Algorithmic Musings...

Thoughts on the mathematics behind music

Discussion:

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• 1/30/2008 - Hello World - Chris - Started wiki. For the first phase of this, I think we should read up and post and relevant souces. Next we will need to make definitions, and then we can begin to decide on the scope of our project. I think this is very important, for instance if we wanted to generate every possible type of music, and all music is defined as all noise, then we will have to possibly look at audio samples (digital) as a single element that we will be looking at for generation. On the other hand, if we define the type of music we want to generate as bebop jazz music with a limited instrument ensemble (drums, keys, bass, sax), we could find more concrete patterns such as analyzing chord progressions for the piano, style over, rhymic patterns of the drums, sax soloing styles and patterns, and therefore it would be a more concrete example. However, I think this is mearly a start into what exactly we would want to accomplish which comes to our first overall task: find out what problem/question we want to solve/answer.

• 1/30/2008 - Sumanth - It seems that the essence of our 'problem' is 'creating music algorithmically'. Stated as a question, it becomes, "Can we create algorithmic music? Is it possible?" As we discussed, it's incredibly easy to accomplish this task, however, creating *enjoyable* music, or music with a high "goodness" factor, is a much harder problem.

Psychology and perception play important roles too. It is embarrassing to admit, but after listening (not by choice) to a Backstreet Boys album a number of times, it started to somewhat seem at some level, enjoyable.

Remember how "awesome" NES graphics seemed; how great 8-bit audio sounded (sounds!). How important is expectation in creating the overall experience?

• 1/2/2008 - Sumanth - Thinking about things further, it seems like one can almost declare, "music does not exist!" (dramatic pause). Or maybe, music does not exist in a physical sense, instead, it is exists as a percept. Playing the same series of sounds to two different people, one may find them unlistenable, the other may actually enjoy Indian music. We can let the word 'sound' do most of the heavy lifting, since it already bridges the gap between the physical phenomena, waves, and the stochastic percept that occurs in our minds. But then again, I may just be throwing around words that I am not familiar with.

• 2/13/2008 - Sumanth - Wait a second. Isn't music already algorithmic? Isn't that why mashups work so well? Everyone is following similar rules...
• 2/13/2008 - Chris - I don't think "Music" is algorithmic, but rather the way we play it has a certian procedures and rules. So essentially we could use those 'rules' or 'procedures' to make an 'algorithm' to model how an actual human would play the music... the procedures for a Jazz keyboard player to comp along with a lead sheet are different than that of a classical harpsichordist trying to read baroque-styles figured bass lines... but essential they are both 'reading a losely defined program' and then 'improvising or interpreting based on prior knowledge'. This is fundamentally where the AI comes in... we need to give the computer context. If we are just making voice leading for a SATB choir... we can use predefined rules that some people wrote down in music theory books, but is that really being creative? Can a computer program be creative?.....
• 2/24/2008 - Chris - http://www.fm3buddhamachine.com/ ... Interesting...
• 3/31/2008 - Sumanth - "hey, just going way out there, but... could a regular radio be considered a type of 'algorithmic musical device'? in the sense that there is nothing inside the radio box that is inherently musical. the circuitry is, in essence, generating music magically out of thin air. isn't this basically what we want our device to do? the logical argument is to say that the radio is playing back information created at another location, and our device will be creating this information 'on the fly', but is it really? as my brain starts to heat up, i get back to the question of, where the EFFWORD are these words i am typing coming from? how is my brain generating them? is it generating them 'algorithmically'?"
  • ... words, words, words ...
  • Chris - "Essentially if we downloaded somebody's brain into a computer. Then we 'ran' the brain and told the brain to generate music... would that be algorithmic?"
  • What I think you did is hit upon the ideal solution, and simultaneously, the most difficult one.
    • Wiki's are kind of pain in the asses, aren't they.

• 4/1/2008 - Chris - (copied from Sumanth's instant message) - "i guess the way humans create music now is sort of a genetic algorithmic process. no one really just pumps out a tune, right? you give a sequence of notes a shot, then listen to how it sounds, tweak, loop. if i'm not wrong (i don't write music), then an algorithmic music generator should probably use a similar process. feed it a list of things that it knows sounds 'good', then have it create a bunch of sequences using these rules, then it should evaluate them. so, i guess, we can break it down into these three steps.

each is a huge task in itself, but it seems like it would be a guide. also, i think this is how people solve similar AI problems now."

• I agree, and I think this is an example : http://en.wikipedia.org/wiki/Evolutionary_music
• The fitness function however, would be difficult... what is good and bad music?
• 4/1/2008 - Chris - I think at this point, we are trying to define algorithmic music starting at something akin to Peano's Axioms. Many people have tackled algorithmic music, but their algorithm has limited scope. This is essential what a musician does (or most do) they limit their scope, its easier, and faster, and gets results. I think if every musician had to pick every note, dynamic, time signature, tempo,etc one by one for each instrument for each quantitzed moment in time, composition would be like a filtered random function. Then we hope the composers fitness function would be adequate, and assume the composer has loads of time on his/her hands. I think at this point, we could try to define the whole entire lot of 'algorithmic music' which we still don't know what algorithmic means, could mean any sort of musical composition, we could formalize the whole system and write a book, then write/give examples of each subset of algorithmic music in the form of a neat C/pd program that would exhbit that functionaltity. Or we could pick a piece... try a subset that would make really good sounding music (using our own fitness function) and sell it to the music industry. I guess we need some direction here.

Random Ideas:

• Adaptable algorithm that learns 'good' music and 'bad' music. Output music, post on web, have users rate, and then use that feedback to make better music. Vary audience, construct perfect pop song, make $$$.
  • See "audioscrobbler" and similar systems: http://www.last.fm/
• http://en.wikipedia.org/wiki/Markov_chain_Monte_Carlo
• http://en.wikipedia.org/wiki/Markov_chain#Music
• This technique applied to literature... http://www.eblong.com/zarf/markov/
  • interestingly enough, literature sampled from vastly different sources, kinda sounds blotchy... maybe this will work with music samples from different genres... -cg
  • this is awesome. so, they are basically analyzing the syntax of a human language, and mimicking it. This is reminding me of AI reading I've done. I'll try to cite some more sources. -sp

Definitions:

A good foundation for any theory is a solid set of terms and definitions. These terms help us create an ontology for music.

• Technical
  • Music
  • Noise
  • Song
  • Structure
  • Genre - what is the concept of "genre", and is it separate from the series of notes that comprises a "song"? For example, the same set of notes played through different filters/at different speeds/with different instruments seem to be able to constitute different "genres" of music. i.e. Cover songs.

• Perceptual
  • "Goodness" (as in music)
  • Quality
  • Mood

Todo:

• Research
• Document
• Collaborate

Tools:

• pd
• brain
• ears

References:

Note: Please post any references used in this section and cite in any sections that you post.

1. Music: A Mathematical Offering - http://www.maths.abdn.ac.uk/~bensondj/html/music.pdf [9.7MB]
2. Linear Algebra and Music - http://web.mit.edu/18.06/www/Essays/linear-algebra-and-music.pdf [100.1KB]
3. The Art of Noises - http://ubu.com/historical/gb/russolo_noise.pdf 3MB
4. The Echo Nest - http://the.echonest.com/analyze.html
5. Sumanth Peddamatham aka Shameless plug - http://www.bafoontecha.com