[MMM] EDOs in "atonal" music (was: Non-Bach and the wide world of influences)

I'm not sure why we would use EDOs at all for music we want to call
"atonal". Someone -- Igs? Chris? -- said they think writing truly
atonal music is hard, and I can see why, especially with EDOs.

If you're going to step back from 3- and 5-limit harmony, as it seemed
Schoenberg wanted to do, why not step back from 2-limit while you're
at it? Use (say) 11 equal divisions of 1800 cents or something
instead. Each step is 163.63636 cents, and you don't line up
particularly well on any traditional 2, 3, or 5-limit consonance that
I can see. The notes will "show how little they are concerned"....

On 3/18/11, Aaron Krister Johnson <aaron@...> wrote:
> Hey Wad-lobber,
>
> I think now you are throwing up smokescreens, because the argument was done
> a while ago...it's all moot. I think I showed in a very clear and
> unambiguous way that Schoenberg didn't give a damn about traditional
> consonant and dissonant structures when he wrote 12 tone music, in fact, he
> favored dissonant structures. Directly in contrast to your claim that
> "emancipation of dissonance" wasn't about being as dissonant as possible.
> So, it's you vs. Schoenberg about how to understand Schoenberg. I gave you
> all the relevant quotes.
>
> I mean, I gave about 3 or 4 direct source quotes from the man himself. Now
> you are saying I was claiming and arguing things that I wasn't even talking
> about. I already agreed with you about the overtone series, but pointed out
> that it was moot. Now you're all over the map, dude. You're not arguing any
> one thing anymore, but having an argument with yourself, claiming I said
> things I didn't even say, or more to the point, didn't even care about for
> this whole conversation.
>
> I'm not even trying to discredit Schoenberg as you claim, either his
> writings or his theories, although the sense that Carl has that he's a bit
> of a hack when it comes to musical cognition and acoustics is probably not
> far from the truth.
>
> Here's what happened:
>
> 1) I claimed 11 or 13 edo would be a good way to do neo-Schoenbergian
> serialism. I mentioned "emancipation of the dissonance"
> 2) You said "emancipation of the dissonance" is not about "being as
> dissonant as possible"
> 3) I said it didn't matter since Schoenberg didn't worry about consonance
> and dissonance in the traditional sense, only about row structure and
> identity.
> 4) You then started claiming that I missed the point, and that it was about
> overtones. Which was and is completely moot.
> 5) I then gave you a series of direct quotes which backed up my points about
> Schoenberg's conception of serialism, including a quote which suggested that
> he did favor "being as dissonant as possible" by favoring dissonant
> harmonies in simultaneous tones.
> 6) You then again claimed I was missing the point, and that it was about
> overtones. Again, not listening to what I was saying, what Schoenberg
> himself was saying, or even what you were saying, and now having a
> completely orthogonal conversation.
> 7) Exasperated, I re-quoted Schoenberg.
> 8) Exasperated, you said it was about higher overtones.
> 9) Here we are, and you still haven't realized that Schoenberg didn't
> consider harmony when he wrote serial row music. And that he favored
> dissonances to show "that the voices didn't care" (direct quote), etc. You
> are still pointing out 13/8, 11/8, etc. Why?
>
> In short, I don't see what your point is. I was only trying to point out
> that 11-edo and 13-edo are perfect for abolishing, in the Schoenbergian
> sense, traditional associations. Period. And that idea still stands, and in
> essence, I don't see why you are huffing and puffing about anything, since
> you seem to agree with me about this basic point.
>
> You can chase your tail all you want talking about other moot things, but I
> will simply re-post all these points, which are *Schoenberg's own words*,
> until you see what I've (he has) been saying....
>
> Also, I stand corrected---you did mention "Probleme der Harmonie" in the
> first episode way back, before this thread really got going. :)
>
> I also said you were ignoring my direct Schoenberg quotes...you now say:
>
> "Not ignoring your quotes. Trying to explain to you the nature of what
> Schoenberg meant by dissonance."
>
> I'm baffled why you think I'd take your words over his own words, especially
> when they are in direct contradiction at times. I agree with you what he
> meant by dissonance---higher partials. But so what? How are they used? This
> is where you say it would be meaningless to consider a tuning that had no
> consonances. I'm showing you it wouldn't be meaningless, because Schoenberg
> didn't find the distinction between consonance and dissonance important to
> his process, and furthermore, he favored dissonance.
>
> Best,
> AKJ
>
>
> On Thu, Mar 17, 2011 at 11:00 PM, lobawad <lobawad@...> wrote:
>
>>
>>
>> --- In MakeMicroMusic@yahoogroups.com, Aaron Krister Johnson <aaron@...>
>> wrote:
>> >
>> > Lobawad,
>> >
>> > On Thu, Mar 17, 2011 at 10:54 AM, lobawad <lobawad@...> wrote:
>> >
>> > >
>> > > "Man kann nun sagen, und kann diesen Satz ziemlich weitgehend erproben
>> und
>> > > beweisen, dass alle musikalischen Geschehnisse sich auf die
>> Obertonreihe
>> > > zurueckfuehren lassen, so dass alles sich darstellt als Ausnuetzung
>> > > eifacherer un komplizierterer Verhaeltnisse dieser Reihe."
>> > >
>> > > Followed by a "13-limit JI" structure, you can make a JI diagram from
>> it.
>> > >
>> > > I already said where to find this stuff- Probleme der Harmonie, 1927.
>> > >
>> > >
>> > This is the first time in this thread you mentioned "Probleme der
>> Harmonie".
>>
>> No it is not.
>>
>> /makemicromusic/topicId_26794.html#26889
>>
>>
>>
>
>> > But more to the point--you are ignoring my quotes which are direct
>> >evidence
>> > that Schoenberg considered consciously used dissonance "to show how
>> >little
>> > the lines are worried".....
>> >
>> > And, I think you could have at least translated to English for
>> > >me...this
>> > passage doesn't really tell us anything. I never said Schoenberg >didn't
>> talk
>> > about the harmonic series. I said that his use of consonance and
>> >dissonance
>> > was such that the distinction between them was irrelevant, and in >fact,
>> as
>> > we are discovering, he actually favored dissonance. So we were both
>> > incomplete in our assessment....the naive view that he wanted to >make
>> things
>> > "as dissonant as possible" is actually, judging from his written >words
>> on
>> > the subject and also the type of textures he wrote, closest to the
>> >truth.
>>
>> Not ignoring your quotes. Trying to explain to you the nature of what
>> Schoenberg meant by dissonance.
>>
>> And he was correct in proposing that ratios from higher in the harmonic
>> series can be implemented as "central" ratios. The 11-edo piece I did uses
>> 9:7 as the simplest central ratio and seems to be pretty, pleasant and
>> downright catchy to "civilians".
>>
>> We were talking about tunings. Whether or not a tone row is comprehesible
>> as such is an interesting topic, but it is a tangent. You are trying to
>> use
>> this, which I don't think Schoenberg ever even claimed, as an argument to
>> discredit Schoenberg's theories. Bogus approach.
>>
>> The tuning ideas in question can be tested. I'm testing them, you're
>> really
>> just giving me Hallmark Greeting Card wisdom about "what people like".
>>
>>
>>
>>
>> ------------------------------------
>>
>> Yahoo! Groups Links
>>
>>
>>
>>
>
>
> --
> Aaron Krister Johnson
> http://www.akjmusic.com
> http://www.untwelve.org
>
>
> [Non-text portions of this message have been removed]
>
>

Sure, non-octave serial sets are possible, if that kind of sound is your
bag.

I think serialism is a valid general technique. Of course, the results vary
widely in quality depending on the choices made.

AKJ

On Fri, Mar 18, 2011 at 8:12 AM, Jake Freivald <jdfreivald@...> wrote:

> I'm not sure why we would use EDOs at all for music we want to call
> "atonal". Someone -- Igs? Chris? -- said they think writing truly
> atonal music is hard, and I can see why, especially with EDOs.
>
> If you're going to step back from 3- and 5-limit harmony, as it seemed
> Schoenberg wanted to do, why not step back from 2-limit while you're
> at it? Use (say) 11 equal divisions of 1800 cents or something
> instead. Each step is 163.63636 cents, and you don't line up
> particularly well on any traditional 2, 3, or 5-limit consonance that
> I can see. The notes will "show how little they are concerned"....
>
> On 3/18/11, Aaron Krister Johnson <aaron@...> wrote:
> > Hey Wad-lobber,
> >
> > I think now you are throwing up smokescreens, because the argument was
> done
> > a while ago...it's all moot. I think I showed in a very clear and
> > unambiguous way that Schoenberg didn't give a damn about traditional
> > consonant and dissonant structures when he wrote 12 tone music, in fact,
> he
> > favored dissonant structures. Directly in contrast to your claim that
> > "emancipation of dissonance" wasn't about being as dissonant as possible.
> > So, it's you vs. Schoenberg about how to understand Schoenberg. I gave
> you
> > all the relevant quotes.
> >
> > I mean, I gave about 3 or 4 direct source quotes from the man himself.
> Now
> > you are saying I was claiming and arguing things that I wasn't even
> talking
> > about. I already agreed with you about the overtone series, but pointed
> out
> > that it was moot. Now you're all over the map, dude. You're not arguing
> any
> > one thing anymore, but having an argument with yourself, claiming I said
> > things I didn't even say, or more to the point, didn't even care about
> for
> > this whole conversation.
> >
> > I'm not even trying to discredit Schoenberg as you claim, either his
> > writings or his theories, although the sense that Carl has that he's a
> bit
> > of a hack when it comes to musical cognition and acoustics is probably
> not
> > far from the truth.
> >
> > Here's what happened:
> >
> > 1) I claimed 11 or 13 edo would be a good way to do neo-Schoenbergian
> > serialism. I mentioned "emancipation of the dissonance"
> > 2) You said "emancipation of the dissonance" is not about "being as
> > dissonant as possible"
> > 3) I said it didn't matter since Schoenberg didn't worry about consonance
> > and dissonance in the traditional sense, only about row structure and
> > identity.
> > 4) You then started claiming that I missed the point, and that it was
> about
> > overtones. Which was and is completely moot.
> > 5) I then gave you a series of direct quotes which backed up my points
> about
> > Schoenberg's conception of serialism, including a quote which suggested
> that
> > he did favor "being as dissonant as possible" by favoring dissonant
> > harmonies in simultaneous tones.
> > 6) You then again claimed I was missing the point, and that it was about
> > overtones. Again, not listening to what I was saying, what Schoenberg
> > himself was saying, or even what you were saying, and now having a
> > completely orthogonal conversation.
> > 7) Exasperated, I re-quoted Schoenberg.
> > 8) Exasperated, you said it was about higher overtones.
> > 9) Here we are, and you still haven't realized that Schoenberg didn't
> > consider harmony when he wrote serial row music. And that he favored
> > dissonances to show "that the voices didn't care" (direct quote), etc.
> You
> > are still pointing out 13/8, 11/8, etc. Why?
> >
> > In short, I don't see what your point is. I was only trying to point out
> > that 11-edo and 13-edo are perfect for abolishing, in the Schoenbergian
> > sense, traditional associations. Period. And that idea still stands, and
> in
> > essence, I don't see why you are huffing and puffing about anything,
> since
> > you seem to agree with me about this basic point.
> >
> > You can chase your tail all you want talking about other moot things, but
> I
> > will simply re-post all these points, which are *Schoenberg's own words*,
> > until you see what I've (he has) been saying....
> >
> > Also, I stand corrected---you did mention "Probleme der Harmonie" in the
> > first episode way back, before this thread really got going. :)
> >
> > I also said you were ignoring my direct Schoenberg quotes...you now say:
> >
> > "Not ignoring your quotes. Trying to explain to you the nature of what
> > Schoenberg meant by dissonance."
> >
> > I'm baffled why you think I'd take your words over his own words,
> especially
> > when they are in direct contradiction at times. I agree with you what he
> > meant by dissonance---higher partials. But so what? How are they used?
> This
> > is where you say it would be meaningless to consider a tuning that had no
> > consonances. I'm showing you it wouldn't be meaningless, because
> Schoenberg
> > didn't find the distinction between consonance and dissonance important
> to
> > his process, and furthermore, he favored dissonance.
> >
> > Best,
> > AKJ
> >
> >
> > On Thu, Mar 17, 2011 at 11:00 PM, lobawad <lobawad@...> wrote:
> >
> >>
> >>
> >> --- In MakeMicroMusic@yahoogroups.com, Aaron Krister Johnson <aaron@
> ...>
> >> wrote:
> >> >
> >> > Lobawad,
> >> >
> >> > On Thu, Mar 17, 2011 at 10:54 AM, lobawad <lobawad@...> wrote:
> >> >
> >> > >
> >> > > "Man kann nun sagen, und kann diesen Satz ziemlich weitgehend
> erproben
> >> und
> >> > > beweisen, dass alle musikalischen Geschehnisse sich auf die
> >> Obertonreihe
> >> > > zurueckfuehren lassen, so dass alles sich darstellt als Ausnuetzung
> >> > > eifacherer un komplizierterer Verhaeltnisse dieser Reihe."
> >> > >
> >> > > Followed by a "13-limit JI" structure, you can make a JI diagram
> from
> >> it.
> >> > >
> >> > > I already said where to find this stuff- Probleme der Harmonie,
> 1927.
> >> > >
> >> > >
> >> > This is the first time in this thread you mentioned "Probleme der
> >> Harmonie".
> >>
> >> No it is not.
> >>
> >> /makemicromusic/topicId_26794.html#26889
> >>
> >>
> >>
> >
> >> > But more to the point--you are ignoring my quotes which are direct
> >> >evidence
> >> > that Schoenberg considered consciously used dissonance "to show how
> >> >little
> >> > the lines are worried".....
> >> >
> >> > And, I think you could have at least translated to English for
> >> > >me...this
> >> > passage doesn't really tell us anything. I never said Schoenberg
> >didn't
> >> talk
> >> > about the harmonic series. I said that his use of consonance and
> >> >dissonance
> >> > was such that the distinction between them was irrelevant, and in
> >fact,
> >> as
> >> > we are discovering, he actually favored dissonance. So we were both
> >> > incomplete in our assessment....the naive view that he wanted to >make
> >> things
> >> > "as dissonant as possible" is actually, judging from his written
> >words
> >> on
> >> > the subject and also the type of textures he wrote, closest to the
> >> >truth.
> >>
> >> Not ignoring your quotes. Trying to explain to you the nature of what
> >> Schoenberg meant by dissonance.
> >>
> >> And he was correct in proposing that ratios from higher in the harmonic
> >> series can be implemented as "central" ratios. The 11-edo piece I did
> uses
> >> 9:7 as the simplest central ratio and seems to be pretty, pleasant and
> >> downright catchy to "civilians".
> >>
> >> We were talking about tunings. Whether or not a tone row is
> comprehesible
> >> as such is an interesting topic, but it is a tangent. You are trying to
> >> use
> >> this, which I don't think Schoenberg ever even claimed, as an argument
> to
> >> discredit Schoenberg's theories. Bogus approach.
> >>
> >> The tuning ideas in question can be tested. I'm testing them, you're
> >> really
> >> just giving me Hallmark Greeting Card wisdom about "what people like".
> >>
> >>
> >>
> >>
> >> ------------------------------------
> >>
> >> Yahoo! Groups Links
> >>
> >>
> >>
> >>
> >
> >
> > --
> > Aaron Krister Johnson
> > http://www.akjmusic.com
> > http://www.untwelve.org
> >
> >
> > [Non-text portions of this message have been removed]
> >
> >
>
>
> ------------------------------------
>
> Yahoo! Groups Links
>
>
>
>

--
Aaron Krister Johnson
http://www.akjmusic.com
http://www.untwelve.org

[Non-text portions of this message have been removed]

--- In MakeMicroMusic@yahoogroups.com, Jake Freivald <jdfreivald@...> wrote:

> If you're going to step back from 3- and 5-limit harmony, as it seemed
> Schoenberg wanted to do, why not step back from 2-limit while you're
> at it? Use (say) 11 equal divisions of 1800 cents or something
> instead. Each step is 163.63636 cents, and you don't line up
> particularly well on any traditional 2, 3, or 5-limit consonance that
> I can see. The notes will "show how little they are concerned"....

Actually, that scale is just 3-out-of-22-EDO with the "octave wrap" removed, or in other words 22 equal divisions of 8/1. There are going to be lots and lots of 3, 5, and 7-limit consonances that pop up in the higher registers. Even in the first "octave" of the scale, you get a decent 6/5, 4/3, 8/5, and 7/4. Might be harder to use this way, but there are still going to be consonances (and thus "tonality"). Eliminating the octave doesn't really make for scales/tunings that are less consonant. If anything, it means that there's a chance for consonant intervals to "sneak in" in higher registers.

Nothing personal, Jake (I know you're still new to this stuff), but I hate that most psychoacoustic theorists consider the octave a "consonance". That's like saying water has a delicious flavor. 2/1 to me has a nil value in terms of consonance or dissonance--it's "tasteless". And by this way of thinking, 1/1 is "even more consonant" than 2/1, so if we really want to escape consonant harmonies, we need to get away from the 1-limit!!!!

Anyone want to point me to a scale with no pure 1/1's?

;-p

-Igs

untempered JI? Just don't force any thing to an octave.

Anyone want to point me to a scale with no pure 1/1's?

;-p

-Igs

>

That would be me.
Truly random rhythm and pitch would be probably the best approximation
of atonal and one single continuous pitch ultimate tonal consonance.
Every other shade of tonality is on a continuum between the two.

Chris

On Fri, Mar 18, 2011 at 9:12 AM, Jake Freivald <jdfreivald@...> wrote:

I'm not sure why we would use EDOs at all for music we want to call
"atonal". Someone -- Igs? Chris? -- said they think writing truly
atonal music is hard, and I can see why, especially with EDOs.

--- In MakeMicroMusic@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> That would be me.
> Truly random rhythm and pitch would be probably the best approximation
> of atonal and one single continuous pitch ultimate tonal consonance.
> Every other shade of tonality is on a continuum between the two.

I think demanding randomness is going overboard. If you want to being statistics into it, it seems to me you could define 5-limit triadic harmony (for example) as atonal if by statistical test no tonal center is present. This could be accomplished by random movement of the chord to related chords on dual of the Riemann Tonnetz; that is, eg, allowing the triad to move only to triads it shares at least one note with.

Of course usually people amalgamate a lack of consonance with the lack of a tonal center. If you want to do that with an edo, choosing one without any very good subgroups would be a good start. That's the mistake people make when latching immediately onto 11 or 13. Why not 14, where you get to have the 2.11/9.17/3.19/9 subgroup, and good luck with that? 14 is probably the suckiest edo larger than 12, though it seems for some reason to have its fans. Time for some 14edo serialism!

On Fri, Mar 18, 2011 at 8:01 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In MakeMicroMusic@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
> >
> > That would be me.
> > Truly random rhythm and pitch would be probably the best approximation
> > of atonal and one single continuous pitch ultimate tonal consonance.
> > Every other shade of tonality is on a continuum between the two.
>
> I think demanding randomness is going overboard. If you want to being statistics into it, it seems to me you could define 5-limit triadic harmony (for example) as atonal if by statistical test no tonal center is present. This could be accomplished by random movement of the chord to related chords on dual of the Riemann Tonnetz; that is, eg, allowing the triad to move only to triads it shares at least one note with.

I kind of did something similar hear, except I used Rothenberg minimal
sets to imply diatonic modes and only moved it to modes that shared
(usually) two notes in common:
http://www.mikebattagliamusic.com/music/ModalResolutions.mp3

> Of course usually people amalgamate a lack of consonance with the lack of a tonal center. If you want to do that with an edo, choosing one without any very good subgroups would be a good start. That's the mistake people make when latching immediately onto 11 or 13. Why not 14, where you get to have the 2.11/9.17/3.19/9 subgroup, and good luck with that? 14 is probably the suckiest edo larger than 12, though it seems for some reason to have its fans. Time for some 14edo serialism!

Bwuh? What? You like 14 less than 13? Huh? Where is Gene? Who are you?

-Mike

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

> Bwuh? What? You like 14 less than 13? Huh? Where is Gene? Who are you?

With 13, you can do 2.11.13/5.17/5.19/5 harmony, which has some possibilities. With 14, you get something which pretty much sucks at everything. Of course, if you are Herman or Igs and think beep is an actual temperament, you think that's good.

All I'm saying Gene is that true atonal music - without a tonal center - is
hard to write. Just doing something like repeating a note enough times
implies a tonal center. In other words, in my view all music are shades of
grey with regard to tonality between the one solution for complete tonality
and the one solution for complete atonality. It is my working premise. Now
of course this was said with 12 equal in mind. I would think it is just as
true of any tuning even if the tuning tends towards one shade of almost
white of one shade of almost black or somewhere in between.

In Urbana we are doing 11 edo serialism - isn't that atonal-ish enough? Why
bother with 14 edo?

Chris

On Fri, Mar 18, 2011 at 8:01 PM, genewardsmith
<genewardsmith@sbcglobal.net>wrote:

>
>
>
> --- In MakeMicroMusic@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...>
> wrote:
> >
> > That would be me.
> > Truly random rhythm and pitch would be probably the best approximation
> > of atonal and one single continuous pitch ultimate tonal consonance.
> > Every other shade of tonality is on a continuum between the two.
>
> I think demanding randomness is going overboard. If you want to being
> statistics into it, it seems to me you could define 5-limit triadic harmony
> (for example) as atonal if by statistical test no tonal center is present.
> This could be accomplished by random movement of the chord to related chords
> on dual of the Riemann Tonnetz; that is, eg, allowing the triad to move only
> to triads it shares at least one note with.
>
> Of course usually people amalgamate a lack of consonance with the lack of a
> tonal center. If you want to do that with an edo, choosing one without any
> very good subgroups would be a good start. That's the mistake people make
> when latching immediately onto 11 or 13. Why not 14, where you get to have
> the 2.11/9.17/3.19/9 subgroup, and good luck with that? 14 is probably the
> suckiest edo larger than 12, though it seems for some reason to have its
> fans. Time for some 14edo serialism!
>
>
>

[Non-text portions of this message have been removed]

> Nothing personal, Jake (I know you're still new to this stuff),

It's cool, Igs, even if I weren't. :)

> Actually, that scale is just 3-out-of-22-EDO with the "octave wrap"
> removed, or in other words 22 equal divisions of 8/1.

Did you misspeak? If I have 11 divisions getting me to less than an
octave, how can 22 of those divisions get me to 3 octaves?

> There are going to be lots and lots of 3, 5, and 7-limit
> consonances that pop up in the higher registers.

I don't deny that, but, it seems to me, the farther apart two tones
are, the less connected they seem to be. Four octaves + a fifth seem
less well-connected than one octave + a fifth, which is less
well-connected than a tone and its fifth.

On the other hand, this highlights an interesting point: People talk
about finding intervals they like based on given ratios -- sometimes
pretty complex ones -- and then temper them to be "almost" those
ratios. As you allow more primes, more tempering (even to the "small"
extent we allow in 12-TET), and more complex ratios, the fewer spots
there are in around some tone that don't bear some relationship to
that tone. After a while, it seems like scale structure has to matter
a whole lot more than individual dyads.

Funny thing: I tried to construct an "atonal" scale a few months back.
I took a list of a bunch of 2-to-7-limit ratios (I had a few hundred,
with exponents no higher than two for 3, 5, and 7, and no higher than
8 for 2 -- something like that), and put them in order from smallest
to biggest. Then I found the largest gaps between consecutive ratios.
Then I took the average of those two consecutive ratios, which gave me
a tone right between them. That gave me a more-than-12-tone scale, so
I took the twelve with the largest denominators, using that as a proxy
(in Excel, so this is not precise) for the greatest number of primes
(regardless of limit).

I was going to name the scale "Jeltz", after the Vogon who was
responsible for blowing up Earth in _The Hitchhiker's Guide to the
Galaxy_; the Vogons make the universe's third-worst poetry, and
they're the galaxy's bureaucrats, so it seemed appropriate.

Unfortunately, every mode (except the one I had explicitly defined)
was riddled with consonances. It was like designing the Locrian mode
in order to be unstable, and discovering that if I started on C or A
or G instead of B, everything sounded good. (Well, almost like that.)

> Even in the first "octave" of the scale, you get a decent 6/5, 4/3,
> 8/5, and 7/4.

This entire scale sounded weird to me, but I think I have different
expectations for "decent" than you do.

> Might be harder to use this way,

Only if you're trying to make tonal music. If you're trying to make
atonal music, then it's no easier or harder to use the scale in, say,
serial construction, but you're less likely to hit an accidentally
strongly tonal interval.

Or so it seems to me. :)

> I hate that most psychoacoustic theorists consider the octave a
> "consonance". That's like saying water has a delicious
> flavor.

I don't see it that way. Water doesn't change the flavor of a dish,
but sometimes you really need the water to make the meal; that said,
even a soup is insipid if your only flavor is water. Some flavorings
are more impactful than water, because they bring out the flavors of
the things they're with: salt might be an example. (Analogy: 5th?)
Others have a stronger flavor, like fish sauce, and could overwhelm a
food if not used judiciously. (Pick a more dissonant interval.)

An octave doesn't have the power to change the flavor of the note it's
with as much as a fifth does, but it still adds to the sound in a way
that's significant.

Again: "in my opinion" or "so it seems to me."

> we need to get away from the 1-limit!!!!

Hilarious! That would be a perfect fake thesis for someone....

Regards,
Jake

On 3/18/11, cityoftheasleep <igliashon@...> wrote:
> --- In MakeMicroMusic@yahoogroups.com, Jake Freivald <jdfreivald@...> wrote:
>
>> If you're going to step back from 3- and 5-limit harmony, as it seemed
>> Schoenberg wanted to do, why not step back from 2-limit while you're
>> at it? Use (say) 11 equal divisions of 1800 cents or something
>> instead. Each step is 163.63636 cents, and you don't line up
>> particularly well on any traditional 2, 3, or 5-limit consonance that
>> I can see. The notes will "show how little they are concerned"....
>
> Actually, that scale is just 3-out-of-22-EDO with the "octave wrap" removed,
> or in other words 22 equal divisions of 8/1. There are going to be lots and
> lots of 3, 5, and 7-limit consonances that pop up in the higher registers.
> Even in the first "octave" of the scale, you get a decent 6/5, 4/3, 8/5, and
> 7/4. Might be harder to use this way, but there are still going to be
> consonances (and thus "tonality"). Eliminating the octave doesn't really
> make for scales/tunings that are less consonant. If anything, it means that
> there's a chance for consonant intervals to "sneak in" in higher registers.
>
> Nothing personal, Jake (I know you're still new to this stuff), but I hate
> that most psychoacoustic theorists consider the octave a "consonance".
> That's like saying water has a delicious flavor. 2/1 to me has a nil value
> in terms of consonance or dissonance--it's "tasteless". And by this way of
> thinking, 1/1 is "even more consonant" than 2/1, so if we really want to
> escape consonant harmonies, we need to get away from the 1-limit!!!!
>
> Anyone want to point me to a scale with no pure 1/1's?
>
> ;-p
>
> -Igs
>
>

--- In MakeMicroMusic@yahoogroups.com, Jake Freivald <jdfreivald@...> wrote:
>
> > Nothing personal, Jake (I know you're still new to this stuff),
>
> It's cool, Igs, even if I weren't. :)
>
> > Actually, that scale is just 3-out-of-22-EDO with the "octave wrap"
> > removed, or in other words 22 equal divisions of 8/1.
>
> Did you misspeak? If I have 11 divisions getting me to less than an
> octave, how can 22 of those divisions get me to 3 octaves?

8/1=3600 cents. 3600/22=163.6363... You said 11 equal divisions of 1800 cents.

> > There are going to be lots and lots of 3, 5, and 7-limit
> > consonances that pop up in the higher registers.
>
> I don't deny that, but, it seems to me, the farther apart two tones
> are, the less connected they seem to be. Four octaves + a fifth seem
> less well-connected than one octave + a fifth, which is less
> well-connected than a tone and its fifth.

Yes, it is true that this scale will be awkward and difficult to use musically. However, the difficulty comes not from a lack of consonances, but (as you pointed out) a "lack of connection". Or, in other words, the "complexity" of the consonances.

> On the other hand, this highlights an interesting point: People talk
> about finding intervals they like based on given ratios -- sometimes
> pretty complex ones -- and then temper them to be "almost" those
> ratios. As you allow more primes, more tempering (even to the "small"
> extent we allow in 12-TET), and more complex ratios, the fewer spots
> there are in around some tone that don't bear some relationship to
> that tone. After a while, it seems like scale structure has to matter
> a whole lot more than individual dyads.

Bingo!

> Funny thing: I tried to construct an "atonal" scale a few months back.
> I took a list of a bunch of 2-to-7-limit ratios (I had a few hundred,
> with exponents no higher than two for 3, 5, and 7, and no higher than
> 8 for 2 -- something like that), and put them in order from smallest
> to biggest. Then I found the largest gaps between consecutive ratios.
> Then I took the average of those two consecutive ratios, which gave me
> a tone right between them. That gave me a more-than-12-tone scale, so
> I took the twelve with the largest denominators, using that as a proxy
> (in Excel, so this is not precise) for the greatest number of primes
> (regardless of limit).
>
> I was going to name the scale "Jeltz", after the Vogon who was
> responsible for blowing up Earth in _The Hitchhiker's Guide to the
> Galaxy_; the Vogons make the universe's third-worst poetry, and
> they're the galaxy's bureaucrats, so it seemed appropriate.
>
> Unfortunately, every mode (except the one I had explicitly defined)
> was riddled with consonances. It was like designing the Locrian mode
> in order to be unstable, and discovering that if I started on C or A
> or G instead of B, everything sounded good. (Well, almost like that.)

Yes. This is exactly the result I've gotten with every single theorist's attempt at designing for me a "scale with no consonances". It's impossible to escape consonance unless you use a scale with very few notes very widely-spaced. The best I've been able to do is a quarter-tone version of the diminished scale, i.e. 0-250-300-550-600-850-900-1150-1200 cents, but even then there's still a diminished 7th chord, which is pretty weak but not entirely unusable.

> This entire scale sounded weird to me, but I think I have different
> expectations for "decent" than you do.

Again, more to do with the step-size and the "structure" of how the consonances relate to each other than with any lack of consonant dyads.

> > Might be harder to use this way,
>
> Only if you're trying to make tonal music. If you're trying to make
> atonal music, then it's no easier or harder to use the scale in, say,
> serial construction, but you're less likely to hit an accidentally
> strongly tonal interval.

That is probably true. But the same could be said of 8-EDO.

> > I hate that most psychoacoustic theorists consider the octave a
> > "consonance". That's like saying water has a delicious
> > flavor.
>
> I don't see it that way. Water doesn't change the flavor of a dish,
> but sometimes you really need the water to make the meal; that said,
> even a soup is insipid if your only flavor is water. Some flavorings
> are more impactful than water, because they bring out the flavors of
> the things they're with: salt might be an example. (Analogy: 5th?)
> Others have a stronger flavor, like fish sauce, and could overwhelm a
> food if not used judiciously. (Pick a more dissonant interval.)

I guess that's where my idea of "consonance" differs from others. I see consonance as something that sounds "good", not something that sounds...unnoticeable. I'll grant that the octave is a very important ingredient in how we make music. But the idea that the "most consonant"--i.e. "most pleasant-sounding" interval is 1/1, followed by 2/1, 3/1, 4/1, and 5/1, and THEN 3/2, etc.--seems ass-backwards to me. To say that 1/1 sounds *better* than 2/1 and so on seems like nonsense. Even more so the idea that 2/1 sounds better than 3/2. In truth, the whole idea of quantifying musical intervals on a one-dimensional continuum seems nonsensical. Does salt taste *better* than fish sauce? Does water taste *better* than salt?

-Igs

14 does 6:7:9 decently enough.

-Igs

--- In MakeMicroMusic@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
> --- In MakeMicroMusic@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
>
> > Bwuh? What? You like 14 less than 13? Huh? Where is Gene? Who are you?
>
> With 13, you can do 2.11.13/5.17/5.19/5 harmony, which has some possibilities. With 14, you get something which pretty much sucks at everything. Of course, if you are Herman or Igs and think beep is an actual temperament, you think that's good.
>

--- In MakeMicroMusic@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> 14 does 6:7:9 decently enough.

Oh, sure. 14 has the same cheesy fifth as 7, 16.24 cents flat, which means the 9 is twice as flat. The 7 is 26 cents flat. Color me not impressed. I don't recall ever hearing a 14 piece I liked, which is not true for 11 or 13. What do the 14 notes add to 7, the washed-out diatonic scale?

The fact there’s some center doesn't necessarily mean it's tonal
center. It needn't to be connected with tonality. I would call this
just hierarchy.

Otherwise I have the same opinion as you, Schonberg's idea of
atonality and equaling all notes is nonsense and can't be constructed
in reality. In music there's always some hierarchy.

Same with Haba's athematic work. by using lot of motifs and themes in
sequence. It there are themes and motifs, it's not athematic despite
missing thematic work, development etc.

Daniel Forro

On Mar 19, 2011, at 9:21 AM, Chris Vaisvil wrote:

> All I'm saying Gene is that true atonal music - without a tonal
> center - is
> hard to write. Just doing something like repeating a note enough times
> implies a tonal center.

The 7/6 is only about 10 cents flat, and the 9/7 is only about 6 or 7 cents flat. Both of these are more accurate than the 5-limit intervals in 12-TET. Sure, the 3/2 is 16.24 cents flat. But for 6:7:9 chords, you don't find a significantly better approximation among the EDOs until you get to 22.

I do agree that good pieces in 14-EDO are pretty much non-existent. This, I attribute to the fact that no one has really used hemifourths[9] (or whatever you want to call the 2.3.7 subgroup that tempers out 49/48 and acts like Godzilla without any 5-limit harmony). The few compositions in 14 that exist really neglect its tonal side.

-Igs

--- In MakeMicroMusic@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
> --- In MakeMicroMusic@yahoogroups.com, "cityoftheasleep" <igliashon@> wrote:
> >
> > 14 does 6:7:9 decently enough.
>
> Oh, sure. 14 has the same cheesy fifth as 7, 16.24 cents flat, which means the 9 is twice as flat. The 7 is 26 cents flat. Color me not impressed. I don't recall ever hearing a 14 piece I liked, which is not true for 11 or 13. What do the 14 notes add to 7, the washed-out diatonic scale?
>

On Fri, Mar 18, 2011 at 3:49 PM, cityoftheasleep
<igliashon@...> wrote:
>
> Nothing personal, Jake (I know you're still new to this stuff), but I hate that most psychoacoustic theorists consider the octave a "consonance". That's like saying water has a delicious flavor. 2/1 to me has a nil value in terms of consonance or dissonance--it's "tasteless". And by this way of thinking, 1/1 is "even more consonant" than 2/1, so if we really want to escape consonant harmonies, we need to get away from the 1-limit!!!!

My jazz piano teacher would frown on chord voicings with lots of
doubled octaves in them. In general, the jazz viewpoint is that the
two notes that are needed to convey most of the relevant "information"
in a chord are the third and the seventh, and maybe only the fifth if
a diminished fifth is involved. The idea to omit the fifth in certain
cases goes back to common practice harmony, anyway.

I think it's because the octave and fifth are low enough in entropy to
be a little bit redundant. Entropy isn't just a fantastic word that we
like to throw around here, it actually has a specific meaning in
information theory; it's roughly equivalent to a measure of "how much
information" is present in the signal. 2/1 and 3/2 have a lower
information content than other intervals in the chord, so if you're
trying to find a compression algorithm to enable a complex chord to be
played with only 10 fingers on a piano, those are the first to go,
because they're not contributing any useful information.

This might also have more to do with the structure of the diatonic
scale than with HE; the fifth and octave are so common that they can
pretty much disappear. For other scales, this might not be the case.

> Anyone want to point me to a scale with no pure 1/1's?

Use phi timbres. H0h0h0!

-Mike

--- In MakeMicroMusic@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> The 7/6 is only about 10 cents flat, and the 9/7 is only about 6 or 7 cents flat. Both of these are more accurate than the 5-limit intervals in 12-TET. Sure, the 3/2 is 16.24 cents flat. But for 6:7:9 chords, you don't find a significantly better approximation among the EDOs until you get to 22.

I don't think this makes the diminished chord of 14 better than that of 12, because of the importance of the 3. And in any case, 17 is significantly better than 14, so this claim isn't true. And 19 and 21 beat it also.

> I do agree that good pieces in 14-EDO are pretty much non-existent. This, I attribute to the fact that no one has really used hemifourths[9] (or whatever you want to call the 2.3.7 subgroup that tempers out 49/48 and acts like Godzilla without any 5-limit harmony). The few compositions in 14 that exist really neglect its tonal side.

I'd call that scale "something for which 19 or 24 do a clearly better job than 14, and for which 24 is just about perfect". Which means you could take the wonderful music people aren't writing in that scale, retune it to 24, and get it to not sound like crud.

I think we agree - you are just drawing a distinction - I think you
are saying "tonal" requires some functional harmony where as a
"resting point" tonal center doesn't and really represents a
hierarchy.

Do I understand correctly?

Thanks,

Chris

On Sat, Mar 19, 2011 at 9:46 AM, Daniel Forró <dan.for@...> wrote:
> The fact there’s some center doesn't necessarily mean it's tonal
> center. It needn't to be connected with tonality. I would call this
> just hierarchy.
>
> Otherwise I have the same opinion as you, Schonberg's idea of
> atonality and equaling all notes is nonsense and can't be constructed
> in reality. In music there's always some hierarchy.
>
> Same with Haba's athematic work. by using lot of motifs and themes in
> sequence. It there are themes and motifs, it's not athematic despite
> missing thematic work, development etc.
>
> Daniel Forro
>
>
> On Mar 19, 2011, at 9:21 AM, Chris Vaisvil wrote:
>
>> All I'm saying Gene is that true atonal music - without a tonal
>> center - is
>> hard to write. Just doing something like repeating a note enough times
>> implies a tonal center.
>
>
> ------------------------------------
>
> Yahoo! Groups Links
>
>
>
>

--- In MakeMicroMusic@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:

> I'd call that scale "something for which 19 or 24 do a clearly better job than 14, and for which 24 is just about perfect". Which means you could take the wonderful music people aren't writing in that scale, retune it to 24, and get it to not sound like crud.

Of course, the 24 version of 6-7-9 is really more an inverted barbados triad if you've been following that stuff. And if you take that point of view, maybe you'll like 29 even better than 24. I think the barbados point of view on this chord is really better, because it's too far out of whack in semphore (49/48) tempering.

--- In MakeMicroMusic@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:

> I don't think this makes the diminished chord of 14 better than that of 12,

Who's talking about diminished chords? I'm talking about subminor triads.

> And in any case, 17 is significantly better than 14, so this claim isn't true. And 19 and 21
> beat it also.

I don't think 17 or 19 or 21 sound significantly better. They all improve on the 3/2, but individually weaken either the 7/6, the 9/7, or both. I think it's more important to weight in favor of the more complex intervals.

>
I'd call that scale "something for which 19 or 24 do a clearly better job than 14, and for which 24 is just about perfect". Which means you could take the wonderful music people aren't writing in that scale, retune it to 24, and get it to not sound like crud.
>

I really don't think it sounds significantly better in 19 or 24. 19's sounds better melodically, but I find the harmonies in 14 to be a good bit sweeter. Maybe I can bang out a musical example to compare the three today. But in any case that's beside the point; the point is 6:7:9 chords sound plenty good in 14, not "like crud", and I'd say they sound a good bit sweeter than anything in 11 or 13.

-Igs

Tonal center needs to have tonality, so yes, one of signs of tonality are "normal" triad chords in strictly defined functional relations.

Then there can be other type of centering in composition as an automatic result of hierarchy - if we use some music element in some piece more than the others, this element starts to be considered as a kind of center, takes our attraction and is considered to be more important. It can be one tone, or longer note, or repeated note, or some articulation type, or any chord with any structure which returns more often (even in transposition), or some rhythmic pattern, sound color, dynamic level (loud notes are always emphasized in comparison with quiet), formal element...

I wouldn't call such type of centre "resting point" because it can be dissonant chord.

Daniel Forro

On Mar 20, 2011, at 8:56 AM, Chris Vaisvil wrote:

> I think we agree - you are just drawing a distinction - I think you
> are saying "tonal" requires some functional harmony where as a
> "resting point" tonal center doesn't and really represents a
> hierarchy.
>
> Do I understand correctly?
>
> Thanks,
>
> Chris
>

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

> I don't think 17 or 19 or 21 sound significantly better. They all improve on the 3/2, but individually weaken either the 7/6, the 9/7, or both. I think it's more important to weight in favor of the more complex intervals.

I wonder if anyone else agrees with you about that? Mike has been talking up the 17 version of the chord in connection with the island business, and the 24 version even more.

> I really don't think it sounds significantly better in 19 or 24. 19's sounds better melodically, but I find the harmonies in 14 to be a good bit sweeter.

Sweeter? You've got a perverse notion of that.

Ok, this sounds to me more like thematic development then tonality. "I
wouldn't call such type of centre "resting point" because it can be
dissonant chord."

Let me try my view. By tonal center I do mean a resting point - (most) music
is about creating tension and relaxation. If there is a note or sonority
that feels like a resting / ending point then I would consider that my tonal
center - and it doesn't have to be the same throughout a piece - it is
something that is constantly being defined and redefined through development
in every musical aspect that is being manipulated. Even very dissonant music
(Carl Ruggles for example http://www.youtube.com/watch?v=GFD-pza4Jys or
http://www.youtube.com/watch?v=da-N9YbN5rI or even better
http://www.youtube.com/watch?v=7ig5Ql2iNQk&feature=related ) goes through
development that changes the tension and emotion of a piece.

It is all relative - as a composer in my view I tell a story based on
tension and release and sometimes the most beautiful passages are from what
surrounds them
- such as the choir in Ives' 4th symphony 4th movement
http://www.youtube.com/watch?v=oAjJf45fkTc&feature=related (or organ in the
3rd movement)
or the alleluia choral entrance and beyond in Stravinsky's Symphony of
Psalms http://www.youtube.com/watch?v=9AOFN65Q0Us&feature=related.
(the whole piece http://www.youtube.com/watch?v=1gijCz39Wts&feature=related
and http://www.youtube.com/watch?v=P9gxxFaAW3g&feature=related)

Its a big world and there are as many ways understand and love music as
there are ears. But this is part of my personal view and how I compose. And
it is based on what I love in the music I have heard and made me feel and
how I understand why I loved those passages. Which I guess comes down to,
when I write for myself, I try to write music I want to hear. (And that does
NOT always work out, believe me.)

Chris

On Sat, Mar 19, 2011 at 9:21 PM, Daniel Forr� <dan.for@...> wrote:

>
>
> Tonal center needs to have tonality, so yes, one of signs of tonality
> are "normal" triad chords in strictly defined functional relations.
>
> Then there can be other type of centering in composition as an
> automatic result of hierarchy - if we use some music element in some
> piece more than the others, this element starts to be considered as a
> kind of center, takes our attraction and is considered to be more
> important. It can be one tone, or longer note, or repeated note, or
> some articulation type, or any chord with any structure which returns
> more often (even in transposition), or some rhythmic pattern, sound
> color, dynamic level (loud notes are always emphasized in comparison
> with quiet), formal element...
>
> I wouldn't call such type of centre "resting point" because it can be
> dissonant chord.
>
> Daniel Forro
>
>
> On Mar 20, 2011, at 8:56 AM, Chris Vaisvil wrote:
>
> > I think we agree - you are just drawing a distinction - I think you
> > are saying "tonal" requires some functional harmony where as a
> > "resting point" tonal center doesn't and really represents a
> > hierarchy.
> >
> > Do I understand correctly?
> >
> > Thanks,
> >
> > Chris
> >
>
>
>

[Non-text portions of this message have been removed]

On Sat, Mar 19, 2011 at 8:16 PM, cityoftheasleep
<igliashon@...> wrote:
>
> > And in any case, 17 is significantly better than 14, so this claim isn't true. And 19 and 21
> > beat it also.
>
> I don't think 17 or 19 or 21 sound significantly better. They all improve on the 3/2, but individually weaken either the 7/6, the 9/7, or both. I think it's more important to weight in favor of the more complex intervals.

17's subminor triad doesn't have the subminor "feel" to it. It sounds
more like a normal minor triad to me. 19's sounds more like an
inverted barbados triad than a subminor chord for sure. But in any
case, if you prefer an unweighted error, such that the error for 7/6
is just as important than the error for 3/2, then what you're saying
is true. On the other hand, I feel that most people around here hate
beating the most, which suggests something like 1/N weighting.

> I really don't think it sounds significantly better in 19 or 24. 19's sounds better melodically, but I find the harmonies in 14 to be a good bit sweeter. Maybe I can bang out a musical example to compare the three today. But in any case that's beside the point; the point is 6:7:9 chords sound plenty good in 14, not "like crud", and I'd say they sound a good bit sweeter than anything in 11 or 13.

Except for the 4:7:9:11's in 11.

-Mike