Our early arithmetic lessons told us 2 goes into 4 evenly, meaning no fraction was in the result. Perhaps the authors mean 'even' harmonics in the same way. Namely as integer multiples (2, 3,4,5, etc.), because an exact number of cycles fits within one cycle of the fundamental frequency.
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Whereas a non-integer multiple is regarded as an 'odd' harmonic? It isn't the clearest use of the English language but sometimes we have to make accommodations.