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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

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.