Music Mathematics Part I. Timeless Music Theory: Timeless Sinatra

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Originally for WFMU dj Vicki Bennett’s People Like Us Radio

Let’s explore music that is neither slow nor fast and for which time is arbitrary. To do so, we travel into the basics of what music is made from.

Let’s start with a building block of 19 seconds from Frank Sinatra’s “It’s a Lonesome Old Town” with a bit of background by arranger Nelson Riddle.

I selected this bit because it’s simple, only voice and a bit of instrumentation, and because a great performer like Sinatra uses subtle shading and attacks that develop features at different time scales. A sine wave is still a sine wave when you change speed: with Sinatra, however, if we slow the recording 8 times so that the word “around” lasts nearly 10 seconds,  you hear a beautiful glissando, while the vocal vibrato at the end of the syllable of “round” nearly becomes a melody itself.

Here’s an easy way to make “fast” and “slow” irrelevant, by playing the phrase at different speeds simultaneously. This is the phrase played at 7 speeds, at each multiple of 2 from the 8 times slower to 8 times faster.

So we have to call that tempo slow, fast, and many shades in between.

Here’s another playback at multiple time scales that overlap to produce new features. I hear something like a church bell that tolls five times.

That was Sinatra’s phrase at 7 speeds, in multiples of three:  9 times slower than normal, 3 times slower, original speed, and 3, 9, 81, and 243 times faster than normal. You might have discerned new patterns in the 10 seconds we just heard. These result, for example, from the peak of one soundwave superimposed on the peak of another to produce a sound that wasn’t in the original. Less noticeably, some of the soundwaves are out of phase and cancel out some of the original pattern.

A stopwatch says that little piece was 10 seconds long. But I think the length of the music, in contrast to the length of the original which is genuinely 19 seconds, is ambiguous. While you heard Sinatra at seven different time scales, we used 2 seconds of overlapping speeds repeated 5 times. The original phrase was ~20 seconds, the kernels that makes up the piece range from one 81^st of a second to 2 seconds, and ALL  the information ise heard in 2 seconds. So any length greater than 2 seconds, like the 10 second length we just heard, is arbitrary.

More provocatively, you may have heard patterns that last longer than the 2 second loop duration! For instance, I hear a slow melody repeated two and a half times: this is like a Middle Eastern geometric art form in which tiles in a mosaic produce patterns that are welcomed but not intended by the artist.

Here’s another time scale overlap of the same material, which somehow contains the sound of a train.

In that case, multiple one second loops of each of the different speeds from the previous piece contained all of the information of the entire piece. So the piece we just heard could be performed for any length of time longer than a second, unless you perceive patterns that are longer than a second.

The above was an intuitive introduction to fractal music composition: much more to come.