music physics: rhythms

Fri 03 January 2014

[caption id="" align="alignright" width="300"]English: Heart diagram with labels in English.... 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.


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
[latex]frac{1}{4}[/latex] Sixteenth Note sixteenth note / semiquaver
[latex]frac{1}{2}[/latex] Eighth Note eighth note / quaver
1 Quarter Note quarter note / crotchet
2 Half Note half note / minim
4 Whole Note whole note / semibreve
[latex](1+frac{1}{2})[/latex] initial value . dotted note


  • dotted notes can also be dotted (duration: [latex](1+1/2)Big((1 + 1/2) \text{initial value}Big)[/latex])
  • 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"]English: Shattered remants of broken guitar wi... 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
[latex]frac{1}{2}[/latex] z Z
[latex]1[/latex] a A
[latex]2[/latex] b B
[latex]4[/latex] 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"]image7 Guatacando[/caption]

aAzzZz zZaB

To be continued...

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