Interested In Music? Have fun with Matrices
Markov chains (a discrete random process with the Markov property) are employed in algorithmic music composition, particularly in software programs such as CSound or Max. In a first-order chain, the states of the system become note or pitch values, and a probability vector for each note is constructed, completing a transition probability matrix (see below). An algorithm is constructed to produce and output note values based on the transition matrix weightings, which could be MIDI note values, frequency (Hz), or any other desirable metric.
A second-order Markov chain can be introduced by considering the current state and also the previous state, as indicated in the second table. Higher, nth-order chains tend to "group" particular notes together, while 'breaking off' into other patterns and sequences occasionally. These higher-order chains tend to generate results with a sense of phrasal structure, rather than the 'aimless wandering' produced by a first-order system.
URL: http://en.wikipedia.org/wiki/Markov_chain#Music
Who don't like music? No matter which genre? We all like it!!!
Patrick Daou.
Patrick, we all do indeed love music!!!!!! :) Who can live without it??
ReplyDeleteWonderful contribution indeed! Thanks a lot!
Zeina
actually, one of my friends is a guitarist
ReplyDeleteand he himself uses matrices in a programme called guitar pro or something like that which helps him produce better notes or something like that. and i checked the programme myself , thought matrices arent clear in it if u read how the programme started it was by matrices !
and of course, i love music 2 :)
frederic mourad
Hello. this site is indeed very interesting, as I was looking through the different posts, I saw music, which interests me a lot.
ReplyDeleteKnowing that also music is affected by matrices is very surprising as I thought, matrices were only used for things related very much to science work.
This post lead me to looking up where matrices are also used and this is where I found a very interesting matter.
Matrices are used in 3D animation and graphics, thus, all the new 3D movies we are watching these days are based on matrices.
They are used to transform the vertices of 3D objects.
There are 3 types of transformations that you can do:
- translation (moving an object),
- scaling (resizing an object)
- rotation.
You can set up a matrix in a particular way to perform all the transformations that you need. This can be any combination of translation, scaling, and rotation to be performed on the x,y or z components of the vertices. The matrix is multiplied by the vertex, and the result is a new vertex with the appropriate operation done to it.
It almost seems like magic. When you apply the matrix to all the vertices in an object, the entire object is translated and/or scaled and/or rotated.
To conclude it all, I think matrices are very much important in our life. They are not only math. They produce MAGICAL and BEAUTIFUL things (music and animation).
URL:
http://www.gamedev.net/reference/articles/article695.asp
http://www.gamedev.net/reference/articles/article415.asp
PS: there is a post on this blog that talks about 3D animation.
http://ndu2009algebra.blogspot.com/2010/01/3d-transformation-matrix-compression.html
MICHELLE ESTEPHAN, LAU
very good idea, and my self i use the guitar pro but at first i didn't know the matrices inside that program but know everything is clear.
ReplyDeleteAnthony choucair
NDU