No. Its the fundamental harmonic. Anyways, you start counting from the (n+1) multiple right? So a wave of twice the fundamental frequency would be the first harmonic, thus it cant be odd.
This is the Wikipedia definition of a harmonic: A harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency, i.e. if the fundamental frequency is f, the harmonics have frequencies 2f, 3f, 4f, . . . etc.
So, the second harmonic is 2 times the fundamental.
But 1 is also an integer and it is an odd number. So, the fundamental is the 1st harmonic and it is an odd harmonic.
This is from Wikipedia's article on overtones:
Frequency........ Order ..........Name 1 ............Name 2 ............Name 3
1 · f = 440 Hz.....n = 1.........fundamental tone 1st harmonic ......1st partial
2 · f = 880 Hz.....n = 2 ........1st overtone.......2nd harmonic ......2nd partial
3 · f = 1320 Hz....n = 3 .......2nd overtone ......3rd harmonic ......3rd partial
4 · f = 1760 Hz ...n = 4 .......3rd overtone .......4th harmonic.......4th partial
Woops - I meant zeroth overtone. Which I think is what chaoseverlasting was referring to. He was injecting his own special bit of chaos :-)
You are, of course, correct that the first harmonic would have to be the fundamental.
So anyway, who cares? Does the name you give it affect its properties?
What you can say about odd and even harmonics is that a waveform consisting only of odd harmonics (including 1st) will look symmetrical whereas one with a fundamental plus even harmonics will look asymmetrical.
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