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**Acoustics & Music Theory**

• Acoustics - the physics of soundwaves

• Physiology of Hearing - the function of hearing as it relates to the form of the ear

• Music Theory - the language used to describe the above

• *Intervals* are the ratio of two frequencies (reduced to their simplest form). Only specific ratios sound *Consonant* (such as the *Major* and *Perfect Intervals*).

• A sound (or "*Fundamental*") produces "*Overtones*" or "*Harmonics*" (i.e.: multiples of that frequency). The *Fundamental* and all of the *Harmonics* taken together are called an "*Overtone*" or "*Harmonic Series*". Taking two adjacent *Harmonics* gives all of the different kinds of *Intervals*.

*Dissonance* (such as the *Interval* of a *Tritone* by itself) is caused by:

-Beating because waves of each *Note* don't nest within each other (numbers in *Interval* are co-prime?)

-Fewer shared "strong" *Harmonics* between the two *Notes* (i.e.: those that come first in the *Overtone Series*)

• "*Intonation*" is the set of *Intervals* that used to tune an instrument. Again, in this case, think of the *Intervals* are ratios of two frequencies. "*Just Intonation*" is when those ratios are made up of small whole numbers. The "limit" of different kinds of *Just Intonation* are which prime number we go up to when forming those ratios, for example:

3-limit: 2, 3

5-limit: 2, 3, 5

7-limit: 2, 3, 5, 7

...etc.

*Equal Temperament* "tempers" all *Notes* equally. In other words, it makes all of them slightly out of tune. This is so we can play in different *Keys* without having to re-tune an instrument.

*Timbre* is determined by how the shape and material of an instrument makes a different *Overtone Series* for each *Note* (i.e.: the *Harmonics* are different volumes for each instrument). Or to put it another way, their *ADSR Envelopes* are different from one another. This is why two instruments could play the same *Note*, but sound completely different from one another.

Likewise, the *Notes* in a *Chord* are also determined by an *Overtone Series*. It is as if we took the higher *Harmonics* of a sound and squished them into the same audible range.