Topic: Harmonics (Pythagoras)

Why do melodies make us doze off like in the works such as Symphony No. 41  by classical era composer Wolfgang Amadeus Mozart, while others bring chills down our spine like romantic composer Hector Belioz’s Dream of a witches Sabbath? Greek philosopher and mathematician Pythagoras found that the frequency a note produces is proportional to the length of the string (or column for wind and brass instruments). Depending on the placement of a player’s finger(s) on the string, or the placement of finger(s) on the keys of a wind or brass instrument creates a fixed ratio by the length of the column and string vs the division (placement of fingers).

In other words, the ratios are as follows

Unison (musicians playing together): 1:1 (Math as to why to come later)

Octave (In musical composition scales are a progression of eight notes. A complete concert* scale starts with a lower frequency of one note and ends with a higher frequency of the same note. This is called an octave) 2:1

Dissonance** (What allows for ‘eerie’ chords) 15:16

Essay Style: I plan on writing this combining my experience as a [classically trained] musician and a mathematician. In other words, alongside explaining how sound is related to geometry I’ll be talking shop as far as music theory (no worries, terminology will be explained) to explain how sound works, and mathematics to explain why some notes sound melodic, while others sound eerie (Ie.. why major chords sound pleasant whereas minor chords aren’t so pleasant)  

*There are many types of scales in music used across all musical styles, and music from around the world. The concert is the scale everyone is familiar with. I will however also be concentrating on Chromatic and Pentatonic scales for the purpose of this paper

**I’ll mention this further in my paper. But I should note that dissonance as used in musical composition isn’t the same as dissonance in physics. Similar but different

Harmonics https://en.wikipedia.org/wiki/Harmonic

Pythagorean Intervals https://www.phys.uconn.edu/~gibson/Notes/Section3_2/Sec3_2.html

Circle of fifths https://www.musical-u.com/learn/how-to-use-circle-fifths/