Re: drifting Sibyllea

Hello, there, everyone, and here's an adaptive 5-limit JI version of
the Prologue of Orlando di Lasso's _Prophetiae Sibyllarum_ which I did
last summer using Vicentino's second tuning for his 36-note
archicembalo, taken as two manuals in 1/4-comma meantone at 1/4 comma
apart to produce "perfect fifths" and "perfect thirds."

In this approach, which might serve as one model for vocal intonation,
no shifts of larger than 1/4 syntonic comma (~5.38 cents) are
required.

http://value.net/~mschulter/lasso001.mid

Please let me caution that some proofreading and debugging might yet be in
order, but I wanted to post promptly in view of the topicality, inviting
any corrections (I can check an ASCII translation of the MIDI coding, but
not listen to the file, which would require a sound card or the like).

This solution might be of special interest because Lasso's piece is
often dated to around 1551, or more generally to the early 1550's,
while Vicentino's apparent scheme for vertical JI on keyboard is
described in his treatise _Ancient Music Adapted to Modern Practice_
(1555), and also a circular advertising his arciorgano or "superorgan"
(1561).

Most appreciatively,

Margo Schulter
mschulter@value.net

--- In tuning@y..., "M. Schulter" <MSCHULTER@V...> wrote:

/tuning/topicId_36554.html#36554

> Hello, there, everyone, and here's an adaptive 5-limit JI version of
> the Prologue of Orlando di Lasso's _Prophetiae Sibyllarum_ which I
did
> last summer using Vicentino's second tuning for his 36-note
> archicembalo, taken as two manuals in 1/4-comma meantone at 1/4
comma
> apart to produce "perfect fifths" and "perfect thirds."
>
> In this approach, which might serve as one model for vocal
intonation,
> no shifts of larger than 1/4 syntonic comma (~5.38 cents) are
> required.
>
> http://value.net/~mschulter/lasso001.mid
>
> Please let me caution that some proofreading and debugging might
yet be in
> order, but I wanted to post promptly in view of the topicality,
inviting
> any corrections (I can check an ASCII translation of the MIDI
coding, but
> not listen to the file, which would require a sound card or the
like).
>
> This solution might be of special interest because Lasso's piece is
> often dated to around 1551, or more generally to the early 1550's,
> while Vicentino's apparent scheme for vertical JI on keyboard is
> described in his treatise _Ancient Music Adapted to Modern Practice_
> (1555), and also a circular advertising his arciorgano
or "superorgan"
> (1561).
>

****Hello Margo!

Thank you so very much for posting this interesting Lasso file. It
really sounds fantastic. Too bad you can't hear it.
Since "adequate" sound cards are only about $30 nowadays perhaps you
should consider having one installed. You might even be able to find
a "donated" one, since there are so many everyplace.

Thanks again!

Joe Pehrson

--- In tuning@y..., "M. Schulter" <MSCHULTER@V...> wrote:
> Hello, there, everyone, and here's an adaptive 5-limit JI version of
> the Prologue of Orlando di Lasso's _Prophetiae Sibyllarum_ which I
did
> last summer using Vicentino's second tuning for his 36-note
> archicembalo, taken as two manuals in 1/4-comma meantone at 1/4
comma
> apart to produce "perfect fifths" and "perfect thirds."
>
> In this approach, which might serve as one model for vocal
intonation,
> no shifts of larger than 1/4 syntonic comma (~5.38 cents) are
> required.
>
> http://value.net/~mschulter/lasso001.mid
>
> Please let me caution that some proofreading and debugging might
yet be in
> order, but I wanted to post promptly in view of the topicality,
inviting
> any corrections (I can check an ASCII translation of the MIDI
coding, but
> not listen to the file, which would require a sound card or the
like).
>
> This solution might be of special interest because Lasso's piece is
> often dated to around 1551, or more generally to the early 1550's,
> while Vicentino's apparent scheme for vertical JI on keyboard is
> described in his treatise _Ancient Music Adapted to Modern Practice_
> (1555), and also a circular advertising his arciorgano
or "superorgan"
> (1561).
>
> Most appreciatively,
>
> Margo Schulter
> mschulter@v...

HOORAY FOR MARGO!!!! if i have any weight to throw behind everything
margo said and did here, consider it thrown. margo happens to be
*the* expert on early music tuning, at least when it comes to the
community of english speakers on the internet. i'd take this
unusually brief and typically understated response from her as
*DEFINITIVE* -- and read and listen to its contents three times a
day, preferably after meals :)

--- In tuning@y..., "M. Schulter" <MSCHULTER@V...> wrote:
> Hello, there, everyone, and here's an adaptive 5-limit JI version
of
> the Prologue of Orlando di Lasso's _Prophetiae Sibyllarum_
which I did
> last summer using Vicentino's second tuning for his 36-note
> archicembalo, taken as two manuals in 1/4-comma meantone
at 1/4 comma
> apart to produce "perfect fifths" and "perfect thirds."

[...]

Margo, thanks for the file, and to all for some suggestions! As an
owner of a harpsichord (and having laid down quite a couple of
temperaments) I was able to inform the group about
meantonesque intonation quite a while ago, so this foundation
is built - so we'll see where this will lead us to...

Now off I go to the Gesualdo threads!

One question to Margo though:
you say you used two manuals - wouldn't I need three to get the
36-note thing? (Now juggling with my two available MIDI-claviers)

All the best
Michael

--- In tuning@y..., "M. Schulter" <MSCHULTER@V...> wrote:
> Hello, there, everyone, and here's an adaptive 5-limit JI version
of
> the Prologue of Orlando di Lasso's _Prophetiae Sibyllarum_
which I did
> last summer using Vicentino's second tuning for his 36-note
> archicembalo, taken as two manuals in 1/4-comma meantone
at 1/4 comma
> apart to produce "perfect fifths" and "perfect thirds."

[...]

Margo, thanks for the file, and to all for some suggestions! As an
owner of a harpsichord (and having laid down quite a couple of
temperaments) I was able to inform the group about
meantonesque intonation quite a while ago, so this foundation
is built - so we'll see where this will lead us to...

Now off I go to the Gesualdo threads!

One question to Margo though:
you say you used two manuals - wouldn't I need three to get the
36-note thing? (Now juggling with my two available MIDI-claviers)

All the best
Michael

Hello, there, Michael and everyone, and thank you for the opportunity
to clear up a possible misunderstanding about the MIDI file of Lasso's
Prologue from the _Prophetiae Sibyllarum_ while also expressing a bit
of due modesty about my keyboard playing:

> One question to Margo though: you say you used two manuals -
> wouldn't I need three to get the 36-note thing? (Now juggling with
> my two available MIDI-claviers) All the best

Here I should clarify that the MIDI file wasn't recorded on any
musical keyboard instrument, but rather programmed with a computer
keyboard using Manuel Op de Coul's fine Scala program available free
on the Internet.

Having defined a 38-note tuning corresponding to Vicentino's adaptive
JI scheme taken as based in 1/4-comma meantone, I then typed a text
file coding the notes of Lasso's Prologue, which Scala translated into
a MIDI file using the EXAMPLE command.

To map this ideal 38-note scheme onto a musical keyboard, one approach
might be the one that Vicentino followed for the most part on his
archicembalo, and presumably also his arciorgano: two 19-note manuals
(Gb-B#) with split keys for the five usual accidentals, plus levers
for E# and B#. The notes on the upper manual are tuned in "just
fifths" to those on the lower manual.

In practice, Vicentino couldn't fit the E# and B# levers into the
upper manual, so he wound up with 36 notes per octave. This wouldn't
be a problem for the Lasso piece, which has a basic range of Eb-A#, or
14 notes. The sharpmost fifth is D#-A#', with the apostrophe (')
representing Vicentino's "comma sign" here likely showing a note
raised by a quartercomma or so to form a pure fifth. (The amount by
which a meantone fifth is tempered is one of Vicentino's definitions
of a "comma.")

Thus the rendition in my computer-generated MIDI file _could_ in
theory have been performed on Vicentino's instrument in its adaptive
JI tuning.

Your request for a clarification not only gives me a chance to explain
that this MIDI file was indeed generated using a computer keyboard
rather than a musical one -- historically authentic or otherwise --
but to invite some discussion about issues that often come up when
early music meets modern technologies.

Also, as I discuss below, it is quite possible to have a useful
24-note set on a musical keyboard for Lasso's Prologue with just
fifths in lots of positions; the main issue might be how well a human
player can navigate such a scheme in real time.

First of all, to address your immediate query, I do indeed use a
24-note arrangement on synthesizer with two 12-note meantone manuals
(Eb-G#) a diesis apart for "Xeno-Renaissance" music -- a very useful
subset of Vicentino's enharmonic 31-note cycle, but different from his
adaptive JI scheme.

As it happens, Vicentino's own enharmonic pieces using dieses or
fifthtones can each fit within such a 24-note gamut with two manuals a
diesis apart. While I use Eb-G#/Eb*-Ab as "standard" (the * showing a
note raised by a 128:125 diesis, about 41.06 cents), Vicentino often
uses a range of Bb-D#/Bb*-Eb, as in his complete motet _Musica prisca
caput_. One madrigal section uses Ab-C#/Ab*-Db.

While I'm not aware of any historical precedent for a 24-note
archicembalo in this arrangement, I find it very attractive for
enharmonic music; but the fifths are tempered at a usual 1/4-comma.

Please let me add with due modesty that I use this arrangement mostly
for "Xeno-Renaissance" improvisations, and for playing brief and
simple examples from Vicentino and Colonna. What an accomplished
keyboardist could do with it is something else again.

Likewise, for Lasso's Prologue, I simply arrange two manuals in Eb-G#
and F-A#, the equivalent of split keys for Eb/D# and Bb/A# -- usual
meantone, as opposed to adaptive JI. Again, trying to play through it
and enjoying the process is one thing, and playing fluently something
else again.

Now let's consider an adaptive JI solution for Lasso's Prologue on a
24-note keyboard with two 12-note manuals. This calls for a bit of
"untidiness," since we don't have quite enough notes for a complete
system over the range of this piece, but let's try for a reasonable
compromise solution.

If we wanted a symmetrical 24-note system, we could tune the lower
manual Eb-G# in 1/4-comma, and then tune each note of the upper manual
to a "just fifth" above a note on the lower manual, as in Vicentino's
38-note scheme, giving us Eb-G#/Bb'-D#' (the 'again showing a note
raised by a quartercomma to produce a pure fifth with the lower
keyboard).

Here our basic gamut is Eb-A#, so the above scheme would leave us with
an A# problem. A rough and ready solution is to settle for a usual
tempered meantone fifth Eb-Bb on the lower manual, and tune the upper
manual F'-A#'. This gives us only tempered forms for the two fifths at
the extremes of our gamut, Eb-Bb and D#'-A#', but just alternatives
for all the others, from Bb-F' to G#-D#'.

As someone whose main idea of "tuning" is entering numbers for a
microtuning table, I give advice on how this might be done on a
harpsichord or the like with due caution. However, a basic approach
might be to tune the lower manual in 1/4-comma meantone at Eb-G#, and
then tune the notes F'-D#' on the upper manual in pure fifths with the
notes Bb-G# on the lower manual. Then A#' could be tuned a pure major
third above F#'.

Here's a general map of this adaptive JI gamut:

75:64
81 275 585 778 971
C#' D#' F#' G#' A#'
C' D' E' F' G' A' B' C'
5 198 391 508 702 895 1088 1205
3:2 15:8
------------------------------------------------------------------
25:16
76 310 579 773 1007
C# Eb F# G# Bb
C D E F G A B C
0 193 386 503 697 890 1083 1200
5:4

I'll also add a Scala file for this 24-note set at the end of this
message, in case it might be useful.

In practice, I suspect that the main issues might concern not so much
the merely tempered rather than just fifths Eb-Bb and D#'-A#', but the
practical complications of negotiating the intricacies of adaptive JI
in real time.

(For example, there are some 5-cent quartercomma shifts between notes
in certain sonorities easy to program in Scala, but maybe "nontrivial"
to handle fluently on a musical keyboard.)

Certainly a skilled performer can get striking just sonorities a good
part of the time; the question might be how often, how reliably, and
with what effort. Since the distinction between JI and meantone might
be most telling with prominent and sustained sonorities, where finding
the right notes might be easiest, we need not assume flawless and
relentless JI to appreciate such pure fifths and thirds could have a
captivating quality -- in 1555, or 2002.

Whatever conclusions one might draw from the experiences of performers
who try this -- a skill worthy of cultivation for period performers --
I am impressed by how Vicentino's 16th-century system for adaptive JI
seems to fit so smoothly with 21st-century MIDI technology which can
manage the intricacies of sounding the right note at the right time.

This is just a quick answer which I hope addresses some of your
immediate questions, and invites much more dialogue. I'd be fascinated
to learn about your meantone keyboard playing, and any 24-note tunings
you might try.

Again, to sum up, I've found a 24-note "enharmonic archicembalo"
tuning with two manuals a diesis apart to be delightful: you get lots
of fifthtone steps a la Vicentino, plus the various kinds of
"proximate" intervals he described a diesis larger or smaller than
usual -- although not in every position, unlike his 31-note circle or
that of Fabio Colonna (1618).

With Vicentino's adaptive JI, my approach has been using computer
coding to generate MIDI files. However, with a 24-note instrument and
a tuning like Eb-G#/F'-A#', it should be possible to get just fifths
and minor thirds, as well as the pure major thirds of 1/4-comma, for
most of Lasso's Prologue. How well a player could do this in real
time, or how helpful a reference it might be for a flexible-pitch
ensemble (e.g. for certain prominent sonorities), I'd leave to
experienced keyboardists to test by experiment and experience.

Most appreciatively,

Margo Schulter
mschulter@value.net

P.S. The following Scala file is basically a quick edit of a file for
Vicentino's ideal 38-note scheme, coming down to the 24-note
compromise described above.

----------------------------- Scala file follows ----------------------

! qcmlji24.scl
!
24-note adaptive JI (Eb-G#/F'-A#') for Lasso's Prologue to _Prophetiae_
24
!
5.37657
76.04900
81.42557
193.15686
198.53343
75/64
310.26471
5/4
391.69029
503.42157
508.79814
579.47057
584.84714
696.57843
3/2
25/16
778.00400
889.73529
895.11186
971.16086
1006.84314
1082.89214
15/8
2/1

---- Scala file includes blank line below last line of text "2/1" ----