One of the many items lodged in my musical memory (and it’s been there for forty years) is the ‘ritornello’ heard at the beginning of Bach’s Fifth Brandenburg Concerto, all 121 notes of it. You can see it notated here. (I didn’t have it quite perfect, it turns out; I thought the eighth-note ‘e’ at the end of the second bar was two sixteenth-notes.) I can play it through in my ‘mind’s ear’ at will, or sing it (though the range, of over 2 octaves, makes that a bit tricky). It’s not ‘random-access’: I basically have to start from the beginning.

Now,  to represent this tune in a straightforward computer-friendly way would occupy about 4096 bits. But, obviously, its brain-based representation is nothing like what a computer would use.

In one sense there is far less information content than the note-for-note calculation would imply: the tune is ‘memorable’ precisely because it is a tune; it makes musical sense. An arbitrary sequence of 121 notes chosen from a span of 2.1 octaves would be virtually impossible to memorize. In a real tune, the choices for each successive note are limited; we could draw an analogy with the predictive algorithms by which the email app on your phone offers you a few likely choices for each word in your message based on what has gone before.

But consider what this means for the brain-based representation of the tune: it is tied in subtle ways to a whole subsystem of musical knowledge.

Just ponder the implications for the gap between the fact-of-the-matter about connections between neurons and the meaning that those connections represent. More to come on this topic.

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One Response to Ritornello

  1. Depaver Jan says:

    Hi Phil, Good that you’ve done another essay, and doubly good it’s on music! The beginning of the Concerto is something familiar to me that I thought I could hum part of, but the piece rapidly gets complex. As you know I don’t read music except for my crude song sheets. Do you know why all my compositions are short and are just songs? — because the paper runs out and I always feel I’ve done quite a bit to fill up one 8 1/2 x 11 sheet of paper in my notebook! I’ve occasionally written essays on music and its potential for social change. I’m still a believer, but I’ve not written a full song since June (and that one after maybe a year of no completions). I found a nice performance of #5, Croatian Baroque Ensemble at https://www.youtube.com/watch?v=BnjqGhAlFzs — 1.6 million views since 2012 is impressive. I have a thing for harpsichord, especially when ‘60s rock groups used it! I hope to get more involved in music again soon. Keep playing the piano! Jan


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