Young

Has anyone heard the recording of Young's Well-Tuned Piano? I've
never been able to find it at stores and it's a bit of an
investment at 5 discs. What's it like?
!#%$!#%$!#%$!#%$!#%$!#%$!#%$!#%$!#%$
#@#@^%#@#@^%Erik Nauman(*%&%(*%&%(*%&%
%&$*^%&$*^%&$*^%&$*^%&$*^%&$*^%&$*^
The Rice School/La Escuela Rice
Houston

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Brian says:
> Gary Morrison stated recently that he judged this tuning
> forum a place for recitations of personal experience

Actually my comment regarded what does, rather than what should, get
discussed here. I suggested mostly that Brian's concern that Paul Rapoport
rarely quotes from Xenharmonikon, is perhaps better stated that only a handful
on this tuning list quote from anywhere.


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From: mclaren
Subject: Using the harmonic series in music theory courses
--
Neil Haverstick has as usual greatly contributed to the
discouse of this forum with his extremely perceptive
comments. In particular, Neil's suggestion that the harmonic
series be used as the basis of teaching music theory (rather
than the current peculiar combination of Guidonian hand
mnemonics, Naziistic intimidation, and Orwellian
"rewriting" of musical history to eliminate any trace of
evidence for past use of non-12-TET) is an excellent one.
It's obvious, however, why there's MAJOR resistance to
this method of teaching music theory. Once the sacred 12
tones get the heave-ho, the entire edifice of the modern
concert hall & "music appreciation" classical CD
racket starts to crumble & collapse.
In a lecture at UCLA in 1966, Harry Partch said "It has been
stated in public print that if my ideas were to become
dominant in music courses, music as we know it would
cease to exist."
Harry was, as usual, correct. Teaching music on the basis
of the harmonic series would detonate "music as we know it"
like a .357 hollow-point slug blowing apart a rotten
watermelon.
The current generations of music theory "experts" would flail
like insects stuck in yogurt, unequipped for and unable to
deal with ear-training or composition or analysis of non-12
music. Almost every Ph.D. in the most prestigious music departments
& the most sainted conservatories throughout the land would
be summarily ejected as grossly incompetent (except in the
tiny subspeciality of 12-TET composition & performance).
Uh...something tells me this ain't gonna happen without a
struggle, Neil.
The outrage that has already resulted from my standard talk
about the facts of music history can scarce be described.
When author after respected author of respected music history
texts is revealed to be ignorant of the actual realities of
intonation in any given period of musical history, many in the
audience lunge to their feet with tears of indignation gleaming
in their eyes.
Not a pretty sight.
Telling the truth in public is one of the hallmarks of a degenerate
mind & a depraved sensibility, and would create untold chaos
throughout the university system were it to become common
practice in teaching music history, music theory, or contemporary
composition.
Indeed, those few students who've already been exposed to some
of the actual scientific research on how the ear non-linearly
warps and distorts perception of melodies, intervals, rhythms,
time and silence in music (students of Warren Burt's psychoacoustics
course at ACAT in Australia) have reportedly staggered away brain-
boggled and bushwacked, mind-blown & aghast.
This is *not* the way to maintain the status quo, Neil.
Such students wind up producing music that's (gasp!)...
imaginative. They end up demonstrating (may the gods save
us)...enthusiasm.
Ever since the trial of Socrates, enthusiasm and imagination
have been well-known as the most heinous crimes
an individual can commit against the state.
Yet now you propose a method of teaching music which would
encourage these qualities...?
This won't do, Neil!
It simply won't do!
--mclaren



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Brian's and Neil's advocacy of a new direction in music theory instruction
is certainly welcome. I have taught the harmonic series in music theory,
computer music, world music and other classes whenever I have been able to.
And, despite Brian's characterization of university professors as a
monolithic bastion against such ideas, I know of other professors who also
think that a revision of standard music theory curricula is long overdue.
But there are problems:

1) Large-scale revisions of multi-semester sequences taught by different
people are very difficult to implement (especially by young, untenured
instructors). If the semester 3 instructor is expecting the students to
know what a Neapolitan sixth is, then that's something the semester 2
instructor is obliged to include. Enough of these obligations and there's
little time left for the harmonic series. There may also be connections and
expectations outside of the sequence, with music history classes for
example. The difficulty of forging a very new consensus is certainly part
of what gives academic institutions their reputation for conservative
inertia.

2) Let's not forget the students. In my (admittedly limited) experience,
they come in three basic flavors:
a) The students who are basically non-music majors who are mainly
interested in learning to read music, understand chords, and know harmonic
progressions well enough to write their own pop songs. A few of the more
technically-minded find the information on the harmonic series interesting,
but ultimately useless for their purposes.
b) The students who are mostly music majors who are mainly interested in
spending time in the practice room and understand that they have to go
through the drudgery of recreating Bach chorales before they can graduate.
Some are interested in understanding the way the music they play was
composed, but many don't really care to know the compositional significance
of a particular unusual chord in the Brahms piano piece they're playing,
let alone the harmonic series.
c) The really insightful ones who want to know the fundamental basis of
their art and have the creativity of thought to try to apply this knowledge
in beautiful and innovative ways. In my experience this type of student is
a happy, but all too uncommon, find.

I'm not really trying to bash students. Like all of us, they have certain
goals in their lives that drive their decisions. Very often they don't see
how things like the harmonic series serve those goals (and in many cases
they are right). I don't think that university educators should necessarily
pander to them, but I think it's unrealistic to expect a music school to
completely flaunt the students' educational goals and instead force another
curriculum on them.

I agree that the time and attention devoted to the minutiae of harmonic
practices of European art music in the eighteenth and nineteenth centuries
in most music programs is seriously disproportionate. In my opinion, much
of that time would be better spent on tuning systems, acoustics, and music
of other cultures and traditions.

I don't want to give the impression that the situation is hopeless either.
These concepts can be given limited exposure in standard classes, much more
exposure in classes outside the regular curriculum, and even more through
personal contact with enthusiastic, intelligent students.

Bill

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^ Bill Alves email: alves@hmc.edu ^
^ Harvey Mudd College URL: http://www2.hmc.edu/~alves/ ^
^ 301 E. Twelfth St. (909)607-4170 (office) ^
^ Claremont CA 91711 USA (909)621-8360 (fax) ^
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^




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I seem to recall somebody saying the Paul Hindemith professed to teach
composition in terms of the harmonic series, although (as far as I know)
strictly within the 12TET system.

Anybody know any more on that?


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I found Bill Alves' comments on innovation in University Music education a
welcome dose of realism. It's good to hear an insider's take on where some of
the difficulties lie. Even though my formal Music education (beyond untold
hours of private lessons and reading on more advanced topics) stops at the
traditional Freshman and Sophomore Theory and Ear-Training classes, I've seen a
lot of what Bill's mentioned from a student's perspective. Many of us have I'm
sure.

One factor in all of this that I find encouraging, perhaps surprisingly or
even ironically, is community colleges. They have some advantages over
full-blown Universities with regard to innovative curricula:
1. In most US states anyway, they are paid by enrollment, so they are always
scrounging for ways to keep students' interest rather than to weed them
out.
2. They have somewhat less pressure to provide specific knowledge to feed into
Junior- and Senior-level courses.
3. A fair percentage of their student body consists somewhat older adults who
are taking music (or whatever) courses simply because they want to, rather
than to begrudgingly fill some required slot in the curriculum.
4. Most community colleges have fewer distractions (football for one, but
let's not get into that!).
5. Since they lack the tenure system, they're a little more open to hiring
innovative instructors.

Of course, they have disadvantages as well, especially the overall quality of
student (and instructor to a fair degree) they attract. Some are quite good
though, my bassoon teacher back in high school was one.

Well, it's something to bear in mind anyway.


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I am under the impression that the main reason for our usual higher-education music curricula to devote 4 semesters to
tonal harmony is the bulk of the greatest music ever composed can be described in terms of tonal functions or modal relations.
This attitude is the natural consequence of a causal relationship where the great works are first and the theoretical interest
afterwards.
It would seem equally natural, then, that there is no interest for a generalized practice of educating music students in
the *how-to*s of some "exotic" intonation systems for which there is no significant corpus of real masterpieces. So again, it
seems to me that our local American educational establishment's lack of concern (with some exceptions here and there) for
disseminating alternative intonations through its channels is a valid statement that asserts the perceived irrelevance of the
subject in relation to music as a body of --mostly modal and tonal-- compositions. In other words, maybe alternative intonations
will receive some attention when there is a large body of concerned compositions, including, of course, many significant
masterpieces. Now, I don't necessarily thrive in this state of affairs, but I have to recognize that this is a valid (if
generally just quietly unstated) view ... --certainly not illogical, or some sort of evil conspiracy like Brian seems to imply
sometimes (though, as I have said before we should take Brian's rhetorical fireworks with a grain of salt, i.e., assume that his
form is an emphatic way to get you to his content ... ).
Enrique Moreno

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Enrique Moreno wrote:

> I am under the impression that the main reason for our usual
>higher-education music curricula to devote 4 semesters to
>tonal harmony is the bulk of the greatest music ever composed can be described
> in terms of tonal functions or modal relations. ...
> It would seem equally natural, then, that there is no interest for a
>generalized practice of educating music students in
>the *how-to*s of some "exotic" intonation systems for which there is no
>significant corpus of real masterpieces.

I disagree strongly with these statements. First, I don't believe that "the
bulk of the greatest music ever composed" lies within the last 300 years or
so of Western European culture. When the world's music is viewed as a
whole, certainly ideas such as tonal harmony, 12TET, and counterpoint are
the "exotic" concepts. Even within this tradition, harmony is only one
aspect of theory, and yet it absolutely dominates our curricula. (Certainly
one reason for this dominance is that it has nice, objective rules that can
be taught in a textbook and graded.)

I try to teach my students that THERE IS NO "corpus of real masterpieces."
I teach certain pieces because I happen to like them and because they
provide good illustrations of the concepts I need to get across. I
encourage all students to make their own decisions about the "masterpieces"
that they like. My job is to get the students to understand pieces, and
perhaps come away turned onto a piece or type of music that they were
previously unaware of, or to see an old favorite in a new light.

Finally, I don't teach tuning systems so that students will understand
Harry Partch, for example, or other composers who use "exotic" intonation
systems. I teach them because they are a fundamental part of all
pitch-based music. I much prefer to teach the "whys" that lie behind even
common-practice theory (as far as is known) than to have students memorize
chord spellings and rules.

For example: Why is singing in parallel octaves not considered polyphony?
Why is an augmented chord dissonant, if all its component intervals are
consonant? What is the meaning of the title The Well-Tempered Clavier? Why
does a string quartet suddenly have to adjust in a common-tone modulation
to some foreign keys? Each of these questions, perhaps trivial in
themselves and easily ignored by a theory instructor, betrays a lack of
understanding of the harmonic series and tuning systems.

Bill

^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
^ Bill Alves email: alves@hmc.edu ^
^ Harvey Mudd College URL: http://www2.hmc.edu/~alves/ ^
^ 301 E. Twelfth St. (909)607-4170 (office) ^
^ Claremont CA 91711 USA (909)621-8360 (fax) ^
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^




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From: mclaren
Subject: Several more worthwhile papers
--
The journal "Music Perception" , Winter 1984, 2(2),
pp. 131-165, carried the article "Tonal Schemata
in the Perception of Music in Bali and in the West,"
It's an interesting paper, but not nearly as useful as
you'd imagine from the title--alas.
The authors confined themselves to extremely
low-level questions as: How well can Balinese
listeners identify the place of a missing western
pitch in a western scale as opposed to how well
a western listenre can identify the place of a
missing gamelan pitch in a gamelan scale?
The Balinese audience memebrs tested were
reportedly members of a remote village with
no previous exposure to western music. This
sounds unlikely on the face of it, and one is
inclined to question the study on that basis.
Nonetheless it's worth reading.
>From Music Perception, Winter 1984 , 2 (2),
pp. 245-264, the article "Studies in Musical
Cognition: Comments from a Music Theorist"
offer some enlightening criticisms of current
higher-level experiments designed to elucidate
elements of human melodic and harmonic
audition.
"A great many of the difficulties in psychology
experiments have come from an ignorance of or
naivete wth regard to tonality. Four examples
will be given.
"First, length was assumed until recently to
be an important factor in both the `memorable-ness'
and the `tonal-ness' of tunes; longer tunes carried
more information than short ones. This has been
shown to be a false assumption."
You'd think this was obvious. Yet it seems to have
come as a revelation to music cognition researchers.
C'mon, guys! Obviously Mozart's 41st symphony 1st
movement theme, while *long*, is *easy* to remember,
whereas the much *shorter* theme of the first
movement of Webern's symphony is obviously vastly
*harder* to remember. Has anyone heard of the words
"implied harmonic cues" and "tonal landmarks"?
Jeez.
"Second, so called `tonal' tunes have thus far for
the most part been defined simply as those
consisting of pitches drawn from some major-
mode diatonic collection, whereas `atonal' tunes
are obtained by drawing random pitches from the
12-tone chromatic collection. The notions that
tunes could be diatonic but only weakly tonal
or chromatic but also tonal have only begun to
be articulated and refined."
Yow.
You'd think this would be obvious.
Listening--that's the key, folks. Ya gotta *listen* to those
psychoacoustic test melodies before you use 'em...
"Third, in music the relationship between frequency
(pitch) distance and function distance is a
complex one..." Again, a very clearly obvious
point--pitches a 12-TET semitone apart represent
opposing harmonies even though the notes are
melodically close, while pitches 7 12-TET semitones
apart represent harmonies close together even
though the notes are melodically distant.
Duh.
Yet researchers are only now catching onto this...?
"Fourth, tunes in the psychological literature,
whether tonal or atonal, are still all too often
characterized as sequences of signed note-to-note
intervals. Few notions of melodic structure
(certainly none based on a well-founded theory
of implicit harmonic structure) have emerged."
[Hantz, E., "Studies in Musical Cognition: Comments
from a Music Theorist," Music Perception, Winter
1984, 2(2), pp. 245-264.]
These objections seem to explain very clearly why
much of the current psychoacoustic and psychological
and music cognition research in microtonality has
failed so miserably to produce results as revelatory or
enlightening as simply LISTENING TO NON-12 MUSIC.
In study after study, otherwise reliable reserachers
like Carol Krumhansl come to obviously wacky
conclusions about such tunings as 48-TET, 19-TET,
36-TET, etc.
The reason for these obviously wrong concusions is
that the researchers assume [1] that melodies in
other tunings must exhibit the same melodic
structure as 12-TET; and [2] melodies in other
tunings msut exhibit the same implied harmonic
structure as 12-TET, with identical modes,
etc. etc.
Ivor Darreg pointed out long ago, as did Easley
Blackwood, that other tunings often turn the
rules of western harmony *upside-down.* Some
tunings require that major thirds be treated as
unstable dissonances which resolve DOWN until
major seconds (17-TET) or UP into perfect
fourths (Pythagorean ji). Some tunings require
that the fifth be treated as a dissonance (13-TET,
18-TET, 23-TET, many of Erv Wilson's higher-order CPSs),
while other tunings require that the fifth be treated
as a consonance (22-TET, standard-limit ji arrays).
In some tunings root progression by fifths produce
the most powerful and convincing cadences (19-TET,
7-limit ji) while in other tunings root progressions
by other intervals produce the most powerful and
convincing cadences (some of Erv Wilson's higher-
level CPSs, 15-TET, varius non-just non-equal
tunings like the metal tube scale or the free-free
metal bar scale).
This explains why Krumhansl and other respected
researchers keep "discovering" that 12-TET is "the
best tuning" for melodies. When you measure everything
by a 12-TET yardstick, 12 looks best.
You'd think that none of this would be controversial
or astonishing, yet these ideas seem to wallop
the psychoacoustics community with the force of
divine revelation. These folks are only now
slowwwwwwwwwwwwwwwwwwwly awakening
to the idea that you can't usefully measure non-12
melodic or harmonic properties according to 12-TET
melodic and harmonic standards.
Wow.
What a surprise, eh?
Incidentally, these same considerations explain why
Markov-chain analysis produces junk when you use it
to analyze a piece of music and then compose an
algorithmic piece. Markov chains are blind to the
the melodic contour, the implied harmonies, the
sense of balance and unbalance, of parry and riposte
in a melody. In this regard Larry Polansky's morphological
metrics represent a major advance--so, naturally, no
psychoacoustical researcher has yet employed Larry's
breakthrough concept in any tests of microtonal melodic
perception.
--mclaren


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From: mclaren
Subject: "The Art of Noises"
--
Came across the book "The Art of Noises" by
Luigi Russolo. "Translated from the Italian
with an introduction by Barclay Brown." Pendragon
press, New York, 1986, Monographs in Music No. 6.
This book is a collection of short essays written
by the Italian futurist Russolo.
Creator of the orchestra of noise-makers known
as intonarumori, Russolo is one of the founts
from which springs modern music.
(Great names for the instruments: "Sobbers," "wailers,"
"shriekers." Sort of like the New Yorker music critic
at one of Johnny Reinhard's concepts.)
It is less well known that Russolo was a radical and
persistant microtonalist.
In the paper entitled "The Conquest of Enharmonicism,"
Russolo sets forth explicitly his dissatisfaction with
12-TET and his militant advocacy of UNtempered
harmonic series-based tunings.
"After the introduction of the tempered system
in music, only the word Enharmonicism remained
to indicate the values that no longer found corres-
pondence in musical reality. Indeed, the difference
between an E sharp and an F, and a B sharp and a C
are called enharmonic, while the tempered system,
in rendering the semitones equal, has removed this
difference and made the two notes into the same
sound.
"But unfortunately, the inconvenient result of the
tempered system does not lie only in the word.
Once that the octave was divided into only *twelve*
*equal* fractions and applied in the tempred scale,
there resulted a considerable limitation of the number
of practical sounds and a strange artificiality in
those that were adopted. The difference between
the scale of the tempered system and hte natural
one are well known. (..) With wind instruments,
which produce the harmonic series of the fundamental
note, the 7th, 11th, 13th and 14th harmonics are
likewise corrected in their intonation to produce what
we call closed sounds.
"In the tempered system, therefore, the difference
between the large and small whole tone (9/8:10/9 = 81/80)
has disapperaed. Similarly, the differences between the
diatonic semitone (16/15) and the chromatic ones (23/22
and 25/24) has also vanished. (..)
"A tempered harmonic system can be compared in a sense
to a system of painting that abolishes all the infinite
gradations of the seven colors (red, orange, yellow, green,
blue, indigo and violet) and accepts only their type of
color, having only one yellow, one green and so on."
This is a remarkable passage. It almost exactly
parallels several passages from Harry Partch. In
"A Quarter-Saw Section of Motivations and Intonations,"
Partch talks in almost exactly the same way about
a rainbow of colors being collapsed down into dull
simplistic hues.
Moreover, it's clear that Russolo knew very well the
intricacies and advantages of just intonation, and that
he thought the so-called natural (read: harmonic series-
based) tuning superior to the tempered one.
It's interesting that when this debate between harmonic-
series-based and expanded equal-temperament (viz.,
48-TET, 41-TET, 72-TET, etc.) occurred in Russia between
1917-1928, the Russian expanded equal-temperament
faction won out. But when this debate occurred in Italy
between 1917-1928, the Italian futurists made the
fascinating choice of chucking tonality entirely in
favor of noise. During the same period in Germany,
Schoenberg resolved the debate by chucking tonality
in favor of an elaborate scheme of statistically
distributing the familiar 5-limit equal-tempered
12 pitches. In Mexico, Novaro and Carrillo resolved
this debate by choosing the Russian option but using
live acoustic instead of electronic instruments.
Thus the claim that "Schoenberg solved the dilemma
of the exhaustion of tonality" is untrue, insofar as
MANY solutions were implemented in various different
countries. The only solutions which survive to this
day are the Russian one (represented today by folks
who compose & perform microtonal music on synthesizers)
and the Mexican one (represented today by folks who
compose & perform microtonal music on acoustic
instruments.)
Needless to say, the German "solution" to the exhaustion of
12-TET tonality didn't last beyond 1978, and post-Webern
serial composition is now a dead art form with no attraction
for contemporary composers.
Clearly, someone should do a 1/1 article on Russolo
& his advocacy of ji as an Italian solution to this problem.
--mclaren


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From: mclaren
Subject: construction of a 19-tone m'bira
--
The Sonic Arts Gallery is constantly boiling with
new ideas and plans for new instruments, so it
came as no surprise when Jonathan Glasier began
work on a 19-tone m'bira.
Patterend after Bill Wesley's "array m'bira," this
instrument is to an african thumb piano as a 747
is to the Wright brothers' biplane.
Bill Wesley's "array" arrangement of tines places
consonant intervals closest to one another, while
putting dissonant intervals far apart. Thus if you
stroke the tines of one of Bill's m'biras at random,
you get a set of fifths, rather than a jangle of
semitones.
This has had some interesting effects when
translating the "array" into 19 tones to the octave.
Originally designed by Pythaogrean intonation,
the 2-D "array" of crisscrossing 5th and 4ths
seems to accomodate well the 19-tone system.
No doubt this is because 19 boasts fine fifths,
only 7 cents flat of the just 3/2. The array would
probably also work as a keyboard arrangement for
17, 22, 27, 29, 31, and most of the other equal
temperaments with good fifths.
The real surprise, though, is how close this
microtonal acoustic instrument sounds to its 12-TET
cousin. The 19-tone equal tempered scale truly is
the first step outside 12.
--mclaren



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From: mclaren
Subject: Randy WInchester's remarkable
collection of microtonal compositions
--
Some months ago one of the forum subscribers
sent me a remarkable tape. It contained
compositions in every equal temperament
from 7 through 23 tones per octave, except
for 18 and 16.
This collection of compositions seems to me
one of the best such collections ever done.
It's outstanding.
What makes the collection even more noteworthy
is the fact that it was done on an "obsolete"
analog synthesizer. Oddly enough, this gives
the recordings a certain sonic sheen not present
in sequaky-clean digital timbres.
Overall, Randy's collection is remarkable and
I've listened to it more than half a dozen times.
Other forum subscribers (to whom I've sent
copies with Randy's permission) agree.
If there's any justifce in the world, Randy's
collection will be issued on commercial
CD or cassette.
For my mney, it's right up there with Easley
Blackwood's and Ivor Darreg's collections.
--mclaren


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From: mclaren

Boomsliter and Creel are well known for their provocative
papers "The Long Pattern Hypothesis in Harmony and Hearing"
and "Extended Reference."
However B&C wrote three other readily available papers
which might also prove of interest.
"Hearing With Ears Instead of Instruments" dates from 1970
and was published in the Journal of the Audio Engineering
Society in August 1970, Vol. 18, No. 4, pps. 407-412.
This articles offers little new information, but it does
give important background on B&C's ideas and motivations
behind their "extended reference" work. Of particular
import: B&C's emphasis on the ear as a non-linear
receiver. "The Seashore team [8] at Iowa found that
intonation is not a simple matter. Singers and violinists
who are free to choose their tuning do not use any one
scale. They make systematic departures in tuning,
and these vary from melody to melody." [pg. 408]
In any case this article will doubtless prove of interest
to those fascinated by the thought processes that
gave rise to Boomsliter & Creel's "extended reference"
hypothesis.
"Time Requirements For the Tonal Function" is a letter
to the Journal of the Acoustic Society of America which
emphasizes the experimental data in favor of the
periodicity hypothesis of hearing.
This article is of slightly less interest. We now know
that no one model of human hearing is supported by
all the evidence, and some evidence contradicts all
3 major competing hypotheses about human hearing.
The third and last article, "Research Potentials In
Auditory Characteristics of Violin Tone," by
Paul C. Boomsliter & Warren Creel, was published
in the Journal of the Acoustical Society of America,
Vol. 51, 1969, Number 6 (part 2), 1972, pp. 1984-
1993.
B&C point out that violin intonation is not easy
to quanitfy since "the doctrine that frequency
governs pitch, virtually alone, and that partial-tone
structure governs quality, virtually alone, does apply
to notes studied in solation, but in melody every note
of the melody participates..." [pg. 1992]
B&C cite experimental data from the brains of
anaesthetized cats (!) showing that "an incoming
signal evokes generation of temporally patterned
recurrences (..) The normal human nervous system,
with many neurons responding only to a change, is not
a steady-state apparatus, yet it uses temporal
recurrence with an appetite for regularity. Human
preference for regularity and change can be observed
when a master plays a violin which is thus
physiologically controlled." [pg. 1984]
This view of memory is likely over-influenced
by the view of the brain as an electrical circuit
(popular during hte 60s and 70s), whereas it is
now known that many different varieties of
neuotransmitter molecules also play a role in
the operation of the brain, and that some
neurotransmitters act to prevent other
neurotransmitters from having an effect at
receptor sites in the brain.
Regardless, the article may prove of interest
as a discussion of the potential real-world
applications of B&C's "extended reference"
hypothesis (viz., performance of a solo
melody on a violin).
--mclaren



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From: mclaren
Subject: combining different tunings simultaneously
--
In Topic 2 of Digest 706 William Alves wrote:
"I also wonder what, exactly, is Brian's dividing point for deciding when a
tuning is a combination of tunings? It doesn't seem to me to be a
straight-forward question."
This strikes me as an extremely insightful comment by Bill Alves.
Theoretically, meantone tuning is a combination of tempered and
just intervals--so theoretically it ought to be heard as a combination
of two types of different tunings. But it never sounds that way to
these old ears.
The issue of categorical perception is an important one. There's a
well-known range within which intervals can be "mistuned" yet
still heard as members of the scale.
Lastly, there's the issue of combining separate tunings as whole
entities, each of which boasts its own internal structure.
When combining 7/oct and 5/oct, for instance, the result does
not sound to my ears as though it's two different small equal
temperaments. Rather, it sounds like a gapped subset of 35/oct.
However, in a composition which combined 15/oct and 17/oct
my ears heard 17/oct alternating with 15/oct in a regular way.
The first composition used a piano timbre, though, while the second
used timbral and registral alternation to keep the tunings audibly
separate, so this might not be a fair test.
Na'theless, my experience is that when two relatively simple
tunings are combined simultaneously, the ear often preceives
them as a single complex tuning.
The reasons why this will occur under some circumstances,
while it doesn't occur under other circumstances, remain obscure.
This suggests that it is not obvious how a 24-tone subset scale
embedded in a 72/oct composition will be heard. Timbre, rhythm
and tonal fusion will almost certainly play a part, along with
tessitura and dynamics.
--mclaren


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From: mclaren
Subject: Jacques Dudon's new JI CD
--
Jacques Dudon is a French composer who uses
patterned glass disks to generate music.
By spinning the disk and shining a light through
it onto a photoreceptor, Dudon is able to produce
periodic waveforms which become audible (when
amplified through a loudspeaker) as timbres.
Dudon's instrument has been featured in the journal
"Experimental Musical Instruments" on many
occasions.
By moving a slotted scrim between the light source and
disk, any by moving from the inner to the outer section of
the disk & vice versa, he is able to produce series
of pitches.
Now Jacques Dudon has come out with a CD of his
music.
The CD is called "Lumieres Audibles" (Audible Light)
and it consists entirely of just intonation music.
You might think that music created in this way would
be synthetic-sounding and fairly dull. Just the
opposite.
For many years, Dudon has been working with a computer
to generate exotic patterns for his spinning photo-acoustic
disks, and he now has a collection of some 500 of 'em.
Morevoer, he uses fractal patterns to generate fractal
waveforms along with irregular Walsh-series slotted
disks which produce extremely evanescent and organic-
sounding timbres.
"Lumieres Audibles" is remarkable, both for the quality of
the timbres and the artistry of the compositions.
The sounds on this CD are hard to describe. They sound
akin to some of the more sophisticated timbres that
can be produced with an anlog synthesizer, but more
ethereal and in some cases more "digital-sounding" than
standard analog timbres. In other cases, particularly
the fractal waveforms, Dudon conjures up timbres whose
only close relatives are timbres generated by elaborate
computer algorithms.
Jacques favors a tuning system which makes his pieces
sound middle eastern; he also uses drones, drum-like
timbres, and repeated tabla-type patterns generated from
interfering and cross-rhythmed slowly rotating glass
disks. (Dudon apparently uses some disks as "sequencer
disks" at a slow rate of rotation, and other disks as
"timbral" disks rotating much faster. By using 6 or
7 different photodiodes and rotating disks, along
with volume pedals to switch between the different
timbres/sequences, Dudon can produce sonic tapestries
of remarkable subtlety and sophistication.)
For more about Dudon's just intonation tunings, see
the 1/1 article "7 Limit Slendro Mutations," Vol. 8,
No. 2, 1994.
This CD is *highly* recommended.
You can order one of these CDs from Jacques Dudon
at Atelier d'Exploration Harmonique - les Camails,
83.340 LE THORONET - phone number 94.73.87.78
--mclaren





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From: mclaren
Subject: MusicWorks 64 CD
--
As some of you may know, Gayle Young is a Canadian
just intonation composer who builds her own JI
instruments, performs in multimedia dance spectacles,
raises a kid, and runs the best new music magazine in
Canadia.
Along with the magazine MusicWorks, subscribers can
opt to receive a MusicWorks CD containing recordings
of compositions by the composers featured in each
issue.
For MusicWorks 64, Gayle Young's own JI compositions
'Harmonium' for string quartet is featured.
This is a splendid piece of music, full of exotic and
vibrant high-limit just intonation chords.
Ms. Young is a fine composer, and it's splendid to be
able to hear her work on CD.
My main complaint is that the piece is too short!
In any case, both the magazine MusicWorks (which often
features xenharmonic composers and their work) and
the MusicWorks 64 CD is *highly* recommended.
[P.S.: MusicWorks 60 contains the single finest
explication of Erv Wilson's CPS method of scale
generation, along with nonpareil photos of geometric
models and diagrams by Erv himself. The article is
"Just Shape, Nothing Central" by the nonpareil Paul
Rapoport. This article is a *must-have* for anyone
interested in non-12 tunings.]
Back issues and back CDs/cassettes of MusicWorks
are available from:
MusicWorks
179 Richmond Street West
Toronto, Ontario
CANADA M5V 1V3
Telephone 416-977-3546
Fax 416-204-1084.
--mclaren


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From: mclaren
Subject: Indian music
--
"Intonation in Present-Day North Indian
Classical Music" by N. A. Jairazhboy and
A. W. Stone, BUlletin of the School of
Oriental and African Music, 1963, pp.
119-132, raises some interesting
evidence about Alain Danielou's claims
that North Indian music is based on
just intonation.
Jairazhboy measured the intervals
sa-re, re-ga and sa-ga in recorded
performances of various ragas. From
this information (gleaned by examination
of oscillograms), he concluded that
modern Indian music does not make use of
the 22 microtonal srutis which in various
Sanskrit texts are described as the basis
of Indian music.
Did Jairazhboy dispose adequately of the
errors introduced by changes in the motor
driving the film through the oscillograph
camera, or the changes in speed of the
tape recorder motor?
Hard to say. He claims to have done so,
but I've got my doubts.
Moreover, he makes some brash claims:
"The ready acceptance and popularity of the
keyboard insrument, the harmonium, as an
accompiment to the voice, should be
adequate proof that the North Indian
octave is, in fact, divided into 12 semitones."
This doesn't parse.
It could equally mean that North Indian
popular music is being Westernized, or it
could mean that audiences tolerate a distortion
of the "correct" sruti-derived svaras for the
convenience of chords offered by the harmonium,
just as the wide acceptance of the awful-sounding
Hammond organs was due largely to issues of
cost and conveience, rather than the excellence
of their tone quality.
In the same way, it has been shown by record
company surveys that audiences will consistently
prefer a mediocre performance of a classical
work recorded in a studio to a superb performance
of a classical work recorded live with coughs and
sneezes disrupting the listerner's attention.
There seems to be a huge amount of controversy
surrounding the intonation of North Indian music,
and time hasn't dispelled it.
Regardless, Jairazhboy concludes: "In view of the
findings in this paper, is seems unlikely that
musicians would play these fine [just] intervals
consistently and accurately enough to form the
basis of any such theory, and that this interpretation
is closer to fiction than fact." [pg. 132]
This 1963 article is worth citing because, remarkably,
it's one of the few objective measurement *by an
Indian* of the intonation of North Indian music (in
English). Virtually everything that's been done wrt
the intonation of North Indian music is either by
white guys or non-quantitative and largely subject
to varagaries of the researcher's opinion.
How about it, folks?
Isn't it time for some new quantitative studies of the
intonation of North Indian music with modern equipment?
--mclaren



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From: mclaren
Subject: Raga pitches
--
In Tuning Digest 712, Bruce Gilson mentions:
"The book "Ragopedia" was mentioned on the digest of the 10th of last
month. I've seen it, and unfortunately it is next to useless for tunings.
Everything is reduced to normal scale notation, with no clue as to which
notes are to be played sharper or flatter than 12-tET."
Thanks for the info, Bruce.
Alas, this accords with my suspicions.
My experience in perusing Western books about Karnatic Indian music
is that Western authors almost universally assume that the ignorant
Indian musicians are trying to play the Western diatonic scale and
getting it just a bit wrong, poor dears. The "errors" are generally
"corrected" by writing down the pitches in standard Western
notation.
This appears to have had untoward results. To wit, Carol Krumhansl
has written an article in which she makes the amazing claim that
"the seven pitches of the Indian scale are identical to the
pitches of the Western diatonic scale."
If you have some CDs or cassettes of Karnatic Indian music
lying around, you might want to give 'em a listen. Ask
yourself whether Carol Krumhansl knows what she's talking
about.
Inasmuch as Krumhansl is a purportedly reputable researcher
who is thought to have done some significant work on
music perception and cognition, this is not a trivial
issue.
--mclaren



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From: mclaren
Subject: Xenharmonic melodic theory vs. harmonic theory
--
In Tuning Digest 715 James McCartney suggested:
> It seems to me there is too much discussion of pitch sets, and scales
> and not enough on harmonic progression and voice leading which seems to
> me to be the more interesting problem. I mean, just choose the pitch set
> you like and be done with it! -- James McCartney
This is one opinion.
Another opinion is that western music theory is already overburdened
with theories of harmonic progression and voice leading. After
a thousand years of obsessing over harmony to the utter exclusion
of melodic theory, it seems to me long past time to concern ourselves
with horizontal structures.
Clearly, James McCartney has another opinion--and quite a lot of
justification for it. Harmony has traditionally be considered a
more fundamental subject for music theory than melody.
The question is whether this notion is valid.
There is at least one musical culture which elevated melodic theory
far above harmonic theory: classical Greece.
As best we can ascertain, the Greek thought melodic theory infinitely
more fundamental to music than the theory of vertical intervals.
Were the Greeks right or wrong?
No way to tell. The question may not even be meaningful, given the
iridescence and multidimensionality of the act of composing music.
In the meantime, I shall continue in my posts to emphasize
melody over harmony, the better to redress the long-standing
theoretical imbalance twixt the two.

--
Also in Tuning Digest 715 McCartney posted:
> I came to this list because I was interested in compositional ideas arising
> out of tuning. I don't think I've seen one article that got past selecting
> the notes. -- James McCartney
McCartney may not have seem 'em, but many *many* such posts exist.
About a year ago I posted a long series of compositional ideas and
compositional techniques for non-12 tunings. Warren Burt has also
posted many such ideas, as have other forum subscribers. Gary Morrison
has posted quite a few discussions on xenharmonic composition.
It might be advisable for newer subscribers to read over past digests
before they post. People who've been on this forum for some time
would probably not appreciate it if I (or others) were to continually
re-post old messages for the benefit of the newer subscribers.
If James can't find those older posts on compositional ideas &
techniques in non-12 tunings, I can easily re-post them, however.
If there's sufficient interest, I can also post articles by Ivor Darreg
on compositional techniques in various non-12 intonations. Ivor
was a vertibale fountain of new ideas for xenharmonic composition,
and his articles on the subject are a "must-read" for budding
xenharmonists.
--
Also in TD 715, Greg Scheimer asked for Csound compositions
in non-12 intonations. I have a few of 'em, but they're long--
in excess of 100 kilobytes of ASCII. Thus it seemed inadvisable
to post them on the Mills ftp site, since Dave Madole is already
fighting the Attack Of The Files That Ate My Disk.
Another issue supervenes, however:
Many of the subscribers to this forum have done non-12 Csound
compositions, but they're reluctant to give out scores for
copyright reasons. I myself requested a number of subscribers
to post Csound scores of their microtonal computer music
compositions.
Every single composer demurred, citing copyright concerns.
--mclaren


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It is also well documented that stretched octaves are preferred to just
octaves. But all these studies tend to focus of melodic rather than harmonic
intervals, or else tones with weak harmonics. The fact that "stretched"
intervals are preferred to just intervals in a context where beating between
partials is not the most prominent determinant of consonance may indicate
that Terhardt's hypothesis about a "stretched" harmonic template is correct.
The ear, when presented with a multiplicity of pure tone components (in
Parncutt's version, the prenatal ear hearing the mother's voice), is known
to slightly stretch the intervals between them, and one hypothesis is that
this stretching is "expected" even when a meager stimulus is presented.
Goldstein studied the precision with which frequency information is
transmitted by the brain's central pitch processor by measuring residue
("virtual") pitches produced by two pure tones, but I think his approach
assumed symmetrical errors and did not pay attention to systematic biases in
the allowable mistuning of the pure tones. I wonder if such a study would
reveal that judgments of harmonic relationships are easier to make when the
distances are stretched somewhat. In any case, it may be a case of the
archers aiming for the bullsye, but a steady wind blowing the arrows off
course. The aesthetic of stretched intervals must be somewhat compromised in
practice: phenomena such as second-order beating and combination tones can
be disturbing for significant departures from harmonicity.

The "small integers" concept of consonance that McLaren "disproves" is a
rather extreme, Partchian version. Which is more consonant, 300001/200000,
or 11/9? While the former clearly involves larger integers, it is also very
close to 3/2, and is likely to be heard as such. He also extends the small
number theory to chords of more than two notes, where the use of frequencies
vs. periods can determine which chord is calculated to be more consonant.
Observe:

Frequencies:

Major - 4:5:6
Minor - 10:12:15
Suspended - 6:8:9

Periods:

Major - 10:12:15
Minor - 4:5:6
Suspended - 6:8:9

Using either frequencies or periods, the suspended triad comes out in
between major and minor; the fact that the suspended triad is more dissonant
is related to the fact that when the intervals are looked at individually,
it requires higher numbers. Moreover, McLaren seems to love neutral thirds
and hate tritones; I have to strongly disagree with his consonance judgments
here. But consonance is a very subjective judgment, and the art of
composition can be just as effective (or more so) when based on flawed or
subjective premises. . . .


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From: mclaren
Subject: Neil Haverstick's evaluation of Partch as
a composer
---
Neil Haverstick is one of the most talented guitarists
I've had the pleasure to hear. His "MicroStock" in
Colorado has rapidly become one of the most important
microtonal concert venues in the U.S., and Neil is
the prime mover in that effort.
However, permit me to join with Denny Genovese in
disagreeing Neil's opinion of Partch as a composer.
Neil said something to the effect that Harry Partch
was a genius "in a certain way," but that he didn't
find Partch to be a great composer.
Having heard a fair amount of Partch's music, it's
clear to me that Partch is at the very least a first-
rate composer. Whether you want to call him "great"
probably depends on the judgement of future
generations...but in my opinion it's safe to say that if
*any* of the composers of the 20th century should be
called "great," Partch certainly should.
"Daphne of the Dunes" sends shivers down my spine. It's
just that good. The intricate cross-rhythms and the
adroit use of timbre and small vs. large just intervals
seem to me astonishingly adept.
"Two Pieces On Ancient Greek Scales" is one of Partch's
most widely recorded compositions, and it seems to me
in every way the equivalent of Bach's best two-part
Inventions.
"And On the Seventh Day, the Petals Fell In Petaluma..."
has always struck me as a virtuoso display of compositional
ability, right up there with Josquin DesPres and Johannes
Ockeghem. Remember that Partch composed "Petals" so that
some of the duets overlapped into quartets...doing this with
a string quartet or a wind quintet is challenging enough, but
to do it *by yourself* using *only two tape recorders* in a JI
tuning which no one else had ever heard before, and to make
it work musically...well, this is an achievement that leaves
me speechless.
Partch was obviously a genius. In my judgment he was also
a great composer.
This is just one person's opinion, but it seems to me that Neil
hasn't fully appreciated the beauty and the power of Partch's
music.
On the other hand, let me point out that this says nothing about
Neil Haverstick's judgement. Neil's compositional style is
*very* different from the academic "serious" so-called
"highbrow" compositional style with which many of the
academic subscribers to this forum are most familiar.
Neil is an excellent composer, however. Oddly enough, many
of Neil's pieces tend in the direction of what the French
call "spectral composition," a new music movement that
doesn't have its own name in this country (but does have
some brilliant exponents, foremost among them William
Sethares).
Neil's use of the guitar with heavy signal processing has
influenced me in my recent use of guitars as "resonant
bodies" with extreme signal processing. By beating the
back of the guitar with a rubber mallet, placing knitting
needles between the strings, and running various objects
along the strings (paper, tin foil, picks, felt sticks) while
subjecting the signal to extravagant signal processing
with a reverb unit, remarkable and almost orchestral
sounds can be obtained from almost any guitar.
Neil's work with guitars particularly in 34/oct pointed
the way for us (Adam Cline has done a lot of work with
prepared guitars at the Sonic Arts Gallery), and serves
as a continual inspiration.
Perhaps Neil comes from such a different mindset
to Partch's that it's difficult for Neil to fully appreciate
Partch's music.
--mclaren


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From: mclaren
Subject: a purportedly "serious error"
--
John Chalmers posted the following in Tuning Digest 718:
"I want to correct a serious error in one of Brian McLaren's recent
posts. While not a peer-reviewed journal, XENHARMONIKON welcomes
contributions from academics." -- John Chalmers
John's "correction" of my purportedly "serious error" is itself
in error.
The statement which John characterized as a "serious error" was:
"...Xenhamonikon is published and vetted completely outside
academia." -- mclaren, Tuning Digest 717
This statement is true as it stands.
The journal Xenharmonikon is not published under the auspices under
any academic institution. No faculty peer review committee scrutinizes
the papers submitted to Xenharmonikon. John Chalmers does not
have an appointment in the music department of any university.
Whatever Xenharmonikon's origins, it is not now affiliated with
any institution of higher education.
All of these facts remain facts. Therefore John Chalmers was
incorrect when he claims that my above statement is a
"serious error." I will repeat my factual statement for the
record: Xenharmonikon is published and vetted entirely outside
academia.
Please do not take this to mean that Xenharmonikon is any
less scrupulous in checking its facts than a so-called "serious"
new music journal. In my experience, John Chalmers does a
superb job of fact-checking. On occasion Your Humble E-Mail
Correspondent helps out.
Moreover, Xenharmonikon is more interesting IMHO than the
so-called "serious" new music journals (many of which cannot
be taken seriously) because Xenharmonikon accepts articles
on areas of tuning theory and microtonality which are truly
adventurous and imaginative.
John *is* correct in pointing out that academics often publish
articles in Xenharmonikon, primarily because the 12-TET-obsessed
"new music journals" have traditionally seldom accepted articles
which venture outside the Sacred Twelve Tones.
Bear in mind that I never said that Xenharmonikon doesn't publish
articles by people in academia. What I said was that Xenharmonikon
is not published under the auspices of any university and does not
have a faculty peer review committee to vet submissions, and both
of these statements remain factually correct.
However, with Musical Quarterly and 20th Century Music and
Perspectives of New Music having recently printed articles about
non-12 music, this "12-TET only" policy in the so-called "serious"
new music journals might be breaking down.
Only time will tell.
--mclaren


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Message written at 23 Jun 1996 17:35:49 +0100
In-reply-to:
(message from John Chalmers on Thu, 20 Jun 1996 10:17:30 -0700)

I noted that Brian said...
Many of the subscribers to this forum have done non-12 Csound
compositions, but they're reluctant to give out scores for
copyright reasons. I myself requested a number of subscribers
to post Csound scores of their microtonal computer music
compositions.
Every single composer demurred, citing copyright concerns.

It is possible that i do not count as a composer, but I am completely
willing to post my only complete work in non-12ET as a csound orc/sco,
and am not concerned about copyright -- I do not expect to make money
on it anyway. Indeed after its premier this August I will place it on
the web. Thinking about it, the other complete csound work only has
one note so I am not sure of its scale....

==John

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From: mclaren
Subject: The French spectral composers
--
A while back, Johnny Reinhard mentioned in
passing the French "spectral composers."
This is a movement that doesn't yet have
a name in America.
In France, the two most prominent spectral
composers are Gerard Grisey and Tristan
Mureil.
These composers consider psychoacoustics
more important to composition than Fortean
pitch-class matrix serialist theory or other
non-sensory-based methods of ordering notes
and timbres.
The result of Grisey's and Mureil's work
has been a series of remarkable compositions
which blend almost-just pitches into a set
of tonally fused timbres which shift in
a prismatic and uncanny way.
I say the pitches are "almost just" because
Tristan Mureil, Gerard Grisey, and their most
prominent disciple, Philliphe Hurel, don't use
true small-whole-number ratios in their music.
Instead, they round off the just values to the
nearest eighth- (sometimes sixteenth-) tone
and notate and have the music performed that
way.
The result is sometimes peculiar, from a pure
hard-core American JI perspective. However,
all three of these composers are extremely
talented and their work is well worth listening
to.
However, it's hard to get hold of. IRCAM has put
out a CD of Phillipe Hurel's pieces performed
by the Ensemble Contemporaine at the Espace
Projection in Paris. Other than that CD, there's
little available in this country. (I heard Grisey's
"Joure, contre-jour" and some Mureil pieces whose
names escape me off cassette at a friend's house.
The friend had just returned from Paris.)
This is one instance where the French seem to
be ahead of us Americans. While isolated voices
like John R. Pierce and James Dashow and
William Sethares have been talking about the
musical and compositional benefits of fitting
timbre to tuning, there is as yet no organized
movement of "spectral composition" in America.
This is peculiar, inasmuch as virtuoso groups like
Johnny Reinhard's AFMM exist in prominent American
cities, and these performers can *easily* perform
high-limit just ratios on traditional acoustic
instruments.
Listening to Johnny Reinhard quadratic just intonation
string quartet "Cosmic Rays" made my jaw drop. These
performers can hit *any* pitch, and do it at top speed,
and do it consistently.
You'd think with these kind of musicians available in
this country, we'd have a full-blown "spectral
composition" movement.
To give you an idea of how important the spectral
composition movement is in French avant-garde
circles right now, consider the following quote
from Denis Cohen:
"I tried to show in an article I wrote ("Ulysses
and the Mermaids") that the contrast often made
in France between serial music and spectral music
was probably useful conceptually, but was
incomplete and bore littel relation with reality."
In America, the contrast is between the New Complexity
and minimalism of one sort or another. But in
France, the lines of division are drawn between
Fortean set-theory serialism and spectral
composition.
--
Another (non-spectral) French composer of note
is the aforementioned Denis Cohen. I mention
him because IRCAM has released a new CD of
his music, the last track of which is microtonal.
"Il SOgno Di Dedalo" (1990-1991).
According to Richard Toop's liner notes,
"Without venturing a key to the labyrinth of
Il Sogno Di Dedalo, one can at least draw
attention to some recurrent elements: loping,
almost *ethnic* percussion rhythms, rapid
melodies in (mostly) four-part harmony,
little brass glissandi, falling (and later,
rising) microtonal scales, and throbbing
Varese-like brass chords." [Toop, R., liner
notes to "Il Sogno Di Dedalo]
This is a fine piece of music and distinctly
xenharmonic.
This is Musique France d'Ajourd Hui CD sponoserd
by the SACEM and Radio France. It is probably
available from Harmonia Mundi as an import.
Highly recommended.
--mclaren

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From: mclaren
Subject: Paul Erlich's insightful comments
--
Kudos to Paul Erlich. Having seived through
hundreds of my posts and thousands of my posted
quotes, references, tables, numbers, equations
and citations, he has succeeded in finding
2 errors. (Actually one of 'em is not an
error, but a sly joke.)
The 1ere error in question involves my calling
phi a transcendental number. As Paul astutely
points out, phi is the solution of a simple
algebraic equation with rational coefficients
and real rational exponents: x^2 - X - 1 = 0.
This means that phi is by definition an
algebraic irrational, rather than a
transcendental irrational number.
Thanks, Paul.
As mentioned on many another occasion,
Your Humble E-Mail Correspondent is a
mathematical idiot. This means I make plenty
of flubs when it comes to math--like my infamous
statement that "i is the square root of -1."
(Of course -i also qualifies, as Manuel Op de
Coul pointed out.)
This also means that I'll make plenty of mathematical
flubs in the future.
Thanks in advance to everyone who'll be on the lookout
for my math errors. It's important, when speaking
about mathematics, to catch the errors before they
propagate.
Here's Erlich's reaction to my little joke (which he
must have misunderstood as an error):
"Brian McLaren wrote:

>As the final and most bizarre demonstration of the properties
>of extended Wilson CPS scales, observe the tuning which
>falls out of the 3,8 [1.22222, 2.33333, 3.444444, 4.55555,
>5.666666, 6.777777, 7.888888, 8.99999].
>According to Manuel Op de Coul's SCALA program, this
>Wilson CPS produces the 9-tone equal-tempered scale.
>--mclaren

"It does not. However, [2^1.22222, 2^2.33333, 2^3.444444, 2^4.55555,
2^5.666666, 2^6.777777, 2^7.888888, 2^8.99999] is all the notes in the
9-tone equal tempered scale, and combination product sets of this will,
trivially, produce 9-tone equal tempered scales. Nothing bizarre about it.
Brian McLaren reminds me of a Ludwig Plutonium on some of the sci.
newsgroups, and Albert Silverman on rec.music.compose. Long,
self-aggrandizing posts filled with factually incorrect and useless
examples and lots of whining about the establishment, accompanied by
a complete lack of ability to communicate with the other members of
the group." -- Paul Erlich, Tuning Digest 719


Let us re-examine EXACTLY what I said:

"According to Manuel Op de Coul's SCALA program, this
Wilson CPS produces the 9-tone equal-tempered scale." -- mclaren

My statement above is correct as it stands.
There's a bug in Manuel's SCALA program version 1.0 which
produces a fairly humorous result for the CPS function when
you input a Wilson 3,8 CPS with generators [1.22222, 2.33333,
3.444444, 4.55555, 5.666666, 6.777777, 7.888888, 8.99999]
It doesn't take a rocket scientist to figure out that these
generators cannot possibly produce a 9-TET scale--or
so I assumed.
It seemed so obvious to me that the result I gave was
comically wrong, that it would be immediately apparent
to any forum subscriber that I was poking a tiny bit of
fun at the beta version of Manuel's SCALA program.
The tip-off, of course, being the last sentence of my post--
a sentence which Erlich deliberately left off when
he misrepresented my post:

"According to Manuel Op de Coul's SCALA program, this
Wilson CPS produces the 9-tone equal-tempered scale.
It is left as an exercise for the enterprising xenharmonist
to determine why and how.
--mclaren"

My expectation was that at least one "enterprising xenharmonist"
would actually feed my numbers into SCALA, discover that
SCALA gave an incorrect result, and report that fact in the
properly amused tone.
Instead, Erlich compares me to someone called "Ludwig Plutonium,"
whoever that is.
Let us re-read the last sentence of my post:

"It is left as as an exercise forthe enterprising xenharmonist
to determine why and how." -- mclaren

This is peculiar way of describing what should be a straightforward
scale-generation procedure. Tongue in cheek, anyone? The "why"
is simple: there's a bug in SCALA 1.0. The "how" is less simple--
it appears to involve an ADA routine which assumes that only
integers will be entered.
I did not expect anyone to penetrate that deeply into the arcana
of my sly little joke; and of course no one did.
Thus, when Erlich complains (Tuning Digest 719) about
"Long, self-aggrandizing posts filled with factually incorrect and
useless examples..." it is of some interest to examine his plaint.
Presumably Erlich wants people to believe that my posts are
"filled" with "factually incorrect" examples.
Yet out of my hundreds of posts and thousands of facts, Erlich
has been able to find only 2 errors--one of which wasn't even
an error.
Out of my thousands of facts and hundreds of posts, Erlich pounces
on 1 (one, count it--one) error. (I incorrectly identified phi as
a trascendental irrational rather than an algebraic irrational.)
On the basis of this 1 (one, count it--one) error, Erlich
rants:
"Brian McLaren reminds me of a Ludwig Plutonium on some of the sci.
newsgroups..."
Okay.
Now I think we've all got the picture.
Make 1 error out of several hundred posts, and you're a charlatan.
One (count it, 1) error identified out of thousands of facts,
tables, quotes, citations...and *this* means that my posts are
"filled" with "factually incorrect" examples.
Need I say more?
Does *anyone* out there require convincing that Paul Erlich
is less concerned with the facts than with ad hominem attacks
on Your Humble E-Mail Correspondent?
While we're on the subject of errors, turnabout is fair play.
So let's examine one of Paul Erlich's own posts,
and see whether it contains any "factually incorrect" examples...
Paul Erlich stated in Tuning Digest 718 that subharmonics are
not present in the spectra of acoustic instruments.
This is not only false, it demo
hates that Erlich has not done
little (if any) Fourier analysis of real-world instrument sounds.
One of the hard facts is that book learning will only take
you so far when you apply DSP techniques to the study of
real sounds. Then you've got to get your hands dirty out in
the real world and find out that 90% of what you
learned in those books applies only in special cases,
or doesn't apply at all.
Ralph David Hill has written a Fourier analysis/
resynthesis software system which is capable of
detecting, analyzing, and resynthesizing quasi-
harmonic sounds.
Yesterday I visited Dave at his home and he ran
me through a demo of his system. He resynthesized
a trombone note with and without the octave-below and
2-octaves below subharmonic. The notes resynthesized
without both subharmonics sounded noticeably different
from the original sound, and significantly less
realistic.
Dave reported this at the 1982 ICMC, so it's very old news.
Clearly Paul Erlich needs to learn something about
signal processing, real-world timbres, and the
limitations of using off-the-shelf Fourier
analysis software.
--
--mclaren


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From: mclaren
Subject: Microtonal Varese
--
The following excerpts from lectures and letters
by Edgard Varese, never published, appeared in
Soundings. Ran across 'em the other day:
Varese foresaw electrical instruments which
promised
"Liberation from the arbitrary, paralyzing tempered
system: the possibility of obtaining any number of
subdivisions of the octave, consequently the formation
of any desired scale, unsuspected range in low and
high registers, new harmonic splendors obtainable
from the now impossible use of subharmonic
combinations..."
Sounds as though Varese would have been right at
home on this tuning forum.
In discussing "Integrales," Varese mentioned:
"While in our musical system we deal with
quantities whose values are fixed, in the
realization that I conceived the values would be
continually chaning in realtion to a constant. In
other words, this would be like a series of
variations, the changes resulting from slight
alterations of the form of a function or by the
transposition of one function into another. A
visual illustration may make clear what I mean:
Imagine the projection of a geomtrical figure
on aplane with both figure and plane moving in
space, each with its own arbitrary and varying
speeds of translation and rotating. The immediate
form of the projection is determined by the
relative orientation between the figure and the
plane to have motions of their own, a highly
complex and seemingly unpredictable image
will result. Further variations are possible
by having the form of the geometrical figure
change as well as the speeds."
This is uncannily akin to a description of music
produced by one of Erv Wilson's higher-dimensional
just intonation lattices using changing timbres.
--mclaren



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From: mclaren
Subject: software synthesis
--
Congratulations to John Fitch for putting one of
his xenharmonic Csound compositions on his web
page.
To my knowledge no one else has composed anything
in 100-TET, so John Fitch is likely the first.
John says "the composers on this forum can
probably do better."
I doubt that.
John has shown himself a brilliant programmer and
an insightful subscriber to this tuning forum. I'd be
surprised if his compositions were less than
excellent.
Speakingt of insightful posts, John mentioned in
Tunign Digest 712 "surely the answer is to use
software synthesis."
A recent article by Roger Dannenberg in Computer
Music Journal supports John's contention.
Dannenberg does some quick calculations that show
that hardware DSP implementations of synthesis
algorithms must run at least 40 (!) times faster
than the same routines in software to give any
kind of real-world payoff in less time than it
takes to develop a usable software interface for
the DSP hardware.
The net result?
Dannenberg concludes that "the days of hardware
synthesis are over." General-purpose CPUs are
increasing in computational power too quickly to
allow DSP hardware to survive.
This is extremely good news for micorotnalists.
The more general-purpose the CPU, the fewer the
restrictions on tuning.
This means that within a very years all the synthesis
algorithms that now require special-purpose hardware
to run in real time will run on standard desktop boxes
in real time. Not only that, we'll be able to detewelvulate
at will--in real time--with sophisticated computer music
timbres on cheap general-purpose computers.
I can hardly wait.
--mclaren


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Said Brian M., quoting John Fitch:
> Speaking of insightful posts, John mentioned in
> Tuning Digest 712 "surely the answer is to use
> software synthesis."

I suppose that depends on what the question was. Do you recall John?


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>>>>> "Gary" == Gary Morrison <71670.2576@compuserve.com> writes:

Gary> Said Brian M., quoting John Fitch:
>> Speaking of insightful posts, John mentioned in
>> Tuning Digest 712 "surely the answer is to use
>> software synthesis."

Gary> I suppose that depends on what the question was. Do you recall John?

I think I was reacting to the complexities of persuading MIDI
synthesisers to play in "non-standard" tunings. For simple sounds I
can use samples and Csound to play them at any frequency. I can play
a set of Bosendorfer piano samples from my MIDI keyboard in real time
(but I am a bad keyboard player).

When I started to use computers for music some years ago I assumed i
would use MIDI. As it turned out I almost never do, and would rather
synthesise ab initio.

At the time of writing Csound in realtime is almost possible on simple
computers. It should not be long now. Until then I will work in
non-real time in order to get the sounds at the frequencies I (think
I) want.

==John

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Gary wrote:
>Paul E. said:
>> Didn't I qualify this to say that apparant
>> subharmonics can result when a note is itself a harmonic, i.e., all notes

on
>> brass instruments? You're right though, I haven't done any actual
fourier
>> analysis of musical instruments.

> Uhmmm... Perhaps mean "undertones" rather than subharmonics? If the
"note
>is itself a harmonic", then the statement is inherently true by definition,
>since harmonics of subharmonics are subharmonics of harmonics.

Not really. You could conceive of a "perfectly" performed brass tone, where,
say, the odd modes of vibration were completely absent. Then you would have
a harmonic (a note an octave above the fundamental pitch of the instrument)
without subharmonic content. However, there is no such thing as a
"perfectly" performed brass tone, and this applies to winds as well.
However, string instruments typically perform in their fundamental mode of
vibration; did you find subharmonics in string timbres as well, after
controlling for Nyquist effects?

In the case of brass and wind instruments, clearly the expected effect
according to my argument is undertones, not necessarily subharmonics. These
undertones would form an overtone series above the fundamental mode of
vibration of the instrument, and not a subharmonic series below the note
being played.

There is also a technique of playing brass instruments (or singing) so that
a buzzy note results which is a subharmonic of the intended note, but is not
an overtone of the fundamental mode of vibration. I believe Benade describes
this phenomenon in his book on acoustics. A brass instrument with a
fundamental frequency of 100 can produce buzzy notes at 125, 133.3, 150,
250, 266.7, 375. But again, the final product is a harmonic series (above
the "subharmonic"), not a subharmonic series.


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As for whether more tones have subharmonics than don't... Well, I suppose
that may depend on whether you're counting notes available on each unique
instrument type, or notes present in existing repertoire. Or maybe there isn't
really all THAT much disparity between the two.

I based my statement that more musical tones in the orchestra have
subharmonics than don't, upon the what I saw in my (roughly 300-tone) test suite
for my program. It contained typically about 20 notes across the range of each
instrument in the usual orchestra, and other instruments. So the orchestral
strings appeared as 4 of 15 or so instruments in the test suite. Counting them
that way, certainly more have subharmonics than don't, from what I saw.

But I suppose one could argue something along the lines that:
1. There is more repertoire for strings than for winds.
2. There are more stringed instruments - even orchestral ones - out there
than just violins, violas, 'celli, and basses.
3. Although the strings represent only four instrument types of instruments,
the orchestra nevertheless contains more chairs for more strings than for
winds.
Arguing from those perspectives, I suppose the question becomes harder to
quantify.


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From: mclaren
Subject: Paul Erlich's innovative & insightful ideas in Digest 749
--
In Tuning Digest 749, Paul Erlich pointed out that
"A typical way of evaluating equal temperaments is to
measure the smallest possible tuning deviation of several
just intervals of interest. The problem with this approach
is that it does not guarantee that the approximating
intervals are consistent with one another." -- Paul Erlich
This is an excellent point, and it's not clear that anyone
else has made it so cogently. In fact this could serve
as the basis of a fascinating article, were any of the
12-TET-obsessed music theory journals interested in
publishing such an article. (You never know. Sometimes
they relent.)
The earliest reference to an idea similar to this one
appears to be found in Mersenne's Harmonicorum Libri...
(1636), pp. 126-127 (last pagination of 2nd ed., 1648).
Mersenne defines each interval as equal to a certain
number of commas, and some of the commas are
incompatible with one another.
This is in the same ballpark as, but clearly not identical
to, Erlich's insight.
--
Gary Morrison's conceptual difficulties in working with
multiple simultaneous tunings are probably what
Ivor Darreg used to call a "pseudo-problem." In other
words, something that conceptually seems like
an unimaginably difficult issue but which, in real
life, turns out to be largely irrelevant or trivial.
(Playing 19-TET or 22-TET on a 7-white-5-black
keyboard is such a "pseudo-problem." In both cases,
the answer is to use open-voiced chord with third
and root played by the left hand, fifth by the right
hand. Simple. Trivial. What's the problem?)
In combining 12-TET and 19-TET, for instance,
we in the Southern California Microtonal Group
have found it useful to view 19-TET as a gapped
nondiatonic scale with some very xenharmonic
ornamental tones.
As I've pointed out before (and as Paul Erlich's
experiments with his roomate demonstrate), listeners
hear the whole-tone portion of a 19-TET diatonic
scale as very reasonable and familiar-sounding, but
the 2/19 of on octave "semitones" (a misnomer, since
this term presupposes that whole tones are
divided into 2 parts whereas in 19-TET they are
divided into 3 parts) always make folks squirm.
They sound...weird. "Out-of-tune" is the typical
description.
The solution, in my experience, is to fracture the
mislabelled "semitone" intervals in the 19-TET
approximation of the 12-TET diatonic scale into
1/19s of a tone. Thus a typical melody in 19-TET
will proceed by whole steps which sound very
reaonable in combination with 12-TET. Then
a constellation of 1/19-octave steps are used
to bridge the gap twixt the next "island" of
whole steps in the 19-TET approximation of
the diatonic scale.
This seems to work reasonably well *provided*
that 12-TET semitones and 19-TET 1/19s of
an octave don't play simultaneously. If, instead,
these intervals "trade off" between different
players (the way good jazz players will trade
off playing flatted blues thirds), the 12 + 19
combo seems to work well.
Another trick that seems to work is to play
melodies full of familiar 12-like intervals
in 19-TET, but to go above or below the last
note of the melody by 1/19 of an octave.
This works well, by the way, for many
incommensurable ETs: 15 and 12, 14 & 17,
15 & 17, 19 & 22, etc.
Many ETs are, however, commensurable--
that is, one forms a subset of the other,
or both form gapped subsets of a much
higher division of the octave.
When combining 5-TET and 7-TET, for
instance, it is often useful to throw
in 35-TET chromatic passages. This
emphasizes that the tiny intervals
heard between 5-TET and 7-TET pitches
that happen to occur vertically are not
accidental, but part of the coherent
35-TET scale.
The issue of combining non-just non-
equal-tempered scales with xen ETs,
or combining, say, all 3 different
classes of tuning simultaneously,
is more complex. I'm still feeling
my way along in this regard.
--mclaren


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From: mclaren
Subject: Enrique Moreno's 1995 PhD thesis
--
Enrique Moreno wrote a thesis in 1995 entitled
"Embedding Equal Pitch Spaces and the Question
of Expanded Chromas: An Experimental Approach."
This is available as Report No. STAN-M-93 from
the Stanford Unviersity Music Dept., CCRMA,
Stanford CA 94305-8180.
This dissertation is one of the most interesting
and provocative theses about microtonality to
come out of Stanford. It stands as the equal
of Elizabeth Cohen's and Douglas Keislar's
fascinating theses (both highly recommended).
The heart of the thesis can be found on pages 50
through 52:
"We need to see that the tuning has a unique
organization, and that its intervals and chords
are, in justice, as unique as the tuning itself
may be, even when the tuning may contain
very closely approximated versions of some
familiar intervals. The main difference comes
perhaps not so much from the intervals of the
tunig t hemsleves but from the *context* that
the whole tuning as an entity provides for every
interval in it. In this sense, to attempt to classify
the new intervals as variations of twelve-tone-to-
the-octave equal intervals (or of just intervals)
woudl constitute perhaps a reasonable mistake.
"It would be reasonable because it is reasonable
to attempt to understand unknown things in terms
of the things we know, especially if there exists
a certain resemblance. It is reasonable to judge
the world according tothe categories of our
experience, but it is not logical to assume that
our categories are the ultimate representation of
reality. (..)
"Follwoing the same ine of thought, we realize that
notating this tuning with the aid of symbols that
make reference to our usual twelve-tone-to-the-
octave tuning or to historical tunings would be
more or less absurd. Imagine having to interepret
the signs ^b, ~#, as "not so flat" and "not so sharp",
or -b+++ as "quasi-flat plus three syntonic commas,"
or whatever. In short, regardless that some of the
intervals, chords, and even chord progressions may
resemble certain well-known intervals, chords, and
chord progression,s this tuning and many others
(although not necessarily all) deserve a fresh
departure point."
This is the stronget and clearest statement I have
yet found of one extreme of the attitude toward
microtonality--namely, that we should approach
the intervals and the tunings anew and search our
their properties without preconceptions. This is
clearly not entirely possibe--it remains a fact
that the human ear/brain system has measurable
properties and various intervals will have predictable
*sensory* effects on the auditory system--but in
making this point Enrique gets at an extremely
important truth.
Namely, that the *sensory* affect of an interval or
a tuning is not all necessarily the same as the
*musical* affect of that interval or tuning.
N0orman Cazden made much the same point in
the article "On Sensory Consonance," Int. Journ. of
Aesthetics and Art Criticism, 1980, but Cazden
was mainly concerned with demolishing Helmhotlz's
influence. Enrique's point is much farther-reaching.
Now, the other end of the spectrum can be seen
in Easley Blackwood's and Paul Rapoport's writings
on microtonality. "When investigating a tuning for
which there is no repertoire or tradition of any kind,
the most illuminating approach is to look for conenctions
between the new tuning and 12-note equal. All the other
tunings contain many extremely discordant intervals,
and are amenable to row music, or to other non-tonal
compositional techniques. But hte most interesting are
those that include tonal elements--ie., major and minor
triads, and seventh chords, which may be arranged in ways
similar to, but not exactly like, 12-note equal." [Blackwood,
Easley, "Research Notes, NEH Grant RO-29376-78-0642,
1980, page 1]
Clearly this approach has a lot of problems. For example,
Blackwood reveals fundamental bias when he states
that "major and minor triads" are his primary criteria.
This causes him to completely overlook the neutral mode
and neutral triads on tunings like 17-TET and 21-TET,
and as a result Blackwood makes many verifiably false
statements--for example, Blackwood discusses *only*
the major and minor triads in 17-TET. He never discusses
the neutral triad, formed from a third with 5 steps of
70.588235 cents each. Fortunately, Paul Rapoport revises
this oversight--but Paul's overall approach remains
relentlessly Pythagorean and 12-TET-based, which is
simply not appropriate, say, with melodic modes in 19-TET,
or harmonies in 21-TET, or with 9-TET or 7-TET or 10-TET
or many other tuning which cannot be jammed into the 12-TET
mold.
In 17-TET, the neutral melodic mode is an important
resource. Blackwood completely overlooks it. He does
not discuss 8- or 9-tone melodic modes, nor does he
discuss pentantonic modes except in 23-TET, to his
credit.
Thus the great drawback of trying to force all equal
temperaments into the conceptual framework of 12-TET
is that it leads the composer to completely overlook
many useful (but highly non-twelvular) melodic and
harmonic resources.
On the other hand, Easley Blackwood's and Paul Rapoport's
approach to non-12 also has many advantages: by
identifying points of similarity with 12, it gives them
a place to start analyzing harmonic progressions and
melodic modes.
The great weakness of Enrique Moreno's position is that
he does not provide a conceptual framework for harmonic
progressions and melodic modes.
The basic idea of Enrique's thesis (to do it gross injustice
by boiling it down to a few words) is that non-octave
tunings can be characterized by the Nth root of K, where N and
K are integers. In many cases, K then takes on the audible
characteristics of the 2:1 (octave) ratio in the twelve-tone
equal temperament. Thus, Enrique contends--and has data
from psychoacoustic experiments to prove--that in many
cases the K:1 ratio exhibits many of the properties of the
octave 2:1 ratio in 12-tone equal temperament. The particular
property on which Enrique concentrates is chroma--that is,
the property according to which a perceived pitch remains
"the same" perceptually if it is displaced up or down by
that ratio. Thus, in 12-TET, a C4 is heard as "the same"
as a C3 and a C5; similarly, in the 12th root of 3, Enrique
claims (and has data to demonstrate) that a pitch
displaced up or down by 3:1 also "sounds the same."
This gives a starting point for harmony in non-octave
scales, since inversions can now be analyzed, melodic
modes can be described, etc.
Enrique's approach seems especially praiseworthy because
[1] it involves psychoacoustic data, and thus has some
connection to the real world--unlike so much mental-
masturbation "modern" 12-TET music theory; [2] it has
the courage to leave behind 12-TET preconceptions.
If it seems utopian that listeners might be expected to utterly
abandon 12-TET conventions when listening to mirotonal
music, it's well to remember Heinz Werner's paper in
the 1940 Journal of Psychology, cited a few posts back.
Wener found that, given enough time to familiarize themselves
with a microtonal tunings, *every* listener he tested
was able to make the leap into hearing the new intervals
on their own terms.
Further proof is provided by everyday experience--William
Schottstaedt, for example, has pointed out that after working
with 11-TET for an extended period, he found that 12-TET
sounded "strange" when he returned to it.
In sum, Enrique's thesis is a major contribution to microtonal
theory. It also adventurously extends some of the conventional
notions of music theory (i.e., octave equivalence) without
becoming a slave to 12-TET ideas.
--mclaren



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From: mclaren
Subject: Paul Erlich's points about inharmonic
tone complexes - post 1 of 2
--
John Chalmers informs me that some folks
object to the idea of matching inharmonic
timbres to inharmonically-derived tunings.
Apparently, your contention is that the
inharmonic tone complexes tones will be heard
as having a virtual pitch entirely different
from that of their component inharmonic
partials. Paul Erlich seems typical in
these respects.
On the surface, this sounds like a good
argument. More: Erlich apparently claims
that inharmonic tone complex will fail
to exhibit spectral fusion and will fall apart
into a set of discrete partials if they're highly
inharmonic. Thus it would seem pointless
to attempt to match a non-just non-equal-
tempered tuning to a n-j n-e-t timbre, since
the resultant inharmonic timbre will never
be heard as having a fundamental pitch
related to the pitches of the n-j n-e-t scale
from which it is drawn.
Is this claim correct?
It turns out that it isn't.
Paul Erlich strikes me as a smart fellow with
some knowledge of acoustics and pyschoacoustics.
Alas, as a newly-minted graduate much of Paul's
knowledge is book learning only. And, as it turns
out, much of what has been written about complexes
of inharmonic tones is either wrong, irrelevant
to xenharmonic composition, or the result of
peculiar and non-musical experimental conditions.
This issue is important. James Dashow, Jean-Claude
Risset, William Sethares, myself, and a number of
other composers have produced a substantial body
of compositional work in which non-just non-equal-
tempered timbres and tunings are used. If Paul's
claims (and some of the available psychoacoustic
literature about inharmonic tones) are correct,
then the theoretical and musical justification for
much of this compositional work collapses.
As will be seen, however, there is a great deal
of evidence *against* Paul Erlich's view, and
many of the psychoacoustic papers which purport
to "prove" that inharmonic tone complexes do not
audibly fuse are lethally flawed.
Let us begin with the alleged evidence *against* the
coherent audibility of inharmonic tone complexes:
Rayleigh, in his 1876 2-volume text "Acoustics," points
out that the fundamental pitch of orchestral timpani
is a frequency not present in the partials produced
by this instrument. Rayleigh explained this by
pointing out that the ear hears some of the upper
partials of timpani as belonging to a fragment of
an harmonic series; the ear extrapolates from
this harmonic-series fragment a lower pitch
which is heard as the fundamental though not
physically present. Other partials, which are
physically present, are heard as "hum" notes
which do not contribute to the sense of musical
pitch of the note.
Rayleigh noted the same phenomenon with regard
to bells: here again, the lowest several inharmonic
partials are heard as "hum" notes, but do not make
musical contribution to the sense of pitch of
the bell.
65 years later Schouten demonstrated in
an elegant experiment that the human ear often
heard a fundamental pitch not physically present in
a musical sound. "He had constructed a sort
of optical siren (Figure 6-4) by means of which
he could produce sounds with various waveforms.
Using this, he produced sounds with harmonically
related partials. (..) Then, by proper adjustments,
he could cancel out the fundamental frequency...
I could hear this fundamental frequency come and
go, but the pitch of the sound did not change at
all. In some way, my ear inferred the proper
pitch form the harmonics..." [Pierce, J. R., "The
Science of Musical Sound," 2nd ed., 1992, pg. 92]
The paper "Pitch of the residue," by J. F. Schouten,
R. J. Ritsma and B. L. Cardozo, J. Acoust. Soc. Am.,
Vol. 34, pp. 1418-1424, 1962, presents these
results concisely. "Whenever a sound consists
of a small number of frequencies, spaced
sufficiently widely, subjective sound analysis
allows us to hear each Fourier component as a
separate pure tone with corresponding pitch
(Ohm's acoustical law). If, however, the
frequencies are narrowly spaced, the ear
fails partly or completely to analyze the
Fourier components into corresponding pure
tones and, instead, hears one single percept
of sharp timbre. If, moreover, the frequencies
are harmonics of one fundamental frequency,
the percept may have a decidedly low pitch."
[Schouten, J. R., J. Ritsman, B. Lopes Cardozo,
"Pitch of the Residue," J. Acoust. Soc. Am.,
Vol. 34, No. 8, September 1962, pg. 1418.]
Schouten et al. go on to point out that "The
phenomenon of the reside necessarily leads
to a hypothetical pitch extractor different
from and subsequent to the analyzer. As a
consequence of the pitch shifts, the operation
of the pitch extraction in the frequency
domain is highly improbable. Therefore, the
hypothetical pitch extractor probably
operates in the time domain (e.g., with
delay-line tehcniques)." [ibid., pg. 1424]
Further evidence for the existence of
periodicity (or "virtual") pitch is found
in "Periodicity Pitch for Interrupted White
Noise--Fact or Artifact?" by Irwin Pollack,
J. Acoust. Soc. Am., Vol 45, no. 1, 1969,
pp. 237-238. The author concludes that
switching transients cannot provide a
reasonable explanation for the perceived
ability of listeners to accurately match
the pitch of the interrupted noise despite
the fact that "The long-term spectrum of
an interrupted white noise shows no
sepctral peaks at the frequency of
interruption." Consequently "The results,
therefore, suggest that the periodicity pitch
of interrupted noise is factual, no artifactual."
[Ibid., pg. 238]
The book "Frequency Analysis and Periodicity
Detection in Hearing," ed. R. Plomp and G. F.
SMoorenburg, A. W. Sithoff, Leiden, 1970,
adduced further evidence in favor of virtual
pitch as the primary pitch extractor in the
human auditory system. Franz Bilsen
concludes "The perceptual similarity between
a sound with its repetition and a pure periodic
signal can be represented in a general model
for the perceptibility of pitch and timbre. Like
the explanation of repteition pitch, time
separation pitch, and peridocity pitch, the model
finds its description in the time domain." [Bilsen,
F., "Repetition Pitch: Its Implications for Hearing
Theory and Room Acoustics," Frequency Analysis
and Periodicity Detection In Hearing--Ed. R. Plomp
and G. F. SMoorenburg, A. W. Sithoff, Leiden, 1970,
pp. 291-299]
Schouten himself points that the earlier (Helmholtz)
explanation of fundamental perception by nonlinear
production of difference tones between higher
harmonics fails: "The case of the missing fundamental
was solved for the time being (the 1860s-1920s)
by a modelmaker's brainwave that the nonlinearity
of the ear could produce the missing fundamental as
a difference tone between the higher harmonics. Both
Fletcher (1929) and von Bekesy (1934), now as
observers, proved this point by the method of best
beats. Sadly enough, the method of best beats is
unreliable unless one knows "who beats whom."
(..) In a way the discovery of the residue confirmed
Seebeck's "wider interpretation" that the high
harmonics might contribute somehow to the
fundamental tone, except that it is not the
fundamental tone itself which is enhanced but a
different subject component: the residue.
"As a modelmaker, the author (Schouten) ascribed
the low pitch of the residue to the *period* in the
time pattern of the joint harmonics striking a
particular area of the basilar membrane (Schouten,
1940s). This amounted to a revival of many older
assumptions, except that the initial quasi-Fourier
analysis was left standing in full glory.
"If a set of harmonics is shifted collectively over
a small distance in the frequency scale, the pitch
of the residue shifts *in proportion* to the
constituent frequencies (Schouten, 1940c). This
crucial experiment (now called the first effect
of pitch shift) kills two birds with one stone. It
implies that pitch is determined neither by the
*spacing* of the harmonics, nor by the *time*
envelope of the wave pattern since both remain
invariant. Hence, in the realm of modelmaking,
it must be anouther form of periodicity detection
in the time domain. This notion goes back to some
etent to Seebeck's (1844a) idea of 'the periodic
recurrence of an equal or similar state of movement'
and to Hermann's (1912) 'intermittence tones.'"
[Schouten, J., "The Residue Revisited," Frequency
Analysis and Periodicity Detection in Hearing, Ed.
R. Plomp and G. F. Smoorenburg, A. W. Sithoff,
Leiden, 1970, pp. 41-58]
These papers provided apparently convincing
proof of the residue's primacy in determining
perceived pitch. Such was the power of the
residue pitch hypothesis that, from the late
1960s to the present, Ernst Terhardt
produced an influential series of papers based
on his model of virtual pitch detection: "Zur
Tonho"henwarnehmung von Kla"ngen I.
Psykoakustische Grundlagen" [Concerning the
perceived pitch height of sounds: I. Psychoacoustic
Foundations]" Acustica, Vol. 26, No. 4, 1972, pp.
175-186] and "Zur Tonho"henwarnehmung von
Kla"ngen II. Ein Funktionschema," Acustica,
Vol. 26, No. 4., [Concerning the perceived pitch
height of sounds: II. A functional model].
Terhardt's theory essentially relegates the
residue or "virtual" pitch to the role of a
"secondary sensation," ascribing the primary
mechanism of pitch detetction to the well-worn
place theory, which accords the operation of
the basilar membrane primacy in determining
pitch. "The pitch of simple tones and the
"residue" pitch of complex tones exhibit quite
different properties. The pitch of simple tones
may be xplained by the principles of the 'classical'
place theory. The 'residue' pitch is closely related
to the pure tone pitches of partials. It is
concluded that the 'residue' pitch may be regarded
as a 'seondary sensation,' derived from the pure
tone pitches of dominant partials." [Terhardt, E.,
op. cit., pg. 174]
Terhardt went on publish a series of papers in
which he elaborated the "residue" pitch as a
secondary sensation: "Pitch consonacne, and
harmony," J. Acoust. Soc. Am., 1974, Vol. 55,
pp. 1061-1069; "On the perception of periodoic
slund fluctations (roughenss)," Acustica, 1974,
vol. 30, pp. 201-213. "Ein psychoakusitche
begru"ndetes Konzept der Kusikalisches
Konsonanz," Acustica, 1976, Vol. 36, pp. 121-
137, "The two-component theory of musical
consonance, in "Psychophysics and physiology
of hearing," ed. E. F. Evans & J. P. Wilson,
London: Academic press, 1977; "Psychoacoustic
evaluation of musical sounds," Perception &
Psychophysics, Vol. 23, pp. 483-492; "Algorithm
for extraction of pitch and pitch salience from
complex tonal signals," J. Acoust. Soc. Am.,
J. Acoust. Soc. Am., Vol. 71, No. 3, March 1982,
pp. 679-688; Terhardt, E., Stoll, G. and Seewann,
M., "Pitch of complex signals according to virtual-
pitch theory: tests, examples, and predictions,"
J. Acoust. Soc. Am. Vol. 71, pp. 671-678, 1982.
This would all seem to be very convincing.
Clearly Erlich *must* be correct...right?
Inharmonic tones complexes exhibit either
a virtual pitch which has nothing to do with
the frequencies of their component partials,
or the inharmonic tone simply falls apart and
fails to fuse into a single acoustic percept...
don't they?
As it turns out, not so.
The first cracks in apparently impregnable
facade of the residue pitch hypothesis began
to appear during de Boer's research. In 1976,
de Boer's monumental study (he calls it "a
textbook inside a book") of the residue pitch
defined the field: "On the 'Residue' and Auditory Pitch
Perception," in Handbook of Sensory Physiology,
Volume 5, No. 3, Springer-Verlag, Berlin-Heidelberg-
New York, 1976, pp. 481-583]
This survey of the residue pitch phenomenon drew
on de Boer's doctoral dissertation and provided an
unparalleled overview: from Seebeck's acoustic
siren to Schouten's and Ritsma's work, to the
evidence from chopped noise (Pollock, op. cit.),
to Smoorenburg's own work.
Here, however, doubt begins to creep in about
the universal validity of the residue hypothesis
as the basis of pitch detection. "Must we say
goodbye to the 'residue'? We might be inclined
to say: yes. In the course of this treatise, we
witnessed the gradual change of meaning of
tjhe term 'resideu,' a change that finally led
to a new and less restrictive definition (see e.g.,
Section E. 10). At the same time the musical
aspects of 'residue pitch' grew more and more
important. (..) What is also new is the
ambiguity involved in residue pitch. This was
recognized rather reluctantly at first (Section
E. 6); later, it was considered an essential feature
of the mechanism (Section E 14). How essential
it is did not become completely clear before the
work on two-tone complexes and musical intervals
(Section H. 2). In last instance, even the harmonic
number n of the lower partial appeared to be
esentially ambiguous (Section H. 6). The ambiguity
involves one other concept that is, in the opinion of
the present reviewer, of the greatest importance. (..)
When we listen to a sound, we do not perceive this or
that aspect of the sound all the time; what we perceive
depends completely on our training. (..) Hence,
the fact that the result of a particular experiment
turns out to be extremely clear-cut does not
necessarily imply that ever naive listener is able
to perceive the signals in the same way. It is not too
difficult to associate a residue pitch with a two-
tone complex presented monaurally. But to do the
same with a two-tone complex presented dichotically
is quite anotehr matter. (..) We may conclude that we
must be extremely cautious in our conclusions."
[de Boer, E., "On the 'Residue' and Auditory Pitch
Perception," Handbook of Sensory Physiology, Vol. 5,
No. 3, Springer-Verlag, New York, 1976, pp. 572-574]
R. J. Ritsma admits as much when he points out
"The pitch behaviour of inharmonic complexes cannot
be described precisely by P = f/n or by the concept
of subharmonics of a dominant frequency
component predicting a pitch P according to equation
1. " [Ritsma, R. J., "Periodicity Detection," in
Frequency Analysis and Periodicity Detection in
Hearing, ed. R. Plomp and G. F. Smoorenburg, A. W.
Sithoff, Leiden, 1970, pp. 251-266]
Further doubts about the validity of the results
of tests on residue pitch were created by Elizabeth
Cohen's and Mathews' and Pierce's work in the
late 1970s and early 1908s.
"In fact, in single tones stretched A = 2.4, one
tended to hear the partials as separated sounds
rather than as fused into a tone of a single
pitch. We believe that such fusion depends on
the phenomenon of residue or periodicity pitch.
This has been noted by Cohen. She has observed
further than the degree of fusion of a stretched
tone depends on the envelope of the tone, and is
greatest for an exponentially decreasing amplitude
which gives a 'struck' quality." [Mathews, M., and
Pierce, J. R., "Harmony and Inhamonic Partials,"
Rapports IRCAM No. 28, 1980, pg. 12]
These results are at first glance mixed: some
of Mathews and Pierce's results appear to
support the residue pitch hypothesis, while
other results--the fact that inharmonic sounds
*can* be made to fuse with the right amplitude
envelope--tend to contravene Erlich's claim.
However, further on the paper strikes a profound
blow to the residue hypothesis:
"Subjects can identify keys of both stretched
and unstretched matierals in an XMXMt test."
The significance of this fact should not be
underestimated.
"If we can detect 'keys' and some form of finality
within a cadence or progressions within inharmonic
tones, then some of the theories of harmony in the
past must not have been as cogent as some of
their proponents have thought them to be."
[Roads, C., "An Interview WIth Max Mathews,"
Computer Music Journal, Vol. 4, No. 4, 1980,
pp. 21-22]
It is impossible to explain key sense and
a sense of finality in harmonic progressions
using inharmonic tones with the residue
pitch hypothesis. Clearly, other auditory
mechanisms must be at work.
This should not be surprising: many other
researchers have run into a brick wall when
they tried to explain all ear/brain phenomena
on the basis of a single proposed mechanism
of pitch detection.
Elizabeth Cohen found similarly mixed results,
and raised even further doubts about the purported
"uselessness" of inharmonic tones for harmony
in her series of experiments.
For one thing, Cohen notes that "Throughout
history musical isntrument ave included not
only sources with integral multiple partials
but also thouse sources with inharmonic partials.
Examples of the latter are stiff strings, bars,
and bells. (..) We already possess convincing
musical examples illustrating that sources with
inharmonic partials have musical potential
outside the confines of western harmony. The
musical legacy of the Balinese gamelan is an
outstanding example. In addition, recent
compositions such as Inharmonique (Jean Claude
Risset) and Stria (John Chowning) have
demonstrated that inharmonic materials can
render musical ideas with exquisite sensitivity
within a more "western" context." [COhen, E.,
"Some Effects of Inharmonic Partials On
Interval Perpcetion," Music Perception, VOl.
1, No. 3, Spring 1984, pp. 323-349]
Cohen searched for a mechanism which could
explain why "Inharmonic tones are not
conventionally part of the infra-structure
of western harmony, but may be used in
the same manner as harmonic tones
under certain conditions."
Cohen notes that a number of her test
subjects had no difficulty perceiving
harmonic progressions in inharmonic
tones, and perceives as "octaves" intervals
far from the 2:1..."Subject GWM shows no
desire to cling to an octave based on a
learned or innate preference for a physical
ratio of 2:1." [op. cit., pg. 337]
She found similar results for inharmonic
"fifths": "The data suggests that GWM, JWG
and JMS tune by matching partials."
Cohen concludes that "The nature of an
instrument having noninteger partials suggests
a need to develop an interval sense on something
other than simple integer ratios or fundamental
doubling. It is suggested here that GWM relied
on an interval sense that was based on
recognizing the consonance determined by
coincident partials and associating this
sound as a particular interval."
Cohen further points out that "If the composer
fuses the sound by controlling the temporal
evolution of the partials, then the composer
can be assured that conventional relationships
and impressions can be made to hold. If the
composer wishes to exploit the inharmonicity
of the stretched tones, yet maintain certain
consonance relations, then the knowledge
that interaction of the partials can successfully
determine interval size will surely be a useful
tool." [op. cit., pg. 347]
This would appear to strike the death blow for
Paul Erlich's argument.
We are now in a position to see why earlier
experiments with inharmonic tones failed to
produce a sense of spectral fusion, and why
earlier experiments (pre-1970s) with
inharmonic tones usually exhibited a residue
pitch unrelated to the frequencies of the
partials:
[1] Early experiments with inharmonic tones
used crude analog electronic tone production
circuits which generated a set of unrelated
iharmonic partials. Typically, FM or AM
was used, or digital counter circuits.
By contrast, the use of digital computers
to generate inharmonic tone-complexes in
the 1970s allowed researchers to generate
inharmonic tones all of whose partials were
related. Clearly this had a profound audible
effect on test subjects.
[2] Early experiments used extremely "electronc-
sounding" lifeless inharmonic tones with very
simple amplitude envelopes. As John Chowning
has pointed out (and as can be heard clearly
in his composition Phone), even perfectly
harmonic sounds often fail to fuse into
a single percept if the envelopes of the
different partials do not share a common
vibrato and tremolo. The effect can be
vividly heard in Chowning's composition:
a set of partials appears from silence and
while harmonic, sounds like an unrelated set
of partials: but when each partials slowly
begins to exhibit common vibrato, the
set of "unrelated" tones gradually fuse into
the unified percept of a human voice.
The same effect was clearly at work in
early experiments with inharmonic tones.
Later experiments, like Cohen's, use
common amplitude and frequency
information "built into" the envelopes
of each inharmonic partial to encourage
the tones to audibly fuse--and experiments
from the 1970s onward show that such
inharmonic tones, so modified, do indeed fuse.
[3] Early experiments with inharmonic tones
use arbitrarily stretched partials. Later,
more sophisticated experiments, (as we
shall see) use sets of partials which
exhibit the properties of an "inharmonic
series" of tones which are related to some
coherent generating method. The ear can
hear this and places the inharmonic partials
within the inharmonic series, producing
a complete and convincing sense of finality
in inharmonic cadences.
As the final nail in the coffin of Terhardt's
apparently all-embracing theory, note the
article "Reivsion of Terhardt's Psychoacoustical
Model of the Root(s) Of a Musical Chord," R.
Parncutt, Music Perception, Vol. 6, No. 1, Fall
1988, pp. 65-94:
"The predictions of Terhardt's octave-
generalized model of the root of a musical
chord occasionally disagree with music theory
(notably, in the case of the minor triad.)"
Thus Terhardt's theory (like so many others
which purported to give 'all the answers'
about how the ear hears) is now crumbling,
and various desperate attempts are being
made to shore it up.
This tells us (as we should have known all along)
that the ear uses more than the virtual
pitch mechanism to ascertain fundamental
pitch of real-world musical sounds. It also
tells us that the operation of the ear is complex
and context-sensitive, and that therefore an
inharmonic tone progression which offers the
ear alternate cues can and often will be heard
as an inharmonic progression within a coherent
yet inharmonic series of timbres.
The second and final post in this series will
discuss the overwhelming evidence *against*
Erlich's claim, and *in favor of* the ability of even
the most naive listener to hear inharmonic
progressions of inharmonic tones as
exhibiting a sense of harmonic closure,
and a fundamental pitch related to the
fundamental of the inharmonic tone complex..
Ideas fundamental to the extension of microtonality
into the realm of timbre.
--mclaren


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From: mclaren
Subject: Enrique Moreno's 1995 PhD thesis
--
Enrique Moreno wrote a thesis in 1995 entitled
"Embedding Equal Pitch Spaces and the Question
of Expanded Chromas: An Experimental Approach."
This is available as Report No. STAN-M-93 from
the Stanford Unviersity Music Dept., CCRMA,
Stanford CA 94305-8180.
This dissertation is one of the most interesting
and provocative theses about microtonality to
come out of Stanford. It stands as the equal
of Elizabeth Cohen's and Douglas Keislar's
fascinating theses (both highly recommended).
The heart of the thesis can be found on pages 50
through 52:
"We need to see that the tuning has a unique
organization, and that its intervals and chords
are, in justice, as unique as the tuning itself
may be, even when the tuning may contain
very closely approximated versions of some
familiar intervals. The main difference comes
perhaps not so much from the intervals of the
tunig t hemsleves but from the *context* that
the whole tuning as an entity provides for every
interval in it. In this sense, to attempt to classify
the new intervals as variations of twelve-tone-to-
the-octave equal intervals (or of just intervals)
woudl constitute perhaps a reasonable mistake.
"It would be reasonable because it is reasonable
to attempt to understand unknown things in terms
of the things we know, especially if there exists
a certain resemblance. It is reasonable to judge
the world according tothe categories of our
experience, but it is not logical to assume that
our categories are the ultimate representation of
reality. (..)
"Follwoing the same ine of thought, we realize that
notating this tuning with the aid of symbols that
make reference to our usual twelve-tone-to-the-
octave tuning or to historical tunings would be
more or less absurd. Imagine having to interepret
the signs ^b, ~#, as "not so flat" and "not so sharp",
or -b+++ as "quasi-flat plus three syntonic commas,"
or whatever. In short, regardless that some of the
intervals, chords, and even chord progressions may
resemble certain well-known intervals, chords, and
chord progression,s this tuning and many others
(although not necessarily all) deserve a fresh
departure point."
This is the stronget and clearest statement I have
yet found of one extreme of the attitude toward
microtonality--namely, that we should approach
the intervals and the tunings anew and search our
their properties without preconceptions. This is
clearly not entirely possibe--it remains a fact
that the human ear/brain system has measurable
properties and various intervals will have predictable
*sensory* effects on the auditory system--but in
making this point Enrique gets at an extremely
important truth.
Namely, that the *sensory* affect of an interval or
a tuning is not all necessarily the same as the
*musical* affect of that interval or tuning.
N0orman Cazden made much the same point in
the article "On Sensory Consonance," Int. Journ. of
Aesthetics and Art Criticism, 1980, but Cazden
was mainly concerned with demolishing Helmhotlz's
influence. Enrique's point is much farther-reaching.
Now, the other end of the spectrum can be seen
in Easley Blackwood's and Paul Rapoport's writings
on microtonality. "When investigating a tuning for
which there is no repertoire or tradition of any kind,
the most illuminating approach is to look for conenctions
between the new tuning and 12-note equal. All the other
tunings contain many extremely discordant intervals,
and are amenable to row music, or to other non-tonal
compositional techniques. But hte most interesting are
those that include tonal elements--ie., major and minor
triads, and seventh chords, which may be arranged in ways
similar to, but not exactly like, 12-note equal." [Blackwood,
Easley, "Research Notes, NEH Grant RO-29376-78-0642,
1980, page 1]
Clearly this approach has a lot of problems. For example,
Blackwood reveals fundamental bias when he states
that "major and minor triads" are his primary criteria.
This causes him to completely overlook the neutral mode
and neutral triads on tunings like 17-TET and 21-TET,
and as a result Blackwood makes many verifiably false
statements--for example, Blackwood discusses *only*
the major and minor triads in 17-TET. He never discusses
the neutral triad, formed from a third with 5 steps of
70.588235 cents each. Fortunately, Paul Rapoport revises
this oversight--but Paul's overall approach remains
relentlessly Pythagorean and 12-TET-based, which is
simply not appropriate, say, with melodic modes in 19-TET,
or harmonies in 21-TET, or with 9-TET or 7-TET or 10-TET
or many other tuning which cannot be jammed into the 12-TET
mold.
In 17-TET, the neutral melodic mode is an important
resource. Blackwood completely overlooks it. He does
not discuss 8- or 9-tone melodic modes, nor does he
discuss pentantonic modes except in 23-TET, to his
credit.
Thus the great drawback of trying to force all equal
temperaments into the conceptual framework of 12-TET
is that it leads the composer to completely overlook
many useful (but highly non-twelvular) melodic and
harmonic resources.
On the other hand, Easley Blackwood's and Paul Rapoport's
approach to non-12 also has many advantages: by
identifying points of similarity with 12, it gives them
a place to start analyzing harmonic progressions and
melodic modes.
The great weakness of Enrique Moreno's position is that
he does not provide a conceptual framework for harmonic
progressions and melodic modes.
The basic idea of Enrique's thesis (to do it gross injustice
by boiling it down to a few words) is that non-octave
tunings can be characterized by the Nth root of K, where N and
K are integers. In many cases, K then takes on the audible
characteristics of the 2:1 (octave) ratio in the twelve-tone
equal temperament. Thus, Enrique contends--and has data
from psychoacoustic experiments to prove--that in many
cases the K:1 ratio exhibits many of the properties of the
octave 2:1 ratio in 12-tone equal temperament. The particular
property on which Enrique concentrates is chroma--that is,
the property according to which a perceived pitch remains
"the same" perceptually if it is displaced up or down by
that ratio. Thus, in 12-TET, a C4 is heard as "the same"
as a C3 and a C5; similarly, in the 12th root of 3, Enrique
claims (and has data to demonstrate) that a pitch
displaced up or down by 3:1 also "sounds the same."
This gives a starting point for harmony in non-octave
scales, since inversions can now be analyzed, melodic
modes can be described, etc.
Enrique's approach seems especially praiseworthy because
[1] it involves psychoacoustic data, and thus has some
connection to the real world--unlike so much mental-
masturbation "modern" 12-TET music theory; [2] it has
the courage to leave behind 12-TET preconceptions.
If it seems utopian that listeners might be expected to utterly
abandon 12-TET conventions when listening to mirotonal
music, it's well to remember Heinz Werner's paper in
the 1940 Journal of Psychology, cited a few posts back.
Wener found that, given enough time to familiarize themselves
with a microtonal tunings, *every* listener he tested
was able to make the leap into hearing the new intervals
on their own terms.
Further proof is provided by everyday experience--William
Schottstaedt, for example, has pointed out that after working
with 11-TET for an extended period, he found that 12-TET
sounded "strange" when he returned to it.
In sum, Enrique's thesis is a major contribution to microtonal
theory. It also adventurously extends some of the conventional
notions of music theory (i.e., octave equivalence) without
becoming a slave to 12-TET ideas.
--mclaren

From: mclaren
Subject: Yet another overlooked (but remarkable)
article on microtonality
--
The Journal of Psychology is not a place you'd
usually think of looking for articles about
xenharmonic music--especially perceptive early
articles which foreshadow many later developments.
But, as it turns out, one such article was published
in Vol. 10, 1940, J. Psych., pp. 149-156, author
Heinz Werner.
The title is "Musical 'Micro-Scales' and 'Micro-
Melodies.'"
In this remarkable article, Werner discusses
what was later to become known as categorical
perception (though in 1940 it did not have that
name). Werner points out that "A subject, when
presented with a arelatively small interval of--let
us say--0.12 of a semitone, at first may hear a
very slight indefinite difference between the two
tones, or even no difference at all. But when the
same interval is repeated a great many times with
the subject deliberately focussing his attention on
the task of discerning a clear-cut interval, there
will almost invariably be reported an apparent
enlargement of the objectively constant interval.
UIsual;ly there is a maximum in this subjective
augmentation: *the maximum is reached
when this small interval has acquired the subjective
character of a semi-tone.* The time necessary
for the attainment of this maximum increase varies
greatly with the individual, but so far not one
individual has been encountered who did not hear
the semi-tone-like quality after more or less
repetition." [Werner, H., "Musical 'Micro-Scales'
and 'Micro-Melodies,'" J. Pych., Vol. 10, 1940,
pp. 149-150]
In this paper Werner goes on to describe a set
of experiments in meldoic recognition performed
with intervals of "less than one-sixth of a
normal semi-tone (16.5 cents)."
Werner foudn a number of fascinating effects:
one which he called "the law of increasing
stabilization" mandated athat "if the subject should
be presented with an ascending-descending interval,
he will at first perceive the ascending phase as
subjectively larger than the one which descends."
Werner also found audible apradoxes--for example,
because the melodic patterns used tended to
acquire a gestalt quality of their own as well
as the effect caused by the pitch of the individual
notes "this leads to a paradoxical statement
frequently made by the [subjects] that even though
Tones 1 and 2 remain constant in character,
nevertheless the interval separating these tones
may audibly vary in size. All this seems to prove
that it is not the position of the tones which is of
primary important and which creates the quality of
the interval. It would seem that it is the quality of
the interval which determines the position of the
tones in the micro-system."
Yet another fascinating effect was observed when
Werner played the ubjects a straight chromatic
cmirotonal scale versus a melody: "When the scale
such was given chromatically, i.e., step by step,
none of these subjects, providing that there were
completely ' in the system,' found any distinction
between te micro-scale and the normal piano scale.
Indivudal differences came to the fore when the
micro-melodies were compared to patterns of the
normal scale. Two of the subjects felt sure
that no difference existed. One observed expressed
the feeling that it was as if she were sitting in a
puppet theater. 'If one keeps on looking at the puppets,
after a while they acquire the full siz eof human
beings!' The other two subjects felt a certain
difference."
This is a fascinating and to my knowledge one of the
only *subjective* records of naive observers'
reactionsn to microtonal melodies. (By "naive" I
mean test subjects who weren't committed
microtonalists).
Moreover, Werner found that microtonal melodies
were perceived with considerable consistency
by the subjects, once they'd become used to hearing
them. Observers could make reliable judgments
about whether two halves of micro-melody "fit"
together, or whether a melody formed an
antepenultimate closure leading to a cadence,
or whether the melody was perceived as
"empty" or not because it used primarily
members of the harmonic series.
Carol Krumhansl has done a great deal of work
with the "probe tone" method of studying
melodic perception. Comparing her work to
Heinz Werner's, however, it seems to me that
Krumhansl's assumptions are crucially flawed.
For one thing, she assumed that when an observer
hears a 12-TET melody with one note missing
and then a series of notes off by various twelfths
of a semitone, the observer willr eact according
to an innate sense of "tonality," rather than
according ot how s/he has been programmed by
a lifetime of listening to 12-TET.
Second, Krumhansl assumes implicitly that no
systematic distinction can be made by test
subjects between one "mistuned" (tuned off
the target 12-TET note by some number of
twelfths of a semitone) note and another.
But Heinz Werner's article proves this is
clearly not so--and our own experience
indicates very clearly that observers can
easily be trained to hear intervals as small
(in my case, anyway_ as 1/100 of an octave.
In fact Jonathan Glasier reliably tuned Pep
Estavane's Harmonry Harp by ear to 1/100
of an octave intervals per string: he had no
trouble hearing a distinct difference twixt
adjacent tones, and he was reliably able
to detect which strings approximated members
of the harmonic series and which did not.
Third, Krumhansl seems to assume that
observers cannot tell whether the probe tone
is bouncing around between different circles
of fifths (each 1/12 of a semitone or 1/72
of an octave belongs to *different* circle
of fifths--and there are *six* different and
entirely incompatible circles of fifths in the
72-tone equal-tempered scale).
But my own experience indicates that this
assumption is probably untrue--and Werner's
evidence supports this contention strongly.
If Werner's subjects were able to hear
difrferences in the implied harmonies of
one 36-TET scale versus another, would
not Krumhansl's test subjects have made
similar judgments about one 72-TET scale
step versus another?
In short, Heinz Werner's article seems to me
a model of its kind. It is amazing that this
article has almost never been cited in the
microtonal literature. It blazes many new
trails and foreshadows quite a few later
developments. In particular, Werner's
briliant idea of giving test subjects *months*
the get used to hearing micro-melodies
completely revolutionized test procedures
for microtonal melodies.
It is in fact shocking that psychoacoutic
and music psychology experiments continue
to be done today using micro-meldoies, but
*without* giving the subjects adequate time
to overcome the inevitable effects of
categorical perception which are known to
apply to any naive listener who hears an
entirely different tuning for the first time.
Heinz Werner's paper did not seem to garner
any attention...it appears to have dropped
into the sea of psychological literature and
vanished.
Yet it would fascinating to follow up on
Werner's experiments today, using modern
equipment, and do a second series of
experiments pushing further along the
lines Werner laid out. In paritcular it
would extremely interesting to compare
subject reactions to micro-harmonies
a well as micro-melodies, after a suitable
period of acclimitization by the
listeners.
This is a truly remarkable paper, and one
which every microtonalist would do well
to study.
Incidentally, there is one other paper by
Heinz Werner I've been able to track down--
"Uber Mikromeloik und Mikroharmonik," in
Zeitschrift f"ur Psychologie, 1926, pp.
74-128. This probably explains the depth
and breadth of Werner's later paper. Clearly
he cut his teeth on microtonality in the
European quartertone movement of the 20s,
then came to America as a refugee before
or during WW II.
It's a shame he never published anything else,
so far as I can tell. Werner was clearly a
first-rate mind, and an amazingly astute
thinker on the perception of microtonal
intervals.
--mclaren

From: mclaren
Subject: Paul Erlich's innovative & insightful ideas in Digest 749
--
In Tuning Digest 749, Paul Erlich pointed out that
"A typical way of evaluating equal temperaments is to
measure the smallest possible tuning deviation of several
just intervals of interest. The problem with this approach
is that it does not guarantee that the approximating
intervals are consistent with one another." -- Paul Erlich
This is an excellent point, and it's not clear that anyone
else has made it so cogently. In fact this could serve
as the basis of a fascinating article, were any of the
12-TET-obsessed music theory journals interested in
publishing such an article. (You never know. Sometimes
they relent.)
The earliest reference to an idea similar to this one
appears to be found in Mersenne's Harmonicorum Libri...
(1636), pp. 126-127 (last pagination of 2nd ed., 1648).
Mersenne defines each interval as equal to a certain
number of commas, and some of the commas are
incompatible with one another.
This is in the same ballpark as, but clearly not identical
to, Erlich's insight.
--
Gary Morrison's conceptual difficulties in working with
multiple simultaneous tunings are probably what
Ivor Darreg used to call a "pseudo-problem." In other
words, something that conceptually seems like
an unimaginably difficult issue but which, in real
life, turns out to be largely irrelevant or trivial.
(Playing 19-TET or 22-TET on a 7-white-5-black
keyboard is such a "pseudo-problem." In both cases,
the answer is to use open-voiced chord with third
and root played by the left hand, fifth by the right
hand. Simple. Trivial. What's the problem?)
In combining 12-TET and 19-TET, for instance,
we in the Southern California Microtonal Group
have found it useful to view 19-TET as a gapped
nondiatonic scale with some very xenharmonic
ornamental tones.
As I've pointed out before (and as Paul Erlich's
experiments with his roomate demonstrate), listeners
hear the whole-tone portion of a 19-TET diatonic
scale as very reasonable and familiar-sounding, but
the 2/19 of on octave "semitones" (a misnomer, since
this term presupposes that whole tones are
divided into 2 parts whereas in 19-TET they are
divided into 3 parts) always make folks squirm.
They sound...weird. "Out-of-tune" is the typical
description.
The solution, in my experience, is to fracture the
mislabelled "semitone" intervals in the 19-TET
approximation of the 12-TET diatonic scale into
1/19s of a tone. Thus a typical melody in 19-TET
will proceed by whole steps which sound very
reaonable in combination with 12-TET. Then
a constellation of 1/19-octave steps are used
to bridge the gap twixt the next "island" of
whole steps in the 19-TET approximation of
the diatonic scale.
This seems to work reasonably well *provided*
that 12-TET semitones and 19-TET 1/19s of
an octave don't play simultaneously. If, instead,
these intervals "trade off" between different
players (the way good jazz players will trade
off playing flatted blues thirds), the 12 + 19
combo seems to work well.
Another trick that seems to work is to play
melodies full of familiar 12-like intervals
in 19-TET, but to go above or below the last
note of the melody by 1/19 of an octave.
This works well, by the way, for many
incommensurable ETs: 15 and 12, 14 & 17,
15 & 17, 19 & 22, etc.
Many ETs are, however, commensurable--
that is, one forms a subset of the other,
or both form gapped subsets of a much
higher division of the octave.
When combining 5-TET and 7-TET, for
instance, it is often useful to throw
in 35-TET chromatic passages. This
emphasizes that the tiny intervals
heard between 5-TET and 7-TET pitches
that happen to occur vertically are not
accidental, but part of the coherent
35-TET scale.
The issue of combining non-just non-
equal-tempered scales with xen ETs,
or combining, say, all 3 different
classes of tuning simultaneously,
is more complex. I'm still feeling
my way along in this regard.
--mclaren

From: mclaren
Subject: More marvellous musical insights from
the musical cognitive elite
--
Without concern for how the music *sounds*,
no system of composition can long survive.
And the endeavour to keep a brain-
dead theory of composition from perishing,
on life support, years after its rationale
has gone, can only lead to brain death.
The latest outbreak of this symptomatic
condition bursts forth in Perspectives of
New Music, Vol. 39, Nos. 1 & 2, 1995,
pp. 554-558.
The article is "Cheered By Battleship," by
James Boros.
It's quite something.
"It ended in an open shaftway, following
LBJ's example. By designating cauldron
19 as their sauce, mirages (against no odds)
vented mighty grams of plenty, and cast
visceral tracking smoke in henceforth
unforeseen celebtrations of danger. Without
too much grinding, her inappropriate spasm
posed as a lofty cur: negation would only
disprove gaiety in instances *not* involving
firecrackers declared inspid by consensual
bigotry. Having agonized under lack of stress,
the rambunctious turnip sought deadening solids
as a means of obtaining `gaslight marginality'
admist dining vocations of porn. Besides, where
in Charlie's hell is there room for another
afghan recorder?" [Boros, James, "Cheered By
Battleship," Perspectives of New Music, Vol.
39, Nos. 1 & 2, pp. 554-555]
Ah, the aroma of modern 12-TET music theory!
Reminiscent of a Tasmanian devil sniffing its
own arse...
In the Alice In Wonderland world of so-called
"serious" modern music theory, *this* is what
passes for profound investigation into the
nature of contemporary music.
Meanwhile, when I write:
"if we've learned ANYTHING by reading the past
60 years of music history, we've learned that there
*isn't* any final stage of musical evolution.
There is no `ultimate style.' There is no
`Single correct way to compose.'"
.. When I write such a sentence, these are the
ravings of an unpleasant crank.
By contrast, James Boros demonstrates sublime
insight into modern music when he blesses us
with these nuggets of immortal wisdom:
"...On and on, reeling in daft plaque via assorted
remora directionality... Semblances, forked like
brazen espresso wallflowers, logged furiously
against the wishes of `kelp,' delegating crap
to wealthy bunglers whose pouches struck
Mickey as naked." [Boros, James, "Cheered By
Battleship," Perspectives of New Music, Vol.
39, Nos. 1 & 2, pg. 555]
The ravings of a tiresome crank:
"The clearest example of this Orwellian and ruthless
state of musical conformity is of course the string
quartet. Offhand, there's no reason at all why 4 fretless
string instruments couldn't perform in any scale desired--
19-TET, 31-TET, 53-TET, 11-TET, the free-free metal
bar scale, the Bohlen-Pierce scale, or any other tuning.
Naturally, any string quartet that gets handed such a score
will burn the offending sheaf of music paper and
bury the ashes. Naturally, all string players have been
programmed to perform in 12, only 12, always 12, forever
12." -- mclaren, Tuning Digest 592
Profound modern music theory:
"Traditions upheld with a pang, we jogged into
sunbeams laden with molten beef, and skimmed
the celebrants' Tuscany while dimming flaps
Prognoses adhered to rougher points (like sawteeth)
despite their having been abused in deep water."
[Boros, James, "Cheered By Battleship," Perspectives
of New Music, Vol. 39, Nos. 1 & 2, pg. 555]
The ravings of an unpleasant crank:
"Moreover, the most important facts
about the equal tempered scales are
not available in and have never been
mentioned in the music theory journals:
Each equal temperament has its
own `sound,' or `mood,' or `sonic
fingerprint.' Ivor Darreg was the
first to point this out, in his 1975
Xenharmonic Bulletin. Over a period
of some 25 years, he made
literally hundreds of different
demonstration cassettes showing
the vivid differences in sound between
different equal temperaments. No
academic music theory journal has
ever referred to these clearly audible
differences between equal temperaments."
--mclaren
Profound modern music theory:
"Upon crossing the lumbar nerve, it noted several
uranium holster supplements making faces at
crossfire emitted from one of the New England
states. Her dance resembled that of a thumbprint,
water-logged janitors aside." [Boros, James, "Cheered
By Battleship," Perspectives of New Music, Vol. 39,
Nos. 1 & 2, pg. 555]
Yes indeedy...
In the Alice In Wonderland realm of so-called
"serious" modern music, black is white,
up is down, dry is wet, ignorance is strength,
freedom is slavery, and gibberish is profundity.
Sho' nuff, chilluns...
Passages like "This grieving advertisement put
'em in a vault with lather and resin, and prayed for
the delivery of wounds" offer incisive illumination
into the nature of modern music (because after all
they appear in a "serious" modern music journal,
Perspective of New Music). Meanwhile, my statements
that 12-TET music theory has descended into
a frenzied spiral of mental masturbation and
glossolalia are the ravings of a crank.
Yes, once we step behind the looking glass and
emerge into the world of modern music theory,
anything is possible.
Anything, it would seem, but common sense, logic,
and sanity.
--mclaren


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From: mclaren
Subject: sound
--
This post deals with the sound of
xenharmonic recordings. As always,
most of you won't like these opinions--
and, as always, many of you will claim
that these statements are false,
ignorant, untrue, delusional, etc.
As usual, this is incorrect and yet
another demonstration that most of
you have ruined your hearing by
listening to far too much rock
music or far too many concerts
of so-called serious electronic
music at far too high amplification
levels. (This proved a critical
probem at the 1992 ICMC concerts.
TA's often pumped up the volume so
loud that the entire audience cringed,
held their ears, and the speakers
distorted.)
A number of forum subscribers have
claimed that most of the music we
all hear is live, rather than
recorded. This claim can only be
explained as the result of mental
illness or hard drug usage, since
it is so indisputably contrary to
everyday reality.
"The pervasive assumption that
support for new music and its
composers equals support for
performances...needs questioning.
(..) Most music is heard at home,
via records, radio and printed
sheet music. Composers have been
getting little support for creation
or presentation of works via these
media to the many people who depend
on them." [Spiegel, Laurie, "A
Non-Performance Viewpoint," New
Music America '81 Festival program
booklet, page 49, 1981]
Since most music is heard at home
via CD, cassette or radio, this
means that the way in which microtonal
music is recorded is *at least* as
important as the microtonal music
itself.
First and most important is the issue
of how the recording is mixed. The hard
cold fact is that you can either mix
for headphones, or for speakers--but
you can't mix for both. A mix that
sounds best when heard over headphones
is likely to sound indistinct, with
an exaggerated sound stage when heard
over speakers. Contrariwise, a mix
that sounds best when heard over
speakers will seem too dry and too
sharp-edged when heard over headphones.
Alas, there is no way around this
dilemma. You cannot mix so that the
recorded sound is optimal on *both*
headphones and speakers.
Unfortunately, even the most expensive
audiophile speakers sound utterly
completely 100% totally different from
headphones. There is no sonic comparison
whatever. This becomes especially clear
when you make binaural recordings using
mikes placed about as far apart as the
ears on a human head. A 2-mike binaural
recording will sound truly startling
in its realism when heard
over headphones, but it will sound
disastrously weird when you hear it
through a pair of speakers.
Headphones isolate one ear from the other;
speakers blend the output of both channels
in the air and throughout all reflecting
surfaces in the room.
The result? Speakers usually tolerate far
less reverb in the mix. A subtle touch of
BBE or Aphex aural enhancement will also
greatly help the clarity of a mix
heard through speakers. Even drastic
processing like the Carver sonic holography
process will sound acceptable. But the same
"enhancements" will produce an unpleasant
in-your-face edginess and dryness when heard
over headphones.
Thus, you must decide which source you're
mixing for *before* you starting mastering
your CD or cassette. Moreover, you must
stick with that decision. Nothing sounds
worse than one track of a CD optimized
for listening over speakers and another
optimized for listening over headphones.
--
The next issue is dynamic range. Headphones
take maximum advantage of a recording with
a large dynamic range, while speakers
cruelly punish a recording with vast dynamic
range. Over speakers, much of a xenharmonic
composition like William Schottstaedt's
"Water Music" is either inaudible or
ear-shattering...yet the same composition
becomes clearly audible when heard
over headphones.
A recording with large dynamic range pretty
much demands headphone listening (The
alternative is a whisper-quiet listening
environment with ultra-high-quality loudspeakers
in a place where the neighbors won't protest
jet-plane-takeoff sound levels. Very few
listeners have such a loudspeaker environment
available.).
Thus, wide dynamic-range xenharmonic recordings
intended to be heard over loudspeakers must,
as a practical matter, employ some compression.
Unfortunately, compression always changes the
sound of a composition. This is especially
noticeable in commercial pop music, where
the maximum dynamic range is about 5 dB.
In such recordings, changes in timbre take
the place of changes in loudness, and this
may require corresponding changes in
you orchestration of a piece of music with
a very wide dynamic range.
One salient point about compression:
it must be applied without regard for the
settings of the equipment, but with
concern only for whether the final result
approximates the original sound of the
live recording. My experience is that
drastic alterations are often required
to get a recording to sond like a live
performance. Often, radical compression,
sonic enhancement, dynamic noise reduction
and gain riding are needed to produce a
recording which when heard over loudspeakers
approximates what you heard in live
performance. Alas, loudspeakers are wildly
non-linear transducers whose measured response
curves bear no relation whatsoever to the
sound you hear. (The reason is simple: graphs
of loudspeaker response vs. frequency give
data *only* on the magnitude of the frequency
response, *never* on phase response at that
frequency, and as Fourier's theorem tells us,
both magnitude *and* phase data are required
for a full reconstruction of the original
signal. Equally important, loudspeaker response
is measured in an anechoic chamber using a
microphone which stays in a fixed position
relative to the loudspeaker. In a real listening
situation, each listener will hear the loudspeaker
from a different position and in a different
sound-absorbing and sound-reflecting environment.
Thus, the graphs typically published in hi-fi
magazines are meaningless as an index of the
actual sound of a pair of loudspeakers. These
graphs are as ludicrous as a graph of the
reflectivity of 450 nm light from Rembrandt's
"The Night Watch" from a photomoter fixed 5
cm from the painting's surface as an indication
of the overall "look" of the entire painting.)
Each loudspeaker type (acoustic reflex,
ribbon, horn, electrostatic, etc.) and
each placement and each listening position
and set of amplifiers, recorders and preamps
produces a different overall "sound."
Using a vacuum tube amplifier as opposed to
a solid state amp will significantly change
the sound of a reproduced recording--changing the
loudspeakers from, say, Klipsch horns to
Magnaplanar IIIDs will transform the sound of
the recording to an almost unrecognizable
extent.
This brings up the issue of boom boxes.
Although it seems wildly insane, it remains
a fact that most of your prosepctive audience
will listen to the output of 50,000 dollar
computer music workstations or tens of thousands
of dollars of handcrafted xenharmonic instruments
or a roomful of microtonal synthesizers over 40 dollar
boom boxes. This is a development so weird
as to border on the psychotic, yet it
remains unquestionably true. Because of
the rush-rush-rush nature of our society,
most people listen to xenharmonic music
either on a boom box or in their car.
The best way to mix for this kind of
peculiar playback situation is on a
set of satellite loudspeakers with small
cheap tweeters and the subwoofer EQ'd
nearly off. This reproduces the extremely
poor frequency response and dynamic range
of the average boom box/car stereo.
A piece of microtonal music mixed for
boom box or car stereo playback must be
compressed to about 20 dB dynamic range.
Notice that this is not "20 dB of reduction
in dynamic range," I mean that the entire
range of the composition must be compressed
to fit within the 20 dB of useful dynamic
range available on the average cassette
deck. This means that if you start with
a composition which uses a dynamic range
of 96 dB in 16-bit linear DAT format, you
will have to compress the output of the
DAT recording by at least 76 dB since
(as we all know) most cassette decks
produce garbage output if the recording
level falls below -20 dB. Typical compressors
useful for most musical material include
the dbx 163x series.
This kind of bizarrely extreme 76 dB
compression will produce a large number of
unfortunate artifacts which cannot, alas,
be avoided. The alternative is to refuse
to mix for cassette deck playback, which
means that your recording will (to most
people, whose hearing has been destroyed
by excessive volume levels and who seem
perfectly happy with the exercrable
sound reproduction afforded by a boom
box/car stereo) sound too reverberant,
indistinct or "muddy," and inaudible
throughout much of its length.
--
The next issue to bear in mind when
recording xenharmonic music is that
computer music requires an entirely
different mixing technique than
live music. Computer music typically
uses sine waves or other kinds
of synthetic tones that cut through
a listener's head like a knife;
typical recording levels for a
xenharmonic piece of computer music
should be at least 20 dB lower than
for live music. This is a classic
case of the Fletcher-Munson curve
at work, and when mixing computer
music you should always ignore
the meter levels. Instead, play
back a live piece periodically
to get a general loudness comparison
and set the levels with complete
disregard for the meter readings.
--
Lastly, there remains the issue of Dolby
encoding. As Dolby Labs has admitted,
the Dolby decoding circuits of most
cassette decks are badly miscalibrated
at the factory, or simply left uncalibrated
entirely. If you doubt this, ask yourself:
when was the last time you saw an audio
techician or a sound man with a Dolby B
calibration tape?
Try: "never."
As a result, the poorly calibrated Dolby B
decoding circuits in most cassette decks
turn Dolby encoded recordings into mush.
When poorly adjusted, Dolby B acts as a
drastic low-pass filter. And since
virtually all cassette decks use
uncalibrated or misadjusted Dolby B
encoding/decoding circuitry, this means
that the best solution is always to
*AVOID* Dolby encoding.
Dolby C works well if the same cassette
deck is used to play back the tape as
was used for recording. Otherwise,
Dolby C produces wretched artifacts.
In effect Dolby C is so cassette-deck-
specific as to prove useless in the real
world.
Dolby Spectral encoding is an excellent
method of noise reduction which, alas,
is featured on almost no casette decks
because the fools at Dolby Labs overpriced
the technology outrageously on its
introduction. When DAT arrived, it proved
far cheaper than adding Dolby S to existing
30 ips reel machines, and so Dolby S never
caught on. Yet another example of "how
not to introduce new technology."
--
Because Dolby encoding (even when adjusted
with a factory-authorized calibration tape)
inevitably produces many unacceptable
artifacts in the source material during
playback, some hiss will be evident in all
your recordings (since any sane person will
avoid Dolby encoding like the plague). This
means that it's vital to push the levels
of the recording as high as they'll go during
cassette dubbing so as to minimize noise
during playback.
In my experience, the most important element
in a cassette dubbing chain is the source
quality--preferably DAT--and after that, the
cassette deck. This means that you will get far
more bang out of your bucks by spending them
on a good cassette deck than on a ton of
signal enhancement gear.
It remains a fact, alas, that Nakamichi still
makes the best cassette decks around. Avoid
the high-end Nakamichi decks and buy the
cheapest new model available. The high-end
Nakamichi cassette decks do such a freakishly
good job of reproducing the execrable audio
signal on the crappy cassette format that a
Nakamichi Dragon (for example) will delude
you into EQ'ing the high end of your recording
down much lower than it should be.
The best way to test your recording is to
make the copy on a Nakamichi deck and play it
back on a crappy K-Mart boom box, since this
is the way virtually everyone will listen to
your recordings. Such grotesquely poor
quality playback will quickly bring to light
any EQ or reverb problems with the master
recording--generally you'll have to EQ
the high end up or add considerable amounts
of BBE or Aphex enhancement to make up for
the fact that the average boom box has
less bandwidth that a typical telephone.
The analog compact cassette might not be
the world's lowest-fidelity recording
medium; it's possible that Edison wax
cylinder recordings sounded worse. However,
this question remains open. It is possible
that the analog copmact cassette does actually
the worst possible audio fidelity of any
recording medium ever invented.
Regardless of the outcome of that issue,
it remains an obscene and outrageous fact
that we will reach the 21st century with
most people listening to microtonal music
on ultra-lo-fi analog audio cassettes
with lots of hiss, plenty of wow and
flutter, and enormous amount of distortion.
Thus it behooves us all to produce the best
possible cassette recordings of microtonal music...
a task akin to producing the best possible
buggy whips we can make. Insane, senseless,
bizarre, and outlandish--yet incontrovertibly
necessary given the utter failure of DAT,
MiniDisc or DCC to survive in the consumer
marketplace as affordable viable mass
recording/playback formats.
--mclaren


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> Over speakers, much of a xenharmonic
> composition like William Schottstaedt's
> "Water Music" is either inaudible or
> ear-shattering...yet the same composition
> becomes clearly audible when heard
> over headphones.

When I was working on this and other related pieces,
I was using the Samson box here at CCRMA connected to
a relatively low-fidelity quad speaker setup in a
room next to the old Lab's machine room (this was
the (end of the) era of enormous air-conditioned machines).
The thing sounded great in that environment. Then
we played it in a concert in very reverberant room
in S.F. and it sounded like mush. Then later it
got put on CD, and I listened at home in my kitchen,
and decided it needed to be compressed, so the
latest version has a much smaller dynamic range,
less reverb, less noise, but maybe lost some of the

exuberance. Rats.

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