When is a musical note a different note?

I've been talking a lot about transduction recently.  Transduction is the process whereby a distinction gets maintained.  In engineering, it is the process of taking one form of energy and turning it into another - like an electric transformer. But the point is it produces a boundary.

The idea of transduction is useful because it turns what we usually think of as fixed 'categories' into processes. So think of a category or a subject.. 'maths', 'geography', 'chair', 'happy', 'ill', etc... Now think of the process which makes that category. It turns out that any category has two sides: a category is a boundary. The process of maintaining it works from both sides of the category. If you want to change a category, you have to change the process.

So you want to change the culture in an organisation? You need to understand where the transduction is happening and 'tweak' it.

Transductions are recursive. One category depends on many many other categories. More to the point, a category is not necessarily something that can be expressed in language. All perception is transduction: to perceive a difference is to experience a transduction.

That's useful when we think about music. To differentiate one note from another is to experience a transduction. What does that tell us about how transduction actually works? Well, to distinguish one note from another depends partly on there being multiple descriptions of a note. A note is never a simple thing: it is a multiplicity of frequencies to start with, which give it a timbre or colour. It also has a beginning and an end, it has a volume, and so on. A note is different from a silence. So a single note is perhaps a kind of transduction between a silence and the note. Since a silence also has multiple descriptions (silence has many qualities), a note is the difference between one set of multiple descriptions of something and another set of multiple descriptions of something.

If we were to compare one note with another note, then some descriptions between one note and another note might be the same - they might have the same volume for example. But they might have different frequencies, or they might have different timbres. 'Another' note is a change in the arrangement of multiple descriptions. That is what the transduction does: it shifts from one set of descriptions to another.

What about detecting that a note is "the same" note as another? That's an interesting transduction. To say that it is "the same" is to still detect that it is "different", but it is different in a way where the boundary between one and the other produces a new category of "the same".

A new category? Ah! A new transduction!