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Music and Math
- a single Note, such as C4, as frequency of a string (length as L=1), its 2x frequency C5 (1 octave higher note, length=1/2), double is the frequency of half length of the same string; its half frequency C3 (1 octave lower note, length=1*2 =2)
- we can define: 2/3 length of that C4 string is G4, (which is a note in-between C4 and C5, L=2/3)
- then, start from G4, as frequency of a new string, 2/3 of that length, we get D5 (L=2/3 * 2/3 = 4/9), so if we start with C3 as 2, then D4 = 2*4/9 = 8/9
- then, same circle of C4 (1), G4 (2/3), D5 (4/9) → D4 (8/9), A5 (8/27) → A4 (16/27), E6 (16/81) → E4 (64/81) continues
cycle | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | C | G | ||||||||||||||||||
2 | D | A | ||||||||||||||||||
3 | E | B | ||||||||||||||||||
4 | F# Gb | C# Db | ||||||||||||||||||
5 | C# Db | G# Ab | D# Eb | |||||||||||||||||
6 | D# Eb | A# Bb | F | |||||||||||||||||
7 | F | C | G | |||||||||||||||||
8 | C | |||||||||||||||||||
combine | C | C# Db | D | D# Eb | E | F | F# Gb | G | G# Ab | A | A# Bb | B |
- ref:
- interactive circle: https://pianolit.com/tools/circle-of-fifths