Thank you for this! I am learning this in theory class and I wasn't understanding how to choose notes for the top row. Your video was also just as good at explaining how to fill in the rest of the matrix as well.
I somehow expected this to be linear algebra 😅 Actually we can interpret a 12 tone series as an automorphism of (F2)^12 or as a simple directed graph with 12 nodes and 12 edges. The matrix would be the adjacency matrix of that graph and the matrix of the automorphism. At the same it could also be called a trivial markov chain because all probabilities are 1 or 0. The retrograde matrix would be the inverse. We could generalize 12 tone series to markov chains where the notes are the states and there is a probability to get from each note to the other. Just some ideas for the mathematics in case someone is interested
Omg I figured out this trick on my own when studying theory and moved on with life from that and forgot! Thanks for refreshing my memory on the matrix and 12 tone. Could you also do a whole scale or whole half scale pattern with this instead of using half steps the whole time?
This is the third video I've watched about matrixes and previously no one explains how they choose the top row.... Then you choose completely random notes!? So confused...
Choosing random notes to make the top row is a technique composers have used. If you're composing a piece or just want to make a matrix you basically just need to come up with an order of the 12 chromatic tones you like. Make sure you use all 12 notes and you don't repeat any notes. If you are looking at a piece you need to do some analysis to try and figure out what 12 tone row the composer started with. Hope that helps a bit.
You certainly could. Pieces I have analyzed tend to mix sharps and flats. Possibly to be easier to read by the performer but there is nothing wrong with using all sharps or all flats.
thanks a ton man, got sick and missed class when they went over this lol
Glad it helped!
@@rogerlouismusic me too! lol.
Thank you for this! I am learning this in theory class and I wasn't understanding how to choose notes for the top row. Your video was also just as good at explaining how to fill in the rest of the matrix as well.
I somehow expected this to be linear algebra 😅
Actually we can interpret a 12 tone series as an automorphism of (F2)^12 or as a simple directed graph with 12 nodes and 12 edges. The matrix would be the adjacency matrix of that graph and the matrix of the automorphism. At the same it could also be called a trivial markov chain because all probabilities are 1 or 0.
The retrograde matrix would be the inverse.
We could generalize 12 tone series to markov chains where the notes are the states and there is a probability to get from each note to the other.
Just some ideas for the mathematics in case someone is interested
Omg I figured out this trick on my own when studying theory and moved on with life from that and forgot! Thanks for refreshing my memory on the matrix and 12 tone. Could you also do a whole scale or whole half scale pattern with this instead of using half steps the whole time?
Nice! Yea for sure. You could find where the whole step is and just do all whole steps.
This is the third video I've watched about matrixes and previously no one explains how they choose the top row.... Then you choose completely random notes!? So confused...
Choosing random notes to make the top row is a technique composers have used. If you're composing a piece or just want to make a matrix you basically just need to come up with an order of the 12 chromatic tones you like. Make sure you use all 12 notes and you don't repeat any notes. If you are looking at a piece you need to do some analysis to try and figure out what 12 tone row the composer started with. Hope that helps a bit.
thank you so sos osososos much
how to apply this to the composition?
I want to make a song based off of using serialism but, I’m not sure how to do that :0
Is it better to stick with all sharps or all flats?
You certainly could. Pieces I have analyzed tend to mix sharps and flats. Possibly to be easier to read by the performer but there is nothing wrong with using all sharps or all flats.