Musical Patterns

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gongchime
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Musical Patterns

Post by gongchime » Sat Jul 12, 2008 8:29 pm

If you were wondering just what exactly are the properties which fractals and algorithms have that allow them to generate music similar to what humans make, then this is your place. Frequently it's an aperiodicity but which isn't completely random or even pseudo-random. There's structure but it's often open ended. Remember when there was a thread with a bunch of number sequences in it and the comment was made by me that a person minimally needs 1 hour of music to play in order to be considered a professional performer? Of course several ways of accomplishing that are to listen to CD's, attend concerts, buy songbooks, find teachers etc... and we should persue all of them.Yet just about all of the COMPOSERS in the classical vein, although they always say a trained composer makes better music than any system, have studied the use of fractals, algorithms etc... If you start talking about it, it's not like they say what's that? They've usually already explored it. So, it's not just for programming computers to make music.One of my favorite comments by one such a person was that he liked variety, so it was more interesting to him when, if a system was being used, is if it was broken. Breaking it somewhere around the golden mean seems intuitive (which is yet another system). 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/seque ... s.htmlHere is another one with probably thousands: http://www.research.att.com/~njas/seque ... Aa.htmlNot 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.

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Re: Musical Patterns

Post by gongchime » Sat Jul 12, 2008 10:08 pm

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 lowest 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.What humans seem to like is a balance between simplicity and complexity. This is similar to a fractal: it repeats but in an ever changing way. It's probably not good if the pattern is only identifiable after looking at hundreds or thousands of members in the sequence. So, not every sequence is going to be useable for music that would be appreciable by humans.Here is an interesting example of a pattern that repeats in an ever changing way:100110/0101/1010/01/01/1001/10/10/01If you keep repeating these patterns in this manner, ironically, you end up with a pattern that never repeats.

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Re: Musical Patterns

Post by gongchime » Sat Jul 12, 2008 10:14 pm

Also, we can take note lengths such as short and long and combine them into a structured but never repeating pattern. This is only one of several ways to do this. And both this and the above pattern have already been used by many composers without recourse to a computer. Just an interest in mathematics.SS,LSSS,SL,LSSSSS,SSL,SLS,LSS,LLSSSSS,SSSL,SSLS,SLSS,SLL,LSSS,LSL,LSS

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Re: Musical Patterns

Post by gongchime » Sat Jul 12, 2008 10:27 pm

So, in the first links in this thread there are mathematical sequences found in "nature". One group which seemed promising for a pitch sequence was the Sprague Grundy Values for Dawson's Chess if we assign a number to mean pitches and perhaps the zeros mean rests. I thought it would be good for that because the first line of the string would primarily create a melody that keeps in the range of steps and thirds.It's like this;01120311033224052233011302110 etc...

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Re: Musical Patterns

Post by gongchime » Sat Jul 12, 2008 10:33 pm

It has a cousin called the Sprague-Grundy Values for games of Kayles. I thought it would be good for creating both a pitch series and rhythms where if each rhythm from a chart is assigned a number. The most important rhythms being a 1 etc... You can click the chart to see it larger.Sprague-Grundy for games of Kayles goes; 01231432142641271432146741265 etc...

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Re: Musical Patterns

Post by gongchime » Sat Jul 12, 2008 10:47 pm

The Class Number of Q Series would produce rhythm patterns of ever increasing complexity.111221212424142366434422648445264423688818474etc...

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Re: Musical Patterns

Post by gongchime » Sat Jul 12, 2008 10:51 pm

The Infinite Juggling Sequence seems like it would also be good for rhythms because there would be a balance of repetition and change.3342333342423411etc...

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Re: Musical Patterns

Post by gongchime » Sat Jul 12, 2008 10:54 pm

In "The Number of Factorizations of n into Prime Powers Greater than 1", the repetitions of 1 while the series progresses would help create a sense of unity; 1112111321121115121211321321etc...

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Re: Musical Patterns

Post by gongchime » Sat Jul 12, 2008 10:58 pm

This Infinite Fibonacci Word (there are several) would be good for alternating two pitches or two rhythms in a complex manner;1011010110110101101011011010110110101101011011010110 etc..

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Re: Musical Patterns

Post by gongchime » Sat Jul 12, 2008 11:02 pm

For "The Number of Segments needed to represent 'n' on a Calculator Display" could be an ever rising pitch pattern or an ever increasingly complex rhythm scheme;6 2 5 5 4 5 6 3 7 6 8 4 7 7 6 7 8 5 9 8 11 7 10 10 9 10 11 8 etc...

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