USING TWO-PART COUNTERPOINT FOR

NON-TWELVE-TONE MUSIC

by

Ivor Darreg (1988)

The 20th Century is nearly over with. We have spectacular progress in all the arts--except music, alas. I have done something about this--will you?

Stand near a downtown street-corner for a moment--everybody is in such a hurry that you can't do that for more than a few seconds: cars and people will be rushing past, and every so often--too often indeed--there will be a siren proclaiming another accident. It will happen because both parties are in a hurry--almost every incident.

If you are quite downtown, you will see some joggers or actual runners hurrying down the street with no real destination. You can't escape this even by going out in the country: aircraft will whiz by overhead! Now contrast this with the average instruction in music that most of will have gone through: rule after rule after rule, repeated and repeated to intimidate us. DEAD COMPOSERS EXCLUSIVELY! Moreover: dead composers of the 19th century in central europe, not here in the USA. Nostalgia beyond belief. Why, it amounts to Musical Necromancy--maybe Necrolatry.

Put on the radio or TV--"Golden Oldies" some stations say they are broadcasting. Well, of course I know that doesn't mean the compositions of the Romantic Period in the 19th century, but logically it could. In truth and in fact, much of the popular music of this century is a reprocessed stylized permutation of the Romantic standbys all the way from Europe in 1830 or 1850 or 1870. Dead but not buried; transported by H. G. Wells' Time machine into 20th-century America and set down in the music textbooks and the How To Play the Piano o Guitar or Violin or Ukelele books at your music store, or in more dignified form, given out in conservatory and college courses throughout our fair land.

Walk into your neighborhood supermarket--look on the shelves and you will find Freeze-Dried This and Old Country That. Well, if Atonal Twelve-Tone Serialism and similar styles of music taught in our colleges and universities and discussed at great length in the musical journals isn't Frozen and Dried from the Old Country, what better description can YOU concoct for it? I dare you to come up with anything more apt. and to make matters more annoying, the so-called avant-garde or ultramodern music many students are taught to compose at the piano, which is the epitome of 18th-century technology, engineering, and design, not even the 19th. Why, the very notes and clefs, accidentals, and symbols used to print today's music whether serious/academic or popular/light, were designed in Central Europe during the middle of the 19th century, nothing whatever to do with today's ideals of graphic design. I might as well cut out a few and paste them in here.

The piano and that standard notation are holding back progress and so are most orchestral conventional instruments--not quite all of those. The new electronic keyboards have been imitating conventional ones so closely as to be mere clones in many cases. The new samplers--well, that's emulation. However, this need not be that had: the cloning and slavish emulation of old instruments is mostly the fault of the performers and their not knowing the possibilities of these new instruments, rather than of the instruments themselves. They simply haven't been told of what they CAN NOW DO!

Recent visits to demonstrations of synthesizers and other new instruments, discussions with certain people in new music movements, recent demonstrations of computer music software in action, and recent tapes from various sources, have usually exemplified built-in constraints and limitations slavishly copied from mid-19th-century music and instruments of that period or even earlier. In some cases these limitations can be circumvented or defeated; in other cases they are impossible to alter. The music software for computers is just as bad as the new hardware: and this goes for the graphics programs which print out conventional musical notation--often they cannot do any new symbols such as microtonal accidentals or various avant-garde expression-marks or some composer's graphics inventions.

Maybe some of you think I am yelling and screaming about trivia--but consider the consequences of impersonal soul-less corporations and conglomerates most of whose business sis not music-related at all, and programmers and software houses which have not consulted composers alive and experimenting with new music right now, and money-managers and engineers and record companies and bankers and media experts and manufacturers of assorted equipment who couldn't care less about any advancement or progress or change or experiment in the art of music or its tools and means. Consider that they, consciously or innocently and subconsciously, are telling you and me and all the other persons that we MAY NOT COMPOSE this or that innovative melody or harmony. (As a matter of cold hard fact: some of the new music software cannot play 5/4 meter, let alone 7/4 or 2 notes against 3, so this built-in limitation extends to Rhythm.)

Some composers and some music-theorists have written volumes saying that nobody has the right to compose in the 13-tone equal temperament or to use more 12 pitches at a time out of the 1/4-coma meantone temperament, or to use any resources of a non-twelve-tone-equal-tempered scale beyond what the rules of the ordinary textbooks permit for use in standard Romantic or Classical piano compositions. Others claim they have tried this or tried that and rejected it because they could not do anything worthwhile with it; therefore you and I are also forbidden to try either.

The worst instance of this at present is the offering by some manufacturers of alternative tunings which do not permit using more than a twelve-pitch-class subset of a scale at any one time. When somebody is trying to perform in just intonation this because very irritating and exasperating. I have had to wait for sixty (60) of my 72 years for non-twelve-tone instruments and adequate recording equipment and cannot wait one minute longer!

Another dreadful imposition upon us is the Acoustical Instruments Only Attitude--that composers of anything, to be taken seriously, must not use electronic instruments or new recording studio technology or samplers or effect-boxes or computers, but must stick to the instruments of the 19th century in Europe and never anything else--not even saxophones or marimbas or vibes or kazoos for that matter. The idea of someone in a modern home or apartment playing recordings, let along making their own, or playing an electronic instrument or a guitar refretted to a new scale--why that would be a Mortal Sin! Ironically enough, electronic instruments have aided and abetted the revival of the clavichord and harpsichord and have acquainted millions of people with their sounds who would never have heard them onstage.

Performers have intimidated composers all through the last century and almost killed compositional progress. I have received letter DEMANDING that I never write a non-12-tone-tempered note. This when I was past 50 and the writer was maybe 30! "No performer will play it" this guy said. Now the tables are turned--most any composer can get or borrow recording equipment to produce high-quality copies of recordings without needing to impose on any narrowminded run-of-the-mill performers. Performers still denounce improvising and any kind of do-it-yourselfery, and keep on demanding that every single note be written down before it is ever heard, and they are happy if they can keep others from composing anything that has the slightest chance of ever being heard by other persons.

Listeners for centuries have had to attend performances often at great distances from their homes or do without. The 19th-century in Central Europe is not the End of the Twentieth Century in this country, so times have changed and nothing is gained by denying one-self opportunities out of Purism. So why should I or any other composer alive today have to pretend that only professional performers at public concert-hall can convert my musical ideas into sound?

Now I am ready to get into our main subject: why two-part counterpoint in non-twelve-tone scales? To make the listener have an easier, more enjoyable time with the compositions in a scale that he or she has never heard before. For the sake of new listeners. For people to understand and analyze the new composition and its scale--make it simple! For a composer who decides to de-twelvulate it is just plain common sense to begin with pieces that they can do well without a heavy investment in preparation and from my own personal experience this is where and how to begin!

It's quicker and it's cheaper. It's more "transparent." Also, it is more appealing to certain other musical cultures where one might find listeners or grounds for discussion; and it permits beginning with one moving voice against a drone or very slowly-moving second part.

Overdubbing only two tracks is much easier than overdubbing 3 or more. Playing only 2 notes at once or two voices at once is much easier than playing heavy block chords or 4-part harmonies in a new scales. Some scales are not harmonic! How about that? THINK.

Some people have rejected the 13-tone temperament, for example, after scarcely trying it. Others never bothered to try it at all, or snorted in haughty disdain, usually on theoretical grounds. OK, let's begin there. 13-tone equal temperament is not harmonious. However, if you want new melodies, they are there in great abundance, and it's all free of charge. Consider the reason why somebody rejected 13-tone: it has no fifths, it doesn't have a consonant triad, it deviates so far from just intonation, you have to go to the 11th and 13th harmonics in the overtone series before you get any reasonable match. Another argument you will hear if you dare mention 13 to the average musician is "How would you write it down?" We can take that one up later.

Why do you have to write it down? Set an instrument to 13 and try melodies out till something appeals to you. Turn on the tape machine and record that. Where's the problem? Holy Jumping Catfish! Program a computer to generate random notes in 13--this is possible with several existing kinds of software. Why use 13? Somebody will ask you. Because it's different. We all need new experiences. My reason and somebody else's might be "wounded Pride;" Look, man--the resources of 12-tone equal temperament are just about exhausted--just about everything worthwhile that can be said in 12-tone has been said already, and probably better than you or I could. It is humiliating to think that not just us but for an entire generation or two of composers, we came in late--we get the short end of the stick; we get the few crumbs on the table that might remain; over and over we are humiliated by finding out that this or that brilliant inspiration has already been used in Garstig von Esel's Symphony No. 3, or maybe Gromkoshumoff's Fourth Rhapsody. How could it be otherwise in our lifetimes after thousands of composers have done millions of hours at pianos and writing-desks and violins and horns? We are punished for being born after the first decade or two of the 19th century and in the USA instead of Europe.

So back before I was even born, at the last gasp of the 1900's, Wagnerian chromaticism had piled complication on lushness and the orchestra had hypertrophied to huge mammoth proportions, and the major and minor scales had been contradicted with hordes of accidentals and modulations had run riot. Several people thought of abolishing tonality and the seeds of serialism were planted. The popular music world lagged behind, but eventually has caught up. Now with computers and other high-tech means, it might pass it by. I have heard some of these possibilities, and also the way that they sound too much like one another.

In passing, there is now an affair called new Age Music, which often is not new but reminiscent of the 19th Century Romantics or sometimes of Debussy and the Impressionists. Or it may be like the so-called Minimalists--rather monotonous and long-drawn-out....maybe of a background nature. However, there is hope for it--if it can be (or rather its composers can be) persuaded to use new scales, it could be part of the March of Musical Progress. If it is to belong to a real New Age, it has to develop a new idiom and manner, so why don't we offer the New Agers our new Scales and New Resources?

No, don't jump on me--I did not say that the New Agers or many of the experimental composers were going to turn to 13-tone. Merely, some people will use it when they need its peculiar mood or its melodic possibilties attract them.

I mentioned 13-tone first because of the CONTRAST it offers with 12. Because it is UNTWELVE, NEW MOOD, not harmonic in the ordinary sense, a definite break, a new experience, something to break up the hackneyed symmetrical patterns of the highly divisible number 12--2,3,4 and 6 divide 12 evenly, creating symmetrical patterns called the whole-tone scale, the diminished seventh chord, the augmented triad, and the tritone; and also creating a repetition of sounds in spite of the different notations and names given those sounds in run-of-the-mill standard ordinary twelve-tone-tempered music.

13 is a prime number and cannot be divided evenly, so the 13-tone scale has non-repeating patterns and unexpected turns of phrase and asymmetric combinations. This is also true of some other scales such as 17, 19, and 31, while 23 and 29 which are other prime numbers, may not be as important for the composer--but they are there if that is your cup of tea.

Don't knock it till you've tried it--that means hearing actual pieces of music in 13, 14, 15, and so on as far as convenient. In other publications I have suggested several places to start, depending on your ambitions, resources, goals, and facilities.

Some people have scolded me because they thought I was maligning just intonation, but that just is not true: I use it where it is the way to go. How can anybody look at my Megalyra Family of Instruments with colored fret-lines in in just intonation, and listen to my just intonation tapes and keep on making this false accusation?

Two-part counterpoint can be used as effectively for introducing new people to just intonation as it can be used for getting used to a rich palette of new temperaments, equal and unequal. Two kinds of compositions are NOT under consideration here as they way to start using two-part counterpoint. If they were I could just refer you to them and save paper and ink! Neither the antiquarian scholar's 16th-Century Counterpoint in its Species and the textbook Examples nor the time-honored and esteemed Two-Part Inventions of Johann Sebastian Bach are under consideration here. Whatever I may be, I am not the reincarnation of Ebenezer Prout and now that the world is jam-full of those lovely marvelous computers and sequencers and eager-beaver programmers to get Bach performed perfectly so that you don't have to be tortured by amateur bashings of these difficult pieces, I can go in for Progress instead of Nostalgia and Necrolatry and Reminiscence.

Frankly, I am not enthusiastic about Serialsm, especially the only kind anybody ever does, twelve-tone-equal-temperament played-on-the-piano serialism. Its rules are so strict and since they can now be translated into sound via computer without much human intervention, why should I use up the little valuable composing time that I might have remaining at age 72, trying to do better than the computer and all the good programs that will generate 12-tone serialism in huge quantities? Why should you?

I heard a random 12-tone-pitch selector turn out at great speed a never-ending stream of atonal themes--a simple addition to a program could make these legitimate 12-tone rows and now doubt that is being done all over the country, nay, the world. I heard it back about 1977, and now anybody could do better. Sure I know: there are theoretically Factorial-12, i.e., 479,001,600 possible 12-tone rows so there ought to be that many and more possible different compositions made out of them, but they sound too much alike.

I am quite willing to use Atonality when it is appropriate, or I wouldn't be advocating two-part counterpoint in such scales as 13, 16, 17, 18, and many others which can do atonality supremely well. Serialism may have required human thinking and human action when it was first invented or elaborated from Schoenberg's and others' atonality and still others' work that followed the decline of the key-system and traditional harmony. But serialism today is largely if not entirely capable of total automation. Oh, sure: some college composer will deny that and object, but does any composition of theirs in that style sound different enough from what the computers now can do so well that it would be worth the human composer's time?

Let's face it: the Notation Tail is wagging the Sound Dog! Many people I have met during the last four decades or so value a written score far far far above any realization of that score in audible sounds. So much is done with the mathematical and permutational side of Serialism and strict 12-tone atonality that is visible on the page, but not audible to the concert audience or the tape listeners. Much of what is taught in how to compose with serial 12-tone methods will not help in systems which are not symmetrical as 12-equal is because 12 is so divisible.

Back to the 13 tone scale: first Metachromatic scale beyond 12. It works for atonality, and might work for serialism (my friends agree on that). 13 being prim,e the structure is asymmetrical. Since most chords in it of 3 or more tones are dissonant, this is a good reason to start using 13 by composing 2-part counterpoint. As with the other non-12s, start with a drone against a one-voice melody; then move the drone around, then go to two movable parts. As much to make it easier for your listeners as for yourself. After you are comfortable with two-part counterpoint, first improvise trying out three- and more-part chords and take it from there.

The old rules of 12-tone harmony do not hold for 13, so don't annoy yourself or others with them. Now we come to an extremely important matter which by itself would be justification for this article: timbre determines harmony--dissonant intervals in "normal" qualities of tone can be tamed or even made agreeable by changing the timbre. With modern resources of additive and subtractve synthesis and filtering and evvelope control, it becomes easy to make 13 quite acceptable: marimbas, vibraphones, ocarinas, song whistles, kalimbas, etc. Special synthesized timbres. For 13, don't use reedy tones and penetrating string-tones at first. Get into those later on. Tones with special inharmonic partials are quite possible now. Try that if you have the equipment.

Compensate for the reduction of ordinary harmony by increasing the rhythmic element--more catchy rhythmic figures, enough rests in each part, whatever. After all, contemporary listeners are used to drummers playing something which has no scale at all! This makes all those arguments about 13-tone and some other scales being inharmonic, extremely silly. The public listens to the unpitched percussionists anyhow, so these new scales aren't going to stop them either.

Now for the promised remarks about writing 13-tone and other new scales down. Julian Carrillo, the Mexican innovator, invented one way out: get rid of note-heads. Write the half-notes with BENT STEMS. Use numbers instead of note-heads, and reduce the staff to one line. That system is neutral as to what scale it is for, while traditional notation is in favor of certain systems (12, 17, 19, 31) and very awkward for others (22, 23, 13, 10). Another way will be various typewritten codes compatible with computer keyboards and the ASCII system.

Graph paper is suitable for certain notations already in use by some composers, so again this is a system-neutral way of writing something in a new strange scale. But for the purposes of relatively simple melodies and spontaneous spur-of-the-moment improvisations, we really don't need notation with all the recording equipment now available--we can catch our ideas while they are very hot and avoid this dreadful Music In Cold Blood that so many professors ask their students to compose.

Some of your compositions will work in more than one scale. Mainly, it depends on the MOOD you wish to express. Each tuning-system, especially in the region before 25 notes per octave, has a specific mood. This could not have been predicted by theorists in advance, although once it is discovered by extensive experiment, they can then come up with some of the reasons for the mood. Beyond quartertones--24 notes per octave--the mood-differences gradually decrease. 31 still has a very different mood, but by the time you reach 50 or the much-discussed 53 tones per octave, the differences among the systems shrink and in a realistic live performance setting wouldn't matter. You have to use timbres rich in harmonics and play more and more slowly to show the differences. Given the natural tolerance of the average music listener for mistuning,t eh systems beyond 31 will become more and more like mistunings of one another, till they seem to merge.

Consider the various devices and techniques used to make orthodox 12-tone equal temperament bearable or to soften its restless mood. Reduce the number of harmonics to 1,2,3,4,5,6 & 8. That is what the Hammond gear-wheel organ did back in the 1930s. Make the tones die away very quickly (xylophone, banjo, harpsichord) or not quite that rapidly (piano). Add slightly different pitches as fringes: pipe-organ, synthesizers. Violin section of an orchestra.

Use vibrato--most orchestral instruments vary the pitch up and down 4 to 7 times a second; most synthesizers do; singers are taught to do so. Dull the timbre with filters or muting or construction of the instrument. Use synthetic reverberation and effect-boxes.

In order to bring out the personalities and moods of the new tunings, these cover-up or mitigating devices just listen above have to be used with much more discretion. The object or aim is quite different now. We are not trying to conceal the defects of the 12-tone system, but to allow the contrasts and variegated new shadings of the new scales to come through and assert themselves.

We have to remember that this exploring of new scales and composing new pieces to play in them is extremely and drastically different from the usual subdued monotonous background-music environment most of us are subjected to by radio programs, TV sets, music in elevators or stores or markets, or that Music On Hold stuff some of the new business telephone systems provide.

In terms of film or TV, we are converting to COLOR instead of just black-and-white. You know what a difference that change made! The new keyboards have different timbres at the touch of a button, whereas the piano which used to be in every home 60 years ago, has only one timbre. The regular instruments of the traditional orchestra have certain limitations and are very difficult to learn to use, whereas the new kinds of tones available form today's synthesizers and computers are far more versatile. This access to a rich palette of timbres and yes, noises, has come upon us so suddenly that hardly anyone knows what to do with it all!
This indeed has held back progress toward new scales--not only are some of these scales unsuited to piano tone, but it now would cost millions to have pianos in all the scales from 13 to 31, even if they could be built. Where would you put them, even if you were a multimillionaire who could afford them? All that money wouldn't buy you time enough to practice on them, and nobody would have a place to sit down and listen. Who would keep them tuned? Who would even know how to tune them in the first place?

But it is now perfectly possible to have an instrument play dozens of new scales, going from one to another in a matter of half a minute or less, and so small that it is actually portable. Two such instruments are in this house right now. Guitars fretted to ten different scales hang on the walls here. Form impossible dream to hard reality in less than a decade.

Put all those instruments on a weighing scale and they would not add up to the weight of ONE piano! Wake up. It's here now. The problems have vanished.

No longer where to put them, or the cost of moving and maintenence and tuning. It's now Where do you begin?

I suggest, simple melodies, then two-part counterpoint, and for each scale, experiment till you have the proper quality or qualities of tone fitting each scale. If y our bias is toward harmony, then start with 19 and go to 22 and 31. 17-tone turns the so-called Rules of Harmony upside-down...seconds are more consonant than thirds, and many resolutions go in the opposite direction tow hat one would think. Variety is the spice of life.

What point going to the trouble of studying theory and taking up new instruments in new tunings, if you are going to remain tied up in a prison of old rules having no use nor bearing on the new systems? Some people have tried to make new scales obey all the rules of the ordinary piano-oriented harmony books and have tried to keep the new moods from being heard. Other persons who are captivated by the smoothness and calmness of just intonation have tried to stop all use of tempered scales, 12 or anything else. Still others have pretended that synthesizers and computers were worthless and would go away. Instead it's the other way around! The piano is now too expensive. The new instruments have become much more affordable.

Recently I ran into a new notation for the 72-tone scale. This means that there are at least four ways to write that scale, if not more; but I have seen four. 72 admittedly is one of the best multiples of 12. very well, if you can get the proper computer software ( and before long you will be able to get it), you can hear that scale and experiment with it and with a computer you wouldn't have to try to play 72-tone in Real Time. Anybody that actually can play a guitar knows that 72 frets per octave is impractical on any fretted instrument. Unavoidable inaccuracies in construction and strings and performing would reach or exceed 1/72 octave in many cases. Theoretically you can play 72 on a cello or violin but please be reasonable! The usual violinist's vibrato exceeds that.

What's the point of writing scores and parts in a system with that many tones, when you don't have to anymore? I can see the use of writing out textbook examples in a 72 notation or in some journal article on theory. But expecting a player of a conventional instrument to have expensive rehearsals and practice to attempt to play it when there are sequencers and computers and other new means of performing accurate pitches?

What' s the point of writing scores and parts in a system that many tones, when you don't have to anymore? I can see the use of writing out text-book examples n a 72 notation or in some journal article on theory. But expecting a player of a conventional instrument to have expensive rehearsals and practice to attempt to play it when there are sequencers and computers and other new means of performing accurate pitches?

If trained professional musicians can't play ordinary twelve in tone on stage throughout a performance, dare you ask them to convert to 72? Who's going to pay the money? Who has time to practice even if they could? I wish I didn't have to bring this up here, but if I go up to scales beyond 31 or to use just intonation extended or expanded to the point that it needs over 50 or even over 100 tones per octave, the effort would be used by traditional musicians and critics to make fun of all explorations beyond 12, tarring them all with the same brush.

For 60 years now I've been pelted with straw-man arguments and reductiones ad absurdum, by my colleagues, by my own teachers, by other musicians and composers, so I caution you: don't let ridiculous argument go unchallenged: don't let them stand. One false premise is that if it was good enough for Bach and beethoven, it has to be good enough for us. OK...if all our ambition is to be clone of the past or a reincarnation of Brahms or Schumann or Debussy. Another false argument is that all music must still be performed in concert-halls form printed scores on conventional pre-electronic instruments. Why? We simply cannot afford to anymore!

Of course I want to hear something in 72-tone or even 87 or 171. But I will not have to write it down. I will not have to ask anyone to perform it. Nor need you wait at all either. But I presume that most of your prefer to start at the beginning and also wish to accomodate new listeners as well as yourselves.

Hence I spent time on the 13-tone scale as the first thing beyond 12. Now we are ready to discuss some other nearby scales.

14 = 2 x 7. By that I meant that some people might want to try 14 first, since something in the ordinary 7-tone major scale will usually be still recognizable when played in the Equal 7-tone scale. Major and minor sort of collapse together, and the modes collapse into the keys. That is, a transposition of something in 7-tone-equal into another key is the same thing as going from one of the Church Modes to another in the ordinary 7-tone white-keys scale on an ordinary 12 system instrument.

There is a circle of 7 fifths in 7, 14, and of course in 21, not a circle of 12 fifths. (In 13-tone it's kind of absurd to speak of fifths.) The fifths of 7 or 14 are quite distorted. But using a bland subdued quality of tone the melodies we already know still are usable in a 7-equal scale. Note that the tone-vs.-semitone distinction in the ordinary major scale has vanished. That's why modes and keys have become one. 14 has a second circle of fifths and there is no 14-tone circle of fifths, but TWO 7-tone circles. We can restore something like our familiar whole- and half-step patterns by using the other 7 of our 14.

Haven't you ever stared at a regular piano keyboard and wondered what would happen if there were black keys between B and C and also between E and F? 14 lets you hear what would (and now does) happen. We suggest that you call the first set of 7: C* D* E* F* G* A* B*. You can't very well call them sharps and flats because they are another circle of 7 fifths and NOT reachable by fifths of the 14 system from the naturals. 14 works fine anyhow. Now, with all 14 you can construct very large major thirds and very small minor thirds and play most existing music in 14 if you insist. You may or may not like the effect. Explore. The important matter right now is: 14 has a NEW MOOD that you can use. It sounds different from 10 or 11 or 12 or 13 or 15 or... You don't have to use it if it annoys you. But don't knock it till you have tried it.

On to 15. 12 = 4 x 3; 15 = 5 x 3. So 15 has symmetry to some extent. More important, 15 contains Equal 5-tone which is a very important scale used in many places around the world, and equal 5 is something the Western World has been deprived of. In 15-tone you have 3 sets of distorted fifths but there must be something good about equal 5 when so many widely-separated cultures have tried it or use it now. What to call the notes? Probably just number them 0 through 14 or put 15 = 0 or 0/15 or something on the starting pitch (whatever that is). However: since 15 is 5 x 3 that means that 15 contains the familiar major third of 12-tone which is one-third of an octave. This suggests (but does not compel) having A, C# and F be the three notes of 15 which are to coincide with those notes in ordinary 12-equal. This in turn means that it can be used with an ordinary 12-tone instrument, going from the 15-tone instrument to the 12-tone one back and forth--some composer have done this.

The minor third in 15-tone is excellent. Therefore th major sixth. By the way, 15s mood is not as weird as that of 10 or 20, so probably 15 is a better place to begin using 5.

On to 16. 16 is a very symmetrical scale since 16 = 2 ^{to the 4}. 16 sounds quite weird to many people. It contains 8-equal and the 4-tone chord usually called the diminished seventh chord. A number of people have proposed 16--personally I don't know of many compositions in it. Presumably, those who work with symmetrical patterns will be attracted to it. Definitely a different MOOD, so worth hearing on that account. The contrast with other scales is what matters.

17 has already been mentioned: 17's mood is brilliance, purchased at the price of some harshness. This scale has been used in a number of cultures, or something like it. 17 should appeal to violinists and other string players because of its similarity to the Pythagorean scale which has sharp major thirds, and the fifths of 17 are very slightly sharp instead of flat, as they are in some other scales. What this means is that most of the solos preferred by violinists, violists, and cellists are going to sound fine in 17 and take on an added sheen. The ordinary black-key pentatonic scale, 5-out-of-12, taken on a new colorful zest as 5-out-of-17.

As already mentioned elsewhere, ordinary harmony rules are radically changed, almost turned upside-down, in 17. Seconds and fourths, and chords containing them, improve; thirds and sixths are dissonant. This makes 17 valuable as escape from humdrum hackneyed harmony. If melody is your bag, try 17 first. You have many other scales to use when harmony is the principal consideration. 17 is excellent for the two-part counterpoint we are recommending as your first step in breaking away from 12-tone. But don't close the section with a third or sixth--use a fourth or fifth instead.

Now for 18. 18 is the "third-tone" scale--used and recommended by Haba and Carrillo; recommended by some others, espoused by the noted pianist/composer Busoni, who however didn't live long enough to get down to important business in it, more's the pity. 18 has no real fifth. 12 = 3 x 2 x 2; 18 = 3 x 3 x 2. So 18's symmetry is about the same as that of 12. Carrillo had a grand piano in 18 as well as an upright. A number of compositions exist in 18 by various composers. Busoni wanted 18 because of the value of the "tripartite tone" or third-tone or third-step as I would like to call it. Debussy's whole-tone scale with its vagueness is contained three times in 18 so 18 transmits this mood. Combined with that is the special mood of the 9-tone scale since 18 = 2 x 9.

This is a good place to mention that Busoni wanted to use 36 so that one could accompany an 18-tone melody with harmonies in 12, and now have to give up fourths and fifths. He proposed notations which have very little in common with other notations for 18 and 36. It is unfortunate that these advocates of 18 never heard about the existence or usefulness of either 17 or 19; those systems have fourths and fifths, and are melodically, third-tone systems just as much as 18 is.

The 19-tone scale is next. We have to spend some time on it because it will probably be used more than the others in the 13-through-24 region, the region of systems I would like toe call metachromatic--I have been looking for a good name for some years now. Not microtonal certainly, because the intervals of all the scales up to 24 and perhaps including 24, are still wide enough to be melodically distinct and useful for creating new melodies.

In recommending two-part counterpoint as your early experimenting in these scales, and as concession you well might make to your new listeners, before you go in for heavy chords, doubling, and elaborate lushness at the beginning stage of performing and composing in Non-Twelve Systems, I realize I am going against the recommendations of an important book which tried to promote 19-tone....one recently reprinted by the way: Joseph Yasser's Theory of Evolving Tonality.

Before I dared refute or contest his argument in that book, I have composed and improvised and performed and built and modified instruments in 19-tone, his recommended next step in musical progress or evolution as I guess he would call it. Other people have followed me as well as the considerable number who have preceded me in exploiting the nineteen-tone system. Yasser was more the theorist, who wrote about it--back in the 1920's and 1930's he could not possibly have had access to the resources you and I would not find available.

So let's excuse him for speculating or predicting the course of evolution--he had no crystal ball or time machine to journey into the 90s and hear what people will do with 19 in the next decade. I read the book soon after it got printed and put in the libraries. I have read many many citations of the book. I have corresponded and discussed the book with dozens of people.

Moreover, I have refretted many guitars to 19 and tuned instruments to 19 and constructed tables to assist tuners and refretters. I know about unequal 19 and 19-out-of-31 and stretched-octave 19 and other possibilties--there is considerable potential there. So I speak from practice, not just speculation or silent theory.

in the present article, I recommend that you use ALL the non-12 systems you have time or chance to use, but Yasser had a series--a Fibonacci series by the way, of systems which goes this way: 5 + 2 = 7; 7 + 5 = 12 (the ordinary tuning); 12 + 7 = 19; 19 + 12 = 31; 31 + 19 = 50; and so on indefinitely into the very far future. So he practically forbade any investigation of 13 or 14 or 15 or... and fulminated in harsh terms against the 14-tone scale--if fact, I thought "if Yasser is so angry at 14 and writes so many paragraphs so emotionally against it, there MUST be something in it!" So I built a 14-tone set of metal bars and refretted a guitar to 14-tone and lo and behold! Many people like it when they try it.

He thought that over a thousand years would pass before 12 gave way to 19, and that 31 was too far into the future to write about in his book and 5 and 7 equal temperaments which do exist or approximately still exist in many parts of the world, gave way to 12 about a thousand years ago or something like that. All music HAD TO EVOLVE IN CONFORMANCE TO HIS THEORIES--an never mind the facts! Again: in the 1920s when he was writing and thinking about it, he couldn't possibly have tested all his theories against actual sounds of instruments that didn't even exist yet! Refretted guitars, many of which are electric, synthesizers, new kinds of electronic organs, computers, and all the marimbas and metallophones and tubulongs that now exist in non-twelve scales.

So we mustn't be too hard on him personally. What I really want to emphasize here is the consequences today of many people having read what he wrote in his book and failing to realize that we can now do and importantly can AFFORD to make or buy what he could not possibly have imagined.

Indeed, something I discovered myself in 1962 when I first heard a copy of a tape recording by Joel Mandelbaum who had two pianos put in the 19-tone scale (back keys on both tuned to the same 5 pitches; white keys tuned differently on each piano). I discovered the unique powerful MOOD of 19. Something nobody predicted because they weren't even looking for it.

I would have given up on non-twelve if I hadn't heard the MOODS of a number of non-twelve systems and the wonderful new CONTRAST of them with one another and with ordinary 12.

Yasser predicted or constructed a new set of note-names--adding V W X Y Z to our familiar C D E F G A B. This was to set up a supradiatonic scale of 12 pitch-classes against which the new 7 added pitches of 19 would function as the supra-sharps and supra-flats and therefore the new 7 pitches would have at least two names.

Sorry about that; but it doesn't work out that way for me or at least 10 other persons acquainted with 19. Then he constructed a ten-line staff instead of our 5 lines. That would make lots of money for optometrists!

Well, maybe that is not too important here, but I am leading up to something else which conflicts with my idea here of composers and listeners starting out with two-part counterpoint and listening to dyads before they try triads: Yasser basic chord.

Yasser argued over and over again for gradual evolution by steps over centuries; not sudden jumps to a new system. Yet he JUMPED from a five- to a ten-line staff and worse yet, from a basic triad for today's orthodox harmony to a HEXAD--from 3-note chords to 6-note chords without passing slowly through 4 and 5 on the way to 6.

The listener to the future composers he was laying down the Law for, would be confronted with extremely complex harmonies at the outset. The theoretical basis for this was the members of the Harmonic Series 8:9:10:11:13:14. Some writers on music had speculated that Alexander Scriabin the fellow-Russian Composer, had based his famous chord C-D-E-F#-A-Bb upon those same members of the harmonic or Overtone Series, but this Scriabin matter is moot.

Some recognized writers have analyzed Scriabin's chord as polytonal--the superposition of more ordinary chords from different keys and/or modes. Others have dealt with it in terms of the harmonic series; still others have considered it merely as ambiguous. Since Scriabin's music works anyway, I will not take part in argument.

The poin there is simply that Yasser evidently took the harmonic-series point of view, and because there is no perfect fifth in Scriabin's chord, Yasser thought that the portion of the harmonic series he would use would omit the fifth also--i.e., 8:9:10: - 11:13:14 without any 12 th harmonic (12 being an octave of 6 and 3 of course). Yasser's other reason for omitting the fifth was that the fifth in 19-tone is 7 cents flatter than just instead of only 2 cents flatter than just as it happens to be in 12-tone temperament, so he was worried about this spoiling all 19-tone harmony. Well, there are counter-arguments to that that I didn't have to invent: other people brought these up: No. 1 -- How does Yasser get 9 without first getting 3--or how do you get the interval of a major second or a major ninth without first getting a fifth and piling another fifth on top of it? Or how come the ninth is more important than the fifth? More basic? No. 2 -- Even the 5- and 7-tone equal temperaments have some kind of fifths and of course the fifth in 12 is better--why must we give up such an extremely important interval? No. 3 -- the eleventh, thirteenth, and fourteenth (seventh if you want to disregard the octave) harmonics are very remote compared to the third harmonic that generates the fifth, and even if you are going to add them to your scheme, why not the 7th harmonic first, then the 11th (thus far as Partch did), then the 13th later?

This jump, not evolution by degrees, from triad to hexad. There is a hexad in common use today, however: Debussy's whole-tone scale which is also a chord, therefore it is a hexad. If Yasser had not brought up harmony so much as against melody, and if he hadn't made so much fuss about omitting fifths from his chords, we might let all that pass since the whole-tone or whole-step, as I would prefer to call it, is definitely a melodic interval. The error of the 9th in 19th-tone is twice the error of the fifth of course, so why admit the interval whose error is twice as great? Something funny going on there!

Out of common charity I will not argue about the 19-tone-equal errors in the 11th and 13th and 14th harmonics.

I had to bring Yasser's theories up because I want our new listeners, yours and mine, to have an easier and more pleasant time of it, listening to what we do or will do in 13, 14, 15, 16...on up to 31 or more. Two-part counterpoint will be much more transparent than six-part counterpoint or ordinary solo-and-accompaniment writing with hexads all over the place instead of the triads we ordinary harmonize with. Sure: we will go onward and upward in each scale to more complex things as each scale permits. But first things first! There is too much theory and not enough practice. There is too much history of music and not enough respect for today and the present time.

There is too much tendency to make music very complicated and to take pride in knowledge and look down on the listeners--well, are we merely talking to ourselves in a tiny closed world? Whom are we composing for? In musical composition supposed to be autistic? Ignoring all the other people out there in the world besides the composer?

It's not a question of making all non-twelve music childish. Merely a question of having enough composition of the nature of gradual introductions to each scale for new listeners. When a new scale is used that was hardly ever been heard before, such as 13, 16, 23, 35, and others, the composer can be less fearful of repeating something that has already been done too much in the standard repertoire. This means in turn that what is done in the new scale at first can be less complicated when the risk of accidentally doing what has already been done too many times by others is reduced.

Certain of the new scales are not suitable for transferring existing conventional music into them, which again means that there will be less temptation to do this. Other scales, such as the 19-tone system we are discussing here, are very suitable for playing existing music--which in most cases will remain entirely recognizable. What will happen when existing music is played in 19-tone will be a change in MOOD. This can be for the better or for the worse, and that is hard to predict. Somewhat easier to predict the change improving or degrading the older music when playing it in 17 or 31. In 17, brilliance and maybe harshness increase; in 31, smoothness and perhaps a soporific effect.

This is a good point in the discussion to bring up the subject of INTIMIDATION: reactionary and self-styled "conservative" music teachers and performers are against progress--they usually love the Classical and Romantic periods of the 19th century so fervently and intensely as to want to embalm the old styles for all eternity and discourage anyone living today from the slightest attempt to evolve tor break from the Central Europe of the Past--well, Central Europe today is changed, so we in America shouldn't be afraid to get in tune with our times either.

Generally, the more radical and strange a new religion or cult is in this country, the more they cling to the old hymns and other 19th-century church music so there is this near-contradiction built right into their practices. So don't look for musical progress there! Some years ago I had a book of music that was popular 200 years ago during the French Revolution. I did the experiment of playing some of the short pieces for various people at various places and they thought it was conservative church-organ stuff! Sometimes I dared not reveal what this book said in French on the cover!

The drastic upheavals of the Russian Revolution didn't make for musical progress but rather for a considerable slowdown in music. Various factions in the Left have seldom promoted any change in music, and so political innovation either Left or Right does not seem to foster musical progress, in case you've wondered. Even more remarkable and unexpected is the fact that almost every science-fiction fan or club or aficionado or author that I have ever spoken to seems to be against progress in music--indeed some of them got very hostile and resented that I was going what they thought should only be DREAMT ABOUT in our generation. I have had to stick it out through40 years of this!

Intimidation is possibly the greatest risk you face when beginning to promote xenharmonics or this metachromatic region of new scales just beyond the orthodox customary 12-tone equal temperament. Forewarned is forearmed. Don't look for sympathy or encouragement in certain places where you might think you will get it. I learned that the hard way over a forty-year span. I don't want you to start out as an eager beaver and be suddenly let down and disillusioned and give it up before you have any chance to hear something new or to make something that differs enough from run-of-the-mill stuff to be worth your time and effort.

I don't want to waste my time writing pamphlets like this if some Professional Sourpuss Intimidator on a Power Trip is going to slap you down next Thursday. That's why a warning belongs here. There has been far too much writing ABOUT change in music and next to no DOING it or HEARING it.

There has been a too-often-repeated "scenario," something like this: someone with considerable writing skills recaps music history and various developments in the musical world up to the present. Usually they are well-versed in such things as pianists on the concert stage and famous virtuosi of a hundred years ago and remarkable opera singers of the past and perhaps the writings of Richard Wagner or the "genealogy" of music teachers through the last two centuries passing on to pupils who become teachers passing on to pupils who... Or these authors writing now or recently have themselves taken college courses under professors who usually teach 12-tone compositional methods after the various successors to Schoenberg.

These authors furthermore seldom have contacts among electronic engineers or physicist/acousticians or instrument-makers or inventors or amplifier repairmen or synthesizer designers. If they very recently have been forced to acknowledge the existence of computers, it is only to learn word processing or to have somebody manage their finances via computer or how to run one of those ATM affairs connected with their bank. Hardly ever to get even a layperson's smattering of what computer music is and does and can do that pianos cannot. Their conception of technology is 17th or 18th century in terms of piano actions or maybe 19th century in terms of key-mechanisms on saxophones and bassoons and maybe the valves on a French horn.

If that. Musn't touch. "Real musicians don't fiddle the piano keys." "Leave that to the specialist." "Shoemaker stick to your last." They never question 12-tone equal temperament and suppose that everything else was dead and buried as of 1800 or so. They assume that when the 19th century ran its course, and from elementary tonic-and-dominant chords accompanying melodies it went to Wagnerian chromaticism and then to the whole-tone scale and and complex chords and polytonality, that the era of regular tonality was exhausted, so the only inevitable way to go was atonality and then serialism and Total Serialism where there was no need for inspiration and there was absolutely no other Wave of the Future. Tonality was dead. Except that you must worship dead composers so must continue to play their things.

Popular music lags behind serious music in that respect and its harmonies are generally borrowed from the last 200 years. New instruments and an emphasis on rhythm does give some change of course. The arrogance of the other arts, both "fine" and "commercial" is such that music is supposed to take second or third place as an almost unnoticed background to theatre, cinema, television, radio broadcasts, etc. Distraction to be turned on and off like decorate lighting, for instance.

Photographers for the magazines and lighting specialists are important members of popular entertainment bands! Visual image is almost more important than their Sound. Something is wrong here. One thing is hopeful though: they admit that synthesizers exist, that timbre is important, and that pitch-bending is a factor, while classical romantic ensembles use pitch-bending but ignore it in public and try never to mention it.

So the abovementioned book about promoting the 19-tone scale, Yasser's Theory of Evolving Tonality, was not esteemed or heeded by the serialists and atonalists and 12-tone theorists and the users and worshippers of pianos during the 50 years or so since it was published--they did not think Evolution would ever go in the direction of new scales. No; the only escape from 12-tone equal temperament they were willing to allow was--get this!--NOISE.

There is an unwritten law in the USA that you may not discuss contemporary music without John Cage twice. So now I have mentioned John Cage twice--let's get that out of the way. "Inventor of the Prepared Piano"--so he is celebrated. Not the builder of a radically new instrument or something like Partch's impressive Bass Marimba. No, making fun of the Musical Establishment mercilessly by stuffing assorted oddments into pianos. This does point out the monotony of piano timbre but it's the end of a great era, not the beginning of a new one. It doesn't inspire you or me.

Somebody has to do that, of course, but do you want to be a clone of him? There are thousands of possibilities right in front of us for building NEW instruments. Electric or not. Not necessary to re-work old ones.

We reached 19-tone in our survey so far--it will cost you less to make a set of metal tube or bars or a marimba in 19-tone or to load 19 into a sampler or modify a synthesizer, than to get a piano and try to force it into 19 which is a very poor hopeless makeshift. Two pianos and two performers can do 19 if the tuner can tune them, but that is fantastically expensive these days and it goes nowhere since each new scale you should try at this stage of leaving 12, would be an equally horrendous expense in floor space and time and maintenance whereas new instruments can be designed for 19 at the outset and designed for 13, 14...31, just intonation, whatever. The cold hard realities of COST should be sufficient to deter you from trying to make a piano over. Send the 19th century back where it came from! Are you man or mouse? ALso, why not re-fret guitars? GuitarS plural--I made up fretting-tables for many scales and string-lengths.

Let's get into that for a moment here: there also are such things as interchangeable fingerboards for guitars that have been modified to take them. For steel guitars it is possible to change fret-line-charts under the strings and temporarily hold them in place. That is feasible on the Megalyra Instruments of course.

The advantage of separate guitars for different scales is that one can go from one guitar to another in a few seconds without having to retune the strings to the next scale; therefore the listener has no chance to forget the sound of the scale just quitted. Rapid alternation between two or more scales being compared is possible and convenient. The disadvantage is storage space and floor or wall space.

A scale like those 13 through 18 which have dissonant intervals and some of which lack fourths and fifths, will still be effective on a guitar with short sustain (more rapid decay)--17 is marvelous on a banjo with its brilliant zippy snap. I.e., the type of guitar or fretted instrument can be chosen for the scale to be fretted upon it. Electric guitars with long sustain are suitable for such scales as 19, 22, and 31.

Most theorists will condemn scales like 19-tone without a hearing--literally! They will point to the flat fifths and sharp fourths (7 cents sharp) as Yasser et al. did. They should be fostering musical progress but instead they try to halt it. They usually will cite Just Intonation and the wide deviations of a scale like 19 from just intonation--they won't even mention 17 let alone 13. Why so? because they do mathematical calculations based on HARMONY and try to put Harmony first when it is really in THIRD PLACE--the other is RHYTHM, MELODY, HARMONY, and possible TIMBRE as fourth entity. Whether to set up Envelope (attack and decay, sustain and release) as a separate factor as is now the rule for synthesizers, as a fifth element, and possibly proportion of Noise as a sixth--or shall we include percentage of noise as part of the fourth-place Timbre Entity? All that is up to you.

The importance of the 19-tone-equal intervals different from those of Just Intonation depends upon Timbre, very much. It also depends upon Tempo--how fast will your new piece be played? I began this article with mention of our hurried impatient helterskelter pace of everyday life--it couldn't have been that way in the 17th century in the average European village. Your audience for a new piece is usually someone who is being prodded and goaded and made to rush fast through life, not someone on a farm in the Middle Ages nor yet an Easterner practicing medititation in some religious cloister or temple or monastery. The rules and environment today are different and we have to live in them.

The average person just does not have the money or time to take up learning all the new notations that would be required to write the new scales we are discussing here and nobody has the space to put all the special instruments that would be required to do everything the 19th-century way or acoustic instruments and nobody has the time to practice on 15 or more different kinds of keyboards or wind-instrument mechanisms. So all these scales had to wait for means of fixing improvisations and editing them later. It is out of the question to expect some professional musician to learn 20 or so new scale and practice in them just for you. So that is another reason we have had to wait--till the means of overdubbing and the means of having computers and software superpose parts and automate the tuning and retuning process, appeared and came down in price to some degree.

Why pretend this is still 1870? Or 1680 as some people do? WHy have religious-cult idolatry for the past and contempt for your own time? I'm getting flak from some of these people right now.

Before we go on from 19, ordinary staff notation and names work for 19, so for some people this will be a very comfortable entrance-point for leaving 12...19 has harmonic resources.

On to 20-tone: not much has been done in this system. It is a multiple of 5. So the mood and character of 5-equal is available in it. It has symmetry since 20 is a divisible number. 4 places to transfer to or from 12. Mood is very different from that of 19.

21 is another multiple of 7. The same advantages that occur in 14 because equal-7 is there, obtain in 21. Many melodies already in existence could be played in 21 and still be recognizable. That may or may not be an advantage or improvement, depending on the mood. 3 places to enter or leave 12. This transferring business may be useful to some composers.

On to 22-equal. This is NOT the 22 srutis of India. It does have some resemblance to them, however; also some theorists in India have considered 22-equal or written it. The value an captivating mood of 22 have, alas, remain unknown to the musical world for far too long. Color, character, versatility, and it is much smoother and more restful than the weird quartertone or 24-tone equal temperament that has received the lion's share of attention.

Many things which will work in 24 will also work in 22 and vice versa. Shameful neglect of 22 caused mostly by the difficulty of writing it in notation. WHy not number the tones as Carrillo did for 12, 18, and 24? Works fine.

Don't neglect 22. Well worth your time!

23 is another prime-number scale, very strange--sometimes written about but little-composed-for. Those interested in harmony might double the number of tones to 46 if they have some means of playing it on a computer or the like.

24, the quartertone scale, has some literature and some earlier quartertone pieces are now being revived. It is not suitable for piano tone, so until other timbres became affordable and easy to use, that has held quartertone composition back. It does not leave 12 because it contains 12, twice over. That may or may not be an advantage for a particular composition. Ironically: 19 and 22 have more resources than 24.

Beyond 24, except for the very important 31, no poin there going into detail for each scale. This is not the right pamphlet to do so, and the mood-differences begin to shrink beyond 24-equal and some complicated affair like 41 or 53, despite its obvious value and mood, is not the place to start composing two-part counterpoint for new listeners to the vast territory outside 12.

When I can and I have recorded in scales beyond 24 and also I have recorded in various versions of just intonation, listening to those tapes is much more valuable to you than words words words words.

The 3-limit subset of Just Intonation, i.e., the Pythagorean system, is excellent for two-part counterpoint. It is the system for which our staff-notation, sharps and flats, and the usual name0-system and key-signatures were designed. So you might be able to interest violinists in a Pythagorean piece if they weren't too busy. But don't count on that! After over 55 years of bitter experience trying to get people to perform something, don't expect miracles. Set it up on some electronic affair--I mean something like 24 notes of Pythagorean--and lay down your two tracks.

The 5-limit set of Just Intonation--that which features pure beatless major and minor thirds--is taken up despite all its problems (the difficult of tunign the commas and of using them to prevent those dissonant false fourths and fifths) primarily for the sake of Harmony, rather than Melody. T he comma is quite small for a melodic interval in its own right, so a simple piece of two-part counterpoint--well, use other scales instead and wait a while. One problem at a time, for composer AND for listeners!

Further expansions of Just Intonation, again, to 7--, 11- and further limits, are primarily in search of new Harmonies. Very important for you to work with, but no tin two-part counterpoint as a means of getting new listners interested.

Now for 31-tone and the Meantone Family which it really belongs to, since 1/2-comma regular Meantone and 31 are not audibly different in actual performance. The 31st of an octave is getting small for a melodic interval in its own right, although it is still audible under many conditions, but with rapid tempo or noisy environment it blurs. For the initial stages of two-part counterpoint, a piece in 31 should be played more slowly.

31 really shines when Harmony is the chief consideration. Xenharmonic Bulletin Number Nine discusses this in detail.

It wouldn't have done too much good to have written this article back in 1960 or even 1970--instruments with automatic tuning to new scales and with rapid retuning capability to go from one scale to another, were hardly in existence then. But now this is feasible.

Probably a good idea for you to get a tuning-device even if you are not planning to build an instrument. You need to check the accuracy of whatever instrument you have, of a synthesizer, of computer software for that matter. You need to keep track for drift--most instruments will not be rock-steady forever. Most commercial tuning-devices work in terms of deviations from 12-equal at A=440. You need to check accuracy of fretting on guitars or the like.

If you are in a club or group, perhaps you can share a device.

Learning to tune enough new scales by ear alone is out of the question of course; that is what held back microtonal progress for over 200 years. The old-fashioned HarD Way is not necessary anymore. You can't trust you ear in matters of this kind when you have not even been allowed to hear most of the new scales. Tape recorders are not steady enough to tune by in new scales.

However, tapes work well enough to acquaint you with the sounds of scales up through 24 notes per octave. Some new recording devices about to come out show some promise of sufficient steadiness to be of use in checking new instrument and scales. That remains to be heard.

During the next few years more and more recordings of new compositions in new scales will come out and you can collect them to decide where you want to explore. It's still difficult now to collect enough examples of new composers and new instruments, but this affair can only get better.

Maybe you wonder why I have not put any music-notation examples in here. It would mislead you, that's why. You would "hear ordinary 12 in your mind" and that would ruin all I am trying to help you with here. It's a trap. You cannot imagine what you have never been allowed to hear, especially when you have been programmed/indoctrinated in orthodox 12-tone-equal for all your life. I know for sure it does not work.

One possible way to enter non-twelve is the Ancient Greek Tetrachord Patternss and modern variations of them, especially the Enharmonic Genus and various ways of representing enharmonic patterns via the new scales. John Chalmers has compiled a list of tetrachords recently. Starting with enharmonic tetrachords, add a few more notes as you compose more themes and selections. 22 and 24 tones/octave are the best places to begin that way. CAUTION: ENHARMONIC HERE DOES NOT MEAN TWO NAMES FOR THE SAME PITCH--IT MEANS PITCHES DIFFERENT BY AS MUCH AS 1/31 OR 1/22 OCTAVE OR MORE!

From the point you and I have now reached here, we MUST go to actual sounds on some kind of recording! Otherwise it is a pointless exercise in futility. Demand that all pitches of a new scale be equally and always accessible to you--at least up to 24 pitches always available to you at the same time.

12-out-of-13 or -14 or...is a waste of time and you will give up trying.