this post was submitted on 26 Jan 2025
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Yup. 12 semitones is 1 octave so A2 on the bass guitar's A string. The frequency ratio to A1 is 2:1.
What? No. That's 5 semitones or 500 cents from A1, which is D2, close to a perfect fourth from A1 (frequency ratio 4:3 or 498 cents).
Two octaves would be 24 semitones or 24 frets (not available on most fretted instruments) for a frequency ratio of 4:1, or A3.
No! The 2nd fret is 2 semitones or 200 cents above A1, which is B1, close to a major second from A1 (frequency ratio 9:8 or 196 cents).
3 octaves would be 36 semitones or 3600 cents for a frequency ratio of 8:1, or A4.
Sorry I mean that's where the harmonics are.
For any harmonic, you first need to get a sound source of that frequency such as a tuning fork or speaker. It's best to place the source where you expect an antinode to be. You can try to just pluck the string at that point but that will probably also produce a lots of harmonics you don't want.
For the kth harmonic, there are k antinodes at (2i-1)/(2k) of the string length, where i≤k; i∈ℕ.
Fundamental (A1):
2nd harmonic (1 octave up, A2):
3rd harmonic (perfect fifth from A2 or approx. E3):
4th harmonic (2 octaves up, A3):
8th harmonic (4 octaves up, A4):
Using fractional frets is cumbersome because they are non-linear. You're probably better off with a tape measure or ruler.