m from n-TET

When the aim is to play an alternative tuning upon a retuned synth, I can fully
recognise the need to be restricted to 12 or less pitches. It is painfully
frustrating to navigate a keyboard that has any interval other than the octave
sounding when a pair of keys are pressed that look like an octave apart -- in
other words: when I tune my synth to 19-TET then press what looks like a pair
of C notes twelve keys apart, I hear an interval much smaller than an octave.
The brain-ache comes when trying to remember where each octave of a given note
occurs along the full width of the keyboard as they are all different.

The benefit of an equal temperament as I see it (?? hear it ??) is that
melodies and chords can be played in any key, enabling creative use of
modulation in our compositions. Even though pure harmony can only be
approximated with an ET, sometimes this compromise is worth tolerating for the
benefits I mentioned. Equal temperaments work brilliantly on fretted
instruments for two reasons: firstly, there is no need to restrict the number
of notes as with a keyboard; and secondly, the spacing of intervals remains
unchanged -- it feels fairly normal to play.

What I don't understand is why a musician would restrict themselves to 12 or
less pitches selected from an equal temperament. I have read numerous posts on
this list describing this practice, most recently 11 from 31-TET. Why choose a
subset from within something that was compromised to start with? Why not select
11 pitches according to just intonation? You will get pure harmony rather than
approximations of it. Does this not make more sense seeing as the benefit of
creative modulation has been lost by discarding some of the equally tempered
pitches?

DARREN McDOUGALL

[McDougall, Darren Scott:]
> What I don't understand is why a musician would restrict themselves
to 12 or less pitches selected from an equal temperament. I have read
numerous posts on this list describing this practice, most recently 11
from 31-TET.

I think that most of these are bandied about as (theoretical)
analogues to the familiar (5, 6, 7, ect.) scalular subsets, and while
culled from larger chromatic sets, are not (necessarily) meant to do
away with the rest of the set (pitches).

>Why choose a subset from within something that was compromised to
start with?

If one is finding (or making...) them musically useful, or if they are
animating ones theoretical interest - WHY NOT?

>Why not select 11 pitches according to just intonation? You will get
pure harmony rather than approximations of it. Does this not make more
sense seeing as the benefit of creative modulation has been lost by
discarding some of the equally tempered pitches?

I think this is far from any sort of a black-and-white, makes more
sense/makes no sense issue... for example, some (such as Kraig Grady)
would (I think) object to the idea that equal divisions of the octave
lead to "the benefit of creative modulation," as (I believe) he would
prefer modulations that include comma shifts, thereby offering
distinctly different pitches by way of a 'modulation.' Myself, in the
context of my music, and as it pertains to intonation/tuning -- what
works works -- and as such, I've always tended to regard terms like
"pure" and "tempered" as (loosely) descriptive 'handles' that carry
little in the way of an immutable musical meaning.

Dan

Darren McDougall wrote,

>What I don't understand is why a musician would restrict themselves to 12
or
>less pitches selected from an equal temperament. I have read numerous posts
on
>this list describing this practice, most recently 11 from 31-TET. Why
choose a
>subset from within something that was compromised to start with? Why not
select
>11 pitches according to just intonation? You will get pure harmony rather
than
>approximations of it. Does this not make more sense seeing as the benefit
of
>creative modulation has been lost by discarding some of the equally
tempered
>pitches?

Not quite. For example, meantone temperament is a compromise which has some
benefits over just intonation -- more notes can be made consonant with one
another than in JI (for example, the diatonic scale in meantone has 6
consonant triads, while a JI version can have at most 5). 31-tET is an
excellent approximation of meantone, so choosing subsets of 31-tET is kind
of like choosing subsets of meantone. I agree that once you're choosing a
subset, 31-equal is not necessarily the ideal superset. But since any good
meantone will do, it's convenient to describe the subset in terms of
31-equal. Likewise for some of the subsets of 22-tET I've discussed.

I'd be happy to elaborate on any of this if it unclear.

-Paul Erlich

>Why not select
>11 pitches according to just intonation?

You should look again at my analysis of the 11-out-of-31 scale given. I
showed how one could not put all the tones in JI and still preserve all the
consonant relationships in the scale. It is much like the case with the
diatonic scale, but here there were even more interrelationships and
concords through the 7-limit.