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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.
Impressive piece, Ramon, and most inspiring in its creativity and innovativity.
A few times I get reminded of LvB 9th 1st mvnt, also a rhythmic piece and at other occasions i think of Bartok´s concert for orchestra.
But the piece is truly unique.
Congrats to this achievement.
Kjell
You are very generous, Kjell with your kind comments, and I really appreciate them !
In addition to my main objective, which has been to experiment with Euclidean rhythms, I have set myself two secondary objectives: the explicit construction of melodic themes from motivic units, which has given it a quite tonal character, perhaps for this reason it has given you remembered compositions from the period of classicism (which makes me proud); the other objective has been to combine modal harmony with fourth chords which has given it a more modern character.
I have also listened to your latest compositions made with NotePerformer (on SoundCloud), especially the last one: "Come Into Being Np" (https://soundcloud.com/user-892939153/come-into-being-np). The sound production you get with NP is very good with very correct timbres. The piece sounds very good, it is very beautiful; it is very well structured, very balanced but with strong, dynamic and expansive passages, with an excellent orchestration; it is very pleasant to listen to. You are certainly doing very good works!
Un saludo.
Ramon
Very interesting piece! In spite of its mathematical roots I did not hear it as mainly mathematical, but as a series of interesting contrasting rhythms that's actually pleasant to listen to. It's pretty amazing that you managed to pull off a strongly-rhythmic piece without using any percussion instruments! The 4th-based harmonies make it sound somewhat like Holst or Walton.
I have to admit, though, that towards the end the eccentric rhythm started to grate a little. I wonder if you could have sequenced the rhythms in a more dramatic / climactic way toward the end to give it a more satisfying climax. But that's just my biased uneducated personal opinion, so take it with a grain of salt.
Thank you for listening to my music and for your kind comment.
Certainly, mathematics, being only a secondary tool in the creation of this piece, goes unnoticed.
I understand your disappointment about the end of the work insofar as it does not follow the logic of a crescendo that ends in culmination as it could come off its rhythmic and thematic evolution, but I preferred a final resolution that was not so predictable opting for an ending that was more open and suspensive, since I thought it was more in line with the serenity and ambiguity of the harmony of the work. But perhaps what would have improved the overall arrangement and balance of the work would have been to make its third (and last) part shorter and reduced and that it would not have been a re-exposition so similar to the first part.
Un saludo,
Ramon