Note mapping

****My point was simply that music conceived in 12tet no doubt sounds best in
12tet. (Of course Mozart does not fall into this category) If a painter does
a p

+++My thoughts on this are thus similar, altho what intrigues me is as to if
there is any system weather heuristic, or that of a computer system that can
be programmed to take
compositions in any equal temperament, ESPECIALLY 12 equal temperament, and
map it
to other equal tempermaments.

Thus, we could take a note in the 12 equal tempermament, and round it either
up or down.

David Keenan, I'm sorry to single you out, but in all honesty, you emailed
me once, and told me that this was a very odd question.

I must be blunt with you, why did you say this?

---Sarn.

Sarn Ursell wrote:

>+++My thoughts on this are thus similar, altho what intrigues me is as to if
>there is any system weather heuristic, or that of a computer system that can
>be programmed to take
>compositions in any equal temperament, ESPECIALLY 12 equal temperament, and
>map it
>to other equal tempermaments.
>
>Thus, we could take a note in the 12 equal tempermament, and round it either
>up or down.
>
>David Keenan, I'm sorry to single you out, but in all honesty, you emailed
>me once, and told me that this was a very odd question.
>
>I must be blunt with you, why did you say this?

Dear Sarn,

I didn't. At least not in general. I think you are referring to the time
you proposed rounding 12-tET notes to the nearest 10-tET note. I suspect
you would only have to listen to the result applied to some familiar piece
to know why I thought this a very odd suggestion.

The idea of mapping from 12-tET to certain other "compatible" ETs with
_more_ than 12 notes is not at all odd. I have attempted 12 to 31 myself
with the aim of improving 5-limit consonances. But it is considerably more
complicated than merely rounding to the nearest note. You can read an
introduction to the method at:
http://dkeenan.com/Music/AdaptiveMeantone.htm

As far as going to fewer notes, maybe rounding from 12-tET to 7-tET could
result in some pieces still being recognisable. You have the problem of
deciding which 12-tET note (if any) should align exactly with a 7-tET note,
as you will get different roundings with different choices. But what's the
point? I don't think anyone is likely to consider it an improvement.

Regards,

-- Dave Keenan
http://dkeenan.com

--- In tuning@egroups.com, David C Keenan <D.KEENAN@U...> wrote:

> As far as going to fewer notes, maybe rounding from 12-tET to 7-tET
could
> result in some pieces still being recognisable. You have the
problem of
> deciding which 12-tET note (if any) should align exactly with a
7-tET note,
> as you will get different roundings with different choices. But
what's the
> point? I don't think anyone is likely to consider it an improvement.

Dave (and others) -- "improvement" is not the only possible point of
retuning. Also
possible are exploring new colors and new way of expressing
structural relationships.

One of my first experiences with a wide variety of alternative
tunings was in college with
the BASIC (was it QBASIC?) on the Mac and a built-in demo program
which translated a
"score" file (with traditional-style notation using letter names,
sharps and flats) -- and
the built-in score file was a well-known Bach piece. Fortunately, the
program was easily
modified to change the sizes of whole tones (a-b, c-d, d-e, f-g,
g-a), diatonic semitones
(e-f and b-c), and chromatic semitones (sharps and flats). By setting
whole tones and
diatonic semitones to 1/7 octave and chromatic semitones to 0, a
7-tET rendition was
obtained -- Thai Bach! Rounding to 7-tET wouldn't have acheived this
effect, as some
keys would have been mutated into scales of fewer than 7 tones; but
this Mac BASIC
approach always treated seven letter names as seven distinct pitches.
Sure, all the logic
of the modulations disappeared, and the piece was rather monotonous,
but it was a
great way to experience 7-tET and the properties it has when used as
a diatonic scale
(neutral triads, equal steps, . . .).

Similarly, setting whole tones to 5/31 octave, diatonic semitones to
3/31 octave, and
chromatic semitones to 2/31 octave resulted in a wonderful meantone
rendition of the
Bach that is quite historically appropriate, and no doubt identical
to what Dave Keenan's
approach would have yielded. An improvement in terms of the
smoothness of the 5-limit
consonances, yes. But my violinist roommate didn't like it because
there was no "noise"
(probably a reference to the roughness among the difference tones of
the 12-tET chords)
which he found comfortable. So, although I would hope to convince him
otherwise, at
least at that moment this was not, for him, an "improvement".

I played with many other tunings including pelog-like ones where the
whole tones were
smaller than the semitones, as well as tunings where the semitones
were negative!
Although some of the results were bizarre, some element of the logic
of Bach's music
always came through, and this was due to a consistent mapping of the
diatonic intervals,
which would not have resulted from a simple rounding operation.