IT IS TIME TO RELEASE COMPOSERS FROM HIDDEN CONSTRAINTS
by
Ivor Darreg July, 1982
The last century has witnessed spectacular progress in every field--except music. This is continually brought out by articles like the recent newsmagazine item about Computers in the Arts where the emphasis is on visual art and as an afterthought a TV-type screen is shown aiding a composer in reducing ideas to notation. But notation is for eyes, not ears at all. It is SILENT.
Having been a composer for some 52 years, I should have some right to discuss this situation! No one can expect more patience from me or any other still-living composer than that. Scores and parts written as long ago as 40 or 45 years previously mock me in silent slumber in my filing drawers and boxes--indeed some conductors and others who promised performances never returned some of the MSS. at all and they are lost, since that was before the days of Xerox.
Paradoxically and ironically, that instrument or tool which helped and fostered and further and supported and encouraged and indeed enabled progress in music around the 1800-1840 era and inspired the production of a tremendous musical literature, is now a drag upon progress, a restraint, a brake, a roadblock--of course I mean the piano.
As recently as 1960 it would have been futile to write such an article as this, but light at the end of the tunnel is finally in sight. Economic pressures are finally pricing the piano and other obsolescent instruments out of the market: the piano is not only too costly for the average person to buy at the present time, but is also too expensive to maintain in working order, to tune,a dn even to move when one has to change residence. But its Image remains--alive and well and engraved on the public mind very deeply. The real piano deteriorates into a hopeless mushy fuzzy jangling wreck while the Image remains bright and clear and the Musical Establishment demands that all composers write all their pieces at the piano keyboard, no matter what instrument they might be intended for. If you are so foolish as to waste your time and wear your eyes out writing a score for orchestra or chamber ensemble and submit it to a conductor or whoever is in charge of a musical group and what they are permitted to perform, it is just about absolutely certain that that score will be tried out by a pianist on a piano, regardless of what instruments it is written for, and chances are excellent that the piano will be out of tine and have something wrong with its wooden machinery.
Now maybe composers had to put with this alleged necessity in 1920, but now--in the Electronic Age--the time when nearly everybody has a a tape recorder? When cassette players can be worn rather than carried? All item submitted for publication in newspapers, books magazines, etc., are typewritten nowadays, but the composer is expected to write every not by hand the old-fashioned HARD way. Notation takes up a lot of space and standard size for sheet music is incompatible with today's copying machines and is very expensive to mail at today's high postal rates. Recently I borrowed a book about popular music figures of the 70s and was appalled to find that many of them couldn't even read music, yet were very successful and seemingly quite well off financially. Some of them even boasted of their inability to write and read staff-notation! Well, in a way they have a point: among conventional musicians, notation wields too much power--it constrains and limits, and often misdirects almost every composer since some things are easy to write or obvious patterns from the notation, while other equally good patterns are difficult or next to impossible to write.
Unfortunately, most notation reform schemes introduce new constraints as they remove certain problems inherent in the conventional notation. It is something like, the hump in a carpet or rug that can be pushed down where you are standing in the room, only to reappear somewhere else in the room just as obnoxious as the one you just got rid of! Just this last year I have had the opportunity to examine a wide range of new notations as well as to read through some books on notation and various authors' proposals for new rules for writing music, or pleas for standardization.
Besides the various proposed new notations, there are several alternative notations in actual use, such as the chord symbols for guitar, both the graph-like fret-diagrams and the letter-and-numeral abbreviations. Then there has been a revival of tablature--a kind of diagram which in the case of fretted instruments has a staff -line for each strings and places numbers on or sometimes between those lines to denote the fret at which that string is to be played. There have been tablatures for keyboard instruments and wind instruments also. During the last century, Tonic Sol Fa was popular in England for signers, especially in choir or chorus.
In all these cases, the constraints and limitations of ordinary staff notation were reduced (otherwise there would have been little reason for inventing or using them in the first place) but new constraints inevitably resulted.
Latest notation reform of course is the use of letters or numbers for computer peripheral input--and ordinary these computer codes for music are compatible with standard typewriter keyboards. Probably this is the principal notation, or group of notations, for the future. When one realizes that many of these codings can cause the performance of the composition by the computer or upon a computer-controlled synthesizer, the convenience is obvious.
Graphics attachments to computers have been made to produce conventional staff-notation, more or less faithfully of course; but this is expensive both in hardware and software to implement, and it consumes immense quantities of paper, and often of computer time and facilities. A great deal of effort has been expended upon coding conventional staff-notation for computer by translating it into typewritable or printout-compatible alphanumeric codes. For instance, this has been done for purposes of information retrieval: such stored codes can be addressed by standard search techniques. Much boasting about how up-to-date all this makes musical composition, arranging, and reference for scholarly purposes, has taken place; but the fact that the recording of conventional notation merely piles the restraint of the new codes upon the limitations of the conventional notation, is ignored or glossed over. To be really effective, computer coding must be designed from scratch. I don't suppose anybody will heed me, but let the record say that I tried!
There can't be perfect bug-less computer-music coding any more than there can be an absolutely faithful staff notation, so don't expect impossible perfection. That isn't the point, since there can and will be a number of alternative computer codings and typewriter systems co-existing and indeed there should be, so that they will offer choices as well as escapes from one another's problems and restrictions.
In the Real World Out There, we cannot arbitrarily separate the notation constraints from the limitations of the instruments used and the limitations due to the almost universal imposition upon us of 12-tone equal temperament tuning--in principle if not always in practice.
I brought up the Piano in this discussion because it embodies both its mechanico-acoustic limitations as a musical instrument and the shortcomings of the twelve-tone equal temperament to which it is supposed to be keep tuned. Considering, on top of that, that all composers are always supposed to write and try out and correct and revise all their compositions at a piano, the piano's influence and constraint has ruled far beyond specifically piano literature--it has limited and warped writing for violin, cello, wind instruments, the human voice, organ, and just about every means of musical expression over most of the globe for more than a hundred years.
Piano tones die away--they never build up. The higher the pitch, the faster the tone dies away, till at the very top of the standard keyboard the nose from the hammer is louder than the tinkly little tone. This conditions composers not to write sustained high notes for the instrument. Thus a most valuable resources of voice or violin or organ or flute is wasted and ignored and neglected. The student composer is commanded to imagine orchestral sounds while seated at the piano.. Almost like a punishment or some kind of religious mortification.
It is easy to write a chord in the middle of the piano's compass but very difficult to read, as well as to write, the same chord at the top of the keyboard. Staves on ordinary music paper often do not leave much room for the ledger lines. At the bottom of the keyboard, many ledger lines are required, so the same problem ensues.
While the 8va----- sign as shown above is supposed to obviate this problem, you can see there still are too many ledger lines for the notes at the top of the piano keyboard even with it, and nobody seems to know that there is a 15ma----- sign for two octaves higher or lower than written.
It has been my bitter experience all these years that when I use the 8va sign, nobody seems to heed where it ends even when I write loco to cancel it. With electronic instruments one can go beyond the top of the piano keyboard about another octave before pitch disappears and one just has a mere sound. Also one can go about an octave below the bottom, with pitch getting more and more indistinct, but the very low tones still being of some use.
C-clefs have gone out of use for keyboard instruments and the treble clef an octave lower is still not permitted in piano music, so ledger lines below the treble staff and above the bass staff are multiplied beyond all reason and all endurance. I am very very worried lest this situation be carried over into sheet music for the new synthesizers. I'll be real mad if it does!
The tenor voice, the guitar, and some other instruments are written in treble clef to be performed an octave lower than written, but this is never indicated even though convenience means exist for doing so. One is always in doubt about percussion instruments like glockenspiel and chimes and xylophone and vibraphone etc. as to what octave they really sound in.
Flute and violin music ordinarily does not use the 8va------------- system, so ledger lines abound and the space between staves get awfully crowded.
All these notation vagaries have some influence upon composer and arrangers, aggravating the shortcomings of conventional instruments. I will spare the readers here the tortures of transposing instruments, since I have already sounded off and shrieked in dismay at that horrid custom enough times elsewhere.
Suffice it to say that in a score for band, most of the parts are enciphered--one or more octaves away from the notated pitch and then in some different key. A few composers dare to write scores in C. That is commoner in Europe than in the USA.
I am not going to say much here about "avant-garde" notation such as aleatory and indeterminate and those notations which actually become abstract visual art. That can be discussed elsewhere and later on. Graphs so have certain uses when the music has certain characteristics.
This is not a plea for "anything and everything goes" either. I am trying to make you aware of constraints and limitations which all of us have been taught to ignore, or carefully steered away from asking questions about, or from wondering if there are any restrictions and what those are.
It is a combined effect--the notation plus the mechanism of the piano and some other common instruments, and the way pianos and organs are tuned--the synergistic impact upon composers of all those factors taken together, that I am asking you to heed, and then to do something about.
Such as doing all one's composing on an instrument that cannot sustain high pitches. And such as being at the mercy of piano manufacturers with their frozen rigid 19th-century designs and at the mercy of tuners and repair-persons. Such as being at the mercy of a non-musical electronic engineer in a synthesizer or electronic-organ factory who builds 12-tone equal temperament into an IC chip.
Th piano aided the progress of music around 1830 or 1850. But it stymies it now, since the mechanism of the piano is not amenable to new non-12-tone tunings. I have discussed this elsewhere and will again, so you can refer to other publications for more information.
In 1900 or even 1920, this did not matter too much--there were still fields like complex rhythm, atonality, and serialism to explore. Now even those techniques have been run into the ground. With the computer music and computer aids to composers and arrangers, 12-tone equal temperament will be exhausted far sooner than anyone could have predicted in say 1940. Besides increasing the number of compositions by each composer, it will flood the market with thousands of compositions by computers programmed to compose. No one can hope to compete with so much imitation Mozart and imitation Beethoven and robotized Schoenberg or computer-simulated whomever! If it never makes the concert hall it WILL make TV commercials and Muzak.
I used to say that somewhere in a back room in this or that recording company there was a team of an engineer and a musica hack writer, analyzing Beethoven's Seventh and Fifth Symphonies, feeding them into a computer, and trying to ad them together to get the Twelfth. Of course at the time I was dreaming about this, the techniques weren't good enough to produce top-quality results, but now, some 25 years later, it might be up to salable standards, whether performed by some conventional orchestra, or simulated by computer-controlled synthesizers. I am quite sure they are not holding back for any ethical considerations; they have non! But they might hold back simply because there wouldn't be enough commercial market for that sort of stuff. I have to remain cynical because of certain other phenomena in the so-called classical music field.
A popular music group of course uses effects boxes and all the newer apparatus available in recording studios, but this does not solve the problem of the conventional 12-tone tuning-system approaching exhaustion. It does help to delay the end. Pitch-bending is a subconscious groping for sounds outside the 12-tone scale. It isn't called that by performers or teachers of classical music, but it is substantially the same thing. In conventional music and popular music alike, pitches are altered for expressive purposes, and like the musica ficta of earlier times, standard notation ignores it and the Establishment pretends it never happens. Thus it becomes a sort of clandestine understanding between teacher and pupil, or among a rock group or other ensembles.
The r3cognition of the real potential of non-12-tone-tempered pitches, and the introduction of new instruments or new modifications (e.g., refretting of guitars) of existing instruments, will take us from the haphazard and unofficial non-system of bending pitches, to a new state of system and order. In fact we can have quite a number of tuning-systems, each with its unique mood, unheard before. The situation up to now has been that the performer bends pitches which have been written down as "normal" 12-tone tempered pitches, thus technically violating the official meanings of the written notes. The composer has been forbidden for a very long time to write any signs or symbols calling for unorthodox pitches. He might of course tell the performers to bend here and there if he is on the scene. But this would still be "illegal." There is a shameful amount of fear and intimidation here.
Ironically enough, Russolo and Marinetti, the Futurists of 70 years ago, realized the existence of non-12-tone or enharmonic pitches in the sounds of the machines which were coming into use, and the need to notate them, along with their Art of Noise. It's sure been a long wait indeed!
Up to the 60s, the avant-gardists have shrunk from the use of non-12 systems and instead gone in for noises and strident sounds. They continued to worship the piano and to use it and write for it, while insulting it and often wrecking or damaging during their performances. No, I dare not call that Quiet Desperation. It was strictly forbidden ever to ask "WHY 12?"
Composers are ordered to take the status quo for granted, and not to question it in any way. Everything has changed between 1790 and 1982 but composers are supposed to operate under all the restrictions which were inevitable in 1790 or 1840 or 1870 and to use only the symbols and signs of a bygone period and only the instruments available in that period, and to spurn everything being invented today or even what was invented since 1900. We live and/or work in the experimental architecture of the early 20th century, and no longer commute on horseback but the composer is supposed to behave like an ascetic reclusive religious masochist and act as though all the limitations and hardships of the 18th or 19th century were still in force. Those who demand such self-abasement of composers are not composers themselves, nay, they put performers and conductors and concert managers above composers and try to keep today's composers from ever being heard. It is rather like blackmail: if you give in to their demands, they still reject you and demand more and more till it is impossible to go on--and that is exactly what they want--that only the composers of a limited period of the past, roughly 1790-1890, shall be heard.
Conventional instruments were not designed for one another--the winds fight the strings and piano is not comfortable (in its 1850 and after forms) with either. A piano concerto with orchestra is a duel or battle. The composers are expected never to question this sad estate of affair, and are afforded no way to fight back or to have any voice in the design or development of instruments. Instruments are designed and manufactured and sold for performers, insomuch as they are not designed or sold for interior decorators or furniture dealers. How else explain the degrading of piano tone and retrogression built into the so-called spinet or vertical or console midget pianos? Nobody had the sense to retrace the piano's evolution to the more delicate instrument of Mozart's day, for instance.
The composer is thus at the mercy of a number of persons and groups working at cross-purposes, none of whom has any real respect for any composer. Manufacturers, their hired engineers, technicians, sales organizations, the home furniture industry, concert managers, performers, music teachers, music textbook writers, orchestra conductors, church organists, the audio hi-fi industry, piano tuners, music publishers, popular music promoters, the recording industry, the broadcasting industry, TV executives, the list is endless, and most of these parties have only contempt for composers living here and now. It is thus not remarkable that the composer's quandary is bad; it is a miracle it isn't even worse!
I don't know what you are going to do about it ,but I can tell you what I already have done. I have gone to tape recorders and overdubbing and also to the designing of new instruments and making modifications in existing instruments. I will go on to computer music if I am ever able to do so, and to synthesizers and electronic organs and various combinations of these ideas, so that a composer will have the same privileges and status as the painter or sculptor already has. Strangely enough, many of my instruments have already been exhibited as visual art in art galleries! Today's art world welcomes these instruments for their appearance and their compatibility with other contemporary art-objects, while the musical world continues to spurn new instruments and the new melodic and harmonic possibilities afforded any user of these instruments.
You and I are never going to get any medal or rewards or prizes or respect for denying and torturing ourselves. Why, then, waste time and money and energy and other people's time etc. in conforming to needless constraints and restrictions? The test has already been made, I understand, some time ago: scores or piano versions of famous composers' works have been copied into MS. form and submitted to publishers or to conductors or recital artists, and always rejected--and the embarrassment of the expose has invariably been suppressed. The converse of this test has been conducted a number of times also: the best-known instance, where Fritz Kreisler attributed a group of his own compositions to Italian composers and "got away with it" for years. Somebody ought to blush but they won't.
That is, even if you conform to these demands from without, you are only humiliated and punished all the more! The disrespect and lack of consideration or compassion or empathy is what hurts most. The way in which non-composers can order composers not to do this and not to do that, culminating in not doing anything at all. The meekness and abject submission of composers to all this abuse and disrespect. Nobody dares tell a painter not to use this or that color. There is no law ordering sculptors to use only marble under the chisel. But the obsolete pianos and the incompatible hodgepodge of 18th- and 19th-century orchestral instruments is imposed upon composers, together with obsolete nonsensical notational practices and prohibition of writing certain things to be heard. Adding insult to injury, the composer is told not to expect to have anything performed--it is supposed to be reward enough if the composition teacher in some University reads the score in dead silence without making any musical tones at all. Music is thus converted into a visual art and the means has become the only end.
Most libraries have books on notation showing that indeed musical notation and abstract drawing have merged so that you cannot tell whether certain drawings are performance scores or merely silent visual artifacts. Meanwhile the tape recorder has developed and flourished and its "notation" is the invisible magnetic encoding of musical sounds. This gives the composer freedom at last from the demands and obstacles of interpreters and those who manage and control such interpreters and the concert-hall.
Naturally enough this new freedom is resented by the promoters of disk records. The public apparently is fighting back, since they seem to prefer videocassette machines that can record to the Videodisc which cannot be recorded upon by the private individual at home. The pendulum is swinging back: in the 16th and 17th centuries music was made at home; in the late 19th and early 20th centuries music making and instrument-making were confined to factories and the homebody was supposed to be totally passive, only listening, never performing, and never at all even dreaming of composing. The Do-it-Yourself Movement is growing and it is now including music and instruments and recording. Not surprising, then, that the obsession with 19th-century music is beginning to decline, and interest in pre-Bach music is growing--interest in that period when music was made at home instead of being exclusively confined to professionals in the concert hall. If we have freedom of speech and freedom of the press, and some people are enjoying these rights in new ways--for instance this article is taken to a copying store to be reproduced a few copies at a time instead of putting oneself at the mercy of a big publishing house or an expensive printshop using letterpress--then why not the same freedom of composition and musical expression, and indeed the cassette machine and cassette copying affords also.
In 1820 or other 1800s there were not so many people on earth as there are today, and so not so much composing and the piano was comparatively new, and its resources still largely unexplored. So there was plenty of room for any composer living then, to produce new music without slavishly repeating his predecessors. Today we have many times the number of people in the world, and worry ourselves sick over overpopulation and energy shortages. By now, many times more composers have produced practically every possible distinctly-different piano composition within the 12-tone equal temperament tuning. There is nowhere else to go within that system; thus today's avant-garde investigates nose and bizarre hardly-musical or frankly nonmusical phenomena; and even that is quickly reduced to cliche. No wonder the antics of performers, the effect-boxes of the rock groups, the light-shows and other visual effects in concert-halls, and various advertising and publicity gimmicks take precedence over the music and also over that Forgotten Person, the Composer.
The piano had to run its course and now it is going downhill--the turning-point can be put somewhere around the Great Depression of 1929 and concomitant phenomena of the time--the virtual extinction of the player-piano (there has been a nostalgic revival lately, though) along with rapid growth of the radio and then the electrification of the phonograph. Instead of rescuing the piano, the introduction of the previously mentioned "spinet" things aggravated the situation. The encouragement of merely passive home listening for several decades worsened matters by providing a whole generation of musical illiterates--it has now gotten to the point where some highly successful performers cannot read music and even boast of it.
But the new electronic scene provides an escape from this difficulty to some extent--it is now possible to improvise into a tape recorder and then to edit the tape or reprocess it, so that being able to notate one's performances is not so absolutely necessary, even for serious music, as it once had been. This gets the performers and conductors and music publishers off the composer's back or out of the composer's hair, however you wish to put it.
No, we do not mean that the performers all have ill-will toward composers. Rather, just like the composers, they are the innocent unwitting victims of programming. Hitherto, we did not enjoy the battery of computerese "buzzwords" to help in discussing matters like this--the best we had before would be phrases like "psychological conditioning." Now we have the more powerful concept of "software" as opposed to "hardware"--the computer will not work without a program--it cannot digest the data without one anymore than the termite can digest wood without microorganisms. The human being cannot get music out of a violin without undergoing training--and thanks to computers we now can reword the above into "the person cannot play a violin agreeably and acceptably without having been programmed to do so." There is nothing evil about programming per se. But in this particular case, of people being programmed to perform and interpret music on certain instruments, the programs with which the teacher indoctrinates them are too much like unscientific narrowminded religious rituals. They are too obsessively focussed upon the middle of the nineteenth century. They lead the performer away from many of the possibilities available upon the instrument beign taught. The violin and cello even the human larynx are fitted out with imaginary frets for the 12-tone equal temperament when such is not part of the physical structure of these non-piano instruments. Because they are hidden constraints, once programmed into the individual, they are almost impossible to override. It becomes impossible for the person to think outside the limits of the programmed-in territory. To become aware of this, try to pronounce a sound of a foreign language you have not learnt. You have the same potential in your vocal organs of producing it, but you have been programmed for so many years to English sounds that you cannot fight against this indoctrination, therefore you lack the commands to fight against this indoctrination, therefore you lack the commands to produce that sound. Moreover, you have been similarly programmed to English phonemes, so that you cannot hear the foreign sound other than as a variant of an English sound--you mis-hear it and utter an ENglish sound in its place, usually and cannot hear the difference between the familiar sound you actually produce and the one you should have produced in order to be able to learn to speak the foreign language.
Similarly those of us who have been trained to 12-tone tempered pitch-classes mis-hear quartertones or other non-twelve pitches and call them out-of-tune or defective performances.
Yet this musical case is more hopeful since we were not indoctrinated in 12-tones-per-octave for quite so long, and in today's environment of all manner of noises and non-musical as well as musical sounds, we hear many sliding pitches and definite pitches which are not members of 12-tone equal temperament. Practice deviates from theory; all instruments are not tuned dead-on. This has saved the situation, frankly. Only in the last few years has the average listener been exposed to accurate precision 12-tone based on A = 400 Hz to any extent.
By making people conscious of this programming component of music instruction, we can help them overcome the indoctrination to a considerable extent, and thus be ready to accept music in non-12-tone scales and even to perform and compose in such scales.
As the piano gradually relinquishes its lofty pedestal occupied from about 1800 to 1960, and as more kinds of new instruments, many of which are electronic and thus not constrained to 12-tone tuning mechanically, come into use, it will be easier and easier for composers to avail themselves of non-12-tone scales. For instance, as re-fretting becomes affordable, guitarists can take up new scales with ease. IT is nothing like having to accustom oneself to a new keyboard layout. There is no need for a special tuning device, since the open strings are tuned close to the familiar pitches in most cases. The fretting takes care of the other tuning-problems for the life of the instrument, so there is no problem of retraining piano and organ tuners. Electronic organs and synthesizers can be made such that they can be retuned to other scales automatically. One such scheme has used counting circuits like those n computers, to derive very accurate stable pitches from which can be selected the pitches needed for any of a large number of possible tuning-systems.
By producing tapes for training listeners to recognize new intervals, the new scales can be put to work soon. For much existing music is playable in non-12-tone systems and in some cases existing musica can be improved by so performing it. There is thus no abrupt break from present practice; continuous progress, rather than having to scrap the old entirely, is practicable. No need to abandon all the treasury of printed music, but merely to add to it and to be able to escape outworn restrictions.
It is time now to examine the restrictions of the 12-tone scale as currently used. Why leave it now? How is the present time different from a century ago? Why do I say HIDDEN CONSTRAINTS? The standard staff-notation and the names for its notes were not designed for the 1q2w-tone equal temperament, but for a scale usually known as Pythagorean--a tuning-system with infinitely many pitches obtained by an endless series of perfectly-tuned fifths (ratio 2:3). Pythagorean B-sharp is not identical with C, nor is G-sharp identical with A-flat--instead of a circle of 12 fifths, there is an endless line stretching forever in both directions, to more sharps than you can imagine and more flats than you can imagine.
If you are uncomfortable with this infinite line, imagine instead a spiral staircase from which you can look down upon a large clock-face with the familiar twelve numbers--you come back with each revolution new where you started, but a trifle above it. For keyboard and fretted instruments, it is generally cheaper and more practical to use distorted intervals than perfect ones, and the cheapest system that will produce a variety of worthwhile music happens to be that which slightly contracts these fifths till 12 of them exactly match 7 octaves. Certain exotic cultures have chosen circles of 5 or 7 fifths for even greater economy of means, but the distortion is quite noticeable and these scales are not very harmonious.This notation and name-system fit certain other scales also: the 12-tone equal in general use, but not so efficiently since now we have many names for one pitch, such as D-double-flat, C, B-sharp, and A-triple-sharp and so on. It fits the 17-tone equal temperament and the 19- and 31-tone systems also. It does not fit quartertones since there then have to be more names and new accidental signs to put on the staff, for now here are two circles of 12 fifths each of which do not intersect. IT can be adapted to many of the possible or desirable tuning-systems we could take up, in some cases easily, and in other cases with problems.
Twelve-tone temperament is an expedient like Daylight Savings Time or those reformed calendars where a Blank Day was to be inserted between the last day of December and the firs tone of January so that all years would begin on Sunday. Or the Interest Year of 360 days used before we had computers to figure out bank loans, etc. It was not brought down by angels from Heaven, that's sure.
Normal musical tones contain the Harmonic Series, some members of which are noticeably different from the standard 12 pitches, so that we are always being exposed to intervals no tin the 12-tone equal temperament. Faintly and subconsciously, but there nevertheless. This lack of certain harmonics in the 12-tone-equally-tempered scale produces a restlessness, a harshness due to the beats between the harmonic pitches and the tempered pitches. Usually this is a semiconscious roughness which prevents 12-tone harmonies (if correctly temepred, of course) from ever coming truly to rest. As a result, the mood of the 12-tone equal temperament is a brilliant restlessness. It is possible to mitigate this by various means, and for composers the most important of these means to know about are (1) tones which die away rather than sustaining--piano, guitar, banjo, harpsichord; (2) heavy vibrato; (3) slightly out-of-tune added sounds to give a pitch-fringe; (4) abnormal qualities of tone not having normal harmonic structures--xylophone, bells, marimba, chimes. From the 1930s to the 1960s, the Hammond gear-wheel organ and some other electronic instruments used additive synthesis with tempered imitation-harmonics to smooth out 12-equal.
So: if we wish to use intervals or harmonies derived from the Harmonic Series, we can go to either extended just intonation or to certain equal and unequal temperaments which have approximations to certain harmonics better than those of 12. It ordinarily amounts to what engineers call a trade-off: you give up this to get that, and in musical terms you change the overall mood and you bias the array of tones toward harmony or toward melody. If you want to have your cake and eat it too, then you must use a large number of tones per octave, as in just intonation carried out far enough to allow for melody and new harmonies and also modulations.
Systems with fewer tones will usually sacrifice one interval for the sake of another, as 12 sacrifices the thirds and sixths, bot major and minor, for the sake of the fifths and fourths. The poin there is that you now have choices you never had before, since it is easier to implement new tunings, and you are not longer tied down to the mechanical and financial restrictions of the piano which prevent redesigning it to handle non-12. You don't have to shoot your entire wad on just one non-twelve system, which means you can have several of them and a wider range of moods and compromises between harmony and melody and freedom of modulation than you ever could have had before. That is, some of the Hidden COnstraints are going or completely gone.
Hitherto, you might have lamented the flat fifths of 19=tone as compared with the practically perfect fifths of 12-tone; now you need not agonize over a momentous choice. Before electronic instruments and other contemporary methods, you might have had to commit yourself to just one non-12 system because of the money and time and trouble each new system would have cost you. Now you can afford a range of systems since tuning is easier and with specially-fretted instruments, tuning is set permanently. There have been experiments with interchangeable fingerboards on guitars, and no doubt there will be electronic organs with interchangeable programs for each tuning--slip in a punch-card or select ROMs with a switch. Computers can go from one system to another with stored programs.
So one of the greatest Hidden Constraints has been the fact that instruments were expensive and an instrument had to be dedicated to just one tuning-system. It will injure a piano to keep retuning it from one system to another; it cannot be tuned to certain systems because of its mechanical construction. A reed-organ can only be retuned so many times. A pipe organ *** well, you get the idea! Until electronics and easy calculations for such things as refretting, the very imagining of of changing the tuning brought up automatic objections of it costs too much, why it's impossible.
That is, the freezing of designs and freezing of tunings in hardware has stymied musical progress for a long time. Now tuning become software, not altering the mechanical construction of the instrument, and we have a whole new ballgame. Another kind of software has existed for a long time--we would not call it the fact that most musicians are programmed to 12-tone; we might have said in the past that they were trained or brought up on it or indoctrinated with it. This is a serious hidden constraint when you must as a composer work only through performers; but with tape recorders and other means for composers to reach listeners without imposing upon performers or going against their training, this no longer should stop you from working in non-12.
But the indoctrination of musicians in 12-tone is not airtight and not all that neat and perfect; strings players are taught to deviate--in particular, to sharpen leading-tones such as the seventh degree of the scale or chromatic passing-notes tending upward. Wind-players humor the tone, and brass players are somewhat influenced by the harmonic series of the tubing in various kinds of horns. A chorus will try to hit just chords if not led astray by the ubiquitous piano accompaniment. By making all these deviations conscious, we can lay the groundwork for introducing people to non-12-tone scales which systematize the new pitches for their own sake, rather than maintaining a sort of haphazard deviation from the alleged norm.
It cannot be mere coincidence that interest in non-12-equal should grow just after various advanced technologies have given us accurate 12-tone-equal tuning in more cases than ever before in history. The tolerance of mistunings of 12 is what has kept it bearable--until just lately. Piano-tuners still tune by ear and stretch octaves and their actual result is seldom perfect-- simply compare the pianos about you with the new electronic tuning-devices. Manufacturers hedge their bets; they build synthesizers with 12-tone embedded in the circuitry, then provide some kind of "pitch-bend" lever to get around it. Electronic organs almost since the beginning of such, have incorporated wide vibrato way beyond what would be considered legitimate from a pipe organ.
Let us now turn to the patterning of the 12-tone equal temperament. WHat constraints does its structure impose upon those who use it? As just mentioned, violinists and cellists are taught to sharpen leading-tones to get a more brilliant effect in melody and in chromatic passages. But the pianist is helpless--the tuner set the temperament on that piano some time ago, and the organist is also at the mercy of the tuner, or on today's electronic, a complete slave to whatever tuning-device was designed into the organ's innards at the factory.
Never mind--the composer is not allowed to tell the violinist through the notation to sharpen or NOT to sharpen this or that note--establishment Etiquette commands the composer to leave all that stuff up to the performer and submit meekly to the way the piano whish is de rigueur for all composers is theoretically supposed to be tuned. The composer is commanded to imagine that all instruments have frets or keyboards for 12-tone. Including the human voice! One is never allowed to wonder WHY. Certainly not to ask why. Even in 1982 when the resources of 12-tone have been worn threadbare by myriads of composers in the past. Even when tone-bending and blue notes and tolerated deviations by performers show that exhaustion is near. The fact that musical notation provides separate symbols for G-sharp and A-flat is not explained, and is usually glossed over with some fiction about Bach inventing 12-tone equal temperament. No scientist would ever tolerate such slipshod non-thinking!
Pianists have traditionally been put through miles and miles of finger-exercises and trivial studies like Hanon and Czerny ad Kohler and you name it. The dulling and numbing effect of these tempered pitches pounded out for hours all one's life just has to be worse than even the effect of tuning pianos professionally. Thus the originality, creativity, and inspiration is drained and trained out of composers long before they are supposed to be old enough to start a career on their own. They may end up mere arrangers rather than composers proper. They may be condemned to an entire lifetime of writing background music for radio or TV or more likely, will become piano teachers or other music teachers and all composing becomes a mere hobby which their alleged friends regard with an amused smirk and/or sneer.
I have witnessed this sort of thing personally: I attended many student concerts at universities and colleges where compositions were presented and could hear first-hand the lack of originality and the snuffed-out creative spark that wasn't there anymore in people who should have been bright-eyes and bushy-tailed in the 20s. I went home and grieved all night, helpless to rescue any one of them. I pored through Ebenezer Prout and the other music-textbook who theoretically knew all there was to know about the great composers, having dissected them under the microscope; but where are the master recordings of the Czerny or Prout Symphonies? I witnessed the pathetic attempts of two of my then neighbors, 35 years ago, who had just retired, to take a correspondence course in How to Compose and become a husband-and-wife team of symphony...opera, and chamber music writers with dreams of being lionized at Philharmonic Hall or some famous New York auditorium. I don't have to tell you what happened--they never completed the course, of course, and after a few finished lessons returned to the school, they defaulted on the correspondence school contract and quietly died. Any resemblance to harmony from their old beat-up piano was purely accidental.
From all I could learn from them while they were actually filling out and returning the correspondence-school materials, it was all about Vintage 1870. No atonality--are you kidding? No Debussy whole-tone either. Strictly Central European mid-nineteenth-century Romantic Period practice, having no relevance to to what goes on in Los Angeles or New York today. The Course, then, was How To Succeed in 1890 at the latest, and about as profitable or productive as a course in How To Make and Sell Buggy-Whips would have been. Writing for an audience which has been in its respective graves for for about a century. Treating the practice of the mid-nineteenth century as if it were Eternal, Forever. As if it were on the same plane as the law of gravitation or the periodic table of the chemical elements.
Hiding the fact that these rules were the after-the-fact analysis by uninspired textbook-writers, deduced from what composers did in the late 18th century and the beginning of the 19th--i.e., before Wagner. Therefore, Hidden Constraints, which is right on our subject here. Something like forcing people to take examinations and answer questions in a science class, out of astronomy books published in 1880, which supposed that Venus and Mercury kept the same faces toward the Sun. Only recently do we know differently, but most science teachers would correct the errors in old textbooks, whereas music teachers mulishly will not. No chemistry professor today would teach the Phlogiston Theory with a straight face, but our music theory and instruction is about as ridiculous and obsolete as phlogiston is today.
One of the chief Hidden Constraints imposed by 12-tone equal temperament is the symmetry of 12-tone patterns. Take the whole-tone scale. Debussy practically began it; he practically ended it since 6 tones per octave have far fewer resources than 12 could. Almost every attempt to use the 6-tone or whole-tone scale today sounds like mere fainthearted rehashing of what Debussy accomplished--anticlimactic. With its equal spacing between its tones, no one of the 6 pitches can be definitely the tonic. The notation can make it appear that a certain notes starts the series of six, but as we said already, this notation is Pythagorean and not 12-equal. The very use of different "spellings" of the six pitches betrays that:
While some of the above "spellings of the pitches would have been against the 1870 rules and regulations, you can find them all through the works of Debussy and his imitators and emulators, and in atonal and serial works of course. So the above staff-notation examples hide the symmetry-constraint of 12-tone equal temperament and to some extent mislead the composer and the student. Let's free the cat from the bag be more honest and open; let's number the 12 pitches as Julian Carrillo and many of the serialists do nowadays:
0 2 4 6 8 10 0
4 6 8 10 0 2 4
4 6 8 10 0 2 4
0 2 4 6 8 10 0
3 5 7 9 11 1 2
1 3 5 7 9 11 1
This should unmask the lack of variety in using only 12 pitches per octave, as against the conventional notation's implying that there are more. Just for the heck of it, let's number the 19 pitches in the 19-tone equal temperament and take the first staff example on the preceding page and set it out in numbers:
0 3 6 9 12 15 18 and then compare it with the second staff-example which in 19-tone equal temperament would go:
0 3 6 9 12 16 0
Six whole-tone in 19 fail to get to the octave, whereas in 17 -tone, they would exceed the octave. Since 17 and 19 are prime numbers, there is now way of dividing either number evenly and so these overly-symmetrical patterns of 12-tone (12 is divisible by 2, 4, 3 and 6) are broken up and this replaces monotony by variety.
But the same conventional staff notation is suitable for both 17 and 19 despite the radically different meanings in those two systems: in 17, G-sharp is sharper than A-flat but in 19, G-sharp is flatter than A-flat. No amount of staring at staves and notes and clefs till you wear out your eyes will ever reveal that this conventional notations works for unconventional scales like 17, 19 and 31. So hardly anyone has tried them. Here is another hidden constraint!
The whole-tone scale contains the augmented triad. This can be spelt many ways. Rimskii-Korsakov used it extensively in his opera Le Coq d'Or (The Golden Cockerel, Zolotoi Petushok) and you will find all kinds of examples of it in harmony books. In 12-tone, there are 4 augmented triads, not 12, even though more than 12 of them can be spelt in traditional staff-notation. That is, it repeats. 12 = 4 x 3 and that is that. If you attempt the a traditional method of constructing chords by stacking major or minor thirds one on top of another, in the manner in which the chords of the seventh, ninth, eleventh and thirteenth are built in harmony textbooks, to make the augmented triad into an augmented-seventh chord and then a doubly-augmented ninth, you get nothing on your piano but a tiresome repetition of the three notes of the augmented triad at the bottom of the stack. 0 4 8 0 4 8 forever. But in 19-tone you could go on till you had a stack of all 19 pitches! THUS:
0 6 12 18 5 11 17 4 10 16 3 9 15 2 8 14 1 7 13 and only now do you get back to 0.
I earnestly hope you get my message right. Perhaps I am risking ridicule by writing triple-flats and octuple-sharps on the preceding page; I have had to take a lot of insult and invective for much less than that during the past half-century. Maybe I will get panned for even setting out the augmented-seventh chord, as C E G# B#, because it is nonsense in 12-tone tuning, but it is perfectly good sense in 19 and 31.
I can't describe how it sounds in non-12 systems--you have to hear a tape or have access to an instrument. Thus I lose some of the persuasive power I really need here and now. I have now been using non-12 systems like 19 and 31 for 20 years, so that is surely long enough that I can ask you to try them for yourself and take my word for it that they do work. (Quartertone or 24-tone does not have a series of 24 major thirds, nor even the augmented-seventh tetrad, since its 12 extra tones are intercalated between the first set of 12 tones and do not alter them.)
I can't expect you to imagine how non-12 sounds, let one the many different sounds of the different kinds of non-12 that you can now use. 12-tone training cripples the imagination. "Outside our Church there is no salvation!" has been thundered from many pulpits for a very long time. And 12-tone-ism is a religious cult in many ways. Harmony and composition textbooks order composers not to do many things, and push them around something terrible. Honestly, haven't you any self-respect at all? Do you have to put with such intimidation? Music textbooks are not scientific, and they are not a new religion either, so why the authoritarian attitude of virtually all of them?
Another way we can look at the symmetry of 12 is afforded by the New Math introduced in grade schools a while back (sometimes it is no longer called new math, but never mind--there has been some progress in elementary teaching nevertheless). The Theory of Sets and "modulo" arithmetic is relevant here. We can use the familiar clock face (soon to be obsoleted by all those digital clocks and watches, perhaps!) as a map of the 12-tone equal temperament. Imagine for example, that the Circle of Keys is laid out on a big dial with C at the 12 position and G at one o'clock and F at 11 o'clock and so on, so that F-sharp = G-flat in 12-tone-equal is at six o'clock on our imaginary dial. Then if we tune 12 fifths up as C G D... B# we find on our dial that we have merely made one revolution and are back where we started. So if we modulated from one key to another by traditional methods we could, in terms of the New Math, be said to be adding, since there is no number higher than 12 on the clock-face and 12 is the same as 0 in arithmetic modulo 12, modulating by major thirds reduces to 4 + 4 = 8 as in ordinary arithmetic, but 4 + 4 + 4 = 0 modulo 12 so that we do not escape the 12 pitches of the 12 major keys. If we went by major thirds down, to A-flat and then to F-flat major which we would immediately re-name E in order to conform to the Authorities which we have meekly accepted, then we get back to C by 0 - 4 - 4- 4 = 0, which you won't find in an old elementary algebra book, but will find in many books on popularized mathematics.
Furthermore, -6 = +6 modulo 12, or F-sharp equals G-flat, in 12-tone.
The familiar clock-face on the 12-tone circle of fifths or circle of keys diagram above will serve to help you realize the divisibility of the number 12. When the notion of set-theory "modulo" arithmetic is added to this, as in our explanation, you can use your experience with figuring out time-intervals to appreciate modulo-12 addition and subtraction. For instance, what is five hours before 1 o'clock? What is six hours after ten-o'clock? Just count around the dial and you have it, and similarly, what key is six places sharpward from B-flat major? Or what key is five places flatward from D major? And the composer who uses the 12-tone tuning-system can do it by this clock-dial arithmetic. IT is also familiar to us how the clock-face can be easily divided into halves, thirds, quarters, and sixths.
Now, look at the 19-tone circle of fifths or circle of keys above and it should be obvious that none of the 19 points around the circle standard at exact halves or quarters or thirds or anything else except nineteenths. All nineteenths are in lowest terms--i.e., the fractions 1/19, 2/19, &c. are as simple as they can be. But only some of the twelfths are in lowest terms, for while 1/12 is, 2/12 = 1/6 and 3/12 = 1/4 and so on. This means that the circle of major thirds in 12-tone has only 3 members, but the circle of major thirds in 19-tone has 19 members. So for other intervals.
The microtonal systems produced by dividing the 12-tone system, or the 6-tone system as was done by Carrillo, Haba, and others, are more divisible than 12 is, so still have the repeating patterns like the augmented triad and the diminished-seventh chord which repeat before they exhaust the tones in the system. Indeed, the quartertone system does not cure this defect of the 12-tone system, but adds another situation of this sort, the 8-tone scale, since 24 = 3 x 8.
Another reason for showing the clock-face with the 12-tone circle of fifths is that the serialists and some other atonalists have remained inside 12-tone equal temperament and evolved elaborate theories and systems along with a special "in" jargon of esoteric terms, and new meanings for some of the older musical terms. For instance, Hexachord.
Various mathematical operations, some of which are highly relevant to sets and to the modulus 12, use the symmetry of 12-tone as shown on the clock-face and as exemplified by numbering the 12 pitch-classes and by correlating staff-notation with those numbers and using various aids to structural visualization, so that the symmetry of 12, and the fact that it is 2 x 6 and 3 x 4 and 2 x 2 x 3 is continually brought before the reader. A person who has been taught with these notions will have a hard time transferring these structural ideas to a prime number of tones or some number such as 14 or 22 which is not as divisible as 12, so that discourages experimentation--here is another Hidden Constraint on Composers.
There is no real basic reason why serial composition has to be 12! Certainly there is no reason why free atonality (which, by the way, is becoming more popular lately, now that strict serialism and tone-rows have slightly loosened their iron grip upon composition students) should not be practiced in 11 or 13 or 16 or 19 or 21 or any other system as well as the almost inevitable 12. Atonality in 13 would mean that you didn't have to be continually on your guard lest you slip into a tonal key-system habit pattern inherent in the 12-tone system and in the material used to teach practically all conventional instruments. This would be true of a very large number of equal and unequal tunings.
The serialists' and atonalists' obsession with 12 and ONLY 12 for all the time they have been in power and all the time they have had academic prestige and status, has created the misconception that 12 has something to do with serial methods or with the non-key-system or that no other number of tones per octave works. This just plain is not true. The obsession with 12 tones per octave acts as a Hidden Constraint, since the immense piano and other musical literature intended to be played in 12-tone temperament have pre-empting most of the striking and telling themes and ideas for worthwhile musical compositions. In avoiding and escaping this tremendous volume of what has been written before, the atonal or serial composer is almost forced to sound like every serialist or atonalist, so long as he or she is tied down to Twelve. The excessive attention paid to written notation by atonalists helps hide the Hidden Constraints since many of these works are read silently rather than getting performed, and the public hears but little of them. So a large portion of even the musical world is almost unaware of this problem.
Probably the reason for this restriction to 12 has been the ubiquity of the piano at the time that atonality first began to take hold in music-teaching establishments. The pianos were there. Good pianos were expensive; now they are priced out of all reason. There were no books telling how to compose in non-12...no books either on who to refret guitars or build non-12 electronic organs or how to retune existing instruments nor those that might be specially built. The composers meekly submitted to what they thought was Eternal Divine Law Forevermore. Actually, fear lurked in dark corners of everybody's mind: it would have cost too much to build or change instruments for other scales, and to house them and maintain them and learn new keyboards and to teach tuners to keep them tuned in the new scales. Thus yet another, financial, Hidden Constraint. With computers and electronics and tape recording and electronic tuning devices, we should at last be free of those problems.
While it is true that almost all present-day synthesizers have keyboards, and keyboards with the piano's 12-tone pattern and the piano's rigidly-frozen dimensions and spacings, many of them can be re-adjusted from 12, such as 11 or 13 through 24 tones per octave, mapped onto the 12-tone keyboard. Other synthesizers are not adjustable or indeed have the 12-tone temperament or an excellent approximation to it, built right into their internal circuitry. To use an unequally-=spaced temperament or a selection of just-intonation pitches, is usually much more difficult on a synthesizer, if not quite impossible. So here we have the newest family of Hidden Constraints Upon COmposers. Be well aware of it and demand from all and sundry that they provide you with more freedom! Why should I write this and go the trouble and expense of having it xeroxed at all, if not to get some of you at least to help me get a few words in edgewise to the makers and customizers of new instruments?
We are the composers. We are those who produce the music and without us there would be nothing for performers to do. Nothing to listen to. No recording industry or concert-hall or instrument-making. True, the non-composers are ruining the show so far as the public ever knows. The retailers of the Past have tried to shut us up forever. But in recent years it has become possible for some composers to make their own instruments and/or do their own recordings, so we can be heard at least on a small scale. Others of us improvise so we don't even need to write anything down, especially with tape recorders and cassette-copying.
When I began composing around 1929 or such a matter, there were many constraints. Why pretend that they are still in place? The majority of those problems are fading away, and many of them are mere ghosts. The composers of the past are only ghosts, even if they get heard more than us. How about asking people why they prefer ghosts (and most of them don't even believe in ghosts) to us who are still alive and breathing and walking around? They better have a good explanation! There is a serious lack of feedback in the music situation. So I often stress that point where challenged to debate or argue. You can't thank Beethoven for the symphonies and sonatas and quartets, but you can drop a line to a live composer. Clapping for the performer is not enough! Which came first? Often the performer improvises and is then the composer and is then entitled to two helpings of feedback.
Classical composers' ghosts don't bother us contemporary composers; at least they never hurt me. It's the self-appointed middlemen who slap us down. And the more obnoxious ghost is the Piano's Ghost--the contemporary situation where the Public's Image of the Piano is untarnished and full of nostalgia for 1870 or such a matter, while real pianos in real homes and apartments and concert-halls and studios and even broadcasting and recording establishments are going to rack and ruin and often are completely kaputt. They don't make 'em like they used to either.
That's bad enough, Piano's Ghost No. 1. Piano's Ghost No. 2 is more of a Hidden Constraint Upon Composers: it is the practice of manufacturing a brand-new instrument, even a new design like these above-mentioned Synthesizers and Electronic Organs and other keyboards, with the same tired old frozen design of a piano keyboard made in 1870. That is, the manufacturer or engineer or designer or custom-builder or even home-craftsperson copies slavishly those features of the keyboard which were determined by the piano's action--that obsolescent piece of wooden machinery held together with glue. My hands are really too small for the standard piano keyboard yet I must put up with it. Why now, with miniaturized electronic innards? WHy must a new instrument's keyboard have to look like and feel like a piano keyboard? Why must it remain the same size, even though there is no clumsy mechanism in there anymore? Why must stasis prevail and progress never start up against since 1870? These new keyboards are not pianos. THose who need pianos can still get them if they have money enough, so why imitate the piano's faults? That is hardly honoring its memory, nor is it preserving the glory of its past. One of the most ridiculous Piano's Ghost stores I have heard lately was in a magazine ad for an electronic imitation-piano, boasting that its highest notes had no damping--i.e., imitated the after-sound of the highest piano notes which do not have any dampers. That is, the consumer is being asked to pay a substantial sum for this imitation-piano and is being told he has no right to control the sound of the instrument he is commanded to purchase! The manufacturer is biting the hand that feeds him! Insulting everyone who pays the bills and keeps him in business. Hardly how to make friends.
Further hidden constraints are embodied in the enormous number of conventional instruments still in composers' studios and still in place elsewhere, whether they still function properly or not at all. TO become conscious of what has been stated here is more than half the battle. Then you will not be so meek and submissive, and will not be seduced by the weight of centuries and the sheer bulk and presence of bygone things of bygone days surrounding you in the studio.
Be aware that you have been programmed. That suffices to throw some of the programming off, or defuse it and de-emphasize it, or allow you to compose in more freedom. Just becoming conscious of these constraints is some release.
Now for a moment: back to the symmetry of 12 and the asymmetry of some other systems. The quarter-of-an-octave exists in 12 as the imitation minor third of that system. I say imitation, because a real 5:6 minor third has 316 cents, or is 16 cents or about a twelfth-tone sharper than this 300-cent version. TUning a piano involves putting jillions of these minor thirds out of tune and making them harsh and restless instead of serene and calm. A 19-tone minor third is almost perfect and comes well within the margin for unavoidable errors in tuning. Same for the inversion, which is the major sixth, of course.
Since a 12-tone imitation minor third is a quarter of an octave, this gives rise to the diminished triad of two of these quarter-octaves, and the diminished-seventh chord (or its "enharmonic equivalents"). A pile of minor thirds, like the pile of major thirds in 12-tone that we discussed earlier, repeats itself forever. C E-flat F-sharp A C... or 0 3 6 9 0 3 6 9 ... endlessly, as Carrillo would write it in his number notation. Thus this chord uses up only 4 of the 12 tones. Only two more different chords exist of this kind: 1 4 7 10 and 2 5 8 11. All these chords have many spellings. The diminished-seventh chords became a tiresome cliche long ago because it was a rapid means of modulating to distant keys by calling its notes different names at will. iT is not as dissonant in its 12-tone form as it is in its possible just-intonation forms, which means that the contrast between dissonance and consonance is reduced at both ends by the errors of the 12-tone equal temperament. Both dissonances and consonances are blunted and fuzzed-up.
The minor third of 19-tone is somewhat larger than a quarter of an octave, so a pile of them exceeds the octave by one degree of the system. Next minor third piled on lands you on a major tenth! Putting this into numbers like the serialists or Carrillo, we get, in terms of 19ths of an octave, 0 5 10 15 1 6 11 16...going through all the 19 pitches if you want to take it that far. Or, in terms of note-names, C E-flat G-flat B-double-flat (= A-sharp) C-sharp E G B-flat... Dr. M Joel Mandelbaum, in the tape accompanying his doctoral thesis at Indiana University, put a long chain of minor thirds into one of his 9 19-tone preludes--big surprise when you hear it the first time.
Now we get variety. In 31-tone and in 22-tone we also get variety with the diminished-seventh chord and longer piles of minor thirds. In these and some other tuning-systems, each spelling means a different sound, rather than the one sound with four or more spellings in 12-tone. Alexander J. Ellis in his Appendix to Sensations of Tone by Helmholtz, attempted to provide just-intonation-based theoretical explanations for the popularity of the diminished-seventh chord and for its conventional theoretical explanation, viz., that it is a minor-ninth chord with the root omitted. He sort of gave up after sincerely trying--it is easier just to consider it to be a 12-tone artifact, or the 4-tone-temperament which 12 contains three times over. I recently stumbled on another explanation which could have some bearing on it: the diminished-seventh chord is the best chord on toy-pianos using metal rods and on tubular chimes and certain kinds of bells. Their abnormal timbre contains approximate major sixths instead of a harmonic series, so when such instruments are played this chord is implied, and thus becomes part of our environment subconcsiously. These sixths are not exactly 12-tone, so that furnishes slight relief from the monotony of the 12-tone form.
These six forms all identical in sound in 12-tone, but all different in 19 and 31.
19 minor thirds: Preceding applies only to the 19-tone system--tremendous variety of chords can be made from this series.
PILE OF MINOR THIRDS: In the 19-tone system, a stack of 5 minor thirds yields a major tenth; in the 31-tone system is gives a neutral tenth, neither major or minor.
In previous publications such as Xenharmonic Bulletin #5, and on some tapes, I have gone into the subject of the MOODS of various tuning-systems. There is almost nothing int eh theoretical literature about the moods and emotional effects which help to contrast one tuning-system with the others. So here is yet another Hidden Constraint--you have probably had to make do with just the 12-tone equal temperament and this has one mood, that of brilliance and restlessness.
There are various ways to override this one mood, but many of these are under the performer's control, not the composer's so the performer is the one making the final decisions. Since the composer is not supposed to indicate deviations from standard tuning int eh score, and since there will be changes in mood, sometimes for the better, by such pitch-deviations, the composer lacks an essential parameter of the work. Anyone who has had a performance by others will now what I mean.
The popular groups' effect-boxes and the drastic equalization in recording studio s and the various manipulations that can be affected by recording engineers doubtless have come into being to override the basic mood of twelve-tone tuning. The quest for noise is another symptom of this. With conventional instruments such devices as the soft pedal and various kinds of mutes are used to create a gentler mood. I might cite here the fact that the mutes used on violins are adequate but those generally sold for cello do not do enough of a job, but the cosmetic scruples are allowed toe defeat the purposes of the proper heavy mute that should be used on a cello, but is disdained for its ungainly appearance, not its sound. Doublebasses go unmuted for similar reasons.
We now have reached the topic of some of the hidden constraints upon performers, so have a little sympathy for them, too. The old wornout pianos mentioned earlier in this article are a shame, and often defeat the performer as well as the composer. Both parties are at their mercy and can be completely frustrated. SInce 95% of what the average person hears in a normal day, is the way of music, has been recorded and reproduced and/or broadcast, the general public judges live performances in terms of recordings. Many groups complaint hat they are forced, when they give concerts, to sound like their records as much as possible--that the freedom to take advantage of the live performance situation has been snatched from them. For a long time now, many people have collected different recordings of the same "classic" and care more about the interpreters than the composers, and you know whose name gets into the big type of the covers of such albums! Or into the record-review column.
I dare to predict that when more tuning-systems are available to composers, the contrast of moods will be a most powerful addition to any composer's vocabulary. This wide dimension has been denied us for much too long. It could not have been predicted theoretically, and with conventional instruments its realization would have been much too difficult as well as too expensive. In the case of more flexible instruments such as the violin family, the trouble has been in the programming of performers, and the modern practice of forcing them back to conform to keyboard instruments--and that in turn goes back to the unthinking custom of making all composers do their thing at the piano.
It would be inappropriate to conclude without mentioning the dependence of the so-called rules of harmony, and to some extent melody, upon timbre. Both conventional and the various reformed notations have no adequate or systematic means for indicating timbres, this being indicated if at all by words in ordinary languages that are necessarily too vague to do any good. The closest thing we have today is verbal directions for organ registration, but this is almost destroyed by the not-so-peaceful coexistence of pipe organs and reed organs and electronic organs, the latter really being many different instruments with different design philosophies, ranging all the way from the ridiculous to the sublime. The systematization of timbre and achieving full control over it are the most important immediate task facing us as composers. This ties in with the utilization of the New Moods mentioned above.
