RE: [tuning] infinite/finite

>Just compare
>the terms in a simple lattice of 3's and 5's extending infinitely on either
>axis with a corresponding harmonic series: after the origin, each term in
>the former will be larger than the corresponding term in the latter.

Huh?

> >Look, Haverstick complained about JI going high up in the harmonic
series.
> >Erlich responded with:
>
> >"you don't need to go infinitely high in the harmonic series
> >to get an infinite JI set of pitches"
>
> >which is nonsense.
>
> It's not nonsense at all. If all voices and instruments only produced the
> first 6 harmonics, we'd still have the same, infinite 5-limit JI lattice.
>

When the tones in that lattice are described as members of a harmonic series
whose "1" is at the extreme southwest, it both (a) continues infinitely high
up in that harmonic series, and indeed, (b) each successive term is larger
than the corresponding successive term in a simple harmonic series.

I really think you're making the wrong argument with Haverstick. You could
have written:

"you don't need to use infinitely high factors to get an infinite JI set of
pitches" (trivial but true)
or:
"with any small set of simple JI intervals, you can generate an infinite JI
set of pitches" (another way of saying the same)
or
"JI systems can use a small set of simple intervals locally, generating a
potentially infinite set of pitches globally" (which starts to suggest how
this works in real musics).