It gets confusing when the fundamental frequency f, is described as having a first harmonic at 2*f.
The fundamental is really the first or “fundamental” harmonic of the harmonic series.
The fundamental at frequency f, has a second harmonic is at 2*f, the third at 3*f, etc.
There is no energy present in the spectrum between the integer harmonics of a vibration.
Broadband energy between the harmonics is called noise.
http://en.wikipedia.org/wiki/Harmonic
Any repetitive vibration can be analysed as a fundamental frequency with integer multiple harmonics.
The higher harmonics are usually generated by non-linear characteristics of the oscillator.
Different generation mechanisms often effect the odd and the even numbered harmonics differently.
Modification of the amplitude of harmonics will change the perception of the sound.
Some vibrations are tuned, while some are determined by engine RPM.
Subsonic beats can occur between the harmonics of different frequency vibrations at different RPM.