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
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
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,
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
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
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)
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
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
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
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.
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
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.
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
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
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
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
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
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.
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
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
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
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.
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
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,
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
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,
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
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
