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Instructions and Help about Far matrix
Hey guys welcome to twelve-tone today we're going to talk about twelve tone matrices and if you stick around till the end we'll have some tips on turning a row into an actual composition like a lot of serialism this gets a little mathy but don't worry it doesn't really go beyond basic arithmetic on that note let's talk about notation up to now we've been using standard note names with letters and accidentals but those names are derived from tonal systems we use seven letters because our scales have seven notes and accidentals signified deviations from those scales but twelve-tone music is a tonal every note is equal so when we get deep into it those names stop being useful instead we just use the number zero to eleven signifying how many half steps above see the note is so zero is C 1 is C sharp or D flat 2 is D and so on once you get to 12 you're back at C so we reset to zero and continue up again this system lets us easily visualize intervals which is more important here than whether a note is sharp or flat this is just for composition though when you're transcribing a piece to be played you should switch back to regular notation that's way easier to read with that in mind let's talk about the matrix this is a useful tool for visualizing the structures available to you and it works like this you start with a 12 by 12 grid in the top line you write your prime rows starting on then going down the first column you write your inversion a handy trick to find this is to take each number in your prime row and subtract it from 12 so this 4 inverts to an 8 this 3 becomes a 9 and so on then for each of the remaining squares you add the number at the top of the column to the one at the beginning of the line so this 4 plus this 8 would be 12 or this 3 plus 8 is 11 this 4 plus 9 is 13 or 1 and so on this takes a little time but once you're done it should look something like this so what's the point well if you read across each of the lines you have every possible transposition of your primer row if you read down the columns you have every inversion reading a line backwards gives you your retrogrades and reading columns from bottom to top gives you the retrograde inversions this grid shows you all 48 possible transformations of your starting row making it a useful reference for quickly determining your available options and that's a 12 tone matrix I promise we're done with math for now some of you have already asked what the next step is to quote one viewer many twelve-tone guides just say here are the row forms now get out and.