
> > sound.
>
> Do you think that the music is in a minor key? Why say it's in dorian?
> My answer is that the alteration of degrees happens only in special
> situations like cadences.

Because the feeling of the key that a song is in isn't only determined
by its root note and the quality of the tonic triad. You, or at least
I, are/am also always aware of the other chords that are "nearby" the
tonic. For instance, Stevie Wonder's "Uptight" has a minor v chord and
features bVII often. Not only does this create an entirely different
feeling than if the song had a major V chord, but to play the bVII
scale degree over the root will sound a million times more appropriate
than playing a standard major vii (if you have to choose one, that
is). Likewise, the Sibelius composition uses IV so often that it
becomes part of the background vibe of the song, and in that way it
creates a different feeling than if they were mashing on bVI instead.
And to be honest I think it sounds amazing, and I wish the classical
repertoire made more use of that effect.

The idea we're discussing is that a note doesn't actually need to be a
part of the bare tonic triad in order to influence the sense of "mode"
or "key" that a composition is in. For further theoretical
justification of this idea, A song can be in a "major" or a "minor"
key even if the guitar is just playing power chords; the other notes
and chords that are played will "clue you in" to whether the song is
in major or minor. Despite that you aren't actually playing ever
playing the tonic triad, your brain puts the pieces together and
figures out what the triad -would be- if you did play it.

Who's to say that this process is limited to root, third, and fifth?
My brain seems to put -all- the notes played recently together to form
the holistic gestalt of an entire mode, not just a 1-3-5 triad. If
you're in minor and you've played a major 6th recently, I'll remember
that, and know that that's a part of the scale. If you've played a
major 6th and a minor 7th, I'll know this is partly Dorian (unless
you've played a #4, in which case it's Dorian #4, a mode of harmonic
minor).

What is important is that to habitually play a major 6th over a minor
chord actually makes the music -feel- different. These alterations
aren't just random emotionless contrivances of melody; they actually
influence the feeling of the music by changing the character of the
harmonic ambience that is presented. To say that "this piece is in
Dorian" communicates information about that ambience and its
associated feeling. This is not a trivial statement.

You can say that this piece is in D Aeolian and just happens to
"cadentially alter" it to Dorian every time he hits that B natural.
You can likewise say the same thing about Come Together, that it's
really D aeolian with some "cadential modulations" into dorian. I
would be very surprised if the average person actually heard it that
way, with a Bb there "naturally," and the note B being a departure or
modulation from that.

-Mike

🔗bobvalentine1 <bob.valentine@...>

🔗Kalle Aho <kalleaho@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> Kalle - my opinions have changed a bit, see my Father example for more
> of my thinking now.
>
> Kalle wrote:
> > > With the bass it sounds a lot different. If you changed the melody on
> > > the last chord from F#-G# to G-G#, e.g. sharp the top note on the
> > > penultimate chord, I predict it'll make the whole thing stronger.
> >
> > If the top note is sharpened by the chroma L-s the penultimate chord
> > becomes an ~7:8:9:10 and to my ears the resolution doesn't sound
> > stronger.
>
> Can you post an example? And does sharpening the top note by L-s turn
> the melodic motion in the top voice for the last two chords into 2\22?
> Because if not I say to hell with the chroma!

Why not just say "s" instead of "2\22"? The example is not in
22-equal, you know. But yes, the upper motion is by s.

Listen to this file:

/tuning/files/KalleAho/Cadence.mp3

The first one is the same one I used in the SoundCloud example.

You probably hear the second one as the strongest. In meantone terms
it sounds like a sweet V9-i(add6). In a decatonic context it doesn't
sound as convincing to me as the first one:

http://soundcloud.com/kalleaho/decatonic-progression-version

As a bonus I've included a third progression where the tones move by
L-s. That's around 66 cents which is near the supposedly optimal 1\17
leading tone. Despite this the third one sounds weakest of the lot to
me.

> > > > I'm pretty sure other modes of pentachordal (and probably
> > > > symmetrical) decatonic can be tonicized in some way too but are the
> > > > pentachordal major and minor really the most tonal as Paul's theories
> > > > suggest? I don't know.
> > >
> > > I just can't get into scales anymore. Haha, I'm sorry. I think it's
> > > just too limiting of a paradigm. If they had stuck to the diatonic
> > > scale when working out minor harmony, music today would absolutely
> > > suck.
> >
> > Because?
>
> Because they'd have to be on crack to ignore something as obvious as
> V-i. Arbitrary limitations and preconceptions have never served
> anyone.

Or perhaps it would have sounded melodically more like traditional
folk music (e.g. of Ireland). And I'm still not convinced that
universal reasons like human psychoacoustics would have selected V-i
as the strongest possible minor key progression in all possible
histories of Western music. I believe that in actual history it's
just that the conventions of musica ficta period carried to the
following major-minor system. In musica ficta (literally "false" or
"contrived" music, haha!) leading tones were sharpened at cadences
and the composers took this practice to the new style.

> > > I wish we could all focus on our efforts on finding whatever
> > > these tonal "features" are directly without trying to find them in
> > > scales. If we get lucky and there's one scale that has them, great. If
> > > not, then we can always use parallel scales like they did with minor.
> > > Why not?
> >
> > I don't really know what this non-scale approach would be like. How
> > are the tonal features found "directly"?
>
> Kalle, all I'm saying is that when they started to mess around with
> modern, cliche, "tonal" harmony, they opted to DITCH the aeolian scale
> and start using things like V-i. They left the scale because V-i
> improved the "tonalness" of the harmony. Hence, this is a "tonal
> feature" that they "directly" found and that lies outside of the
> scalar structure of aeolian mode.

That's funny because aeolian was probably never used strictly in the
period between gregorian chant and tonal harmony. In fact the 19th
century revival of modes used them much more strictly than music in
renaissance because the 19th century composers wanted a stronger
distinction from major and minor.

> For melody, rather than using aeolian and forcing the harmony into
> that, they opted instead to use a rotating cast of heptatonic scales
> for harmony, and let the melody be as it will. If you have some kind
> of reservation to this objection, I'd love to hear why, and why the
> answer couldn't just be that perhaps there's more to tonality than
> Paul laid in the Pajara paper.

Where exactly in that paper did Paul command us to stick to aeolian
scale? He discusses "altered" scales in the paper after all.

> I am more than willing to admit that scale structure may play a role
> in this, and my recent experiments with Father suggests that it may.
> But it may simply have more to do with "leading tones" than some sort
> of holographic tonalness scale property. The fact that 17-equal seems
> to be universally recognized as having excellent melodic properties,
> and 19-equal as well if you sharp the leading tone by 1\19, suggests
> that there is some kind of psychoacoustic component to what makes
> leading tones work. Leading tones can exist outside of a scale.

Of course they can! Does the third cadence example sound melodically
good to you? To me it doesn't.

> The fact that you can sort of hear inflections of majorness and
> minorness in 7-equal is noteworthy as well, not sure how that relates
> to anything.

Let's just not bring that complication to this discussion, OK? :)

> > Also, I don't think of minor as three parallel "scales" (even if that
> > concept makes some sense melodically). For me a minor key has seven
> > degrees some of which are mutable.
>
> OK, that's what I was trying to say, but the way you put it is more
> elegant. They generally make the choice of heptatonic scale conform to
> the harmony, changing the 6th and 7th degrees as appropriate.
>
> > Melodic movement by chromatic semitone sounds instantly like
> > going outside the basic seven degrees while typical use of the minor
> > doesn't.
>
> What do you mean "typical use of the minor?"

The usual sort like using different scales when ascending and
descending.

> > > Dorian mode can be tonicized by just throwing the V chord in there
> > > sometimes, and using melodic minor instead of harmonic minor. Is it
> > > cheating? If so, I am a dirty cheater! But did you hear the Sibelius
> > > example I posted? He does the same thing, and I think the result is
> > > beautiful. To my ears, that's what music would have sounded like if
> > > we'd gone with Dorian instead of Aeolian harmony - instead of having
> > > natural, harmonic, melodic minor, we'd just have dorian and melodic
> > > minor. Instead of using bVI we'd be using IV more. I really like the
> > > sound.
> >
> > Do you think that the music is in a minor key? Why say it's in dorian?
> > My answer is that the alteration of degrees happens only in special
> > situations like cadences.
>
> Because the feeling of the key that a song is in isn't only determined
> by its root note and the quality of the tonic triad. You, or at least
> I, are/am also always aware of the other chords that are "nearby" the
> tonic. For instance, Stevie Wonder's "Uptight" has a minor v chord and
> features bVII often. Not only does this create an entirely different
> feeling than if the song had a major V chord, but to play the bVII
> scale degree over the root will sound a million times more appropriate
> than playing a standard major vii (if you have to choose one, that
> is). Likewise, the Sibelius composition uses IV so often that it
> becomes part of the background vibe of the song, and in that way it
> creates a different feeling than if they were mashing on bVI instead.
> And to be honest I think it sounds amazing, and I wish the classical
> repertoire made more use of that effect.
>
> The idea we're discussing is that a note doesn't actually need to be a
> part of the bare tonic triad in order to influence the sense of "mode"
> or "key" that a composition is in. For further theoretical
> justification of this idea, A song can be in a "major" or a "minor"
> key even if the guitar is just playing power chords; the other notes
> and chords that are played will "clue you in" to whether the song is
> in major or minor. Despite that you aren't actually playing ever
> playing the tonic triad, your brain puts the pieces together and
> figures out what the triad -would be- if you did play it.
>
> Who's to say that this process is limited to root, third, and fifth?
> My brain seems to put -all- the notes played recently together to form
> the holistic gestalt of an entire mode, not just a 1-3-5 triad. If
> you're in minor and you've played a major 6th recently, I'll remember
> that, and know that that's a part of the scale. If you've played a
> major 6th and a minor 7th, I'll know this is partly Dorian (unless
> you've played a #4, in which case it's Dorian #4, a mode of harmonic
> minor).
>
> What is important is that to habitually play a major 6th over a minor
> chord actually makes the music -feel- different. These alterations
> aren't just random emotionless contrivances of melody; they actually
> influence the feeling of the music by changing the character of the
> harmonic ambience that is presented. To say that "this piece is in
> Dorian" communicates information about that ambience and its
> associated feeling. This is not a trivial statement.
>
> You can say that this piece is in D Aeolian and just happens to
> "cadentially alter" it to Dorian every time he hits that B natural.
> You can likewise say the same thing about Come Together, that it's
> really D aeolian with some "cadential modulations" into dorian. I
> would be very surprised if the average person actually heard it that
> way, with a Bb there "naturally," and the note B being a departure or
> modulation from that.

No no no, I wasn't claiming it's not in dorian. I agree about that but
what I claim is that it is in dorian because the alterations happen
only in special occasions.

Kalle

🔗cityoftheasleep <igliashon@...>

🔗Kalle Aho <kalleaho@...>

🔗genewardsmith <genewardsmith@...>

🔗Kalle Aho <kalleaho@...>

🔗genewardsmith <genewardsmith@...>

🔗Kalle Aho <kalleaho@...>

🔗Mike Battaglia <battaglia01@...>

On Sun, Jun 5, 2011 at 5:17 PM, Kalle Aho <kalleaho@...> wrote:
>
> Why not just say "s" instead of "2\22"? The example is not in
> 22-equal, you know. But yes, the upper motion is by s.

I didn't want s, I wanted a decent leading tone. In 19-equal, 1\19
often makes for a better leading tone than 2\19, despite that 2\19 is
the diatonic "s." But if s is close enough it'll do.

> Listen to this file:
>
> /tuning/files/KalleAho/Cadence.mp3
>
> The first one is the same one I used in the SoundCloud example.
>
> You probably hear the second one as the strongest. In meantone terms
> it sounds like a sweet V9-i(add6). In a decatonic context it doesn't
> sound as convincing to me as the first one:
>
> http://soundcloud.com/kalleaho/decatonic-progression-version

I do hear the second one as being strongest. As far as the new
decatonic progression example vs the original, there is definitely
something that I like about the original, although I don't know
exactly what, but the altered one is also strong, just in a different
way. But what if you flatten the second-top in the penultimate chord
by "s," so that it sounds like a b9 resolving to a m6 chord in
meantone terms?

> As a bonus I've included a third progression where the tones move by
> L-s. That's around 66 cents which is near the supposedly optimal 1\17
> leading tone. Despite this the third one sounds weakest of the lot to
> me.

The third one sounded weird initially because the second-last chord is
so discordant, but after listening to it a few times I actually really
like it. In a certain way I like it more than the other ones. I don't
know if the strength of the resolution would have increased if you
made them move by s instead of 66 cents, but I do like the flattening
of the seventh on the penultimate chord (I guess you're altering 7/4
to 12/7?).

After listening to the example on repeat a bunch of times I actually
like the last one more than the others; the supermajor 6th gives it a
whole new color and it resolves beautifully to the minor 6 chord at
the end. The 66 cents leading tone might actually be too narrow,
although I'm not sure why.

> > Because they'd have to be on crack to ignore something as obvious as
> > V-i. Arbitrary limitations and preconceptions have never served
> > anyone.
>
> Or perhaps it would have sounded melodically more like traditional
> folk music (e.g. of Ireland).

OK, good point. I should have caught this one, being as I just wrote a
song in pretty straight Aeolian that tries to nail the Irish folk song
feel, but didn't think anything of it when I posted this. So you're
right.

> And I'm still not convinced that
> universal reasons like human psychoacoustics would have selected V-i
> as the strongest possible minor key progression in all possible
> histories of Western music.

The strength of a resolution seems to have something to do with
learning. For instance, you apparently have to "learn" to hear
decatonic progressions as sounding decatonic; otherwise they just
sound diatonic. I have no idea what the difference is, because they
all sound the same to me. I also hated the third progression in the
sample you posted above, but liked it a lot after hearing it a few
times. However, there has to be some reason why 1\17 seems to function
as The Greatest Leading Tone Ever, and psychoacoustics is a natural
fit for why that might be. But perhaps it has to do with cognition as
well - if we were all used to 17, then maybe we'd think that 22 was
The Greatest Leading Tone Ever or something.

> I believe that in actual history it's
> just that the conventions of musica ficta period carried to the
> following major-minor system. In musica ficta (literally "false" or
> "contrived" music, haha!) leading tones were sharpened at cadences
> and the composers took this practice to the new style.

But don't you agree that the two have different musical effects? There
is a certain sense in which V-i is different from v-i. What aspects of
the contrast between the two do you think are psychoacoustic and what
aspects do you think are learned?

> > Kalle, all I'm saying is that when they started to mess around with
> > modern, cliche, "tonal" harmony, they opted to DITCH the aeolian scale
> > and start using things like V-i. They left the scale because V-i
> > improved the "tonalness" of the harmony. Hence, this is a "tonal
> > feature" that they "directly" found and that lies outside of the
> > scalar structure of aeolian mode.
>
> That's funny because aeolian was probably never used strictly in the
> period between gregorian chant and tonal harmony. In fact the 19th
> century revival of modes used them much more strictly than music in
> renaissance because the 19th century composers wanted a stronger
> distinction from major and minor.

I should have said the diatonic scale. They ditched the diatonic
scale. Rather than continuing to search for scale patterns in the
diatonic scale, they opted to change it. And when we get into 20th
century extended harmony, they even got the diminished scale involved,
and used the altered scale over dominant chords.

> > For melody, rather than using aeolian and forcing the harmony into
> > that, they opted instead to use a rotating cast of heptatonic scales
> > for harmony, and let the melody be as it will. If you have some kind
> > of reservation to this objection, I'd love to hear why, and why the
> > answer couldn't just be that perhaps there's more to tonality than
> > Paul laid in the Pajara paper.
>
> Where exactly in that paper did Paul command us to stick to aeolian
> scale? He discusses "altered" scales in the paper after all.

Paul discusses tonality as stemming from the rare step sizes in a
scale. I ask you how you reconcile this paradigm with the fact that
tonality in minor doesn't seem to have anything to do with a single
scale. Do you think that it comes from the scalar structures of the
three parallel minor scales? Or do you think that there are no
parallel minor scales, and if so, where does tonality emerge from?

> > I am more than willing to admit that scale structure may play a role
> > in this, and my recent experiments with Father suggests that it may.
> > But it may simply have more to do with "leading tones" than some sort
> > of holographic tonalness scale property. The fact that 17-equal seems
> > to be universally recognized as having excellent melodic properties,
> > and 19-equal as well if you sharp the leading tone by 1\19, suggests
> > that there is some kind of psychoacoustic component to what makes
> > leading tones work. Leading tones can exist outside of a scale.
>
> Of course they can! Does the third cadence example sound melodically
> good to you? To me it doesn't.

Given a brief training period, it'll sound melodically good to you
too! Just wait for it... :)

I think the strength of the melody could be improved by making the
leading tones a little bigger though.

> > > Melodic movement by chromatic semitone sounds instantly like
> > > going outside the basic seven degrees while typical use of the minor
> > > doesn't.
> >
> > What do you mean "typical use of the minor?"
>
> The usual sort like using different scales when ascending and
> descending.

I'm not sure I follow - what are the basic seven degrees, the bare
diatonic scale? Because I hear melodic minor as being different from
the diatonic scale, obviously. So I'm a bit confused.

> > You can say that this piece is in D Aeolian and just happens to
> > "cadentially alter" it to Dorian every time he hits that B natural.
> > You can likewise say the same thing about Come Together, that it's
> > really D aeolian with some "cadential modulations" into dorian. I
> > would be very surprised if the average person actually heard it that
> > way, with a Bb there "naturally," and the note B being a departure or
> > modulation from that.
>
> No no no, I wasn't claiming it's not in dorian. I agree about that but
> what I claim is that it is in dorian because the alterations happen
> only in special occasions.

But there are no alterations. The alteration happens when the B
finally changes to Bb, at which point it moves away from Dorian and
into Aeolian. They don't play a single Bb until almost the last phrase
of the song. The melody is in Dorian throughout, and the only
alteration until that Bb is that they move the C up to C# so as to put
you at the major V chord.

-Mike

🔗Kalle Aho <kalleaho@...>

Back to this...

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Sun, Jun 5, 2011 at 5:17 PM, Kalle Aho <kalleaho@...> wrote:
> >
> > Why not just say "s" instead of "2\22"? The example is not in
> > 22-equal, you know. But yes, the upper motion is by s.
>
> I didn't want s, I wanted a decent leading tone. In 19-equal, 1\19
> often makes for a better leading tone than 2\19, despite that 2\19 is
> the diatonic "s." But if s is close enough it'll do.

In message #99766 you said:

"And does sharpening the top note by L-s turn the melodic motion in
the top voice for the last two chords into 2\22? Because if not I say
to hell with the chroma!"

2\22 is the small step in 22-equal decatonics.

> > Listen to this file:
> >
> > /tuning/files/KalleAho/Cadence.mp3
> >
> > The first one is the same one I used in the SoundCloud example.
> >
> > You probably hear the second one as the strongest. In meantone terms
> > it sounds like a sweet V9-i(add6). In a decatonic context it doesn't
> > sound as convincing to me as the first one:
> >
> > http://soundcloud.com/kalleaho/decatonic-progression-version
>
> I do hear the second one as being strongest. As far as the new
> decatonic progression example vs the original, there is definitely
> something that I like about the original, although I don't know
> exactly what, but the altered one is also strong, just in a different
> way. But what if you flatten the second-top in the penultimate chord
> by "s," so that it sounds like a b9 resolving to a m6 chord in
> meantone terms?

In which one of the progressions? And don't you have any means for
trying that out for yourself? (A rhetorical question, I know you do!)

> > And I'm still not convinced that
> > universal reasons like human psychoacoustics would have selected V-i
> > as the strongest possible minor key progression in all possible
> > histories of Western music.
>
> The strength of a resolution seems to have something to do with
> learning. For instance, you apparently have to "learn" to hear
> decatonic progressions as sounding decatonic; otherwise they just
> sound diatonic. I have no idea what the difference is, because they
> all sound the same to me. I also hated the third progression in the
> sample you posted above, but liked it a lot after hearing it a few
> times. However, there has to be some reason why 1\17 seems to function
> as The Greatest Leading Tone Ever, and psychoacoustics is a natural
> fit for why that might be. But perhaps it has to do with cognition as
> well - if we were all used to 17, then maybe we'd think that 22 was
> The Greatest Leading Tone Ever or something.

How can decatonic progressions with their consecutive semitone-like
steps sound diatonic to you? Chromatic maybe, but diatonic?!

And where's the evidence that everyone thinks that 1\17 is the best
leading tone, was there a survey that I missed?

> > I believe that in actual history it's
> > just that the conventions of musica ficta period carried to the
> > following major-minor system. In musica ficta (literally "false" or
> > "contrived" music, haha!) leading tones were sharpened at cadences
> > and the composers took this practice to the new style.
>
> But don't you agree that the two have different musical effects? There
> is a certain sense in which V-i is different from v-i.

Of course.

> What aspects of the contrast between the two do you think are
> psychoacoustic and what aspects do you think are learned?

I'm not that sure about the meaningfulness of the distinction but
at least the contrast between the chord qualities of minor and major
is psychoacoustic.

I'd say (again) that it's the raising of the seventh degree that
allows the fifth chord (and especially its' seventh chord version) to
take the function of dominant. v doesn't quite sound like a dominant,
really! In an unaltered aeolian scale that function is more likely
taken by the nominally subdominant minor sixth chord, or so I
maintain. Note that this sort of talk where the dominant function is
not tied to a position of a fifth above the tonic has a precedent at
least here:

http://en.wikipedia.org/wiki/Flamenco#Harmony

Also, people talk about substitute dominants and those are not in
a fifth relationship to the tonic.

> > > Kalle, all I'm saying is that when they started to mess around with
> > > modern, cliche, "tonal" harmony, they opted to DITCH the aeolian scale
> > > and start using things like V-i. They left the scale because V-i
> > > improved the "tonalness" of the harmony. Hence, this is a "tonal
> > > feature" that they "directly" found and that lies outside of the
> > > scalar structure of aeolian mode.
> >
> > That's funny because aeolian was probably never used strictly in the
> > period between gregorian chant and tonal harmony. In fact the 19th
> > century revival of modes used them much more strictly than music in
> > renaissance because the 19th century composers wanted a stronger
> > distinction from major and minor.
>
> I should have said the diatonic scale. They ditched the diatonic
> scale. Rather than continuing to search for scale patterns in the
> diatonic scale, they opted to change it. And when we get into 20th
> century extended harmony, they even got the diminished scale involved,
> and used the altered scale over dominant chords.

But they already had ditched the strict use of the diatonic scale
before tonal harmony. Musica ficta.

> > > For melody, rather than using aeolian and forcing the harmony into
> > > that, they opted instead to use a rotating cast of heptatonic scales
> > > for harmony, and let the melody be as it will. If you have some kind
> > > of reservation to this objection, I'd love to hear why, and why the
> > > answer couldn't just be that perhaps there's more to tonality than
> > > Paul laid in the Pajara paper.
> >
> > Where exactly in that paper did Paul command us to stick to aeolian
> > scale? He discusses "altered" scales in the paper after all.
>
> Paul discusses tonality as stemming from the rare step sizes in a
> scale.

That's only a half-truth. Remember the characteristic dissonances!

> I ask you how you reconcile this paradigm with the fact that
> tonality in minor doesn't seem to have anything to do with a single
> scale. Do you think that it comes from the scalar structures of the
> three parallel minor scales? Or do you think that there are no
> parallel minor scales, and if so, where does tonality emerge from?

Personally, I don't have any strong opinions about the emergence of
tonality. Paul would probably say that if any new (compared to the
unaltered scale) intervals are avoided in use then they don't count
when observing his rules for tonality.

> > > > Melodic movement by chromatic semitone sounds instantly like
> > > > going outside the basic seven degrees while typical use of the minor
> > > > doesn't.
> > >
> > > What do you mean "typical use of the minor?"
> >
> > The usual sort like using different scales when ascending and
> > descending.
>
> I'm not sure I follow - what are the basic seven degrees, the bare
> diatonic scale? Because I hear melodic minor as being different from
> the diatonic scale, obviously. So I'm a bit confused.

The seven degrees are more abstract entities in that they can be
inflected. The minor melodies may use different inflections
depending on the melodic direction. But if this inflecting is done
directly by playing a tone and its' chromatic inflection
consecutively then the music sounds chromatic. Doesn't that make
sense to you?

> > > You can say that this piece is in D Aeolian and just happens to
> > > "cadentially alter" it to Dorian every time he hits that B natural.
> > > You can likewise say the same thing about Come Together, that it's
> > > really D aeolian with some "cadential modulations" into dorian. I
> > > would be very surprised if the average person actually heard it that
> > > way, with a Bb there "naturally," and the note B being a departure or
> > > modulation from that.
> >
> > No no no, I wasn't claiming it's not in dorian. I agree about that but
> > what I claim is that it is in dorian because the alterations happen
> > only in special occasions.
>
> But there are no alterations. The alteration happens when the B
> finally changes to Bb, at which point it moves away from Dorian and
> into Aeolian. They don't play a single Bb until almost the last phrase
> of the song. The melody is in Dorian throughout, and the only
> alteration until that Bb is that they move the C up to C# so as to put
> you at the major V chord.

And why isn't that a description of alteration at a special occasion?

Kalle

🔗Mike Battaglia <battaglia01@...>

On Sun, Jun 12, 2011 at 5:14 PM, Kalle Aho <kalleaho@...> wrote:
> >
> > > Listen to this file:
> > >
> > > /tuning/files/KalleAho/Cadence.mp3
> > >
> > > The first one is the same one I used in the SoundCloud example.
> > >
> > > You probably hear the second one as the strongest. In meantone terms
> > > it sounds like a sweet V9-i(add6). In a decatonic context it doesn't
> > > sound as convincing to me as the first one:
> > >
> > > http://soundcloud.com/kalleaho/decatonic-progression-version
> >
> > I do hear the second one as being strongest. As far as the new
> > decatonic progression example vs the original, there is definitely
> > something that I like about the original, although I don't know
> > exactly what, but the altered one is also strong, just in a different
> > way. But what if you flatten the second-top in the penultimate chord
> > by "s," so that it sounds like a b9 resolving to a m6 chord in
> > meantone terms?
>
> In which one of the progressions? And don't you have any means for
> trying that out for yourself? (A rhetorical question, I know you do!)

In the last one, the weird one, but really all of them. As for means
of trying it out for myself - until recently, I didn't, as I've been
traveling back and from Brooklyn armed only with my new Mac. I'm not
sure how to use Macs yet really and don't have any audio software for
it. I only finally got my AXiS up and running last night. If you could
send me a MIDI file I'll try it though.

> > The strength of a resolution seems to have something to do with
> > learning. For instance, you apparently have to "learn" to hear
> > decatonic progressions as sounding decatonic; otherwise they just
> > sound diatonic. I have no idea what the difference is, because they
> > all sound the same to me. I also hated the third progression in the
> > sample you posted above, but liked it a lot after hearing it a few
> > times. However, there has to be some reason why 1\17 seems to function
> > as The Greatest Leading Tone Ever, and psychoacoustics is a natural
> > fit for why that might be. But perhaps it has to do with cognition as
> > well - if we were all used to 17, then maybe we'd think that 22 was
> > The Greatest Leading Tone Ever or something.
>
> How can decatonic progressions with their consecutive semitone-like
> steps sound diatonic to you? Chromatic maybe, but diatonic?!

They don't really sound fully chromatic, not like 12-tone serialist
music or anything like that. They sound, you know, mostly "diatonic"
with some extra notes thrown in there. To be honest it just sounds
like, let's call it, "extended diatonic harmony," like the kind they'd
use in jazz standards or early 20th century pop music and so on.

> And where's the evidence that everyone thinks that 1\17 is the best
> leading tone, was there a survey that I missed?

It's not 1\17 specifically, it's just that around that area leading
tones seem to resolve really well. For example, take 19-equal vs
12-equal - to my ears, the ti->do resolution, if left unaltered, is
much weaker than that of 12-tet. However, if you sharpen the leading
tone by 1\19, it's much stronger, and suddenly 19-equal seems to have
excellent melodic properties. I'm not the first person to notice this,
and I've seen references to this scattered all over the place, both on
and off this list, but if you disagree I won't argue the point as I'm
not an expert on it.

The point with 17-equal is that it puts the small step in the diatonic
scale equal around this spot, so no alteration is required. Hence
17-equal is often said to have good melodic properties (I think George
Secor originally brought this point up), and that's how it sounds to
me as well, and I've never heard anyone disagree with it. Does that
not seem to be true for you?

> > But don't you agree that the two have different musical effects? There
> > is a certain sense in which V-i is different from v-i.
>
> Of course.

Do you think they would have been aware of these different effects in
the musica ficta period, and that that's why they sharpened the
leading tones?

> I'd say (again) that it's the raising of the seventh degree that
> allows the fifth chord (and especially its' seventh chord version) to
> take the function of dominant. v doesn't quite sound like a dominant,
> really!

I do now agree with you that something about the concept of "leading
tone" is what's important, but I'm having trouble seeing the big
picture. In the diatonic scale, the leading tones also happen to be
the "rare intervals." In Pajara, however, the leading tone-sized
intervals are -not- the rare intervals, but rather they're everywhere.
You can't get away from them, which is partially why the whole thing
sounds so incoherent to me sometimes.

Maybe the secret is just to keep leading tones as rare intervals in
the scale - this way, they aren't played so much that you get
desensitized to them, and also the rare intervals are also leading
tones inasmuch as they carry minimal spectral overlap. In fact, this
seems to be what I naturally like about the scales that I said were
awesome - Keemun[7] and Father[8]. Keemun is 4L3s, and Father is 5L3s,
and both of them consist of nice smooth whole tones with some jarring
leading tones to fracture the scale up thrown in there. And I notice
that although the large steps are rare in Mavila[7], they're
definitely not ideal leading tones (although Mavila is nice for other
reasons).

I've also liked this about hedgehog as well, which is 6L2s - try the
LLsLLLsL mode in 22-equal. Note the LLsL pentachord sounds like a very
flat version of the same LLsL pentachord that exists in the diatonic
scale, except now the 5/4 is replaced with 6/5, the 9/8=10/9 replaced
with 10/9=11/10, the 4/3 replaced with 9/7, and the 3/2 replaced with
10/7, 4:5:6 in general replaced with 5:6:7, and 8:9:10:12 replaced
with 10:11:12:14. (Holy crap)

Actually, I didn't realize this until I started typing the above just
how crazy that is. WTF crazy property of LLsL is this that lets it
works out this neatly? If you do the same thing with 7:9:11 as the
base chord, does it work out that neatly? The LLsLLL machine[6] scale
of 11-equal gives us that, and that's another one of Igs' magic
"screwed up diatonic scales" - the 10/9=9/8 becomes 9/8=8/7, the 5/4
becomes 9/7, the 4/3 becomes 11/8, the 3/2 becomes 11/7, the 4:5:6
becomes 7:9:11, and the 8:9:10:12 becomes 7:8:9:11. WTF?

> In an unaltered aeolian scale that function is more likely
> taken by the nominally subdominant minor sixth chord, or so I
> maintain. Note that this sort of talk where the dominant function is
> not tied to a position of a fifth above the tonic has a precedent at
> least here:
>
> http://en.wikipedia.org/wiki/Flamenco#Harmony

In what sense do you mean that the function is "dominant?" I hear Fmaj
-> Em in the Andalusian cadence as resolving very strongly, perhaps
rivaling dominant in strength, but if dominant just means "strong
resolution" then what does subdominant mean? "Weak resolution?"

> > I should have said the diatonic scale. They ditched the diatonic
> > scale. Rather than continuing to search for scale patterns in the
> > diatonic scale, they opted to change it. And when we get into 20th
> > century extended harmony, they even got the diminished scale involved,
> > and used the altered scale over dominant chords.
>
> But they already had ditched the strict use of the diatonic scale
> before tonal harmony. Musica ficta.

OK, good point.

> > > Where exactly in that paper did Paul command us to stick to aeolian
> > > scale? He discusses "altered" scales in the paper after all.
> >
> > Paul discusses tonality as stemming from the rare step sizes in a
> > scale.
>
> That's only a half-truth. Remember the characteristic dissonances!

Hmm... perhaps I need to go through and read it again. But to be
honest, in the porcupine examples I laid out in 22-equal, setting the
dominant chord equal to 4:5:6:7 made it resolve more strongly than
setting it to 1/1 5/4 3/2 9/5, whatever that might be. The latter is
more dissonant, but the 9/5 on top resolving to the 5/4 of the I chord
was much weaker than the 7/4 resolving, despite that the first one had
the diminished fifth as 16/11 on top (which Paul chose as being more
dissonant than 7/5), and the second had it as 7/5. But the first one
gives you a better leading tone, which is more dissonant than any of
these intervals.

> > I ask you how you reconcile this paradigm with the fact that
> > tonality in minor doesn't seem to have anything to do with a single
> > scale. Do you think that it comes from the scalar structures of the
> > three parallel minor scales? Or do you think that there are no
> > parallel minor scales, and if so, where does tonality emerge from?
>
> Personally, I don't have any strong opinions about the emergence of
> tonality. Paul would probably say that if any new (compared to the
> unaltered scale) intervals are avoided in use then they don't count
> when observing his rules for tonality.

What do you mean new intervals?

> > I'm not sure I follow - what are the basic seven degrees, the bare
> > diatonic scale? Because I hear melodic minor as being different from
> > the diatonic scale, obviously. So I'm a bit confused.
>
> The seven degrees are more abstract entities in that they can be
> inflected. The minor melodies may use different inflections
> depending on the melodic direction. But if this inflecting is done
> directly by playing a tone and its' chromatic inflection
> consecutively then the music sounds chromatic. Doesn't that make
> sense to you?

OK, yes. And that's how I hear Pajara as sounding as well.

> > > No no no, I wasn't claiming it's not in dorian. I agree about that but
> > > what I claim is that it is in dorian because the alterations happen
> > > only in special occasions.
> >
> > But there are no alterations. The alteration happens when the B
> > finally changes to Bb, at which point it moves away from Dorian and
> > into Aeolian. They don't play a single Bb until almost the last phrase
> > of the song. The melody is in Dorian throughout, and the only
> > alteration until that Bb is that they move the C up to C# so as to put
> > you at the major V chord.
>
> And why isn't that a description of alteration at a special occasion?

It's a description of an alteration towards Aeolian away from Dorian.
I thought you were saying that any minor piece is naturally in
Aeolian, and any time someone plays a raised sixth that that's an
alteration. I was making the point that they never play the flat 6
until the very end, and then it's Aeolian that sounds like the
alteration, not the other way around.

-Mike

🔗Mike Battaglia <battaglia01@...>

🔗Kalle Aho <kalleaho@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Sun, Jun 12, 2011 at 5:14 PM, Kalle Aho <kalleaho@...> wrote:
> > >
> > > > Listen to this file:
> > > >
> > > > /tuning/files/KalleAho/Cadence.mp3
> > > >
> > > > The first one is the same one I used in the SoundCloud example.
> > > >
> > > > You probably hear the second one as the strongest. In meantone terms
> > > > it sounds like a sweet V9-i(add6). In a decatonic context it doesn't
> > > > sound as convincing to me as the first one:
> > > >
> > > > http://soundcloud.com/kalleaho/decatonic-progression-version
> > >
> > > I do hear the second one as being strongest. As far as the new
> > > decatonic progression example vs the original, there is definitely
> > > something that I like about the original, although I don't know
> > > exactly what, but the altered one is also strong, just in a different
> > > way. But what if you flatten the second-top in the penultimate chord
> > > by "s," so that it sounds like a b9 resolving to a m6 chord in
> > > meantone terms?
> >
> > In which one of the progressions? And don't you have any means for
> > trying that out for yourself? (A rhetorical question, I know you do!)
>
> In the last one, the weird one, but really all of them. As for means
> of trying it out for myself - until recently, I didn't, as I've been
> traveling back and from Brooklyn armed only with my new Mac. I'm not
> sure how to use Macs yet really and don't have any audio software for
> it. I only finally got my AXiS up and running last night. If you could
> send me a MIDI file I'll try it though.

I don't use MIDI files. Here:

/tuning/files/KalleAho/cadence2.mp3

> > > The strength of a resolution seems to have something to do with
> > > learning. For instance, you apparently have to "learn" to hear
> > > decatonic progressions as sounding decatonic; otherwise they just
> > > sound diatonic. I have no idea what the difference is, because they
> > > all sound the same to me. I also hated the third progression in the
> > > sample you posted above, but liked it a lot after hearing it a few
> > > times. However, there has to be some reason why 1\17 seems to function
> > > as The Greatest Leading Tone Ever, and psychoacoustics is a natural
> > > fit for why that might be. But perhaps it has to do with cognition as
> > > well - if we were all used to 17, then maybe we'd think that 22 was
> > > The Greatest Leading Tone Ever or something.
> >
> > How can decatonic progressions with their consecutive semitone-like
> > steps sound diatonic to you? Chromatic maybe, but diatonic?!
>
> They don't really sound fully chromatic, not like 12-tone serialist
> music or anything like that. They sound, you know, mostly "diatonic"
> with some extra notes thrown in there. To be honest it just sounds
> like, let's call it, "extended diatonic harmony," like the kind they'd
> use in jazz standards or early 20th century pop music and so on.

12-tone serialism is not what "chromaticism" typically refers to.
"Mostly diatonic with some extra notes thrown in there" is actually a
good working definition for chromaticism.

And if you think using common practice harmony in novel temperaments
is xenharmonic, then so is using "extended diatonic harmony" (or
rather something sounding like it) in those temperaments.

> > And where's the evidence that everyone thinks that 1\17 is the best
> > leading tone, was there a survey that I missed?
>
> It's not 1\17 specifically, it's just that around that area leading
> tones seem to resolve really well. For example, take 19-equal vs
> 12-equal - to my ears, the ti->do resolution, if left unaltered, is
> much weaker than that of 12-tet. However, if you sharpen the leading
> tone by 1\19, it's much stronger, and suddenly 19-equal seems to have
> excellent melodic properties. I'm not the first person to notice this,
> and I've seen references to this scattered all over the place, both on
> and off this list, but if you disagree I won't argue the point as I'm
> not an expert on it.
>
> The point with 17-equal is that it puts the small step in the diatonic
> scale equal around this spot, so no alteration is required. Hence
> 17-equal is often said to have good melodic properties (I think George
> Secor originally brought this point up), and that's how it sounds to
> me as well, and I've never heard anyone disagree with it. Does that
> not seem to be true for you?

I'm just skeptical about it. Is it really an interval of minimal
spectral overlap or something like that? Doesn't that honour actually
go to Phi? And if it's some local metastable interval then there are
others as well and it is not singled out as something universal. The
size of the steps in the third progression is right there between
1\17 and 1\19 so why doesn't it sound that great?

> > > But don't you agree that the two have different musical effects? There
> > > is a certain sense in which V-i is different from v-i.
> >
> > Of course.
>
> Do you think they would have been aware of these different effects in
> the musica ficta period, and that that's why they sharpened the
> leading tones?

No, the period spans centuries and multiple styles starting at 12th
century when there was no triadic harmony. At first the ficta were
used to avoid offending intervals like tritones but soon they were
also used in cadences which were dyadic progressions from imperfect
to perfect consonances. As to why they did that, I don't know.

> > I'd say (again) that it's the raising of the seventh degree that
> > allows the fifth chord (and especially its' seventh chord version) to
> > take the function of dominant. v doesn't quite sound like a dominant,
> > really!
>
> I do now agree with you that something about the concept of "leading
> tone" is what's important, but I'm having trouble seeing the big
> picture.

But I don't think leading tones are universally important to all
tuning systems and in my opinion that something that is important
about leading tone in the minor tonality is that the raised seventh
degree produces another tritone in the scale so that we have a V7
chord that leads in contrary motion to i chord, contrary motion being
the strongest of motions. One of the scale degrees the tritone
expands to is the tonic, that doesn't happen in the natural minor
cadence.

Another reason for harmonic minor was probably the need for
functional symmetry between major and minor tonalities so that
melodies could be modulated between major and minor with the same
order of harmonic functions, one of the great dramatic techniques of
common practice music.

> In the diatonic scale, the leading tones also happen to be
> the "rare intervals." In Pajara, however, the leading tone-sized
> intervals are -not- the rare intervals, but rather they're everywhere.
> You can't get away from them, which is partially why the whole thing
> sounds so incoherent to me sometimes.
>
> Maybe the secret is just to keep leading tones as rare intervals in
> the scale - this way, they aren't played so much that you get
> desensitized to them, and also the rare intervals are also leading
> tones inasmuch as they carry minimal spectral overlap. In fact, this
> seems to be what I naturally like about the scales that I said were
> awesome - Keemun[7] and Father[8]. Keemun is 4L3s, and Father is 5L3s,
> and both of them consist of nice smooth whole tones with some jarring
> leading tones to fracture the scale up thrown in there. And I notice
> that although the large steps are rare in Mavila[7], they're
> definitely not ideal leading tones (although Mavila is nice for other
> reasons).

Maybe Mavila should be tuned so that the large step is some local
interval of minimal spectral overlap?

> I've also liked this about hedgehog as well, which is 6L2s - try the
> LLsLLLsL mode in 22-equal. Note the LLsL pentachord sounds like a very
> flat version of the same LLsL pentachord that exists in the diatonic
> scale, except now the 5/4 is replaced with 6/5, the 9/8=10/9 replaced
> with 10/9=11/10, the 4/3 replaced with 9/7, and the 3/2 replaced with
> 10/7, 4:5:6 in general replaced with 5:6:7, and 8:9:10:12 replaced
> with 10:11:12:14. (Holy crap)
>
> Actually, I didn't realize this until I started typing the above just
> how crazy that is. WTF crazy property of LLsL is this that lets it
> works out this neatly? If you do the same thing with 7:9:11 as the
> base chord, does it work out that neatly? The LLsLLL machine[6] scale
> of 11-equal gives us that, and that's another one of Igs' magic
> "screwed up diatonic scales" - the 10/9=9/8 becomes 9/8=8/7, the 5/4
> becomes 9/7, the 4/3 becomes 11/8, the 3/2 becomes 11/7, the 4:5:6
> becomes 7:9:11, and the 8:9:10:12 becomes 7:8:9:11. WTF?

I'll try these sometime.

> > In an unaltered aeolian scale that function is more likely
> > taken by the nominally subdominant minor sixth chord, or so I
> > maintain. Note that this sort of talk where the dominant function is
> > not tied to a position of a fifth above the tonic has a precedent at
> > least here:
> >
> > http://en.wikipedia.org/wiki/Flamenco#Harmony
>
> In what sense do you mean that the function is "dominant?"

Creating an instability that strongly suggests the tonic as the most
satisfying resolution.

> I hear Fmaj -> Em in the Andalusian cadence as resolving very strongly,
> perhaps rivaling dominant in strength, but if dominant just means "strong
> resolution" then what does subdominant mean? "Weak resolution?"

You mean Fmaj -> Emaj, right?

In this context subdominant has multiple meanings that can be
dissociated: a chord that has the tonic as its' dominant, predominant
etc. But how we name the functions is not that important, my point is
that harmonic functions should not be equated with scale degrees or
root relations.

> > > > Where exactly in that paper did Paul command us to stick to aeolian
> > > > scale? He discusses "altered" scales in the paper after all.
> > >
> > > Paul discusses tonality as stemming from the rare step sizes in a
> > > scale.
> >
> > That's only a half-truth. Remember the characteristic dissonances!
>
> Hmm... perhaps I need to go through and read it again. But to be
> honest, in the porcupine examples I laid out in 22-equal, setting the
> dominant chord equal to 4:5:6:7 made it resolve more strongly than
> setting it to 1/1 5/4 3/2 9/5, whatever that might be. The latter is
> more dissonant, but the 9/5 on top resolving to the 5/4 of the I chord
> was much weaker than the 7/4 resolving, despite that the first one had
> the diminished fifth as 16/11 on top (which Paul chose as being more
> dissonant than 7/5), and the second had it as 7/5. But the first one
> gives you a better leading tone, which is more dissonant than any of
> these intervals.

The ~5:7 in 22-equal is identical to the tritone we are used to in
12-equal and the tritone is the characteristic dissonance of the
diatonic scale.

> > > I ask you how you reconcile this paradigm with the fact that
> > > tonality in minor doesn't seem to have anything to do with a single
> > > scale. Do you think that it comes from the scalar structures of the
> > > three parallel minor scales? Or do you think that there are no
> > > parallel minor scales, and if so, where does tonality emerge from?
> >
> > Personally, I don't have any strong opinions about the emergence of
> > tonality. Paul would probably say that if any new (compared to the
> > unaltered scale) intervals are avoided in use then they don't count
> > when observing his rules for tonality.
>
> What do you mean new intervals?

Ones not present in the unaltered scale.

> > > I'm not sure I follow - what are the basic seven degrees, the bare
> > > diatonic scale? Because I hear melodic minor as being different from
> > > the diatonic scale, obviously. So I'm a bit confused.
> >
> > The seven degrees are more abstract entities in that they can be
> > inflected. The minor melodies may use different inflections
> > depending on the melodic direction. But if this inflecting is done
> > directly by playing a tone and its' chromatic inflection
> > consecutively then the music sounds chromatic. Doesn't that make
> > sense to you?
>
> OK, yes. And that's how I hear Pajara as sounding as well.

As seven alterable degrees or chromaticism or what?

> Also, do you feel like these pieces do the job of being "tonal?"
>
> http://www.youtube.com/watch?v=y8MXbFtw4rM
> http://www.youtube.com/watch?v=KV_MzdtU2WQ

I hear a tonal center. Does that suffice? I don't know. It also sounds
modal in the sense of not being in traditional major or minor.

Kalle

🔗duckfeetbilly <billygard@...>

🔗Mike Battaglia <battaglia01@...>

Here we go!

-Mike

On Thu, Jun 16, 2011 at 4:05 PM, Kalle Aho <kalleaho@...> wrote:
>
> I don't use MIDI files. Here:
>
> /tuning/files/KalleAho/cadence2.mp3

Alright, after listening to this with a clear head, the second one is
strongest to me. The last one sounds cool, and I like it, but I do
understand what you mean in that the sharpening of the one tone and
flattening of the other tone means the interval between them is closer
to a fifth - not a tritone. The same thing happens in 16-equal, where
if you do G7->Cmaj - and you make the B-C move by 1\16, and you also
make the F-E move by 1\16 - the tritone becomes a 675 fifth, and the
strength of the resolution is completely destroyed. So touche, Mr.
Aho, you win this time. Foiled again!

There is one thing though - check out the mavila experiments I posted
again, I saw you commented on them in Facebook:

http://soundcloud.com/mikebattagliamusic/sets/the-mavila-experiments

In these experiments, when you're in minor - which now has become
major - and when you'd normally sharpen the minor 7th to get you the
leading tone, you end up flattening the now neutral 7th to get the new
"leading" tone. That is, in mavila major, the normal 7th scale degree
is 1043 cents (in 23-equal, which is what they're tuned to). Any piece
that would "sharpen" this originally ends up flattening it, and your
new altered 7th scale degree is 991 cents, meaning your "leading tone"
becomes 208 cents. This ends up doing four things:

1) It means that the ti-do resolution now becomes the "rare" interval
in the scale, except the rare interval is the large step or 208 cents.
2) Since the leading tone is 208 cents, it also now means that the
leading tone is moving by a much more consonant sounding interval than
before.
3) The diminished fifth now becomes 730 cents, and the augmented
fourth now becomes 469 cents.
4) V-i now becomes v-I.

I think that while these pieces work out nicely, the flattening of the
leading tone doesn't make the resolutions sound any stronger; rather I
think it makes them sound weaker. I think that, despite the fact that
the leading tone ends up become the "rare" interval, this rare
interval doesn't signal the tonic, and that if I went back to each one
of these pieces and systematically changed the flattened leading tones
to sharpened ones, the resolutions would sound stronger (this would be
hell to do). What are your thoughts?

I should add that #3 could be changed somewhat by putting it in
16-equal, where the diminished fifth would now be 750 cents, and the
augmented fourth would now be 450 cents.

> > They don't really sound fully chromatic, not like 12-tone serialist
> > music or anything like that. They sound, you know, mostly "diatonic"
> > with some extra notes thrown in there. To be honest it just sounds
> > like, let's call it, "extended diatonic harmony," like the kind they'd
> > use in jazz standards or early 20th century pop music and so on.
>
> 12-tone serialism is not what "chromaticism" typically refers to.
> "Mostly diatonic with some extra notes thrown in there" is actually a
> good working definition for chromaticism.

OK, then yeah, that's what it sounds like to me.

> And if you think using common practice harmony in novel temperaments
> is xenharmonic, then so is using "extended diatonic harmony" (or
> rather something sounding like it) in those temperaments.

You must be referring to my functional porcupine harmony examples. I
think that those sound xenharmonic because the structure of the comma
pump causes the very fabric of the universe to sound like it's
inverting on itself, and you don't know whether up is down or down is
up, and you seem to be going on a rollercoaster that's shaped like a
Klein bottle, and then suddenly BAM, you're at the IV chord, IV V I.
Hell yes, that's xenharmonic. On the other hand, I wouldn't say that
it's the pinnacle of xenharmonicity either - it does sound a bit like
boring old common practice harmony in other ways. But it was a
starting point for me to explore porcupine MODAL harmony, which is
definitely xenharmonic. See this -
http://www.youtube.com/watch?v=XSfnyr1MhXE

And please ignore me mumbling and screwing up the explanation, it was
like 5 AM :)

Pajara offers a similar experience by way of doing tritone subs, which
were definitely xenharmonic when they were first discovered in
12-equal. I'm just saying that I don't hear it sounding radically
different, that's all, I'm used to them because 12-equal already has
them. I think that Pajara is great because it provides some kind of
theoretical explanation for what's going on with this other sound that
was discovered in 12-equal in the early 20th century. But I still
can't get the hang of hearing this Pajara[10] MODMOS as offering a
bold new sensory experience that I've never heard before.

I will say one interesting thing - the Pajara standard pentachordal
scale, if you reframe it as a 2.3.5.17 subgroup temperament, suddenly
does open up a whole new world in my mind, even though it's playable
in 12-equal. You can play C C# D E all at the same time and it'll
"fuse" very slightly (!) into 16:17:18:20. It's good enough to hint at
the sound. That is, you start to hear C# as a rooted interval over the
C, not as some kind of borrowed note from Phrygian or whatever. Then
you can get to G# and that's a fifth up, and F# is a fifth down. It's
like a new way of conceptualizing the notes in the scale. The C C# D E
F F# G G# A B C mode seems to be the magical one here (all relative to
12-equal, you can put it in 22-equal as you want). So maybe it's just
that I'm used to 7-limit harmony because the concept of hearing a
dominant 7 chord as "otonal" was already discovered in 12-equal, but
the 17-limit version was not. Just a thought. I have a recording from
several years ago of the concept here:
http://rabbit.eng.miami.edu/students/mbattaglia/Senior_Recital/1-01%20Sand%20Prism.mp3

It hints at 17-limit harmony in the way I'm describing above.

> > The point with 17-equal is that it puts the small step in the diatonic
> > scale equal around this spot, so no alteration is required. Hence
> > 17-equal is often said to have good melodic properties (I think George
> > Secor originally brought this point up), and that's how it sounds to
> > me as well, and I've never heard anyone disagree with it. Does that
> > not seem to be true for you?
>
> I'm just skeptical about it. Is it really an interval of minimal
> spectral overlap or something like that?

It's an interval of nearly maximal harmonic entropy, which is
obliquely related in that it means it's an interval that is maximally
inharmonic. I think it's the global maximum, right? Not that I think
that HE is precisely accurate enough to really model this over
anyone's own hearing, but I'm just pointing that out.

> Doesn't that honour actually
> go to Phi? And if it's some local metastable interval then there are
> others as well and it is not singled out as something universal. The
> size of the steps in the third progression is right there between
> 1\17 and 1\19 so why doesn't it sound that great?

I don't know, but the version with the sharpened leading tone sounds
stronger to my ears. It could be that the 550 cent interval sounds
kind of like a fourth to my ears in the context that it's being used,
whereas the raised leading tone version sounds like a tritone. Which
seems to mean that the tritone works best even if we're supposed to be
accepting tritones as consonant now, because they're in 7-limit
tetrads, and which is also consistent with the fact that as I
mentioned before using 600 cents in 22-equal ended up giving a more
convincing resolution than 650 cents even for 5-limit harmony.

> > Do you think they would have been aware of these different effects in
> > the musica ficta period, and that that's why they sharpened the
> > leading tones?
>
> No, the period spans centuries and multiple styles starting at 12th
> century when there was no triadic harmony. At first the ficta were
> used to avoid offending intervals like tritones but soon they were
> also used in cadences which were dyadic progressions from imperfect
> to perfect consonances. As to why they did that, I don't know.

You honestly don't think that it just had a different musical feeling,
the same one that caused them to sharpen it even when they started
using harmony?

> > I do now agree with you that something about the concept of "leading
> > tone" is what's important, but I'm having trouble seeing the big
> > picture.
>
> But I don't think leading tones are universally important to all
> tuning systems and in my opinion that something that is important
> about leading tone in the minor tonality is that the raised seventh
> degree produces another tritone in the scale so that we have a V7
> chord that leads in contrary motion to i chord, contrary motion being
> the strongest of motions. One of the scale degrees the tritone
> expands to is the tonic, that doesn't happen in the natural minor
> cadence.

OK, I can see that. I guess I just am not convinced of the possibility
of using 550 cents as a substitute for 600 cents, that's all. Although
7/5 "fuses" better than 11/8, there is a sense in which the former is
more dissonant, and this is what makes it suitable for resolutions to
my ears. I don't know what that sense is. It could be the fact that
11/8, if played with the root doubled down a few bass notes, becomes
something like 2:4:8:11, which is pretty simple, whereas 7/5 becomes
5:10:20:28, which is less. So perhaps tonalness has to do with it.
Honestly, no matter how much I listen to Pajara, I can't get into the
sound of 11/8 as a characteristic dissonance, nor can I get into the
sound of 8/7 as a leading tone. I've been trying for years.

> Another reason for harmonic minor was probably the need for
> functional symmetry between major and minor tonalities so that
> melodies could be modulated between major and minor with the same
> order of harmonic functions, one of the great dramatic techniques of
> common practice music.

OK, I agree with this too.

> > Maybe the secret is just to keep leading tones as rare intervals in
> > the scale - this way, they aren't played so much that you get
> > desensitized to them, and also the rare intervals are also leading
> > tones inasmuch as they carry minimal spectral overlap. In fact, this
> > seems to be what I naturally like about the scales that I said were
> > awesome - Keemun[7] and Father[8]. Keemun is 4L3s, and Father is 5L3s,
> > and both of them consist of nice smooth whole tones with some jarring
> > leading tones to fracture the scale up thrown in there. And I notice
> > that although the large steps are rare in Mavila[7], they're
> > definitely not ideal leading tones (although Mavila is nice for other
> > reasons).
>
> Maybe Mavila should be tuned so that the large step is some local
> interval of minimal spectral overlap?

Maybe, but I think it's also about dissonance - the local maximum of
harmonic entropy between 9/8 and 8/7 just doesn't sound as dissonant
to me as 25/24 does. But this is the mysterious part of the
"categorical perception" of intervals that we labeled the "Big
Masturbatory Theoretical Question" last week, so I don't think anyone
has the answer. I'm not entirely sure it has anything to do with
harmonic entropy. I've just noticed that if you're in 19-equal,
sharpening the leading tone by 1\19 makes it a million times more
convincing, and also happens to push the leading tone towards the
global maximum of HE. Perhaps it's a false correlation.

> > > http://en.wikipedia.org/wiki/Flamenco#Harmony
> >
> > In what sense do you mean that the function is "dominant?"
>
> Creating an instability that strongly suggests the tonic as the most
> satisfying resolution.

OK. Perhaps that's been the cause of some confusion, because to me the
dominant means the v or V chord, and subdominant means the iv or IV
chord.

> In this context subdominant has multiple meanings that can be
> dissociated: a chord that has the tonic as its' dominant, predominant
> etc. But how we name the functions is not that important, my point is
> that harmonic functions should not be equated with scale degrees or
> root relations.

OK, fair enough.

> > Hmm... perhaps I need to go through and read it again. But to be
> > honest, in the porcupine examples I laid out in 22-equal, setting the
> > dominant chord equal to 4:5:6:7 made it resolve more strongly than
> > setting it to 1/1 5/4 3/2 9/5, whatever that might be. The latter is
> > more dissonant, but the 9/5 on top resolving to the 5/4 of the I chord
> > was much weaker than the 7/4 resolving, despite that the first one had
> > the diminished fifth as 16/11 on top (which Paul chose as being more
> > dissonant than 7/5), and the second had it as 7/5. But the first one
> > gives you a better leading tone, which is more dissonant than any of
> > these intervals.
>
> The ~5:7 in 22-equal is identical to the tritone we are used to in
> 12-equal and the tritone is the characteristic dissonance of the
> diatonic scale.

If 650 cents is supposed to be more dissonant than 600 cents,
shouldn't it work even better? But that's not the case. And why does
it seem to be universally accepted that 17-equal has better melodic
properties than 12-equal, a better leading tone, etc? What I'm saying
is, if it was really 100% about learning, why this consistent response
towards 17-equal? There does seem to be some kind of way to make
things resolve "even more," and that approach isn't met by changing
600 cents to 650 cents in 22-equal, but it is when you move to
17-equal which has a tritone of 635 cents and a leading tone of 60
cents. Why...? I seriously don't know.

> > > The seven degrees are more abstract entities in that they can be
> > > inflected. The minor melodies may use different inflections
> > > depending on the melodic direction. But if this inflecting is done
> > > directly by playing a tone and its' chromatic inflection
> > > consecutively then the music sounds chromatic. Doesn't that make
> > > sense to you?
> >
> > OK, yes. And that's how I hear Pajara as sounding as well.
>
> As seven alterable degrees or chromaticism or what?

Both.

> > Also, do you feel like these pieces do the job of being "tonal?"
> >
> > http://www.youtube.com/watch?v=y8MXbFtw4rM
> > http://www.youtube.com/watch?v=KV_MzdtU2WQ
>
> I hear a tonal center. Does that suffice? I don't know. It also sounds
> modal in the sense of not being in traditional major or minor.

It does suffice, yes. It's basically the mavila equivalent of this
meantone progression:

Except since we're in mavila, the Bb becomes a B. That is, you can
think of Gmaj as V, and the Bb/F as IV/IV. In meantone, when V moves
to IV/IV, the root goes up by 6/5. In mavila, instead, it goes by 5/4.
So the roots in the mavila version are C - G - A - G - B - F - C,
where B-F is still 3/2.

I also play this comma pump in mavila that's like Cmaj - Emaj - Bmaj -
Fmaj, again where B-F is 3/2. So it's like a mavila I III VII IV.

My question is, now that I've explained the progression, would you say
that the mavila one sounds "modal" and the meantone one sounds
"tonal?" Or that they both sound modal, or that they both sound tonal?
To my ears, they both sound tonal, with this one colorful IV/IV thrown
in there.

-Mike

🔗Kalle Aho <kalleaho@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> On Thu, Jun 16, 2011 at 4:05 PM, Kalle Aho <kalleaho@...> wrote:
> >
> > I don't use MIDI files. Here:
> >
> > /tuning/files/KalleAho/cadence2.mp3
>
> Alright, after listening to this with a clear head, the second one is
> strongest to me.

To me there is something unsatisfactory in the second one, I hear the
first one as the strongest.

> The last one sounds cool, and I like it, but I do
> understand what you mean in that the sharpening of the one tone and
> flattening of the other tone means the interval between them is closer
> to a fifth - not a tritone.

I don't know where I said this but OK. :)

> The same thing happens in 16-equal, where
> if you do G7->Cmaj - and you make the B-C move by 1\16, and you also
> make the F-E move by 1\16 - the tritone becomes a 675 fifth, and the
> strength of the resolution is completely destroyed. So touche, Mr.
> Aho, you win this time. Foiled again!
>
> There is one thing though - check out the mavila experiments I posted
> again, I saw you commented on them in Facebook:
>
> http://soundcloud.com/mikebattagliamusic/sets/the-mavila-experiments
>
> In these experiments, when you're in minor - which now has become
> major - and when you'd normally sharpen the minor 7th to get you the
> leading tone, you end up flattening the now neutral 7th to get the new
> "leading" tone. That is, in mavila major, the normal 7th scale degree
> is 1043 cents (in 23-equal, which is what they're tuned to). Any piece
> that would "sharpen" this originally ends up flattening it, and your
> new altered 7th scale degree is 991 cents, meaning your "leading tone"
> becomes 208 cents. This ends up doing four things:
>
> 1) It means that the ti-do resolution now becomes the "rare" interval
> in the scale, except the rare interval is the large step or 208 cents.
> 2) Since the leading tone is 208 cents, it also now means that the
> leading tone is moving by a much more consonant sounding interval than
> before.

Are you saying that a melodic (i.e. tones are successive, not
simultaneous) interval can sound consonant/dissonant? That might
happen in arpeggiated chords but what about melodic movements by
step? I don't feel that there is anything consonant or dissonant
about them.

> 3) The diminished fifth now becomes 730 cents, and the augmented
> fourth now becomes 469 cents.
> 4) V-i now becomes v-I.
>
> I think that while these pieces work out nicely, the flattening of the
> leading tone doesn't make the resolutions sound any stronger; rather I
> think it makes them sound weaker. I think that, despite the fact that
> the leading tone ends up become the "rare" interval, this rare
> interval doesn't signal the tonic, and that if I went back to each one
> of these pieces and systematically changed the flattened leading tones
> to sharpened ones, the resolutions would sound stronger (this would be
> hell to do). What are your thoughts?

Maybe. The pieces sound fine as they are now though. Could you make
some simple example where the effects of flattening and sharpening
are compared, perhaps a phrase from one of the example pieces?

> I should add that #3 could be changed somewhat by putting it in
> 16-equal, where the diminished fifth would now be 750 cents, and the
> augmented fourth would now be 450 cents.

It bothers me that none of the optimal tuning methods we have
considers the tuning of the dissonances, they just let them land
where they may. For example, in TOP Mavila the characteristic
dissonance is closer to 2:3 than the Mavila fifth and that's just
wrong!

> > And if you think using common practice harmony in novel temperaments
> > is xenharmonic, then so is using "extended diatonic harmony" (or
> > rather something sounding like it) in those temperaments.
>
> You must be referring to my functional porcupine harmony examples. I
> think that those sound xenharmonic because the structure of the comma
> pump causes the very fabric of the universe to sound like it's
> inverting on itself, and you don't know whether up is down or down is
> up, and you seem to be going on a rollercoaster that's shaped like a
> Klein bottle, and then suddenly BAM, you're at the IV chord, IV V I.
> Hell yes, that's xenharmonic. On the other hand, I wouldn't say that
> it's the pinnacle of xenharmonicity either - it does sound a bit like
> boring old common practice harmony in other ways. But it was a
> starting point for me to explore porcupine MODAL harmony, which is
> definitely xenharmonic. See this -
> http://www.youtube.com/watch?v=XSfnyr1MhXE
>
> And please ignore me mumbling and screwing up the explanation, it was
> like 5 AM :)
>
> Pajara offers a similar experience by way of doing tritone subs, which
> were definitely xenharmonic when they were first discovered in
> 12-equal. I'm just saying that I don't hear it sounding radically
> different, that's all, I'm used to them because 12-equal already has
> them. I think that Pajara is great because it provides some kind of
> theoretical explanation for what's going on with this other sound that
> was discovered in 12-equal in the early 20th century. But I still
> can't get the hang of hearing this Pajara[10] MODMOS as offering a
> bold new sensory experience that I've never heard before.
>
> I will say one interesting thing - the Pajara standard pentachordal
> scale, if you reframe it as a 2.3.5.17 subgroup temperament, suddenly
> does open up a whole new world in my mind, even though it's playable
> in 12-equal. You can play C C# D E all at the same time and it'll
> "fuse" very slightly (!) into 16:17:18:20. It's good enough to hint at
> the sound. That is, you start to hear C# as a rooted interval over the
> C, not as some kind of borrowed note from Phrygian or whatever. Then
> you can get to G# and that's a fifth up, and F# is a fifth down. It's
> like a new way of conceptualizing the notes in the scale. The C C# D E
> F F# G G# A B C mode seems to be the magical one here (all relative to
> 12-equal, you can put it in 22-equal as you want). So maybe it's just
> that I'm used to 7-limit harmony because the concept of hearing a
> dominant 7 chord as "otonal" was already discovered in 12-equal, but
> the 17-limit version was not. Just a thought. I have a recording from
> several years ago of the concept here:
> http://rabbit.eng.miami.edu/students/mbattaglia/Senior_Recital/1-01%20Sand%20Prism.mp3
>
> It hints at 17-limit harmony in the way I'm describing above.

The Pajara temperament itself is moderately xenharmonic because it
doesn't temper out 35:36 or 80:81 and while Pajara[10] is in a sense
a better tuned version of something already found in 12-equal,
12-equal doesn't contain the characteristic dissonances found in
22-equal and 2D Pajara although we may disagree about their
importance.

BTW, I'm not really a xenharmonic thrills junkie like you because
that lifestyle will ultimately disappoint. You are just going to seek
weirder and weirder comma pumps and become a recluse because your
dopaminergic xenharmonicity neurons will only fire when you hear
something that respectful people can't even comprehend or stomach!

> > > The point with 17-equal is that it puts the small step in the diatonic
> > > scale equal around this spot, so no alteration is required. Hence
> > > 17-equal is often said to have good melodic properties (I think George
> > > Secor originally brought this point up), and that's how it sounds to
> > > me as well, and I've never heard anyone disagree with it. Does that
> > > not seem to be true for you?
> >
> > I'm just skeptical about it. Is it really an interval of minimal
> > spectral overlap or something like that?
>
> It's an interval of nearly maximal harmonic entropy, which is
> obliquely related in that it means it's an interval that is maximally
> inharmonic. I think it's the global maximum, right? Not that I think
> that HE is precisely accurate enough to really model this over
> anyone's own hearing, but I'm just pointing that out.

You keep on talking as if this idea of melodic intervals sounding
dissonant or consonant was common music theory parlance. And it is
not clear to me by what mechanism this would aid in establishing
tonality.

> > Doesn't that honour actually
> > go to Phi? And if it's some local metastable interval then there are
> > others as well and it is not singled out as something universal. The
> > size of the steps in the third progression is right there between
> > 1\17 and 1\19 so why doesn't it sound that great?
>
> I don't know, but the version with the sharpened leading tone sounds
> stronger to my ears. It could be that the 550 cent interval sounds
> kind of like a fourth to my ears in the context that it's being used,
> whereas the raised leading tone version sounds like a tritone. Which
> seems to mean that the tritone works best even if we're supposed to be
> accepting tritones as consonant now, because they're in 7-limit
> tetrads, and which is also consistent with the fact that as I
> mentioned before using 600 cents in 22-equal ended up giving a more
> convincing resolution than 650 cents even for 5-limit harmony.

See below (as you essentially wrote the same thing twice).

> > > Do you think they would have been aware of these different effects in
> > > the musica ficta period, and that that's why they sharpened the
> > > leading tones?
> >
> > No, the period spans centuries and multiple styles starting at 12th
> > century when there was no triadic harmony. At first the ficta were
> > used to avoid offending intervals like tritones but soon they were
> > also used in cadences which were dyadic progressions from imperfect
> > to perfect consonances. As to why they did that, I don't know.
>
> You honestly don't think that it just had a different musical feeling,
> the same one that caused them to sharpen it even when they started
> using harmony?

Of course it had a different musical feeling but just having a
different musical feeling is not sufficient reason to sharpen
consistently. Just having a different musical feeling would imply
sometimes sharpening and sometimes not, just for variety's sake,
don't you think?

"Started using harmony"? Harmony was already in use way before this
sharpening started.

> > > I do now agree with you that something about the concept of "leading
> > > tone" is what's important, but I'm having trouble seeing the big
> > > picture.
> >
> > But I don't think leading tones are universally important to all
> > tuning systems and in my opinion that something that is important
> > about leading tone in the minor tonality is that the raised seventh
> > degree produces another tritone in the scale so that we have a V7
> > chord that leads in contrary motion to i chord, contrary motion being
> > the strongest of motions. One of the scale degrees the tritone
> > expands to is the tonic, that doesn't happen in the natural minor
> > cadence.

Adding to this: the two tritones also produce a diminished seventh
chord and that is something extremely common in common practice minor
tonality, often replacing the V7 in function even though it's most
often "rooted" on the raised seventh degree of harmonic minor.

> OK, I can see that. I guess I just am not convinced of the possibility
> of using 550 cents as a substitute for 600 cents, that's all. Although
> 7/5 "fuses" better than 11/8, there is a sense in which the former is
> more dissonant, and this is what makes it suitable for resolutions to
> my ears. I don't know what that sense is. It could be the fact that
> 11/8, if played with the root doubled down a few bass notes, becomes
> something like 2:4:8:11, which is pretty simple, whereas 7/5 becomes
> 5:10:20:28, which is less. So perhaps tonalness has to do with it.
> Honestly, no matter how much I listen to Pajara, I can't get into the
> sound of 11/8 as a characteristic dissonance, nor can I get into the
> sound of 8/7 as a leading tone. I've been trying for years.

I'm using TOP Pajara in my example and the characteristic dissonance
is 532.833 cents which is more like 11:15 than 8:11. Also the rare
interval in Pajara is not the ~7:8. It's an ~9:10.

> > > In what sense do you mean that the function is "dominant?"
> >
> > Creating an instability that strongly suggests the tonic as the most
> > satisfying resolution.
>
> OK. Perhaps that's been the cause of some confusion, because to me the
> dominant means the v or V chord, and subdominant means the iv or IV
> chord.

What about theorists who regard both IV and ii as subdominant
(or predominant) and both V and vii as dominant? That's pretty common
in German music theory.

> > > Hmm... perhaps I need to go through and read it again. But to be
> > > honest, in the porcupine examples I laid out in 22-equal, setting the
> > > dominant chord equal to 4:5:6:7 made it resolve more strongly than
> > > setting it to 1/1 5/4 3/2 9/5, whatever that might be. The latter is
> > > more dissonant, but the 9/5 on top resolving to the 5/4 of the I chord
> > > was much weaker than the 7/4 resolving, despite that the first one had
> > > the diminished fifth as 16/11 on top (which Paul chose as being more
> > > dissonant than 7/5), and the second had it as 7/5. But the first one
> > > gives you a better leading tone, which is more dissonant than any of
> > > these intervals.
> >
> > The ~5:7 in 22-equal is identical to the tritone we are used to in
> > 12-equal and the tritone is the characteristic dissonance of the
> > diatonic scale.
>
> If 650 cents is supposed to be more dissonant than 600 cents,
> shouldn't it work even better? But that's not the case. And why does
> it seem to be universally accepted that 17-equal has better melodic
> properties than 12-equal, a better leading tone, etc? What I'm saying
> is, if it was really 100% about learning, why this consistent response
> towards 17-equal? There does seem to be some kind of way to make
> things resolve "even more," and that approach isn't met by changing
> 600 cents to 650 cents in 22-equal, but it is when you move to
> 17-equal which has a tritone of 635 cents and a leading tone of 60
> cents. Why...? I seriously don't know.

I hear 1/1 5/4 3/2 9/5 as more dissonant but it sounds very different
from a typical meantone V-I so that might influence our judgment.
Maybe it's just not convincing as a meantone-like V-I, whatever
merits it has outside that context.

> > > Also, do you feel like these pieces do the job of being "tonal?"
> > >
> > > http://www.youtube.com/watch?v=y8MXbFtw4rM
> > > http://www.youtube.com/watch?v=KV_MzdtU2WQ
> >
> > I hear a tonal center. Does that suffice? I don't know. It also sounds
> > modal in the sense of not being in traditional major or minor.
>
> It does suffice, yes.

Why are you so sure? Modal music is tonal in the sense of having a
tonal center but 'tonal' probably should mean something more than
just having a tonal center.

That second Gmaj doesn't sound like a structurally important chord,
it's more like a passing chord. Just pointing out.

> Except since we're in mavila, the Bb becomes a B. That is, you can
> think of Gmaj as V, and the Bb/F as IV/IV. In meantone, when V moves
> to IV/IV, the root goes up by 6/5. In mavila, instead, it goes by 5/4.
> So the roots in the mavila version are C - G - A - G - B - F - C,
> where B-F is still 3/2.
>
> I also play this comma pump in mavila that's like Cmaj - Emaj - Bmaj -
> Fmaj, again where B-F is 3/2. So it's like a mavila I III VII IV.
>
> My question is, now that I've explained the progression, would you say
> that the mavila one sounds "modal" and the meantone one sounds
> "tonal?" Or that they both sound modal, or that they both sound tonal?
> To my ears, they both sound tonal, with this one colorful IV/IV thrown
> in there.

They both sound more modal than tonal to me but I hear that IV/IV as
sticking out so maybe there is some sense of chords belonging or not
belonging to a key.

Kalle

🔗Mike Battaglia <battaglia01@...>

On Wed, Jul 6, 2011 at 10:44 AM, Kalle Aho <kalleaho@...> wrote:
>
> > Alright, after listening to this with a clear head, the second one is
> > strongest to me.
>
> To me there is something unsatisfactory in the second one, I hear the
> first one as the strongest.

They're both great to me. The first one is more chilled out, the
second is more sinister. They differ in modality.

> > The last one sounds cool, and I like it, but I do
> > understand what you mean in that the sharpening of the one tone and
> > flattening of the other tone means the interval between them is closer
> > to a fifth - not a tritone.
>
> I don't know where I said this but OK. :)

It was a poorly worded sentence - I just meant that the last one
doesn't evoke some kind of dissonance between the intervals that are
moving. But now that I'm listening to it again, I actually like it, it
sounds really exotic.

> > 1) It means that the ti-do resolution now becomes the "rare" interval
> > in the scale, except the rare interval is the large step or 208 cents.
> > 2) Since the leading tone is 208 cents, it also now means that the
> > leading tone is moving by a much more consonant sounding interval than
> > before.
>
> Are you saying that a melodic (i.e. tones are successive, not
> simultaneous) interval can sound consonant/dissonant? That might
> happen in arpeggiated chords but what about melodic movements by
> step? I don't feel that there is anything consonant or dissonant
> about them.

Yes, I am saying that. Sooner or later I'm confident people will admit
it as well. When you arpeggiate C-E-G, it's more consonant than if you
arpeggiate C-Eb-Gb. When you arpeggiate Bb-C-D-F, it's more consonant
than if you arpeggiate Bb-B-D-F. When you arpeggiate Bb-C-D, it's more
consonant than if you arpeggiate Bb-B-C. And even if we're talking
about just two notes, if you arpeggiate Bb-C, it's more consonant than
if you arpeggiate Bb-B.

> > I think that while these pieces work out nicely, the flattening of the
> > leading tone doesn't make the resolutions sound any stronger; rather I
> > think it makes them sound weaker. I think that, despite the fact that
> > the leading tone ends up become the "rare" interval, this rare
> > interval doesn't signal the tonic, and that if I went back to each one
> > of these pieces and systematically changed the flattened leading tones
> > to sharpened ones, the resolutions would sound stronger (this would be
> > hell to do). What are your thoughts?
>
> Maybe. The pieces sound fine as they are now though.

It also sounds fine if you replace every V-i resolution in a piece of
classical music with v-i. It'll sound different, but it won't sound
un-fine, especially if you listen to it a hundred times and get used
to it.

> Could you make
> some simple example where the effects of flattening and sharpening
> are compared, perhaps a phrase from one of the example pieces?

I've been meaning to do this for a while, but have no time right now,
sorry. I'll try messing with Fur Elise when I get the chance.

> > I should add that #3 could be changed somewhat by putting it in
> > 16-equal, where the diminished fifth would now be 750 cents, and the
> > augmented fourth would now be 450 cents.
>
> It bothers me that none of the optimal tuning methods we have
> considers the tuning of the dissonances, they just let them land
> where they may. For example, in TOP Mavila the characteristic
> dissonance is closer to 2:3 than the Mavila fifth and that's just
> wrong!

Yeah. Got to go by ear, I guess. I think 25-equal might be melodically
ideal for Mavila in a certain sense.

> > It hints at 17-limit harmony in the way I'm describing above.
>
> The Pajara temperament itself is moderately xenharmonic because it
> doesn't temper out 35:36 or 80:81 and while Pajara[10] is in a sense
> a better tuned version of something already found in 12-equal,
> 12-equal doesn't contain the characteristic dissonances found in
> 22-equal and 2D Pajara although we may disagree about their
> importance.

The characteristic dissonance in the version you posted was 532 cents,
which as a mavila and 9-ET junkie is alright with me.

What I'm saying is that my brain has snapped instantly into
mavila-tonality mode, and it hasn't yet for Pajara-tonality mode. Why?

> BTW, I'm not really a xenharmonic thrills junkie like you because
> that lifestyle will ultimately disappoint. You are just going to seek
> weirder and weirder comma pumps and become a recluse because your
> dopaminergic xenharmonicity neurons will only fire when you hear
> something that respectful people can't even comprehend or stomach!

That sounds like me now...

> > It's an interval of nearly maximal harmonic entropy, which is
> > obliquely related in that it means it's an interval that is maximally
> > inharmonic. I think it's the global maximum, right? Not that I think
> > that HE is precisely accurate enough to really model this over
> > anyone's own hearing, but I'm just pointing that out.
>
> You keep on talking as if this idea of melodic intervals sounding
> dissonant or consonant was common music theory parlance. And it is
> not clear to me by what mechanism this would aid in establishing
> tonality.

Arpeggiated chords can be consonant or dissonant, and arpeggiated
dyads can be consonant or dissonant too, just like chords and dyads
themselves can be when the notes are played simultaneously. But I'm
basically throwing ideas out, because for me, Mavila works and Pajara
doesn't. This is an extrapolation of the George Secor 17-equal optimal
leading tone thing. But I've since changed my mind about a few things
since I've written this.

I have a question for you: why do you think that all of this stuff
with rare interval sizes and characteristic dissonances matters? In my
experience, my brain, for your example, has smashed the characteristic
dissonance into the "perfect fourth" category. Clearly the dissonance
of 533 cents alone is not enough to signal my brain to the fact that
this is some kind of hot potato "avoid" interval that needs to
disappear after it's played. The notion that I will be able to learn
to hear it that way after "just a little more training" is
unfalsifiable. What do I do to learn to hear Pajara tonality? Do you
really hear some kind of radical switch when the decatonic scale is
played?

In fact, I'll post an experiment up sometime when I have a second to
think: where a piece of music gets dynamically retuned from 12-equal
to 17-equal to 22-equal to 27-equal all the way up to 42-equal and
then 5-equal, with the fifth getting wider each time and L:s
increasing in the diatonic scale. When you get to 5-equal, you can
still hear 0-480-720 as a really stretched major chord and 0-240-720
as a minor chord after that epic buildup. At the 5-equal point, the
fact that s now equals 0 leads to some distortions of perception, but
not as much before that, even when the difference between a major
third and a perfect fourth is like 28 cents. So consonance and
dissonance doesn't act like a signal for anything to my brain.

Perhaps some kind of initial exposure to consonance and dissonance
would do the trick to "burn" the categorical perception into my brain,
and then I'll be able to recognize the pattern in subsequent
exposures. Perhaps a different tuning for Pajara would make it sound
different, something like 22-equal or even 32 perhaps.

> > You honestly don't think that it just had a different musical feeling,
> > the same one that caused them to sharpen it even when they started
> > using harmony?
>
> Of course it had a different musical feeling but just having a
> different musical feeling is not sufficient reason to sharpen
> consistently. Just having a different musical feeling would imply
> sometimes sharpening and sometimes not, just for variety's sake,
> don't you think?

Which is exactly what people have since started doing, to add variety.
I reference you to noted music theorists Earth Wind and Fire, with the
use of the minor v chord:

http://www.youtube.com/watch?v=_XOY7lsBVpo

And "Louie Louie"

http://www.youtube.com/watch?v=7Vae_AkLb4Q

etc. They could have also used Dorian and Phrygian and such, but
didn't. Or they could have stuck with Aeolian and used bVII7, as
Celtic folk music does, all of which to add variety. Why not? That
wasn't the feeling that was in style at the time.

> > OK, I can see that. I guess I just am not convinced of the possibility
> > of using 550 cents as a substitute for 600 cents, that's all. Although
> > 7/5 "fuses" better than 11/8, there is a sense in which the former is
> > more dissonant, and this is what makes it suitable for resolutions to
> > my ears. I don't know what that sense is. It could be the fact that
> > 11/8, if played with the root doubled down a few bass notes, becomes
> > something like 2:4:8:11, which is pretty simple, whereas 7/5 becomes
> > 5:10:20:28, which is less. So perhaps tonalness has to do with it.
> > Honestly, no matter how much I listen to Pajara, I can't get into the
> > sound of 11/8 as a characteristic dissonance, nor can I get into the
> > sound of 8/7 as a leading tone. I've been trying for years.
>
> I'm using TOP Pajara in my example and the characteristic dissonance
> is 532.833 cents which is more like 11:15 than 8:11. Also the rare
> interval in Pajara is not the ~7:8. It's an ~9:10.

Sorry, I meant 10/9 for the rare interval. But I thought this was
22-equal - maybe the fact that the dissonance is only 533 cents has
something to do with it.

> > OK. Perhaps that's been the cause of some confusion, because to me the
> > dominant means the v or V chord, and subdominant means the iv or IV
> > chord.
>
> What about theorists who regard both IV and ii as subdominant
> (or predominant) and both V and vii as dominant? That's pretty common
> in German music theory.

OK, we can call it that too. I just want to make sure we're talking
about the same thing.

> > If 650 cents is supposed to be more dissonant than 600 cents,
> > shouldn't it work even better? But that's not the case. And why does
> > it seem to be universally accepted that 17-equal has better melodic
> > properties than 12-equal, a better leading tone, etc? What I'm saying
> > is, if it was really 100% about learning, why this consistent response
> > towards 17-equal? There does seem to be some kind of way to make
> > things resolve "even more," and that approach isn't met by changing
> > 600 cents to 650 cents in 22-equal, but it is when you move to
> > 17-equal which has a tritone of 635 cents and a leading tone of 60
> > cents. Why...? I seriously don't know.
>
> I hear 1/1 5/4 3/2 9/5 as more dissonant but it sounds very different
> from a typical meantone V-I so that might influence our judgment.
> Maybe it's just not convincing as a meantone-like V-I, whatever
> merits it has outside that context.

And I think that the thing about it that sounds different is that it
doesn't resolve as well.

> > > I hear a tonal center. Does that suffice? I don't know. It also sounds
> > > modal in the sense of not being in traditional major or minor.
> >
> > It does suffice, yes.
>
> Why are you so sure? Modal music is tonal in the sense of having a
> tonal center but 'tonal' probably should mean something more than
> just having a tonal center.

I was taught that tonality is when you perceive the pitches in a piece
of music as being organized around one central, main pitch, which is
the "key." That's what it means to me. Other than that, people seem to
use the word to denote a piece of music that has that feature, but
that lacks the "variety" that you mentioned above and sticks only to
the common practice's harmonic vocabulary. I doubt the use of IV/IV
destroyed the perception of the piece having a tonal center for you,
and I'm sure that no matter how far out I went with this piece, it
would still sound to you like C was the key the song is in. But the
use of IV/IV is a departure from the common practice norm.

It is.

> > My question is, now that I've explained the progression, would you say
> > that the mavila one sounds "modal" and the meantone one sounds
> > "tonal?" Or that they both sound modal, or that they both sound tonal?
> > To my ears, they both sound tonal, with this one colorful IV/IV thrown
> > in there.
>
> They both sound more modal than tonal to me but I hear that IV/IV as
> sticking out so maybe there is some sense of chords belonging or not
> belonging to a key.

OK. Well, I don't hear it that way. I hear the IV/IV as a temporary
modulation in the same way that I hear meantone Cm -> Bbmaj -> Abmaj
-> Gmaj -> Cmaj as containing a modulation when the Bb in the Bbmaj is
supplanted by the B natural in the Gmaj. It doesn't destroy the
perception that C is a tonal center in any event.

-Mike

🔗lobawad <lobawad@...>

🔗Kalle Aho <kalleaho@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Wed, Jul 6, 2011 at 10:44 AM, Kalle Aho <kalleaho@...> wrote:
> >
> > > Alright, after listening to this with a clear head, the second one is
> > > strongest to me.
> >
> > To me there is something unsatisfactory in the second one, I hear the
> > first one as the strongest.
>
> They're both great to me. The first one is more chilled out, the
> second is more sinister. They differ in modality.

Differ in modality? What does that mean?

> > > The last one sounds cool, and I like it, but I do
> > > understand what you mean in that the sharpening of the one tone and
> > > flattening of the other tone means the interval between them is closer
> > > to a fifth - not a tritone.
> >
> > I don't know where I said this but OK. :)
>
> It was a poorly worded sentence - I just meant that the last one
> doesn't evoke some kind of dissonance between the intervals that are
> moving. But now that I'm listening to it again, I actually like it, it
> sounds really exotic.

The interval between the pitches that are moving is an ~9:14 and it
moves into an ~3:5.

> > Are you saying that a melodic (i.e. tones are successive, not
> > simultaneous) interval can sound consonant/dissonant? That might
> > happen in arpeggiated chords but what about melodic movements by
> > step? I don't feel that there is anything consonant or dissonant
> > about them.
>
> Yes, I am saying that. Sooner or later I'm confident people will admit
> it as well. When you arpeggiate C-E-G, it's more consonant than if you
> arpeggiate C-Eb-Gb. When you arpeggiate Bb-C-D-F, it's more consonant
> than if you arpeggiate Bb-B-D-F. When you arpeggiate Bb-C-D, it's more
> consonant than if you arpeggiate Bb-B-C. And even if we're talking
> about just two notes, if you arpeggiate Bb-C, it's more consonant than
> if you arpeggiate Bb-B.

Yes, if you arpeggiate. That's what I said. But think about a tritone
expanding into a minor sixth in contrary semitonal motion: do you hear
the semitonal motions as somehow dissonant? That makes no sense to
me.

> > The Pajara temperament itself is moderately xenharmonic because it
> > doesn't temper out 35:36 or 80:81 and while Pajara[10] is in a sense
> > a better tuned version of something already found in 12-equal,
> > 12-equal doesn't contain the characteristic dissonances found in
> > 22-equal and 2D Pajara although we may disagree about their
> > importance.
>
> The characteristic dissonance in the version you posted was 532 cents,
> which as a mavila and 9-ET junkie is alright with me.

Are you saying that when playing in decatonics your brain categorizes
it into the same interval class as the intended ~3:4s? Even if all the
intended ~3:4s are much better tuned?

> What I'm saying is that my brain has snapped instantly into
> mavila-tonality mode, and it hasn't yet for Pajara-tonality mode. Why?

Given what you said about tonality (pitches organized around a
central pitch), do you mean that you don't hear the decatonics as
tonal or what?

> I have a question for you: why do you think that all of this stuff
> with rare interval sizes and characteristic dissonances matters? In my
> experience, my brain, for your example, has smashed the characteristic
> dissonance into the "perfect fourth" category. Clearly the dissonance
> of 533 cents alone is not enough to signal my brain to the fact that
> this is some kind of hot potato "avoid" interval that needs to
> disappear after it's played. The notion that I will be able to learn
> to hear it that way after "just a little more training" is
> unfalsifiable. What do I do to learn to hear Pajara tonality? Do you
> really hear some kind of radical switch when the decatonic scale is
> played?

It matters because to me both the diatonic scale and the decatonics
seem to work exactly as Paul explains. There probably are ways to
tonicize any mode of the scale but when the characteristic
dissonance is played Paul's intended resolutions of it really sound
like the most satisfying ones. That's really all there is to it.
I don't understand why you expect "some kind of radical switch".

> > > You honestly don't think that it just had a different musical feeling,
> > > the same one that caused them to sharpen it even when they started
> > > using harmony?
> >
> > Of course it had a different musical feeling but just having a
> > different musical feeling is not sufficient reason to sharpen
> > consistently. Just having a different musical feeling would imply
> > sometimes sharpening and sometimes not, just for variety's sake,
> > don't you think?
>
> Which is exactly what people have since started doing, to add variety.
> I reference you to noted music theorists Earth Wind and Fire, with the
> use of the minor v chord:
>
> http://www.youtube.com/watch?v=_XOY7lsBVpo
>
> And "Louie Louie"
>
> http://www.youtube.com/watch?v=7Vae_AkLb4Q
>
> etc. They could have also used Dorian and Phrygian and such, but
> didn't. Or they could have stuck with Aeolian and used bVII7, as
> Celtic folk music does, all of which to add variety. Why not? That
> wasn't the feeling that was in style at the time.

That's your explanation for the consistent sharpening in cadences in
Musica Ficta? OK, but then you are now basically saying that the
properties of the leading tone had nothing to do with it. You are
saying that in Musica Ficta the practice was just the fashion of the
time while in common practice tonality the leading tone suddenly has
magical properties that make V-i the preferred cadence in minor
tonality.

> > > OK, I can see that. I guess I just am not convinced of the possibility
> > > of using 550 cents as a substitute for 600 cents, that's all. Although
> > > 7/5 "fuses" better than 11/8, there is a sense in which the former is
> > > more dissonant, and this is what makes it suitable for resolutions to
> > > my ears. I don't know what that sense is. It could be the fact that
> > > 11/8, if played with the root doubled down a few bass notes, becomes
> > > something like 2:4:8:11, which is pretty simple, whereas 7/5 becomes
> > > 5:10:20:28, which is less. So perhaps tonalness has to do with it.
> > > Honestly, no matter how much I listen to Pajara, I can't get into the
> > > sound of 11/8 as a characteristic dissonance, nor can I get into the
> > > sound of 8/7 as a leading tone. I've been trying for years.
> >
> > I'm using TOP Pajara in my example and the characteristic dissonance
> > is 532.833 cents which is more like 11:15 than 8:11. Also the rare
> > interval in Pajara is not the ~7:8. It's an ~9:10.
>
> Sorry, I meant 10/9 for the rare interval. But I thought this was
> 22-equal - maybe the fact that the dissonance is only 533 cents has
> something to do with it.

Something to do with what?

> > > My question is, now that I've explained the progression, would you say
> > > that the mavila one sounds "modal" and the meantone one sounds
> > > "tonal?" Or that they both sound modal, or that they both sound tonal?
> > > To my ears, they both sound tonal, with this one colorful IV/IV thrown
> > > in there.
> >
> > They both sound more modal than tonal to me but I hear that IV/IV as
> > sticking out so maybe there is some sense of chords belonging or not
> > belonging to a key.
>
> OK. Well, I don't hear it that way. I hear the IV/IV as a temporary
> modulation in the same way that I hear meantone Cm -> Bbmaj -> Abmaj
> -> Gmaj -> Cmaj as containing a modulation when the Bb in the Bbmaj is
> supplanted by the B natural in the Gmaj. It doesn't destroy the
> perception that C is a tonal center in any event.

So what? If I hear the IV/IV as sticking out (perhaps as a temporary
modulation like yourself), that doesn't mean that it destroys the
perception of the tonal center.

Kalle

🔗Mike Battaglia <battaglia01@...>

On Fri, Jul 8, 2011 at 5:59 PM, Kalle Aho <kalleaho@...> wrote:
> >
> > They're both great to me. The first one is more chilled out, the
> > second is more sinister. They differ in modality.
>
> Differ in modality? What does that mean?

They just sound different. In meantone parlance, the first one sounds
like G phrygian to C dorian, the second one sounds like G phrygian
dominant to C dorian. In terms of Pajara MODMOS's I'm not sure what
the equivalent would be. They sound fine, they just both sound
different.

> > It was a poorly worded sentence - I just meant that the last one
> > doesn't evoke some kind of dissonance between the intervals that are
> > moving. But now that I'm listening to it again, I actually like it, it
> > sounds really exotic.
>
> The interval between the pitches that are moving is an ~9:14 and it
> moves into an ~3:5.

Is it really 14/9? It sounds like it's going E-B -> Eb-C, to me I hear
a 3/2 between those notes.

> > Yes, I am saying that. Sooner or later I'm confident people will admit
> > it as well. When you arpeggiate C-E-G, it's more consonant than if you
> > arpeggiate C-Eb-Gb. When you arpeggiate Bb-C-D-F, it's more consonant
> > than if you arpeggiate Bb-B-D-F. When you arpeggiate Bb-C-D, it's more
> > consonant than if you arpeggiate Bb-B-C. And even if we're talking
> > about just two notes, if you arpeggiate Bb-C, it's more consonant than
> > if you arpeggiate Bb-B.
>
> Yes, if you arpeggiate. That's what I said.

You also said that it doesn't apply to melodic intervals. Arpeggiated
dyads are melodic intervals. Are you changing your opinion now?

> But think about a tritone
> expanding into a minor sixth in contrary semitonal motion: do you hear
> the semitonal motions as somehow dissonant? That makes no sense to
> me.

I hear them as suggesting "new notes" that are separate from the last
one. It's not so much that they are directly dissonant, it's that they
signal your brain into that the note after the leading tone is not a
part of the previous arpeggiated chord. C-C#-D doesn't sound like it's
arpeggiating a chord, C-D-E does. Even dyadically, C-C# doesn't sound
like it's arpeggiating anything in particular, C-D does.

I think that the dissonance of the semitone causes us to hear motion
by that interval as emphatically NOT being part of an arpeggiated
chord, which is why it's so useful for a "leading" tone or a
resolution, and why I don't think that scales that have all half steps
with whole steps as the rare intervals will work as well, and also why
I think it works better in 17-equal than 19-equal. For example, I
think it's like this - imagine you play a major scale:

C (ok!)
D (how nice, a major second)
E (we're arpeggiating a consonant C-D-E structure)
F (BREAK. The E-F semitone means it doesn't sound like we're
arpeggiating anything anymore. Now we're temporarily at a "new tonic,"
which is F)
G (how nice, a major second over F)
A (we're arpeggiating F-G-A)
B (now we have this duality where you're arpeggiating F-G-A, or maybe
G-A-B, or perhaps the whole F-G-A-B, sort of ambiguous and wondering,
sounds kind of "floaty")
C (BREAK. The B-C semitone doesn't sound like we're arpeggiating
anything anymore. Now we're temporarily at a "new tonic" again, which
is the same as that tonic I remember from before! high five bro)

That's how I think it works, and that's how I hear the major scale. I
don't hear the large steps in Pajara as signifying a similar "break" -
I actually hear breaks for all of the small steps, and the large step
is the only time I can get away from that! But I do hear sporadic and
manageable breaks in Father[8] and Keemun[7], which serves to fracture
the scale into different temporary tonics, and I like those a lot.

> > The characteristic dissonance in the version you posted was 532 cents,
> > which as a mavila and 9-ET junkie is alright with me.
>
> Are you saying that when playing in decatonics your brain categorizes
> it into the same interval class as the intended ~3:4s? Even if all the
> intended ~3:4s are much better tuned?

That's how I heard it, like it was a well temperament or something. I
also doubt my brain has built in categories for ratios at all.

> > What I'm saying is that my brain has snapped instantly into
> > mavila-tonality mode, and it hasn't yet for Pajara-tonality mode. Why?
>
> Given what you said about tonality (pitches organized around a
> central pitch), do you mean that you don't hear the decatonics as
> tonal or what?

I meant that I don't hear the large step as signaling a new tonic,
which seems to be fundamental to the idea of Pajara tonality,
analogously to how the small step works for meantone, right?

> > I have a question for you: why do you think that all of this stuff
> > with rare interval sizes and characteristic dissonances matters? In my
> > experience, my brain, for your example, has smashed the characteristic
> > dissonance into the "perfect fourth" category. Clearly the dissonance
> > of 533 cents alone is not enough to signal my brain to the fact that
> > this is some kind of hot potato "avoid" interval that needs to
> > disappear after it's played. The notion that I will be able to learn
> > to hear it that way after "just a little more training" is
> > unfalsifiable. What do I do to learn to hear Pajara tonality? Do you
> > really hear some kind of radical switch when the decatonic scale is
> > played?
>
> It matters because to me both the diatonic scale and the decatonics
> seem to work exactly as Paul explains. There probably are ways to
> tonicize any mode of the scale but when the characteristic
> dissonance is played Paul's intended resolutions of it really sound
> like the most satisfying ones. That's really all there is to it.

If that's how you hear it then I'm not going to argue with you. This
so far doesn't apply to me. Sometime I'll have to mess around it with
different tunings of Pajara and see if there's some magic one where
the characteristic dissonance is most dissonant and it all makes
sense. Once I get it to make sense for the first time, I'm sure it'll
continue to make sense in every other tuning for Pajara.

> I don't understand why you expect "some kind of radical switch".

It sounds like I'm supposed to have my brain switch into some
alternate bizarro-universe where 10/9 signals new tonics and the small
steps in the scale don't sound like a sea of chromaticism.

> > Which is exactly what people have since started doing, to add variety.
> > I reference you to noted music theorists Earth Wind and Fire, with the
> > use of the minor v chord:
> >
> > http://www.youtube.com/watch?v=_XOY7lsBVpo
> >
> > And "Louie Louie"
> >
> > http://www.youtube.com/watch?v=7Vae_AkLb4Q
> >
> > etc. They could have also used Dorian and Phrygian and such, but
> > didn't. Or they could have stuck with Aeolian and used bVII7, as
> > Celtic folk music does, all of which to add variety. Why not? That
> > wasn't the feeling that was in style at the time.
>
> That's your explanation for the consistent sharpening in cadences in
> Musica Ficta? OK, but then you are now basically saying that the
> properties of the leading tone had nothing to do with it. You are
> saying that in Musica Ficta the practice was just the fashion of the
> time while in common practice tonality the leading tone suddenly has
> magical properties that make V-i the preferred cadence in minor
> tonality.

No, I'm not saying that. I'm saying that there's more than one way to
skin a cat, and that's the way they went. Part of it is the leading
tone thing, and part of it is that it made minor sound much darker and
more intense overall, and they liked both of them. But when people
talk about the sharpening of the 7th as though it only has a melodic
effect, and not a huge and intense harmonic effect, I have to point
this out.

> > Sorry, I meant 10/9 for the rare interval. But I thought this was
> > 22-equal - maybe the fact that the dissonance is only 533 cents has
> > something to do with it.
>
> Something to do with what?

With why the characteristic dissonance sounds like a slightly sharp
fourth that doesn't bother me or make me want to get rid of it.

> > OK. Well, I don't hear it that way. I hear the IV/IV as a temporary
> > modulation in the same way that I hear meantone Cm -> Bbmaj -> Abmaj
> > -> Gmaj -> Cmaj as containing a modulation when the Bb in the Bbmaj is
> > supplanted by the B natural in the Gmaj. It doesn't destroy the
> > perception that C is a tonal center in any event.
>
> So what? If I hear the IV/IV as sticking out (perhaps as a temporary
> modulation like yourself), that doesn't mean that it destroys the
> perception of the tonal center.

OK, so if the whole piece has a clear tonal center... what else do we
want? It's tonal!

-Mike

🔗Kalle Aho <kalleaho@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> Is it really 14/9? It sounds like it's going E-B -> Eb-C, to me I hear
> a 3/2 between those notes.

You know what Mr. Goldenears, I made a mistake and the interval is a
sharp fifth of about 730 cents! The lower voice moves by a step of 41
cents and the upper voice by 107 cents.

> > > Yes, I am saying that. Sooner or later I'm confident people will admit
> > > it as well. When you arpeggiate C-E-G, it's more consonant than if you
> > > arpeggiate C-Eb-Gb. When you arpeggiate Bb-C-D-F, it's more consonant
> > > than if you arpeggiate Bb-B-D-F. When you arpeggiate Bb-C-D, it's more
> > > consonant than if you arpeggiate Bb-B-C. And even if we're talking
> > > about just two notes, if you arpeggiate Bb-C, it's more consonant than
> > > if you arpeggiate Bb-B.
> >
> > Yes, if you arpeggiate. That's what I said.
>
> You also said that it doesn't apply to melodic intervals. Arpeggiated
> dyads are melodic intervals. Are you changing your opinion now?

I said "steps".

> > But think about a tritone
> > expanding into a minor sixth in contrary semitonal motion: do you hear
> > the semitonal motions as somehow dissonant? That makes no sense to
> > me.
>
> I hear them as suggesting "new notes" that are separate from the last
> one. It's not so much that they are directly dissonant, it's that they
> signal your brain into that the note after the leading tone is not a
> part of the previous arpeggiated chord. C-C#-D doesn't sound like it's
> arpeggiating a chord, C-D-E does. Even dyadically, C-C# doesn't sound
> like it's arpeggiating anything in particular, C-D does.
>
> I think that the dissonance of the semitone causes us to hear motion
> by that interval as emphatically NOT being part of an arpeggiated
> chord,

What if you arpeggiate a maj7 chord voiced so that there is a
semitone?

> which is why it's so useful for a "leading" tone or a
> resolution, and why I don't think that scales that have all half steps
> with whole steps as the rare intervals will work as well, and also why
> I think it works better in 17-equal than 19-equal. For example, I
> think it's like this - imagine you play a major scale:
>
> C (ok!)
> D (how nice, a major second)
> E (we're arpeggiating a consonant C-D-E structure)
> F (BREAK. The E-F semitone means it doesn't sound like we're
> arpeggiating anything anymore. Now we're temporarily at a "new tonic,"
> which is F)
> G (how nice, a major second over F)
> A (we're arpeggiating F-G-A)
> B (now we have this duality where you're arpeggiating F-G-A, or maybe
> G-A-B, or perhaps the whole F-G-A-B, sort of ambiguous and wondering,
> sounds kind of "floaty")
> C (BREAK. The B-C semitone doesn't sound like we're arpeggiating
> anything anymore. Now we're temporarily at a "new tonic" again, which
> is the same as that tonic I remember from before! high five bro)
>
> That's how I think it works, and that's how I hear the major scale. I
> don't hear the large steps in Pajara as signifying a similar "break" -
> I actually hear breaks for all of the small steps, and the large step
> is the only time I can get away from that! But I do hear sporadic and
> manageable breaks in Father[8] and Keemun[7], which serves to fracture
> the scale into different temporary tonics, and I like those a lot.

What if you play the major scale downwards: do B and E then sound like
temporary tonics?

> > > The characteristic dissonance in the version you posted was 532 cents,
> > > which as a mavila and 9-ET junkie is alright with me.
> >
> > Are you saying that when playing in decatonics your brain categorizes
> > it into the same interval class as the intended ~3:4s? Even if all the
> > intended ~3:4s are much better tuned?
>
> That's how I heard it, like it was a well temperament or something. I
> also doubt my brain has built in categories for ratios at all.

I don't intend to mean that it has. But if all the ~3:4s are tuned
the same, I think it should be possible to hear that 532 cents (or
the ~8:11 of 22-equal) as going to a different class. Also, I don't
know if this is important but purely scale-theoretically (as opposed
to subjective impressions) it is in the same *generic* interval class
as the tritones.

> > > What I'm saying is that my brain has snapped instantly into
> > > mavila-tonality mode, and it hasn't yet for Pajara-tonality mode. Why?
> >
> > Given what you said about tonality (pitches organized around a
> > central pitch), do you mean that you don't hear the decatonics as
> > tonal or what?
>
> I meant that I don't hear the large step as signaling a new tonic,
> which seems to be fundamental to the idea of Pajara tonality,
> analogously to how the small step works for meantone, right?

I don't know how much importance Paul gives to this feature and he
says the large steps act "as "signposts" if not necessarily leading
tones per se."

> > I don't understand why you expect "some kind of radical switch".
>
> It sounds like I'm supposed to have my brain switch into some
> alternate bizarro-universe where 10/9 signals new tonics and the small
> steps in the scale don't sound like a sea of chromaticism.

I'm pretty sure it is not intended to signal new tonics exactly the
same way as leading tones do because in the pentachordal major the
tonic is not adjacent to a large step.

> > > Sorry, I meant 10/9 for the rare interval. But I thought this was
> > > 22-equal - maybe the fact that the dissonance is only 533 cents has
> > > something to do with it.
> >
> > Something to do with what?
>
> With why the characteristic dissonance sounds like a slightly sharp
> fourth that doesn't bother me or make me want to get rid of it.

What if it is more clearly a different interval like in 22-equal?

> > > OK. Well, I don't hear it that way. I hear the IV/IV as a temporary
> > > modulation in the same way that I hear meantone Cm -> Bbmaj -> Abmaj
> > > -> Gmaj -> Cmaj as containing a modulation when the Bb in the Bbmaj is
> > > supplanted by the B natural in the Gmaj. It doesn't destroy the
> > > perception that C is a tonal center in any event.
> >
> > So what? If I hear the IV/IV as sticking out (perhaps as a temporary
> > modulation like yourself), that doesn't mean that it destroys the
> > perception of the tonal center.
>
> OK, so if the whole piece has a clear tonal center... what else do we
> want? It's tonal!

By your definition, yes. So?

Kalle

🔗Mike Battaglia <battaglia01@...>

On Sat, Jul 9, 2011 at 8:32 AM, Kalle Aho <kalleaho@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > Is it really 14/9? It sounds like it's going E-B -> Eb-C, to me I hear
> > a 3/2 between those notes.
>
> You know what Mr. Goldenears, I made a mistake and the interval is a
> sharp fifth of about 730 cents! The lower voice moves by a step of 41
> cents and the upper voice by 107 cents.

Aha, I knew it! Well I like the sound. It's a new color.

> > > > Yes, I am saying that. Sooner or later I'm confident people will admit
> > > > it as well. When you arpeggiate C-E-G, it's more consonant than if you
> > > > arpeggiate C-Eb-Gb. When you arpeggiate Bb-C-D-F, it's more consonant
> > > > than if you arpeggiate Bb-B-D-F. When you arpeggiate Bb-C-D, it's more
> > > > consonant than if you arpeggiate Bb-B-C. And even if we're talking
> > > > about just two notes, if you arpeggiate Bb-C, it's more consonant than
> > > > if you arpeggiate Bb-B.
> > >
> > > Yes, if you arpeggiate. That's what I said.
> >
> > You also said that it doesn't apply to melodic intervals. Arpeggiated
> > dyads are melodic intervals. Are you changing your opinion now?
>
> I said "steps".

Melodic steps are arpeggiated intervals. I'm saying that successive
melodic major seconds, like C-D-E, lends itself to an interpretation
where it's fleshing out C-D-E as a chord, and throwing a minor second
in there doesn't lend itself to that kind of interpretation.

> > I hear them as suggesting "new notes" that are separate from the last
> > one. It's not so much that they are directly dissonant, it's that they
> > signal your brain into that the note after the leading tone is not a
> > part of the previous arpeggiated chord. C-C#-D doesn't sound like it's
> > arpeggiating a chord, C-D-E does. Even dyadically, C-C# doesn't sound
> > like it's arpeggiating anything in particular, C-D does.
> >
> > I think that the dissonance of the semitone causes us to hear motion
> > by that interval as emphatically NOT being part of an arpeggiated
> > chord,
>
> What if you arpeggiate a maj7 chord voiced so that there is a
> semitone?

I'll need to explain my experience a little further before I can
answer that. It has to do with this other form of consonance that's
often mentioned, which is "musical consonance," which really means
musical context. I can only explain my experience so feel free to tell
me if your experience differs from mine.

There's always a "root" that I'm imagining in my head the whole time
while these notes are played. For any sequence of notes that you play,
as long as I can comfortably imagine the same root underneath the
whole thing, I can hear it as an arpeggiation. When you play a new
note that DOESN'T sound like it fits over the same root, you throw
some "noise" into this process, and my brain gives up and starts over
at a new root. It's like you've sent a TCP/IP RST flag or something.
You string a few of these RST's together and you now have a chord
progression. Too many RSTs all at once makes the line sound atonal.

So as for your major 7 example above: note that I said that I will
aggregate a note into an arpeggiated chord if it is "comfortable" to
imagine the same root over the whole thing. This "comfortableness" is
context dependent - if we're playing common practice music, and
suddenly there's a cadenza, and the guy arpeggiates a maj7 chord, I'm
note sure if I'll hear the minor second as an arpeggiation. It'll
probably sound something like

C (establish C root)
E (strengthen C root)
G (strengthen C root)
B (WTF THIS IS OUT OF PLACE, retroactively remember the last note and
reframe the root as G, with maybe E as a very slight secondary option)
C (the confusion doesn't last long, C is the root again)

On the other hand, if we're playing jazz, I'll probably hear it like

C (establish C root)
E (strengthen C root)
G (strengthen C root)
B (C still dominates, but also establish secondary weaker notion of G
root and perhaps E, how I love kaleidoscopic major 7 chords.)
C (still a C maj7 chord and life goes on)

I'm going to start a spinoff thread about what I think this means
cognitively and psychoacoustically.

> What if you play the major scale downwards: do B and E then sound like
> temporary tonics?

My brain constructs the chords from the bottom down:

C (ok, C!)
B (no tonic. you could play C B F# E G# Bb Z H & from here on out for
all my brain knows)
A (A-B is consonant, maybe the root is A)
G (no, wait! Now I get it, the root was G all along! G-A-B is really
consonant! Nice.)
F (wait, no, what? The root is F now. Or maybe slightly G? But mostly
F. Cue Lydian floaty land!)
E (RESET EVERYTHING. Lydian floaty land is done. focus on the note E)
D (D-E, is consonant, maybe the root is D)
C (C-D-E is consonant! Aha!)
B (RESET EVERYTHING, focus on B)

etc. That's how I hear it, anyway.

> > That's how I heard it, like it was a well temperament or something. I
> > also doubt my brain has built in categories for ratios at all.
>
> I don't intend to mean that it has. But if all the ~3:4s are tuned
> the same, I think it should be possible to hear that 532 cents (or
> the ~8:11 of 22-equal) as going to a different class. Also, I don't
> know if this is important but purely scale-theoretically (as opposed
> to subjective impressions) it is in the same *generic* interval class
> as the tritones.

I think it is possible, and I've heard that sort of thing happen with
other scales, like diminished[8], where the major third and perfect
fourth share a category. As a side note though, the generic interval
class flip flop doesn't seem to have anything to do with my perception
of the interval, because I play diminished[8] and the altered scale
(7th mode of melodic minor) over dominant 7 chords all the time. Maybe
in 22-equal the whole thing will make more sense.

> > > > Sorry, I meant 10/9 for the rare interval. But I thought this was
> > > > 22-equal - maybe the fact that the dissonance is only 533 cents has
> > > > something to do with it.
> > >
> > > Something to do with what?
> >
> > With why the characteristic dissonance sounds like a slightly sharp
> > fourth that doesn't bother me or make me want to get rid of it.
>
> What if it is more clearly a different interval like in 22-equal?

Well, if either of us ever gets time to make some examples nowadays,
we'll find out!

> > OK, so if the whole piece has a clear tonal center... what else do we
> > want? It's tonal!
>
> By your definition, yes. So?

Is that an unsatisfactory definition of a tonal piece of music? A
piece with a tonal center that is strong enough that you can leave it
and come back to it and feel like you're home again?

-Mike

🔗Mike Battaglia <battaglia01@...>

On Sun, Jul 10, 2011 at 4:16 AM, Mike Battaglia <battaglia01@...> wrote:
> On Sat, Jul 9, 2011 at 8:32 AM, Kalle Aho <kalleaho@...> wrote:
>
> There's always a "root" that I'm imagining in my head the whole time
> while these notes are played. For any sequence of notes that you play,
> as long as I can comfortably imagine the same root underneath the
> whole thing, I can hear it as an arpeggiation. When you play a new
> note that DOESN'T sound like it fits over the same root, you throw
> some "noise" into this process, and my brain gives up and starts over
> at a new root. It's like you've sent a TCP/IP RST flag or something.
> You string a few of these RST's together and you now have a chord
> progression. Too many RSTs all at once makes the line sound atonal.
//snip
> I'm going to start a spinoff thread about what I think this means
> cognitively and psychoacoustically.

I'm going to put the psychoacoustic explanation off for a bit because
I'm having trouble uploading this example to soundcloud. But here's
what I'm getting at: after playing music for all of our lives, we
build a sense of harmonic reasoning that enables us to imagine the
concordance of arpeggiated chords. This sense is learned (e.g. not
involuntary f0 estimation) and we continue to develop it as time goes
on, and when I have some time to get my psychoacoustic spinoff thread
together, I'll show some examples of how this can break down for
unfamiliar tuning systems.

We somehow manage to keep track of the notes that were previously
played, imagine a "root" underneath them, and sum them into the
sensation of there being a unified "background chord" when possible.
As a result, we have nice things like Alberti bass lines and two part
inventions that imply triadic harmony.

When some sneaky tone jumps in there that is so out of place that it
doesn't fit, we either ignore it (a "passing note") or stop this
process and start building a new root (a "leading tone"). As a result,
we have nice things like chromaticism and chord progressions.

Meantone is great, because not only is C-E-G concordant as 4:5:6, but
C-D-E is concordant as 8:9:10. There's concordant stuff all over the
place for melodies, and then there are some very sparse "breaks" that
fracture the scale into separate tonal centers. Pajara, on the other
hand, makes life extremely difficult for me, because most intervals in
the scale consist of breaks and I just hear "RST RST RST RST RST oh
hey! a large step! cool RST RST RST RST." If I'm not hearing RST RST
RST packets being pounded directly into my brain, then I'm instead
hearing "passing notes" everywhere as my brain futilely tries to pick
out any type of harmonic logic that it can and ignores the noise.
There is too much information being thrown around, and it does not
allow this integrative holistic mechanism any opportunity to work. The
same applies to augmented[9] in 12-equal. It does not apply to
Keemun[7], nor to Father[8], nor to Blackwood[10], nor to Mavila[7],
nor to Mavila[9]. That is what I am getting at. So far, 4 years of
training hasn't helped me find any better solution with Pajara,
despite that I know the scale like the back of my hand, can rip lines
out on it in 12-equal, hear "imprints" of Pajara harmony in 10-equal,
etc.

Tangentially, I started to like Pajara a lot in 12-equal when I
started experimenting with 16:17:18:20 cluster chords and tried to
train myself to hear the small step as a rooted harmonic interval (try
this!!), but that has more to do with 17-limit harmony than 7-limit
harmony. Once you get used to the sound of C major with a C# on top
(and some clever voicings to massage away the pain), the sound of A
minor with C# on top is like a whole new world.

-Mike

🔗Kalle Aho <kalleaho@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> > > > Yes, if you arpeggiate. That's what I said.
> > >
> > > You also said that it doesn't apply to melodic intervals. Arpeggiated
> > > dyads are melodic intervals. Are you changing your opinion now?
> >
> > I said "steps".
>
> Melodic steps are arpeggiated intervals.

Huh? There is a perceptual distinction between hearing an arpeggiated
chord and hearing a melodic line. Just think about some polyphonic
texture of multiple melodic lines moving mostly by seconds, the lines
can meet as vertical chords but do you really hear the melodic lines
themselves as arpeggios? Or in a texture consisting entirely of a
sequence of arpeggiated chords where you hear the tones segregating
into melodic streams, do you hear those melodic streams as arpeggios?
I don't.

> I'm saying that successive melodic major seconds, like C-D-E, lends
> itself to an interpretation where it's fleshing out C-D-E as a chord,
> and throwing a minor second in there doesn't lend itself to that kind
> of interpretation.

I'm willing to admit that such an interpretation is perceptually
possible (given add2 chords) but I doubt that it is some kind of
prerequisite for the intelligibility of the diatonic scale. For one
thing, in common practice harmony, D would be heard as a nonchord
tone against C. How could that happen if hearing D as rooted in C was
necessary for the diatonic scale's intelligibility?

> > > I think that the dissonance of the semitone causes us to hear motion
> > > by that interval as emphatically NOT being part of an arpeggiated
> > > chord,
> >
> > What if you arpeggiate a maj7 chord voiced so that there is a
> > semitone?
>
> I'll need to explain my experience a little further before I can
> answer that. It has to do with this other form of consonance that's
> often mentioned, which is "musical consonance," which really means
> musical context. I can only explain my experience so feel free to tell
> me if your experience differs from mine.
>
> There's always a "root" that I'm imagining in my head the whole time
> while these notes are played. For any sequence of notes that you play,
> as long as I can comfortably imagine the same root underneath the
> whole thing, I can hear it as an arpeggiation. When you play a new
> note that DOESN'T sound like it fits over the same root, you throw
> some "noise" into this process, and my brain gives up and starts over
> at a new root. It's like you've sent a TCP/IP RST flag or something.
> You string a few of these RST's together and you now have a chord
> progression. Too many RSTs all at once makes the line sound atonal.

I had to look that up, geek.

> So as for your major 7 example above: note that I said that I will
> aggregate a note into an arpeggiated chord if it is "comfortable" to
> imagine the same root over the whole thing. This "comfortableness" is
> context dependent - if we're playing common practice music, and
> suddenly there's a cadenza, and the guy arpeggiates a maj7 chord, I'm
> note sure if I'll hear the minor second as an arpeggiation. It'll
> probably sound something like
>
> C (establish C root)
> E (strengthen C root)
> G (strengthen C root)
> B (WTF THIS IS OUT OF PLACE, retroactively remember the last note and
> reframe the root as G, with maybe E as a very slight secondary option)
> C (the confusion doesn't last long, C is the root again)
>
> On the other hand, if we're playing jazz, I'll probably hear it like
>
> C (establish C root)
> E (strengthen C root)
> G (strengthen C root)
> B (C still dominates, but also establish secondary weaker notion of G
> root and perhaps E, how I love kaleidoscopic major 7 chords.)
> C (still a C maj7 chord and life goes on)

This doesn't really answer my question because at the point of
potential confusion, namely B, no semitones have been played yet!

> I'm going to start a spinoff thread about what I think this means
> cognitively and psychoacoustically.
>
> > What if you play the major scale downwards: do B and E then sound like
> > temporary tonics?
>
> My brain constructs the chords from the bottom down:
>
> C (ok, C!)
> B (no tonic. you could play C B F# E G# Bb Z H & from here on out for
> all my brain knows)
> A (A-B is consonant, maybe the root is A)
> G (no, wait! Now I get it, the root was G all along! G-A-B is really
> consonant! Nice.)
> F (wait, no, what? The root is F now. Or maybe slightly G? But mostly
> F. Cue Lydian floaty land!)
> E (RESET EVERYTHING. Lydian floaty land is done. focus on the note E)
> D (D-E, is consonant, maybe the root is D)
> C (C-D-E is consonant! Aha!)
> B (RESET EVERYTHING, focus on B)
>
> etc. That's how I hear it, anyway.

I don't see what the semitone and especially its' size has to do with
this. Can this type of analysis explain why minor pentatonic is one
of the preferred modes of the meantone pentatonic scale?

> > > > > Sorry, I meant 10/9 for the rare interval. But I thought this was
> > > > > 22-equal - maybe the fact that the dissonance is only 533 cents has
> > > > > something to do with it.
> > > >
> > > > Something to do with what?
> > >
> > > With why the characteristic dissonance sounds like a slightly sharp
> > > fourth that doesn't bother me or make me want to get rid of it.
> >
> > What if it is more clearly a different interval like in 22-equal?
>
> Well, if either of us ever gets time to make some examples nowadays,
> we'll find out!

But shouldn't you already know given your years of training with
Pajara/decatonics?

> > > OK, so if the whole piece has a clear tonal center... what else do we
> > > want? It's tonal!
> >
> > By your definition, yes. So?
>
> Is that an unsatisfactory definition of a tonal piece of music? A
> piece with a tonal center that is strong enough that you can leave it
> and come back to it and feel like you're home again?

I don't have any strong opinions about the meaning of the words
'tonal' and 'modal'. OK, it has that property, so?

Kalle

🔗Kalle Aho <kalleaho@...>

🔗Mike Battaglia <battaglia01@...>

🔗Kalle Aho <kalleaho@...>

🔗Mike Battaglia <battaglia01@...>

🔗Kalle Aho <kalleaho@...>

🔗Mike Battaglia <battaglia01@...>

On Sun, Jul 17, 2011 at 10:03 AM, Kalle Aho <kalleaho@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > Well, since we're talking about Paul's claims for Pajara, and I'm
> > telling you that the way I described it is how I hear it instead, I
> > hope there's more to it just than that "I'm different." I mean, I'm
> > probably not going to stop hearing it like that any time soon! And
> > besides, I like the way things sound now. It would be a drag to switch
> > it up and start hearing C-D-E like they didn't have anything to do
> > with each other.
>
> I ask again: then what's the problem?

The problem is that none of this is part of how the decatonic scales
are "supposed" to work, but that this is how I hear it.

> Because in the other branch of this thread you claimed that decatonics can't be decomposed into
> these harmonic segments and now it seems to me that you are saying
> the opposite.

First off, this is purely melodically. Harmonically, this scale leads
to a lot of great chord progressions, all of which I like and have
started using in my own playing in 12-equal a lot. I'm only talking
about my perception of the scale as it pertains to melody.

1) At first, I heard standard pentachordal major as being completely
atonal and chromatic. It sounded like every note in 12-equal except
for Eb and Ab, which made it sound about as atonal as the 12-equal
chromatic scale where I just avoid playing two of the notes for some
reason. The 22-equal version sounded more or less like the same thing
with better intonation and didn't "snap" my brain into any radically
new perception of it. This was early on.

2) I quickly discover that this scale leads to ridiculously awesome
chord progressions. This changes my perception of the scale, which I
now start hearing as a generally tonal scale with some "passing notes"
in it. The C# and F# in C pentachordal major sounded like passing
notes that weren't particularly related to anything, and the B as
well. If I take all of the passing notes out of it, I end up with
mixolydian. I now decide that Pajara in 22-equal is the least
xenharmonic scale of all time. This is where I was at up until about a
few weeks ago.

3) This discussion we're having inspires me to start exploring
12-equal as a 2.3.5.7.17.19 subgroup temperament. I discover that if I
play full harmonic series-ish chords and then cluster chords on top
like C-C#-D-D#-E, the cluster chord takes on an "otonal" and "rooted"
quality and sounds like 16:17:18:19:20. I discover that C-C#-D-E can
snap into the same perception. I "train" myself to "look" for this
perception, which gets easier with time. Now I start hearing the "C#"
in the C-C#-D-E beginning of pentachordal major as being weakly
related to the fundamental via this perception, kind of like how I
think common practice folks heard the "D" in C-D-E.

I have finally conquered the previous "confusion." I haven't played it
in 22-equal since this very dramatic perceptual shift and so I can't
comment on whether I hear 16/11 as a characteristic "dissonance" with
this perception. In fact, the entire scale now sort of sounds like one
huge arpeggiated otonal chord to me. This is sort of cool and
exploring this perception leads to some new possibilities in 12-equal,
like playing C# over C major, and then playing it again over A minor.
It doesn't sound as chaotic and noisy this way, but still requires
more effort to keep that C-C# in the right "frame."

4) I still don't hear the large steps in the scale as "signaling"
anything. And, all things considered, I don't like this scale as much
for melody as something like Semaphore[9], which is awesome, or
Mavila[9], which is fantastic, or Keemun[7] which I love, or
Father[8], etc. Especially Keemun[7], which just seemed to "snap into
place" immediately for me without much training at all. Pajara[10] and
the pentachordal MODMOS's on the other hand don't really sound as
immediately good. I have to work a bit harder and force my brain into
this new 17-limit "sound" to get it to really make sense.

As a final example, something like Augmented[9] sounds to my brain
like Pajara does - confusing, requires me to think more, etc. But
Triforce[9] just "works" instantly. So there's more to it just than
that all new microtonal scales require lengthy training periods.

The record has now been set straight.

> Also, the 17-limit interpretations of the decatonic intervals are
> explicitly mentioned in Paul's 22-tone paper.

Thanks for mentioning, I didn't remember that. But even so, my
approach to get past the initial confusion of this scale was to force
myself to get used to the 17-limit, which is a somewhat fragile
perception. How will I hear 16/11 and 11/8 as "characteristically
dissonant" if I'm forcing myself to swallow a 17-limit pill?

> > Let me ask you a question, Kalle - in your view, what works better for
> > melody: standard pentachordal major or Father[8]? If you think that
> > they're both "potentially equal" with enough training, which one do
> > you think would be more immediately comprehensible?
>
> Probably Father, at least at first because monophonically played it
> gives an impression of having diatonic sounding snippets. So?

How about 2 1 2 1 2 1 2 in 11-equal vs Pajara?

I think that the "diatonic sounding snippets" that you are referring
to are more than just "parts of a familiar whole." These "snippets"
are made up of features that the diatonic scale and the father[8] MOS
both happen to have. The LLs tetrachord that's present in both scales
isn't just a diatonic snippet, but a series of two consonant sounding
"whole tones" that make a "5/4" and then have a "leading tone" at the
end.

My brain hears that as "join join break!" And the periodic breaks
fracture the scale into different stable points of melodic repose, and
make it more efficient for melody to imply something like a root shift
or a chord progression. Of course, you're saying you don't hear C-D-E
that way, so I'm not sure what to make of that, but that sure is how
it works for me.

-Mike

V - i

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