For context, bass guitar strings are tuned 3 octaves lower than that. The frequency of the A string is 55 Hz. You can't even reach 220 Hz using the 12th fret on the highest (G) string. Tuning a bass A string to 8 times the frequency would require increasing its tension ~~almost 3 times~~ 64 times. The guitar body ~~should~~ will not survive such forces but the string will snap long before you reach 110 Hz.

Edit: got the quadratic formula the other way around

You can do the experiment on a non-bass guitar: "shorten" the high E string (330 Hz) by 5 frets to reach close to 440 Hz. It's a chromatic scale and not a perfect fifth (error of +0.02 semitones) but that can be corrected without damage by holding the 5th fret and tuning the string to exactly 440 Hz. This shorter string will then react to the tuning fork as intended.

[–] Frozengyro@lemmy.world 2 points 1 week ago (1 children)

Or you can just use harmonics.

[–] ChaoticNeutralCzech@feddit.org 7 points 1 week ago* (last edited 1 week ago) (1 children)

I think that would make a standing wave with a series of nodes/antinodes on the string, and how well it works would strongly depend on where the tuning fork is along the string. This has the potential to be more interesting but it's not as easy. See my other comment for a table at which frequencies a standing wave occurs on the A1 string.

[–] Frozengyro@lemmy.world 2 points 1 week ago (1 children)

So the 12th fret is 1 octave up, 5th is 2 octaves, and just past the second fret is 3 octaves.

[–] ChaoticNeutralCzech@feddit.org 2 points 1 week ago (1 children)

the 12th fret is 1 octave up

Yup. 12 semitones is 1 octave so A2 on the bass guitar's A string. The frequency ratio to A1 is 2:1.

5th is 2 octaves

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.

just past the second fret is 3 octaves

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.

[–] Frozengyro@lemmy.world 2 points 1 week ago (1 children)

Sorry I mean that's where the harmonics are.

[–] ChaoticNeutralCzech@feddit.org 3 points 1 week ago

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):

½ the string length (fret 12)

2nd harmonic (1 octave up, A2):

¾ the string length (fret 4.98)
¼ the string length

3rd harmonic (perfect fifth from A2 or approx. E3):

⅚ the string length (fret 3.15)
½ the string length (fret 12)
⅙ the string length

4th harmonic (2 octaves up, A3):

⅞ the string length (fret 2.32)
⅝ the string length (fret 8.14)
⅜ the string length
⅛ the string length

8th harmonic (4 octaves up, A4):

15/16 the string length (fret 1.12)
13/16 the string length (fret 3.59)
11/16 the string length (fret 6.49)
9/16 the string length (fret 9.96)
7/16 the string length
5/16 the string length
3/16 the string length
1/16 the string length

Using fractional frets is cumbersome because they are non-linear. You're probably better off with a tape measure or ruler.