My Korean composition professor, who is a big fan of Eastern European classical music especially the Polish composer Lutoslavski, told me to write ALL of my rhythms for classical music using the golden mean/fibonacci series in a certain way. Where, for example, 3/4s of the way through there was some variety within two measures. Then again at 3/4s through 4 measures which includes the first two already discussed. And again at 3/4s through 8 measures.
Anyway, if you’re so inclined to search for meaning within mathematical "systems", I came across this page which has about 147 number sequences 1/3rd of the way down the page.
http://www.research.att.com/~njas/sequences/Seis.html
Here is another one with probably thousands:
http://www.research.att.com/~njas/sequences/Sindx_Aa.html
Not all of them seem musically useful to me and I only looked at the one’s with an asterisk which are supposed to be frequently resorted to by mathematicians making them more important in the math world.
How to translate these into musically meaningful ideas will be the topic of the next posts in this thread.
One definition of a pattern is: a succession of local similarities.
Pattern recognition software such as speech recognition, or face recognition use some of the same things we’ll be talking about here. There is also software for identifying patterns within music, which can be difficult because sometimes a repetition of a pattern is so altered that it could just as easily be defined as a new pattern.
They usually say that musical patterns are based on contour, pitches and rhythm. Once a pattern is identified, the third repetition of a pattern can be found merely from it’s contour even if the melodic and rhythmic aspects are significantly distorted.
A note or group of notes make poorly perceptible patterns only when they cannot be related to more salient patterns. Simple suffixes and prefixes of patterns cannot be considered new patterns.
The importance of a pattern within the music is a product of it’s length and the frequency of it’s recurrence. Another musical pattern they talk about is that the degree of slowing reflects the importance of a boundary. So, if either you’re playing a longer note such as a whole note at the end of a tune, that usually signifies it’s the most important boundary in the composition, or if the tune is performing a ritardando after the climax and approaching the final pitch and rhythmic event.
Some of the most basic patterns in music are if a note begins and ends a piece.
If it’s in a metrically important position, is louder than the rest and if it’s accented.
If it has a long duration and if it’s repeated.
If it’s the highest lowers or pivotal within a defining pattern.
Or a member of the harmonic relations, octave, fifth or fourth even if they are only consecutive.
More complex patterns would be motifs, antecedent phrases, consequent phrases, and sections.
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