Re: [tuning] infinite/finite

Writing, for the moment, not as a constructivist, but as a transfinitist, if
you have an infinite set of JI pitches, their membership will correspond one
to one with the membership of the (likewise infinite) harmonic series, even
though the first series is a sieved subset of the second... 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.

Perhaps the more relevant points for Haverstick are that (1) most JI systems
will be constructed from relatively small sets of generating intervals, each
interval being audibly distinct, identifiable, and verifiable, and (2) the
variety of musical contexts into which particular interval relationships may
be audibly projected is unknown; it is not true to say that a given
interval is not perceptible so long as we still know so little about the
modes and limits of musical production and reception. La Monte Young's
extended duration sound environments are examples of compositional
innovation allowing previously unheard-of relationships to be made
perceptible.

Daniel Wolf
http://home.snafu.de/djwolf/

> Neil -- just intonation does not have to be thought of as being a
> represenation of the harmonic series. It can simply be thought of as a
> tuning system built up from the most acoustically blending intervals,
which
> turn out to be simple ratios such as 3/2, 5/3, etc. Also, the infinite
> lattice Polychroni was referring to could simply be an infinite chain of
> 3/2s and 4/3s, or a 2-dimensional grid of 3/2s and 5/4s, or a 7-limit
> lattice, etc.; you don't need to go infinitely high in the harmonic series
> to get an infinite JI set of pitches. -- Paul
>

>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.