DON'T FENCE ME IN!

by

Ivor Darreg (1988?)

I am a composer, and have to stand up for the other composers' rights as well as my own: the exploration of non-twelve-tone tuning has entered a new phase, with the coming of better electronic musical instruments and new computer software for musical purposes.

Formidable financial obstacles have now retreated: redesigning the piano for new scales having more than 12 tones per octave has been an impractical dream for all the piano's useful life, but now that we no longer are tied to wooden machinery of piano-actions and heavy cast-iron frames and now that the price of real pianos built the nineteenth-century way has gone completely out of sight, and the price of new kinds of instruments and computers has come down and indeed crossed over the astronomically rocketing-into-the-sky piano price, it makes no sense to hold the musical world in nostalgic captivity to bygone restrictions. The limitations of the piano and most other conventional instruments belong in the history-books, not in your living room nor in my studio!

The electronic instrument doesn't care what it is tuned to. no strings to break. Any limitations of tuning will be put there by non-musician factory engineers and manufacturers who may or may not know what the public wants. The fact that most synthesizers now have some kind of pitch-bending lever or control, should be evidence enough that people out there are groping for some new effects. These bending controls would never have been put on if nobody wanted new pitches! Oh, sure, some old-fogy is going to argue that pianos have gotten along without them for century and a half, but they forget about the clavichord, which had pitch-bending built into every single key! These antiquarians better not say that what was good enough for Bach ought to be good enough for you and me, because Bach used clavichords and must have done some pitch-bending on them.

That makes moot the theoretical/historical arguments about whether Bach did or did not ask for exact 12-tone equal temperament. The clavichord, even if exactly so tuned, could bend any note upward at will and this escape the rigid theoretical tuning at any time. The counter-argument you are likely to hear at this point would be that the harpsichord cannot bend; but after all, the violin can. What I am trying to point out here is that the idea of bending pitches on a keyboard instrument is older than the piano, so this is a revival rather than unheard-of new trend. No theoretical scale was observed as rigidly and uncompromisingly as the mathematical and theoretical writers on the subject of tuning-systems make it seem.

If tone-bending were the main consideration, I could stop right here; it would be sufficient to point out the Hawaiian steel guitar and the blues-singers and the concert violinists and other soloists who take this or that note sharper or flatter. Traditionally, composers have not been allowed to notate a bent pitch! This freedom has been extended only to performers. The composer living today has been forbidden to do anything not sanctioned by what we inherit from DEAD Romantic and Classical composers.

The anachronistic incongruity is outrageous! Go into a bookstore--here is a book on how to build electronic devices using the latest parts, but if the device is a keyboard electronic instrument, the music it will produce is for melodic and harmonic possibilities about 200 years old. That is, day before yesterday's music shown cheek-by-jowl with tomorrow's electronic technology often not yet in full production. Now look over the other racks and you will see How To This and How To That and almost any other Do-It-Yourself booklet will have really modern stuff in it. Everything except music.

So most composers today are kept from knowing what is available and affordable and feasible right now. Knowledge is suppressed; they are held back. They may try to invent something based on conventional instruments, and of course do not know that that was thought of long ago. That is, interdisciplinary feedback is suppressed. External cosmetic features of instruments designed to attract attention on a rock concert stage get all the manufacturers' efforts and the needs of the composer are ignored.

For fully fifty years I have been doing something about this: I didn't wait for someone else to. My electronic keyboard oboe is 52 years old. It still has features which the mass-produced synthesizers do not have. Without feedback there can be no progress. If the composer and the instrument-maker have no common terminology, they cannot communicate. So they haven't been on speaking terms. The only way I could make progress was by learning electronics as well as music theory and composition.

Believe me: it is harder to tell someone else how to build a new instrument than to build it yourself.

At the present time, there are widely divergent motivations and reasons for going outside the conventional standards of music-making such as the twelve-tone--or better, the twelve-pitch-class equal temperament--that has been an accepted ideal or standard or norm for some two centuries. No wonder, then, that the non-12 people don't always understand one another. No wonder either that there has been so little progress till very very recently. Most of you probably have heard of the quartertone piano pioneers, some of whom began in the 1920's--it never really caught on, but the motivation was there. (I have dealt with the reasons elsewhere in several writings.) Carrillo and Haba went further, to real microtones--sixth, eighth, even sixteenth-tones (96 pitches per octave). If you were a piano manufacturer or organ-builder or music-store proprietor, your wallet-nerves would be jumping like conniption fits over the very thought of such complications. And although it's considered a grave breach of etiquette to mention financial considerations, once you go beyond 12 pitches per octave the costs could escalate to the whole National Debt or the 22nd century's Space Program. Or so the average practical person will think.

There is what we might call the software problem also: how do you write down the new scales? How do you teach them? How do you get performers to practice them? And capping the climax, how to get any piano-tuner to tune them? These problems seemed to be the crushing final answer to all composers and experimenters--Get Lost!!! and often this scathing rejoinder was delivered with more than three exclamation-points. Total Impasse--B.T.R. (Before Tape Recording.)

Yet another version of the chicken-or-the-egg dilemma. How can you construct non-12-tone harmony without instruments to hear such harmonies? But why would anybody build such an instrument without a demand for it? The mass-production manufacturer will not build a one-of-a-kind instrument, of course; that is a "given." If the question should be one about public demand, well, the public is now allowed to hear any new tunings or scales if the Musical Establishment can possibly prevent it. however, our contemporary sound environment contains numerous sounds which do not conform to the the standard Western European musical scale we are taught to use.

This impasse has been broken by tape recording, then effect-boxes and overdubbing and modifying of instruments and multiple tracks and better yet, editing recording--then copying them in one's own studio--no censorship, no martinet self-appointed Authority looking over your shoulder to nip all your creativity in the bud.

This way the composer can now get through to the listeners without the interposition of conservative, reactionary or hostile performers, which has been unhappily the usual situation for over a century--i.e., when music in the home declined, and was turned over to the professionals, and the public became passive consumers and their desires to create music were discouraged. The arrogance of some performers toward composers is incredible. Happily, I don't have to put up with it anymore. If the performers doesn't want to play my stuff, he can go right back tot he 19th century and stay there: I do not need him! In return, I will not have the slightest desire to upset his status quo or attitude or lifestyle. Since tape recording, no performer can ever say I imposed upon him or her.

Elevating the performer above the composer is humiliating: so the tape machine has put the composer up to a status comparable to that of painters and sculptors--and that should be so.

This should dispose of the frequent objection that performers cannot be expected to read new notations nor master new techniques which go against their years of practice and training. Now, even the composer doesn't have to go against his training, since the performance, if desired, may forgo real-time and be done by a computer. Dehumanizing? Well, don't bring that up! What can be more dehumanizing that keeping composers lonely and in silence for forty or fifty years, not allowing their melodies and harmonies to be heard by others?

Now for the motivations: one of the older reasons for having more than 12 notes per octave is to get just intonation. usually this has been to improve the sound of previously-existing music. many advocates of just intonation have not cared about living composers at all. They have studied acoustics and theory of tuning and mathematics and have come to understand what distortion is caused by the intervals of twelve-tone equal temperament in roughening and spoiling consonant chords. So they reason, if the classical and romantic repertoire were always performed with mathematically-perfect intervals, every music listener would be in heaven or at least Utopia.

The century-old book, Helmholtz's Sensations of Tone, with what amount to a long treatise on theory of tuning by the translator, Alexander John Ellis, presented a comprehensive series of arguments for just intonation. It has been harshly criticized and seriously misunderstood for the entire century since it was published. It was much more practical and realistic than these critics would ever admit. A 5-limit array was presented--i.e., the subset of just intonation implied by ordinary harmony, which would call for just (pure, beatless, untempered) major thirds and fifths. The modulations to other keys implied in the ordinary classical and romantic music would be taken care of by an array of some 117 tones per octave if one were so finicky as to demand very fine distinctions. But this was not the actual demand made in the book at all. An array of 24 tones was worked out by Prof. Helmholtz and actually tuned on a two-manual harmonium--this fully a century ago!--and that would do for a very wide range of existing music of that period. An equal temperament of 53 tones per octave was proposed by several investigators, after Mercators early discovery of this possibility, and the differences between those 53 tones and 117 in the 5-limit array are trivial--while they can be heard under laboratory conditions, they would not be heard in any realistic musical performance. No matter now in 1988: a computer could get very close to perfection. Some new instruments already do.

This subset of just intonation which does not contain any ratios involving primes greater than 5, would not take care of septimal intervals which use the prime factory 7. So the very common dominant seventh chord would be out of tune. However, there is a rough approximation available int eh 5-limit, and the 53-tone-equal imitation is 5 cents sharp of the true value of the 4:7 interval. Some composers, notably the late Harry Partch, went one step further, demanding new intervals based upon the prime number 11. Partch's just array had 43 pitches, but since it had to include so m any 7- 11-based intervals, could not modulate very far. With new instruments now available, this would not longer be the case--the array could be shifted anywhere one wished to go. However during Partch's lifetime and with his insistence on acoustic instruments, the limitations were severe. For him and many of his would-be followers, there was a painful dilemma--extending just intonation meant a cruel cramping sacrifice of modulation. It is very important to point out that this is no longer necessary.

Those who do not want to hear any music written since 1900 or even 1850, refuse to admit the use for chords involving ratios containing 7. This even though the use of 7 would improve a great part of older music. And thus the advocates of just intonation are quite divided and often attack one another with wicked polemics and constant invective. One book even called 7-based intervals "dangerous" as if they would drive you crazy. Are we going to destroy all clarinets and most horns to placate this theorist? The 7th harmonic is an essential part of their timbre. And how about Barbershop Quartets? They sing 7-based intervals with no harm at all.

That is to say, the Barbershop Quartet singers are not constrained by the tuning of instruments in the way that, say, a church choir accompanied with a pipe organ would be. The same person might be now and then in both environments and behave differently, of course.

Up to now, the actual instances of just intonation that get heard by an average listener are "lucky accidents" in spite of the usual constraints of conventional musical instruments which are tuned some other way. So for most people such phrases as "pure intervals" or "exact tuning" or "just intonation" or "untempered music" are empty words with no concrete examples stored in your memory or the other fellow's knowledge either. Since the advocates of various just systems have such widely different objectives, they cannot co-operate and do not present a United Front against the Music Establishment. Indeed, they waste most of their energy and time fighting one another!

This situation has come about because there was no accessible equipment for most musicians or listeners or theorists or experimenters to try different forms of just intonation out objectively and with "repeatibility"--i.e., such that one person experimenting in Massachusetts would have the same sounds and the same results and impressions as another experimenter in Oregon. Until the recent profliferation of tape machines and the easy copying of cassettes, there was no assurance that you were hearing anything like what the other person was experimenting with. It was all SILENT arguments on purely visual paper-and-ink. Hence no progress.

Just a few weeks ago I read a letter to technical journal by some academic in a university, condemning just intonation without a hearing. LIterally. This letter could not prove his argument: it could not disprove that of the just-intonation advocates either!

Soon, recordings will become generally available. Then it will be unnecessary to argue silently with typewriter and geometrical diagram and computer printouts.

There are now certain synthesizers and keyboard instruments which offer a tiny piece of just intonation. That is to say, they have the usual keyboards with 12 tones per octave and no more, so 12 pitches are set up which are related to untempered intervals. It is then claimed that this is all you need of just intonation. Then it is compared with the ordinary 12-tone temperament and found wanting because certain of the intervals in the ordinary C-major scale are obviously very much out of tune. If A-flat is tuned to permit playing C minor, then there is no room to put the G-sharp needed by A minor. The F-sharp needed for the ascending A-minor scale will not do for the F-sharp needed to modulate to G major. And the A needed for G major is not the same as the A required to play C-major just chords. You will not get this information from most music textbooks. If one chord is put in tune, it puts the other chord(s) out of tune, and so long as only 12 pitch-classes per octave are all that is furnished, the cause of just intonation is sabotaged by trickery. There is even a semi-official standard found in some textbooks, giving the just C major scale with a very out-of-tune fifth between D a and A in that scale--very much too flat. Now either you could have two different D's to play in C major without modulation, or you simply do not have the ability to play a consonant chord on the second degree of that scale!

Boredom will set in very quickly if you are forbidden to go to even the nearest neighbors of a key. So by stacking the cards this way, or rather leaving cards out of the deck entirely, some persons and firms are thwarting progress and denying composers any room for growth or any escape from merely parroting what has already been "said."

In most cases, this is not deliberate or malicious: the firms offering these incomplete truncated deficient scales don't know any better. Hardly anyone has ever heard any standard important piece of music of reasonable length performed in just intonation. It was financially as well as mechanically and technically impossible to do it in any studio or concert hall. Nobody would have the practice-time and rehearsal-time to do it, given available equipment till now and given present economic conditions. besides that, a considerable number of 'classics" would not be improved by just tuning--there might be insoluble problems or more likely, extreme yet justifiable disagreement over which tuning this or that chord should have. But we can state that the 12-out-of-just tunings now offered for certain new instruments would ruin these classics and induce the audience (if any!) to leave. So all that is going to get heard, and all that can be composed, for such tunings, amounts to acoustic exercises.

Recently a scheme was patented for using computer-style logic circuitry to retune a 12-tone tempered organ to "justify" automatically the chord being sounded at the moment by sensing what type of chord it was, and lowering the too-sharp major third and even lowering the seventh in a seventh chord to the theoretical harmonic-series value. This would work for typical church-organ music pieces, certainly. But it would offer little room for progress to composers today. WIthin its proper field--the smoothing out and calming-down of 19th-century and some earlier church-organ music without the organist having to learn too many new principles--this is still an excellent idea. But there is no way to implement it on a guitar (Ivor is correct when he speaks of acoustic guitars. If, however, a guitar is used as a MIDI controller and connected to a computer which appropriately process the incoming MIDI data stream, guitars can indeed produce just intonation with a virtually unlimited set of pitches -- Editor), and it wouldn't have helped Harry Partch, and it would actually have to be overridden by a contemporary composer who did not want to sound like his distant precursors. It will not work for purely melodic music, and there is an enormous body of music all around the world which need not and should not be harmonized. To put it another way, it would not do for the storm-scene in an Italian opera and it would not take care of a melody from India or the South Seas. It does represent a very ingenious way to get more than 12 pitches out of a 12-tone keyboard and allow many of the conventional church-music modulations.

In my Xenharmonic Bulletin No. 9, published in 1978 but still available, I took up the hornet's-nest icky thorny subject hinted at in the above discussion of different kinds of just intonation: the Ptolemaic or Syntonic Comma whose ratio is 81:80 and which is the difference between a note tuned by four pure beatless fifths upward and that reached by one pure beatless major third upward. Since the Bulletin is still available, I need not repeat my discussion here to any extent. I will merely say that is comma of about one-fifty-fifth octave is still big enough to make or break the consonance of ordinary harmony in just intonation, and if the two pitches a comma part are not available instantly, then any performance without them is going to be disagreeable. On a violin, the finger-movement required to make a comma pitch-difference is almost invisible. Frets a comma apart on a guitar are so close together that there have been very few attempts to provide them. In short, this comma is a nuisance to regular musicians and so you cannot hope to sell them the idea nor to impose it upon them by fiat. Crusading will get you nowhere. Having played in orchestras and ensembles as long as 55 years ago, and having tuned pianos for 48 years, I should know what the real-world conditions are!

Let me save you some time and disappointment, and anguish: do not waste your efforts trying to get just intonation out of a piano! The bass strings are out of tune with themselves! It is mechanically an financially impossible to rebuild a piano to accomodate notes a comma part. Even if it were feasible, the effect would be blurred. In this age of electronics, it simply would be futile and ridiculous to spurn the means now at hand.

The principal outlet for new just-intonation compositions will be to forgo real-time performances and compose into a computer that can play all the exact or extremely-close-to-perfect pitches that you will need. More than you can ever distinguish.

The usual way to eliminate the comma nuisance and the need for extremely slight differences in pitch, will be some kind of temperament, equal or unequal. historically,t he first such to get used was Meantone, so-called because its "whole-tone" or whole-step or major second is the "geometric mean" of the two whole-tones of just intonation, that whose ratio is 9:10 and that whose ratio is 9:8. Thus its ratio is 1:1/2 (square root of 5) Well, that's too esoteric, isn't it?--let's restate it as being the equal half of a pure, just, smooth, untempered major third.

Now for the sad news: too many instruments and recordings and printed music examples and discussions in magazines and books, present only a crippled, sick, damaged, incomplete, truncated, emasculated, distorted, rip-off, defective version of meantone, and promulgate blatant falsehoods and lies such as "meantone can't modulate beyond 7 major keys and three minor keys," when as a matter of fact, meantone is capable of an enormous number of keys you never heard of nor read about. The above limitation to 7 major and 3 minor is only true if you are presented with only 12 of its pitches.

Sure, that's all you can tune on a piano. But why pretend that the piano is the Ultimate Instrument, now that we don't need it anymore? Very well, how many pitches of meantone are necessary? For a considerable amount of older music, 15 or 17 will do. For most existing music that would be plenty. Is there an equal temperament with this meantone principle? Certainly--the 31-tone equal temperament. There are new keyboards for it. Guitars can be fretted to it. The difference between meantone and 31 is very small and of no consequence in any musical performance. Only under special conditions would it matter. That is, unrealistic precision and stability of tuning is required to make this difference audible in playing real music.

The wow and flutter in tape and disk and other methods of sound recording is often greater than the difference between the thirty-first fifth tuned from C in 31-equal or in meantone. So even a laboratory demonstration will be compromised by recording it and copying the recording and playing the copy on the listener's machine.

In asking for more than 12 notes per octave, I am not crusading for some impossible dream. I am basing my stand upon what I already have accomplished in more than 50 years. I am basing my stand upon the accomplishments of everyone in an informal xenharmonic network of people who have existed as such for over 25 years, and this Network has grown and grown and continues to represent a variegated range of opinions and attitudes and instruments both built and modified. I am not asking anybody to build something for me, nor to do experiments in some laboratory, or to go against their training and forsake their connections and squander a fortune bucking the Establishment. I don't have to! These people who have formed a new movement did not need to organize formally. They found one another through new channels of communication which did not exist 40 or 50 years ago. It is just as well that the reactionary backward-looking Establishment of musicians and teachers and textbook-writers did not know that such a network was coming into being, for it is now too late for them to stop it. Indeed they pretend that we do not exist.

Well, why fight them? They have nothing to offer that would induce us to quit, and there is no point in our presenting new scales or extended just intonation in ordinary concert-halls to listeners who only want dead composers and will not listen to anything written since 1900. Frankly, even if it were possible, it would cost too much! The classical and romantic period music and its instruments and orchestras have priced themselves out of the market. We can expand our activities without disturbing theirs. We seek a different audience and most of this audience can play cassettes in t heir own home or even on the run.

They are followers; we are self-starters. Most of us can build our own instruments and are getting into computer music and also new developments in recording. new magazines have sprung up. I write for them. Other kinds of artists are willing to communicate with us and offer the fellowship and understanding that the hidebound traditional music experts may deny us. For instance, many of us have been accepted as members of the Sound Sculpture Movement--musical instruments which also have visual-art appeal.

Up there at the beginning, I said that the exploration of non-12-tone tuning-systems had entered a new phase. Let's get on with specifics. In the 1920's and 30's there was a flurry of quartertone piano activity. It faded away and didn't set the world on fire. It did produce compositions by Julian Carrillo and Alois Haba and Ivan Vyshnegradsky--it is only lately that the important quartertone compositions of Charles Ives at that period received proper performances and recordings that the public could access. Well, if you had had to spend 48 years of your life tuning pianos you wouldn't be enthusiastic about a piano with twice as many strings (2 x 210 = 420) and think what horrible cuss-words a piano-mover would have to say about it! Bad enough; but the timbre of the piano does not do justice to quartertones. It should have been harpsichords. Well, no matter: if I want to play or compose with quartertones today I take one synthesizer and tune it a quartertone sharper or flatter than the other one--no sir! I don't have to tune any individual notes! Just turn the know or flip the tone-bender lever on one of the synthesizers--both have 12-tone-tempered built into them at the factory. INSTANT quartertones. No muss no fuss no bother no hassle. Why, some music stores might let you put one synthesizer or electronic imitation-piano or other keyboard a quartertone off from another--or somebody will have done it already. Oh, sure--at some places they might toss you out on your Whatever, but ordinarily this sort of instant quartertone happens almost without planning or thinking.

You don't even have to wait to re-fret a guitar: put two E strings and two B strings and two G strings on it and tune each such pair a quartertone apart and experiment. Better, of course, to re-fret, but this experiment won't hurt the guitar and won't cast anything but time.

So here is one way beyond 12 notes per octave: merely double them. I have added quartertone frets to quite a number of guitars. When taking up the cello back in the 1930s I practiced quartertones on it and drove my teacher flaming bananas. The electronic keyboard oboe built in 1936 has always had a quartertone key on it--now a row of microtonal pushbuttons. (Actually, since 1938.)

Whether quartertones are for you depends on your attitude: quartertones are great for melody, but do not expand harmonic resources as much as you might think. Partly, they still keep the original twelve, and therefore do not really escape 12. No improvement whatsoever in thirds or sixths, either major or minor: those intervals so essential to ordinary harmony. The quartertone version of the 7th harmonic is still pretty far off. It can be used better than the 12-tone minor seventh, but is nothing to brag about. The quartertone version of the 11th harmonic is just about perfect. Errors in tuning might exceed its deviation from the truth. Note that quartertones do not make any distinction between such notes as A-sharp and B-flat, or B-double-flat and A, or C-sharp and D-flat...the two-names-for-one-and-the-same-pitch situation of ordinary twelve-tone temperament remains. There are dozens of ways of writing quartertones: I use Mildred Couper's variant of the Vyshnegradski system.

Good place right here to state that it's harmony VERSUS melody! Some tuning-systems are very good for harmony and not so hot for melody. Other tunings are excellent for melody and poor or bad or even impossible for harmony--for instance, 13-tone. Twelve-tone-equal-temperament tuning is biassed toward melody and not very good for harmony and moreover, its harmonic resources have now been mined to exhaustion by tens of thousands of composers for over three centuries. It's a matter of Wounded Pride--because we were not born in 1770 or 1813, almost everything worthwhile in 12-tone has already been said, leaving us with pitiful crumbs from the tables of the Masters. Atonality? We'll get to that in a moment--better non-twelve than within twelve. Serialism--well, it looks neat on paper, but how many people want to listen to Serialism in 12-tone temperament? 'Fess up now: how many serialist melodies get hummed and whistled? Have you made any friends or gained admirers because of your Serialist 12-tone pieces? It's Music in Cold Blood, that's why. You have to avoid anything that might suggest the cliche's of tonality. Try singing serialist tone-rows. I dare you.

I don't condemn atonality--but there is Free Atonality, and there are quite a number of non-harmonic scales such as the above-mentioned 13-tone-equal, jim-dandy for atonal compositions. 13 can be tamed by using a bland mellow timbre for its instruments or on a synthesizer.

There are other scales like 5, 10, 15, or 7 and 14 with strange harmonic biasses and tendencies. That is, melodies or themes that run through your head will tend to go in a direction absolutely unthinkable for orthodox twelve. All of us are in a rut--a timbre-rut due to 200 years of piano timbre, a pitch-rut due to 12-equal, melodic ruts due to the symmetry of 12-equal: the number 12 is divisible for 2, 3, 4 and 6, which causes symmetrical patterns that repeat--and in addition, patterns which do not use up all 12 tones. The diminished seventh chord, or the 1/4 octave pattern, has been just about exhausted. The whole-tone scale, or 6-tone temperament, has also been "run into the ground"--can you say something in it that Debussy never thought of? Level with me now!

How about practical implementation of new tunings: some synthesizers can be reprogrammed. Most computers can be hooked up to sound-generators and a few even have built-in music and sound facilities. There is no limit to the number of possible programs that can be written to get music out of computers. In theory, some of these synthesizer pitch-making facilities and computer programs and hardware facilities for pitch-generation are not exactly settable to exact pitches of either just intonation or the temperaments we are discussing here; but the pitches are usually so close together that no error is big enough to spoil a musical performance. After all, few pianos are in exact tune and after a couple of months, all pianos go out more or less. So the ordinary 12-tone equal temperament is an ideal rather than a perfect reality every time. We don't refuse to look at the TV screen because we know the picture is made up of lines instead of being perfectly fine microscopic detail. Perfectionists never get any fun out of life. Their only pleasure is a twisted Power Trip--making other people dissatisfied and therefore unhappy when they had been contented enough before.

Guitars can be refretted so that they are in other equal or unequal temperaments: a small number of just pitches or a portion of the Harmonic Series can also be fretted. The practical limit is about 31 frets per octave, although 41 has been done. Fretless fingerboards are quite feasible; so are movable frets of various kinds. With the popularity of electric guitars and basses, many people will find this the easiest way to investigate non-12-tone scales.

Many new keyboards have been invented, and some of them actually put onto instruments. However, it is not necessary to wait for them. Ordinary keyboards such as come on electronic organs, synthesizers, and some other instruments, can often be "mapped-onto" or reassigned to another other scale, equal or unequal. Or two keyboards can be used at once to provide up to 24 pitches per octave. I have been doing this since 1962. Why wait for perfection? Are you a doer or just a dreamer? WIth the intensive activity in the computer field, all kinds of new keyboards not originally intended for music can be easily adapted for music, so we may expect many developments soon. If you are willing to forgo real time, then you can type our codes for notes and computer software will play them for you.

Switches and pushbuttons and various kinds of touch-plates are now readily obtainable devices and they come in a bewildering variety of sizes and colors, so there is no limit anymore to possible keyboards that can be assembled from standard parts. most of the timeworn objections to leaving 12-equal are pseudo-problems with no real basis.

Most of the criticisms are based on limitations which no longer exist, or opinions by persons who have never heard any non-12-tone music whatever.

The difficulties are psychological now rather than physical or financial. Refretting a guitar is trivial cost-wise. Once the new fret positions were calculated by me and others, it's just a matter of sawing kerfs in new locations. Frequency tables have been calculated, and some of the work can be done on a pocket calculator. Piano-tuning is a skill that takes months to learn, but now tuning can be built right into the new instruments--no need to use one's ears at all. Tunings devices accurate to cent (1/1200 octave or 1/100 ordinary semitone) are widely available now. So are frequency counters that go way above audibility with fantastic accuracy.

One of the most important advances in composition now is that we don't notation for everything: we can record improvisations and our trials and corrections as we make them and preserve them indefinitely--no need to stop to write things out and lose inspiration or notate inaccurately--and especially as we said, no need to learn new notations for new scales. The tape machine does not care what tuning is recorded into it; it will play it bach faithfully anyway! Composers can get feedback from other persons by giving out or mailing out tapes. Thus we know right away which compositions or themes are acceptable and which are questionable; we don't have to imagine what some hypothetical Posterity might think or humiliate ourselves by slavishly imitating mannerisms of Brahmoven or Mendelburt or Ravellusi or Turnitoffsky! Let the computer wizards do that! Composers should use their valuable time working with sounds, not squirting ink on paper and hoping in vain that it might be performed after their demise.

Really good news is that expanding the tonal world by having many new scales and systems to compose and perform in, increases the composer's pride and self-respect by making it less likely that the new work was already created or substantially anticipated by some composer of the past.

Even better news is that many of the new scales have MOODS. Play a theme in 12-tone and it will be more aggressive and have more zonk than it would in 31. Choose 31-tone for more soothing, calm and peaceful compositions. Use 17 to rouse your listeners--to give hard edge and sparkling brilliance. Try 16 for a weird mood. 12 and 24 are restless. 18 is rather vague. The mood of just intonation depends on how far it is carried out--are ratios of 7 present or not? (For example.) Some scales have not been used enough yet to predict their moods. 22 has a valuable mood that contrasts with the others. That's why we need you in on this. Cut-throat competition and professional jealousy among composers will be greatly reduced by providing everyone with so many new choices. No need to be paranoid about copyright protection and fearing that others are going to steal your thunder.

But insist, demand, that you have all the notes of the new scale at least up to 31--and a small subset of tones from these scales is not enough. Don't let the killjoys and spoil-sports hold you back. Don't let them fence you in!