Yahoo Tuning Groups Ultimate Backup makemicromusic Books on composition

This is a very personal response to a personal topic.

These are a few of the books more-or-less directly about composition
to which I have returned frequently over the years; in most cases,
content about intonation is implicit rather than explicit:

Cowell, Henry, _New Musical Resources_
De la Motte, Diether, _Kontrapunkt_ (This, unfortunately, has not yet
been translated into English).
Erickson, Robert, _The Structure of Music, A Listener's Guide_
(Erickson's later book, _Sound Structure in Music_, mostly about
timbre, is also interesting, but for whatever reasons, I have never
returned to it)
Harrison, Lou, _Lou Harrison's Music Primer_
Morley, Thomas, _A Plaine and Easy Introduction to Practical Music_
Mozart, W.A., _Attwood-Studien_ (The harmony and counterpoint
notebooks of Mozart's student Thomas Attwood)
Seeger, Charles, _Harmony_ (Sadly, very difficult to find!)
Seeger, Charles, _Dissonant Counterpoint_ (article)

These come from the visual arts, and say nothing explicit about
musical composition, let alone tuning, but I can't imagine not having
them near:

Klee, Paul, _Pedagogical Sketchbook_
Wechsler, Lawrence, _Seeing is Forgetting the Name of the Thing One
Sees: A Life of Contemporary Artist Robert Irwin_

I'm not alone among composers in having found this valuable:

Thompson, D'arcy, _On Growth and Form_

These are more recent additions to my library, so have not yet faced
the test of time, but are certainly worth a look:

Tenzer, Michael, _Gamelan Gong Kebyar: The Art of Twentieth Century
Balinese Music_
Wolff, Christian, _Cues/Hinweise_
Lucier, Alvin, _Reflections/Reflektionen_

One of my students recommends this so strongly that I include it here
despite my own reservations:

Mathieu, W.A., _the Harmonic Experience_

Best regards,

Daniel Wolf

--- In MakeMicroMusic@yahoogroups.com, Alexandros Papadopoulos
<Alexmoog@o...> wrote:
> Hello
> Which book on composition would you suggest reading , that is not very
> specific to 12ET ?
> I don't know if such thing exists .
> I have read a little of Hindemith's "system of music composition" and
> it begins with some suggestions on tuning , leaning towards just
> intonation , and bashes(is this the right word?) 12ET.
>
> Thanks

🔗Carl Lumma <ekin@...>

🔗Joseph Pehrson <jpehrson@...>

🔗Joel Rodrigues <jdrodrigues@...>

Hello Alexandros !

This is the (english & french) composition shopping/reading list I've
been putting together. I took this out of my journal/notepad, and has
things mentioned, like no. of pages. You may want to look for these at
http://www.abebooks.co.uk

I've been adding these to my list based on reviews, descriptions,
excerpts, and recommendations.

- Joel

Cantagrel, Gilles et Brigitte François-Sappey (Dir Biographie...
Guide de la mélodie et du lied (1994)
Librairie Arthème Fayard, 928 pages, ISBN 2-213-59210-1

Cook, Nicholas
Analysis Through Composition : Principles of the Classical Style (21
November 1996)
Oxford University Press, 258 pages, 276mm x 228mm, spiralbound
paperback, ISBN 0-19-879013-9

Cowell, Henry
New Musical Resources
Cambridge University Press, 195 pages, 205 x 140 mm, ISBN 0521499747

Fux, Johann Joseph, Navarre, Jean-Philippe (tr)
Gradus ad Parnassum [1725]. Texte original intégral. (2000)
Mardaga (coll. Amicus), 378 p. 326 exemples, ISBN 2870097425

Hindemith, Paul
Craft of Musical Composition: Book One, Theoretical Part (4/e December
1942)
European Amer Music Dist Corp, (inches) 1.00 x 9.25 x 6.25, paperback,
ISBN 0901938300

Hindemith, Paul
Craft of Musical Composition: Book Two, Exercises in Two Part Writing
(January 1941)
European Amer Music Dist Corp, (inches) 0.50 x 9.25 x 6.25, paperback,
ISBN 0901938416

Mabry, Sharon
Exploring Twentieth-Century Vocal Music : A Practical Guide to
Innovations in Performance and Repertoire (2002)
Oxford University Press, 208 pp., 26 music exx., 6-1/8 x 9-1/4, ISBN
0-19-514198-9

Owen, Harold
Modal and Tonal Counterpoint From Josquin to Stravinsky (1/e March 1992)
Wadsworth Publishing Company, 389 pages, (inches) 0.89 x 11.06 x 8.51
Paperback, ISBN 0028721454

Schoenberg, Arnold; Strang, Gerald & Stein, Leonard (eds.).
Fundamentals of Musical Composition (1967/paperback 1970)
London: Faber, 224 pages, over 73⁄4" - 93⁄4" tall, ISBN 0571196586

Schoenberg, Arnold; Eithne Wilkins and Ernst Kaiser (tr); Erwin Stein
(ed)
Letters [1909 to 1951] (1987)
University of California Press, 309 pages, Paperback, ISBN 0520060091

Schoenberg, Arnold
Structural Forms of Harmony (reprint 1989)
Faber and Faber, 203 pages, over 7¾" - 9¾" tall, ISBN 0571130003

Smith Brindle, Reginald
Serial Composition (1968)
Oxford University Press, 218 pp., musical examples, paper, ISBN
0-19-311906-4

Xenakis, Iannis
Formalized Music : Thought and Mathematics in Composition (revised
edition 1992)
Pendragon Press, 6" x 9", 401 pp., illus., music ex., ISBN 0-945193-24-6

---
Some articles/web pages :

This seems to be an often referenced and important article :
Gyorgy Ligeti: ‘Metamorphoses of Musical Form’, Die Reihe, 7 (tr1965),
pp5–19.

Koenigsberg, Christopher K.
Karlheinz Stockhausen's New Morphology of Musical Time
http://www.music.princeton.edu/%7Eckk/smmt/index.html

(A very basic, rudimentary article :)
GRADE V THEORY COMPOSITION
An introduction by Joan Gregory
http://www.musicteachers.co.uk/resources/5comp.pdf

This website may be useful :
Music Composition Resource
http://www.und.edu/dept/mcr/
----------------------------------------------------------------------------------

On Monday, April 26, 2004, at 11:23 , MakeMicroMusic@yahoogroups.com
wrote:

> Alexandros Papadopoulos <Alexmoog@...>
>
> Hello
> Which book on composition would you suggest reading , that is not very
> specific to 12ET ?
> I don't know if such thing exists .
> I have read a little of Hindemith's "system of music composition" and
> it begins with some suggestions on tuning , leaning towards just
> intonation , and bashes(is this the right word?) 12ET.
>
> Thanks

🔗Joel Rodrigues <jdrodrigues@...>

On Monday, April 26, 2004, at 11:23 , MakeMicroMusic@yahoogroups.com wrote:

> From: Alexandros Papadopoulos <Alexmoog@...>

A couple more references :

(I've seen many recommendations for this)
Russo, William; with Jeffrey Aines and David Stevenson
Composing Music : A New Approach (1983)
University of Chicago Pres, 230 pages, ISBN 0-226-73216-9

and the Xenakis' book in the original french is :
Musiques formelles (1963, reissued 1981)
Editions Stock, 232 pages 261 pages

Strange that it doesn't seem to be easy to find, even
http://www.editions-stock.fr seems to have no trace of it.

I know you asked specifically for composition books relevant to non-2^(1/12) music, but I think these books would be helpful no matter what scales one chooses to work with.

If anyone has any comments about any of the books I mentioned, please respond !

Cheers,
Joel

🔗Daniel Wolf <djwolf1@...>

Carl Lumma wrote:

> >Hello > >Which book on composition would you suggest reading, that is not very
> >specific to 12ET?
>
> Daniel Wolf recommends Lou Harrison's Music Primer.
>
> I recommend you do NOT read anything about composing.
>
> -Carl
>

I hope that my name on a recommendation does anything but diminish the reputation of Lou's little book! Carl's point is well-taken, but I hope folks would've noticed that my own list did not include a single book with "composition" in the title. It would have been easy to throw in _New Music Composition_ by David Cope (who I value as a friend and teacher) or even Schoenberg's _Fundamentals of Musical Composition_; but the truth is, I have not found either helpful for learning/thinking about my composing, although either may serve well as references on particular issues (for example, Schoenberg is an excellent reference on traditional Viennese styles). On the other hand, the practical, "can-do", attitude of Lou's book has always inspired me, even if my own music uses techniques only distantly related to Lou's. The poet and teacher Charles Olson famously said "I teach posture"; ultimately, composing is about posture, it's about being able to present a piece of work to your fellow citizens and to identify yourself completely with that work. By definition, I believe, books can't teach posture, but they can be examples thereof.
I just re-read an interview with the composer Robert Ashley. Ashley complains about not being able to keep up with activities in the other arts, for example, in not being able to keep up with what his colleagues in literature were doing. He sees it as a matter of not having enough time, as the time he has is already full with his musical work. That's legitimate for him and probably for many others, but just not for me. I just can't imagine a life without always having four or five open books around the house, stashed as if by plan in each of the places where one might end up reading. Some "serious" lit (Pynchon or Carter Scholz or The Tale of Genji), Marshall Hodgson on Islam, a trashy political-thriller, a handbook on organ building, a lushly illustrated guide to dim sum, or a new grammar of Javanese... what things we fill our musics with!

Daniel Wolf

🔗Alexandros Papadopoulos <Alexmoog@...>

Thank you all for the recomendations , I hope nobody left the group because of my post!
I already ordered three of the books..
On Apr 27, 2004, at 3:30 PM, Daniel Wolf wrote:

> Carl Lumma wrote:
>
>>> Hello
>>> Which book on composition would you suggest reading, that is not very
>>> specific to 12ET?
>>
>> Daniel Wolf recommends Lou Harrison's Music Primer.
>>
>> I recommend you do NOT read anything about composing.
>>
>> -Carl
>>
>
> I hope that my name on a recommendation does anything but diminish the
> reputation of Lou's little book!
>
> Carl's point is well-taken, but I hope folks would've noticed that my
> own list did not include a single book with "composition" in the title.
> It would have been easy to throw in _New Music Composition_ by David
> Cope (who I value as a friend and teacher) or even Schoenberg's
> _Fundamentals of Musical Composition_; but the truth is, I have not
> found either helpful for learning/thinking about my composing, although
> either may serve well as references on particular issues (for example,
> Schoenberg is an excellent reference on traditional Viennese styles).
> On the other hand, the practical, "can-do", attitude of Lou's book has
> always inspired me, even if my own music uses techniques only distantly
> related to Lou's. The poet and teacher Charles Olson famously said "I
> teach posture"; ultimately, composing is about posture, it's about
> being able to present a piece of work to your fellow citizens and to
> identify yourself completely with that work. By definition, I believe,
> books can't teach posture, but they can be examples thereof.
>
> I just re-read an interview with the composer Robert Ashley. Ashley
> complains about not being able to keep up with activities in the other
> arts, for example, in not being able to keep up with what his > colleagues
> in literature were doing. He sees it as a matter of not having enough
> time, as the time he has is already full with his musical work. That's
> legitimate for him and probably for many others, but just not for me. > I
> just can't imagine a life without always having four or five open books
> around the house, stashed as if by plan in each of the places where one
> might end up reading. Some "serious" lit (Pynchon or Carter Scholz or
> The Tale of Genji), Marshall Hodgson on Islam, a trashy
> political-thriller, a handbook on organ building, a lushly illustrated
> guide to dim sum, or a new grammar of Javanese... what things we fill
> our musics with!
>
> Daniel Wolf
>
>
>
>
>
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> ------------------------------------------------------[MMM info]
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>
>

🔗George D. Secor <gdsecor@...>

--- In MakeMicroMusic@yahoogroups.com, Joel Rodrigues
<jdrodrigues@P...> wrote:
> ...
> If anyone has any comments about any of the books I mentioned,
please
> respond !

I have a comment regarding this one:

> Hindemith, Paul
> Craft of Musical Composition: Book One, Theoretical Part (4/e
December 1942)
> European Amer Music Dist Corp, (inches) 1.00 x 9.25 x 6.25,
paperback,
> ISBN 0901938300

Paul Hindemith spent some 20 pages "demonstrating" that musical
harmony above the 5-limit is impractical in an equal division of the
octave. A couple of choice quotes:

<< In the distances between the tones, there must be some clear
order. The smallest interval thus far is the minor second between E
and F, and it should not be hard to establish this as the smallest
interval in our scale. But the new smallest interval E-flat-minus
[7/6] to E-flat [6/5] would assert its claims. And since it would
not do to provide only one or two tones of the scale with auxiliary
tones which were simply slight flattenings of the original tones,
every tone of the scale would have to be provided with a similar
auxiliary. And these auxiliaries would have to have other tones at a
similar distance below them, and so on, until we should have a
hundred or more separate tones to the octave. Such a structure would
be impractical, and instrumental technique could not cope with it.
To realize to the fullest extent how meaningless it must remain for
practical music, one need only imagine a singer hopelessly struggling
with such small intervals.

In the play of harmonic intervals -- that is, in chord-progressions --
every tone of the scale must be capable of being used not only as a
root but also as any other factor of a chord. To this rule the tones
derived from the seventh overtone could be no exception. And every
one of them would support an overtone series of which the seventh
overtone must be treated like the seventh of the original series.
The result would be chaos. >> [pp. 37-38]

<< I have shown that to reckon with overtones above the sixth leads
to chaos. The system cannot be enlarged in this direction. The
twelve-tone chromatic scale is, as far as we can humanly tell, the
most complete solution of the problem -- at least for harmonic
purposes. >> [pp. 50-51]

We are therefore presented with the conclusion that microtonality is
incompatible with harmony. Unfortunately, misinformation of this
sort, disseminated by musical "authorities," is all too common.

--George

🔗Paul Erlich <perlich@...>

--- In MakeMicroMusic@yahoogroups.com, "George D. Secor"
<gdsecor@y...> wrote:
> --- In MakeMicroMusic@yahoogroups.com, Joel Rodrigues
> <jdrodrigues@P...> wrote:
> > ...
> > If anyone has any comments about any of the books I mentioned,
> please
> > respond !
>
> I have a comment regarding this one:
>
> > Hindemith, Paul
> > Craft of Musical Composition: Book One, Theoretical Part (4/e
> December 1942)
> > European Amer Music Dist Corp, (inches) 1.00 x 9.25 x 6.25,
> paperback,
> > ISBN 0901938300
>
> Paul Hindemith spent some 20 pages "demonstrating" that musical
> harmony above the 5-limit is impractical in an equal division of
the
> octave. A couple of choice quotes:
>
> << In the distances between the tones, there must be some clear
> order. The smallest interval thus far is the minor second between
E
> and F, and it should not be hard to establish this as the smallest
> interval in our scale. But the new smallest interval E-flat-minus
> [7/6] to E-flat [6/5] would assert its claims. And since it would
> not do to provide only one or two tones of the scale with auxiliary
> tones which were simply slight flattenings of the original tones,
> every tone of the scale would have to be provided with a similar
> auxiliary. And these auxiliaries would have to have other tones at
a
> similar distance below them, and so on, until we should have a
> hundred or more separate tones to the octave. Such a structure
would
> be impractical, and instrumental technique could not cope with it.
> To realize to the fullest extent how meaningless it must remain for
> practical music, one need only imagine a singer hopelessly
struggling
> with such small intervals.
>
> In the play of harmonic intervals -- that is, in chord-
progressions --
> every tone of the scale must be capable of being used not only as
a
> root but also as any other factor of a chord. To this rule the
tones
> derived from the seventh overtone could be no exception. And every
> one of them would support an overtone series of which the seventh
> overtone must be treated like the seventh of the original series.
> The result would be chaos. >> [pp. 37-38]
>
> << I have shown that to reckon with overtones above the sixth leads
> to chaos. The system cannot be enlarged in this direction. The
> twelve-tone chromatic scale is, as far as we can humanly tell, the
> most complete solution of the problem -- at least for harmonic
> purposes. >> [pp. 50-51]

Hindemith was clearly talking out of his @$&#*!%. As far as equal-
tempered scales go (which allow the complete flexibility of use that
Hindemith requires), 22-equal already provides a very clear and
striking distinction between 7/6 and 6/5 (a fact I love to use in
music, and is easy to sing along with). Even 15-equal can, in my
opinion, make this distinction -- with only three more notes than 12-
equal!! Among systems where the syntonic comma vanishes, and that
therefore behave in traditional Western common-practice ways, 31-
equal most definitely and 19-equal probably have this feature as
well.

> We are therefore presented with the conclusion that microtonality
is
> incompatible with harmony. Unfortunately, misinformation of this
> sort, disseminated by musical "authorities," is all too common.

And, frankly, I'm sick of it!!!

🔗Daniel Wolf <djwolf1@...>

🔗George D. Secor <gdsecor@...>

--- In MakeMicroMusic@yahoogroups.com, Daniel Wolf <djwolf1@a...>
wrote:
> George D. Secor wrote:
>
> > Paul Hindemith spent some 20 pages "demonstrating" that musical
> > harmony above the 5-limit is impractical in an equal division of
the
> > octave. A couple of choice quotes:
>
> To Hindemith's credit, Alois Haba praised Hindemith's "mastery" of
the
> quartertone intonation in playing the viola parts in several works
of
> Haba. Hindemith was apparently very modest, and kept asking Haba
for
> his approval. Another case of watch what he does, not what he says,
I
> suppose -- and very different to Menuhin, who would request the
removal
> of quartertones from a Bartok score!

The second quote I gave was in fact taken from a passage in which
Hindemith discussed his feelings about quartertones:

<< Will the musician forever be satisfied with this [12-ET] tonal
material? Will there not be within some reasonable time a further
enlargement of it? To many, the introduction of the quarter-tone
system is the answer to this question.

Scales may arise, as we have seen, in either of two ways: through the
filling out of the octave with intervals measured by the proportions
of the overtone series, and through the arithmetical division of the
octave. This book recommends the first of these, and the only way in
which this system of scale-construction could be expanded would be by
the use of the seventh overtone, for there is no compelling reason
why we should choose arbitrarily among the proportions offered us by
the overtone series, or skip over one of the overtones and choose the
next one as a basis for further reckoning. But I have shown that to
reckon with overtones above the sixth leads to chaos. The system
cannot be enlarged in this direction. The twelve-tone chromatic
scale is, as far as we can humanly tell, the most complete solution
of the problem -- at least for harmonic purposes.

The quarter-tone system proceeds from the second method of scale-
construction. It takes the equally tempered twelve-tone system as
its point of departure. That is a mistake. We have seen that equal
temperament does not offer a single scale-interval in pure form. But
what can be borne in a twelve-tone system becomes intolerable in a
system in which there are twice as many tones that contradict
nature. Anyone who has heard quarter-tone music frequently,
especially on keyboard instruments, knows that this is true, if his
sense of hearing is healthy, and he has not allowed it to be clouded
by preconceived opinions. Stringed instruments can make this music
barely tolerable, since even when working with these intervals they
can so place the comma that the ear hears pure intervals instead of
an uninterrupted series of mistuned ones. But this must contradict
the intention of the quarter-tone composer, for the correction of one
of his intervals by the size of a comma is, proportionately, a
considerable "clouding" of the interval. >> [The Craft of Musical
Composition, Book I, pp. 50-51]

From this last paragraph I would gather than Hindemith must have been
(at least initially) uncomfortably cautious in playing Haba's
quartertone music, but clearly his musical abilities were up to the
challenge.

--George

🔗George D. Secor <gdsecor@...>

--- In MakeMicroMusic@yahoogroups.com, "Paul Erlich" <perlich@a...>
wrote:
> --- In MakeMicroMusic@yahoogroups.com, "George D. Secor"
> >
> > Paul Hindemith spent some 20 pages "demonstrating" that musical
> > harmony above the 5-limit is impractical in an equal division of
the
> > octave. ...
>
> Hindemith was clearly talking out of his @$&#*!%. As far as equal-
> tempered scales go (which allow the complete flexibility of use
that
> Hindemith requires), 22-equal already provides a very clear and
> striking distinction between 7/6 and 6/5 (a fact I love to use in
> music, and is easy to sing along with). Even 15-equal can, in my
> opinion, make this distinction -- with only three more notes than
12-
> equal!! Among systems where the syntonic comma vanishes, and that
> therefore behave in traditional Western common-practice ways, 31-
> equal most definitely and 19-equal probably have this feature as
> well.

It appears that Hindemith was completely ignorant of 31-ET, because
it would have satisfied all of his requirements (and then some) for
an expanded harmonic system, particularly in light of its close
association with the meantone temperament.

However, Hindemith did know about 19, and here's what he had to say
about it:

<< Of the systems of more than twelve tones (tempered or using
natural intervals), the one closest to the twelve-tone one and yet
entirely independent is a system with nineteen tones within the
octave. It has the distinction of having been calculated and
proposed -- since its first appearance shortly after 1600 -- more
often than any other unusual system, but in spite of this it has
remained theory -- and theory in its vaguest form at that. It is one
thing to propose tonal systems; another to prove their
practicability. Has anyone ever reported on his successful
experiences with a nineteen-tone system, actually sung (and sung many
times) by an _a cappella_ chorus? No. Tonal systems grow and live
like languages. They may develop from primitive forms into extremely
involved idioms; worn-out systems may disappear. But they cannot be
manufactured and put into use like motors and crackers, nor can they
be enforced like laws. >> [_A Composer's World_, p. 92]

In contrast to his observations about 24-ET, he had absolutely
nothing to say about the characteristics of the 19-ET tuning
itself!!! Instead, he argues for some sort of musical evolutionary
process in which we are collectively involved, but over which we, as
individuals, have little no control.

--George

🔗Gene Ward Smith <gwsmith@...>

This is what I get for reading out of sequence--this is the faux
mathematical proof I referred to, and which I've mentioned before.

> << In the distances between the tones, there must be some clear
> order. The smallest interval thus far is the minor second between
E
> and F, and it should not be hard to establish this as the smallest
> interval in our scale. But the new smallest interval E-flat-minus
> [7/6] to E-flat [6/5] would assert its claims. And since it would
> not do to provide only one or two tones of the scale with auxiliary
> tones which were simply slight flattenings of the original tones,
> every tone of the scale would have to be provided with a similar
> auxiliary. And these auxiliaries would have to have other tones at
a
> similar distance below them, and so on, until we should have a
> hundred or more separate tones to the octave.

Here Hindemith claims, in effect, that unless 36/35 is a comma of
your 7-limit system of harmony, it will necessarily blow itself up.
Assuming this makes it easy to show 12 is the most practical system
for trying to work what 7-limit harmony we can into the picture, but
the premise is of course false. One could produce a similar argument
in 7-equal, in connection with 5/4 and 6/5 and 25/24 as a comma,
and "prove" that musical harmony above the 3-limit makes sense only
to the extent 7-equal will accomodate it.

🔗Joseph Pehrson <jpehrson@...>

--- In MakeMicroMusic@yahoogroups.com, Joel Rodrigues

/makemicromusic/topicId_6263.html#6300

<jdrodrigues@P...> wrote:
>
> On Monday, April 26, 2004, at 11:23 ,
MakeMicroMusic@yahoogroups.com
> wrote:
>
> > From: Alexandros Papadopoulos <Alexmoog@o...>
>
> A couple more references :
>
> (I've seen many recommendations for this)
> Russo, William; with Jeffrey Aines and David Stevenson
> Composing Music : A New Approach (1983)
> University of Chicago Pres, 230 pages, ISBN 0-226-73216-9
>
>
> and the Xenakis' book in the original french is :
> Musiques formelles (1963, reissued 1981)
> Editions Stock, 232 pages 261 pages
>
> Strange that it doesn't seem to be easy to find, even
> http://www.editions-stock.fr seems to have no trace of it.
>
>
> I know you asked specifically for composition books relevant to
> non-2^(1/12) music, but I think these books would be helpful no
matter
> what scales one chooses to work with.
>
> If anyone has any comments about any of the books I mentioned,
please
> respond !
>
> Cheers,
> Joel

***I've always enjoyed the *photographs* in the Xenakis book (the
architecture and such like) and he personally autographed it for
me... but I think one would have to have the math background of Gene
Ward Smith or Paul Erlich to use it seriously as a compositional
tool...

🔗Joseph Pehrson <jpehrson@...>

--- In MakeMicroMusic@yahoogroups.com, "George D. Secor"

/makemicromusic/topicId_6263.html#6310

<gdsecor@y...> wrote:
> --- In MakeMicroMusic@yahoogroups.com, "Paul Erlich" <perlich@a...>
> wrote:
> > --- In MakeMicroMusic@yahoogroups.com, "George D. Secor"
> > >
> > > Paul Hindemith spent some 20 pages "demonstrating" that musical
> > > harmony above the 5-limit is impractical in an equal division
of
> the
> > > octave. ...
> >
> > Hindemith was clearly talking out of his @$&#*!%. As far as equal-
> > tempered scales go (which allow the complete flexibility of use
> that
> > Hindemith requires), 22-equal already provides a very clear and
> > striking distinction between 7/6 and 6/5 (a fact I love to use in
> > music, and is easy to sing along with). Even 15-equal can, in my
> > opinion, make this distinction -- with only three more notes than
> 12-
> > equal!! Among systems where the syntonic comma vanishes, and that
> > therefore behave in traditional Western common-practice ways, 31-
> > equal most definitely and 19-equal probably have this feature as
> > well.
>
> It appears that Hindemith was completely ignorant of 31-ET, because
> it would have satisfied all of his requirements (and then some) for
> an expanded harmonic system, particularly in light of its close
> association with the meantone temperament.
>
> However, Hindemith did know about 19, and here's what he had to say
> about it:
>
> << Of the systems of more than twelve tones (tempered or using
> natural intervals), the one closest to the twelve-tone one and yet
> entirely independent is a system with nineteen tones within the
> octave. It has the distinction of having been calculated and
> proposed -- since its first appearance shortly after 1600 -- more
> often than any other unusual system, but in spite of this it has
> remained theory -- and theory in its vaguest form at that. It is
one
> thing to propose tonal systems; another to prove their
> practicability. Has anyone ever reported on his successful
> experiences with a nineteen-tone system, actually sung (and sung
many
> times) by an _a cappella_ chorus? No. Tonal systems grow and live
> like languages. They may develop from primitive forms into
extremely
> involved idioms; worn-out systems may disappear. But they cannot
be
> manufactured and put into use like motors and crackers, nor can
they
> be enforced like laws. >> [_A Composer's World_, p. 92]
>
> In contrast to his observations about 24-ET, he had absolutely
> nothing to say about the characteristics of the 19-ET tuning
> itself!!! Instead, he argues for some sort of musical evolutionary
> process in which we are collectively involved, but over which we,
as
> individuals, have little no control.
>
> --George

***Gathering only from the cited paragraph, I would guess that he
really hadn't studied it very well...

J. Pehrson

🔗Joseph Pehrson <jpehrson@...>

--- In MakeMicroMusic@yahoogroups.com, "Gene Ward Smith"

/makemicromusic/topicId_6263.html#6312

<gwsmith@s...> wrote:
> --- In MakeMicroMusic@yahoogroups.com, "George D. Secor"
> <gdsecor@y...> wrote:
> > --- In MakeMicroMusic@yahoogroups.com, Joel Rodrigues
> > <jdrodrigues@P...> wrote:
> > > ...
> > > If anyone has any comments about any of the books I mentioned,
> > please
> > > respond !
> >
> > I have a comment regarding this one:
> >
> > > Hindemith, Paul
> > > Craft of Musical Composition: Book One, Theoretical Part (4/e
> > December 1942)
> > > European Amer Music Dist Corp, (inches) 1.00 x 9.25 x 6.25,
> > paperback,
> > > ISBN 0901938300
> >
> > Paul Hindemith spent some 20 pages "demonstrating" that musical
> > harmony above the 5-limit is impractical in an equal division of
> the
> > octave. A couple of choice quotes:
>
> This is what I get for reading out of sequence--this is the faux
> mathematical proof I referred to, and which I've mentioned before.
>
> > << In the distances between the tones, there must be some clear
> > order. The smallest interval thus far is the minor second
between
> E
> > and F, and it should not be hard to establish this as the
smallest
> > interval in our scale. But the new smallest interval E-flat-
minus
> > [7/6] to E-flat [6/5] would assert its claims. And since it
would
> > not do to provide only one or two tones of the scale with
auxiliary
> > tones which were simply slight flattenings of the original tones,
> > every tone of the scale would have to be provided with a similar
> > auxiliary. And these auxiliaries would have to have other tones
at
> a
> > similar distance below them, and so on, until we should have a
> > hundred or more separate tones to the octave.
>
> Here Hindemith claims, in effect, that unless 36/35 is a comma of
> your 7-limit system of harmony, it will necessarily blow itself up.
> Assuming this makes it easy to show 12 is the most practical system
> for trying to work what 7-limit harmony we can into the picture,
but
> the premise is of course false. One could produce a similar
argument
> in 7-equal, in connection with 5/4 and 6/5 and 25/24 as a comma,
> and "prove" that musical harmony above the 3-limit makes sense only
> to the extent 7-equal will accomodate it.

***The paragraph immediately above seems very important to me, but I
need some more elaboration. Could somebody please provide a bit
of "genespeak" translation or elaboration, maybe on another list if
not this one??

Tx!

🔗George D. Secor <gdsecor@...>

--- In MakeMicroMusic@yahoogroups.com, "Joseph Pehrson"
<jpehrson@r...> wrote:
> --- In MakeMicroMusic@yahoogroups.com, "Gene Ward Smith"
> >
> > Here Hindemith claims, in effect, that unless 36/35 is a comma of
> > your 7-limit system of harmony, it will necessarily blow itself
up.
> > Assuming this makes it easy to show 12 is the most practical
system
> > for trying to work what 7-limit harmony we can into the picture,
but
> > the premise is of course false. One could produce a similar
argument
> > in 7-equal, in connection with 5/4 and 6/5 and 25/24 as a comma,
> > and "prove" that musical harmony above the 3-limit makes sense
only
> > to the extent 7-equal will accomodate it.
>
> ***The paragraph immediately above seems very important to me, but
I
> need some more elaboration. Could somebody please provide a bit
> of "genespeak" translation or elaboration, maybe on another list if
> not this one??

See my original (untranslated) message:
/makemicromusic/topicId_6263.html#6306
plus Paul Erlich's reply:
/makemicromusic/topicId_6263.html#6307
in which he mentions a few divisions in which 7/6 is differentiated
from 6/5.

Any equal division of the octave will satisfy Hindemith's requirement
of allowing any tone to be used as any factor of a chord, so
Hindemith's "proof" can be refuted simply by finding one or more EDOs
with a reasonable number of tones/octave in which the 3rd, 5th, and
7th harmonics are well represented. Both 22 and 31 not only meet,
but exceed Hindemith's requirements by including the 11th harmonic as
well.

--George

🔗Paul Erlich <perlich@...>

--- In MakeMicroMusic@yahoogroups.com, "George D. Secor"
<gdsecor@y...> wrote:
> --- In MakeMicroMusic@yahoogroups.com, "Joseph Pehrson"
> <jpehrson@r...> wrote:
> > --- In MakeMicroMusic@yahoogroups.com, "Gene Ward Smith"
> > >
> > > Here Hindemith claims, in effect, that unless 36/35 is a comma
of
> > > your 7-limit system of harmony, it will necessarily blow itself
> up.
> > > Assuming this makes it easy to show 12 is the most practical
> system
> > > for trying to work what 7-limit harmony we can into the
picture,
> but
> > > the premise is of course false. One could produce a similar
> argument
> > > in 7-equal, in connection with 5/4 and 6/5 and 25/24 as a
comma,
> > > and "prove" that musical harmony above the 3-limit makes sense
> only
> > > to the extent 7-equal will accomodate it.
> >
> > ***The paragraph immediately above seems very important to me,
but
> I
> > need some more elaboration. Could somebody please provide a bit
> > of "genespeak" translation or elaboration, maybe on another list
if
> > not this one??
>
> See my original (untranslated) message:
> /makemicromusic/topicId_6263.html#6306
> plus Paul Erlich's reply:
> /makemicromusic/topicId_6263.html#6307
> in which he mentions a few divisions in which 7/6 is differentiated
> from 6/5.
>
> Any equal division of the octave will satisfy Hindemith's
requirement
> of allowing any tone to be used as any factor of a chord, so
> Hindemith's "proof" can be refuted simply by finding one or more
EDOs
> with a reasonable number of tones/octave in which the 3rd, 5th, and
> 7th harmonics are well represented.

That won't quite do it. 12-equal (especially if compressed a bit) can
be said to satisfy this. Hindemith was specifically referring to
distinguishing 7/6 from 6/5, something 12-equal can't do. Gene's
point, above, took off specifically from *this* observation.

How are you doing, Joseph? :)

🔗George D. Secor <gdsecor@...>

--- In MakeMicroMusic@yahoogroups.com, "Paul Erlich" <perlich@a...>
wrote:
> --- In MakeMicroMusic@yahoogroups.com, "George D. Secor"
> <gdsecor@y...> wrote:
> >
> > Any equal division of the octave will satisfy Hindemith's
> requirement
> > of allowing any tone to be used as any factor of a chord, so
> > Hindemith's "proof" can be refuted simply by finding one or more
> EDOs
> > with a reasonable number of tones/octave in which the 3rd, 5th,
and
> > 7th harmonics are well represented.
>
> That won't quite do it. 12-equal (especially if compressed a bit)
can
> be said to satisfy this. Hindemith was specifically referring to
> distinguishing 7/6 from 6/5, something 12-equal can't do. Gene's
> point, above, took off specifically from *this* observation.

Yes, I was assuming that, but forgot to say it. And should we
continue at the 7 limit with the same procedure Hindemith followed in
deriving a 12-tone octave based on 5-limit intervals, we would
probably also require that 8/7 be distinguished from 7/6, and also
7/5 from 10/7; i.e., our EDO should be 7-limit unique.

It looks like it would have to be 31.

--George

🔗Paul Erlich <perlich@...>

--- In MakeMicroMusic@yahoogroups.com, "George D. Secor"
<gdsecor@y...> wrote:
> --- In MakeMicroMusic@yahoogroups.com, "Paul Erlich" <perlich@a...>
> wrote:
> > --- In MakeMicroMusic@yahoogroups.com, "George D. Secor"
> > <gdsecor@y...> wrote:
> > >
> > > Any equal division of the octave will satisfy Hindemith's
> > requirement
> > > of allowing any tone to be used as any factor of a chord, so
> > > Hindemith's "proof" can be refuted simply by finding one or
more
> > EDOs
> > > with a reasonable number of tones/octave in which the 3rd, 5th,
> and
> > > 7th harmonics are well represented.
> >
> > That won't quite do it. 12-equal (especially if compressed a bit)
> can
> > be said to satisfy this. Hindemith was specifically referring to
> > distinguishing 7/6 from 6/5, something 12-equal can't do. Gene's
> > point, above, took off specifically from *this* observation.
>
> Yes, I was assuming that, but forgot to say it. And should we
> continue at the 7 limit with the same procedure Hindemith followed
in
> deriving a 12-tone octave based on 5-limit intervals, we would
> probably also require that 8/7 be distinguished from 7/6, and also
> 7/5 from 10/7; i.e., our EDO should be 7-limit unique.
>
> It looks like it would have to be 31.

Or 27, if one could tolerate those wide fifths (711 cents).

One could go even lower if one dropped requirements of octave-
equivalence and/or consistency.

But now we're knee-deep in theory stuff.

Out of courtesy to this list and its mission, please put anything
further on the tuning or tuning-math list.

🔗Gene Ward Smith <gwsmith@...>

🔗Joseph Pehrson <jpehrson@...>

--- In MakeMicroMusic@yahoogroups.com, "George D. Secor"

/makemicromusic/topicId_6263.html#6338

<gdsecor@y...> wrote:
> --- In MakeMicroMusic@yahoogroups.com, "Joseph Pehrson"
> <jpehrson@r...> wrote:
> > --- In MakeMicroMusic@yahoogroups.com, "Gene Ward Smith"
> > >
> > > Here Hindemith claims, in effect, that unless 36/35 is a comma
of
> > > your 7-limit system of harmony, it will necessarily blow itself
> up.
> > > Assuming this makes it easy to show 12 is the most practical
> system
> > > for trying to work what 7-limit harmony we can into the
picture,
> but
> > > the premise is of course false. One could produce a similar
> argument
> > > in 7-equal, in connection with 5/4 and 6/5 and 25/24 as a
comma,
> > > and "prove" that musical harmony above the 3-limit makes sense
> only
> > > to the extent 7-equal will accomodate it.
> >
> > ***The paragraph immediately above seems very important to me,
but
> I
> > need some more elaboration. Could somebody please provide a bit
> > of "genespeak" translation or elaboration, maybe on another list
if
> > not this one??
>
> See my original (untranslated) message:
> /makemicromusic/topicId_6263.html#6306
> plus Paul Erlich's reply:
> /makemicromusic/topicId_6263.html#6307
> in which he mentions a few divisions in which 7/6 is differentiated
> from 6/5.
>
> Any equal division of the octave will satisfy Hindemith's
requirement
> of allowing any tone to be used as any factor of a chord, so
> Hindemith's "proof" can be refuted simply by finding one or more
EDOs
> with a reasonable number of tones/octave in which the 3rd, 5th, and
> 7th harmonics are well represented. Both 22 and 31 not only meet,
> but exceed Hindemith's requirements by including the 11th harmonic
as
> well.
>
> --George

***Thanks so much, George! Yes, I understood *your* post and Paul's
response right away. I had a little more trouble with Gene's, but
now, in the context of your discussion, Gene's is making sense too
(albeit a bit abstractly...) Thanks so much!

Joseph

🔗Joseph Pehrson <jpehrson@...>

--- In MakeMicroMusic@yahoogroups.com, "Paul Erlich" <perlich@a...>

/makemicromusic/topicId_6263.html#6343

wrote:
> --- In MakeMicroMusic@yahoogroups.com, "George D. Secor"
> <gdsecor@y...> wrote:
> > --- In MakeMicroMusic@yahoogroups.com, "Joseph Pehrson"
> > <jpehrson@r...> wrote:
> > > --- In MakeMicroMusic@yahoogroups.com, "Gene Ward Smith"
> > > >
> > > > Here Hindemith claims, in effect, that unless 36/35 is a
comma
> of
> > > > your 7-limit system of harmony, it will necessarily blow
itself
> > up.
> > > > Assuming this makes it easy to show 12 is the most practical
> > system
> > > > for trying to work what 7-limit harmony we can into the
> picture,
> > but
> > > > the premise is of course false. One could produce a similar
> > argument
> > > > in 7-equal, in connection with 5/4 and 6/5 and 25/24 as a
> comma,
> > > > and "prove" that musical harmony above the 3-limit makes
sense
> > only
> > > > to the extent 7-equal will accomodate it.
> > >
> > > ***The paragraph immediately above seems very important to me,
> but
> > I
> > > need some more elaboration. Could somebody please provide a
bit
> > > of "genespeak" translation or elaboration, maybe on another
list
> if
> > > not this one??
> >
> > See my original (untranslated) message:
> > /makemicromusic/topicId_6263.html#6306
> > plus Paul Erlich's reply:
> > /makemicromusic/topicId_6263.html#6307
> > in which he mentions a few divisions in which 7/6 is
differentiated
> > from 6/5.
> >
> > Any equal division of the octave will satisfy Hindemith's
> requirement
> > of allowing any tone to be used as any factor of a chord, so
> > Hindemith's "proof" can be refuted simply by finding one or more
> EDOs
> > with a reasonable number of tones/octave in which the 3rd, 5th,
and
> > 7th harmonics are well represented.
>
> That won't quite do it. 12-equal (especially if compressed a bit)
can
> be said to satisfy this. Hindemith was specifically referring to
> distinguishing 7/6 from 6/5, something 12-equal can't do. Gene's
> point, above, took off specifically from *this* observation.
>
> How are you doing, Joseph? :)

***So far, I'm following this, even the "gene part" now... but I was
also hoping that George Secor had an "easy fix..." :)

🔗Joseph Pehrson <jpehrson@...>

--- In MakeMicroMusic@yahoogroups.com, "Paul Erlich" <perlich@a...>

/makemicromusic/topicId_6263.html#6346

wrote:
> --- In MakeMicroMusic@yahoogroups.com, "George D. Secor"
> <gdsecor@y...> wrote:
> > --- In MakeMicroMusic@yahoogroups.com, "Paul Erlich"
<perlich@a...>
> > wrote:
> > > --- In MakeMicroMusic@yahoogroups.com, "George D. Secor"
> > > <gdsecor@y...> wrote:
> > > >
> > > > Any equal division of the octave will satisfy Hindemith's
> > > requirement
> > > > of allowing any tone to be used as any factor of a chord, so
> > > > Hindemith's "proof" can be refuted simply by finding one or
> more
> > > EDOs
> > > > with a reasonable number of tones/octave in which the 3rd,
5th,
> > and
> > > > 7th harmonics are well represented.
> > >
> > > That won't quite do it. 12-equal (especially if compressed a
bit)
> > can
> > > be said to satisfy this. Hindemith was specifically referring
to
> > > distinguishing 7/6 from 6/5, something 12-equal can't do.
Gene's
> > > point, above, took off specifically from *this* observation.
> >
> > Yes, I was assuming that, but forgot to say it. And should we
> > continue at the 7 limit with the same procedure Hindemith
followed
> in
> > deriving a 12-tone octave based on 5-limit intervals, we would
> > probably also require that 8/7 be distinguished from 7/6, and
also
> > 7/5 from 10/7; i.e., our EDO should be 7-limit unique.
> >
> > It looks like it would have to be 31.
>
> Or 27, if one could tolerate those wide fifths (711 cents).
>
> One could go even lower if one dropped requirements of octave-
> equivalence and/or consistency.
>
> But now we're knee-deep in theory stuff.
>
> Out of courtesy to this list and its mission, please put anything
> further on the tuning or tuning-math list.

***Oh...could I please request that if any of these discussion move
somebody puts in a "migration link..." Otherwise I might miss
something if I'm not always checking...

Thanks!

Books on composition

🔗Alexandros Papadopoulos <Alexmoog@...>

🔗danieljameswolf <djwolf1@...>

🔗Carl Lumma <ekin@...>

🔗Carl Lumma <ekin@...>

🔗Joseph Pehrson <jpehrson@...>

🔗Joel Rodrigues <jdrodrigues@...>

🔗Joel Rodrigues <jdrodrigues@...>

🔗Daniel Wolf <djwolf1@...>

🔗Alexandros Papadopoulos <Alexmoog@...>

🔗George D. Secor <gdsecor@...>

🔗Paul Erlich <perlich@...>

🔗Daniel Wolf <djwolf1@...>

🔗George D. Secor <gdsecor@...>

🔗George D. Secor <gdsecor@...>

🔗Gene Ward Smith <gwsmith@...>

🔗Gene Ward Smith <gwsmith@...>

🔗Joseph Pehrson <jpehrson@...>

🔗Joseph Pehrson <jpehrson@...>

🔗Joseph Pehrson <jpehrson@...>

🔗Joseph Pehrson <jpehrson@...>

🔗George D. Secor <gdsecor@...>

🔗Paul Erlich <perlich@...>

🔗George D. Secor <gdsecor@...>

🔗Paul Erlich <perlich@...>

🔗Gene Ward Smith <gwsmith@...>

🔗Joseph Pehrson <jpehrson@...>

🔗Joseph Pehrson <jpehrson@...>

🔗Joseph Pehrson <jpehrson@...>

🔗Joseph Pehrson <jpehrson@...>