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Hello everybody.
This is a piece that I just composed:
The rhythmic aspect of this composition is based on Euclidean rhythms (a salutation to theGreek mathematician Euclid!). In 2005 Goldfried Toussaint published the article "The Euclidean algorithm generates traditional musical rhythms"(http://cgm.cs.mcgill.ca/~godfried/publications/banff.pdf). In this article he defines and explains the concept of Euclidean rhythm . These rhythms are so called because they can be obtained using the famous Euclid algorithm that allows us to obtain the greatest common divisor of two numbers. Using this algorithm, rhythms are achieved in which the accented beats of the measure are evenly distributed among the non-accented beats and the uniformity that is achieved is the maximum possible. The interest is that many of the prominent rhythms of world folk music have this Euclidean rhythm arrangement. Specifically, in this piece I have used four Euclidean rhythms, corresponding to the following popular music: "Cumbia Colombiana", "Tresillo Cubano", "Cinquillo Cubano", a bell rhythmfrom West Africa.
With a pair of numbers, the first indicating the number of downbeats and the second the total number of beats in the measure and using the sign x to represent the accented beats and the sign . for the weak, the cited rhythms can be represented like this:
"Cumbia Colombiana" : E (3,4) = [x. x x]
" Tresillo Cubano ": E (3,8) = [x. . x. . x.]
" Cinquillo Cubano ": E (5,8) = [x. x x. x x.]
West African bell rhythm: E (7,12) = [x. x x. x. x x. x.]
The intention has been to obtain a festive music for a certain celebration.
To contrast with such joy and to give a little more variety, in the harmony I have used more ambiguous and somber elements such as the fourth chords and also the four musical modes that I have used: Dorian, Aeolian, Phrygian and Locrian.
In the symphonic instrumentation, it is worth highlighting the inclusion of four saxophones, two sopranos and two tenors and also the absence of percussion instruments with the intention of achieving strong rhythmic sensations implicitly only with melodic instruments.
Replies
You have given us a wonderful piece here Ramon, thank you! I also appreciated your explanation of your approach to this compostion. I don't hear anything particularly mathematical about this, to my ears it sounds tonal, albeit not CPP tonal, but accessible with some mildly eccentric but engaging rhythms that most composers would probably be tempted to add percussion to but I think you have successfully avoided the need for that. Good work!
Thank you very much Ingo for listening to my music in detail and for your comments as kind as always. I appreciate you taking the time to do this.
It is true that it is tonal music but moving away from the Common practice period, for two reasons:
1. In defining scales and harmonic progression, modern modes are used (in particular Dorian, Aeolian, Phrygian and Locrian).
2. The harmony is based on the fourth chords.
It is also true that, although I usually use mathematical elements in my compositions, I try it is not noticeable in the way it sounds.
Un saludo.