The Sounds of Mathematics

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.

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

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.

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

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

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

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

F C G D A E B F

Or Using Garage Band on iPad Smart Strings – Chords E m A m D m G C F B b B dim

Convert Your Name to Mod 8 C = ≡ 3 mod(8) → G y = ≡ 1 mod(8) → F n = ≡ 6 mod(8) → E t = ≡ 4 mod(8) → D h = ≡ 0 mod(8) → F i = ≡ 1 mod(8) → F a = ≡ 1 mod(8) → F

Cynthia iPad Piano Garage Band

Using the notes or chords we can build a musical phrase

Using Symmetry Properties Translation: GFEDFFF GFEDFFF GFEDFFF

Vertical Reflection GFEDFFF FFFDEFG

Horizontal Reflection GFEDFFF

180 Degree Rotation

4/4 Time How many rhythm combinations? GFEDFFF

Note choices Whole notes 4 counts Half notes 2 counts Quarter notes 1 count Eighth notes ½ count Sixteenth notes ¼ count

Whole Notes

Half Notes

Quarter notes

Eighth notes &1 &2 &3 & Rest

Sixteenth Notes 1e&a 2e&a

Triplets 1&a 2&a 3 rest

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

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

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

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

Bongo Your Name Convert your name to base 3 C = y = n = t = h = i = a =

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

STEAL OTHER PEOPLE’S IDEAS! From ABACABA Music GFEDFFF G GFFG GFEEFG GFEDDEGF GFEDFFDEFG GFEDFFFFDEFG GFEDFFFFFFDEFG

Cynthia in Base 4 C = y = n = t = h = i = a =

Measure pattern 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

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

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