Editing Additive synthesis (section)

== Explanation ==
The sounds that are heard in everyday life are not characterized by a single [[frequency]]. Instead, they consist of a sum of pure sine frequencies, each one at a different [[amplitude]]. When humans hear these frequencies simultaneously, we can recognize the sound. This is true for both "non-musical" sounds (e.g. water splashing, leaves rustling, etc.) and for "musical sounds" (e.g. a piano note, a bird's tweet, etc.). This set of parameters (frequencies, their relative amplitudes, and how the relative amplitudes change over time) are encapsulated by the ''[[timbre]]'' of the sound. [[Fourier analysis]] is the technique that is used to determine these exact timbre parameters from an overall sound signal; conversely, the resulting set of frequencies and amplitudes is called the [[Fourier series]] of the original sound signal.

In the case of a musical note, the lowest frequency of its timbre is designated as the sound's [[fundamental frequency]]. For simplicity, we often say that the note is playing at that fundamental frequency (e.g. "[[middle C]] is 261.6 Hz"),<ref>{{Cite web|url=http://www.liutaiomottola.com/formulae/freqtab.htm|title=Table of Musical Notes and Their Frequencies and Wavelengths|last=Mottola|first=Liutaio|date=31 May 2017}}</ref> even though the sound of that note consists of many other frequencies as well. The set of the remaining frequencies is called the [[overtone]]s (or the [[harmonic]]s, if their frequencies are integer multiples of the fundamental frequency) of the sound.<ref>{{Cite web|url=http://www.physicsclassroom.com/class/sound/Lesson-4/Fundamental-Frequency-and-Harmonics|title=Fundamental Frequency and Harmonics}}</ref> In other words, the fundamental frequency alone is responsible for the pitch of the note, while the overtones define the timbre of the sound. The overtones of a piano playing middle C will be quite different from the overtones of a violin playing the same note; that's what allows us to differentiate the sounds of the two instruments. There are even subtle differences in timbre between different versions of the same instrument (for example, an [[upright piano]] vs. a [[Grand Piano|grand piano]]).

Additive synthesis aims to exploit this property of sound in order to construct timbre from the ground up. By adding together pure frequencies ([[sine wave]]s) of varying frequencies and amplitudes, we can precisely define the timbre of the sound that we want to create.