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Microtonal Musings

The ability to accommodate microtonal tunings may look good on the spec sheet of your favourite synth, but what use is it to you? Scott Wilkinson reads between the lines.

Interested in alternative tunings and scales, but unsure about how to use them? Read on to discover the practical applications of microtonality.

IF YOU'VE BEEN reading MT over the past couple of years, you'll be aware of the growing interest in microtonality - the ability to play the notes "in between" the standard 12-tone scale. Microtonality offers the promise of new musical dimensions for composers, performers and listeners alike.

I know what you're thinking: "isn't it mainly for making weird, avant garde music? What exactly can I use it for?" Well, lend an ear (or rather, an eyelash) and I'll tell you about the wide range of microtonal applications that any musician can use to enhance the quality of his or her music.

Background Music

MANY PEOPLE BELIEVE microtonality is about scales that consist of very small musical intervals. In fact, these scales comprise only a part of the world of microtonality. A more accurate assessment would be that microtonality is concerned with any interval, particularly those intervals not found in 12-tone equal temperament. Many of these intervals differ from those in equal temperament by very small amounts, hence the term microtonality.

When you stop and think about it, there is an infinite number of musical pitches available to composers and performers. Trombonists, fretless string players (such as violinists) and singers know this instinctively because they can produce any pitch of any frequency with equal ease (as long as it's within their range). And yet, virtually all of the music composed and performed in the Western world during the last 200 years has been created using only 12 distinct pitches that are repeated in all of the octaves audible by human ears. The reasons for this 12-tone limit are found in the history of Western scientific and musical development.

As a musician, you probably know that the distance between any two notes is called an interval. One of the most common and easily recognised intervals is the octave. In this interval, the frequency of the higher note is exactly twice the frequency of the lower note. As a result, the two notes are said to be in a ratio of 2/1. In a perfect fifth (such as C up to G), the frequency of the higher note is exactly 1 1/2 times the frequency of the lower note. This interval is described by the ratio 3/2 (or 1 1/2). The comforting thing about ratios is that they can be used to describe intervals without regard to the actual notes that make them up. Any two notes that form an octave will always be in the ratio of 2/1.

Figure 1. The harmonic series based on the fundamental C. The intervals and ratios have been adjusted to compensate for the different octaves in which they occur. Notice the interesting pattern in the ratios describing the consecutive intervals.

The ratios of various intervals can be found in the harmonic series. The intervals between consecutive harmonics become gradually narrower as you ascend the series. The first interval in the series is the octave, followed by the perfect fifth, perfect fourth, major third, minor third and so on. The first 12 members of the harmonic series and the intervals that they form with the fundamental (C in this example) as well as between consecutive harmonics are shown in Figure 1.

As you can see, the harmonics in one octave are repeated in all higher octaves with the addition of new harmonics. The intervals in the harmonic series are known as "pure" intervals because the ratios that describe them are composed of two whole numbers. An entire diatonic scale can be constructed from the members of the harmonic series. This is one form of "pure" or "just" Intonation.

In the days of ancient Greece, the famous scientist Pythagoras constructed scales in a different way by generating consecutive perfect fifths. For example, he might have started on C, moved up to G, then to D, A, E, B and so on around the "Circle of Fifths" that music students study to this day. If you are or were such a student, you probably remember that the Circle of Fifths closes on itself, returning to the starting point of C (actually, to its enharmonic equivalent B#) after 12 perfect fifths (and the appropriate octave adjustments).

However, Pythagoras discovered a problem with this procedure. If the fifths used are truly in tune (that is, exactly in the ratio of 3/2), the Circle of Fifths does not close on itself. By the time he got to B#, it was almost a quarter tone sharp with respect to the starting note C. When using truly in tune (or "pure") perfect fifths, the Circle of Fifths becomes the Spiral of Fifths.

This error in the Circle of Fifths when using pure fifths, known as the Pythagorean Comma, is one of the main reasons why pure intonation does not allow the performance of diatonic music in any key. In order for any of the 12 key signatures to be available, the circle must close on itself. The octave must be preserved. This means that the Pythagorean Comma must be placed somewhere else in the scale.

One way to close the Circle of Fifths is to divide the Pythagorean Comma into 12 equal parts and subtract this very small interval from each of the pure fifths in the Circle. This results in 12-tone "equal temperament" that we have grown to know and accept as the only alternative. You can also derive 12-tone equal temperament by dividing the octave into 12 equal intervals (called semitones). The fifths in this tuning are slightly flat and the major thirds are noticeably sharp (not to mention that all the other intervals except the octave are also impure).

As you might imagine at this point, there are many other ways to divide the octave into a scale. By exploring these other alternatives, the intervals that are important to Western music can be made more pure and harmonious to the ear.

Improved Intonation

ONE OF THE most important but least understood applications of microtonality is improved intonation for "normal" Western music of any style including (but not limited to) pop, rock, jazz and classical. Today's musicians and listeners alike have come to accept the imperfect intonation of 12-tone equal temperament because it has been used almost exclusively for the last two centuries. Our ears have become culturally accustomed to the imperfect fifths and sharp major thirds that are inherent in our standard scale.

Pure tunings such as just intonation derived from the harmonic series provide the opportunity to create music with greatly improved intonation. Perfect fifths are indeed perfect, and major thirds are noticeably lower than their equal tempered counterparts. More to the point, these and the other intervals used in Western music are truly in tune when played in a pure tuning. Music performed with pure intervals and chords has a shimmering quality and a conspicuous absence of the "beating" given by imperfectly tuned notes.

Of course, the reason that pure tunings such as just intonation were abandoned was that only a small number of key signatures sounded good in any particular tuning (although it's important to remember that these keys sounded much better in fact than in equal temperament). This is due to the fact that each note performs different functions in different harmonic contexts. For example, C acts as the third in the key of Ab major and the dominant seventh in the key of D. In order to maintain pure intonation in both harmonic contexts, two slightly different Cs must be used. The difficulty of retuning an instrument for a piece in a different key (not to mention the increasingly popular modulations within a single piece) made the compromise of equal temperament more and more attractive. How would you like to retune the grand piano on stage between each piece at a gig?

Equal temperament, however, is a double-edged sword. While all key signatures sound equally good, they also sound equally bad. Except for the octave, no interval played in equal temperament is purely in tune. This is the price we have paid for musical flexibility.

One solution to this problem is to divide the octave into many more than 12 equal parts. It turns out that other equal divisions of the octave produce the important intervals (such as the perfect fifth and fourth as well as the major and minor third) with greater purity than 12-tone equal temperament. Such divisions include 31, 53, 65 and 118 equal intervals per octave. Within these large scales are hidden the specific intervals that allow performance in any of the 12 keys with improved intonation over 12-tone equal temperament.

"Microtunable synthesisers provide a facility never before available in the history of keyboard instruments: instant retuning."

The problem with these tunings is that they don't map well onto the standard musical keyboard. Instrument designers throughout the ages have come up with a variety of keyboards that are better suited to playing these large tunings, but none have ever enjoyed widespread acceptance. Sort of like the Dvorak typewriter keyboard, eh?

Microtunable synthesisers provide a capability never before available in the history of keyboard instruments: instant retuning. If you write a piece for synthesisers that starts in C minor and modulates to A major, and you wish to use just intonation so that the intervals and chords in both keys are pure, you can change the base key of the tuning with ease. This can be done manually on the front panel of the instrument or, in some cases, by sending a program change message that recalls a preset with an associated tuning.

Another, even more useful, prospect on the horizon is the development of a standard MIDI microtuning file format. Carter Scholz and Robert Rich (two regular contributors to MT's American sister magazine and members of the American body, the Just Intonation Network), have proposed a microtuning file format that codifies the specific characteristics of any tuning into SysEx messages. Similar in principle to the MIDI Sample Dump Standard, this file format will allow synthesisers from different manufacturers and computers to share microtuning data.

With such a file format, you would be able to send entire tuning tables from your sequencer to any compatible synth or sampler. In addition, the proposed format includes provisions for real-time control that will allow you to tune individual notes in any compatible synthesiser on the fly. This has far-reaching implications for improving intonation in any musical style and will revolutionise the way in which tunings are implemented in electronic music.

Things Ethnic

ALTHOUGH IT MAY sometimes be hard to imagine, there's a whole world of music that has little or nothing to do with diatonic scales and 12 key signatures. The indigenous musics of Asia, Africa, Australia, India, the Pacific islands, the Middle East and South America are rich with melodic, harmonic and rhythmic elements not found in the Western musical tradition. These elements are now being incorporated into the music of contemporary American and European composers such as Terry Riley, and Eberhard Schoener.

Wendy Carlos is another composer who uses elements from various ethnic sources in her music. In particular, she has pioneered the use of non-Western tunings and scales with electronic instruments. Her album Beauty In The Beast is a stunning example of how these tunings can be incorporated into an electronic setting. Using such instruments as the Synergy, MuLogix Slave 32 and Kurzweil 15OFS, Carlos uses imitative synthesis to recreate the sounds of instruments from different parts of the world and plays these sounds with tunings appropriate to the cultures from which they came. She also mixes her metaphors for a wonderful hybrid effect as in one section of 'Poem For Bali', which is a mini-concerto for Gamelan and Symphonic Orchestras.

Another area ripe for the picking (or plucking, banging, bowing or blowing) is found by reaching into the past. Elements of historical music can be extracted and used in contemporary composition. New age artists are using historical instruments such as recorders and harpsichords to establish a certain elegant feeling. The tunings from these bygone eras can also be used to enhance the historical perspective of this music.

Microtunable synthesisers offer some very attractive possibilities to music educators and early music specialists as well. If you teach music history or keyboard performance, synths and samplers with historical tunings can be used to illustrate the music as it was meant to be heard. Various principles of acoustics can also be demonstrated with these instruments.

Performers of early music can use synthesisers to try out different tunings before they commit their harpsichord or pianoforte to any particular one. Electronic instruments are also much easier to take to rehearsals and hold their tuning perfectly, unlike their acoustic counterparts.

Experimental Music

NOW YOU'RE THINKING: "here comes the weird stuff". Well, some of us like to get outside from time to time. Besides, if no one ever experimented with new musical ideas, we'd all still be listening to bones and skins (apologies to any drumbores out there - your contributions illustrate that music is a cumulative art).

One area of experimental music that has yet to be fully explored involves the use of psychoacoustics. This rather esoteric branch of psychology deals with how we perceive sound. There are several very interesting psychoacoustic effects that can be easily generated with microtonal synths to enhance your music.

Figure 2. A pure C major triad in root position based on middle C produces several combination tones below the triad.

One of the most common psychoacoustic effects results in what are known as "combination tones". When pure intervals and chords are played, our brain actually manufactures additional tones that we perceive from the interaction of the primary tones. For example, if you play a C major triad in root position with pure intervals, most people will hear the G a fourth below the root and the Cs one and two octaves below the root in addition to the primary tones (see Figure 2). While this might not seem very experimental, it does help to reinforce the purity of intonation. A more experimental application would be to compose a piece in which combination tones are produced to provide the melody by varying the primary tones.

Another interesting effect is known as "binaural beats". You're probably aware of the regular beats that occur when two slightly out-of-tune notes are played together. In fact, this phenomenon can be used to good effect in experimental composition. However, binaural beats provide even more interesting possibilities. They arise when two tones of slightly different frequencies are played separately into the two sides of a set of headphones without interacting electronically or acoustically. Under these conditions, you might expect to hear the two tones as separate and distinct. Surprisingly, you don't. Binaural beats are perceived as a single tone that circles around inside your head with an almost chorus-like effect. This is quite startling; it also suggests an entire genre of music intended solely for headphone listening that makes extensive use of binaural beats and other binaural effects.


IF YOU INTEND to experiment with some of the ideas presented in this article and you use a Macintosh computer, I'd highly recommend you contact Robert Rich at Soundscape Productions, P.O. Box 8891, Stanford, CA 94309, USA. Aside from working on the MIDI Tuning Dump Standard, he has also developed a HyperCard stack called JI (Just Intonation) Calculator that facilitates the design of any tuning with up to 48 notes per scale (and scales need not be octave repeating). The Mac's sound chip can be used to hear the results of different tunings and the stack even sends its tuning tables to the Yamaha DX7ll, TX802 and TX81Z over MIDI. The best part is, it only costs $10.

Another product of interest to microtonal explorers is the Tune Up tuning library for the TX81Z from American company Antelope Engineering. This program is available for IBM PC and Macintosh computers and includes 100 historical, ethnic and contemporary tunings that can be downloaded into the TX via MIDI. Tune Up is available for $49 from Antelope Engineering, 1048 Neilson St, Albany, CA 94706, USA.

There you have it: a brief introduction to the applications of microtonality. Perhaps your curiosity has been aroused and you'll even consider using these ideas in your own music. Perhaps we'll even get some microtonal demos sometime.

Happy tuning.

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Steinberg Cubase

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Anatek Pocket FX

Music Technology - Copyright: Music Maker Publications (UK), Future Publishing.


Music Technology - Aug 1989

Feature by Scott Wilkinson

Previous article in this issue:

> Steinberg Cubase

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> Anatek Pocket FX

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