Techniques of Polytempic Polymicrotonal Music Creation: Just Noticeable Difference, part X

 What is JND?

Just Noticeable Difference, which has nothing to do with just intonation, btw, is a psychoacoustic metric associated with the smallest interval detectable by the human ear. There is no point in making microtonal scales that can not be heard at their smallest division. Or is it? 

The Greek schisma is a 2-cent interval created by subtracting the Syntonic Comma at 22 cents from the Pythagorean Comma, at 24 cents (Ditonic Comma). Ben Johnston used this 2-cent interval in his music. To truly hear a 2-cent interval, one would have to count the beats in between this narrow structure. I believe it was Marin Mersenne who discovered counting beats for intervals back in the 1600s, and this technique was discussed in Ellis-Helmholtz. Nevertheless, if Johnston used the schisma, then what stops the rest of us from using the cent itself? 

Ellis-Helmholtz suggested the ten-cent threshold, while David Whaley, in his 1975 dissertation on the microtonal capability of the Horn 1975, wrote his dissertation on this very topic, and found that musicians consistently landed in the 13-16 cent range. 16 cents is the 12th tone. In fact, Aristoxenus used the 16.6 cent 12th tone for his "unit," of which 30 were used to divide the tetrachord. Actually, it was his student Cleonides who created this system on Aristoxenus's behalf, as it was the latter's teachings. 

Even the theorist Llewelyn Lloyd contested that the human ear can hear any interval provided it lasts longer than a hundredth of a second. This is, in fact, true. I myself created a 1200-cent polymicrotonal synthesizer in Max, while at the University of Illinois, and I discovered that a one-cent interval lasted several seconds, enough time that I could hear literally the entire overtone series sound as the close proximity phase cancellations went by my ears. (Another failed post-doc study opportunity). At one cent, I could hear the flavor, design, and curvature of the series. That's how slowly the one-cent interval operates. This, of course, is at middle C. I still have this polymicrotonal synth. I ought to make a piece just using one cent in different registers. Even on Scala, there exists no 1-cent scales. If I were to create a one octave piece of 1200 1-cent rising tones, at @ 8 seconds long, on average, it would take about 160 minutes to complete the octave. Talk about minimalism...

What does this have to do with Space Travel? Well, in a polymicrotonal composition, the point is to have many competing tuning or microtonal systems. The sky is the limit. I choose four-part polyphony, in keeping with standard contrapuntal practice, and as a drummer, I have only four limbs to use in polyrhythmic-metric structures. Secondly, I believe it is important to broach the topic as a practical concern. What CAN we hear? As a matter of fact, could the educated listener truly hear when the subject of a fugue was being altered and transposed in the development section? No. I really do not think even the educated listeners truly knew what Bach was doing at the note level. They just knew it was awesome. Does any educated listener hear Schönberg's rows? No. People just like the music. Therefore, does it matter if these intervals are truly and easily perceptible to the ear? No. However, people will (and can) hear the compression of small intervals as a sound mass down to the polychromatic line. The use of microtones at their most basic unit is still generally avoided in favor of keeping the standard chordal tonal structures, only retuned according to the taste of the composers themselves. 

But I do care about the performers who will object to these systems because they are outside their comfort zone. As discussed before, I would have to inculcate the performers, lest they already have a microtonal background and are amenable to this philosophy and aesthetic. 

JND, however, becomes very important with respect to the future topic of polymicrotonal modulation, which will require a "near unity" within 16 cents of a pitch's berth to complete a transfer of tuning. Ivor Darreg called microtonal modulation "migration" or "immigration," instead, because for him, modulating microtonal scales was like leaving one country for another. 

The three genera of Greece were also modulated by pivot tone, from one genus to another. This is an early form of tuning modulation, as the point of the genera was specific intervallic sizes down to quarter and third tones, in the Aristoxenian sense. In fact, this same musical practice is exactly what Arabic maqamlar are about, borrowing all from the Greeks. 

Further to the point, the multiple time streams help differentiate the blocks of stratified microtonal intervals. The unpredictable groups of verticalities can be considered indeterminate, which can and will open up new types of chords. 

to be continued...