Steve F wrote

Acoustics" by Arthur H. Benade, and he makes it very clear that the term
"partial" is used for any "part" of the sound produced, including the
fundamental.  It's a necessary way of looking at things because not all
sound coming from the same source are necessarily musically related, e.g.,
Mr. Benade's example of hitting a skillet and listening to the resulting
sounds.  All such sounds are parts, and therefore partials, of the total
sound being produced.  In a musical context where the partials are
mathematically related (or nearly so, at any rate), the fundamental, the
first harmonic, and the first partial all refer to the same pitch.

***********
Your usage of these terms corresponds to the standard scientific
usage.   Unfortunately, many people use the term "overtone."
The first overtone is the second harmonic.   Other people, typically
harpists and guitarists, use the term "first harmonic" to mean
a note an octave higher than the fundamental. This usage is so
ingrained that there is probably no way to correct it, short of
hitting the miscreants over the head with a heavy metal object.
Alas! Where are Benade and his skillet now that we need them?

Gotta go,
Cabbfegge 
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