post for Brian McLaren

From: mclaren
Subject: practical vs. theoretical
implementations of microtonality
--
A microtonal composer on this forum
recently slammed head-on into the real world
of synthesizers in a particularly unpleasant
way, so it's time to discuss the humungously
vast difference between the theoretical
ideal ivory tower notions of microtonality
on currently available MIDI synthesizers
as opposed to the hard cold realities.
--
Let's start with the basic upper limit
on the number of pitches per octave
on a MIDI synthesizr.
If you have only one pitch table on
your synthesizer or sampler, you will
be limited to no more than 17 tones per
octave.
How so?
Let's do the calculation (which, since
it's obvious, has never been posted
by any of the illustrious PhDs on this
forum):
The instrument of the orchestra with
the largest pitch range is the piano:
88 notes, a little more than 7 octaves.
The maximum number of pitches which can
be generated with one pitch table limited
to 127 MIDI notes on such an instrument is:
127/88*12 17.3 pitches per octave.
To get more pitches per octave than
this, you must either [1] reduce the
range of your instrument from 7 octaves
down to some smaller ambitus; [2] use
multitracking with SMPTE sync and
create multiple MIDI files which break
up portions of your composition into
different keyboard ranges, and then
build up the entire composition out
of multiple passes via multitrack
recordings; [3] use an instrument
with multiple pitch tables; or [4]
pull the samples into a program like
Alchemy and sample-rate-convert them
to use less memory...which also
produces lower audio fidelity.
--
These are your only choices.
Reducing the range of the instrument
is usually not an option. If you
want to compose a piano sonata in,
say, 41 tone equal temperament,
this limits you to a 3 octave
range. Most composers would not
accept such a limitation.
As for using multitrack with SMPTE
sync to create a microtonal compostion
via multiple passes in the recording
studio, this is so harrowing and so
arduous and so difficult that no
microtonal composer has ever done
it. Thus it is so complex and so
tortuous that it is effectively
impossible.
Few MIDI synthesizers have multiple
pitch tables. Only the EPS samplers,
the VFX and TS-10 synthesizers, and
the TX802 have more than one pitch table.
Of these, only the TS-10 and ASR-10
samplers are currently manufactured.
This leaves most microtonal composers
with no options.
--
In the real world, things are very
different from the realm of pure theory.
Let's take a hard cold example--let's
say you want to compose a piano sonata
in 41 tone equal temperament.
The best piano sample bank around is
the Akai Steinway D bank on Volume 1
of Akai's "Complete Piano" series.
Clearly, this is the piano sample
to use.
This bank takes up 32 megs of sample
RAM.
As we've seen, the maximum limit for
1 MIDI channel is 17 pitches per
octave. To get 41 pitches per octave,
we need 3 different retuned sample
banks on 3 different MIDI channels,
requiring a minimum of 96 megabytes
of sample RAM.
No current sampler allows this much
RAM except for the astronomically
expensive Kurzweill K3000 sampler.
This sampler lets you add up to
128 megs of RAM and the sampler
itself costs about $4500. With
128 megs of RAM, the cost rises above
$6000. Since no microtonalist
has this kind of cash to spend merely
to produce a single composition, you're
pretty much out of luck.
The alternative is to use 8 Ensoniq
ASR-10 samplers, at an approximate
cost of $20,000. Those of you who have
twenty thousand dollars to spend on
a single composition, raise your hands...
The other alternative is to use one
ASR-10 sampler and break up the
Akai piano sample into 8 different
blocks, then realize the entire
composition in fragments by writing
software to break up your MIDI file
of the composition into 8 different
MIDI channels and re-assemble the
whole composition one fragment
at a time via digital multitrack
with SMPTE sync, changing piano samples
between each take.
No microtonalist has yet accomplished
such an incredibly convoluted and
difficult feat; in the real world,
therefore, such an option does not
realistically exist.
--
If you want to use a sampler without
a pitch table--say, the Akai S-2000--
you're *really* up the creek.
In this case you can only break out of
12-tet by using a sample map to map
each sample to a different pitch and
each pitch to a separate key.
This requires that you use 127 different
samples...one for each MIDI note.
Since the Akai Steinway D piano bank
uses 1 sample for each whole note
(44 whole notes total in the bank)
with a total of 32 megs, you would need
32 megs * 127/44 92.36 megabytes of
sample RAM to get 127 MIDI microtonal notes.
If we're in 19-tone equal temperament,
127 MIDI notes still isn't very much:
that's only 127/19 6.68 octaves, less
than the range of a conventional grand
piano. Yet the Akai series of samplers
permit only 32 megs per sampler. This
means that you would either have to
buy 3 Akai samplers, or multitrack
the composition sync'd to SMPTE--as we've
seen, an impractical option so difficult
and so arduous as to be effectively
impossible.
--
What are the other alternatives?
Well, theoretically we could feed
the Akai piano bank samples into
a program like Alchemy or Sound
Forge and sample-rate-convert them
to take up less room. Downsampling
from 44.1 khz to 22.05 khz would
double the number of notes per
megabyte of sample. However, this
would degrade the audio quality of
the piano sound, and it would
also take up an impractical amount
of computer time.
How much time?
As Leibniz suggested, "Gentlemen,
let us calculate."
Say 5 minutes per 800 kilobyte piano
sample to convert from 44.1 khz to
22.05 khz--and the Akai piano sample
has 44 different multisamples, so this
is 220 minutes or 3 hours 10
minutes. Add on file naming,
saving to disk, etc., and we
get roughly 4 hours of work.
Of course, this is only for
one intonation--41-tet. If we
want sample-rate-converted
smaller-size piano samples
re-mapped for every equal
temperament from 5 through
53 tones per octave, that
will take 192 hours of work,
or 8 days working non-stop
8 hours per day. If we
work 4 hours per day (a more
realistic estimate--say,
after you come home from your
job) it would take 16 days
to finish that task.
This still gives you only 1
timbre--piano timbre, in 5
through 53 tones per octave.
For 64 different timbres (a
reasonable though modest
sound-pallette) you would need
to spend 1024 days, or 2.8
years working 4 hours per day,
7 days per week, 52 weeks per
year.
At this point we've slammed
head-on into the practical
limitations of the real
world.
--
The difference between the
theoretical ideal of microtonality
and the practical reality is vast.
It's as large as the differene
between the theoretically finite
possibility that a pot of water
will freeze when you put it over
a fire, and the practical reality
that this NEVER happens. In the
real world, the pot always boils...
ALWAYS. Without exception.
And so when various forum subscribers
clamor that my facts are incorrect
or my conclusions are wrong, it's
well to remember that they are fantasizing
about some ideal theoretical pie-in-the-
sky realm, and NOT talking about the real
world.
--
We can use the 17-pitch-per-
MIDI-channel limit to do some
other calculations which tell
us some revealing things about
synthesizers and MIDI.
72 pitches per octave seems like
a reasonable maximum for a
microtonal composer. Some
members of this forum (myself,
John Fitch with 100/oct, William
Schottstaedt with 144/oct) have
composed pieces of music using
much larger numbers of tones
per octave, but such compositions
remain rare exceptions. Most microtonal
music uses 72 tones/octave
or less.
If we accept 72 pitches per octave
as a practical maximum, how many
MIDI channels are needed to
realize such a composition, given
the 127 MIDI note limitation?
The answer is 72/17 4.23,
or, rounding up, 5 MIDI channels.
Thus 5 MIDI channels represents
the minimum number that should
be available on a sampler.
We can use this result to tell
what the minimum amount of sample
RAM should be on a sampler so
as to allow us to compose with
up to 72 pitches per octave:
Given that most sample banks
now average about 32 megs of
RAM, we would need at least
5*32 megs of sample RAM.
So 160 megabytes is the minimum
amount of sample RAM which would
be useful on a sampler if you
want to compose microtonal music
with it.
Alas, no sampler allows this much
RAM.
The Enqoniq ASR-10 is limited
to 16 megs maximum, ditto the
Digidesign Sample Cell. The
Kurzweill 2000 allows 64 megs
maximum, while the Kurzweill
3000 allows 128 megs maximum.
Now we run into another limitation
of the real world: pitch tables,
and the lack thereof.
The Ensoniq ASR-10 is the only
sampler on the market which
currently has pitch tables. All
other samples are locked via hardware
into 12 pitches per octave--in
some samplers you can vary those
12 pitches, but you're still
restricted to 12.
At this point various forum
subscribers will predictably
claim that they can force 12/oct
samplers to do microtonal things
using some exotic combination of
hardware and software.
This is false.
While in an ideal world it is
theoretically possible to use some
exotic software systemm to tweak
an Akai or Kawai or Kurzweill or
Roland synthesizer/sampler so
that it produces microtonal music,
in the real world the cold hard
fact is that these exotic kludges
*do not* produce acceptable results.
Either pitch-bend messages/
sys-ex messages clog the MIDI
channels and turn chords into
arpeggios, or pitch-bends turn
every note-on into a twang (an
ugly sound, especially with
percussive timbres), or you get
only a few notes out of N at a
time.
Thus, in the real world, these
schemes don't work. In the
real world, I need all 41 pitches
of 41-tet available at once.
I want to do 5 octaves of
41-tone per octave note
clusters. I want to do complex
chromatic polyphony at high
speed. I want to run from the
highest pitch to the lowest
in chromatic progression while
harmonizing with 13th chords.
None of these strange sys-ex
or pitch-bend schemes will
permit this.
Thus, in the real world such
onerous kludges simply do not work.
They enforce such drastic
limitations on the composer
as to be unacceptable. Either
the composer must edit every
note to insert a sys-ex message
by hand, or the MIDI channels
get so choked with sys-ex info
that the synthesizer starts
missing notes, or you're limited
to a maximum of 16 notes/MIDI
channels at a time, or some other
crippling problem arises.
--
This points up the *enormous*
gap between practical and
theoretical implementations
of microtonality.
While pitch-bend and sys-ex
schemes are theoretically
possible, in the real world
they just don't work out.
The hard cold brutal reality
of microtonal composition is
that it's so difficult and
so complex and so demanding
for us (the first generation of
microtonal composers using
MIDI instruments) to write
music outside of the 12 Sacred
Tones that if a scheme requires
a composer to spend more than
a day or two tweaking a synthesizer
to get non-12, we simply won't use
it.
The reason for this is the hardware
we're battling, as well as our own
mental software. We were all taught
to compose in 12, and that programming
is very strong. Thus it's doubly hard
for us, as the first generation of xenharmonists
with instant access to ALL possible tunings,
to fight *both* our 12-tet programming AND
the current neolithic generation of
microtonal synth hardware.
Right now synthesizers are mostly hardware.
In the future, this will change drastically.
Soon synths will be mostly software, and this
will make it much *much* easier to compose
in real time in scales like Partch 43 or
41-tet. In the meantime, however, we must
do the best with the hardware we've got.
Remember...MIDI is only 13 years old.
--
Amid this blizzard of numbers, it's important
to keep sight of our priorities--as this tuning
forum often does NOT.
Numbers and ratios and algorithms are
NOT what microtonal music is all about.
Words and equations and psychoacoustics
papers are NOT the ultimate destination of
xenharmonics.
Microtonality is about MUSIC.
As composers, we cannot afford to
get sidetracked into a tarpit of
endless sys-ex tables and synth
set-ups and individual note-edits.
More than a few hours of this prior
to a composition or performance is
impractical. In the real world,
a couple of days of this kind
of hassle at most is about the
limit of what the average xenharmonic
composer can stand per tuning.
What we need is pretty much something
like what an ordinary 12-tone composer
has: you sit down at the piano and you
play. If 12-tone composers had to
spend 3 weeks busting hump with sample
editors and sys-ex tables and the rest
of that rigamarole before they could
even start to compose, there wouldn't
be much 12-tone music.
This is just the hard cold reality.
People who dwell in ivory towers or
who spend their lives as programmers
(not composers) of course don't
understand this. But for the rest of
us, it's a very real fact. When the
amount of work required to get a
synthesizer to do something microtonal
rises above some arduous level--say,
a couple of days of effort--we as composers
will say "The hell with it!" and move on.
This is why so little microtonal music
has been written for the FB-01. That
synth required that a separate sys-ex
tuning message be sent with each
note-on, and it was simply far far *FAR*
too much work. Composers just gave
up and turned to other synthesizers that
had tuning tables. Life's too short
to spend it beating your head against
intractable digital hardware.
--
This means that synthesizers and samplers
with pitch tables are the minimum
requirement for microtonality. While
it is in an ideal world theoretically
possible to get synths which are locked into
12 pitches per octave to do something
microtonal, in the real world it's so
difficult and so complex and introduces so
many crippling limitations that in practical
terms it's impossible. For microtonality,
you MUST have a synthesizer with a pitch table.
--
It's a matter of some interest to use
the 17 pitch per octave limit to calculate
how many MIDI notes *would* have been
required to let us get 72 pitches per
octave. It turns out that the number
of MIDI notes we really needed in the
MIDI spec was X 72*88/12 528.
The assumptions here are, as usual,
that we won't need a single instrument
with a wider range than a grand piano
(88 notes) and that we must restrict
ourselves to a single MIDI channel.
It's heartbreaking to realize that if
only the original MIDI spec had used
10 bits for pitch instead of 7, we would
today be able to easily get 72 pitches
per octave without any trouble. In fact
with 1023 MIDI notes we'd be able to
get 7 octaves of 139 pitches per octave...
plenty for almost any practical
microtonal composition.
Just think of it--if the original MIDI
protocol had used 16 bits per MIDI byte
instead of 8 bits, we would have had
15 bits available for pitch. That would
have given us 32767 pitches, far more
than enough for any conceivable xenharmonic
tuning. Our problems would have been
solved.
Alas, Wold's Law applies: Erling Wold once
said that all standards in the personal computer
industry are created by taking the cheesiest
sleaziest lowest-cost kludge that will
do the job at some grotesquely sub-minimal
level and etching it in adamantine diorite.
Once again, with MIDI, Wold's Law has
proven correct...if only MIDI had been
delayed until 16 bit processors and
16 bit bytes became the standard in
the desktop computer industry...!
(Sigh.)
--
At this point Johnny Reinhard and his
New York friends will predictably claim
that the answer is to eliminate MIDI
synthesizers and compose for pure
acoustic ensembles. Of course, Johnny
and friends overlook the vitally
important fact that MIDI synths have
become *indispensable* in composing microtonal
music. A MIDI synth allows a composer
to *hear* those new microtonal harmonies
and microtonal melodies before committing
them to paper. This is absolutely necessary
because history shows that every microtonal
theorist who ever made a judgement about
a scale *without* hearing it wound up
being completely mistaken. The cold deaf
mute silent numbers NEVER tell you what a
tuning will *sound* like. Thus, J. Murray
Barbour dismissed 19-tet as "too insipid"
because of its "overly pure" minor thirds...
but in fact 19-tet is today one of the most
popular equal temperaments, due to its distinctive
and memorable and very aggressive "sound" or
"mood." Fox-Strangways disdained Partch's 43
note just intonation because of the purported
"problem" with different notes having the same
name--but as anyone who's heard Partch's music
knows quite well, this is simply a non-problem.
As a triad moves from I to IV to V to I, different
notes with the same name play musical chairs
inside the chords. It works perfectly, sounds completely
straightforward. Again: 15-tet was pooh-poohed by
countless music theorists because of its 720-cent
fifths, but 15-tet turns out to have a vivid
and lovely "sound" or "mood"--as Easley Blackwood,
Ivor Darreg, and many others have proven conclusively
by composing superb music in the tuning.
And so on.
Thus, microtonal synthesizers are here to
stay. It is not practical to roll the clock
back and banish them from the composer's
studio or the concert hall.
This makes the 127-note MIDI limit a
particularly huge probem. MIDI syths
are everywhere--in fact they are largely
responsible for the formation of this
tuning forum--and this means that the
17-pitch-per-octave limit is something like
the speed of light...it is built into
microtonal synths at the hardware level,
and we must *all* deal with it. (The
only exceptions are those lucky few with
access to the Samson Box. Even the KYMA
system is limited to 127 MIDI notes.)
--
Efforts to expand the number of MIDI notes
have proven disastrously misguided. The
recent ZIPI proposals by the Berkeley CNMAT group
headed by David Wessel suggested sending
pitch as an unsigned multi-byte float instead
of as an unsigned 7-bit int. This was an
astoundingly BAD idea because the great
virtue of MIDI note numbers is that they
are just that--numbers, not connected to
any particular pitch. This leaves the
individual synthesizer free to interpret
the numbers and that means that a microtonal
composer has maximum flexibility. Using
simple integers as MIDI numbers means
that a composer can very simply and easily
set up elaborate pitch tables merely by
filling up the linear array of midi note
numbers in any way desired. For example, a
microtonal composer can fill one pitch
table of a MIDI synth with a 5/oct pitch
table, another pitch table with 7/oct,
and yet a third with a 35/oct pitch table.
This allows a composer great freedom in
moving between tunings--all you need
do is switch MIDI channels.
Interpreting MIDI notes as simple integers
(which are really pointers to an array)
without reference to pitch makes possible
such exotic compositional strategies as
composing in (say) 13-tone equal temperament
melodically with just intonation vertical
harmonies for each note.
All you need to do is fill one pitch table
with 13-tet and two other pitch tables with
the same pitches transposed a 5/4 higher and
a 3/2 higher.
To regress and devolve by interpreting notes as pitch
rather than numbers is a giant step BACKWARDS
which makes many kinds of microtonal composition
much more complex than they ought to be.
But the worst aspect of CNMAT's ZIPI proposal
is that it puts the burden of setting pitch on
the shoulders of the controller manufacturers.
And we all know EXACTLY what will happen five
minutes after ZIPI becomes the official pitch
protocol for synthesizers: the controller
manufacturers would take one look at the
pitch protocol, say "To hell with this!" and
lock their controllers into strict 12-tet to
save time and money in manufacturing their
keyboards.
The end result?
ZIPI would sound the death knell for
microtonality on digital synthesizers.
--
And so the situation looks bleak for microtonality
on synthesizers. Those who want to explore
large numbers of tones per octave (> 17 pitches
per octave) are up against some cruel practical
limitations. And now that Ensoniq has fired
its entire R&D staff, the future of microtonal
innovation on synthesizers is very much in question.
Instead of having more pitch tables on synths
(as we desperately need), we are likely to have
*fewer* in the future.
John Fitch's Extended Csound spec looks like it's
arriving just in time.
--mclaren



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