IVOR DARREG

Defining One's Terms

June, 1988

In the last two years or so, the number of people interested in non-twelve-tone tunings of various kinds has grown. Certain commercial instruments and computer-music software have begun to offer alternative tunings. More magazine articles have appeared. Alas! Much of this has been misleading. In particular, a tuning which REQUIRES more than 12 pitch-classes per octave being available ALL the time, is often crippled by providing only a few of its pitches, and preventing any progress in the use of that tuning since 12 pitches are no longer enough if you use the 12-tone equal temperament, for instance.

The misleading labelling of a small number of pitches as "Just Intonation" is even more serious and prevents progress with just intonation as well as forcing the playing of dissonances when a simple consonant interval such as the Fifth, 3:2, is needed. The claim that it is not possible modulate to other tonics in just intonation is false and indeed unconscionable! Providing only 12 pitch pitches of the Meantone Temperament, or similar systems, is also cruelly misleading and it spreads the misinformation that one cannot modulate very far in meantone and/or that one must put up with the "wolf," a seriously out-of-tune fourth or fifth or major third in not so very remote keys such as B major or A-flat major or F minor or C# minor.

The Piano is mechanically incapable of having many tones per octave and keeping them in tune since tuners are justifiably unwilling to learn how to tune a multitude of new tuning-systems. But with refretted guitars and electronic keyboards and computer music this is no longer a necessary constraint. Then why pretend we are back in the 18th or 19th century? That is frankly, INTOLERABLE.

With recording machines and the ability to get recording copied, notation and nomenclature problems should no longer be allowed to stymie progress in music. WHy write out compositions when nobody can perform them? Or when most musicians refuse to perform music anywhere out of the ordinary 19th-century style? Or when they will perform new music incorrectly and mislead the listeners? All that has happened to me hundreds of times during the last 57 years and I am sick and tired of it! It has happened to dozens of other people to whom I have talked or whose letters I have received over the years.

With the influx of newcomers to xenharmonics and just intonation systems and instrument-building and the newcomers who come, not from the musical Establishment, but from handicrafts and computer science and physical sciences and mathematics and communications fields, many musical terms have lost their original meanings and new terms have been coined at a rapid pace. Needed inventions and new software and new instruments are being designed by those who never had to study the Musical Establishment's terminology, and so why must they conform to obsolete 19th-century lingo?

Here is an example I have used before: MODULATION. In electronic and radio engineering, this means modifying a carrier with a signal, as for instance in radio broadcasting where speech or music is caused to alter a steady high-frequency signal. In conventional 18th or 19th-century music, this means going from one key (tonality) to another, or changing mode, as from minor to major. If you are in a public-speaking class, it would mean proper control of pitch and intensity patterns of your voice. In other contexts, it might mean to control, to soften, to "tone down."

Back in the 1930s or 1940s, no big deal. Musicians didn't go around to engineers in broadcasting studios and debate which meaning of "modulation" might be the TRUE one! The engineer wouldn't know a change from E minor to C major even when heard it and wouldn't care what it was called. The musicians wouldn't know how to use an overmodulation indicator on the dial-panel of the radio station and wouldn't even WANT to know how it worked.

Now it's another story. Synthesizers often have something labelled MODULATION among their controls. Computer music necessarily involves several meanings of the word MODULATION.

...In case you wondered, Why all this fuss now? We got along well enough in 1847 or 1920 or 1931 and music is music and what are you making such a damn commotion about? Well, this is the Computer Age and the Electronic Age and it is time for music to progress as every other art and science has progressed, and new words are necessary and new definitions for old words.

No, I don't hold any special privileged position of Authority to make you use all the words exactly as I do. That is not the point. Don't accuse me of grandiose ideas I never had!

I don't have time to be Official Music Lexicographer. So all I want to do in this publication is to STIPULATE some meanings that I use in my own writings and you don't have to use these meaning if they repel you. WIth several hundred compositions, and having built many instruments, and having published tables for tuning and theory and other musical-instrument data, and having issued many Xenharmonic Bulletins and articles on aesthetics and audible communication, I have had to employ technical terms of both science and art, and often have had to coin new ones.

There cannot be any final glossary right now--now way! In over forty years of writing and discussing I have had to change my mind, and so have you, and these changes of meaning will be worse in the very near future.

Indeed I wish the Premature Standardizers would stop their dictatorial demands. We are in a very lively State of Flux.

Let's begin with some of the common words that have been ruined.

TONE: This word, not only in English but in French, German, Spanish, Russian and heaven knows what else, has too many meanings. I am going to use that words as little as possible from now on. I can't quit entirely, of course, but there are many acceptable substitutes of more explicit meaning.

For instance: Why use WHOLE-TONE when you can say WHOLE-STEP or sometimes MAJOR SECOND?

If you mean what is sometimes called tone-quality or tone-color, how about the French word TIMBRE? If you don't believe me about there being too many meanings, look in the nearest ordinary dictionary.

MICROTONE: Dictionaries and encyclopaedias disagree--some say anything smaller than a semitone and others say smaller than a quarter-tone and there are still other definitions. We can't stumble along that way. It's now too vague. MICRO- suggests exactitude and accuracy and precision while in the metric system it means "one-millionth" and that doesn't help us either. Too late; so if you want a vague indefinite word, go ahead, but I won't use it anymore.

Some Europeans use the term micro-interval. That might do--it hasn't been run into the ground yet.

SEMITONE: So long as most people use it to mean one-twelfth of an octave, and so long as non-twelve scales have been seldom used, it can be taken as 1/12 octave unless otherwise indicated. But in discussions of new scales, we have to qualify it everytime. Even traditional nomenclature affords us AUGMENTED PRIME and MINOR SECOND and in such a system as 19-tone temperament we have to say what kind of "semitone" we mean, and why not take advantage of those other more exact names?

JUST INTONATION: A system where interval-ratios are exact and not distorted by temperament. Also called PURE INTONATION. Nobody agrees on what "exact" means here and I do not have time to argue.

TEMPERAMENT: A system of tuning that distorts one or more of the intervals which it contains. Theoretically an infinite number of temperaments can be constructed. Actually hundreds can exist such that a musician could hear them as different--sometimes the differences are great, and sometimes the differences are teenyweeny or almost not there. Some differences between one temperament and another are important for theorists and mathematicians but cannot be heard in any conceivable musical performance. Example: the difference between ordinary meantone temperament (sometimes called 1/4-comma) and 31-tone equal temperament. A difference can be heard under laboratory conditions and measured with special equipment, but in a concert-hall the ambient noise and errors in tuning and the normal speed of playing any regular music would mask it out.

The principle of distorting values to make them come out even is found in many other disciplines than music. This type you are now reading is tempered! Clothing sizes are tempered. Electronic parts come in tempered sizes. Each spoken language has a tempered set of distinctive speech-sounds called PHONEMES.

Note that it is quite possible to have a tempered temperament. Indeed, pianos are not tuned to a simple temperament but the octaves are stretched, and the stretch in its turn is stretched.

DEGREE: Traditionally, any line or space on the musical staff or on or between the ledger-lines and below it. Or a degree of a scale is a pitch included in that scale. New meaning: one unit in a tempered system, especially an equal temperament. For example: a fifth in the 5-tone equal temperament is 3 degrees from the starting note or degree 3 if the first starting point is 0 (zero), or degree 4 if you call the starting note 1. If the 7-tone system, a fifth is 4 degrees wide [my expression for getting out of useless arguments about whether the starting-note shall be called 0 or 1] and in the standard 12-tone equal temperament a fifth is 7 degrees wide. In 19-tone it has 11 degrees, and in 31-tone it has 18. Since the just scale has theoretically an infinite number of pitches, we cannot count them and must resort to other measuring-methods. Harry Partch modularized integer ratios so that for the interval we would call a just fifth he would write 3/2 and I might write 2:3 or 3:2 depending on which way I was looking at it at the time. 3/2 or 2:3 or 3:2 all mean that one sound is vibrating exactly two times while the other higher-pitched sound is vibrating exactly three times. Our term "fifth" does not have anything to do with the fraction 1/5 but means five consecutive degrees of the ordinary staff counting INCLUSIVELY.

OCTAVE: I use the ordinary definition which is that a sound one octave above another has twice the frequency, or the ratio of one octave is 2:1, or a sound one octave lower has one-half the frequency.

In the Real WOrld of practical instrument-tuning and actual musical performance, whether people or computers, there is a small TOLERANCE such that he octave may be slightly sharp or very slightly flat: say less than 1% sharp or something less than 0.5% flat will still be called an octave.

I do not use Partch's private definition of an octave as a distance on a keyboard. If an octave is somewhat out of tune I still call it an octave, and I cannot call it a 2/1 as he did when it is not exactly 2/1 and that should be obvious.

We are stuck with the name OCTAVE because it meant eight degrees on the staff counting INCLUSIVELY, or eight white keys on a keyboard counting INCLUSIVELY, or eight letter-names counting inclusively so that the eighth letter-name is the SAME as the FIRST letter-name. After 63 years of agreeing with most people what an octave is, there is not use my changing it. Physicists have now officially agreed to use the term OCTAVE to mean a ratio of 2:1 or a doubling or halving of frequencies even beyond the audible range, so it is even more standardized than it was during Partch's lifetime.

HERTZ: one cycle per second. Used by stating pitches and frequencies and officially adopted by the United States Bureau of Standard several years ago (before that they used cycles per second, which of course took more time and space than hertz) or its abbreviation Hz). Cycle means a complete vibration or period of a repetetive waveform in most cases. Endless confusion in a number of countries was caused by the term VIBRATION since this was various defined as a whole cycle or a half-cycle and so there was a very confusing term "double vibration" in old textbooks. There is a new physical term bequerel (abbreviation Bq) for events per second of the kind that are not uniformly repeating but may be irregularly-spaced.

CENT: 1/1200 of an octave or .01 of the 12-tone equally-tempered semitone. Introduced a century ago by Alexander John Ellis. Certain European countries such as France use other measurements for small intervals such as the savart. Millioctaves or 1/1000 octave have been used by some theorists.

XENHARMONICS: Any system of tuning which does not sound like the ordinary standard twelve-tone equal temperament. That is,a tuning is xenharmonic if most musically-trained or musically-inclined listeners to a permanence hear it as different from a performance in 12-tone equal temperament. Nearly all just-intonation performances are xenharmonic. The only exception would be where so few just pitches are used that no interval noticeably different in a real performance of apiece of music from the nearest 12-tone-tempered interval can be heard. (The subset of just intonation called Pythagorean by most writers, if not carried out to many pitches, might be too close to the 12-tone tempered pitches for the average music-listener to call it different enough.)

Certain of the 12-tones-per-octave-only-and-no-more UNequal temperaments would not be called xenharmonic because the deviation from 12-equal is too trivial to be heard in a normal performance. A wild style of performing with wide vibrato and/or deviations from 12-tone-equal or the use of pitch-fringes and double-tracking, would not be xenharmonic even though small intervals occurred, because there would still be only 12 pitch-classes and no use of that tiny intervals to progress beyond the limitations of the 12-tone equal temperament.

The just intervals 18:17 and 19:16 have been used in fretting guitars to approximate 12-tone temperament and even though they might theoretically be just, this is not xenharmonic. Nor is the complicated interval 89:84 or 196:185 as used in the Hammond gear-wheel organ. Most contemporary definitions of just intonation exclude complicated intervals used merely to simulate 12-equal. But if I don't spell this out here to the point of annoyance, somebody will complain.

Most non-twelve-tone equal and unequal temperaments are xenharmonic. Obviously quartertones (the 24-tone equal temperament) is tied to 12 and cannot be as xenharmonic as 23-tone or 25-tone. 6-tone equal temperament is CONTAINED in 12, and therefore cannot be xenharmonic.

We can't provide a perfectly airtight definition because all human beings have different ears and hearing, and the same person hears differently at different times. It's like demanding to know what day and month and year I became bald, or do I still have enough hair on the sides of my head to be considered not quite bald? Does fuzz count or not? Such hairsplitting nonsense will not advance music one iota!

So the present definition of XENHARMONIC says that nearly all just intonation is xenharmonic and most equal and unequal temperaments are xenharmonic and most pitch-deviations caused by organ vibrato and effect-box chorusing and flanging and most slight bends by violinists are not xenharmonic because they do not leave the 12-equal standard tolerance range.

TRANSFER: When more than one tuning-system is used in the same piece or performance item, it will be said to transfer from one tuning-system to another. "Modulation" will not do in such cases. POLYSYSTEMIC means the simultaneous playing in more than one tuning system at the same time. (Similar to the conventional term POLYTONALITY: a piece in two keys at the same time.)

ORGAN: Another word ruined beyond any hope of repair! As late as 1930 it meant something; now the image of the organ is lost forever. It's unfortunate when you can't trust people and you can't any longer compose serious organ music without the risk that it will be played on something unworthy of it. And the listeners condemn you, the composer, not the manufacturers of some stripped-down affair.

Many people today have never heard a genuine pipe-organ. Until the coming of certain new synthesizers, they had not even heard a serviceable acceptable imitation either! Most of the great organ literature pre-supposes or takes for granted certain aspects of pipe-organ tone and now most things called "organs" lack these aspects. For example: a certain amount of wind-noise which differs with different stops; spatial separation of sound-sources [this is being resupplied now by using stereo amplifier systems]; slight deviations of pitch from one stop to another so that adding stops is not merely increasing loudness; contrast between one keyboard and the other(s)--too many instruments now which offer no such contrast at all--we may kind of contrast ANTIPHONY. In contrapuntal organ music this is necessary, not a frill that manufacturers may omit at their pleasure to economize! Under modern economic and other social conditions obviously the regular pipe-organ of previous centuries is too expensive and impossible to put in homes or apartments or even many public buildings of today. So imitations are now required, but it is now possible to get decent imitations and to go beyond what the pipe-organ can do, so there is no excuse any longer for the dreadful imitations of the 1940s and 1950s! The fact remains, that it is useless for me or any other composer to issue or have published, compositions for ORGAN when they are almost certain to be played on an instrument that simply cannot deliver the goods. Ironically enough, the new system called MIDI restores to electronic keyboards the COUPLER system used on pipe-organs for several centuries. So what's new?

PIANO: The definition of what is and what is not a piano is now going through the same agonizing degeneration that ORGAN when through since 1930. While this process of Degradation of the Image is not so complete yet as the ruination of the Organ's Image now is, it is too late already to do anything about it. Twenty-three years ago this subject was covered pretty well in my monograph Shall We Improve the Piano?, and sad to say, my success in predicting what was going to happen is spoilt by the horrible state of pianos today in most places, and the proliferation of poor imitations, and the utterly thoughtless copying of the piano's defects and shortcomings and fundamental constraints into new electronic keyboards which instead should break away from piano restrictions.

NOISE: One official definition is unwanted sound. This is meant for instance when giving the noise level as so many decibels. Noise on a synthesizer or in a computer-music system will ordinarily mean some device for injecting unpitched sound or random frequencies into the signal being generated. The nose of hammers in a piano or the tangents in a clavichord or the jacks and quills in a harpsichord indeed distinguish these instruments more than the timbre of the "tone" or regular-vibration part of their sound. The Italian Futurists of some 80 years ago actually built mechanical noisemaking instruments called INTONARUMORI to create a new Art of Noise--the Intona- part of this Italian word however presupposed giving a tone or pitch to their new noises. Much as a truck going up a hill makes pitches along with the various noises, or an electric motor starting up a piece of heavy machinery slides up the scale of pitches. WHITE NOISE is a sound engineers' term meaning noise which contains all color. PINK NOISE has more energy at the bass than does white nose and is more like normal ambient random sounds, because it does not slight the lower octaves.

BENDING: (more fully, Pitch-Bending) This is the term now being used on new instruments and elsewhere for some kind of wheel or level or control that sends pitch or down from the norm (usually this norm is the 12 pitch-classes or 12-tone equal temperament) and often such controls are spring-loaded so as to return to the sacred 12-tone norm whether the performer wants them to or not. Pitch-bending ordinarily means some kind of capricious or random or accidental or controllable deviation from the theoretical Standard Tuning. It is mostly used for popular music and the classical musicians and music teachers avoid the term and use something else to conceal what they are doing! Wind-players often call bending "humoring the tone;" string-players speak of sharpening leading-tones going up, and so on. New tuning-systems can systematize bending and bring it out into the open instead of sub-rosa underground hiding the facts. New tuning-systems can put order and reasons for having pitches outside the ordinary norm, instead of the present chaos and belittling of the idea. Often where to bend the pitch is a secret doctrine never written down in the sheet music and just a tacit compact between teacher and pupil how to inflect the pitch without letter the rest of the musical world in on this technique.

VIBRATO: A regular or cyclic variation of frequency and hence pitch up and down from an average or center point. Electronic-organ specialists usually took 7 Hz as their norm for the vibrato rate. In real life it can be much slower or somewhat faster--say from 4 Hz to about 10. The electronic engineer will call this type of vibrato "frequency modulation" because in engineerese this is quite correct--a low infrasonic frequency is used to send the frequency of the main signal up and down from the center frequency it would have without vibrato.

The defect of recording and playback machines called FLUTTER is the unwanted vibrato from unsteadiness in the revolution of a turntable or motion of a tape, for instance. The defect called WOW is simply a very slow vibrato that would not ordinarily be used by a musician on an instrument.

Performers of music will vary the rate of vibrato as the music needs, and also the WIDTH of the vibrato. Unfortunately most organ and synthesizer vibrati can become boring and monotonous because they are too steady and/or cannot be turned off.

TREMOLO: This term is quite ambiguous. To a violinist or cellist it is really a combination of somewhat-interrupted tone with extra noise from the rapid reversals of bow-stroking. Other conventional musicians might use tremolo to mean rapid reiterations of a tone which in many cases involves actual interruption of the tone at each repetition, while in other cases it will be mere AMPLITUDE MODULATION in the engineer's parlance. Tremolo on a piano involves rapidly repeated hammer-strokes, and on a banjo or mandolin it is the norm for long notes. On the pipe-organ a tremolo stop will cause the wind-pressure to fluctuate, and this in turn will cause the pipe-sounds to go up and down in amplitude AND frequency at the same time.

On some instruments and effect-boxes and amplifiers, tremolo can be pure amplitude modulation without any frequency effects. That is a pure variation in loudness without any added noise or frequency wobbling. The vibraphone or "vibes" for short consists of metal bars with shutters mounted between them and their pipe-resonators, such that an electric motor causes a fluctuation in loudness as the shutters revolve and alternately allow the resonators to increase the apparent loudness and close off the resonators so that the bar-sound appears to be softer. So this "vibes" effect is about as close as the ordinary non-electronic musician will come to pure amplitude modulation or Loudness Variation Without Pitch Variation. The engineer or acoustician may declare that there is a Joker hidden here--amplitude modulation produces SIDEBANDS or frequencies on either side of the main frequency. One percussionist devised a special vibraphone whose shutters could be driven very fast, and then the sidebands become clearly audible as extra pitches! Conversely, if beats are deliberately caused, as in the Voix Celeste or Unda Maris stops on pipe organs, by supplying slightly slightly higher pitches or slightly lower pitches or both, this is what we might call artificial sidebands; and so the celeste or pitch-fringe effect shades into the loudness-variation effect and the definition of these terms becomes somewhat moot.

I want to define all my terms clearly, but the Real World will not let me. bad enough that artists and scientists disagree on semantics, but worse yet, engineers disagree with both, and then much of music and musical-instrument lore becomes a fanatical Religion, and reason flies out the window and there is no harmony at all--just polemic and disputation and arguing far into the night! If music experts practiced peace and harmony, I would not have to write this pamphlet at all.

BEATS are alternate increases and decreases in apparent loudness when two tones of slightly different pitch interfere with each other. These may be harmonics rather than fundamentals--the beating of harmonics permits tuners to tune complex tones. Now that most music is heard through amplifiers and recording and playback machines and now that effect-boxes and sound-processing equipment is used so much, beating is heard many times more often than in the pre-electronic world. This is the result of INTERMODULATION DISTORTION or IM for short. Passing certain signals through certain equipment causes them to chop each other up or at least to roughen and curdle each other to some extent. Nineteenth-century experimenters had only acoustical and mechanical equipment, so had to go to great and special effort to hear beats that now with electronics can be so loud as to overpower the tones causing them! Difference-tones have a frequency which is the difference between their generators--subtract the lower frequency from the higher to obtain the frequency of the beats or difference-tone (depending upon whether eh difference is infrasonic or within the audible range). There is a SUMMATION-TONE which until the above-mentioned recording machines and amplifiers and fuzzboxes and other sound-processing equipment, was almost impossible ever to hear. Now it can be heard ever once in a while, thanks to the new distortion methods, intention or accidental. To find the summation frequency, ADD the lower frequency to the higher. Difference-tones and summation-tones are instances of the sidebands mentioned above.

PITCH-FRINGES or VOIX CELESTE EFFECT are thus deliberately-caused SIDEBANDS producing beats and this is not too different from CHORUS EFFECT. The main problem today is how to turn them OFF! They are being overused. The string section of a symphony orchestra, or a choir, produce chorus effect by random variations in slightly-different pitches. Pianos have three strings to a note in part of their compass for this purpose--the unisons, however carefully made identical by the piano-tuner, soon go out and give this effect. When it gets too much, the pianist sends for the tuner--or SHOULD.

DISTORTION: Intermodulation distortion has already been discussed. Of importance to musicians is HARMONIC DISTORTION. When a vibration in certain musical instruments (metal bars struck very gently, tuning forks, air blown across the neck of a bottle gently, soft whistling, &c.) or an alternating current has but one frequency, there is no harmonic distortion. Such a sound is said to be dull--it has no zonk, zest, nor zip. When displayed on a cathode-ray oscilloscope, it shows what the engineer calls a sine wave because of the way this wave shape can be described mathematically. It looks something like this:

Most practical and useful musical tones are not simple like that--they have more complicated waveforms. However, most of them can be analyzed into a series of such simple waves having 1, 2, 3, 4,... times the frequency of the fundamental component. If these components are really exact multiples of the lowest frequency, they are called HARMONICS. In some musical instruments they are not exact--the piano, for instance. In other cases, such as bells and chimes, there may be inharmonic components.

The acoustician takes the simple waveform as ideal and anything else is "distorted" in relation to it. If you put too large a signal into an amplifier or other equipment, overloading it, it will distort. Harmonic distortion on single tones may be all right up to point--at first it merely changes timbre or adds some "brightness" to a dull sound. Soon it becomes irritating, as rock groups often show us.

Harmonic distortion and other kinds of distortion occur inside many conventional instruments. This is normal, so don't be misled by the engineer's Ideal of no distortion at all. Technically or theoretically an unfaithful response to different frequencies is distortion, but this is exactly what makes a brass instrument or a woodwind or violin useful for music--the original vibrations of the string or reed if they were faithfully picked up and amplified would probably be too harsh or at least unfamiliar--the body of the instrument removes some frequencies and reinforces others. So in the electronic instrument where this also can be done to the performer's taste.

The 1930's terms High Fidelity is not necessarily a blessing or virtue. The 'audiophiles" insist of nearing the piano dampers falling and fuzzy-buzzing as they settle back on the strings, and harpsichord jacks falling and making an unpleasant humping noise after the last note of the piece is released, and they want to hear key-clicks on clarinets and saxophones and that horrid screech when a guitarist slides between hand-positions--well, as a composer I have no use for that kind of "fidelity" and would just as soon it never happened. This is what happens when the MEANS are over-glorified and both the beginning and the end, that is, the composer and listener, are totally forgotten and ignored.

Maybe this is why most orchestras and classical performers want all their composers DEAD--so they can't talk back.

FORMANTS: While it is possible to synthesizer most tone-qualities by adding simple components both harmonic and inharmonic, it is usually more convenient to use what is called SUBTRACTIVE SYNTHESIS--generate a sound more complex than what you want and REMOVE this or that portion with FILTERS. The mutes that can be plugged into certain kinds of horns are acoustic filters. The mute that can be clamped onto a violin bridge is another kind of filter. Many electronic organs contain filter circuits called formants. So do certain synthesizers. It is even possible to insert filters in the recording channel at a recording studio and turn one instrument into another.

The formant principle is as old as Mankind: vowels require two or three formants to distinguish one vowel from another. The human vocal tract filters the vibrations of the vocal cords and the noises of the consonants into our accepted speech-sounds.

What is new about formants is the CONTROL we now can have by using equalizers (EQ) and the filters built into new electronic instruments and various types of amplifiers. Filters can also be simulated by computer software and called for when a composition is done on a computer. The pianist has been at the mercy of the tuner and the repairman the manufacturer and utterly helpless to change the voicing and the timbre of the instrument. So for early organs and electronic organs, where the manufacturer economized by not providing enough control over timbre. Not it's a different story. Not surprising, then, that the performer of today is bewildered by all these new powers conferred at once without warning, and no music-teacher prepared anyone for this to happen. So the new capabilities go unused in many cases.

The composer has never been allowed to specify or to get control of the way the composition should sound! Now it is possible for the composer to use instruments and/or computers and work as the sculptor or painter has been able to: full control of the parameters and no distortion by unwilling performers who were not taught how to perform new music, and certainly not taught about using new tunings and scales!

The so-called RULES OF HARMONY are mere deductions from 16th- through 19th-century practice of certain composers considered important enough to have their practice analyzed and codified by legalistic textbook-writers. The newcomer to music or instruments of computer music often does not realize this, and confuses these arbitrary legalistic "rules" with the Laws of Physics or Natural Law. That just isn't so. Why should a harmony teacher writing a book be allowed to dictate what instruments shall be built or what today's composers working hundreds of years later may do? That is to say, the Rules of Harmony are long long After the Fact, and what city would tear down all its freeways and garages because there were no automobiles in 1700? What office building would rip out all the electric wiring because there wasn't any electric lighting nor any elevators back in 1658? But as a composer for the past 50 years, I have been scolded hundreds of times because traditionalists think I have no right to put down a single note that cannot be played on a piano or French horn or bassoon. Every legal and illegal means of intimidating me and my fellow-composers has been tried. If you want merely to parrot the greats of the 16th through 19th centuries, then these Rules deduced by non-composers may suffice. But they forbid any progress; and there is no point in me or my colleagues composing at all if we may not progress. I repeat: the Rules of Harmony are NOT Laws of Physics! They are mere deductions and analyses of long-gone periods in history.

ATONALITY: An etymologist might complain that this term should mean pure noise. I.e., no tonal or regularly-vibrating sounds, but just random waves in the air. Maybe it should been "ATONIC." That is, without a tonic degree of the scale or a tonal CENTER. For good or ill, we're stuck with it. Now, when exploring new scales and tuning-systems, we find certain of them can be used with a key-system such as most composers have been doing. This is true for just intonation and for the 17-, 19-, 22-, 24- and 31-tone equal temperaments. But other tunings such as 13-tone equal temperament are inharmonic and so Atonality is an excellent choice for using these tunings and instruments and composing on them.

Some other scales such as 14- or 13-tone equal temperament, will present intermediate situations between the atonality of 13 and the intense tonality of 31. Also, there is a considerable body of composition now which employs random pitches or very irregularly pitch-series. Between tight-tolerance definite pitch and random noise there is a complete continuum with no gaps or breaks at all. There is also musique concrete, which uses sounds from the environment and may or may not impose timbre and pitch constraints upon them.

Atonality may be free, despite the widespread notion that Atonality is the same thing as TWELVE-TONE SERIALISM. Indeed, Serialism need not be twelve-tone-tempered at all. It can even be applied to a just system. Twelve-tone Serialism may well be defined as MUSIC IN COLD BLOOD. Everything neat and coldly calculated in advance and thoroughly premeditated. Whatever might suggest a cliche Romantic or Classical harmonic or melodic pattern is usually carefully avoided. The standard twelve-tone equal temperament was not invented for the purposes of Serialism or Atonality, and atonalists will be much better off using non-twelve scales. Doing Serialism in 12-tone temperament is simply "because the piano was THERE!"

There is nothing wrong in principle with serialism or atonality--only with the tying of either to the piano and 12-tone tuning which were not indeed nor designed for such uses. Must airplane pilots fly always directly over city streets and century-old roads which strictly follow the limitations of the terrain? It's ridiculous.

I knew a composer who dressed to look like Schubert. He was afraid to be himself. WHen his hearing went bad, he started dressing and putting on fits of temper like Beethoven. I don't whether he changed to any other composer when or if he got fitted with good hearing-aids. Another composer dressed up like Schumann. And learned German to do the act better. Must we view all music through a rear-view mirror?

Compare this fanatic obsession with History to what has happened in nearly all other sciences and arts. Just take a little time and see how music has been held back! Why? The real tragedy is that some schools are training all the creativity out of musicians. They are making written notation or printed sheet-music more important than any sounds. They are training people for jobs which no longer exist.

I do not let my 48 years of tuning standard 12-tone on pianos, organs, and harpsichords cloud my judgment on the need to get outside that tuning-system now that we have the technology to leave it and the means of sparing traditionally-trained musicians from having to learn special notations for new scales. Most of the problems are pseudoproblems that don't really matter in the Real World of 1988.

WELL TEMPERAMENT: This neologism is being denounced by many writers who think it is improperly-formed. That may be, but again we are stuck with a new phrase which has to be defined here, even if it is incorrect in terms of English grammar or style. This is an article on definitions and not a schoolbook for teaching grammar and syntax. If there were a better phrase now in use I would use it. But I cannot wait for some expert to invent a better phrase. I need somethign NOW while still alive. As of Fall 1988, Well Tempermanet means a way of unequally spacing 12 pitch-classes on a standard keyboard instrument such as harpsichord or piano so that certain keys of traditional music will sound smoother the expense of certain other remote keys such as F-sharp major or E-flat minor. The phrase is adapted from the title of Bach's Preludes and Fugues, the "48" usually in two books, The Well-Tempered Keyboard. The "well" has been taken by many scholars of the last few decades to mean a variation of 12-tone equal temperament such that the smoothness or harmonious quality of the nearby keys such as C, F, and G major is improved enough to notice without ruining the remote keys like E-flat minor and F-sharp major so terribly that they can't be endured anymore. If those keys are made really discordant, as by the WOLF that results from yanking only 12 pitches out of meantone temperament and playing G-sharp instead of A-flat in an E-flat major composition, then that unequal 12-tone temperament is not "well" in this new meaning.

These scholars of the last few decades referred to above different from standard 19th century opinion, which was that Bach demanded perfect EQUAL 12-tone temperament at all times. These scholars think that well did not mean perfectly-equal spacing of pitches, but allowed for "character in keys" and some slighting of the less-used keys. It is not for me to judge here. Frankly I don't care! I am a composer and I do not want to repeat what bach or Beethoven already did very well and I want instead to do what has not been heard before and could not have been heard before. What earthly use being a conformist clone? What would that do for music or for society or for you or anybody else?

I would like to extend the meaning of Well Temperaments but I suppose I will get slapped down by the self-appointed authorities who think they rule me and own me and you. Suppose we took the 19-tone equal temperament and distorted or warped it in such a way that the nearby keys sounded smoother, say like keys in 31-tone, and the remote keys like A-sharp major or B-sharp minor were not that smooth? This has already been done. George Secor constructed such temperaments, and there is still another way to do it by basing the temperament on something other than the octave.

My main reason for defining WELL TEMPERAMENT here is simply to show that I don't need it in 12-tone versions, and I do not promote it for 12-tone instruments because I haven't time to tune it for others' and furthermore it DOES NOT ALLOW FOR PROGRESS BY TODAY'S COMPOSERS and in the ordinary meaning of well temperament now, does not give anyone the ability to get out of twelve. If I had kept silent on this phrase, I might have seemed to be including it in xenharmonics and non-twelve and Ideas For you To Progress. It is not Xenharmonic because it cannot diverge that much from 12-equal and still be "well"!

So much for WELL TEMPERAMENT: Now what would a SICK temperament be like? Alas alack-a-day! I had a chance to hear it about 8 years ago in a college auditorium when somebody played a grand piano through a Ring-Modulator--this is a device which can be set up to suppress the original signal (the normal piano tuning and tone in this case) and output an inverted section of the Audio Spectrum. The high notes became low and the low ones high; the chords all became inharmonic; the harmonic partials all became inharmonic partials so that all timbres were very abnormal. It outdid John Cage by miles.

PITCH-CLASS: If the number of keys on an instrument are restricted as with normal fretted guitars and mandolins and our standard pianos and organs, then we may re-define "pitch" to take this quantization and also the customary notations and nomenclatures into account. Quantization is a form of digitization in a way--instead of regarding musical pitch as a continuous spectrum, we arbitrarily cut it up into discrete segments and anything a certain small distance above or below these segments' center-points will be admitted into a PITCH-CLASS, while something too far away will be entirely rejected or ignored, or assigned to the next pitch-class above or below. Actually, there already are devices which will take somebody singing or playing an instrument and impose the 12 pitch-classes of the 12-tone equal temperament on the input and "correct" anything and everything to the 12-tone points. This is truly QUANTIZING in the usual engineering sense. Another meaning of pitch-class is with respect to the nomenclature: DO RE MI or C # D or 0 1 2 or however one names or numbers the notes of a tempered scale. One might ignore all octave-differences and put all instances of C in one class and all instances of C# in another, and so on. Another meaning might not involve quantizing: it might instead deal with wide or narrow BANDS of frequencies and call "C" something which is close enough to the standard center-point to be taken as "C" by the listener, whether "corrected" or not. In many cases, it would have to be exactly on C-semiflat or C-semisharp not to be admitted to the C-class and thus only exact quartertones would get refused admission to the twelve pitch-classes usually set up. Remember also that wide vibrato is common enough and this would cause endless trouble, were it not for setting up classes within which a group of pitches could comfortably reside.

Now, we could define xenharmonic as having more or less than 12 pitch-classes, in many cases if that is our pleasure.

In a system like 19-tone or 31-tone temperament or unequal temperament beyond twelve, we can have 19 or 31 or 22 or some other number of pitch-classes up to a certain point. This point is somewhere around 45 or 55 equally-spaced tones. When using unequal systems with certain very small intervals, then one begins to wonder: are the two b's a comma apart in just intonation or in, say, the 53-tone temperament, within one pitch-class or two? So there very well may be more tones per octave than there are pitch-classes.

I'll leave this with a theory question you can torment your enemies with: is a bent note still a member of the pitch-class from which it was bent? Or does it start a NEW pitch-class? Or what?

DIATONIC: I only have to comment briefly--just to point out that in certain temperaments such as 5, 7, and 14 and possibly some others, the MODES collapse into the KEYS. Indeed that makes equal-7 and equal-14 useful for their strange moods. A familiar melody can be played the 7- or 14-tone equal temperament and there will be whole-steps between each letter-named pitch, and no alternation of whole-steps and half-steps as there is in 12-tone with the 7-note diatonic scale. The melody will still be recognizable. BUT: there is no difference between transposing it into a higher or lower key and playing it in another MODE, whereas with the very same diatonic melody in the 12- or 17- or 19-tone temperament there will be many modes, and each mode available to be transposed into 12 or 17 or 19 different keys. Debussy anticipated this with his whole-tone scale of 6 equally-spaced pitches in each octave.

CHROMATIC: This is the Greek term for "colored" and originally referred to a certain tetrachordal pattern. Now it usually means the complete 12-tone scale. With this heavy Establishment bias now in effect and with inevitable ambiguities resulting from exploring new scales with different-sized unit-intervals, xenharmonists will have to be careful about using "chromatic" lest they be misunderstood. If you have a quartertone instrument, what's "chromatic"? 12 out of 24? All 24? Something like 17 out of 24? This is a real world question now. What about 19-tone? Is it all 19? 12 out of 19? Some other number?

ENHARMONIC: The original meaning of this word in Ancient Greek was "suitable" or "in keeping" and by extension, it became attached to a certain musical figure--then to a tetrachord pattern which contains two small intervals. If that were still its only meaning or set of meanings, I could have used it to great advantage in referring to certain scales which contain small intervals on the order of a third-step or quarter-step...say from about 1/16 octave to 1/25 octave.

Sadly and regrettably, this was not to be. To the conventional 19th-century music teacher and student, and right up to now in the 20th century, the only meaning they give to "enharmonic" is "two or three names for the same pitch." Examples in the standard twelve-tone equal temperament would be C-sharp and D-flat, or F-doublesharp, G natural, and A-doubleflat. Look into many textbooks and dictionaries and you will never see the real meaning of ENHARMONIC. Just a few books will tell you. So, yet another example of a word that has been ruined beyond repair.

Why would such names as C-sharp and D-flat have been invented in the first place if there were not two distinct pitches that they could mean? Well, there are, in many systems of tuning, and in other systems of tuning they DO mean the same pitch, and still other systems, they have no meaning because the conventional name-system does not fit such systems as 13 tones per octave.

In the 12-tone system C-sharp means the same pitch as D-flat; in the 17-tone system, C-sharp is very much higher than D-flat, and in the 19-tone system C-sharp is much lower than D-flat. Sure, this is confusing. If that bothers you too much, why not number the tempered tones? For Just Intonation you might use ratio-numbers as Partch did. The computer-user will have some kind of code that can be typed in numerals and/or letters like what you are now reading, and evade the sharps-vs.-flats problem very neatly that way. Indeed, if someone has a computer and is able to use the 171-tone system (which has been done a few times) it would be absurd to name all the pitches! What listener would WANT to know all those names? Any more than the centipede needed which leg came after which.

With tape recorders and new recorders yet to come, we can avoid notation for the most part. Why ask performers to go against their indoctrination and training, when the machine has no prejudice? So I don't bother writing down all my compositions anymore--I just go ahead and play them and record them and copy the tapes. No muss no fuss no hassle and no imposing on other musicians. No begging no pleasing no waiting.

METACHROMATIC: This is a possible term for something smaller than 1/12 octave but not really MICRO. Meta means "beyond" in Greek and Chromatic is a Greek word like dozens more of our musical terms. A few people have used ULTRACHROMATIC for systems like 24 or 31 notes per octave. Another possibility is HYPERCHROMATIC for extremely small intervals like 1/60 or 1/100 octave--when it gets too small to be a melodic interval and much too small to speak of separate pitch-classes. We are proposing METACHROMATIC for the region of systems 1/13 to 1/24 octave where the unit-intervals are still usable and recognizable melodic intervals, giving us new songs and new tunes. Metachromatic does not "beg the question" and does not say this is too small to hear or whether the system is just or tempered. For "microtone" look back on Page 3.