Re: Vicentino's adaptive JI: all vertical fifths are just

Hello, there, and this is just a quick clarification about Vicentino's
just intonation system for his archicembalo with 36 or 38 notes per
octave.

In Vicentino's JI tuning, if carried out on a 38-note version of his
instrument, _all_ vertical fifths are just -- assuming that a performer
could consistently reach the right notes on both keyboards. Obviously with
an automated method of performance, whether a mechanical "player
archicembalo" with rolls or an electronic arrangement such as some MIDI
system using sequencer input, this complication should no longer be a
problem.

In this tuning, the 19 notes of the first or regular keyboard are tuned in
1/4-comma meantone (very close to 31-tet), Gb-A#. Then the 17 or 19 notes
of the second keyboard -- Vicentino wanted 19, or 38 for the whole
instrument, but settled for 17 (36 in all) because of technical problems
-- are tuned in pure fifths with the first 19.

On Vicentino's 36-note instrument, there will be two notes on the lower
keyboard with only tempered meantone fifths rather than pure ones -- B#
and E#, as I recall. A 38-note instrument solves this problem, and
obviously a modern electronic implementation could go to 62 notes for a
complete 31-note meantone plus pure fifths above every step.

Thus Vicentino-style adaptive JI -- putting aside the B#/E# question on
his 36-note instrument -- means pure vertical fifths everywhere.

The melodic intervals are based on meantone, requiring a melodic
adjustment of 1/4 syntonic comma (~5.38 cents) to cope with syntonic comma
shifts.

As has been pointed out, diesis shifts (e.g. G# vs. Ab) are a different
problem if one seeking a 19th-century equivalence between these notes --
or opportunity, if one wishes to use Vicentino's enharmonic (fifthtone)
style with dieses as deliberate intervals, and at the same time to enjoy
vertical JI.

Vicentino's JI tuning should not be confused with his 31-note division of
the octave, where 31 notes of the 36-note or 38-note instrument are used
to make a near-equal division of the octave into fifthtones, with the
remaining 5 or 7 notes used to provide a _few_ just fifths. In the
adaptive JI tuning for his instrument, we have only 19 basic pitches, with
pure fifths supplied consistently (apart from E# and B#).

Again, especially in an automated performance, one can get the best of
both systems by using 62 notes -- 31 basic notes (like his first tuning)
each with its pure fifth (like his second tuning).

Most respectfully,

Margo Schulter
mschulter@value.net

Margo, thanks for the concise explanation of Vicentino's
tuning scheme! Now I *finally* understand what he was doing!

I've read Kaufmann's articles on Vicentino, and still could
not glean the actual tuning. Did I miss it? Please cite the
sources which explain it as you do.

(references to your own List postings are also appreciated:
I already have one on the Sonic Arts website,
http://www.ixpres.com/interval/td/schulter/vincento.htm
but I know there are many more.)

> [Margo Schulter, TD 525.15]
> Thus Vicentino-style adaptive JI -- putting aside the B#/E#
> question on his 36-note instrument -- means pure vertical
> fifths everywhere.

So then there should be some way for John deLaubenfels to
'ground' his retuning scheme to a set of 2:3s so that it
will result in Vicentino's tuning... right? Anyone (Paul?)
care to clarify?

-monz

Joseph L. Monzo Philadelphia monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
--------------------------------------------------

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Thanks to Margo Schulter for clarifying Vicentino's work in TD 525.15.
I didn't realize he had BOTH a circular 31-tET meantone proposal AND
a 38 (or 36) note mixture of meantone and pure fifths. No doubt, had
it been possible to construct a reasonable 62-note per octave
instrument, he'd have put the two together, as we now can with
computers.

It sure would be nice if some talented member of this list would program
the 62-note effect (hint, hint!). I'd love to hear it!

JdL