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Pedro Kroger - Music for Geeks and Nerds

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Pedro Kroger Music for Geeks and Nerds
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Are you interested in learning more about music but have found most material condescending or to present things magically instead of logically? The good news is that much of music can be understood with programming and math, two things youre already good at! In this book youll learn some elements of music from a programmers perspective. Youll learn about the primitives of music such as notes and duration, the means of combining those primitives into motives and chords, operations such as transposition, retrograde, and inversion, and the means of abstraction (phrases and form) using Python and some basic math. Every concept in this book is explained in English with a corresponding implementation in Python, using the Pyknon music library.

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Contents
Introduction

I have a lot of friends who are computer scientists and engineers, andthey are always asking me for books to learn more aboutmusic. Unfortunately, I have never found a good book torecommend. There are good books out there, but they present thingsmagically instead of logically and tend to be kind of patronizing.

Because music is an ancient art with more than 2500 years of recordeddata, it has a lot of baggage. Things like tetrachords that the Greeksused more than 2500 years ago are still used today. This is good, butsometimes it is difficult to separate what is natural (such asfrequencies); logical (such as the math used fortransposition and inversion); from what is the result of socialconventions and usage over hundreds of years (such as intervalnames). In this book, I clearly separate these three things. If you area nerd like me, you will find that you can learn the natural andlogical stuff pretty quickly.

I am heavily influenced by Hal Abelson and Jerry SussmansStructure and Interpretation of Computer Programs(http://bit.ly/sicp-book), in which they state that every powerfullanguage has three mechanisms for combining simple elements to formmore complex ideas:

  • primitive expressions, which represent the simplest entities the language is concerned with,
  • means of combination, by which compound elements are built from simpler ones, and
  • means of abstraction, by which compound elements can be named and manipulated as units.

In the same way that we can apply these mechanisms to programming,I like to apply them to music. In fact, I use this idea in teaching bothcomputer science and music composition, and I find it verypowerful. Well explore some of these ideas in this book.

Another similar font of inspiration is the talk Why Programming is aGood Medium for Expressing Poorly Understood and Sloppily FormulatedIdeas by Gerald J. Sussman (http://bit.ly/why-programming) in which heuses programming to teach electrical engineering. In this book we willuse programming to learn music.

We will see some music notation in this book, but dont worry. If youhave never seen music notation before, read chapter. If you dont feel like learning musicnotation at all, its no problem; you should be all right by readingthe text and code examples.

Getting Started

This book has quite a few code and audio examples. You can downloadthem at our resources webpage.

The sound examples in this book are in both MIDI and MP3 formats. Iused a high quality sampler library to generate the MP3s from MIDI, soit should sound good.

To play the MIDI files youll create using the genmidi module,youll need a MIDI player. Windows and Ubuntu should play MIDI filesby default when you double-click on them. On a Mac you may need toinstall QuickTime Player 7. Another option is to use a music notationprogram. A music notation program may be useful even if you dont knowhow to read music, as itll help you spot crazy outputs. Musescore is a free program (as in speech and beer)that runs on Linux, Mac, and Windows. Finale is a commercial notation program forWindows and Mac that is more polished than Musescore, but itsexpensive. Their trial version is fully functional and works for 30days.

Acknowledgments

This book would not be possible without the encouragement of manypeople. Id like to thank the nice folks who took my tutorial at the2012 PyCon. The tutorial was based on an earlier draft of this book,and their participation was essential in cleaning the material andinspiring me to finish this book. Id like to thank Vilson Vieira,Marcos Sampaio, Alexandre Passos, and Tiago Vaz for their invaluablesuggestions. Finally, Id like to acknowledge Mara for herpatience, love, and support.

Introduction to Music Notation in n Seconds or Less

Music notation is both simple and complex, not unlike mathnotation. In this chapter well learn enough music notation tounderstand the examples in this book.

The first thing to know about music notation is that time isrepresented from left to right while pitch is represented from bottomto top:

As youd expect, there are symbols to represent different things. Themain symbols are the clef, the time signature, the note head, and thestem, as you can see in the following image:

The time signature shows how many beats are in a measure and the notevalue of the beat. For instance, in the previous image we have sevenbeats (represented by the number 7) of quarter notes (represented bythe number 4). Naturally, we can subdivide a beat into smaller notevalues (see section ).

The actual pitch of a note is determined by the position of a notehead on the staff and the clef being used. Clefs solve the problem ofcramming 80+ notes into five lines. There are three kinds ofclefsG-clef, F-clef, and C-clefand they indicate the pitch nameon a specific line. For instance, the treble clef (the one used in thetwo previous images) indicates that the second line from the bottomhas the note G, while the bass clef indicates that the fourth linefrom the bottom has the low F note.

In the following image we can see six notes in the same graphicalposition in the top staff. Because each note occurs after a differentclef, they will represent different pitches. The arrows show theposition of each note on the piano, while the bottom staff shows wherethese notes would be placed in the treble clef. The sub- andsuperscript eight indicates that a note will sound one octave below orabove than written, respectively.

The note shape and the number of beams (the horizontal linesconnecting two or more notes) indicate the note duration. In thefollowing example the notes have shorter duration as the musicprogresses (see section ). Unlike Python, butlike the C programming language, space is not significant, but it is used to make a score easyto read. Notice how the space between the first and second note isgreater than the space between the third and fourth note. This isbecause the first note is longer than the third:

Finally, you may see symbols above or below a note such as a dot, agreater than (>), a line, or a fermata (on the last note in thefollowing image). They are symbols of expression to tell theperformer how the note should be played. There are dozens ofexpression symbols, but we dont need to worry about them in thisbook:

In this chapter we had the shortest introduction to music notation inthe history of introductions, but this is pretty much all you need toknow to follow the music examples in this book.

The Primitives of Music

In this chapter well see an overview of notes, intervals, and durationsand how to represent them in Python.

Notes

A note is a symbol representing a musical sound.

Pitch is the combination of a frequency in Hertz and a note name. Forinstance, central A has a frequency of 440Hz. This combination issomewhat arbitrary. In the past, the frequency of central A wouldchange depending on the region. In some places, it was equal to 315Hz,for example.

An octave is the interval between two pitches where their frequency has aratio of 2:1. For example, central A has a frequency of 440Hz and theA one octave above has a frequency of 880Hz. Two notes an octaveapart are in a sense alike, being different only in their relativeregisters and often seeming to blend into one another . Inmost cultures the two frequencies are perceived as the same pitchin different registers. In the following image we have twooctaves. Notice how the pattern of black keys is repeated in each octave:

There are many ways to divide an octave. In fact, octave division has beenan important component in music theory for 2500+ years. Today, themost common way to divide the octave is into 12 equal parts, theso-called equal temperament. The equal temperament became prevalent inthe 18th century, and before that many others temperaments were used(see section )

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