Musical Patterns Three

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:

10
01

10/01
01/10

10/01/01/10
01/10/10/01

If you keep repeating these patterns in this manner, ironically, you end up with a pattern that never repeats.

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,L
SSS,SL,LS
SSSS,SSL,SLS,LSS,LL
SSSSS,SSSL,SSLS,SLSS,SLL,LSSS,LSL,LSS

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...

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...

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

111221212424142366434422648445264423688818474etc...

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

3342333342423411etc...

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...

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

1011010110110101101011011010110110101101011011010110 etc..

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...

As would "The Number of Letters in English names of length ’n’";

4 3 3 5 4 4 3 5 5 4 3 6 6 8 8 7 7 9 8 8 6 9 9 11 10 10 9 11

I forget the name but the code for this one in the second link is AO72203 would produce only stepwise pitch motion if each number is assigned a pitch;

1 2 1 2 1 2 3 2 1 2 3 4 3 2 1 2 3 4 5 4 3 4 3 2 1 2 3 4 5 6 7 6 5 4 3 4 3 4 3 2 1 etc...

as would "The Number of Runs in a Binary Expansion of n";

1 2 1 2 3 2 1 2 3 4 3 2 3 2 1 2 3 4 3 4 5 4 3 2 3 4 3 2 3 2 1 etc...

and "Roman Numbers for n" with occasional motion by third and even more rare by fourth;

1 2 3 2 1 2 3 4 2 1 2 3 4 3 2 3 4 5 3 2 3 4 5 4 3 4 5 6 4 3 4 5 6 7 5 2

Some Cellular automata would produce various patterns, some that involve simultanaeities where some voices would linger, some drop out, and some appear. It could be interesting for experimental voice motion/chord construction.

Expert and Real Music Based Systems

More recently, systems have been created which take input from actual music, even a live improvisation, and can create a meaningful response in real time. The computer takes the previous improvisation as input, performs transformations on it lightening fast and then gives a performance of its own nano seconds later. It’s these systems that are fooling experts, especially when they’re combined with a knowledge base such as a hundreds of licks which can also have transformations performed on those patterns as well.

The programmers don’t need to tell the computer to test for fitness before the computer puts out the music. If good music is used to initiate the system, then good music is coming out. Initiating an expert system with a fractal or a second order Markov chain just does not produce music as good as if it’s initiated with quality music. In that case, the computer is doing almost exactly the same thing that you’re favorite guitar god did to come up with all their albums. The computer listened to existing music and then changed it.

It’s not exactly the same though. A human’s musical cortex can be FAR more flexible and nuanced than a computer’s. And can process at a high level unconsciously and even while a person sleeps. But to get it that way takes tons of practice, intelligence and the capacity to memorize a lot of music. Yes, a computer can become an expert but it cannot do it at the same LEVEL of expertise that is possible by some very special humans and it cannot become an unconscious competent the way people can. If you ask some experts to teach you how to compose music the same way they do it, they can’t tell you. Or they say it’s all intuition. It’s not going too far to say that they actually consciously forgot how they learned what they do. They literally can’t remember. It was a lot of work and it has all been internalized. It’s proprioceptive now. Most of what they learned bypasses all of their conscious thought processes and takes a direct channel from the subconscious. It’s a huge benefit to them as a composer because everything has been streamlined. If you ask a computer how it’s composing music, there’s never a point in time when it can’t tell you exactly what it’s doing. That’s a huge benefit if you’re a student.

Experts are operating in the stratosphere and computers and beginning students are operating in the dust. If the computer was a beginning student, would the expert start at the level of the stratosphere in his lessons to it? A better approach might be to ask the question, “What parameters would an expert educator and musician give to a novice or intermediate student so that they can create a lot of good music quickly and easily but not get into too much trouble?”

It just needs to be good ENOUGH. If you demand the optimum, then yes, you need to study hard at Berklee for several years and pay the tuition. If you can double your investment after graduation it might be worth it. For some people it will work. For others it won’t. If you want to save time and test the market first with a smaller investment of time and money, yet still have your music take you and your listeners somewhere interesting then this course has what you need.
For the purpose of this course, what the real music initiated expert systems are doing is good enough for us at this point in time, until you can put in the practice to memorize a lot of music and acquire other compositional skills. Even then, there’s no guarantee that you’re musical cortex will create the desired output, although naturally it’s always fun to try.

The Evolutionary Approach
In the evolutionary approach the programmers say that being close to the style of songs that were put in is not good enough for high quality and creative new music. So, they extract sequences of notes that are conceived as melodic words within that style. Using them puts a limit on notes that can be adjacent to each other.

The “genes” of two different songs or two different styles can be mixed such as Bach and Jimi Hendrix and during the breeding process the computer introduces musically meaningful operations such as retrograde, inversion, transposition, augmentation, etc... This overcomes the truly horrible results with other methods that introduced "corruption" through random procedures. The genes in this case are the melodic and rhythmic series which are extracted from the music and not DNA.

The fitness of the results are judged by their adherence to voice leading rules. Some of the other rules used for evaluating fitness are the desired level of syncopation, melodic density, beat repetitions, the number of new notes, maximum interval sizes, the number of changes of direction, and types of note transitions. They also use "musical grammars" to narrow down the number of results that humans are given to pass or fail. Then about 1/3 of the weakest carriers of the material are killed off so the music would theoretically get better and better over time.
I wanted to say that I've met some people who resist thinking about their music consciously like the plague. Some people believe that doing it without thinking is best. But for many people, while they're trying to do that, their career is floundering and wasting precious time just like a lot of us have done. Some people are unconscious competents (they consistently write good music without thinking about it too much), some are conscious competents (who are good at explaining what the unconscious competents are doing) and some are incompetent (and need no introduction).
The unconscious competents can't tell us what they're doing. Hopefully that's who you're listening to. The conscious competents can tell us what the unconscious competents are doing. Hopefully they were our teachers. The incompetents hopefully aren't recording or teaching and god help that they're not us.

A few people have difficulty becoming competent through the conscious method. But it doesn't hurt them as a musician to try. Their intuition hasn’t gone anywhere just because they switched their brains on. If the unconscious method isn’t working for them, ragging on the people who study it consciously isn’t helping them one bit.
If you want to be a brain surgeon, you don't just wing it. You study hard everything that there is to know about it. If you have the instincts from listening and playing a lot of great music that causes you to write good music all the time or that allows you to break the "rules" for a good reason yet still come up with excellent music, then analyzing too much might get in the way. Most people aren't the Beatles.

For you to use the transformational methods that I’m recommending, it implies being able to either get your hands on a song book; in guitar tablature, traditional notation or some other way of presenting it. Or being able to transcribe the sounds you hear into notes on a page in some kind of notation. What kind of notation you use is not important. Actually, for some people, it’s not even necessary to use notation.

There’s a story about the origins of Jazz Bebop music. My friend Leandro from Argentina who I met in Bali told me an anecdote that he heard from an American musician. The story goes that the players who used to perform Bop had played the tunes so much and knew them so well, they would play musical games from the tunes when hanging out with their friends after a gig. They would challenge each other to try and play a song they knew backwards and if that was too easy, then they would try to play it backwards three times faster. According to him, that became the origins of Bebop. Clearly, they didn’t use pencil and paper to do that.

These transformational methods are what allowed them to come up with a new style of music and allowed me to produce more music than I needed for my first album. But I didn’t use an expert computer system. I did it on paper by hand. It was fast, fun and easy. I recorded a CD of metal gongs and xylophone music called "Garden of Contemplation" with Aparna Panshikar, a vocalist who was world music artist of the year in both Korea and India. It was under my Traditional Independent Record Label: Gongchime.

My arrangement of the "Kang Ding Love Song" and my composition "Vietnamese Melody" were forwarded at the largest independent A&R Company in the world, Taxi, to a Fitness and Yoga Meditation listing. In 2006 my tunes Vietnamese Melody and Champa were in the top 10 on the website Broadjam in the Asian category for several months. In 2007 my tune "Visiting Shaman" was in the #1 position in the Asian chart. Later my tunes Vietnamese Melody and Champa were accepted into a music library available to TV and film producers.
So, I’m convinced these methods work because they already worked for me and worked for the creators of Bebop. They can work for you too. Have a look at the compositional chart I used to create the music that was both forwarded and accepted.

Expert Systems, Fractals, and Algorithms,

Some programmers initiate music composition systems with fractals or algorithms which the computer then performs transformations on, such as playing the input backwards, upside down, upside-down and backwards, faster, slower etc… And then the program performs transformations on the transformations.

If you were wondering just what exactly are the properties which fractals and genetic algorithms have that allow them to generate music similar to what humans make, it's an aperiodicity but which isn't completely random. There's structure, but it's often open ended and infinitely long. This is somewhat similar to human music but not spot on. Sometimes in order to identify the structure within an algorithm, you’d have to look at thousands of individual members within it before you could find the pattern. Those specific algorithms are not normally used for music composition. So, just because it’s an algorithm doesn’t mean it’s good. Even a good algorithm only creates pseudo-human-like music. It might repeat patterns in an ever changing way, which could be mildly interesting at times, but they never fool experts into thinking the music was created by another human let alone by another expert. It usually sounds quite amateurish.

Below is only one quarter of an example of a gene sequence. Computer programmers can assign different musical parameters to the recurrences of the amino acids adenine, guanine, cytosine and thymine to create different effects.

… 1 ggcagtggtg ctgggagtgt cgtggacgcc gtgccgttac tcgtagtcag gcggcggcgc
61 aggcggcggc ggcggcatag cgcacagcgc gccttagcag cagcagcagc agcagcggca
121 tcggaggtac ccccgccgtc gcagcccccg cgctggtgca gccaccctcg ctccctctgc
181 tcttcctccc ttcgctcgca ccatggctga tcagctgacc gaagaacaga ttgctgaatt
241 caaggaagcc ttctccctat ttgataaaga tggcgatggc accatcacaa caaaggaact
301 tggaactgtc atgaggtcac tgggtcagaa cccaacagaa gctgaattgc aggatatgat
361 caatgaagtg gatgctgatg gtaatggcac cattgacttc cccgaatttt tgactatgat

Just about all of the contemporary composers in the classical vein that you might run into at a university, although they always say a trained composer makes better music than any system, have studied the use of the Fibonacci series, fractals and algorithms etc... If you start talking about those, it's not like the classical composers will say, “What are those?” They've usually already explored genetic algorithms and such. So, it seems fractals and the like are not just for computers.