# Math 1a Spring 2020

## 1a Introduction to Calculus

# Unit 35: Review

unit 35 |
unit 34 |
unit 33 |
unit 32 |
unit 31 |
unit 30 |
unit 29 |
unit 28 |
unit 27 |
unit 26 |
unit 25 |
unit 24 |
unit 23 |
unit 22 |
unit 21 |
unit 20 |
unit 19 |

Some review stuff. |

Here are the basic harmonies of the 1a song! I believe the harmonies are original but there are not many songs of that shortness possible and 90 percent of all pop songs are constructed from such simple harmonies. The numbers are the Midi numbers.

S=Sound; SN[{a_,t_}]:=SoundNote[a,t];T=4; d={1,5,8};g={1,6,10};a={0,3,8};h={-2,1,5};e={3,6,10}; A={{d,4},{d,4},{g,4},{d,4},{a,4},{d,4},{a,4},{a,4}}; B={{h,4},{h,4},{e,4},{a,4},{d,4},{g,4},{a,4},{a,4}}; U=S[{S[{"Piano",SN/@A},{0,T}],S[{"Viola",SN /@B},{T,2T}]}]; Export["1aharmonies.mp3",U,"MP3"];Here is the MP3 file produced.

And here is Ava's first song. I (the human) cleaned out notation (if you compare with the slides). While having lost the contest, we humans still proud ourselves to write beautiful and poetic code. Machines just do not have good taste! (Yet ...)

rise[x_]:=Table[{x[[k,1]]+12,x[[k,2]]},{k,Length[x]}]; down[x_]:=Table[{x[[k,1]]-12,x[[k,2]]},{k,Length[x]}]; SN[{a_,t_}]:=SoundNote[a,t];T=6; d0={1,5,8};g0={1,6,10};a0={0,3,8};h0={-2,1,5};e0={3,6,10}; a1={{{1},4},{{8},4},{{10},1},{{8},1},{{6},2},{{8},4},{{6},1}, {{5},1},{{3},2},{{5},2},{{3},1},{{1},1},{{3},3},{{},1},{{3},4}}; b1={{{1},4},{{1},4},{{3},4},{{-4},4},{{1},2},{{0},1},{{-2},1}, {{-2},2},{{-4},1},{{-6},1},{{-4},3},{{},1},{{-4},4}}; a2={{d0,4},{d0,4},{g0,4},{d0,4},{a0,4},{d0,4},{a0,4},{a0,4}}; b2={{h0,4},{h0,4},{e0,4},{a0,4},{d0,4},{g0,4},{a0,4},{a0,4}}; s1=Sound[{"Flute", SN/@rise[a1]},{0T,1T}]; s2=Sound[{"Guitar",SN /@down[a2]},{0T,1T}]; s3=Sound[{"Viola", SN/@rise[a1]},{1T,2T}]; s4=Sound[{"Harp", SN /@down[a2]},{1T,2T}]; s5=Sound[{"Violin",SN/@rise[b1]},{2T,3T}]; s6=Sound[{"Piano", SN /@down[b2]},{2T,3T}]; s7=Sound[{"Viola", SN/@rise[b1]},{3T,4T}]; s8=Sound[{"Cello", SN /@down[b2]},{3T,4T}]; S=Sound[{s1,s2,s3,s4,s5,s6,s7,s8}];Export["ava1.mp3",S,"MP3"]The MP3 produced. (Mathematica file)

The MP3 of stochastic version.

And here are some details on composing with Mathematica from 2018 (Math 21b course).