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The Sounds of Mathematics

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Motivation Help students understand mathematical patterns Help students develop numeric, symbolic, functional and spatial concepts Provide students experiences where they can connect classroom learning to life experiences Enable students to construct knowledge of mathematics through exploration of ideas Foster positive student attitudes.

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Building Music Mathematically involves spatial-temporal reasoning the ability to visualize patterns, come to solutions and understand multi-stop problems.

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Music is one of the most widely-acknowledged uses of spatial-temporal reasoning. Individuals who write music often visualize notes as a large puzzle, fitting different fractions of notes and rests together to create a whole piece of music.

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Using Mathematics to Map Numbers to Musical Notes Understanding of number bases. Understanding of modulo math. The ascii code Functions or equations

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Tools Number bases. Modulo math. The ascii code Functions Symmetry properties Fractals

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Using the Ascii Code Find the decimal representation of the letters of your name C = 67 y = 121 n = 110 t = 116 h = 104 i = 105 a = 97

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Choose a key Key of C C D E F G A B Since Im not teaching music or music theory, I like to keep this part simple. We want to map numbers into notes, beats, or chords.

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F C G D A E B F 1 2 3 4 5 6 7 0

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Or Using Garage Band on iPad Smart Strings Chords E m A m D m G C F B b B dim 1 2 3 4 5 6 7 0

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Convert Your Name to Mod 8 C = 67 67 3 mod(8) G y = 121 121 1 mod(8) F n = 110 110 6 mod(8) E t = 116 116 4 mod(8) D h = 104 104 0 mod(8) F i = 105 105 1 mod(8) F a = 97 97 1 mod(8) F

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Cynthia iPad Piano Garage Band

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Using the notes or chords we can build a musical phrase

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Using Symmetry Properties Translation: GFEDFFF GFEDFFF GFEDFFF

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Vertical Reflection GFEDFFF FFFDEFG

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Horizontal Reflection GFEDFFF

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180 Degree Rotation

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4/4 Time How many rhythm combinations? GFEDFFF

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Note choices Whole notes 4 counts Half notes 2 counts Quarter notes 1 count Eighth notes count Sixteenth notes count

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Whole Notes

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Half Notes

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Quarter notes

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Eighth notes &1 &2 &3 & Rest

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Sixteenth Notes 1e&a 2e&a

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Triplets 1&a 2&a 3 rest

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Fitting Notes to Beats For simplicity use 4/4 time. Each measure has 4 beats Decide on a rule: roll a die, use a formula, use a mathematical pattern

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Fibonacci Numbers Mod (5) 1, 1, 2, 3, 0 3, 3, 1, 4 1 2 3& 4&a r 2&a 3 4e&a

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1, 1, 2, 3, 0 3, 3, 1 1 2 3& 4&a r 2&a 3&a 4

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Building Your Musical Phrase Using Symmetry Properties Translation Verticle reflection Horizontal reflection Rotation

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Bongo Your Name Convert your name to base 3 C = 67 2 1 0 1 y = 121 1 1 0 2 1 n = 110 1 1 0 0 2 t = 116 1 1 0 2 2 h = 104 1 0 2 1 2 i = 105 1 0 2 0 0 a = 97 1 0 1 2 1

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Fractal Music Using L system Variables G F 1 E D F 2 F 1 Create Rules: Let: G F 1 E E DF 2 F 2 F 1 F 1 G D F 2

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STEAL OTHER PEOPLES IDEAS! From ABACABA Music GFEDFFF G GFFG GFEEFG GFEDDEGF GFEDFFDEFG GFEDFFFFDEFG GFEDFFFFFFDEFG

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Cynthia in Base 4 C = 67 1003 4 y = 121 1321 4 n = 110 1232 4 t = 116 1310 4 h = 104 1220 4 i = 105 1221 4 a = 97 1201 4

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Measure pattern1003132112321310122012211201 Counts 1, 2, 3, 4&a 1,2& a, 3&, 4 1, 2&, 3&a, 4& 1, 2&a, 3, 4 1, 2&, 3&, 4 1, 2&, 3&, 4 1, 2&, 3, 4

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Tap Dance your name: 0 = hold 1 = step or tap 2 = shuffle 3 = triplet 1003 step, hold, hold, triplet 1321 - step, triplet, shuffle, step 1232 - step, shuffle, triplet, shuffle 1310 step, triplet, step, hold 1220 step, shuffle, shuffle, hold 1221 step, shuffle, shuffle, step 1201 step, shuffle, hold step

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Graphic Design: 0 = Solid 1 = horizontal stripes 2 = vertical stripes 3 = diagonal stripes I pattern1003132112321310122012211201

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