Final Projects Some simple ideas

Composition

(1) program that "learns" some aspect of musical composition

(2) fractal music that sounds musical

(3) program that creates engaging new styles

(4) vivaldi music maker (scales, arps, sequences, etc.)

(5) program that sets some of Messiaen's ideas into code

(6) real-time transformation of drawing to music

(7) improvisation program

(8) accompaniment program

(9) re-write masterpieces according to some plan

(10) logically replace one of the elements of known music

Analysis

(1) performance attributes of given performers

(2) mapping rhythm, texture, harmonic rhythm, etc.

(3) reduction by mathematics

(4) analysis using 2D cellular automata

(5) statistical representation and comparison

(6) analysis of chromatic versus diatonic content of music

(7) tension analyzing program (Hindemith theories?)

(8) relevance of dynamics to pitch, etc. (i.e., cross dependency)

(9) compare some aspect of music to some aspect of non- music

(10) a composer's use of some attribute over an extended period

Short Paper Well-Documented Code Five Sample Outputs

Presentations due Thursday June 12, 8-11am

Determinacy versus Indeterminacy

Sir Isaac Newton 1726 Principia “Actioni contrarium semper et equalem esse reactionem” “to every action there is always opposed an equal and opposite reaction”

Richard Feynman “it is impossible to predict which way a photon will go”

Murray Gell-Mann “there is no way to predict the exact moment of disintegration”

Werner Heisenberg uncertainty principle “the act of observation itself may cause apparent randomness at the subatomic level”

Albert Einstein “God does not play with dice.”

Cope “Observation alone cannot determine indeterminacy.”

Ignorance? Too complex? Too patternless? Too irrelevant?

Discrete Mathematics

Study of discontinuous numbers

Logic, Set Theory, Combinatorics Algorithms, Automata Theory, Graph Theory, Number Theory, Game Theory, Information Theory

Recreational Number Theory

Power of 9s

9 * 9 = 81

8 + 1 = 9

Multiply any number by 9 Add the resultant digits together until you get one digit

Always 9 e.g., 4 * 9 = = 9

Square Root of Palendromic Numbers

Square Root of = 11111

Square Root of =

Pascal’s Triangle

The sum of each row results in increasing powers of 2 (i.e., 1, 2, 4, 8, 16, 32, and so on). The 45 ° diagonals represent various number systems. For example, the first diagonal represents units (1, 1...), the second diagonal, the natural numbers (1, 2, 3, 4...), the third diagonal, the triangular numbers (1, 3, 6, 10...), the fourth diagonal, the tetrahedral numbers (1, 4, 10, 20...), and so on. All row numbers—row numbers begin at 0—whose contents are divisible by that row number are successive prime numbers. The count of odd numbers in any row always equates to a power of 2. The numbers in the shallow diagonals (from 22.5° upper right to lower left) add to produce the Fibonacci series (1, 1, 2, 3, 5, 8, 13...), discussed in chapter 4. The powers of 11 beginning with zero produce a compacted Pascal's triangle (e.g., 11 0 = 1, 11 1 = 11, 11 2 = 121, 11 3 = 1331, 11 4 = 14641, and so on). Compressing Pascal's triangle using modulo 2 (remainders after successive divisions of 2, leading to binary 0s and 1s) reveals the famous Sierpinski gasket, a fractal-like various-sized triangles, as shown in figure 7.2, with the zeros (a) and without the zeros (b), the latter presented to make the graph clearer.

Leonardo of Pisa, known as Fibonacci. Series first stated in 1202 book Liber Abaci

0,1,1,2,3,5,8,13,21,34,55,89... Each pair of previous numbers equaling the next number of the Sequence.

Dividing a number in the sequence into the following number produces the Golden Ratio 1.62

Debussy, Stravinsky, Bartók composed using Golden mean (ratio, section).

Bartók’s Music for Strings, Percussion and Celeste

Fermat’s Last Theorum to prove that X n + Y n = Z n can never have integers for X, Y, and/or Z beyond n = 2

$1 million prize to create formula for creating next primes without trial and error

Magic Squares

Square Matrix in which all horizontal ranks all vertical columns both diagonals equal same number when added together

Musikalisches Würfelspiele

Number of Possibilities of 2 matrixes is or 45,949,729,863,572, quadrillion

X n+1 = 1/cosX n 2

(defun cope (n seed) (if (zerop n)() (let ((test (/ 1 (cos (* seed seed))))) (cons (round test) (cope (1- n) test)))))

? (cope 40 2) ( )

Tom Johnson’s Formulas for String Quartet

Iannis Xenakis Metastasis

(defun normalize-numbers (numbers midi-low midi-high) "Normalizes all of its first argument into the midi range." (normalize numbers (apply #'min numbers) (apply #'max numbers) midi-high midi-low)) (defun normalize (numbers data-low data-high midi-low midi-high) "Normalizes its first argument from its range into the midi range.” (if (null numbers) nil (cons (normalize-number (first numbers) data-low data-high midi-low midi-high) (normalize-number (rest numbers) data-low data-high midi-low midi-high))))

Class Sonifications

Assignment Sonify a mathematical process me a MIDI file turn in your code.