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
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
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,
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
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
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
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,
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
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
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.
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
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
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,
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
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."
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
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
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
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
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
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
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
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
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
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.
--
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
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
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
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
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
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,
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.
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
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
*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
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
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.
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
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, 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
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
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
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
