musical time

[bachus]

I have been trying to create a "computable" definition of musical time. In doing so I have found it necessary to recognize two distinct types of musical time, rhythmic and arhythmic. Rhythmic time is characterized by a context of temporal expectations provided by a meter. Rhythmic time is displayed/edited in standard notation. Every note event that occurs in rhythmic time is linked to its position in its meter's accent map. Attached is a screen shot of the display of the upper levels of the accent map of 5/4 meter subdivided 2 + 3.

At one extreme arhythmic music has a pulse but no subdivision/accenting of pulse groups. Here accent is either uniform or evolves with a sense of smooth continuity. At its other extreme arhythmic music has little of no accent/pulse at all.

The basic assumption/restriction on time is that all musical events are expressed as an offset from the start of some measure and the offset is given in Chronons which unit is defined as follows: The number of Chronons in a whole note is equal to the least common multiple of all the standard note lengths known to the system including tuplets and tuplets within tuplets.

At present I am using 417372849653760 Chronons to the whole note. Such a definition allows for extremely simple definitions and fast computation of many temporal operations on standard note lengths. However defining a range of tuplets within tuplets can easily exceed the 64 bit limit of the current generation of machines. Still any ordered system of note lengths whether time, percent of measure, etc., could be mapped to Chronons (with the necessary approximations) with out fear of temporal "grain".

By habit I think in terms of music with meter. What alternative divisions of time seem most desirable to others is of great interest to me as would be thoughts regarding meter.

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Zy meter 5-4.JPG
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[bachus]

Here is a partial map of 12/8 compound meter. The bar height represents the strenght of an accent. But a meter's accents define a pattern of expectations not actual note accent values -- eh?

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meter 12-8.JPG
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[bachus]

And here is the map of 8/8 as a meter parsed 2+3+3. Which, with 5/4, should make clear that a time signature is not sufficient to define a meter. Though for simple and compound time the grouping has default values and can be derived directly.

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meter 8-8 2+3+3.JPG
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[nobody]

This looks interesting, but I have to admit I'm not sure I quite follow along.

1. Why find a computable definition of musical time? What is meant by a "computable definition"?

2. What is a chronon?

[bachus]

[Acoustic Interloper]

[bachus]

[Acoustic Interloper]

[bachus]

[Acoustic Interloper]

Thanks! I found out later that the pattern used as an example in the paper is the Brazilian Baion. I learned this fact when I was invited to sit in with a university world percussion ensemble after I finger picked it for the prof on banjo. My finger patterns locked right in with the ensemble's drums with essentially no practice. My guess is that I learned it from listening to Brazillian percussionist Airto Moreiro on some Miles Davis albums from the Seventies.

The subconscious can do wonderful things!

[usw]

what about rational numbers ?

[bachus]

[usw]

Being both symbols and numbers, they allow you to perform arithmetic operations in a very compact/convenient form and save quantization errors for the final stage, when applying them to the discrete time-grid of your choice

[bachus]

Ah! From its definition the number of chronons in a whole note is the common denominator of all note lengths known to the system including, for example, double dotted 13th-tuplets. This allows you to perform arithmetic operations in a very compact/convenient form without quantization errors

[usw]

[Acoustic Interloper]

Ah, blessed temporal harmony among the posters.

I've added a "todo" to dig up some of my 80's vintage texts on temporal logic and see if anything jumps out. It may not contribute here, but it might prove catalytic for my own composing.