Yahoo Tuning Groups Ultimate Backup mills-tuning-list Tuning Preferences

I would like to respond to some of Brian's good points about just
intervals, but before getting into specifics, I would like to talk about
the musical applicability of these studies. I would imagine that if you
asked subjects to state their "preference" between minor seconds and major
thirds, the thirds would be a near unanimous choice. Does this mean that
minor seconds should never be used in music?

Also, I don't think many people since the time of Helmholtz have claimed
that small-number ratios are the only criterion of consonance. Certainly I
have not. Consonance, in a musical sense as well as a strictly
psychoacoustic sense (if there is such a thing) is a very complex
phenomenon that depends on the ratio, on its relationship to the critical
bandwidth, on the relative timbres, the absolute frequencies, the loudness,
and, not least of all, the musical context.

Finally, as John Chalmers has pointed out, these studies are not without
their cultural biases. Though such biases difficult to test, given the
current ubiquity of twelve-tone equal temperament through radio and
television, I think that one is bound to show a "preference" for the
familiar. Some evidence for this comes from the article Brian quoted
earlier: Kessler, Hansen, and Shepard, "Tonal Schemata in the Perception of
Music in Bali and the West" (Music Perception, Winter 1984 V2/2, 131-165).

>[1] [Comparison of sqrt(3/2) to 45/32]

I personally find 45/32 much too high a ratio to be called "consonant," and
I don't really hear it as just. To take a fairer comparison, I do find 7/5
more consonant than a neutral third.

>[2] Tune up 11/9 and compare it to 9/8. Which sounds more
>consonant?

This is true and illustrates my problem with a reliance on LCM analysis.
Because 9/8 is small and, depending on the absolute frequency, may lie
within the critical bandwidth, I find it relatively dissonant. I don't
think that the relative simplicity of the ratios are as much of an issue.

>[3] Tune up a second inversion 4:5:6 chord--that is, a just major
>chord with a 4/3 in the bass, i.e., a 9:12:15 triad. Now compare it
>with a 10:12:15 minor chord.

If one resolves the numbers here you have 4/3 and 5/3 in the first and 6/5
and 3/2 in the second. Based only on the ratios, I find 5/3 and 6/5
equivalent -- they are inversions of each other. That leaves 4/3 and 3/2.
Clearly 3/2 is the more stable because it lies lower in the harmonic
series.

>[4] Tune up the ratio 3:5:7 and then tune up the ratio 18:22:27.
>Which one sounds more consonant?

Here I have to disagree. While they both have distinctive sounds, I find
the 3/5 and 5/7 intervals more consonant than the 11/9 interval of the
second triad.

>This also sidesteps the dilemma of the just perfect fourth.

The dilemma of the perfect fourth is in part a historical artifact of
producing counterpoint by counting intervals relative to the lowest sound
voice (which for simplicity I'll call the bass). Thus the apparent
consonance of the perfect fourth and perfect fifth sounding together if one
only looks at them relative to the bass is taken care of by considering the
fourth dissonant. As is obvious to anyone looking at all the interval
combinations, the dissonance is not so much the fourth as the second
between the two upper voices.

The second reason for considering the fourth relative to the bass a
"dissonance" is to explain the need for the second inversion triad to
resolve. To me, this need for resolution is not so much because the 9:12:15
is "dissonant" as the simplest interval lies higher in the harmonic series
than either the octave or the perfect fifth. Therefore the chord sounds
less stable than one based on a 3/2. Also, some medieval musicians were not
bothered by this relative instability.

>Too, as Norman Cazden points out:
>"Traditional rules of harmony and counterpoint explicitly
>proscribe parallel successions of perfect intervals, though
>with the unaccountable excpetion of that same troublesome
>fourth when it is not in the lowest placement.

Using the stylistic conventions of one musical culture during one period of
history is a weak justification at best. The main reason behind the
prohibition of parallel perfect intervals was to maintain the independence
of the voices sought by European polyphonic composers of the 15th to 19th
centuries.

Parallel octaves causes the texture to suddenly thin because the octave
lies so low in the harmonic series -- which is why we tend to consider men
and women singing in parallel octaves virtually the same as monophony. Put
another way, the upper voices are doubling a harmonic already present in
the lower voices.

So, do we prohibit all parallel intervals, since they must be found in the
same harmonic series of some fundamental somewhere? Of course not. As we
move further up the harmonic series the impression of the two voices
operating "as a single unit" becomes less and less prominent. So where does
one draw the line? Perfect unison? Perfect octave? Perfect fifth? Perfect
fourth? Major third? Minor third? Well, composers of the 15th century chose
the draw the line between the perfect fifth and the perfect fourth.
Incidentally, it is interesting to note that 13th century motet composers
quite intentionally avoided parallel thirds, though parallel fifths and
fourths are often found.

I have nothing against composers who prefer the musical usefulness of equal
temperament or any other type of temperament. Nazir Jairazhboy, the Indian
music master quoted by Brian earlier, points out that he finds that
tempered intervals can give extra tension to a melody in need of
resolution. As Brian has pointed out as well, the Javanese find perfect 2/1
octaves rather lifeless and usually try to compress or expand them.

However, to say that there is some natural predilection for just,
equal-tempered, or any other kind of scale is, I think, to misunderstand
the relationship between nature and art. Certainly one would think Brian
would understand this, having composed in JI himself, according to John.

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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🔗John Chalmers <non12@...>

From: mclaren
Subject: The hideous truth about web searches
for info on the word "microtonality" - post 2 of 2
--
(COMMENT: Predictably, a small vocal minority
will contradict with a great deal of misinformation
every statement made in the last post. Here,
as cold hard proof that no useful info is
yet available to the microtonal beginner on the
WWW, is an actual transcript of a typical web
search session:)

Lycos search: microtonality
66557959 unique documents in catalog.
Your query resulted in 27 relevant documents on 3 pages.

Words searched:
microtonality
These words were ignored:

Just Intonation and Microtonality
http://www.ftech.co.uk/~rainbow/just.html

(COMMENT: This is a dead 404 URL)

Music-Research Digest Fri, 2 Feb 90 Volume 5 : Issue 8
Today's Topics: Call for papers on microtonality
Cognitive Musicology (from: Research Digest Vol. 5, #02)
DARMS parsers/manipulators ...
ftp://cattell.psych.upenn.edu/pub/Music.Research/5.08

(COMMENT: A call for papers on microtonality. Useless
as a source of info.)

EMUSIC-L Digest Volume 13 EMUSIC-L Digest Index to Volume
13 Issue 1 Topics: Musician's dependencies 4-track recommendation
DSP card programming (3 messages) Oberheim Matrix-6 sys-ex ...
http://sunsite.unc.edu/mcmahon/emusic-l/back-issues/vol13/

(COMMENT: An electronic music thread. No discernable relation
to microtonality, except perhaps that one of the synthesizers
mentioned might be retunable.)

CDeMUSIC CDeMUSIC is a worldwide service that gives you
easy, direct-mail access to one of the most comprehensive
selections of compact discs of experimental, exceptional,
and/or electronic music...
http://www.emf.org/emusic.html

(COMMENT: A couple of their discs are microtonal--the
Easley Blackwood "12 Etudes" and the Ivor Darreg
"Detwevulate!"
99% of CDeMUSIC's discs are *not* microtonal.)

ZIA With virtually every major industrial band somehow
interconnected with one another through side projects,
it was only natural for the burgeoning electronic scene
in Boston to also take on ...
http://ftp.std.com/obi/Zines/Chaos.Control/ZIA.html

(COMMENT: Web page for Elaine Walker's ZIA, a 19-tet
and Bohlen-Pierce tuning industrial band.)

Partch's Legacy. Perhaps the obvious subject for this
opening column is Ben Johnston. I was never one to
avoid the obvious. Johnston is of interest to the
Society as one of the ...
http://www.ftech.net/~rainbow/legacy.html

(COMMENT: A dead 404 URL)

Robert Rich Biography Biography for Robert Rich
Music Style: Progressive electronic, Ethnic fusion,
Ambient, Techno-Tribal Instrument: Synthesizers,
flute, guitar, percussion Building his first ...

(COMMENT: Robert Rich web page. Useless as a
source of info on microtonality, though Rich
*is* a microtonalist.)

Interview for ND Magazine Interview for ND Magazine
with Todd Zachritz June 29, 1993 1) First, how did
you become interested in sound construction/music?
Since I started playing music when I was ...
http://www.amoeba.com/rrich/rr/nd.html

(COMMENT: No perceptible relation to microtonality.
He talks about computer musique concrete.)

Frequence Interview Interview with David Bottile
at Frequence 6 March 1995 1) Tell us about your
work in Psychology. I got my university degree
in psychology, focusing on psychophysiology, ...
http://www.amoeba.com/rrich/rr/frequence.html

(COMMENT: No discernible relation to microtonality.
He talks about psychoacoustics and the psychology
of music.)

T Index - MIDI Classics T Index - MIDI Classics
T Product Index TECHNO DANCE/ SMF #3302 SEQ
$26.96 TRADITIONAL CHRISTMAS/ SMF #3299 SEQ
$26.96 TRANSPORT/ MAC- nonlin avid protools
deck #1991 S/W ...

(COMMENTS: Ads for DSP software and MIDI
sequences. NO relation whatsoever to
microtonality.)

ACCA PACKAGES data structure Amsterdam
Catalogue of Composition Algorithms home
page of ACCA home page of Alfa-Informatica
PACKAGES data structure The PACKAGES database
is meant to contain all ...
http://mars.let.uva.nl/ACCA/Database.Packages.html

(COMMENT: Compositional algorithms. NO relation
whatsoever to microtonality.)

Interview with Elliott Sharp [Return to ESTWeb
Home Page] [Return to Interviews Index] An
Elliott Sharp discography exists on the net.
There is also a web page maintained by Extreme
Records. An ...
http://www.ultraviolet.com./zines/est/intervs/sharp.html

(COMMENT: What a shock--this person is actually a
microtonalist. Along with Elaine Walker's ZIA
and the EMF page, that's 3 references that
have *anything* to do with microtonality so far...)

The Noise (Festival) Of American Music The Noise
(Festival) Of American Music Normally, Sacramento
is a pretty sleepy town when it comes to music
and art. I guess I'm talking about culture. Being...
http://beercity.com/heckler/noise.html

(COMMENT: No relation whatsoever to microtonality.
Industrial music festival in Sacramento.)

Industrial Prehistory: Anti-Music ii.Anti-Music
Although it would be nice to trace back the idea
of using noise as an element in music to the
futurist Luigi Russolo's manifesto, The Art of Noises...
http://www.schwa.org/zines/est/articles/prehist5.html

(COMMENT: An industrial music essay. No relation
whatsoever to microtonality.)

SoundCanvas User's Group WWW Help Centre
SCUG - WWW Help Centre! Mr. Web Counter says that
have been helped since June 9, 1996. Roland Go to
Roland's Home Page
http://www.interlog.com/~stilpaul/scug/help/help.html

(COMMENT: Technical details on the Roland Sound Canvas
card. Only the most tenuous connection to microtonality,
since the Sound Canvas can theoretically be retuned. No
info on how to tune it to various temperaments or just
intonations, though.)

BG - What's New Viol o Page Guitar Page What's New
Index: Badi Assad in Boston That's really hot,
Mannis!!! If you are in the Boston area, don't miss it!!!
http://www.cce.ufpr.br/~ofraga/whatsnew.html

(COMMENT: Boston thrash punk bands. No relation whatsoever
to microtonality.)

Date: Monday, 08-Apr-96 01:20:20 GMT Last-Modified:
Thursday, 26-Oct-95 18:28:55 GMT Content-type:
text/html Content-length: 8213 Music 315 Music in
the 20th Century: Music and Technology MUSC ...
http://orpheus.tamu.edu/music.program.web/computer.
music/Mustech.html

(COMMENT: Course offering from Texas A & M University.
The course mentions Harry Partch as a footnote. This is
what you call "getting desperate" in the search for the
word "microtonality"...)

Events - May 1994 To Do & Notice - May 1994 May 1
Special Exhibitions Science Stuff You Can Do with
Beakman and Jax Last Day Based on the internationally
syndicated Sunday cartoon strip that ...
http://www.exploratorium.edu//./events/may_1994.html

(COMMENT: No relation whatsoever to microtonality. How
did this get in here?)

Silence Digest Volume 1 Number 27 Received:
(from daemon@localhost) by zoom.bga.com (8.6.12/8.6.10)
id JAA06515 for silence-digest-outgoing; Thu, 20 Jul
1995 09:55:20 -0500 Date: Thu, 20 Jul 1995...
http://www.realtime.net/~jzitt/Cage/cage0127.html

(COMMENT: A webzine devoted to the inept charlatan
John Cage. No relation whatsoever to microtonality.
How did this get in here?)

Events - June 1994 To Do & Notice June 94 June
1 Interactive Sound Studio Special Exhibition and
Summer Festival Through September 5 A three-month-long
festival of sound and music (previously ...
http://www.ylem.org/./events/june_1994.html

(COMMENT: An ad for some interactive museum exhibit.
No connection whatsoever with microtonality.
How did this get in here?)

List of microtonal music on CD Microtonal music on
CD This list contains microtonal/xenharmonic/non-12
music on CD only and no works in 12-note just intonation,
12-note in historical temperaments...
ftp://mills.edu/ccm/tuning/papers/discs.html

(COMMENT: At long last, something informative...this is
my and Manuel Op de Coul's list of microtonal CDs at
the Mills site.)

Bibliography on synthesizers, Midi, Computer and
Electronic Music Bibliography on synthesizers, Midi,
Computer and Electronic Music Version: $Id:
bibliography,v 1.39 1996/02/05 14:36:15 piet Exp ...
http://www.ircam.fr/biblio/bibliography.html

(COMMENT: No relation whatsoever to microtonality.
How did this get in here?)

ACCA: List of Tools Amsterdam Catalogue of Composition
Algorithms home page of ACCA home page of Alfa-Informatica
List of Tools by and reproduced with permission of
Leonidas Hepis LIST OF TOOLS ...
http://homepage.interaccess.com/~beckwith/d0004/s0000326.htm

(COMMENT: Again, this has nothing to do with microtonality,
and we've seen it before.)

(COMMENT: And b-dat b-dat b-dat b-dat's all, folks!
What an incredible list of non sequitur junk info, eh?
Out of ALL of these references, only 4 had anything
to do with microtonality: [1] Manuel's and my list of
microtonal music on CD, [2] The EMF catalog containing
a couple of microtonal CDs, [3] the Elliott Sharp website,
[4] Elaine Walker's ZIA website.
*Notice that the most useful starting point on microtonality
anywhere on the web--the microtonal bibliography at mills--
was NOT found.*
Good work!
So the search engine turned up VAST amounts of irrelevant
*crap,* but COULDN'T FIND the single most useful source
of info on microtonality on the web.
Hey...that sounds about right.
Web pages on algorithmic composition and industrial music...
a bibliography of books on synthesizers...a "special
exhibition of science stuff" at a museum...
You know, as long as the Lycos search engine was
finding irrelevant trivia in its search for "microtonality"
on the web and *ignoring* the single most useful
source of info *about* microtonality on the web,
why not just go all the way?
I mean, why do things by halves?
Why didn't LYCOS just spit up a list of URLs at random?
The Sudan Web Site...Sex life of frogs web page...
the Chrysler web page...these non sequitur websites
have exactly as much to do with microtonality as
the actual sites puked up by the LYCOS search engine.
Worst of all, this is TYPICAL of the results
for ALL search engines.
Naturally a few of you will vociferously claim
that all these statements are untrue, etc., etc.
Alas, there seem to be a handful of forum
subscribers dedicated to purveying misinformation
and canards whenever and wherever possible. The
brutal fact is that the only way to weed out all
the junk info and bad hits containing websites
irrelevant to microtonality is to refine your
search for the word "microtonality" in such
a sophisticated way that you'd have to already
know what you're looking for. In short, all the
search engines on the web generate useful info
on microtonality *ONLY* if the searcher *already
knows* exactly what s/he's looking for.
But this is *never* going to be the case for
a microtonal beginner. Thus, newcomers to
microtonality are left high and dry--left to
wander for themselves in a blizzard of junkthink,
guitar ads, industrial music reviews and
web pages touting MIDI software which has
*nothing* whatsoever to do with microtonality.
Ladies and gentlemen, you'd have better luck
examining tea leaves in your quest for useful
information about microtonality than in searching
the world wide web.
--mclaren

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🔗John Chalmers <non12@...>

From: mclaren
Subject: Technology drives tuning
--
Having made this claim, it behooves me
to offer proof.
We read in Boethius that Pythagoras
discovered the relationship of fifth
and octave by listening to a blacksmith's
hammers. The weights of the hammers
purportedly produced different pitches
when the blacksmith smote the anvil.
This is of course pure fantasy. Hammers
of different weights striking an anvil
give off the same tone at different
volumes. It is the bell, not the clapper,
which produces a tone, and the pitch of
the tone is not determined by the mass
of the clapper but by the mass and
shape of the bell. (Bells have recently
been designed by computer to sound a
major chord rather than a minor chord.)
In any case, simply doubling the weight
which hangs at the end of a string would
produce a pitch in the ratio of 1.414 to the
original note (Pythagoras was supposed to
have rushed home and performed this
experiment; obviously he did not, nor
did Boethius. Galileo's father did, and
published the results.). Doubling anvil weights
produces an interval not of an octave but
a tritone. As it happens, vibrating metal
bars behave differently from strings, and
so the tale about Pythagoras is a myth.
However, this tall tale shows pretty clearly
the level of technology available in classical
Greece. Pythagoras didn't rush home and
try out his theory on a keyboard instrument
or a zither with 88 different strings at
high tension because the Greeks didn't have
the technology to build such instruments.
For one thing, you have to know a good deal
about metallurgy to produce tough wires as
would be needed in a harpsichord or zither or
piano; for another, the Greeks didn't have
the technology to machine metal as is
required to produce metal screws, iron
frameworks for pianos, etc.
What sort of intonation system is most
appropriate for a technology limited to
lyres with only a few gut strings and
some wind instruments?
Because gut changes its tension with
humidity and because it must be kept at
low tension lest the gut strings break,
the intonation best suited for such
technology would use only the simplest
and most obvious members of the harmonic
series. Plucked gut strings produce harmonic
series timbres, so the second and third
members of the harmonic series would be
most useful in tuning such instruments.
Because of the extremely low tension of
a tortoise-shell lyre (try and add a lot of
strings or tune them to high tension and
either the back of the lyre will collapse
or the gut strings will snap), the sounds
will be faint and only the very lowest
harmonics will be audible. The 5th
harmonic and higher harmonics would
probably have been extremely faint on
a plucked gut string, too faint to tune
to.
Thus the technology of classical Greek
music lent itself primarily to Pythagorean
tuning.
The tuning of auloi is not so limited; however,
it remains unclear what the Greek auloi were.
Some authors claim they were similar to
oboes, in which case they would demand
a tremendous amount of air. Other authors
claims the Greek auloi were more flute-like,
in which case the sound would have been much
louder and the players less sorely taxed.
However, even today it's impossible to calculate
precisely the position of tone holes for simple
wood instruments theoretically; the theory
never matches the actual position. In classical
times, the position of tone holes would have
been a matter of guesstimation, and this
would have necessarily limited the intonational
complexity of Greek auloi.
Net result?
Pythagorean tuning was a technological
necessity for the Greeks, as it was for
the bablyonians and the Sumerians. These
latter recorded a Pythagorean tuning on
tablet U7/80 (Side 2) in the British Museum; it
is almost certain that the tall tales about
Pythagoras mask an intonational tradition
which drifted from the older civilizations
of Egypt and the Euphrates valley to the
newer civilizations of the Mediterranean.
--
Inventions were common in the classical
era of ancient Greece: Ktesibos of Alexandria
build a device to produce "intermittant bird
song" around 270 B.C. It worked by regulating
the flow of water into a closed chamber.
But such devices were very limited in their
musical utility because the air pressure was
low and so the "bird songs" would have
been extremely faint--and when the chamber
designed to catch the streamof water filled
up, the sound would have stopped.
Ktesibos solved this problem by using a
double-barreled water pump he had devised
to fight fires--he modified this pump
to create a continuous source of compressed
air. The roman author Hero reports around
the first century B.C. that Ktesibos used
three components to build his hydraulis
(water organ): a single-cylinder air pump,
a large cistern filled with water, and a smaller
vessel attached to the bottom of the cistern
to act as a regulator to keep constant the rate of
flow of water out of the cistern.
This organ used sliders moving in and out
of slots below each pipe; the sliders
were controlled by the keys of the keyboard
and when a player pressed a key, the hole
in the slider aligned with the opening in
the corresponding pipe. By spring action, the
keys recoiled, dragging each slider back to
its closed position.
Notice several problems with this organ.
First, it must have required at least as
much force to depress a key as would
be required to drag each slider back into
its closed position. Second, the organ
can play only as long as the cistern
contains water. Third, the size of the
cistern and its height determine
the maximum available air pressure and thus
the total number of pipes and the maximum
volume of the sound. But the biggest
problem is that as more and more keys
were depressed, the air pressure would
drop because the regulator at the bottom
of the cistern would prohibit water from
flowing at more than a certain maximum
rate from the reservoir. This means that
if more than one key was depressed, the
overall air pressure of the organ would
drop and the overall pitch of all notes
would fall. It would not have been
possible to remedy this by eliminating
the regulator, since its purpose is to
maintain even air pressure--otherwise
there would initially be high air pressure
as a great mass of water started to
press down on the pump at the start
and the air pressure would continually
fall as the mass of water in the
cistern continually lessened.
Thus Ktesibos' organ would not have
been useful for performing with other
instruments, since its pitch changed
as more keys were depressed. Also,
it could only play for a short time,
and the creaking of the wooden pump
and the burble of water pouring out
of the cistern would have made the
instrument hard to hear.
As a result, the hydraulis was only
a novelty item. Even so it impressed
contemporaries: Athenaeus describes
a feast at which the hydraulis was
discussed: "The sound of the hydraulis
was heard close by. So pleasant and
charming was it that we all turned
towards the sound, fascinating by the
harmony."
The reaction here hints at the surprise
and shock Alexandrian citizens must
have felt at hearing sustained chords.
This was clearly alien to their experience.
It is reasonable to assume that the
hydraulis used Pythagorean intonation;
remember that the pitch changes as
more keys are depressed. This would make
an elaborate tuning system very hard
to tune up. Even Pythagorean was probably
only roughly approximated on such organs.
The Romans used such instruments at
the arena; the oldest archaeological remains
of an organ were unearthed at Aquincum
(near currest-day Budapest), dedicated
in A.D. 228 to the college of weavers there.
Having listened to the hydraulis, the
Pythagorean Philolaus proclaimed: "The
nature of number and harmony admits
no falsehood... But in fact number, fitting
all things into the soul through
sense-perception makes them recognizable
and comparable with one another."
This is a fine statement of the
Pythagorean conception of the universe as
an expression of pure theoretical math.
Music was unpopular with the early
leaders of Christianity. Divine revelation
was preferred to the study of nature.
Early Christian thinkers did not have
much interest in the application of
logic and the study of physical evidence
(an attitude represented on this forum
by Greg Taylor); instead, they preferred
the mystic contemplation of sacred verse,
from which music proved an unwanted
distraction.
Saint Augustine wrote in the early 5th
century that he found music in any form
suspect, but allowed as how "now when
I hear sung in a sweet and well-trained
voice those mleodies...I do, I confess,
feel a pleasurable relaxation. But this
bodily pleasure to which the mind should
not succumb without enervation, often
deceives me.... In these matters I sin
without realizing it."
The message is clear: to the early
Christians, beautiful music was a sin.
(This is an attitude remarkably similar
to that of many academic music theorists
of the modern day.)
--
The first organ to reach Western Europe
after the sack of Rome in 476 was a
gift from the Byzantine emperor
Constantine V to the Frankish king
Pepin in the year 757. The gift
excited amazement because its like
had not been seen for hundreds of
years--a clear indication of how
much knowledge and scientific
thought could be lost forgotten and
how badly the capacity for clear
thinking could erode during the
Dark Ages (a fate which awaits us
all if we follow the prescriptions
of the Eric Lyons and the Greg Taylors
of the world).
Ermold le Noir wrote an epic in which
he proclaimed "Even the organ, never
yet seen in France, which was the
overweening pride of Greece and which
in Constantinople was the sole reason
for them to feel superior to us--even
that is now in the palace of Aix."
The organ was slowly transformed
into an engine of divine worship in
the churches--this took a while, given
the attitude of Augustine: "Whatever
knowledge man has acquired outside
of Holy Writ, if it be harmful it is there
condemned; if it be wholesome, it is
there contained." (An attitude remarkably
similar to that of contemporary music
professors, save that their Holy Writ is
Schoenberg's "Harmonielehre" and John
Cage's "Silence.")
Organs were increasingly optimized for
volume. By the 990s this led to what
Wulstan described as "Like Thunder,
the strident voice assails the ear,
shutting out all other sounds than its
own; such are its reverberations,
echoing here and there, that each man
lifts his hands to stop his ears, unable
as he drawn hear to tolerate the roaring
of so many different and noisy combinations."
Clearly volume came at the price of
intonational precision--the "noisy
combinations" surely describe the
effect of an unsteady air-flow on
the pitches of the individual pipes.
This organ (like most around the 900s)
did not seem to have been
used for music so much as to amaze
and shock the crowd and entice them
into attending church services.
By the 12th century, organs had been
accepted into the church in a feat of
intellectual jiu-jitsu similar to
Thomas Aquinas' introduction of
Aristotle. By this time the organs
clearly had worked up high air
pressure, though the steadiness
of their intonation was probably
still poor: Saint Aelred, abbot at
Rievaulx in Yorkshire, wrote
"What use, pray is this terrifying
blast from the bellows that is
better suited to imitate the noise
of thunder than the sweetness of the
human voice..."
This quote indicates that the organs
were now using bellows--in fact
banks of them, one for each pipe,
with serfs treading on them in time
to the music. This would have greatly
increased air pressure, but it required
the serfs to tread in lockstep and more
to the point the air pressure would still
change over the course of a note as the
bellows emptied. The initial higher
air pressure would, ironically, have
produced a more drastic drop in the
pitch of each note while it sounded.
Moreover, the notes could not sound
for a very long time--only as long
as it took the bellows feeding air to
that pipe to empty.
The overall effect would have been
of a set of notes which dropped in
pitch as they were sounded and
which would have had to be played
in strict robotic meter; however,
the problem of polyphony changing
the overall pitch of the organ had
been solved, and the organs of the
12th century would have sounded much
louder than that of Ktesibos.
Moreover, these 12th-century organs
still didn't have keyboards. They
were played by ramming blocks of
wood forward and back to open up
and cut off the flow of air into each
pipe. Given the size of the pipes,
this would have been a real workout.
Some time between the 11th century
and the 14th century, true keyboards
appeared. These were spring-loaded,
like Ktesibos' keys. They still had
to be bashed with the fist--but they
could now be played more musically.
Given the persistent problems
with changing pitch and lack of any
kind of real keyboard, Pythagorean
intonation was still used into the
12th century according to the organ-
building manuals of that period--even
though modern keyboards had started
to evolve.
However, by the 14th century small
portable foot-pumped organs were
starting to appear. Henri Arnaut
published the best suriviving text
on building medieval organs in
1450; around this time the single
greatest innovation in musical
technology between 100 B.C. and
1800 A.D. was introduced--the
multiple-chamber bellows.
Water-operated organs were clumsy
because they demanded a source of
water and they could only play for
a limited time; bellows were better
because they could be pumped relatively
silently (I've played some of these
portatives and you can't hear the
bellows).
Adding a second chamber onto the bellows
produced constant air pressure. The
second inner chamber of the bellows had
an aperature into which air could be forced
but could exit except through the organ pipes.
Thus, even though the pressure of the primary
bellows constantly changed as it was pumped,
the secondary chamber maintained a relatively
constant air flow.
Around this time Napier also introduced the
logarithm, making possible calculations which
treated musical intervals as portions of the
octave which could be added and subtracted
rather than as messy complex grade-school
fractions which had to be multiplied and
divided.
These two advances had an explosive impact
on intonation.
Within a few generations of the late 1400s,
the Pythagorean intonation was no longer
in widespread use (though it was still taught
in music theory--much as 12-TET is still
universally taught today even thought modern
composers are using it less and less). Organs
with large numbers of pipes became common.
Moreover, serfs no longer needed to tread in
strict time on sets of bellows. By adding
a secondary chamber, all the pipes could be
connected to a single bellows and as long
as it was large enough, the air pressure
would be sufficient that no matter how
many keys were depressed (within some
reasonable limit) the overall air pressure
inside the inner chamber (after the
secondary bellows) wouldn't change.
This not only allowed composers
and performers to explore much wilder
and less regular rhythms, it also allowed
more elaborate intonational schemes
than 3-limit just, and it made possible
the exploration of complex polyphony
with many notes of stable pitch
sounding all at once.
With more notes available on the organ
keyboard, the possibility of modulation
is correspondingly greater. Between
the early 1500s and the middle 1700s
this increasing use of modulation by
composers would have made various
meantone systems particularly popular.
Indeed, Mark LIndley claims that the
early English virginal piece "Ut, Re,
Mi, Fa, Sol, La" by John Bull (written
in the late 1500s) used 1/3-comma
meantone. Bull was a wild-eyed
avant garde composer, the Stockhausen
of his time, and this sounds reasonable
given Bull's penchant for pushing the
outside of the musical envelope.
The next post concludes this examination
of technology's effect on tuning.
--mclaren

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🔗John Chalmers <non12@...>

From: mclaren
Subject: technology and intonation
--
A tenth century text on organ building laid
out the rules for pipe length exactly as
Pythagoras would have in the Greek era.
Start with a pipe and call it C. Divide it
into 4 parts, remove one and you have the
pipe for the low F. Divide the C pipe into
3, throw away one part, and the resulting
pipe sounds a G above C. Divide the G
pipe into three, add one part to it, and
the result is D below G. The instructions
continue in the same way, producing
a completely standard Pythagorean scale
that effectively translates the tuning
of a monochord into fixed ratios of
pipe length.
This is a typical reaction to new
technology. As Marshall McLuhan
pointed out, new forms of technology
typically start by taking on the modes
and habits of older forms of tehcnology.
Only gradually does the new technology
start to develop unique and novel
modes of use.
For example, early printing presses
used type designed to fool its readers
into thinking the letters had been
written by hand. Each letter was
carefully designed to imitate the
shape of a letter written in ink with
a square-nibbed pen; printers of the 1490s
even used multiple typesets with
different inks to produce the effect
of illumination by scribes with red
ink for special words, etc.
Early television programs imitated
plays; early Internet applications
imitate magazines--for example,
this tuning forum. The world wide
web is not limited to ASCII text,
as is this tuning forum, and soon
sounds will be sent attached to
graphics and text as a matter of
course (this still takes too much
bandwidth today--a 44.1 khz stereo
soundfiles demands 10.5 megs of
data per minute).
In the 1450s Duke Philip's organ
designer Henri Arnaut came up with
the idea of modifying the Pythagorean
system to keep as many fifths pure as
possible while still making as many
keys as possible listenable (i.e., triads
without excessive beats). This was
in retrospect a failed attempt to
use the new technology of the modern
organ for polyphonic music; meantone
tuning did the opposite of Arnaut's
procedure, keeping thirds just while
shaving bits off each fifth.
Meantone proved so successful that,
according to Alexander J. Ellis and
others, it remained the dominant form
of tuning through the 1840s.
In between the 1500s and the 1840s,
many different peculiar variants of
meantone were tried.
Example: an organ at Bucksburg, build around
1615, boasts 14 keys per octave. Handel's
harpsichord also uses 14 keys to the
octave. I have pictures in my files of many
peculiar-looking keyboards which have as
many as three tiers of keys--one set of
ordinary white keys, a second set of
black keys with some extra smaller keys
*in between* B and C, and a third tier of
keys, also blac keys, which reproduce the
conventional black keys but translated
by a comma up. Mersenne's Harmonie
Universelle is full of such illustrations,
but many such keyboards were actually
built. Between 1500 and 1800 there was
no such thing as "a standard keyboard
instrument keyboard"--there were a lot
of different types of keyboards, since
all musical instruments throughout that
period were hand-made.
Such extended meantone keyboards flourished
during the 17th and 18th century, a period
when standardization was not the norm,
and when musical tuning--like spelling!--
was considered a matter of individual
taste within the overall limits of the
meantone system. (It's important to
remember that because meantone is
a general method in which fifths are
altered to preserve just thirds, there
are *many* different flavors of meantone.
1/3 comma, 1/4-comma, 1/6 comma,
1/11 comma--known as 12-TET--and
variants such as the irregular circulating
temperaments of Marpurg and Werckmeister
and Kirnberger.)
The next great technological leap was made
by Henry Maudslay, who worked at the
smithy in Woolwich Royal Arsenal in the
early late 1700s.
Joseph Brahma, an entrepeneur who wanted
to build an unpickable lock to cash in on
a highly-publicized series of robberies in
London, hired Maudslay as an apprentice
locksmith. By 1797, Maudslay asked for
a raise of thirty shillings a week (to
support his wife and children) and Brahma
refused, so Maudslay walked out and
started his own workshop on Oxford street
in London.
Maudslay's first product was a new lathe
he had designed.
A lathe is basically a machine which
uses a screw as a moving base for a knife;
the knife can cut wood, or if made of
tempered steel, iron or copper.
The 1800 Maudslay lathe was far larger
than any of its predecessors (which were
mainly used for ornamental work on small
gewgaws) and his sliding tool-rest
was perfectly mounted on accurately
planed triangular bars. Because Maudslay
was a fanatic for accuracy, he built his
lathes to extraordinarily fine tolerances
for the era; but the big suprise was not
that Maudslay's lathe could turn out more
accurate work faster than any other lathe.
The real shock came when people realized
that they could use Maudslay lathes to
machine extremely accurate and regular
screws and bars for use in *other*
lathes, which in turn could produce
*other* machine tools... Starting with
extremely accurate screws, it is
possible to build a huge variety of
precision machine tools. These tools
in turn make possible the creation
of even more precise machine tools.
The process builds on itself in much
the same way as the development of
ever-more-powerful silicon chips has
led to silicon compilers which in turn
allow the construction of even more
powerful computer chips by automated
methods.
The end result of Maudslay's lathe was
that woodworking, metalworking,
manufacture, toolmaking, and factories
were all revolutionized. Maudslay's
lathe changed the nature of warfare
and it made Britain the greatest sea
power in the world. It also made possible
the modern orchestra and the modern
piano.
How so?
Napoleonic warfare depended on the fact
that rifles were inaccurate. They were
inaccurate because there was no way
to rifle barrels with precise accuracy or
to turn out standardized gun parts with
high precision at high speed. This meant
that if you shot at an enemy more than
a few score yards away, your shot probably
wouldn't hit. So Napoleonic warfare depended
on masses of infantry marching in lockstep
toward one another until they got close enough
to mow each other down.
Britain became a great sea power when it built
and equipped enough ships to rule the seas; but
this wasn't possible without turning out more
than 1400 block-and-tackle units to haul sails
up and down *on each and every ship* (and that's
only on 3rd-class ships. First-line ships used
> 2000 blocks!). These blocks and winches and
pulleys were made of wood by hand. There
weren't enough carpenters in Britain (or in
Europe) for all the blocks the British navy
needed, and you couldn't run a ship without
'em.
Marc Isambard Brunel came to Maudslay
in 1800 with an idea to turn out these blocks
for the Royal Navy using his new lathe; by 1808,
the first large-scale mass production
facility in the world, Maudslay's factory,
was turning them out by the truckload.
To string a piano you need huge amounts of
wire, and--even more important--you need
precision machines to build the die through
to draw the wire, and more precision machines
to loop the wire at the ends, and even *more*
precision machines to wind the lower strings.
Maudslay's lathes made it possible to build
such precision machinery, and as a result the piano
rapidly evolved from a relatively thin-voiced
instrument strung at low tension in the 1830s
to a robust instrument with three wires per
note at high tension and wound strings on the
lower octaves by the 1880s--all due to
the tidal wave of change produced in
manufacturing by Madslay's lathe.
Woodwind instrument had always been
nortoriously dicey in their intonation, in large
part due to the problems of precisely boring
amd machining wood (essentially the same
problem as rifling a musket barrel). By the 1880s
woodwinds had reached high standards of
precision (though they still depended crucially
on those temperamental reeds). Moreover,
woodwinds plummeted in price along with brass
instruments as precision machine tools
proliferated.
The valves of brass instrument benefited
most of all from Maudslay's lathe because
of the precision tools built to bend and seal
them.
Eventually, wire strings became so common
that they replaced gut strings in the string
instruments, leading to the godawful
screeching-train sound of modern string
instruments and a corresponding increase
in sheer volume (and a precipitous drop
in listenability--the average violin solo
noawdays sounds like a cat being castrated).
--
The upshot of these precision machine tools
was the 12 tone equal tempered scale. Musical
instruments built by mass production could not
be economically individualized so as to accomodate
dozens of different meantone variants. To make
money turning out modern musical instruments,
you must *standardize*--all exactly alike. When you
build only one or two harpischords per year, you
can easliy afford to use exotic three-tier keyboards
fitted to special custom meantone tuning schemes...
but when you build 100 pianos a year you must
settle on a single rigid standard keyboard. As
soon as musical instruments became mass-market
commodities, their tuning also had to be standardized
to make a profit for the manufacturer.
The result--as Ivor Darreg pointed out for many
years--was that 12-TET was foisted on the
musical world by musical instrument manufacturers,
rather than by musical theorists, performers,
or composers. As Lou Harrison has pointed out, the
advantages of 12-tet are "almost entirely economic."
In fact Ellis reports that meantone "sounds by far
the sweetest" of all the intonations he tried;
clearly *technology* forced 12 equal tones on
musicians, and they went along *reluctantly.*
With the advent of the digitial synthesizer the
iron fist of 12 made itself manifest in the velvet
glove of digital technology. As Ivor pointed out,
once people started to hear pure unadulterated
exactly precise 12, they fled from it in droves.
Pianos and string instruments strayed gracefully from
12, especially in the upper and lower registers--
the octaves on a piano are systematically stretched,
and vioinists tend to bend pitches whenever
they possibly can.
But with the earliest digital synthesizers, there
was no choice--the intonation was burned into
the ROMs and listeners and composers and
performers were stuck with pure perfect 12.
And the beats drove them crazy, so they slathered
on hockey-rink reverb, they used phase shifting
and multitrack tape and echo... And as soon as
retunable synths appeared, a mass exodus from
12 began in earnest.
Today we're in the middle of that intonational
diaspora. It has been created and supported by
the technology used in our instruments. As
computers move ever closer to real-time MIDI
generation of Csound-type timbres, it will
become easier and easier to specify with precision
*both* tuning and timbre--and to control the
interaction of the two.
This will produce the next revolution in tuning,
probably within the next generation or two, based
on the ideas of William Sethares, John R. Pierce,
Jean Clause Risset, J. M. Geary and James Dashow.
Hot diggity!
--mclaren

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🔗alves@osiris.ac.hmc.edu (Bill Alves)

🔗John Chalmers <non12@...>

From: mclaren
Subject: mystery package
--
Recently a mystery package arrived in my mailbox.
Expecting a mail bomb from the Unatuner,
imagine my surprise to discover....
..That the parcel contained the very nearly complete
text of "acoustique musicale," a French book on
xenharmonics and acoustics from the 1950s.
No return address. No letter inside. On a scale
of 1 to 11, my puzzlement at this package scored
somewhere above 11. Examination of the postmark,
however, revealed that the xenharmonic cipher
who sent this little gem was in fact Kami Rousseau.
The book turns out to be an astoundingly rare
item: the internal collection of the CNRS titled
"Acoustique Musicale," from 1959.
This is treasure, containing worthwhile articles
which have not appeared anywhere else.
Thanks, Kami!
--
The contents of this rare volume are so
interesting that it seemed worthwhile to
post my alleged and highly risible "translation"
of the more important articles. (One
at a time. One now, others later) The book
contains articles by Jacques Chailley,
M. Barkechli, Adriaan Fokker, Jacques
Brillouin, R. Tanner, Robert Dussaut,
P. Riety and Fritz Winckel. Chailley was
a Sorbonne professor and director of
the Institute of Musicology of Paris;
Winckel was a pioneer psychoacoustician;
Fokker rediscovered 31-tet and founded
the Netherlands Huyghens-Fokker institute;
R. Tanner was attached to the C.R.S.I.M.
in Marseille and did interesting work on
acoustics and tuning; Barkechli was the
director-general for arts in Iran during
the reign of the Shah, and was one of the
few writers in the 1950s to discuss the
contributions of Zalzal, Farabi and other
Medieval arabic scholars to the development
of modern intonation.
--
N.B.: Forum subscribers are warned that
Your Humble E-Mail Correspondent never
took a course in French. So the many ludicrous
errorsin the following muttonheaded "translation"
are strictly *MY* fault, not the author's.
--
The first article is "The dynamism of scales
and consonances in the principal acoustical
systems and its influence on the development
of music" by Jacques Chailley. This is the same
Chailley who wrote the excellent "40,000 Years
of Music" in 1964, one of the best books on
music history, period.
"Of the various acoustic systems which involve
physical considerations in some way, three
stand out in western musical practice. Up to
the 16th century, musical practice was primarily
Pythagorean; from the 16th to the 18th century,
it was based on Zarlino's work; and from that
era to the present, on 12-tone equal temperament.
"I. The origins of the Pythagorean intonation are
empirical. (This is 100% backwards from the
reality; Aristoxenos, the chief intonational
empiricist of ancient times, vehemently disagreed
with the Pythagoreans and make considerable light
of their reliance on the sacred tetraktys as the
source of all music -- but then, no doubt my
"translation" is hog-wild --mclaren) Clearly there's
no truth to the tale of Pythagoras hearing blacksmith's
hammers (John Chalmers has pointed this out, also
why. For one thing, the anvil would ring and not the
hammers just as the clapper does not ring rather
than the bell. For another thing, vibrating masses
follow a different law of musical ratios than
vibrating strings-- mclaren). Instead he established
the relationship between the size of the interval and
the length of string. Pythagoras deduced that the
octave, the fifth and the fourth were the basis of
all existing music. (Actually the Pythagoreans
worshipped a numerological pyramid made of
the number 1, 2, 3, and 4, called the tetraktys.
M. Chailley's statement is not quite accurate,
but close. Either he has confused the
ecstatic 3-worship of Holy Trinity-influenced
Medieval music theorists like Jean de Muris with
Pythaogras' writings, or my ludicrous "translation"
is to blame -- mclaren) Pythagoras had no
contact with other cultures which did not use such
intervals--such as the American Indians.
"Concerning the list of resonances, Pythagoreans
started their investigation at the second and
stopped at the fourth harmonic. They ignored,
evidently, the harmonic principle discovered
during the 17th century, namely that of the
relationship between consecutive harmonics which
transformed simultaneous consonances into
a posteriori operation. (Hard to see what he's
getting at here. Probably my nonexistent French
is bamboozling me. --mclaren) Superparticularity
was considered the most important relationship,
not the proximity of the sounds in a list of
harmonics--which was ignored when the first
frequencies were calculated. (I've probably got
it scrambled. The gist seems to be that absolute
frequencies are not important but rather their
relationships--which is to say, ratios, and
that superparticular ratios are considered the
most important. --mclaren) And so the 9/8
interval is not defined as the ratio twixt
harmonics 8 and 9, but the difference betwene
the 3/2 fifth and the 4/3 fourth. There was
no consideration of the 5/4 "natural" third,
although it was superparticular, because
the Pythagoreans stopped their investigations
at harmonic 4.
"In arresting his observations at the number 4,
Pythagoras conformed to the most primitve
classification of consonance: category1 (unison,
ocrtave) represents perfect consonance,
while category 2 (fifth, fourth) consists of
imperfect consonances. In the melodic
art of music, this results in a scale whose
structure in the sound-universe of Pythagorean
theory is based exclusively on the cycle of
fifths:
(Here M. Chailley gives an unfortunately
misleading 5-line staff with 7 musical
pitches notated as the conventional 12-TET
notes. The naive reader might be deceived
by this diagram into imagining that the final
B in M. Chailley's diagram--starting pitch
F, ending pitch after 6 just 3/2s B--
corresponds to the familiar B on the piano
keyboard, ratio 2^[6/12] = 1.41414... or
600 cents. In fact, in the Pythagorean
tuning this pitch pitch is not the familiar B
above F but a pitch above F = (3/2)^6 =
11.390625 = 11.390625/8 = 611.73 cents.
The difference between this "B" and the
B on the piano keyboard is clearly audible.
12 cents is not a subtle or indetectable
interval. The point here is that Mssr.
Chailley's diagram entirely leaves out the
fact that in a Pythagorean tuning the
pitches rise by 1.995 cents for each note
prdouced by a leap of a just perfect fifth
as compared to 12-tet. After 6 notes this
adds up to 6*1.995 cents = about 12 cents,
a non-trivial difference. --mclaren)
"The system is fundamentally a succession
of fifths producing 1, 2 and eventually all 7
of the notes of the diatonic scale.
"The cycle stops at 7 notes. Chromaticism
becomes a question of physics in the
continuation of the cycle of just perfect
fifths, rather than a matter of convention
and musical language.
"And so Pythagorean intonation is perfectly
suited to melody, and C-E-G-C' are perfectly
in tune. In the middle ages western
music was melodic and Pythagorean tuning
was popular, but did not last beyond the
16th century. The intonation was
prediminantly minor, since in hexatonic
Pythgorean tuning, the minor Pythagorean
third is much more a point of acoustic rest
than the Pythagorean major third, and
the pentatonic mode was primarily used.
(The Pythagorean major third so-called
is usually calculated as (3/2)^4, = 81/64
= 1.2625625 = 407.82 cents, while
the Pythagorean minor third is usually
calculated as the difference twixt the
9/8 and the 4/3 or 8/9*4/3 = 32/27 =
1.185185 = 294.1349 cents. -- mclaren)
"As far as polyphony goes, the Pythagorean
system was not favorable to the development
of triadic harmony based on its
fundamental intervals, since perfect
consonance was restricted to only two
of these. It was favorable to the
development of counterpoint in independent
lines, where the requirement for perfect
consonance was not great: aside
from the unison and octave, and the
two imperfect consonanances, it was
a matter of indifference in which of the
two classes (fifth or fourth) the intervals
fell. Practically speaking, this made for
primitive polypohony, and throughout the
Middle Ages polyphony was restricted
to such counterpoint, in which all parts
were composed so as to proceed together,
rather than various lines in contrary motion.
(Mssr. Chailley is alluding to fauxbourdon
here, along with plainchant. In fauxbordon
an upper voice duplicates the lower at the
interval of a just fourth, which in plainchant
duplication at the octave was allowed -- mclaren)
In conclusion, the Pythagorean system had
the characteristic, that the semitones
were enlarged compared to the other
intervals and were not considered proper
consonances. The resulting tendency was
for very strongly consonant intervals to
sound on the fifth, the minor third
and the unison, the major sixth above
the octave, the minor sixth above the
fifth or the fourth.
"Plagal cadences were typical. As a result,
Pythagorean intonation was a dynamic system,
whose accentuation of the differences between
intervals emphasized dissonance more than
consonance.
"As a result, certain pitches were often made
more attractive by modification to their
consonance in performance (musica falsa),
and this was the primary function of
chromaticism. Marchetto of Padua (in
the 16th century) used the 5/4 as a chromatic
alteration in this manner instead of the 81/64.
"This could be considered an early Medieval
use of temperament. The Pythagorean major
third is a true dissonance, whose tendency
toward resolution is very strong. Thus
Pythagorean chromaticism represents the
triumph of the large interval as one of
maximum attraction. (Presumably Mssr.
Chailley means here that the 407.8-cent
P maj 3rd tended to resolve to the just
3/2 701.955 cent fifth. -- mclaren)
"Pythagorean triadic harmony was not
consonant; the P maj 3rd was constantly
drawn along a line of strong attraction to
the fifth. The music of the Middle Ages
was characterized by primitive polyphony
and strong dynamism.
"II. Zarlino held a contrary view. He adopted
the major third as a basic consnance, using
harmonic 5 to make three fundamental
consonances instead of 2. (That is, 5/4
along with 2/1 and 3/2 -- mclaren)
"The result was that consonance was extended
to triads, and a major third over the fundamental
satisfied the requirements of proper sonority
in accordance with the model of resonance.
(Presumably this refers obliquely to the fact
that all the members of a just 4:5:6 chord are
harmonics of an unheard fundamental. Or it
might simply refer to the fact that when
just intonation is used, there in a noticeable
increase in the resonance of chords played on
instruments with strictly integer harmonics.
-- mclaren) Harmony in the 16th century
accreted bit by bit from counterpoint and
progressively deviated from a strict adherence
to consonance. The harmonic progressions
did not solely rest on consonances, but did
exhibit a constant relationship to a bass line.
"Zarlino's system was therefore static.
The chromaticism of Zarlino's system
accentuated the character of individual
keys. The chromatic tetrachord of the Greeks
was identified through an error of orthogoraphy
with a description by Boethius, instead of
the intervals of Zarlino's system. (Eh? This
is probably me scrambling the translation...
--mclaren)
"The chromaticism of Zarlino represents the
triumph of the small interval. (Presumably
this refers to the fact that Zarlino's theory
brought thirds into music as consonances and
respectable members of chords -- mclaren)
"Concerning melodic construction, the advent
of Zarlino's system required the modification
of the concept of intonational structure. The
hierarchy of the cycle of fifths must needs be
finite if modulation is to be effected. Thus,
based on classical ideas, Zarlino's method
effected a radical transformation.
"Zarlino divided consonances into three
categories. Harmonic 7 did not fit into
any of these; in fact, the just seventh
was incompatible with the rest of 16th century
theory and practice. As the seventh became
more and more used in music through the 18th
century, it posed grave problems as to its
correct resolution: Rameau's theory dealt
with this question (among others).
"III. It is impossible to construct a practical
system of just intonation using only the first
4 integers. (The organ builders of the 10th through
15th centuries would have been greatly surprised
to hear this. In fact a tenth-century text
lays out the rules in exact Pythagorean fashion:
start with a pipe of whatever length and call
it C, divide ito four parts and remove one--
that's low F. Divide the C pipe into three,
toss out one part, and you have the fifth above
C or G. And so on. Duke Philip's organ designer
Henri Arnaut, around 1450, used a slightly
modified Pythagorean system which concentrated
the dissonance into the interval twixt B and F-sharp.
Under Arnaut's system, only 4 thirds out of the 12
were consonant and the bad fifth is amazingly
awful--a true wolf. Nonetheless, Arnaut's system
represented a workable compromise for the period.
To call a system of tuning employed on organs from
the 10th through the 15th centuries "impractical"
tells me Mssr. Chailley didn't do his homework
here -- mclaren)
"Logically, it is suitable to divide consonances
into four categories, the fourth accomodating
the 7th harmonic. This is not in accord with
Zarlino's 3 categories of consonances.
"That, incidentally, is why the 7th harmonic was
never accepted as a consonance in western
music. (Mssr. Chailley may be barking up the wrong
tree here--the 7th was never accepted as a
consonance because the interval between
harmonic 7 and harmonic 6 is the first interval
in successive members of the harmonic series
which falls within the critical band. The reason
is psychoacoustic, not historical. However, my
alleged and preposterous "translation" might
well be the culprit instead of M. Chailley -- mclaren)
"The sounding of the chord C-E-G-B creates a
dissonance which fails to resolve. The musican,
in assimilating harmonic 7, creates attractive
new intervals but cannot resolve these chords
within the conventional western system. The
7th harmonic does not correspond to any
degree in the western scale; moreover, the
resolution of seventh chords has contributed
to the tyranny of the dominant chord. (vii
usually resolves to V in classical harmony --
mclaren) In classical tonal music, the just seventh
cannot coexist with usual melodies, and is
only found as a suggestion in the traditional
seventh chords.
"IV. Pythagorean intonation is dynamic, while
Zarlino's just triadic harmonic intonation is static.
Equal temperament is neither one nor the other.
It is a compromise, whose intervals do not partake
entirely of either of these systems, and thus
is a somewhat neutral system whose employment
was spurred by the need to find a correct middle
ground between Pythagorean intonation's excellence
for melody and Zarlino's just intonation system's
excellence in harmony. Equal temperament was
not imposed by fiat, but arose from the nature
of the music being made.
"The result is a certain musical ambiguity; the
possibilitity that a given pitch may be taken
in more than one sense. (Das Wohltempierte
Klavier of Bach is an example.)
(Well, Mssr. Chailley has fallen into the trap
of assuming Bach wrote in 12-tet, but we
must grant him parole for that insofar as he was
writing around 1958. People weren't nearly
as aware of the use of well temperament in
the 17t and 18th century back in the 1950s
as they are today, largely due to the efforts
of pioneers like Johnny Reinhard--whose
remarkable yearly Christmas programs of
well-tempered Bach have detwelvulated ears
far and wide -- mclaren)
"Equal temperament greatly facilitated rapid
modulation (for example, listen to
Bach's Kleine Harmonisches Lanyrinth
for organ) and allowed the employment of
modern harmonies. (Presumably Mssr. Chailley
refers also to the use of diminished, augmented
and seventh chords, which certainly can be
found in profusion in the music of Bach --
mclaren)
"Equal temperament formed the character of
the classical epoch of music. (Alexander
John Ellis disputes this, along with Patrizio
Barbieri. Both these scholars cite sources
to prove that meantone survived on pianos
into the early 1840s, while in some parts
of Europe--Italy, for instance--meantone
was used by orchestras into the 1890s --
mclaren)
"By the end of the 19th century, musicians
had begun to explore extremes of ambiguity.
The result was the decadence of fin-de-sicle
tonality. This was a neutral system: it was
opposed to firm tonality. Such departure
from strict tonality led to an increasing
dissolution of the sense of key (for
example, Wagner, Liszt, Debussy). This
ambiguity led to an ensuing agressive
negation of tonality (Schoenberg). The
result was that any combination of
notes was permitted.
"Concerning melodic structure,
temperament proceeded in the same
way. Temperament in and of itself
was not opposed to the continuation of
classical thematicism based on the
C-E-G triad. Moreover, with the
rediscovery and reintroduction of
folk melodies around the end of the
19th century, ancient melodic structures
based on the cycle of pure fifths revived
in popularity. And so some other composers
(Debussy, Bartok, Stravinsky, etc.)
renewed the thematic structure of music
by using harmonies based on primitive
categories of consonance divided into
only 2 classes, highly consonant, and highly
dissonant. (This is an interesting point and
one which I've not seen made before. --mclaren)
"To conclude, equal temperament provided the
necessary conditions (but not sufficient conditions)
for dodecaphonic music. (12-tone serialism,
presumably -- mclaren) Temperament was
definitely an acoustic compromise and marked
the starting point of theoretical department from
historical precendents. Once introduced, it was
not possible to retain the resonance principle
(i.e., Rameau's doctrine that a major chord is
based on integer multiples of an unheard
fundamental -- mclaren) and thus there was
successively greater departure from Pythagorean
models. In the absence of consonances typical
of that system, sounds tends to devolve into
chord-complexes without acoustical rationale,
and this led to new concepts of musical
organization (musique concrete, electronic music,
etc.) as well as serial music (Boulez, Barraque,
Stockhausen, etc.) This evolution would have
been impossible without the initial confusion
introduced by equal temperament.
CONCLUSION
"The historical change in music from acoustic
systems to different ones non-acoustic
in nature was not an accident, but a
continuation of historical practice which
began with the study of acoustical phenomena.
"The essential elements of this evolution were
in place when a language of music and a method of
writing down music emerged." M. Chailley,
circa 1958 (?)
(There is no date visible anywhere in the xerox
which was mailed to me, other than circumstantial
evidence from the dates of the citations. The latest
citations appear to be 1957, so presumably "Acoustique
Musicale" dates from 1958-1960 or thereabouts.)
Thanks again, Kami. Sorry about the ludicrously
bad alleged "translation" but, hey...to me, "Prelude a l'apres
midi d'une faun" means "Prelude to an after ski dune faun.")
--mclaren

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🔗Gary Morrison <71670.2576@...>

🔗John Chalmers <non12@...>

From: mclaren
Subject: Will Grant's interesting post
--
In topic 2 of Digest 810, Will Grant answered
my statement that "Lou Harrison has not explained
how to reconcile these facts [that is, the prevalence
of tunings which cannot be explained easily in
terms of small integer ratios in other cultures] with
the notion that just intonation forms the basis of
world music."
Will Grant pointed out that "an arbitrary octave of 1150
cents does not preclude reference to a just standard."
Will's counter-argument is that "the music I've listened to
from Central Africa...relies on a 'gamut'... of a major
third..." And that "tetrachords carry
inevitably a potential toward modulation... Nevertheless,
sharping thirds can be pleasant. (..) The central African
musics aren't concerned about melodic modulatory
implications... Therefore I do not see that the specific
use of wide octaves can be used to discredit the
theoretical notion of a just standard." [Will Grant]
Will makes some excellent points, with considerable
insight.
First, Will G. is certainly right that in many parts of
Africa the overall "gamut" of pitch is somewhere
in the neighborhood of a third. This is not simply
based on my listening, but on the research printed
in the Journal of Ethnomusicology, etc., the bulk
of which supports Will Grant's statement--for
*many* African musics.
However, this is not the case for *all* musical
traditions in Africa, and may not be the case
for a majority. I don't know enough about
African music to decide whether a majority
of the cultures use a gamut of a third.
However, I do know of several specific exceptions
to that rule--and where there are several
excpetions to a general ethnomuiscological
"rule," experience has taught me that there
are apt to be many more. The "weeping song"
of the Gisalo, if memory serves, exceeds the
compass of a third by a considerable amount,
and the ugubhu is typically played using harmonics
up to 7.
Second:
While Will Grant's argument is ingenious and
very well thought out, it does not appear to apply
to the example cited in my post. Permit me
to quote the full text of my original citation:
"This definition is refused by the practices
of these musicians, who tune their xylophones
using adjacent intervals, step by step. Our
experimentation verified that 'perfect'
consonances are not a consituent of Central
African concept of the scale. These musicians
do not judge a strict octave (1200 cents) to
be better than a large major seventh (1150
cents) in any rgister, probably because of the
roughness it creates on the octaves that are
always played simultaneously with double
sticks in each hand." [Voisin, Frederic, "Musical
Scales in Central Africa and Java: Modeling by
Synthesis," Leonardo Music Journal, Vol. 4,
pp. 85-90, 1994]
This specific quote appears to crush most
of Will Grant's objections. On the other
hand, it's possible that I've misunderstood
the text. In any case Will might want to
study the article in question in detail.
Others examples (some outside Africa):
The panpipes of the 'Are-'are of the Solomon
Islands are tuned in 7 equal-tempered tones
to the octave which cannot be understood
in terms of the harmonic series (unless, of
course, there's something I've overlooked or
not taken account of--always possible); the same
seems to be true of the xylophones of the Kwaiker
indians of central Mexico and Guatamala.
The Burmese oboe-like instruments,
the drums of the Akan in West Africa,
and much of the vocal music of the Kaluli
of highland New Guinea and other music
from sub-Saharan Africa all seem to use
pitches which systematically avoid just ratios.
Of course the most spectacularly non-just
non-equal-tempered musical traditions
are those of Bali and Java, along with
Thailand. No one has succeeded in
explaining these musical traditions
in terms of small integer ratios, to the
best of my knowledge, and so my case
seems to stand. However, it's quite
possible I've made some silly error or
failed to see some crucial point. Perhaps
Will Grant can show me what I've overlooked.
--mclaren

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🔗John Chalmers <non12@...>

From: mclaren
Subject: non-octave scales and octave
equivalence
--
With typical insight, Paul Erlich made a particularly
interesting comment about non-octave scales in topic
6 of digest 797. He wrote: "The point is that if a note
comes close enough to an octave or a multiple octave,
it will sound equivalent, especially in the case of
harmonic partials. For example, an interval of 33 Pierce
steps exhibits equivalence, even though it is a very
different pitch class in the tritave scheme. Even when
the even partials are removed, I believe the virtual
pitch sensation is not very octave-specific."
My ears agree with Paul Erlich's here. Removing
odd or even partials doesn't seem to affect my
perception of the Bohlen-Pierce scale.
However, Paul E. did not mention whether he was
talking about "an interval of 33 Pierce steps"
*melodically* or *harmonically.* That is,
sounding the interval as a vertical dyad or
as two sequential notes one after the other.
Now, my experience is that this makes a *huge*
difference in the perception of octave
equivalence in non-octave scales. My ears
hear sequential (melodic) intervals as
being octave equivalent even if they are
significantly off from the octave--upwards
of 30 or 40 cents in many cases, especially
if the interval is a multiple of an octave--say,
2 octaves, 3 octaves, etc.
However, the range of detuning within which my
ears will accept an interval as octave equivalent
is much smaller when the interval is a vertical
dyad (harmonic): somewhere in the range of 0-18
cents.
As a concrete example, take the Bohlen-Pierce
scale. Play melodically the interval of 8 scale
steps; if you play the melodic interval reasonably
quickly, you'll find that your ear accepts it as
a melodic octave. But if you sound that 8-step
interval as a vertical dyad, it will not sound
like an octave at all since the interval is
1170.4338 cents, outside the acceptable vertical
range for octave equivalence (except at very
low fundamental frequencies).
This brings up an interesting point with regard
to non-octave scales: as most of you know, Enrique
Moreno has a very different conception of non-octave
scales than Gary Morrison or Your Humble E-Mail
Correspondent. Enrique believes that it is pointless
and meaningless to try to assign to the intervals of
non-octave scales familiar categories such as
"third" or "fifth" or "octave." Instead, Enrique
suggests that we accept the intervals of non-octave
scales on their own merits, rather than misguidedly
trying to jam them into familiar but conceptually
and musically limiting categories.
This view has merit. It recognizes the fact that
non-octave scales sound different in a basic way
from octave = 2.0 scales; Gary Morrison has
described non-octave scales as sounding like
"the musical equivalent of thick rich chocolate
milk shakes" and this is true--there's something
unutterably exotic and gorgeously alien about
most non-octave scales. They all share a very
sultry foreign "sound" which renders, say,
the 12th root of 3, the 15th root of 3 and the
13thr oot of 3 and the 25th root of 5 and the
37th root of 31 much more akin to one another
in "sound" or what Ivor Darreg called "mood"
than any trivial considerations of audible
octave equivalence.
On the other hand, there are problems with
Enrique's view of non-octave scale. For one
thing, there exist infinitely many non-octave
scales which are audibly identical to familiar
octave = 2.0 divisions of the octave. For
example: I defy anyone to tell the difference
audibly between 12-TET and the 51st root
of 19, or the 105th root of 431, or the 114th
root of 727, the 122nd root of 1153, or the 126th
root of 1453. THe difference between a 2/1
and the equivalent interval in each of these
"non-octave" scales is less than 1/3 cent--
you *cannot* hear the difference between these
intonations and 12.
There exist infinitely many non-octave scales
audibly identical (not close, *identical* to
the ears, with a 2/1 less than 0.1 cents off
from 1200 cents) to 13-TET, 14-TET, 15-TET,
and so on.
This being the case, we are forced to recognize
that for a significant sub-class of non-octave
Nth root of K scales, there is *no audible
difference whatsoever* between these and
some N-TET octave = 2.0 scale. This being the
case, it would obviously be perverse in a
tuning audibly identical to 12-TET to try to
describe the intervals in exotic Nth root of
K terms rather than in terms of the familiar
fifth, major and minor third, fourth, major
and minor second, and so on.
Thus the situation for non-octave scales is
more complicated than anyone has mentioned
to date.
On the one hand, listeners will tend to hear
intervals in these scales *very* differently
melodically than harmonically if the interval
is slightly off from a familiar interval.
On the other hand, there exist a large class
of non-octave scales which sound audibly
*identical* to familiar dvisions of the octave.
Lastly, there's the question: In a given Nth
root of K non-octave scale, what is the most
consonant interval? That is, what is the
interval which takes the musical and acoustic
place of the 2:1 octave in ordinary divisions
of the octave with harmonic series timbres?
--
There is no simple answer to this question.
A superficial answer is: obviously, if we're
talking about the Nth root of K, then K is the
most consonant interval in all cases.
This is sometimes true, and sometimes clearly
false.
In the 13th root of 3, the 3:1 ratio is clearly the
primary consonant interval. It functions musically
in the same way that a 2:1 does. If you "double"
pitches at an interval of 13 scale steps in the
13th root of 3, you'll get much the same result
as when you double pitches at an interval of 12
scale steps in 12/oct.
In the 21st root of 17, however, the interval
of 21 scale steps is not nearly as great a
point of acoustic rest as the interval of 3 scale
steps.
Moreover, all Ks are not created equal.
Intervals which are low members of the harmonic
series multplied by small integers tend to sound
more consonant than Ks which are high members
of the harmonic series. Thus , an interval of 17:1
sounds less consonant than 6:1 since 6:1 is 3:1 times
2, while 17 is relatively far up the harmonic series.
Even this statement must be qualified, for the
harmonic series exhibits the property that
consonance decreases as one climbs the harmonic
series, then suddenly it begins to increase as one
climbs further, then consonance decreases again,
then it suddenly increases, and so on.
For example: 2, 3, 4, 5, 6 are highly consonant.
7 is less so, intermediate in fact between consonance
and dissonance; 8, 9, 10 are highly consonant, 11
is much less consonant; 12 is highly consonant;
13 is relatively dissonant; 14, as a multple of 7,
is intermediate in consonance; 15, 16 are highly
consonant; 17 is relatively dissonant; 18 is highly
consonant; 19 is quite consonant, ditto
20 and 21; but 22 and 23 are relatively dissonant;
24, 25 are highly consonant; 26 is dissonant,
27 is extremely consonant; 28 intermediate;
29 is dissonant...and so on.
Thus the particular K is question must be considered,
in addition to the issue of whether the Nth root
of K scale contains an interval interval within
the N:1 span that sounds more consonant than
N:1.
One last point is that the absolute size of the
musical interval in question is very important.
Paul Erlich mentioned that an interval of 33
scale-steps of the Bohlen-Pierce scale sounds
like an interval of 4 octaves. However, this
interval comes out to 4828.0396 cents, 28 cents
away from 4 octaves. The ear doesn't tend to
notice this discrepancy for very large intervals
because the two notes are so greatly separated
from one another than there is little opportunity
for the harmonics of the lower and the upper
note to beat with one another. Most acoustic timbres
exhibit very little energy above the 16th harmonic,
and the 16th harmonic is the fundamental of a
pitch 4 octaves above the base note of a dyad.
Thus, while an interval of 33 scale steps in
the Bohlen-Pierce scale is about as far away
from the octave as an interval of 8 scale
steps (28.039 cents for the former as opposed to
29.567 cents for the latter), 8 scale-steps in
the 13th root of 3 sounds very far from octave
equivalence while 33 scale-steps sounds
reasonably close to octave equivalence because
many harmonics of both notes fall within the
critical band in the case of the 8-step interval
while almost no harmonics of both notes fall
within the same critical band in the case of the
33-step interval.
In short, octave equivalence and the question of
which intervals will most tend to function and
sound as points of acoustic and musical rest in
intervals formed from the notes of non-octave
scales are issues more complex than anyone on
this forum appears to have suggested.
--
Paul Erlich goes on to write that "In the case
of inharmonic partials, octave equivalence may
play less of a role, but still exists, and is less
demanding as to intonation." Both my experiments
with additive synthesis inharmonic timbres in
Csound and William Sethares' experiments with
resynthesized Fourier-analyzed timbres with
stretched partials strongly contradict this
statement. In particular William Sethares has
a set of instrument timbres resynthesized with
all harmonics stretched so that the octave is a
ratio of 2.1 instead of 2.0, etc.
Playing a vertical octave dyad with such timbres
produces unbearable dissonance; but playing a
vertical octave whose ratio is 2.1 rather than 2.0
produces the familiar sensation of octave
equivalence. So the evidence *strongly* indicates
that 2:1 octave equivalence goes away when the
timbre becomes inharmonic, and this is confirmed
by William Sethares' mathematical procedure for
finding scale pitches from an inharmonic timbre.
--mclaren

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🔗John Chalmers <non12@...>

From: mclaren
Subject: the future of microtonality
--
While watching a particularly magnificent sunset
with Maxfield Parrish clouds this evening, it occurred
to me how far we've come--and how much there remains
to do.
The history of intonation can be divided into five
eras. The first era, lasting roughly 15,000 years,
began when nomadic hunters first built musical
instruments. Since bone flutes have been discovered
in caves coeval with Neolithic stone tools from
15,000 years ago, it's clear that the act of building
musical instruments predates the discovery of
writing. Thus xenharmonics is an earlier and more
basic activity than reading and writing, and our
pre-school curriculum should be changed from the
"three Rs" to the "three Xs." (Xenharmonic instrument
building, Xenharmonic music-making, and Xenharmonic
'Rithmetic. JI is a superb way to teach fractions because
you can *hear* them.) In the Trois Freres cave in Frances
there is a clear depiction of a performer using a mouth
bow (also called a Jaws Harp), and since none of
these instruments use 12-tone equal temperament
it's also clear that microtonality has been actively
practiced for at least 15,000 years, and probably
longer.
The second era of intonation was inaugurated by
John Napier with his discovery of logarithms in
the mid-16th century. There's no mystery why
the late 16th century witnessed such a remarkable
explosion of interest in different tuning systems--
"Napier's bones" had as vast an impact on composers
and music theorists of the late 16th century as
computers have had on composers and music
theorists of the late 20th century. Vicentino's
and Huyghens' advocacy of 31-TET and Titelouz's,
and Salinas' interest in 19-TET precisely follow
the introduction of logarithms which for the
first time allowed music theorists to easily
calculate added or subtracted musical intervals.
(I mean the 16th century Salinas, not J.A.M.
Salinas here!)
The third era of microtonality was ushered in by
John Henry Maudslay's 1843 invention of the modern
lathe--which led immediately to modern machine
tools, precise and reliably machined tolerances,
and the standardization of machined parts.
Woodwind instruments and keyboard instruments
could not be turned out at simultaneously low cost
and high intonational accuracy prior to the Maudsley
lathe. Even brass instruments and guitars were influenced
by modern precision machine tools: the equipment used
to bent and shape the tubes of which brass instruments
are made and the equipment used to make wound guitar
strings has since the 1840s been entirely machined
by modern precision machine tools. (The valves of
trumpets owe a particular debt to this technology.)
To a large extent, Maudslay's lathe led to the
standardization of 12-TET in the western world and
to the rule of the modern orchestra as the supreme
ideal of western music. And of course large
orchestras with complete families of all instruments
were only possible once the woodwinds and brass
instruments and the piano had been made intonationally
accurate by the Maudsley lathe & its progeny. (This
is why earlier "orchestras" uses primarily stringed
instruments with a few valveless brass instruments.)
The fourth era of microtonality was inaugurated in
1959 by Max Mathews' MUSIC I through IV computer
programs. All current commercial digital
synthesizers are essentially hard-wired subsets of
the Mathews MUSIC N paradigm, with special-purpose
ICs which allow sounds to be calculated in real
time when the keys are pressed.
The fifth era of microtonality dawned when the
first fully retunable digital synthesizers appeared:
the DX7II family in 1987. This was the first time
it was easily possible to explore an unlimited number
of different tunings using many simultaneous
polyphonic notes with a large pallette of different
timbres.
--
It's worth a thought or two. Although we've come
far, we're still at the beginning of the journey. The
most recent advance in intonation only came 9
years ago, when for the first time in human history
it was possible to rapidly switch between different
tunings while playing enough simultaneous notes
on an instrument cheap enough for anyone to afford
in a large enough gamut of timbres to get a reasonable
idea of what each intonation sounds like both
harmonically and melodically.
9 years! That's all!
Retunable MIDI synthesizers offer an almost unbelievable
breakthrough for the microtonal composer. Prior to
1987, composers either had to settle for a very limited
timbral range (retunable analog Moog-type synthesizers)
or a very small number of simultaneous notes (home-built
non-12 guitars, metallophones, etc.) or a fabulously
expensive computer music set-up (prior to the mid-1980s
most computer music facilities were based around DEC
minicomputers costing a quarter of a million dollars each
--or more. Prior to 1980, no privately owned single-user
high-quality 16-bit computer music facility existed
anywhere in the world).
While we've come far, it's sobering to realize that this
latest breakthrough is only 9 years old. To put it another
way, 9.5 years ago, if you wanted to hear the sound of
a string orchestra playing in 27-tone equal temperament
or Partch's monophonic fabric or the free-free metal
bar scale, you would have had to get a doctorate at an
elite computer music institution. Only grad students
at a few elite schools had access to the kind of computer
power that would allow realization of xenharmonic music
with a large number of different timbres and a large
array of different tunings.
Your other choice would have been to bury yourself
in sawdust (like Partch) for 20 years to produce a
set of xenharmonic instruments; but this still meant
confining yourself to a single tuning system. If you
wanted to hear many different tunings played on
many different instruments so as to compare the "sound"
of each intonation, prior to 1987 you either had to
be lucky enough to work as a grad student at IRCAM
or Stanford or Princeton or Simon Fraser University
or the U. of Toronto or Columbia or one or two other
places.
--
In retrospect, our progress has been staggering. For
15,000 years, stasis--hand-built instruments, tuning
by ear. Suddenly, logarithmic calculation of musical
intervals; then, 100 years later, high-speed digital
computers. 30 years later, inexpensive special-purpose
digital computers with built-in tuning tables (these
special-purpose computers are now called "digital
keyboards" but this should not deceive us as to
their lineage or essential function).
Looking forward, what can we see in the
xenharmonic future?
--
Clearly the rapid rate of increase in the speed of
desktop computers means that within 10 to 15 years
every synthesis algorithm currently used in Csound
and its ilk will run in real time. Of course, new
and even more demanding synthesis algorithms
will be developed in the meantime--but within the
next 10 years or so the average person will be
able to use a remarkable array of extremely
sophisticated synthesis techniques to play
notes generated completely in software by
a desktop general-purpose computer in real time.
This will probably be the next era of microtonality.
--
One likely result is that live concerts will
continue to fade away. This has been happening
already, but the trend will accelerate. Johnny
Reinhard has already noticed it. Within a few
years live concerts using traditional acoustic
musical instruments will be priced far out of the
range of the average person's ability to afford
'em, and they'll be available in only a few of
the world's largest cities.
Another of the implications of this next era is that it
will for the first time be possible to calculate
the timbre of a microtonal instrument on the fly.
Thus, it will be of great interest to match timbres
to tunings.
At present William Sethares' work in this area has
gone relatively unnoticed by the microtonal community
because exotic, expensive and wildly time-consuming
programs are needed to analyze and resynthesize
acoustic sounds. As of 1996, it requires anywhere
from a few minutes to several hours to number-crunch
an acoustic sound, manipulate its partials, and
resynthesize them so that the timbre fits the tuning.
Programs like MatLab cost $2000 (yes, two THOUSAND
dollars) and are difficult to use though adequately
flexible; programs like Csound's HETRO and on the
Mac LEMUR cost nothing but are inadequate for
microtonal/musical use because of their lack
of flexibility. (In MatLab you can tell the program
to take input partials and map them to the closest
notes in 19-TET; you cannot do this with HETRO or
LEMUR. Both HETRO and LEMUR prevent the user
from accessing the guts of the program in this way.)
Moreover, all of these programs require minutes
or hours to complete a single analysis/synthesis
cycle of a single note. For multi-sampled notes
spread over an 88-note keyboard, hundreds of
analysis/synthesis cycles are required. And
for (say) 30 different timbres in (say)
30 different tunings, tens of thousands of
different analysis/resynthesis cycles would
be needed. This means years worth of non-stop
computing time even with today's 200 Mhz
CPUs.
Bill Schottstaedt several years ago mentioned
that he felt the need for a machine at least
100 times as fast as the original NeXT cube.
Given the magnitude of the tasks which face
us in matching timbres to microtonal tunings,
that probably represents a very conservative
estimate.
--
Beyond real-time resynthesis and its implied
total timbral & pitch flexibility, what are the
next few eras of microtonality likely to be?
Virtual synthesis and performance environments
are likely to appear.
This implies that a generalized musical controller
represents the next era of microtonality, beyond
the next 10 years. With VR gear it should be easy
enough to produce a virtual theremin or a virtual
marimba (we probably won't be using MIDI, but
a superset thereof, possibly based on FIreWire
or the Uuniversal Serial Bus) or a virtual violin
or a virtual Bosanquet keyboard.
It's unclear whether VR generalized keyboards will
catch on; a large part of musical instrument
performance is muscle memory built by tactile
feedback. VR gear offers no tactile feedback, nor
is there any prospect of adding it to VR gear
at low cost in the foreseeable future. (So much
for teledildonics, gearheads.)
So beyond the next 10 years my guess would be
that the next era in microtonality will be heralded
by new types of controllers, specifically Bosanquet-
type controllers... But it's unclear whether they'll
be physical controllers or virtual instruments.
--
What are the current gaps? What kinds of tools
and theories do we need to push microtonality
beyond the extremely primitive point at we
find ourselves in the late 1990s?
--
First and most important is a generalized MIDI
keyboard. The lack of a true generalized 2-D
keyboard has crippled microtonality to a
devastating extent. Paul Rapoport has pointed
out repeatedly in this forum that it's almost
impossible to perform useful non-12 music
on a standard 7-white-5-black keyboard,
and he's right. A few of us have managed
to produce some highly microtonal music
using conventional keyboards by subjecting
ourselves to a deeply perverted S&M-style
conditioning process whereby we unlearn
conventional fingering techniques and
chord progressions--but this has proven
useful only for the equal temperaments and
just arrays with roughly 22 or fewer notes.
Beyond that point, we've had to flounder
around with solo melodic lines or N-out-of-M
notes of a given intonation.
--
So my first clarion call to the members of this
tuning forum is: someone get to work
commercializing a cheap reliable MIDI
Bosanquet-type keyboard! Harold Fortuin has
already built one, but it's unclear whether
his licensing agreement with STEIM will let
him commercialize it, and it's even more
unclear whether STEIM gives a damn about
driving the cost down on the clavette and
pumping these things out by the thousands.
Probably not. Most large music foundations
have zero interest in doing the tough work
required to move the state of the art forward
and produce tectonic change; large music
foundations prefer to sponsor works of
arts and individuals and thus produce
obvious tangible short-term one-of-a-kind
results.
This leaves it to you, the members of this
tuning forum. Between you, there's more than
enough talent and ability to produce a cheap
commerical reliable MIDI generalized
keyboard.
Who among you will build one that I can
afford to buy?
--
The second enormous gap is in software tools.
Specifically, we need easy-to-use MIDI software
tools which allow us to quickly and efficiently
manipulate xenharmonic MIDI files.
The problem is this: if you're in, say, Partch's
43-tone and you want to modulate to the 3/2,
that means switching to a second MIDI channel
in which all the intervals have been tuned up
by a 3/2. However, there's no easy way to
directly transpose the existing MIDI sequence
on channel 1 and use it harmoniously on channel
2 along with channel 1 without encountering
awkward commas. A human performing such
a modulation in just intonation would know
which notes on channel 2 to omit and which
notes "fit" with channel 1. But MIDI, being
nothing more than a set of note numbers from
1-27, knows nothing of which 3/2-transposed
just pitches on channel 2 "fit" with the original
pitches on channel 1.
Clearly, we need an intelligent MIDI file parser.
This MIDI file parser would offer a simple input
screen and would quickly process input MIDI
files and generate output MIDI files.
In the example above, it would take MIDI notes
on channel 1 and output MIDI notes on channel 2.
Notes on channel 2 which don't "fit" with those
on channel would be left on MIDI channel 1.
This example concerns just intonation, but an
equally important example could be taken from
non-12 equal temperament. Suppose you're
composing a set of variations in 5-TET through
53-TET; you want to play a theme in the nearest
notes to a given set of pitches in each of those
equal temperaments. Your input is a set of
MIDI notes. How do you proceed?
At present, a lot of skull sweat and programming
is required. Again, what we desperately need is
an intelligent MIDI file parser. The parser would
offer a simple input screen (something like: "input
number of tones/oct?" _____ "Number of output
equal temperaments? (1-16)" ____ "Enter output
ET number 1 and track number: " ___ ____ ...."
In other words, this intelligent parser would
accept user input and process a single MIDI
file with a single track and generate an output
MIDI file with multiple tracks. Each output
track would contain the MIDI notes of the
closest notes to a given set of pitches in
a desired equal temperament.
There is nothing like this in existence anywhere
that I know. It is an extremely important
requirement, since many situations arise
every day in which such xenharmonic MIDI
file processing is an absolute necessity.
Let me give another example of badly needed
this kind of intelligent MIDI file parser is:
suppose you have a MIDI synth module like
the Proteus II orcehstral block. This MIDI
synth is basically a playback-only unit. It
contains lots of orchestral samples. Because
these samples are fixed in ROM, they can't
be changed. This means that if you want
to play the Proteus II in Partch 43 tone
monophonic fabric pitches, most of the
samples will sound godawful because they'll
be either far too high or far too low. That is,
the note at which the sample was orginally
recorded becomes farther and farther away
from the pitch played in Partch 43 tone JI
as you move toward the extreme upper and
lower end of the keyboard.
Because the Proteus II has only one tuning
table, you're stuck. The only way around this
problem is an intelligent MIDI file parser.
What you need to do is break up the tuning
table into 4 blocks of 12 out of the Partch
43 just pitches; each track would play
12 of Partch 43 on a different channel.
You then tune the Proteus II to set #1 of
12 out of Partch 43 and play the processed
MIDI track #1 containing MIDI tones
for only 12 out of Partch 43. You record
this to hard disk or ADAT or portastudio.
Then you play back processed MIDI track #2
after returning the Proteus II to the second
12-out-of-Partch-43 pitch table and record
that in simul-sync with the first track.
And so on for 4 complete tracks.
When played back all together, the 4
separate tracks completely avoid the
chimpunking (samples played much too
high or low) and sound as they should.
This can only be done with the aid of
an intelligent MIDI file parser.
We desperately need something like this.
This tuning forum surely boasts a
remarkable overload of programming
talent. Who among you will write
such an intelligent MIDI file parser?
--
A third and extremely important task
that someone needs to do is to tear
down and resynthesize a complete
set of sampled orchestral timbres
so that the altered timbres are
maximally consonant in equal
temperaments 5 through 53 per
octave.
This is an enormous task, requiring
fantastic amounts of processing
power. Who among you will accomplish
this vital task?
--
A fourth extremely important gap
in the xenharmonic toolkit is a set
of MIDI file processing programs
which clean up the output from
non-standard controllers. As we
all know, microtonality accomodates
atypical controllers--wind controllers,
MIDI violin controllers, MIDI theremins,
MIDI guitars. The problem is that most
of these controllers are not yet ready
for prime time. They output loads of
spurious notes and glitches. There
should be easily-available shareware
MIDI file processing programs which
take input MIDI wind controller files
and search-and-destroy all the tiny
brief note-on glitches and spurious
pitch-bends. Ditto MIDI theremin
input tracks: ditto MIDI guitar input
tracks.
Who among you will produce such a
piece of shareware programming?
--
We also need music theory tools to
deal with unanswered questions
in microtonality.
Example: why does a tuning with
"good" numbers like 24-TET sound
so uninteresting while a tuning
with "bad" numbers like 9-TET sound
so musical and so fascinating?
We need better theoretical tools
than crude measurements of this or
that scale against the harmonic series.
As has been pointed out often enough,
the harmonic series is not the be-all
and end-all of music; most musical
cultures throughout the world do not
use pitches derived from the harmonic
series, and psychoacoustic studies
demonstrate that when intervals drawn
from the harmonic series are played,
most people hear them as "impure" and
"not just." Computer analysis of live
performances by expert musicians also
show wild deviations from the target notes,
which deviations are nonetheless heard as
being "in tune."
We need more and better psychoacoustic
research to understand this, and we need
more sophisticated theories of intonation
to explain these results.
We need better music theoretic tools to
quantify the "moods" of the various tunings,
as Ivor Darreg called them. Everyone knows
that 5, 10, 15, 20, 25, 30, 35, and 40-TET
share a similar "sound" or "mood." But we
need to be able to turn it into hard numbers.
Similarly, everyone knows that Ptolemy's intense
diatonic and the scale of Olympos share more
of a "mood" than the enharmonic genus, but again
we need more finely honed theories to quantify
this.
We all know that the "limit" of a just tuning
has an important effect on the "mood" of the
scale. But we need theoretical tools which
will allow finer distinctions to be made
among just tunings than something as coarse
as the "limit" of the tuning. At present, there
is a singular dearth of such theoretical tools.
--mclaren

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🔗John Chalmers <non12@...>

From: mclaren
Subject: Muddy thinking, con artistry, and John Cage
- part I of 2
--
Many thanks to Eric Lyon for falling into
the Bengal tiger trap hidden in my post
in Topic 3 of Tuning Digest 803.
By helpfully committing so many flagrant
logical errors, he has given me leave
to dilate on important points which the
brevity of Topic 3, digest 803 did not permit
me to discuss.
My post stated (in part): "Exactly what is
an experimental composer?
"Which hypothesis does the experimental
composer conduct an experiment to test?
"What is the experimental control? What kind
of statistical methods does the experimental
composer use to analyze hi/r results--linear
regression, chi square, least squares, ANOVA?
"Which laws of nature does the experimental
composer seek to investigate?"
Lyon describes this criticism as "inane"
insofar as "Most of these questions are
irrelevant because musical experimentation
does not equal scientific experimentation."
--
This is a classic example of the slovenly
thinking best satirized in Charles
Dodgson's "Through the Looking Glass" :
"I don't know what you mean by `glory,'" Alice said.
Humpty Dumpty smiled contemptuously. "Of course
you don't-- till I tell you. I meant `there's a nice
knock-down argument for you!'"
"But 'glory' doesn't mean 'a nice knock-down
argument,'" Alice objected.
"When *I* use a word," Humpty Dumpty said, in rather
a scornful tone, "it means just what I choose it to
mean--neither more nor less."
"The question is," said Alice, "whether you *can*
make words mean so many different things."
[Lewis Carroll (nee Charles Dodgson), "Through
the Looking Glass"]
--
In this case the word being grossly misued is
"experimental."
"Experimental" does not have an infinite
variety of possible meanings. It does not
mean just what Eric Lyon chooses it to mean.
The American College Dictionary defines
"Experimental" as: "1. pertaining to, derived
from, or founded on experiment: an experimental
science. 2. based on or derived from experience;
empirical; experimental religion. 3. Of the nature
of an experiment; tentative."
John Cage's use of the word "experimental"
violently contradicts all three of these
meanings.
--
Lyons' logical error is his assumption that
he can misuse and abuse and warp and twist
the word "experimental" at will. (Notably,
this is one of John Cage's most flagrant
errors as well.)
And, like Cage, Lyon has not only misused
the word "experimental," he has demonstrated
his ignorance of the meaning of the word --
and of its profoundly important implications
in our culture.
The word "experimental" inevitably takes on
overtones of the scientific method whenever
it is used nowadays. "Of the nature of an
experiment" (the dictionary definition which
refers to this implication of the word) refers
to the use of experimental technique and
methodology in the course of applying the
scientific method.
What is the scientific method?
Clearly Eric Lyon does know. He states that
"the scientist makes the utmost effort to
*disprove* his hypothesis to determine its
veracity."
This is not the scientific method. It is
never enough merely to "make the utmost
effort to disprose" an hypothesis, since
one's utmost efforts are likely to be futile--
life is short, experiments are complex, and
there are too many possible ways of doing
the wrong experiment.
For example, suppose I hypothesize that light
is a form of electromagnetic radiation. Such
radiation is--as we all know--produced by
accelerating an electric charge or a magnet.
To test this hypothesis, I shake a magnet with
my hand. No matter how rapidly I shake the
magnet, it never emits any light. To do
my utmost to disprove my hypothesis, I
hook up the magnet to a widget which
agitates the magnet over a wide range of
frequencies, up to thousands of times a
second. Having "done my utmost" to disprove
the hypothesis that light is electromagnetic
radiation, I conclude that my hypothesis is
false.
What's wrong with this "experiment"?
The problem is that I would have had to
agaitate the magnet at a rate of about
10^15 cycles per second to get it emit
visible light. Doing "my utmost to disprove"
the hypothesis wasn't remotely adequate,
because I didn't know the range of requencies
required for visible light. Another variant
of such bad science would be to fire up
a radio broadcast tower, transmit over a
wide range of frequencies, and show that
in no case was light ever emitted. Again,
this fails the test of a scientific experiment
because experimental scientists do NOT
try to "do their utmost to disprove the
hypothesis." Rather, in the real world they calculate
an expected result from a mathematical model
and perform repeatable experiments to determine
whether the calculated values match the
observed experimental results.
Moreover, Lyon's claim is obviously false for
another reason. It is *never* possible
to "make the utmost effort to *disprove*"
an hypothesis, since one can never prove
a negative. The effort required to disprove
an hypothesis is infinite and thus the utmost
effort is unending and without limit.
For example, a scientist who hypothesizes
that a psuedorandom number generator
produces a good simulation of an ergodic
stochastic source would--by Lyon's criterion--
have to perform an infinite number of tests
on an infinite number of runs by the pseudo-
random number generator. Otherwise, the
scientist would not be "doing his utmost
to disprove his hypothesis."
Of course, no scientist does what Eric Lyon
suggests because this is not science. Lyon
clearly does not know what science is,
what constitutes an experiment, or the
nature of the scientific method.
"Experiment is the sole source of truth. It
alone can teach us something new; it alone
can give us certainty. These are two points
that cannot be questioned. (..) It is not
sufficient merely to observe; we must use
our observations, and for that purpose we
must generalize. This is what has always
been done, only as the recollection of past
errors has made man more and more
circumspect, he has observed more and more
and generalized less and less. (..) What
then is a good experiment? It is that which
teaches us something more than an isolated
fact. Without generalization, prediction is
impossible. The circumstances under which
one has operated will never again be
reproduced simultaneously. The fact observed
will never been repeated. All that can be
affirmed is that under analagous circumstances
an analagous fact will be produced. To predict
it, we must therefore invoke the aid of analogy--
that it to say, even at this stage, we must
generalize. (..) Experiment only gives us a
certain number of isolated points. They must
be connected by a continuous line, and this
is a true generalization. But more is done.
The curve thus traced will pass between and near
the points themselves. Thus we are not
restricted to generalizing our experiment,
we must correct it. (..) Detached facts cannot
therefore satisfy us, and that is why our science
must be ordered, or, better still, generalized."
[Poincare, Henri, "Hypotheses in Physics," pg.
142, from Science and Hypothesis, Dover
Edition, 1952]
One of the finest mathematicians of all time,
Poincare had a good idea what the scientific
method involved. "Every experiment must
enable us to make a maximum number of
repdictions having the highest possible
degree of probability. The problem is, so to
speak, to increase the output of the scientific
machine. I may be permitted to compare science
to a library which must go on increasing
indefinitely; the librarian has limited funds
for his purchases, and he must, therefore,
strain every nerve not to waste them." [Poincare,
op. cit, pg. 144]
Lyons' claim about the scientific method
grossly violates Poincare's principle of
experimental parsimony. This is as we would
expect, since Lyon understands nothing of
the scientific method; but Poincare makes
it pellucidly clear that quick rejection of
an hypothesis is of the utmost importance.
"Every generalization is a hypothesis.
Hypothesis therefore plays a necessary role,
which no one has ever contested. Only, it
should always be as soon as possible
submitted to verification. ...If it cannot
stand this test, it must be abandoned without
any hesitation. (..) If [the hypothesis] is not
verified, it is because there is something
unexpected and extraordinary about it, because
we are on the point of finding something unknown
and new. Has the hypothesis thus rejected been
made sterile? Far from it. It may even be
said that it has rendered more service than
a true hypothesis. Not only has it been the
occasion of a decisive experiment, but if
this experiement had been made by chance,
without the hypothesis, no conclusion could
have been drawn; nothing extraordinary
would have been seen; and only one fact the
more would have been catalogued, without
deducing from it the remotest consequence."
[Poincare, Henri, op cit., pg. 151]
Notice that this latter pointless activity
is *precisely* what Cage advocates. From
this "experiment...made by chance" without
an hypothesis, no conclusion can be drawn;
the outcome is "without the remotest
consequence." This is not science. This is
not an experiment. It is not "experimental."
Neither Eric Lyon nor John Cage understood
this--because neither of them understood
the meaning of the word "experiment," the
nature of the scientific method, or (apparently)
any of the other technical vocabulary they
have chosen to misuse.
This discussion of the the experimental method
is particularly appropriate to microtonality
because, as we've seen, time and time again
xenharmonic intonations have been
dismissed as "useless" and "impractical"
and "unmusical" on the basis of abstract
calculations--yet these same intonations
prove superbly useful for composers of
microtonal music. Barbour, for instance,
dismissed 19-tet: yet reams of excellent
19-tet music has been composed. Fox-
Strangways dismissed just intonation as
impractical--yet Partch and the members of
the JIN have composed enormous amounts of
beautiful music using ji. 15-tet has been
pooh-poohed as "unmusical," yet Easley
Blackwood has proven that it is not only
musical but fertile ground for microtonal
composition. And so on.
Thus, it is especially vital when discussing
microtonality to have a firm grasp on the
scientific method, for new tunings must
always be *tested* by *experiment* before
they can be accepted or discarded. And
Eric Lyon makes this difficult because he
has given a series of utterly false definitions
of "experiment" and by implication the scientific
method.
Instead, what scientists actually do is to
try to prove their hypotheses by measuring
physical events and comparing the results
with calculations based on mathematical
models derived from their hypotheses.
To proceed in the opposite way, by trying (and
failing) to disprove one's hypothesis, is futile
and in fact a profound logical fallacy. For
Lyon reasons that if a large enough number of
instances in which an hypothesis is not
true cannot be demonstrated, the hypothesis
must be correct. This is obviously false, and it
has been known to be false for more than two
thousand years: Aristotle discussed this logical
error, and it has been used as a textbook example
of faulty reasoning in universities throughout
Medieval Europe, the great institutions of
learning of the Renaissance, and up to the
modern day.
This reasoning is faulty because no matter how
many experiments you perform to disprove your
hypothesis, it doesn't guarantee that *both* your
hypothesis *and* the null hypothesis might be
false, and the truth might be a third possibility
you hadn't thought of.
Notice that this is *exactly* and *precisely*
the same logical fallacy into which critics of JI and
microtonality have consistently fallen; a theorist
here and there attempts to compose in a xenharmonic
intonation, and knowing nothing about the intonation,
produces unlistenable junk. From this they conclude
that microtonal tunings are "useless" and "unmusical."
Barbour is a prime example: his misuse of JI--in which
hs tries to compose a passage which modules from C
to F# without changing any of the pitches by a comma--
does not show that JI is "useless" or "unmusical,"
it merely shows that Barbour's use of JI is
inept, unmusical and willfully ignorant.
This should be so obvious as to require no
explanation, but apparently this kind of
2500-year-old logical fallacy is news to
many of you, including Eric Lyon.
(Sigh)
The scientific method does not stress disproof,
but positive demonstrations, for precisely
this reason. A million pieces of bad music
composed by people ignorant of JI do not
disprove the utility of JI: but one good piece
of music composed by someone knowledgable
of JI *DOES* prove the intonation's utility.
Eric Lyon clearly does not understand the
scientific method, nor the logic behind it. These
concepts are apparently alien to him, just as they were
to John Cage, just as no "experimental" composer
appears to have known what the scientific method
involves or why it is *vitally* important when
dealing with new intonations.
As John Backus pointed out, "terms borrowed
from the field of science must be used with their
precise scientific meanings." Otherwise, the result
will be pseudo-science, "disregard for the accepted
meanings of scientific terms, (..) unintelligibility,
and (..) complete lack of any reference to the results
of other workers as support for (..) statements."
[Backus, J. "Die Reihe--A Scientific Evaluation,"
Perspectives of New Music, Vol. 1, No. 1, pp. 161, 171]
The concluding half of this post deals with
some concrete examples which show why
an understanding of the scientific method
(and use of the word "experimental" in accord
with its specific dictionary definition) is
so crucially important in dealing with microtonal
scales.
--mclaren

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