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New Musical Instruments
Harmonic Series Music
Plans for an International Microtonal Arts Center


I'll describe three of my new musical instruments here.

The first two instruments are extensions, expansions, enlargements, and extrapolations of the Hawaiian steel guitar idea. The third instrument is a contrabass steel guitar.

Very well, what has this to do with xenharmonics? The steel guitar happens to be a popular instrument which at the same time is suited to just intonation and to what I have been calling justified or tempered temperaments. Putting it more bluntly, the steel guitar has snuck just intonation into the musical world by the back door.

Despite the 12-tone fret-pattern painted or silk-screened onto the non-fingerboards of virtually all Hawaiian steel guitars in existence, this fret-chart is by its very nature a mere guide, not a precision pitch-determiner-and-quantizer.

The parallax error in reading the fret-graduations on the board beneath the strings will guarantee continual deviation and inaccuracy in the placement of the steel. This is similar to the error in reading the position of the needle on a voltmeter, since the needle must be an appreciable distance above the surface of the dial which bears the numbered scale.

However much of a disadvantage and problem this may be in the world of electrical measuring equipment, it is a fortunate and happy circumstance where steel guitars are concerned! The ear and not the eye becomes the arbiter of where that steel goes, and this results in just intonation or at least something superior to 12-tone equal temperament, more often than not.

The orthodox uptight world of serious music has of course looked down its collective nose at the Hawaiian steel guitar with a haughty contemptuous sniff, ever since the instrument was invented: indeed they have carefully pretended it never existed!

Let me concede here and now that there have been two good reasons for criticizing the steel guitar: its abuse by untalented novices who do not have sufficient sense of pitch, or who have not been trained; and the restriction of the first commercial models of the instrument to an A-major chord.

Also, at the time when the instrument first became popular, the gulf between serious music and popular music was a much wider chasm than it is today; and the imitation-Hawaiian stuff played on the first steel guitars was definitely not in the mainstream of the jazz or standard or popular music of that time; it was off to one side and something of a novelty or special effect.

During the postwar period and the fifties, the instrument was more or less forgotten. More recently, it has come back in improved forms. Various means have been resorted to permit playing minor chords, for instance: seventh or eighth strings have been added to the original six.

For a while there was a vogue for double, or even triple, necks so that two or three sets of strings could have different tunings.

Finally, someone borrowed the pedals from the elegant status symbol of the late 19th-century concert stage, the Erard double-action harp, and the pedal steel guitar was born.

Those pedal instruments which I have had a chance to examine had two or three sets of ten strings each. The pedals affected only a few of the 20 or 30 strings, raising them a semitone, as on the conventional concert harp, where the pedals raise all the strings of a given name one or two semitones, depending on whether the pedal is locked into the first or second notch. (Ex.: F-flat to F and then F-sharp.)

In effect, this is a case of the 12-tone tuning trying to tame or discipline the steel guitar, by installing something on it that alters the pitch one-twelfth of an octave.

I wonder what Partch would have said about this: Expletive Deleted no doubt. Of more practical importance, the drawbacks of the pedal guitar are that it is less portable, since it must be on a stand of some kind; and it is fabulously expensive -- in the kilobuck region I would presume.

The reason I describe it here, is to clue you in on the state of the art as the patent attorneys or technical journals would say; to indicate the place my new instruments or modifications of them might come to occupy in the contemporary context. Some of you may prefer to go in some other direction than I have.

Also, in a bulletin of this kind where I can't include all kinds of pictures of instruments and where the readers will be of such widely different walks of life, I have to describe my new instruments in terms of what commercial products they resemble, giving similarities as well as differences.

The desirable aspect of the pedal instruments' design is the clean break from the hourglass silhouette and separate neck of the Spanish guitar, since these features are no longer necessary for an amplifying instrument with so many strings, however attractive they may be for regular acoustic Spanish guitars.

But it would be better still if this new affair and perhaps the other forms of the Hawaiian steel guitar were called by some new name or names -- vroomla or maxiwiz or sliggit or whabajee come to mind as possibilities or maybe we can even cook up a different name for each instrument.

The Spanish guitar is digital and the Hawaiian guitar is analog, to put it in modern data-technology idiom. Surely this profound difference is more justification for giving them distinct names, than the calling of the same instrument a dulcimer or a psaltery, depending on whether its strings are struck or plucked.

This lack of a really distinctive name may be one of the reasons why the steel guitar is not adequately described in reference works, and why no one seems to consider its use in the more serious kinds of musical composition.

You cannot write for it in the same way you would write for Spanish guitar, and to make matters worse, much of the music and instrumental material for it is published in a tablature or nonstandard notation, convenient for some performers but devilishly difficult for the composer. As for me I gladly play the instrument, but I will not write for it in that tablature! I promise that I won't emulate Partch in inventing special notations or tablatures for my new instruments...there are other ways out of the situation.

Back to the matter of just intonation:

Because the vast majority of steel guitars are electric, i.e., they have electromagnetic pickups built in, and are amplified, and further because the amplifiers used for such instruments generally have what is called intermodulation distortion by sound and electronic engineers (it was called beat-tones or combination tones or difference-tones by the acousticians of yore), the sounding of two or more pitches at the same time will cause the sounding of additional pitches as well. Difference tones of the first order are the strongest, being equal in frequency to the difference of the two original frequencies, hence the name. These may interact with their generators, producing difference tones of second and higher orders. This used to be text-book stuff, mostly confined to physics labs.

Now, everyone can hear it. You know how loud the rock groups play these days, with their high-power amplifiers. Then there are tinny $8.95 record-players and those ubiquitous transistor radios, all with their quota of intermodulation distortion. (The engineer's modulation has nothing to do with the musical term modulation.)

Even the summational tone, which was extremely rare and mostly a mathematical theorist's curiosity, can be heard nowadays.

The summational tone has a frequency equal to the sum of the two tones generating it, and when heard, is more annoying than difference tones.

Tempered intervals produce false combinational tones, which make the music harsh and coarse. So with the coming of the steel guitar and its amplifier, there is almost a compulsion to tune the chords just, so that the combination tones for the major chord will be a true bass, and the combination tones from minor and other chords will be more tolerable. It greatly improves the general effect to have justly-intoned chords; everything sounds cleaner. It improves the mood.

Over 110 years after Prof. Helmholtz argued and pleaded for some use of just intonation to get rid of those false combinational tones, he is having his revenge in a manner he could never have foreseen. The electronic organs and amplified everything are taking care of that!

So the just intervals and chords have survived in various nooks and crannies of the musical world, and now the alleged villain, intermodulation distortion, bane of all hi-fi addicts, is encouraging some steel-guitar players to tune their strings to exact integer ratios although they may not be conscious of doing so.

Very well; the steel-guitar idea is current, and this instrument is well-suited to demonstrating just intonation, and it can be combined with other instruments, and thanks to amplification, nobody else can drown it out.

Your friendly neighborhood pawn-shop probably has one; so, fellow-experimenters, what are you waiting for? It's a valuable addition to any music theorist's laboratory.

A while ago I acquired some pieces of wood suitable for instrument-building, but only lately have I had time and facilities to go ahead with them.

I was curious to know how far the steel-guitar idea could be carried. Last year, when I built the first four-sided instrument with really long strings (810, 900 and 1200 millimeters' vibrating length instead of the standard acoustic guitar's 650 mm and the usual Hawaiian guitar's stingy 570), I was most pleasantly surprised, and many of my visitors have been favorably impressed. The steel, for those who haven't played on a Hawaiian guitar yet (I understand the instrument is little known outside the North American zone) is a rod smoothly polished on its business end and long enough to be a movable bridge for all the guitar's strings. Something like an overgrown clavichord tangent.

I call attention to this resemblance in order to fill your head with dangerously imaginative, heretical ideas.

Since my instruments are much wider than standard, and the contrabass will be really wide, the steels have to be longer and heavier. The rod doesn't have to be steel: brass, aluminum, aluminum tubing, glass rods, all work with different effects.

You might even get some interesting muffled tones with a wooden steel if I may be pardoned such an expression. Bowing the strings is difficult but sometimes possible. Violinists please note!

My first instrument has this tuning on one side, giving major and minor chords, with the shared bass notes in the center:


(This is actual pitch, not octave-lower.)

With the steel, you can go up about three octaves from those F major and F minor chords, and the natural harmonics are spectacular.

Give the instrument a quarter-turn, to a narrow side, and it has a chord of the sixth, thus:


In ratios, 2:3:4:5:6:7:8:9:10.

All chords are just!

This chord in just intonation with its lower harmonic or subminor or natural seventh and its two major seconds (8:9 and 9:10) takes this instrument out of the silly syrupy cliche cocktail-bar class.

Another quarter-turn and you get a Harmonic Series, numbers 8 through 19:


Notation here is just a practical expedient; I am not trying to force it upon you.

This is a reader's, demonstrator's, and explainer's notation, not a part copied out for a professional performer: hence my bass clef at actual pitch instead of the Spanish guitarists' treble clef to be played an octave lower than written.

This Harmonic Series contains the minor-ninth chord as well as the Yasser Hexad's theoretical just form. Did Scriabin, or didn't he?

This is the wide side (90 mm).

The last quarter-turn brings us to 8 long strings in 2 groups of 4, tuned to:


The very long, very thin tenor E strings have an intriguing sitar buzz throughout the compass. This is a narrow side (65 mm wide).

The second instrument is on a very similar board the same size as the first, 1400 mm long (4 ft. 7 inc.), 65 x 90 mm cross-section. It has 45 strings, while the first instrument has only 41.

On a wide side is a Subharmonic Series -- or as some theorists have said, undertone series -- I do not intend to imply, of course, that undertones exist as components of a complex tone as overtones do. What I mean is that the members of a subharmonic series have some high tone as their partial-in-common in the present case, double high C,3 octaves above Middle C, 2112 Hz.


I was able to squeeze in 13 strings for the 8th to 20th subharmonics of the double-high C, inclusive.

A quarter-turn brings us to a chord of the harmonic eleventh on a narrow side:


The steel of course transposes this tuning to any pitch whatsoever for about three octaves.

Another quarter-turn gives a wide side again, with a just diatonic major scale, the three flats for the tonic minor, the grave or comma-lower [10:9] major second, and the septimal sub-fourth for a 'natural' dominant seventh chord. [4:5:6:7]


The remaining narrow side has a chord of the added sixth which seems to be conventional for the pedal steel guitars discussed above. No doubt this is because the major and relative minor are contained in it.


IMPORTANT 1980 NOTICE: some of the chords on this page have been or will be changed! More instruments have been built with still other tuning-schemes -- design is NOT frozen.

So-called piano-wire or music-wire is used for the strings, in sizes from 0.2 mm (.008 inch) to the sizes used in the treble register of pianos, about 1 mm (.039 inch). It would be much better if guitar wound strings were obtainable in long lengths, but so far I have not found any. If you are willing to content yourself with a shorter instrument, a wide selection of custom gauge electric guitar strings is available at music stores. Their length seldom goes beyond one meter (39 3/8 inches), and then a considerable proportion of this is used up at the tuning-pins or -gears, and below the bridge at the anchor points or tailpiece.

Amplification will be through magnetic pickups.

However, the wood is resonant enough to make the instruments clearly audible in a living-room, and to permit recording through an ordinary microphone.

The strings are tuned with standard piano tuning-pins, and while not as tight as piano strings, the tension is much higher than that in a regular guitar. My estimate would be nearly a ton on each instrument. The heavy tuning-gear-pegs that would have been needed would have been so fantastically expensive as to put the whole project out of the question entirely!

The main reason for putting strings on all four sides of the instrument is to balance this great tension. Another reason is that this gets the greatest variety of chords into a small space and easily-carryable form. The alternative, of course, is to use metal frames and some kind of easily-demountable stands for several of them.

The tuning scheme above is not necessarily the absolute final version for the life of the instruments, although it likely will remain as it is. If more tunings are needed, more instruments will be built.

I am not going into exhaustive detail on certain aspects of these instruments, simply because they are accidents of circumstance, or have to do with my needs at this time, and would not apply to a similar instrument built the way you want it.

For instance, the exact length of the strings and locations of the bridges, and spacing between adjacent strings and height of bridges are all ad hoc. I found two suitable old boards and wanted to get the most out of them for my present purposes and as a demonstration of what unsuspected possibilities lie in the steel-guitar principle.

Now that that has been accomplished, both sooner and better than I anticipated, other instruments can be built with variations on the theme over a very wide range of parameters. Only in the event of mass-producing instruments will there be any need to clamp on the constraints and juggle with the limitations.



Now for an important variation of this idea: the third instrument is a contrabass, as I said before. While writing this I have completed it. It is 2 meters long (6 ft. 7 in.) and has 28 strings, 14 on each side. One side is tuned thus:


That is to say, five strings in unison sound Contra C = 33 Hz, and the remaining groups of strings sound its second, third, and and fourth harmonics, so that any note for more than two octaves up from that can be played with a wide steel with a chorus effect and with the 16-foot-8-foot-4-foot-5 1/3-foot ensemble effect available on the pedal keyboard of many pipe organs and some electronic organs.

In thousands of conventional orchestra scores, the cello and double-bass parts are yoked together in octaves, or as the organist would say, 16- and 8-foot pitches, for long passages. This new instrument imitates that effect very well indeed.

It should be obvious that a large loudspeaker unit in a big enclosure is required to reproduce these low tones. Tiny portable equipment simply will not do! The amplifying pickups used will be described in a later issue. For practicing, the wooden board has enough resonance to give soft tones without any amplification, especially when the instrument is laid on a wooden table or bench.

At present, the 14 strings on the second side of the instrument are tuned as follows:


The steel-guitar principle sliding a movable bridge along a string or group of strings makes frets useless and unnecessary and so is an ideal means of escaping the fetters of 12-tone temperament. Those who are experienced with instruments of the violin family will not need fret-charts on the board beneath the strings. Other persons will want such charts, painted on the board, attached to the metal frame, or on plastic or cardboard to lay on the board underneath the strings, and since this is just another way of using fretting-tables, I will discuss it in later issues when furnishing such tables.

The steel guitar in whatever form is not a frequency-standard or precision instrument: it has to be tuned from such a standard. That does not keep it from being an expressive and valuable musical instrument.

It deserves a better future than the mere retailing of trivial background and the aimless sliding which has given it such a bad name in the past.







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