Lasso example in adaptive-JI

hello all,

i've added a graphic and MIDI-file of the
first 5 measures of Orlando di Lasso's motet
_Ave regina coelorum_, tuned in Vicentino's
adaptive-JI of 1555, to both of these pages:

Tuning Dictionary "adaptive-JI" entry:
http://sonic-arts.org/dict/adaptiveji.htm

my webpage about Vicentino's tuning:
http://sonic-arts.org/monzo/vicentino/vicentino.htm

(Lasso was a contemporary of Vicentino.)

the staff-notation is based on Pythagorean tuning,
and the graphic shows deviations from Pythagorean,
in 1/4-syntonic-comma increments.

the melodic shifts from 5-limit JI are never more
than 1/2-comma (~10.75 cents), and only 1/4-comma in
the cases where a note written by Lasso as a sustained
note is tuned to two different pitches.

all vertical sonorities are in the proportions 4:5:6
for "major" triads and 1/(6:5:4) for "minor" triads,
except for the suspensions before they resolve.

-monz
"all roads lead to n^0"

--- In tuning@y..., "monz" <monz@a...> wrote:
> hello all,
>
>
>
> i've added a graphic and MIDI-file of the
> first 5 measures of Orlando di Lasso's motet
> _Ave regina coelorum_, tuned in Vicentino's
> adaptive-JI of 1555, to both of these pages:
>
>
> Tuning Dictionary "adaptive-JI" entry:
> http://sonic-arts.org/dict/adaptiveji.htm
>
>
> my webpage about Vicentino's tuning:
> http://sonic-arts.org/monzo/vicentino/vicentino.htm
>
>
> (Lasso was a contemporary of Vicentino.)
>
>
> the staff-notation is based on Pythagorean tuning,
> and the graphic shows deviations from Pythagorean,
> in 1/4-syntonic-comma increments.

cool! cool! cool!!
>
> the melodic shifts from 5-limit JI are never more
> than 1/2-comma (~10.75 cents), and only 1/4-comma in
> the cases where a note written by Lasso as a sustained
> note is tuned to two different pitches.

what do you mean, "the melodic shifts from 5-limit JI"? do you simply
mean "the melodic shifts in sustained or repeated pitches"???

i'll take a closer look at this later . . .

hi paul,

> From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
> To: <tuning@yahoogroups.com>
> Sent: Saturday, November 30, 2002 11:45 AM
> Subject: [tuning] Re: Lasso example in adaptive-JI
>
>
> --- In tuning@y..., "monz" <monz@a...> wrote:
> > hello all,
> >
> >
> >
> > i've added a graphic and MIDI-file of the
> > first 5 measures of Orlando di Lasso's motet
> > _Ave regina coelorum_, tuned in Vicentino's
> > adaptive-JI of 1555, to both of these pages:
> >
> >
> > Tuning Dictionary "adaptive-JI" entry:
> > http://sonic-arts.org/dict/adaptiveji.htm
> >
> >
> > my webpage about Vicentino's tuning:
> > http://sonic-arts.org/monzo/vicentino/vicentino.htm
> >
> >
> > (Lasso was a contemporary of Vicentino.)
> >
> >
> > the staff-notation is based on Pythagorean tuning,
> > and the graphic shows deviations from Pythagorean,
> > in 1/4-syntonic-comma increments.
>
> cool! cool! cool!!
> >
> > the melodic shifts from 5-limit JI are never more
> > than 1/2-comma (~10.75 cents), and only 1/4-comma in
> > the cases where a note written by Lasso as a sustained
> > note is tuned to two different pitches.
>
> what do you mean, "the melodic shifts from 5-limit JI"? do you
> simply mean "the melodic shifts in sustained or repeated pitches"???

i felt compelled to put that in because of the F#'s in measure 5
which are labelled "-5/4", which are 1&1/4 syntonic commas flatter
than the Pythagorean F# of ratio 243/128, and thus 1/4 of a comma
flatter than the usual JI F# of ratio 15/8.

the deviation looks rather large in my notation, since it's greater
than a whole comma compared to the Pythagorean basis of the letter-name
notation, but compared to 5-limit JI (which in some ways is the
theoretical basis of the composition anyway) it's still only 1/4-comma.

that whole ornamental figure of G-F#-E-F# has only small deviations
from 5-limit JI.

-monz

--- In tuning@y..., "monz" <monz@a...> wrote:
> hi paul,
>
>
>
> > From: "wallyesterpaulrus" <wallyesterpaulrus@y...>
> > To: <tuning@y...>
> > Sent: Saturday, November 30, 2002 11:45 AM
> > Subject: [tuning] Re: Lasso example in adaptive-JI
> >
> >
> > --- In tuning@y..., "monz" <monz@a...> wrote:
> > > hello all,
> > >
> > >
> > >
> > > i've added a graphic and MIDI-file of the
> > > first 5 measures of Orlando di Lasso's motet
> > > _Ave regina coelorum_, tuned in Vicentino's
> > > adaptive-JI of 1555, to both of these pages:
> > >
> > >
> > > Tuning Dictionary "adaptive-JI" entry:
> > > http://sonic-arts.org/dict/adaptiveji.htm
> > >
> > >
> > > my webpage about Vicentino's tuning:
> > > http://sonic-arts.org/monzo/vicentino/vicentino.htm
> > >
> > >
> > > (Lasso was a contemporary of Vicentino.)
> > >
> > >
> > > the staff-notation is based on Pythagorean tuning,
> > > and the graphic shows deviations from Pythagorean,
> > > in 1/4-syntonic-comma increments.
> >
> > cool! cool! cool!!
> > >
> > > the melodic shifts from 5-limit JI are never more
> > > than 1/2-comma (~10.75 cents), and only 1/4-comma in
> > > the cases where a note written by Lasso as a sustained
> > > note is tuned to two different pitches.
> >
> > what do you mean, "the melodic shifts from 5-limit JI"? do
you
> > simply mean "the melodic shifts in sustained or repeated
pitches"???
>
>
>
> i felt compelled to put that in because of the F#'s in measure 5
> which are labelled "-5/4", which are 1&1/4 syntonic commas
flatter
> than the Pythagorean F# of ratio 243/128, and thus 1/4 of a
comma
> flatter than the usual JI F# of ratio 15/8.
>
> the deviation looks rather large in my notation, since it's greater
> than a whole comma compared to the Pythagorean basis of
the letter-name
> notation, but compared to 5-limit JI (which in some ways is the
> theoretical basis of the composition anyway) it's still only
1/4-comma.
>
> that whole ornamental figure of G-F#-E-F# has only small
deviations
> from 5-limit JI.
>
>
>
> -monz

so you meant "pitch deviation from JI", and not "melodic shifts" at
all. the latter has a specific meaning . . .

since 5-limit JI does not unambiguously assign a ratio to each
pitch class (for example, what's A), i think much more
meaningful and revealing would be to express the pitches in
terms of 1/4-comma meantone and deviations therefrom. this
would also make the system much more intelligible to someone
comtemplating such a realization, since the deviations from
pythagorean are so large and varied, while the deviations from
1/4-comma meantone will be very limited in both size and variety.

also, i see that the largest melodic shift is 1/4-comma, not 1/2
comma. this in fact is the whole point of the tuning system (as an
adaptive JI solution): the melodic shifts are subliminal, and at
the same time the vertical triads are in JI within themselves.

hi paul,

> From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
> To: <tuning@yahoogroups.com>
> Sent: Saturday, November 30, 2002 9:30 PM
> Subject: [tuning] Re: Lasso example in adaptive-JI
>

> --- In tuning@y..., "monz" <monz@a...> wrote:
> > > >
> > > > i've added a graphic and MIDI-file of the
> > > > first 5 measures of Orlando di Lasso's motet
> > > > _Ave regina coelorum_, tuned in Vicentino's
> > > > adaptive-JI of 1555, to both of these pages:
> > > >
> > > >
> > > > Tuning Dictionary "adaptive-JI" entry:
> > > > http://sonic-arts.org/dict/adaptiveji.htm
> > > >
> > > >
> > > > my webpage about Vicentino's tuning:
> > > > http://sonic-arts.org/monzo/vicentino/vicentino.htm
>
>
> so you meant "pitch deviation from JI", and not "melodic shifts"
> at all. the latter has a specific meaning . . .

OK. i'll have to fix the webpage.

> since 5-limit JI does not unambiguously assign a ratio to each
> pitch class (for example, what's A), i think much more
> meaningful and revealing would be to express the pitches in
> terms of 1/4-comma meantone and deviations therefrom. this
> would also make the system much more intelligible to someone
> comtemplating such a realization, since the deviations from
> pythagorean are so large and varied, while the deviations from
> 1/4-comma meantone will be very limited in both size and variety.

OK, your argument makes sense and i guess i can agree with that.

> also, i see that the largest melodic shift is 1/4-comma, not 1/2
> comma. this in fact is the whole point of the tuning system (as an
> adaptive JI solution): the melodic shifts are subliminal, and at
> the same time the vertical triads are in JI within themselves.

it seemed to me at first that melodic shifts would be no
more than 1/4-comma, but i wasn't sure without really examining
the melodic lines of each of the voices. thanks.

just for the record -- even listening closely while looking at
my score, it's hard to tell that the 1/4-comma melodic shifts
occur. so they are indeed subliminal to my ears, and i'd wager
to nearly everyone else's too. the whole selection sounds like
it's in JI to me, but without any drifting of the pitch -- which,
of course, was the whole point behind Vicentino's tuning.
pretty damn clever.

-monz

--- In tuning@y..., "monz" <monz@a...> wrote:

> > also, i see that the largest melodic shift is 1/4-comma, not
1/2
> > comma. this in fact is the whole point of the tuning system
(as an
> > adaptive JI solution): the melodic shifts are subliminal, and
at
> > the same time the vertical triads are in JI within themselves.
>
>
> it seemed to me at first that melodic shifts would be no
> more than 1/4-comma, but i wasn't sure without really
examining
> the melodic lines of each of the voices. thanks.
>
> just for the record -- even listening closely while looking at
> my score, it's hard to tell that the 1/4-comma melodic shifts
> occur. so they are indeed subliminal to my ears, and i'd wager
> to nearly everyone else's too. the whole selection sounds like
> it's in JI to me, but without any drifting of the pitch -- which,
> of course, was the whole point behind Vicentino's tuning.
> pretty damn clever.
>
>
>
> -monz

thanks monz. just to be 100% scholarly, it should be noted that
vicentino's own description is extremely confusing, and seems
to have more than one possible interpretation. i came up with the
same idea independently around dec. '94, after johnny reinhard
told me he had arranged some old piece with the roots in
pythagorean and the chords in vertical JI . . . after some thought, i
realized that a meantone, rather than pythagorean, basis for
adaptive JI would cut the melodic shifts by a factor of 4. much
later, on this list, margo informed me that my proposal appeared
to agree with vicentino's second tuning of 1555, at least as
interpreted by Palisca and/or herself . . .

> From: "monz" <monz@attglobal.net>
> To: <tuning@yahoogroups.com>
> Sent: Sunday, December 01, 2002 9:29 AM
> Subject: Re: [tuning] Re: Lasso example in adaptive-JI
>
>
> hi paul,
>
>
> > From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
> > To: <tuning@yahoogroups.com>
> > Sent: Saturday, November 30, 2002 9:30 PM
> > Subject: [tuning] Re: Lasso example in adaptive-JI
> >
>
> > --- In tuning@y..., "monz" <monz@a...> wrote:
> > > > >
> > > > > i've added a graphic and MIDI-file of the
> > > > > first 5 measures of Orlando di Lasso's motet
> > > > > _Ave regina coelorum_, tuned in Vicentino's
> > > > > adaptive-JI of 1555, to both of these pages:
> > > > >
> > > > >
> > > > > Tuning Dictionary "adaptive-JI" entry:
> > > > > http://sonic-arts.org/dict/adaptiveji.htm
> > > > >
> > > > >
> > > > > my webpage about Vicentino's tuning:
> > > > > http://sonic-arts.org/monzo/vicentino/vicentino.htm
> >
> >
> > since 5-limit JI does not unambiguously assign a ratio to each
> > pitch class (for example, what's A), i think much more
> > meaningful and revealing would be to express the pitches in
> > terms of 1/4-comma meantone and deviations therefrom. this
> > would also make the system much more intelligible to someone
> > comtemplating such a realization, since the deviations from
> > pythagorean are so large and varied, while the deviations from
> > 1/4-comma meantone will be very limited in both size and variety.
>
>
> OK, your argument makes sense and i guess i can agree with that.

i decided to use two illustrations, showing *both* deviation
from Pythagorean as well as deviation from 1/4-comma meantone.

-monz

--- In tuning@y..., "monz" <monz@a...> wrote:

> i decided to use two illustrations, showing *both* deviation
> from Pythagorean as well as deviation from 1/4-comma meantone.
>
>
>
> -monz

cool, dude! now i have two comments:

1. is this the whole motet? if not, you might want to
say "excerpt" . . .

2. would it be possible to do this for _Ave Maria_ by Josquin des
Pres? this is the piece that jonathan walker focuses on in his
_defense of just intonation_, but the idea of *adaptive*, rather than
strict, just intonation seems to have escaped walker's consideration.

http://boethius.music.ucsb.edu/mto/issues/mto.96.2.6/mto.96.2.6.walker
.html

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>
wrote:

> 1. is this the whole motet? if not, you might want to
> say "excerpt" . . .

sorry, dude . . . now that i read the page, i see that you mention
that this is the first five measures . . . please excuse my insolence!

----- Original Message -----
From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
To: <tuning@yahoogroups.com>
Sent: Monday, December 02, 2002 1:43 PM
Subject: [tuning] Re: Lasso example in adaptive-JI

> --- In tuning@y..., "monz" <monz@a...> wrote:
>
> > i decided to use two illustrations, showing *both* deviation
> > from Pythagorean as well as deviation from 1/4-comma meantone.
> >
> >
> >
> > -monz
>
> cool, dude! now i have two comments:
>
> 1. is this the whole motet? if not, you might want to
> say "excerpt" . . .

i do mention on the page that it's "the first 5 measures".

it corresponds exactly to the first two examples from this
piece which Blackwood used in his book. there's one more
example of this piece in Blackwood, from the last 9 measures.
but i don't know how long the piece is, as he numbers the
measures in that illustration 1-9.

> 2. would it be possible to do this for _Ave Maria_ by Josquin des
> Pres? this is the piece that jonathan walker focuses on in his
> _defense of just intonation_, but the idea of *adaptive*, rather than
> strict, just intonation seems to have escaped walker's consideration.
>
>
http://boethius.music.ucsb.edu/mto/issues/mto.96.2.6/mto.96.2.6.walker.html

thanks for that link, paul. i was an active reader and subscriber
to MTO for several months just after that paper was published, and
while i never read it, i follow the subsequent discussion of it
with great interest, and even wrote a long response to Walker
which i never finished or submitted.

anyway, regarding the Josquin piece, here's the score:
http://www.sandtonchoir.com/Ave%20Maria%20SATB.pdf

do i need to do the whole piece, or will an excerpt suffice to
illustrate Walker's commentary?

-monz

--- In tuning@y..., "monz" <monz@a...> wrote:
>
> ----- Original Message -----
> From: "wallyesterpaulrus" <wallyesterpaulrus@y...>
> To: <tuning@y...>
> Sent: Monday, December 02, 2002 1:43 PM
> Subject: [tuning] Re: Lasso example in adaptive-JI
>
>
> > --- In tuning@y..., "monz" <monz@a...> wrote:
> >
> > > i decided to use two illustrations, showing *both* deviation
> > > from Pythagorean as well as deviation from 1/4-comma meantone.
> > >
> > >
> > >
> > > -monz
> >
> > cool, dude! now i have two comments:
> >
> > 1. is this the whole motet? if not, you might want to
> > say "excerpt" . . .
>
>
>
> i do mention on the page that it's "the first 5 measures".

yes, my bad -- i hope you caught my apology on this.

>
> it corresponds exactly to the first two examples from this
> piece which Blackwood used in his book. there's one more
> example of this piece in Blackwood, from the last 9 measures.
> but i don't know how long the piece is, as he numbers the
> measures in that illustration 1-9.

well, it might be cool to include those too . .

>
> thanks for that link, paul. i was an active reader and subscriber
> to MTO for several months just after that paper was published, and
> while i never read it, i follow the subsequent discussion of it
> with great interest, and even wrote a long response to Walker
> which i never finished or submitted.
>
>
> anyway, regarding the Josquin piece, here's the score:
> http://www.sandtonchoir.com/Ave%20Maria%20SATB.pdf

recall that the accidentals were not normally notated then, in the
age of "ficta" -- see walker's paper.

> do i need to do the whole piece, or will an excerpt suffice to
> illustrate Walker's commentary?

my suggestion would be to use only the excerpt that walker himself
proposes strict ji renditions for (with his own ficta
interpretation), so that the adaptive ji rendition will constitute a
direct "rebuttal" . . .

hi paul,

> From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
> To: <tuning@yahoogroups.com>
> Sent: Tuesday, December 03, 2002 12:57 PM
> Subject: [tuning] Re: Lasso example in adaptive-JI
>
>
> --- In tuning@y..., "monz" <monz@a...> wrote:
> >
> > ----- Original Message -----
> > From: "wallyesterpaulrus" <wallyesterpaulrus@y...>
> > To: <tuning@y...>
> > Sent: Monday, December 02, 2002 1:43 PM
> > Subject: [tuning] Re: Lasso example in adaptive-JI
> >
> >
> > > --- In tuning@y..., "monz" <monz@a...> wrote:
> > >
> >
> > i do mention on the page that it's "the first 5 measures".
>
> yes, my bad -- i hope you caught my apology on this.

yes, i did. i sent my response before reading your second
post about it.

> > it corresponds exactly to the first two examples from this
> > piece which Blackwood used in his book. there's one more
> > example of this piece in Blackwood, from the last 9 measures.
> > but i don't know how long the piece is, as he numbers the
> > measures in that illustration 1-9.
>
> well, it might be cool to include those too . .

actually, i'm a huge fan of Lasso's work, and would like to
track down the score to the whole piece and do it right.

> > thanks for that link, paul. i was an active reader and subscriber
> > to MTO for several months just after that paper was published, and
> > while i never read it, i follow the subsequent discussion of it
> > with great interest, and even wrote a long response to Walker
> > which i never finished or submitted.
> >
> >
> > anyway, regarding the Josquin piece, here's the score:
> > http://www.sandtonchoir.com/Ave%20Maria%20SATB.pdf
>
> recall that the accidentals were not normally notated then, in the
> age of "ficta" -- see walker's paper.

good point -- in fact, Blackwood also mentions this, and opts to
retain the editorial F# which i also used in my retuning.

> > do i need to do the whole piece, or will an excerpt suffice to
> > illustrate Walker's commentary?
>
> my suggestion would be to use only the excerpt that walker himself
> proposes strict ji renditions for (with his own ficta
> interpretation), so that the adaptive ji rendition will constitute a
> direct "rebuttal" . . .

OK, cool ... so you're talking about measures 44-53 of the Josquin.
will do, ASAP.

-monz

hi paul,

> ----- Original Message -----
> From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
> To: <tuning@yahoogroups.com>
> Sent: Monday, December 02, 2002 1:43 PM
> Subject: [tuning] Re: Lasso example in adaptive-JI
>
>
> > 2. would it be possible to do this for _Ave Maria_ by Josquin des
> > Pres? this is the piece that jonathan walker focuses on in his
> > _defense of just intonation_, but the idea of *adaptive*, rather than
> > strict, just intonation seems to have escaped walker's consideration.
> >
> >
>
http://boethius.music.ucsb.edu/mto/issues/mto.96.2.6/mto.96.2.6.walker.html

i took a look at Walker's article, and am not sure which
score of Josquin's piece to use as my basis.

Walker's three examples and the PDF score i found all use
different interpretations of the _musica ficta_, so i'm
not quite sure where to put flats or sharps, if any.
please advise.

-monz

--- In tuning@y..., "monz" <monz@a...> wrote:
> hi paul,
>
>
> > ----- Original Message -----
> > From: "wallyesterpaulrus" <wallyesterpaulrus@y...>
> > To: <tuning@y...>
> > Sent: Monday, December 02, 2002 1:43 PM
> > Subject: [tuning] Re: Lasso example in adaptive-JI
> >
> >
> > > 2. would it be possible to do this for _Ave Maria_ by Josquin
des
> > > Pres? this is the piece that jonathan walker focuses on in his
> > > _defense of just intonation_, but the idea of *adaptive*,
rather than
> > > strict, just intonation seems to have escaped walker's
consideration.
> > >
> > >
> >
>
http://boethius.music.ucsb.edu/mto/issues/mto.96.2.6/mto.96.2.6.walker
.html
>
>
>
> i took a look at Walker's article, and am not sure which
> score of Josquin's piece to use as my basis.
>
> Walker's three examples and the PDF score i found all use
> different interpretations of the _musica ficta_, so i'm
> not quite sure where to put flats or sharps, if any.
> please advise.

i looked at example 2 and example 3, and they appear to have exactly
the same pattern of sharps and flats. these would be the relevant
model.

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:

/tuning/topicId_41295.html#41295

> hello all,
>
>
>
> i've added a graphic and MIDI-file of the
> first 5 measures of Orlando di Lasso's motet
> _Ave regina coelorum_, tuned in Vicentino's
> adaptive-JI of 1555, to both of these pages:
>
>
> Tuning Dictionary "adaptive-JI" entry:
> http://sonic-arts.org/dict/adaptiveji.htm
>

***This is just great, Monz. Lassus is one of my very favorites...
It's great, too, to have such "multimedia" illustrations...

Joe Pehrson