Rhythm as a point

(Varning: this blog post might contain content unsuitable for artists, music lovers and others. It includes some quite nerdy ideas related to music and research)

Last week I came across an extraordinary way of describing rhythm. When I first saw it I got a bit upset but when I suddenly realised what a beautiful way of describing a rhythm it is, I almost fell in love with it. OK. It’s got its limitations but as long as you stick to a three note rhythm, it will work beautifully.

The concept is as simple as it is genius. One way of understanding it is this:

Take this rhythm:

The relation between the three note lengths could be expressed

1 : 1 : 2

If we say that the total length of the notes is 100% we could also express the rhythm as

25% : 25% : 50%

Now, lets draw this rhythm using a triangle where the length of each side represents 100% of the total length of the rhythm:

In this way, we can actually represent any three note rhythm in this graph making it possible to study i.e. other divisions than our notation based systems of quarter notes, eight notes, sixteenth notes etc. It is also proven to be very useful when we want to study and visualise rhythmic perception and performance.

If you got all the way to this point and still think it’s interesting, please have a look at the article Structure and Interpretation of Rhythm and Timing where the Henkjan Honing, who designed the concept, describes it more thoroughly.

7 thoughts on “Rhythm as a point

  • 9th November 2021 at 3:43 pm

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  • 15th November 2018 at 7:29 am

    Super intressant !!

    Vad sägs om ett lunchmöte ?

    • 3rd December 2018 at 8:42 am

      Gärna! Vad sägs om en lunch på KMH?

  • 14th November 2018 at 12:22 am

    Cool idea!
    Without having read the article (wouldn’t download to my phone) I guess a four note rhythm can be modeled using a square and applying the same ruleset as for the three note rythm gives a rectangle for each rhythm who’s center will represent the point for the rhythm. Right?
    If so, I think the concept keeps scaleing on, though it is a bit harder to find the center of polygons beyond squares.

    • 3rd December 2018 at 8:41 am

      I don’t know. I would be great to discuss further. I studied Cello instead of math at high school so there are lots of mathematical perspectives I haven’t seen yet. It seems to me that the triangle gives opportunities the square will not, like letting three values be represented by three trajectories and meet in one unique point.
      Would four values in a square rather make up a unique rectangle?

  • 13th November 2018 at 2:48 pm

    Ytterst lite musik använder tre toner. Användbart endast när man konstruerar dörrplångar?
    Hur går man vidare; delar man iterrativt in de följande noterna i grupper om tre?
    Och vilken praktisk nytta kan man ha av detta?

    Vid närmare eftertanke; kanske detta är ett sätt att grafiskt presentera en synkop och “häng” i en jazzrytm?

    • 3rd December 2018 at 8:32 am

      Det är ju helt klart en av modellens största begränsningar, men ändå visar den sig kunna visa väldigt intressanta saker om hur vi strukturerar rytmer som vi hör olika beroende på vilken kultur vi tränats in i. Och precis som du är inne på delar man ofta in respektive slag i underdelningar. Och vilka de är kan nog också variera.


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