There are "minor third bells" (e.g., church bells) and "major third bells".
The correct terminology in the context of bells is "prime" and "tierce" (not "fundamental" and "second harmonic"; as user1079505 notes, "It's not a harmonic if it doesn't follow harmonic series.").
Table 6.2 of Sethares, Tuning, Timbre, Spectrum, Scale (p. 117) gives the partials:
| Name of Partial |
Ideal Minor Third Bell |
Measured Bell |
Ideal Major Third Bell |
| hum |
0.5 |
0.5 |
0.5 |
| prime |
1.0 |
1.0 |
1.0 |
| tierce |
1.2 |
1.19 |
1.25 |
| quint |
1.5 |
1.56 |
1.5 |
| nominal |
2.0 |
2.0 |
2.0 |
| deciem |
2.5 |
2.51 |
2.5 |
| undeciem |
2.61 |
2.66 |
2.95 |
| duodeciem |
3.0 |
3.01 |
3.25 |
| upper octave |
4.0 |
4.1 |
4.0 |
Ibid. p. 116:
Traditional church bells tuned this way are called “minor third” bells because of the interval 1.2, which is exactly the just minor third 6/5. Bell makers have recently figured out how to shape a bell in which the tierce becomes 1.25, which is the just major third 5/4. These are called “major third” bells.
For example, this bell is a very good "minor third bell":
| Name of Partial |
Ideal Minor Third Bell Ratio |
Measured |
Measured Ratio |
| hum |
0.5 |
144 Hz (Re3) = -41,0 dB |
0.51 |
| prime |
1.0 |
284 Hz (Do♯4) = -37,4 dB |
1.0 |
| tierce |
1.2 |
343 Hz (Fa4) = -43,2 dB |
1.21 |
| quint |
1.5 |
431 Hz (La4) = -55,7 dB |
1.52 |
| nominal |
2.0 |
576 Hz (Re5) = -39,1 dB |
2.03 |
| deciem |
2.5 |
717 Hz (Fa5) = -50,1 dB |
2.52 |
| undeciem |
2.61 |
744 Hz (Fa♯5) = -53,5 dB |
2.62 |
| duodeciem |
3.0 |
858 Hz (La5) = -40,8 dB |
3.02 |
| upper octave |
4.0 |
1181 Hz (Re6) = -45,9 dB |
4.16 |
