DIGITAL, ANALOG AND THE MUSICIAN

IVOR DARREG

(1974?)

DIGITAL -- What a fashionable buzzword these days!--digital synthesizers, digital interfacing, digital delay (one of the "effects" in the recording studios), and of course computers are assumed to be digital unless specifically referred to as analog computers (not many of those anymore), and now there is digital recording of the sound entering the Now Scene.

Actually, we have been acquainted, albeit subconsciously, as musicians, with digital techniques for generations, long long before anybody ever dreamt of computers! Indeed, music has been heavily involved in the entire spectrum from analog to digital. The typewriter started out with layouts borrowed from the piano keyboard. Those extremely digital instruments, the harpsichord and the pipe organ, have been around for a very long time.

That is to say, the notes of the pipe organ are digital because they are either on or off with no middle ground--you get louder and softer in steps, not continuously, by pulling out more stops or pushing them in to turn them off--whacking the organ-key harder has no effect. (The swell pedal controlling the swell-box's shutters is only an apparent exception, for most swell-shutters open in six steps or so, not continuously.) The notes of the organ or other keyboard instruments are obviously digital as to pitch also: you go from C to C# to D without passing through the infinite number of intermediate pitches.

In contrast, the human voice is analog, with every possible pitch equally accessible throughout its entire compass, and every possible degree of loudness equally accessible throughout its dynamic range, and incredible range of possible timbres and noises, which in the normal linguistic use of the speaking voice are referred to as vowels and consonants. Printing is digital, with separate pieces of type spelling out words, but the actual original spoken word is analog, with every intermediate speech-sound and voice-glide being audible in between the sounds that the printed letters stand for.

Musical NOTATION, however, is mostly digital, so the notes on the staff stand for discrete pitches belonging to some scale or other, and do not truly represent what the human voice or the violin, viola, cello, or bass actually perform from that notation--so writing down a song or violin piece is analog-to-digital conversion, and performing from the notes is digital-to-analog conversion! Learning to do this is very much like a computer being programmed, and this for centuries before there were computers. What's so new about digital?

The piano represents an intermediate case, since it is analog as to dynamics but digital as to pitch. (The piano-tuner can change pitches of the strings continuously, so while tuning, pitch is analog, but the pianist of course is taught to ignore that.) The same highly-digital musical notation is used for voice, violin, piano, harpsichord, and organ, so this analog-vs.-digital question is submerged in a fog of confusion for most of us.

Now add in all the wind instruments and percussions, still generally written for in the same digital staff notation, and having various degrees of analog or digital nature in their sounds. The confusion is really confounded, when one kind of notation has to serve for so many different instruments and ways of playing them.

The fretted instruments, typified by the guitar, are digital as to pitch just as the piano is, so that leads us to the subject of tempered scales. Most music has an orderly structure. From the chaotic infinite gradations of natural sounds, just a few are selected according to some system to form a scale (a stairway or ladder, rather than a ramp or slope). Since our voice does not have frets, mental frets are installed by the music teacher in the process of voice-training and of learning to read music, or to sing with the sol-fa syllables.

So the digitization process, or analog-to-digital conversion, is often a process of pretending, of make-believe. The engineer or programmer will make this sound more businesslike and scientific by calling it quantizing. The composer, inspired by the wind howling through the threes outside, plays something like this on the piano, writing it down as shown below:

Or the singer's melody is displayed on special machines which draw a continuous (analog) pitch graph, but the quantized graph of the same performance shows stepwise jumps instead of a gradual curve.

Analog Digital

All watches had hands till recently; now we use digital watches which jump from 3:51 to 3:52, pretending that intermediate moments do not exist. Again, this is quantizing process, imagining that things proceed in sudden steps or jumps.

Since we have covered the tempered and just musical scale question in many other publications, we won't go to too much detail here.

Most digitization or quantizing is into equal steps, but in the musical case there are instances of unequal steps--that doesn't meant hat it isn't quantized or digital. Take a look at a guitar fingerboard: the frets are not equally spaced like the lines on a foot rule, but get closer and closer together as they approach the bridge. Yet the interval-spacing of the resulting sounds is equal. This is like the graduations on a slide-rule, and there is a mathematical similarity. The do re mi syllables are obviously digital, although their interval-spacing for the singing of a just or untempered scale is unequal. They have been around for almost a thousand years, and have precursors in Ancient Greece and India.

There are fretted instruments of other cultures which have unequal spacing: a typical example would be the Arabic scale.

Despite such inequality of fret-spacing, there is still an orderly sequence of pitches, proceeding by discrete steps, so this has to be considered digital rather than analog.

Various intermediate situations occur in music: the finger-holes and keys in wind instruments are digital, even though the player can superpose analog modifications such as varying wind-pressure or partly covering a hole. THE valves on a brass instrument such as a trumpet are intended to be digital in nature--to depress the pitch by one or more semitones., and to add up when more than one valve is operated. They don't quite make the theoretical pitches, and upon this form of digital control is superimposed a different digital sequence, the harmonic or overtone series produced by the player's lips and technique. The result is therefore somewhat like analog and this mislead some investigators.

Conventional notation of loudness is digital in the case of the letter series: ppp pp p mp mf f ff fff but there are analog symbols such as crescendo and decrescendo and various directions in Italian and other languages. Different instruments give different loudnesses for the same letter o symbol, and the response of the ear is not linear, so that "as soft as possible" must be interpreted with regard to the concert-hall or home or recording's noise level, as "as loud as possible" might be painful, or overload the equipment, or merely result in severe distortion sometime before the maximum loudness is reached. This situation often tricks composers into asking the impossible, or for directing in some absurd manner deliberately, in order to get the sounds resulting when the performers attempt to follow such directions.

There are many auditory illusions, but psychologists and experimenters have sadly neglected this field, preferring to write nearly all their articles and textbooks and studies on optical illusions, quite as though everyone was deaf! Now that digital recording is becoming common, and some new musical instruments use digital methods to create their sounds, the study of auditory perception and illusions becomes urgent.

The performer on stage is somewhat like a stage magician, often suggesting the impossible. The audience may belive they are hearing something the instrument in question could never do. On the organ, as we stated above, hitting the key harder does not give a louder tone, but the illusion of accent--that a certain one is louder than its neighbors--can be effected by prolonging a note slightly.

The digital imitation of analog phenomena might be understood this way: on Page 2 we gave a notation of a rapid chromatic scale on the piano (it could be some other keyboard instrument) imitating the wind howling. Now the conventional keyboard or fretted instrument has only 12 pitches per octave. This is a rather coarse digitization of a continuous sliding tone such as the wind or a fire siren. The imitation is improved by doing it very rapidly, but in most cases the 1/12-octave steps can be heard--this kind of imitation-glissando, the digital simulation of a continuous pitch-glide, has become a sort of theatrical convention--we know it isn't quite the Real McCoy, but we take it as custom. The violinist or cellist or vocalist can do the Real Thing, true analog. Several years ago we had the good fortune toe acquire a copy of a tape recording of Julian Carrillo's series of microtonal pianos in which the chromatic scale for each piano in everything from third-tones (1/18 octave) to sixteenth-tones (1/96 octave) was played. It was not until the eighth-tones (1/48 octave) and ninth-tones (1/54 octave) were reached that successive pitches melted together into a good illusion of a continuous up-and-down sirenlike glissando.

Remember that the cards are somewhat stacked in this case. Dampers on pianos do not stop the sounds instantly: therefore there is some blurring of each tone in the time of the successor. No matter in the long run: we can get some experiments done later on with a computer and exact control over these factors which are necessarily fuzzy on the conventional piano. The question in this article is mainly, when we use discrete pitches in succession, how close together must they be in order to fool us into haring a continuous pitch-glide? How fine must digital simulations be deceive us into hearing it as analog? At a reasonable keyboard-playing speed, it appears from the Carrillo demonstration to be somewhere over 50 pitches per octave. Vary the experimental conditions and you could alter this either way. The demonstrations were in the middle register without using any extremely low or high notes.

The fact remains that a tuning-system with smaller increments of pitch would give us better imitations of sliding tones along with its other melodic and harmonic advantages which we already have discussed in our Xenharmonic Bulletins.

Another thing of this kind with some practical importance in either electronic musical instruments or computer music would be the simulation of vibrato (analog variation of the pitch above and below the mean or resting, non-vibrato frequency) by small steps of pitch above and below the mean instead of true continuous rise and fall. The author's experiments quite some time ago in this regard appear to confirm that this digital imitation is usually satisfactory.

As for stepwise volume control imitating continuous crescendo and diminuendo, quite a number of stepwise controls have been in use in broadcasting and other sound studios for years and no-one seems to complain.

So for tempo: metronomes are digital since they have little "click" notches where the slider on the pendulum tends to stop. Most of these metronome speeds have been well standardized in printed music.

The player-piano is digital--the roll-perforations say either ON or OFF. There are means for more refined performances from player-rolls, so don't judge present-day digital technology by the honky-tonk player of 1910. The computer will of course make the clumsy bulky heavy player-piano unnecessary, and can do so much more--but we had to bring this Nostalgic Beast up because it got so much digital music into so many places at the turn of the century. Long before computer came on the market, music used digital,. Barrel-organs, music-boxes, the list is long enough. The computer industry can't be accused of digitalizing musicians

and numbering our tones; that happened long ago.

Digital Recording. Before we can discuss the new ways of producing musical tones digitally, it behooves us to examine the digital recording methods now taking hold. You probably can find books and articles on this subject as it progresses, so for the moment we just have to give a slapdash introduction. A disk-record groove is a continuous thing with tiny wiggles all along it corresponding to the sounds recorded on it. In contrast, a digital recording, say a tape, is a series of tiny samples taken frequently--say 40,000 times a second or more often than that. These brief samples are in effect measurements of the amplitude of the electrical signal at an extremely tiny instant, and are then encoded as some kind of numbers--that being why they are called digital. There are quite a number of possible ways to encode a sample, and this is done much as it would be inside a computer.

Once we have a series of code-numbers instead of the continuous analog electrical signal, there are many operations that can be performed on these numbers that would be impracticable or impossible with the ordinary analog-recorded signal. An important aspect is that repeated copying a recording without introducing noise or distortion or degradation is possible, since the numbers can be restored to their original condition where the ordinary analog recording would pick up more and more noise with each generation of re-recording. In the playback process all these samples are decoded, and the intervals between the samples are filled in and smoothed out.

Now, suppose we did not actually sample a tape recording of the ordinary type, or a signal from a microphone. SUppose we used a computer and some other equipment, producing an "artificial" sample--a code-number corresponding to some new or unheard-of sound. Then we could manipulate these samples and then decode them into sounds or analog recordings just as if they had been regular digital recordings. Then we could play impractical scales on impossible instruments! Or create the Martian Language or a Traffic Jam in Galaxy RHF-315.

This is something like what a digital synthesizer or keyboard instrument does, and what is now being done in some new kinds of computer music. Another digital application to music is that of using computer chips to divide a large number, say 7 MHz (seven million vibrations per second), by various divisors through countdown circuits (i.e., counting every 1325th vibration and letting a pulse through, or counting every 748th vibration and letting a pulse through) so that we get the upper notes of a musical scale. Then dividing by 2 in succession by further countdown, we get 7 octaves of tones, played by an organ keyboard or other means. Different sets of divisors would give us different scales, with a very large variety to choose from. Such systems are already on the market, and you may be able to hear them at your music store or on records.

For people who want a simple accompaniment, there are rhythm machines of various sorts, which count the beats and subdivisions of beats and will play drums etc. in various standard rhythmic patterns. This is digital, not all that different from the way your LCD quartz wristwatch takes 32,768 vibrations per second and divides it down to give seconds, minutes, hours and the calendar feature.

Music is a manifold Pattern In Time, and counting takes time, and music teachers make their pupils count. Thus applying all these digital counting concepts to music is quite in keeping with a long tradition. Using digital methods does not mean the abolition of analog methods, for conversion back and forth is an important part of the total picture. The digital organ is used to accompany analog singers.