When you introduce the 4th harmonic let us know that it is two octaves above the fundamental. As it is you only compare it to the 3rd harmonic, which is fine, but I feel each of the overtones should at least be described by comparison to the fundamental. You say it later, but say it when you first introduce it.
This part:
It's a little problematic to say that choirs and especially orchestras use just intonation. It's true that vocal ensmbles singing a capella are going to naturally gravitate toward just intervals when it comes to harmonies. We know from sources as early as the 14th century (Walter of Odington) that singers probably sang just 3rds (5/4, 6/5) even though the prevailing tunings would prescribe the very sharp Pythagorean 3rds. That's just people using their ears and gravitating towards the purest thirds they can hear.The problem with natural overtones (the Just Scale) is that the tuning is different for different scales, and the intervals between notes are not constant. It's actually still used in orchestras and choirs, and this is why orchestras have to retune in between pieces. For modern instruments however, we have adapted the equal temperament tuning. However it's useful to understand the overtones series as this is how music is derived, with a slight tweak to create a continuous and even tuning.
The same thing could be possible for violin family strings and the trombone; string orchestras and trombone choirs might very well have a tendency to play just intervals. But when these instruments are grouped with other fixed pitch instruments then to say that the ensemble tunes to a just scale is probably getting it wrong. Of course with winds and orchestral strings the actual frequencies that come out of each instrument will never be precisely in tune with any scale, but keyboard and fretted instruments are absolutely beholden to a predetermined tuning. So if an orchestra is playing a piano concerto you can bet that they're not tuned to a just scale.
And orchestras do consist of "modern instrument!" btw!
As a side note to all that, from looking at 15th and 16th century sources on the matter it's a safe bet that fretted instruments always utilized some form of equal temperament, even before such a thing had been "discovered" and named. It's just the nature of such an instrument; you're never going to get the whole range of it perfectly in tune with itself.
Third thing is why not talk about what kind of overtones would create "unpleasant" sounds (I personally wouldn't use the subjective terms like you have but it's not a big deal). What I mean is since you've talked how integer ratio related overtones create complex sounds with harmonic spectra, why not give a little space to sounds with inharmonic spectra?
I have one other comment but I'm trying to formulate it in a way that's not too inflammatory. I do think it's important and might help all of your tutorials.
