source file: mills2.txt Date: Wed, 18 Dec 1996 14:04:33 -0800 Subject: post for Brian McLaren From: John Chalmers 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 Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Thu, 19 Dec 1996 07:11 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA04789; Thu, 19 Dec 1996 07:13:20 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA04465 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id WAA09396; Wed, 18 Dec 1996 22:13:17 -0800 Date: Wed, 18 Dec 1996 22:13:17 -0800 Message-Id: Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu