Harmonic just means integer multiples of the fundamental frequency, whether they are odd or even. If you really want to get into musical harmony, the perfect fifth is not an even multiple of the fundamental with an interval ratio of 3:2 and neither is the major third, which is an interval ratio of 5:4. Even order harmonics represent octaves, which strengthen the fundamental which may or may not even be present, giving a larger than life ringing tone. A combination or Tartini tone is most commonly produced using a fundamental and its fifth, in which a common subharmonic is heard psychoacoustically. Overtones are any frequencies above the fundamental frequency.
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