As the terms are defined here, the different numbering systems exist because there is a distinction between an overtone (or partial) and a harmonic. Hamonics are exact multiples of the fundamental pitch, so the fundamental counts as 1. Overtones are partial frequencies relative to the fundamental, so the fundamental is not counted.
For me it is a conventional problem only. Important is understand what is the more clear, simple and obvious method. And I think that we are all agree. Or not?
I agree, it is a matter of convention. For me, numbering based on harmonics makes the most sense, but that is just the way my mind works -- I see it in mathematical and analytical terms. This is probably related to the fact that that my practical thinking about overtones/harmonics is primarily from the point of view of synthesis, rather then natural sources like voice or physical instruments. So I don't expect others to share my perspective if they are approaching it as a performer rather than as a composer of electronic music.
Igor Ezendam singing overtones at sunset at the Buddha Hall in Arillas, Corfu, Greece, with the Buddha Hall house cat. Recorded 2024.03.21If you want to hear...
Hare Krishna Hare Krishna Krishna Krishna Hare Hare Hare Rama Hare Rama Rama Hare Hare Mahamantra , ( Sanskrit : महामन्त्र mahāmantra) means "Great Mantra", ...