TRITONE MISSILES

My April installment left you hanging with Dr. Diana Deutsch and my soap-based friend Jim, who had sent me a Science News report on Deutsch's latest musical research into hearing. He couldn't understand the musical details but hoped I might. I could indeed and was fascinated. So I continue, working Dr.

Deutsch in with some previous ideas on music that I had already planned to explore. In this I am fortified by our own earlier Audio Deutsch article which you may have read--and heard--in our March 1987 issue.

I missed that issue due to eye troubles, now cleared away, but the Editor rushed me a black-and-white copy from the office machine so I might catch up. The bound-in plastic record reproduced very nicely but would not play, being on paper. So I went to my big bound volumes of back Audios, and there was the article in splendid red, white, and blue. But no record. It was removed before binding.

The newer Deutsch study, again, concerns our curious perceptions of up and down in musical pitch-the very foundation of musical notation and hence of live performance and, consequently, our audio that converts it to signal and back again. Practically everything, you see, goes up and down in music. And here is Deutsch, always ready to drop significant bombshells, telling us according to her tests that, lacking certain clues, we can seriously disagree among ourselves as to what goes UP and what goes DOWN! That's like disputing the law of gravity.

Well, I could have told her the same long ago out of my own experience.

But never in the disciplined detail that comes from her kind of research.

Dr. Deutsch doesn't use music. She devises test tones, you might say test tunes, of utter and calculated minimality, patterned and grouped for (mostly) headphone listening, each ear receiving its own channel. Binaural. In this new study, an extension of a 1986 report, she uses no more than two tones at a time. (Two successive tones make a minimum tune, don't they, like the cuckoo's song?) Moreover, these tones are as pure as the driven snow, i.e., sine waves. The most basic frequency shape, minus all distracting harmonics that might confuse the results.

To a musician, these tones are dismally vacuous. No personality compared, say, to the richness of an oboe's sound. But they have the immense advantage of being elemental, the better to aid in pinning down the enormously subtle workings of our sound perception.

Dr. Deutsch offers new bombshells each time she comes out with a study.

And then goes on often to further implications and new testings. We can confuse our musical ups and downs? That was 1986. The new tests, those I referred to in the April issue, find that our perceptions of up and down are strictly related to our spoken language, our local dialect. Where her English testees heard the mini-tune go UP, her American (Southern Californian) listeners said it went DOWN. An unsettling thought--does our music listening vary in any such way? Could be. Here, Deutsch converts what must have rated as an informed hunch into a disciplined proof. She is good at informed hunches. I might add that music and language have been subtly related since the time of the ancient Greeks, whose poets "sang," and probably long before. I expect Neanderthal man did the same, so Deutsch is well within a long tradition.

In her up-down studies she has made use of what she calls the paradoxical tritone. (I assume that this is where my friend Jim admitted defeat.) This is a musical interval-the proportion in frequency between tones-that is well known for its strange, featureless, ambiguous sound, its near-irrational ratio. (You won't find it approximated until the 11th harmonic.) In notation the tritone encompasses three whole steps (tones) in the modern music pitch system, hence the name. It may be heard as an augmented (stretched) fourth, as F to B, or as a diminished (shrunken) fifth, as in B to F. Our musical alphabet is repetitive, so this covers the five piano white notes BCDEF, hence a diminished fifth. But if you continue, FGAB, you have still another tritone, this one an augmented fourth.

Highly ambiguous, even polyguous.

The tritone was shunned in early music. It was the "wolf" in the musical henhouse-the devil in music. But well before the 15th century, a way was found, just one, which surprisingly removed both the wolf-like fierceness and the musical ambiguity. If you put another note 1 1/2 tones lower (i.e., down a minor third), the tritone vanished! You can easily hear this on the piano. Play F and B (a tritone), then add a D below it. The tritone is softened. In its place is a gentle chord which moves easily on to a C or C chord, forming a cadence. In music, a cadence (a falling, from the Latin-not to be confused with a march) says mildly, THE END, or the end of something, a place to take a breath. And so it was long used. The effect is much like the stronger (and later) cadence from the dominant to the tonic. We in the audio/music world would understand this as the third harmonic to the second harmonic and its fundamental an octave lower. Play the note G and then a C, and you'll get the idea. Better, play a G chord and a C chord. The older tritone cadence has no third harmonic at all. It is purely melodic. No simple harmonic relationship.

Please take a small breath! Like all professional terminology, music's is hopelessly polysyllabic and sounds much worse than it is. All of this is ever so simple for the ear. You have heard at least five billion cadences in the music that surrounds us even without going to a concert.

Mathematically, the tritone rates as an interval-relation between two pitches-of a half octave. Play C, F sharp, and the C above, and you will hear that there is indeed a tritone in each direction from the F sharp. But what is the tritone in numeric terms? A bit like the square root of 2. And that is how it sounds. The octave is simple, even basic, 2:1. Not the tritone, 11:8.

Why octave, for tones in the 2:1 relationship? Because if you play eight tones of a scale, eight white notes on the piano, you cover the span of an octave. Likewise, if you play five or three notes, you have fifths or thirds and so on, even when they are small or large-as in major and minor.

Hi-fi makes use of octave relationships to compensate for loudspeakers that cannot reproduce the fundamental. The second and third harmonics are usually present, so thus the ear "manufactures" a facsimile of the fundamental as a difference tone to those harmonics. For example, say a speaker cannot reproduce a 30-Hz tone, but the 60and 90-Hz tones are present.

The difference between these tones is 30 Hz, and the ear hears this as a resultant tone. Organ-builders have used this trick to produce fundamentals without full-length pipes.

To polish off the idea of a cadence, note that around the year 1600, as musical language widened, composers came to the logical thought that they might combine the old, gentle tritone cadence with the newer, stronger dominant-to-tonic cadence, written in harmonic language as V I (five moving to one). (Naming chords, harmonies, we convert to Latin.) The combination of these two cadences was stronger, juicier, more expressive-the dominant seventh, V'! It still has the tritone in it, also the extra covering tone (the Dsee above) and the dominant-chord harmonies. Very familiar, very convincing. I recently found an early one in a madrigal by the young Girolamo Frescobaldi, later a famous organist and keyboard composer. The music was published in Holland in 1608. A newly discovered sound effect.

In musical literature (Western) these tritone ambiguities are wondrously exploited by clever composers from Bach to Debussy, Stravinsky and onward. For this tritone is a kind of musical pun word, which may jump from one meaning to another, startlingly different. Often this is via the augmented sixth chord and its relatives, including a tritone as the unstable element. Here, a minor (small) seventh, e.g., C to B flat, converts to an augmented, stretched, sixth, C to A sharp, the same tones. The other note in such a chord, an E (the chord's third) is a tritone away from that A sharp. See Haydn, Mozart, Beethoven, Schubert, Brahms, et al. for thousands of easily listenable examples.

In addition, the tritone is used melodically to give a somehow exotic, mysterious. or bizarre effect since it does not advertise itself as to what part of an ordinary familiar scale it might belong. The "Prelude to the Afternoon of a Faun" (Debussy), flute solo, faunlike. It plays up and down a tritone. The trained bear in Petrouchka (Stravinsky) does a lumbering dance to a tritoneclumsy tune.

Dr. Deutsch works in two musical dimensions. Her new study, lice that of 1986, is vertical, concerning ups and downs. In our 1987 Deutsch article, the thrust was sidewise, rights and lefts.

Here, too, her test tones, quite different, were devilishly ingenious, aimed at sorting out and pinning down what a single ear, unaided by its teammate on the other side, could do on its own. In nature, in musical listening, our pairs of ears grab at an immensely subtle complex of different clues for direction, as we know when we try to reproduce musical sound. There'll never be an end to our own arguments over sonic directionality or of our intense interest in the practical side, for broadcast and recording. What Deutsch does is to narrow down these multiplicities to clear specifics, once again. Listen to her tests on Audio's bound-in record.

It's all explained in the article. No tritones here, and the "tunes" are much longer, pitch patterns, changing alternations right and left, lots of octaves (jumping up and down contrarily in each ear), chromatic half-step lines, wide jumps up and down, and so on.

Always a different signal to each ear.

Ups and downs but oppositely.

The two ears cannot relate and join these sounds-too different. So they are strictly on their own. What can an isolated ear do for apparent directionality when its partner can't work with it? Very strange, as you might guess.

Sometimes, tones fed to the right ear are heard to be on the left, though the left ear receives no such signal. It's another Deutsch bombshell.

No, you won't set up your coincident stereo mike array and find the violins on the wrong side even though your connections are not crossed. This is music, not testing. In stereo, both ears working on both loudspeakers, there are enough richly assorted directional cues to keep things in place unless you get into flighty changes in phase somewhere along the lines, or faulty volume balances. Deutsch tells us only, as I get it, that the single ear is not merely mono but has a positively unstable directionality when its partner ear is sending noncompatible info to the common brain. Sometimes right is right (in the right 'phone), sometimes it's on the other side of the head.

There are those secondary bombshells that Deutsch sends our way, so intriguingly. One in the Audio article has really raised my consciousness. It says that the way the single ear perceives lefts and rights, right or wrong, has to do with handedness. In the tests, lefties reacted distinctly differently from righties. Now I am a lefty, even a mini-Leonardo. My directional wires are hopelessly crossed at the gut level. Say "QUICK, TURN RIGHT!" and I instantly turn left, traffic allowing. But not if I have time to think. I tread on square-dance toes, creating dance gridlock, because I invariably put the wrong foot forward. And I can write backwards. When I learned longhand with my right, the left hand learned it in reverse automatically. I still can write backwards, but I can't read what I write. Unless in a mirror. The eyes, you see, are on a different circuit.

So go find Diana Deutsch's articles, and listen to her tones too. As for me, I'd better get out to California and have myself checked. I think maybe my left hand is attached to my right arm.

(by: EDWARD TATNALL CANBY; adapted from Audio magazine, Jul. 1991)

= = = =