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Just Guitar It All Comes Down to the Genetic Code for All of Harmony Known As the Harmonic Series

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Just Guitar It All Comes Down to the Genetic Code for All of Harmony Known As the Harmonic Series Special Just Guitar It all comes down to the genetic code for all of harmony known as the harmonic series by John Schneider he guitar has come a long, long way in the last five intervals that are actually, acoustically in tune. Sound obvious? centuries. Certainly the concept is shockingly simple, but its manifes- T History books brimming with instruments of all tation is anything but, as anyone who has ever tried to tune sizes, shapes & stringings scrupulously chart the a guitar can tell you. It all comes down to that innate growth of the body, the number & placement of the struts template for tuning which is inherent in every pitched note, under the soundboard, choice of woods for top, back & sides the genetic code for all of harmony known as the Harmonic etc. But oddly, one of the most important aspects of the Series. guitar – the actual notes produced – are rarely, if ever Every guitarist knows that plucking an open string that is discussed. The usual single sentence reads something like, touched lightly at the 12th fret will produce a note that is “…the strings were stopped by tied frets, like the lute, which one octave higher than the open string, and that after one were replaced by ivory or metal frets in the late 18th removes the left hand finger, the string continues to vibrate. century…,” and that’s it. When tunings are mentioned, it Both halves of the string vibrate at the higher pitch, creating is only the relationship between the open strings that is a sustained tone that can last longer than if the string were shown, because it is taken for granted that of the tuning actually fretted and only one half was sounding. Touching the 12-fretted notes in each octave was and has always been the string at the seventh fret creates the same effect, but modern equal temperament. It turns out, as the Gershwins this time, the string divides into thirds, with the resultant would say, “…it ain’t necessarily so!” In fact, not only were pitch one octave and a fifth above the open string. The same the tied frets of instruments past rarely spaced equally, this pitch also can be produced by touching lightly over the 19th past century has also produced a surprising amount of music fret as well, since that will also divide the string into thirds. for guitars that have been refretted to play notes not possible This process can be repeated over and over again, each time on today’s standard instrument. dividing the string into smaller and smaller equal parts, So-called microtonal music, which uses notes other than with the pitches being produced known as harmonics. those of 12-tone equal tempered scale, uses smaller intervals The great irony is that these equal divisions of a string do from two basic categories – tonal & atonal. The Atonal or not produce a scale of notes that are equal divisions of an ‘Divisional’ class of tunings partitions the octave into an octave. For a musical interval to be acoustically in tune, the increasing number of equally spaced intervals, the most pitch of the higher note must match one or more of the famous being quartertones = 24 tones per octave (imagine harmonics of the lower note. Try this experiment: play the one fret being placed exactly between each one of your harmonic G# just behind the 4th fret on the low E-string, existing frets). Mexican composer Julian Carrillo created a and compare it to the fretted G# found on the first string handful of solo and ensemble works using this instrument fourth fret. Surprised? if the two strings have been properly in the 1920s-30s. The Czech Alois Haba used quartertone tuned before hand, (the first string two octaves higher than guitar in the 1940s, having already composed a substantial the sixth), the fretted note will be sharper than the harmonic. repertoire for 1/5-tone and 1/6-tone string quartet, trombones, But which one is correct? clarinet and even a custom quartertone piano. There have Play an E-major chord using that first string G#, then retune also been a few works for 19-tone equal temperament applied the high string so that the fretted G# matchs the harmonic to guitar, but what all of these divisional systems have in G# - now that’s in tune, acoustically that is. Welcome to the common, regardless of how they divide the octave, is the world of Just Intonation! The fretted G# that is acoustically search for novel musical material – fresh new pitches to in tune with the low E-string is a tonal or ‘just’ microtone create harmonies & melodies that have never fallen on because it has been flattened by a very small amount (14% human ears before. of an equal-tempered semitone) to match the 5th harmonic Tonal or ‘just’ microtones also seek to create original sounds, of the low ‘E’. Simply put, Just intonation matches the notes 42 but from a completely different premise, that of producing of a scale with the harmonics generated by the key or tonic of that scale. One then chooses how high up the to match the tunings of the harps and keyboard instruments harmonic series to tune. For example, if the root-third-fifth of the day. Juan Bermudo went to great lengths to describe of the triads of a key are to be acoustically in tune, that is el arte de entrastar(the Art of Fret Placement) needed to often called 5-limit just intonation, since the fifth harmonic produce the pure fifths of Pythagorean temperament for the used is the highest used. (The E-major chord generated by six & seven course vihuela in his Declaracion de Instrumentos Ex. 1 is spelled E-G#-B, using harmonics #1-#5-#3). If an Musicales (1555), Marin Mersenne diagrammed frettings for E dominant seventh chord was tuned, it would be spelled pure major thirds and fifths in Harmonie Universelle (1637), E-G#-B-D, using harmonic numbers 1-5-3-7, and would occasionally resorting to 19 frets per octave to accurately Special therefore be a 7-limit, since the seventh harmonic is the reproduce the three genera of Ancient Greek music (diatonic, highest used in the chord. Try playing that E7 chord, properly chromatic & enharmonic). But when a fret moves, so do all tuned, on your instrument, using the harmonics of the bass of the notes determined by that fret, unlike the keyboards string to tune each note of the chord on each string. Quite or harps that have one string per note. The first breakthrough a difference! especially the note ‘D’ which is almost a third that allowed individual guitar notes to be tuned came in of a semitone flatter than the standard fretted ‘D’ (-31% of the 19th Century with the invention of the Enharmonic an equal semitone, or -31¢). Over the last century, a handful Guitar. In his Instructions for playing on the Enharmonic Guitar of composers have been struck by the absolute beauty of (1829), General Perronet Thompson describes an instrument these ‘natural,’ unadulterated kinds of musical intervals, which he invented in “…an attempt to effect the execution and have created amazing music with them, including many of correct harmony, on principles analogous to those of the gorgeous works for the guitar. ancient Enharmonic” (throughout European history, the pure But 20th century composers were certainly not the first to intervals of just intonation were invariably evoked by the use so-called ‘microtones,’ since modern equal temperament ancient Greek Enharmonic). In the great tradition of the has only been universally accepted in Western music since Victorian enlightened amateur, the noted Cambridge econ- around the 1820’s, virtually all music before that time could omist, ex-governer of Sierra Leone, Member of Parliament, technically be considered ‘microtonal.’ In fact, all early key- editor of the Westminster Review, and advocate of universal board instruments were tuned much more purely than today, suffrage created a scale using 53 notes/octave “…in a desire but with the great compromise that one could not play in to abate the untuneableness of the common guitar: which, all keys. Bach and his colleagues Werckmeister & Kirnberger though an instrument possessed of many agreeable qualities, famously went to great lengths to find tunings that allowed has the defect of being out of tune to a greater extent than performance in all keys – hence the creation of Well- any other that is played by means of either strings or keys…” Temperament in which the size of the major third was In order to achieve this extraordinary feat, Thompson devised different from key to key, creating an exquisite rainbow of a marvelous system of removable frets whereby the neck key coloration throughout the instrument. was pre-drilled with hundreds of holes, 53 pairs per octave Because the tied string frets of the Renaissance & Baroque for each string, into which staple-like frets were placed in were mobile, the gambists, lutenists, guitarists & vihuelists a pattern determined by which key was meant to be pro- that used them were constantly adjusting their placement duced. Opposite page: Partche's Adapted Guitar II (close-up on 10-string Martin neck) Above: Example 1) Harmonic Series of the low E-string 43 I purchased my original guitar in 1934“ and spent several years (1934- 1942) in the effort to evolve effective frets in Just Intonation. The usual low, Special wire-type frets were not very satisfactory, and I eventually fitted high, stainless-steel frets into slots in a brass plate, which was then screwed onto the neck.
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