### music physics: rhythms

###### Fri 03 January 2014

[caption id="" align="alignright" width="300"] Natural rhythms generator[/caption]

I'm still interesseted in music (de)composition. In this post, I want to focus on rhythm, i.e. only when a note is played and for how many time.

## notation

I will use the usual notation is sheets.

## note duration

In western music, note can last a multiple of the beat. The beat is the basic unit. Notes last mostly a power of two of this unit. We can summarize this in the following table:

 duration (number of beat) notation name $frac{1}{4}$ sixteenth note / semiquaver $frac{1}{2}$ eighth note / quaver 1 quarter note / crotchet 2 half note / minim 4 whole note / semibreve $(1+frac{1}{2})$ initial value . dotted note

Notes:

• dotted notes can also be dotted (duration: $(1+1/2)Big((1 + 1/2) \text{initial value}Big)$)
• equivalent notation exist for silence duration (rest, breve rest, ..., hemidemisemiquaver rest)
• this table is not exhaustive but should be enough for an introduction
• I still don't know how to correctly write music. I'm working on it

## music piece decomposition

[caption id="" align="alignright" width="300"] music decomposition[/caption]

A music piece is cut into beat measures. Usually beat measure are composed of 4 beats. Beat measures are marked out by bars. Note that measures are also called bar.

This bar can be seen as word separation, and group of measures as sentences.

## mathematical modelisation

Due to possible word representation of measure, text mining techniques could be used. Let's define an alphabet.

The requirement are:

• indicate note duration
• indicate rest duration

The following is straigth forward:

• one letter (=symbol) per note indicating the duration (multiple of beat time)
• one letter per rest indicating the duration
• one word separation per bar

I propose:

 duration (number of beat) rest note $frac{1}{2}$ z Z $1$ a A $2$ b B $4$ c C

Note that this is not yet tested and ongoing reflexions.

As an example, given this notation, the first line of the simple sheet names guatacando is:

[caption id="" align="alignright" width="300"] Guatacando[/caption]

aAzzZz zZaB

To be continued...

(Non-)Related articles

Category: maths Tagged: bar beat duration note rhythm Typesetting musi maths