Listen Like a Programmer
From Wave to Note with Mathematics and Code

Kengo Ichiki

Turn sound waves into notes with mathematics and code. A technical book on transcription by ear that relies on method, not on talent — the English edition of the Japanese original 音楽と数理 才能にたよらない耳コピ, translated by the author.

Paperback/Kindle on Amazon.com/Amazon.co.jp: paperbackKindle

Also in Kindle Unlimited.

A yellow sound wave on a dark grid leading into layered pitch tracks above a piano keyboard

From waveform to note, one step at a time

Start with sound and pitch, follow the Fourier mathematics, then see how the program WaoN uses those ideas to transcribe audio into MIDI.

Three paths through one question: how does a wave become a note?

A black sound wave above a piano keyboard on a warm yellow background

Begin with music

Explore sound, pitch, harmony, and playback speed, starting from the musical questions that set the investigation in motion.

Several colored waves converging into a spectrum of frequency peaks on a dark grid

Follow the mathematics

Work through Fourier analysis, the discrete Fourier transform, power spectra, window functions, and phase-vocoder frequency correction.

A stylized program display with a waveform, a frequency spectrum, and the names waon, gwaon, and pv

Use the programs

Work with waon, gwaon, and pv, then compare a traditional transcription algorithm with a neural-network approach.

A layered frequency display and piano keyboard leading into a piano-roll pattern of notes

Choose your path

Read the music chapters, concentrate on the programs, or go deeper into the mathematics. Each route returns to the same question: how does a wave become a note? For curious amateurs who want to enjoy music more deeply through mathematics and code.

What you should bring

This is not a method for training your ear. It is an account of how a sound becomes a note — in music, in mathematics, and in a program you can run. High-school mathematics and a little programming experience are enough to follow the main line; the Fourier chapters reward a slower second reading.

After the book, the tool

The program the book describes now runs on iPhone, iPad, and Mac as わおん — Music Transcriber: waveform, spectrogram, and detected notes on one timeline, editable by hand, exportable as MIDI or MusicXML. The first 30 seconds are free.
About わおん →

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