Henry Cowell's New Musical Resources

Well, finally I had a chance to go through this fairly short theory
book. I particularly enjoyed the emphasis on the overtone series.

I was more troubled, though, by his lengthy section on rhythm. First
off, the whole idea of using different note heads for other
rhythms... triangle notes for "third notes" or one beat (with a stem)
of the meter 3/3 seem a little far-fetched for musicians to adopt.

I think the fact that this book was written in 1919 and, to my
knowledge, none of these suggestions have been seriously implemented
in any way may speak to this difficulty.

Even more troubling is the assumption that rhythm and meter of,
essentially, inharmonic timbres, should follow the pitched overtone
series of multiples (i.e. 1 note per measure, 2 notes per measure, 3
per measure) and should relate in a kind of gestalt theory that
covers everything.

I'm not sure that there is any evidence that an inharmonic sound
being struck at twice the speed of another sound heard at the same
time has the kind of "special relationship" that one finds in the 2x
multiple of vibrations in the pitch spectrum.

Couldn't these things be apples and oranges and not necessarily
involving the same physical principles?

I admit that some of these ideas of organization... say
of "modulating" rhythms according to speed multiples that roughly
correspond to a multiple of the overtone series might be an
intresting way to make some textures.

After all, Charles Ives does this in his Universe Symphony... did he
get the ideas from Cowell or vice versa (probably the latter)

However, to boil all this down to some kind of "unified field theory"
where it all relates, rhythm, meter and pitch, to the simple ratios
of the overtone series *by necessity* seems something of a stretch,
no?

I though the sections on creating tone clusters and the harmonic
implications of those and usage was a considerably more apt and
useful.

Fun summer reading, in any case...

Joseph Pehrson

Joseph Pehrson wrote:
> Well, finally I had a chance to go through this fairly short theory
> book. I particularly enjoyed the emphasis on the overtone series.
>
> I was more troubled, though, by his lengthy section on rhythm. First
> off, the whole idea of using different note heads for other
> rhythms... triangle notes for "third notes" or one beat (with a stem)
> of the meter 3/3 seem a little far-fetched for musicians to adopt.
>
> I think the fact that this book was written in 1919 and, to my
> knowledge, none of these suggestions have been seriously implemented
> in any way may speak to this difficulty.
>
> Even more troubling is the assumption that rhythm and meter of,
> essentially, inharmonic timbres, should follow the pitched overtone
> series of multiples (i.e. 1 note per measure, 2 notes per measure, 3
> per measure) and should relate in a kind of gestalt theory that
> covers everything.
... [much snipt]

Joseph,
Thanks for sharing this with us. Now I know I need not bother
hunting it up (it's been on a "mental list" for, oh, thirty years!
:-) ). Grand theories that fly in the face of facts are at best
useless.

However, the _idea_ of the metre 3/3 escapes me. Was he simply
rebelling against the convention of metres using binary divisions:
dividing whole notes into halves, quarters, etc?

Obviously, you COULD instead divide a whole note into thirds,
fifths, sixths, sevenths ... any other whole number of parts. But
a long, long notational tradition gives us what seem adequate
ways of notating both "perfectus" (threefold) and "imperfectus"
(twofold) metres, and even complex hemiole (three against two)
rhythms.

Do you think using third-notes would make it easier for musicians
to read and play a hemiole?

The last part of your message was interesting - the harmonic
implications of tone-clusters. When improvising at the piano, I've
often found an unintended tone-cluster (I'm clumsy) more
interesting than whatever else I happened to be exploring at the
time, and some of my most satisfyingly sonorous pieces have arisen
in this way. At times, I've been able to jot down some of what
happened, and explore it later. What I invariably find, however
-this _is_ a 12-EDO beast I hammer on - is that I can easily
analyse the harmonies into progressions of nothing more complex
than 13th chords. Which often leaves me feeling - Where next?

Regards,
Yahya

> Joseph,
> Thanks for sharing this with us. Now I know I need not bother
> hunting it up (it's been on a "mental list" for, oh, thirty years!
> :-) ). Grand theories that fly in the face of facts are at best
> useless.
>

***Hi Yahya!

Well, I wouldn't go to that extreme. There are many interesting
parts of this book. I just, personally, don't find the rhythmic part
(the largest) one of them...

> However, the _idea_ of the metre 3/3 escapes me. Was he simply
> rebelling against the convention of metres using binary divisions:
> dividing whole notes into halves, quarters, etc?
>

***Well, he's looking for more divisions, obviously... I don't think
it's a "rebellion" per se, but more a possible "augmentation..."

> Obviously, you COULD instead divide a whole note into thirds,
> fifths, sixths, sevenths ... any other whole number of parts. But
> a long, long notational tradition gives us what seem adequate
> ways of notating both "perfectus" (threefold) and "imperfectus"
> (twofold) metres, and even complex hemiole (three against two)
> rhythms.
>

***Well, exactly. I have to disagree slightly with Carl Lumma that
the lack of adoption of these measures (poor pun!) is in the same
league as the lack of adoption of microtonality.

It is *far* easier for me to teach a performer 1/12th of a whole tone
or 1/6th of a whole tone than it would be the meter 3/3 (three beats
to the measure and a "third note" gets one count) or 5/5 (five beats
to the measure and a "fifth note" gets one count).

The reason is I believe, as you state Yahya, the underlying
background of the rhythm of music being in 2 or 3 as the fundamental
structure. Sure, it can be changed with "brackets" and other
enhancements, which is the way it *should* be done, in my opinion,
but to change the fundamental structure would be like replacing our
five line staff again with a four-line staff, or a six-line staff or
whatever...

(I do note that my friend Joe Monzo has advocated changing the number
of lines of the musical staff, but I am not, personally, in that camp
of campers...)

> Do you think using third-notes would make it easier for musicians
> to read and play a hemiole?
>

***I think, basically, the meter would confuse the "hell" out of
them, to politely use the vernacular for the moment. They would
probably throw the music in my face, and that would be the end of the
rehearsal...

Otherwise, it would be quite a fine time... (literally)

> The last part of your message was interesting - the harmonic
> implications of tone-clusters.

***Well, I had nothing to do with it. These are Cowell's ideas, of
course.

When improvising at the piano, I've
> often found an unintended tone-cluster (I'm clumsy) more
> interesting than whatever else I happened to be exploring at the
> time, and some of my most satisfyingly sonorous pieces have arisen
> in this way. At times, I've been able to jot down some of what
> happened, and explore it later. What I invariably find, however
> -this _is_ a 12-EDO beast I hammer on - is that I can easily
> analyse the harmonies into progressions of nothing more complex
> than 13th chords. Which often leaves me feeling - Where next?
>

***It's a very interesting question, Yahya, but this might be do to
our conditioning to hear only chords that are build in thirds and
which go up to about the thirteenth... After all, we're very
much "conditioned" by our past experiences, naturally.

Thanks for the comments! I enjoyed reading the book and I would
suggest you at least try to check it out of the library, if it can be
found. Maybe on one of those grad library "exchange type" things...

best,

Joseph

Joseph Pehrson wrote:
...
> > However, the _idea_ of the metre 3/3 escapes me. Was he simply
> > rebelling against the convention of metres using binary divisions:
> > dividing whole notes into halves, quarters, etc?
>
> ***Well, he's looking for more divisions, obviously... I don't think
> it's a "rebellion" per se, but more a possible "augmentation..."
>
> > Obviously, you COULD instead divide a whole note into thirds,
> > fifths, sixths, sevenths ... any other whole number of parts. But
> > a long, long notational tradition gives us what seem adequate
> > ways of notating both "perfectus" (threefold) and "imperfectus"
> > (twofold) metres, and even complex hemiole (three against two)
> > rhythms.
>
> ***Well, exactly. I have to disagree slightly with Carl Lumma that
> the lack of adoption of these measures (poor pun!) is in the same
> league as the lack of adoption of microtonality.
>
> It is *far* easier for me to teach a performer 1/12th of a whole tone
> or 1/6th of a whole tone than it would be the meter 3/3 (three beats
> to the measure and a "third note" gets one count) or 5/5 (five beats
> to the measure and a "fifth note" gets one count).
>
> The reason is I believe, as you state Yahya, the underlying
> background of the rhythm of music being in 2 or 3 as the fundamental
> structure. Sure, it can be changed with "brackets" and other
> enhancements, which is the way it *should* be done, in my opinion,
> but to change the fundamental structure would be like replacing our
> five line staff again with a four-line staff, or a six-line staff or
> whatever...

At this point, I'm tempted to switch sides! :-) - but only for such
music that "the underlying background of the rhythm of music" is
NOT "in 2 or 3". For example, it's darn awkward trying to notate
a fairly low-order cross-rhythm of, say, 5 against 7. One of my
earliest pieces notated and realised with NoteWorthy Composer,
called "Cross", has a shifting triplet group, so that in 4/4 a group of
triplet crotchets (quarter-notes) moves through three positions
within the bar (measure) - the first half-bar, the _middle_ half-bar
and the last half-bar. When played against a delayed and transposed
copy of itself, we get a shifting hemiole. This is extremely easy to
notate using just a bracketed triplet. But to do the same with a
group of 5 or 7 is harder to notate and read - limitations of software
and also of our musical expectations both come into it. NoteWorthy
1.x can't notate a quintuplet, tho Sibelius etc can. It would be
simpler to notate, say, 3 against 5, if we could divide the whole note
into 15 equal parts, and thus dispense with the brackets entirely.
But see below ...

> (I do note that my friend Joe Monzo has advocated changing the number
> of lines of the musical staff, but I am not, personally, in that camp
> of campers...)

For increased clarity, placing noteheads only between lines is
one possible way to go - but we'd need ten lines to accommodate
what five lines presently can now in the treble clef, from E4 to F5.

> > Do you think using third-notes would make it easier for musicians
> > to read and play a hemiole?
>
> ***I think, basically, the meter would confuse the "hell" out of
> them, to politely use the vernacular for the moment. They would
> probably throw the music in my face, and that would be the end of the
> rehearsal...

Of course, some musicians ARE keen to go on learning new stuff.
The ones I have little respect for are those who believe that it's
all been done before and that they learned everything they need
to know way back when cocky was an egg.

> Otherwise, it would be quite a fine time... (literally)
>
> > The last part of your message was interesting - the harmonic
> > implications of tone-clusters.
>
> ***Well, I had nothing to do with it. These are Cowell's ideas, of
> course.
>
> > When improvising at the piano, I've
> > often found an unintended tone-cluster (I'm clumsy) more
> > interesting than whatever else I happened to be exploring at the
> > time, and some of my most satisfyingly sonorous pieces have arisen
> > in this way. At times, I've been able to jot down some of what
> > happened, and explore it later. What I invariably find, however
> > -this _is_ a 12-EDO beast I hammer on - is that I can easily
> > analyse the harmonies into progressions of nothing more complex
> > than 13th chords. Which often leaves me feeling - Where next?
>
> ***It's a very interesting question, Yahya, but this might be do to
> our conditioning to hear only chords that are build in thirds and
> which go up to about the thirteenth... After all, we're very
> much "conditioned" by our past experiences, naturally.

And it can be hard to know which parts of that conditioning is
truly useful, and which a hindrance, to making our own music.

> Thanks for the comments! I enjoyed reading the book and I would
> suggest you at least try to check it out of the library, if it can be
> found. Maybe on one of those grad library "exchange type" things...

You're probably right. Man deserves a hearing, doesn't he?

> best,
> Joseph

Regards,
Yahya

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This is a cross-post from MMM...

Hi Joseph,

>I was more troubled, though, by his lengthy section on rhythm.
>First off, the whole idea of using different note heads for other
>rhythms... triangle notes for "third notes" or one beat (with a
>stem) of the meter 3/3 seem a little far-fetched for musicians to
>adopt.
>
>I think the fact that this book was written in 1919 and, to my
>knowledge, none of these suggestions have been seriously
>implemented in any way may speak to this difficulty.

One could say the same thing about microtonality.

>Even more troubling is the assumption that rhythm and meter of,
>essentially, inharmonic timbres, should follow the pitched overtone
>series of multiples (i.e. 1 note per measure, 2 notes per measure,
>3 per measure) and should relate in a kind of gestalt theory that
>covers everything.

Simple ratios fall out of coupled oscillator systems that are
likely candidates for the way the brain represents rhythms. I
don't think Cowell knew that, that but he could hear the way they
sound. I really enjoy the polyrhythms in Cowell's music. The
nature of percussion timbres hardly matters here, especially in
light of the fact that the ratios are not describing simultaneities.

>I'm not sure that there is any evidence that an inharmonic sound
>being struck at twice the speed of another sound heard at the same
>time has the kind of "special relationship" that one finds in the
>2x multiple of vibrations in the pitch spectrum.

The overwhelming majority of percussion parts, as notated, are
made entirely of simple-ratio rhythms. Cowell was suggesting
extending this. Nancarrow apparently did stuff with irrational
rhythms like sqrt(2)... might be a good exercise to dig up that
stuff and listen for it.

>I admit that some of these ideas of organization... say
>of "modulating" rhythms according to speed multiples that roughly
>correspond to a multiple of the overtone series might be an
>intresting way to make some textures.

Glenn Gould was a believer that tempo changes ought to happen at
simple ratios -- in a 1981 (IIRC) interview he describes how he
used this technique between variations in his rendition of the
Goldberg variations. I had always done this on my scores, before
I knew about just intonation or Glenn Gould.

>After all, Charles Ives does this in his Universe Symphony... did
>he get the ideas from Cowell or vice versa (probably the latter)

Or maybe they did it independently... anybody know?

>However, to boil all this down to some kind of "unified field
>theory" where it all relates, rhythm, meter and pitch, to the
>simple ratios of the overtone series *by necessity* seems
>something of a stretch, no?

I don't remember Cowell putting forth such a grand system -- I
remember his approach being one of making suggestions. An
unified theory like this would indeed be a stretch, in my view.

-Carl

> Well, I wouldn't go to that extreme. There are many interesting
> parts of this book. I just, personally, don't find the rhythmic
> part (the largest) one of them...

I thought the notation proposal was one of the most interesting
in the book...

> It is *far* easier for me to teach a performer 1/12th of a
> whole tone or 1/6th of a whole tone than it would be the
> meter 3/3 (three beats to the measure and a "third note"
> gets one count) or 5/5 (five beats to the measure and a "fifth
> note" gets one count).

Whether or not this is true, I'd like to point out that notation
is good for more than being read by "musicians".

> The reason is I believe, as you state Yahya, the underlying
> background of the rhythm of music being in 2 or 3 as the
> fundamental structure. Sure, it can be changed with "brackets"
> and other enhancements, which is the way it *should* be done,
> in my opinion,

Brackets are clumsey, especially for long or nested structures.

> but to change the fundamental structure would be like replacing
> our five line staff again with a four-line staff, or a six-line
> staff or whatever...

Heh... *grunt*

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <clumma@y...> wrote:
> > Well, I wouldn't go to that extreme. There are many interesting
> > parts of this book. I just, personally, don't find the rhythmic
> > part (the largest) one of them...
>
> I thought the notation proposal was one of the most interesting
> in the book...
>
> > It is *far* easier for me to teach a performer 1/12th of a
> > whole tone or 1/6th of a whole tone than it would be the
> > meter 3/3 (three beats to the measure and a "third note"
> > gets one count) or 5/5 (five beats to the measure and a "fifth
> > note" gets one count).
>
> Whether or not this is true, I'd like to point out that notation
> is good for more than being read by "musicians".
>
> > The reason is I believe, as you state Yahya, the underlying
> > background of the rhythm of music being in 2 or 3 as the
> > fundamental structure. Sure, it can be changed with "brackets"
> > and other enhancements, which is the way it *should* be done,
> > in my opinion,
>
> Brackets are clumsey, especially for long or nested structures.
>
> > but to change the fundamental structure would be like replacing
> > our five line staff again with a four-line staff, or a six-line
> > staff or whatever...
>
> Heh... *grunt*
>
> -Carl

***Hi Carl,

Well, I don't want to put a damper on your pedal (accelerator!)... I
enjoy thinking about new things, and always enjoyed the Stockhausen
electronic pieces that had oodles of lines for staves in graphic
form. I also enjoy looking at Monz' quarternote notation.

However, I kinda wish somebody with practical experience like Johnny
Reinhard would "weigh in" on this discussion, since I really think
it's *much* easier to teach a performer microtonal pitch notations
or "cents" notations than fundamental changes in note shapes to
represent fundamental new rhythmic bases for music... Just to get
the job done, that's all! :)

But in a totally *theoretical* world sure, "go for it"! :)

JP

--- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, "Carl Lumma" <clumma@y...> wrote:
> > > Well, I wouldn't go to that extreme. There are many
interesting
> > > parts of this book. I just, personally, don't find the rhythmic
> > > part (the largest) one of them...
> >
> > I thought the notation proposal was one of the most interesting
> > in the book...
> >
> > > It is *far* easier for me to teach a performer 1/12th of a
> > > whole tone or 1/6th of a whole tone than it would be the
> > > meter 3/3 (three beats to the measure and a "third note"
> > > gets one count) or 5/5 (five beats to the measure and a "fifth
> > > note" gets one count).
> >
> > Whether or not this is true, I'd like to point out that notation
> > is good for more than being read by "musicians".
> >
> > > The reason is I believe, as you state Yahya, the underlying
> > > background of the rhythm of music being in 2 or 3 as the
> > > fundamental structure. Sure, it can be changed with "brackets"
> > > and other enhancements, which is the way it *should* be done,
> > > in my opinion,
> >
> > Brackets are clumsey, especially for long or nested structures.
> >
> > > but to change the fundamental structure would be like replacing
> > > our five line staff again with a four-line staff, or a six-line
> > > staff or whatever...
> >
> > Heh... *grunt*
> >
> > -Carl
>
> ***Hi Carl,
>
> Well, I don't want to put a damper on your pedal (accelerator!)...
> I enjoy thinking about new things, and always enjoyed the
> Stockhausen electronic pieces that had oodles of lines for
> staves in graphic form. I also enjoy looking at Monz'
> quarternote notation.
>
> However, I kinda wish somebody with practical experience like
> Johnny Reinhard would "weigh in" on this discussion, since I
> really think it's *much* easier to teach a performer microtonal
> pitch notations or "cents" notations than fundamental changes in
> note shapes to represent fundamental new rhythmic bases for
> music...

Once again, you're thinking of only one possible application
for notation.

Further, I put "musicians" in scare quotes there because the
majority of the world's musicians do not read common-practice
notation with any proficiency.

> But in a totally *theoretical* world sure, "go for it"! :)

Ever use the piano roll view in a MIDI sequencer?

-Carl