As [email protected] mentioned, you can have interesting results by using harmonics - tones that are a whole (k) multiple of the base frequency because then the string vibrates in a standing wave forming a series of k+1 nodes (including ends) and k antinodes equally spaced across its length. Such notes are:
Closest note
Freq.
Harm.
Relation to A
A1
55 Hz
base
(aka fundamental or open string frequency)
A2
110 Hz
2nd
octave above A1
E3 + 2 cents
165 Hz
3rd
perfect fifth from A2
A3
220 Hz
4th
octave above A2
C#4 - 14 cents
275 Hz
5th
major third from A3
E4 + 2 cents
330 Hz
6th
perfect fifth from A3
G4 - 31 cents
385 Hz
7th
far from a note on the chromatic scale
A4
440 Hz
8th
octave above A3
B4 + 4 cents
495 Hz
9th
major second from A4
C#5 - 14 cents
550 Hz
10th
major third from A4
D#5 - 49 cents
605 Hz
11th
very far from a note on the chromatic scale
E5 + 2 cents
660 Hz
12th
perfect fifth from A4
F5 + 41 cents
715 Hz
13th
very far from a note on the chromatic scale
G5 - 31 cents
770 Hz
14th
far from a note on the chromatic scale
G#5 - 12 cents
825 Hz
15th
minor second below A5
A5
880 Hz
16th
octave above A4
Frequencies and relations are exact, closest chromatic (piano) notes other than A are approximate, the deviation is expressed in whole cents (hundreths of semitones). Notes more than 20 cents off the chromatic scale will probably sound off so they are discouraged. You could continue forever but frequencies above that will have a very weak response.
Yes, you will get some resonance on non-integer multiples but way less.
As [email protected] mentioned, you can have interesting results by using harmonics - tones that are a whole (k) multiple of the base frequency because then the string vibrates in a standing wave forming a series of k+1 nodes (including ends) and k antinodes equally spaced across its length. Such notes are:
Frequencies and relations are exact, closest chromatic (piano) notes other than A are approximate, the deviation is expressed in whole cents (hundreths of semitones). Notes more than 20 cents off the chromatic scale will probably sound off so they are discouraged. You could continue forever but frequencies above that will have a very weak response.
Yes, you will get some resonance on non-integer multiples but way less.