Yahoo Tuning Groups Ultimate Backup tuning Ut re mi fa sol la in 2/7-comma meantone

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> I've put up a version of this here:
>
> http://66.98.148.43/~xenharmo/ratwolfmus.html
>
> Persons with more knowledge of music history than I possess are
> invited to either shoot down or support my suggestion that Bull
could
> have used a tuning like this.

An enjoyable sound! But (IIRC) several of the ficta in there are
different from those of the Fitzwilliam text (page 183ff in the
Dover, volume 1). What score/MS was used as source?

And, shouldn't we have a comma shift somewhere, either gradually or
suddenly at several places (downbeat at time index 1:37?, but that's
not where the score puts one)? This is analogous to crossing the
International Date Line; the extra day or comma has to be accounted
for somewhere.... Rather, it sounds to me as if in the MIDI source
the distinctions between enharmonics were all discarded first (input
in 12edo, perhaps?) and they haven't come back into the otherwise
marvelous sound of 2/7.

Methinks I'll go retune my virginal to be all sharps, and see what
effect I get with it. But even then, forcing the whole thing to stay
in sharps instead of flats, I still think we'll need a B# and an Fx
in the fifth go of the cantus firmus; C and G won't do. And on an
instrument that really has only 12 notes per octave, even at slippery
places like the 1:37 (maybe splicing together two recordings that
were
done in separate sets of notes...), there are still wolf major thirds
(diminished fourths) to be dealt with.

Do you know Alan Curtis' recording of 17th century Neapolitan
chromatic music, on the "Nuova Era" label? He did it on a 12-key
harpsichord but spliced together takes from different sessions tuned
differently to simulate the presence of split keys, for extended
regular 1/4 comma.

Brad Lehman

🔗Brad Lehman <bpl@umich.edu>

--- In tuning@yahoogroups.com, "Manuel Op de Coul" <manuel.op.de.
coul@e...> wrote:
>
> Gene on his webpage:
> >It would be easy to conclude that this piece, Ut re mi fa sol la,
> >must be intended for a well-temperament, since it visits the
> >complete circle of fifths,
>
> No circle of fifths. According to Lindley this fantasia is for
> 1/3-comma meantone with more than 12 tones/oct. So it requires a
> keyboard with split semitone keys.

The shtick of Bull's piece is to present "Ut re mi fa sol la", and
then its reverse "La sol fa mi re ut", in twelve different positions
rising by tones. G, A, B, Db, Eb, F; then {rift} Ab, Bb, C, D, E,
F#; then five more occurrences all starting on G playing around with
metric stuff instead of pitch.

The assertion of a keyboard with split keys doesn't ring true, to me,
for this piece. The first note of the Db iteration is notated
between an A and an E (vertically) and we've just finished with an E
major half cadence, such that the A-Db-E then sounds like its
resolution. But, which note is one to play if split keys are
available? If a Db to go with the upcoming stuff, it's a wolf in
this
A-Db-E triad; if a C# coming out of the "old" phrase, it's both
melodically unsatisfactory in the Db..Eb..F... cantus firmus and
harmonically unsatisfactory in Gb-Bb-Db-Gb immediately following the
A-Db-E triad.

Split keys, therefore, do not solve this particular problem.

The piece doesn't modulate all the way around the circle of fifths,
but it does use twelve different pitches as Ut, systematically.
There's a comma shift to deal with: either when we go from B to Db as
our "Ut", or (if we've lied and are really using C#, D#, E# there)
going from E# to Ab. The Pythagorean comma either has to be handled
stepwise somewhere in the piece, or we have to sprinkle little bits
of it around so there's not such a noticeable single step of it.
Furthermore, since melodically our cantus firmus starts on each of
twelve different notes and rises and descends diatonically, there's
simply nowhere to put a single complete Pythagorean comma step into
some tone or semitone without it being noticeable.

This has to be a case of temperament, not extra keys on the 'board to
deliver all or a subset of 19edo. Furthermore, it works very well on
a typically 17th century French/Italianate layout of modified
meantone where the sharps are pretty much "as is" (and/or slightly
raised, to taste, making them more exciting), and F-Bb-Eb are wide
fifths, leaving merely a wolf puppy at the normal Eb-G# position.
The
occurrences of Eb-G# (and their enharmonics) are disguised in weak or
passing parts of the beat, metrically, or hidden under the thickness
of other notes (minor chords are especially useful in this regard),
or touched and released quickly in small note values. Hide that
puppy! Such a modified-meantone layout is not the only available
solution, but it's an easily practical one.

One of Froberger's toccatas from 1649 either has to have a good
temperament or it needs split keys C#/Db, D#/Eb, and G#/Ab. And it's
clearly an organ piece by its liturgical function: for the elevation.

Brad Lehman

🔗monz <monz@tonalsoft.com>

--- In tuning@yahoogroups.com, "Brad Lehman" <bpl@u...> wrote:

> The shtick of Bull's piece is to present "Ut re mi fa sol la",
> and then its reverse "La sol fa mi re ut", in twelve different
> positions rising by tones. G, A, B, Db, Eb, F; then {rift} Ab,
> Bb, C, D, E, F#; then five more occurrences all starting on
> G playing around with metric stuff instead of pitch.
>
> The assertion of a keyboard with split keys doesn't ring true,
> to me, for this piece. The first note of the Db iteration is
> notated between an A and an E (vertically) and we've just
> finished with an E major half cadence, such that the A-Db-E
> then sounds like its resolution. But, which note is one to
> play if split keys are available? If a Db to go with the
> upcoming stuff, it's a wolf in this A-Db-E triad; if a C# coming
> out of the "old" phrase, it's both melodically unsatisfactory
> in the Db..Eb..F... cantus firmus and harmonically unsatisfactory
> in Gb-Bb-Db-Gb immediately following the A-Db-E triad.

if Bull notated a triad as A-Db-E and intended for it
to be a consonance, then it looks like he's using
schismic tuning: in pythagorean, a Db is very close
to a 5:4 C# (only a skhisma flatter).

if that's the case, then we shouldn't be talking about
meantone for this piece at all.

Lindley (in _Mathematical Models of Musical Scales_)
points out that keyboard pieces of the late 1400s were
doing this sort of thing, and he views it as evidence
of this "extended pythagorean" type of tuning -- i.e.,
use of an extended pythagorean chain where 3^-8
substitutes for 5^1 on the lattice.

-monz

🔗Gene Ward Smith <gwsmith@svpal.org>

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

> if Bull notated a triad as A-Db-E and intended for it
> to be a consonance, then it looks like he's using
> schismic tuning: in pythagorean, a Db is very close
> to a 5:4 C# (only a skhisma flatter).

Schismic isn't sometimes using a diminised fourth as a major third, it
is *always* using a diminished fourth as a major third; moreover it
only makes sense if the fifth is either untempered or tempered only to
a very slight degree--less than 12-equal, certainly.

Assuming Bull tuned his fifths regularly, what A-Db-E sounds like
depends on how his fifth is tuned. If he tuned to 2/7-comma, then
the diminished fourth is 433.52 cents, 1.57 cents flatter than 9/7,
and it is that interval which the ear is presumably going to
assimilate this to.

> if that's the case, then we shouldn't be talking about
> meantone for this piece at all.

I think it is absurd to suggest otherwise.

> Lindley (in _Mathematical Models of Musical Scales_)
> points out that keyboard pieces of the late 1400s were
> doing this sort of thing, and he views it as evidence
> of this "extended pythagorean" type of tuning -- i.e.,
> use of an extended pythagorean chain where 3^-8
> substitutes for 5^1 on the lattice.

Doc Bull is hardly writing keyboard pieces of the late 1400s.

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> > I've put up a version of this here:
> >
> > http://66.98.148.43/~xenharmo/ratwolfmus.html
> >
> > Persons with more knowledge of music history than
> > I possess are invited to either shoot down or support
> > my suggestion that Bull could have used a tuning like this.
>
>
> your version sounds fantastic to me!
>
> was this piece written for keyboard?

He may have scored a version for viols, but this is my mutation of a
harpsichord/celesta version (where I turned the celesta into a flute.)
Obviously, that wasn't what Bull orginally wrote either, and I wanted
to make the harmony clearly defined, with sustained tones.

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "Brad Lehman" <bpl@u...> wrote:
> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> > I've put up a version of this here:
> >
> > http://66.98.148.43/~xenharmo/ratwolfmus.html
> >
> > Persons with more knowledge of music history than I possess are
> > invited to either shoot down or support my suggestion that Bull
> could
> > have used a tuning like this.
>
> An enjoyable sound! But (IIRC) several of the ficta in there are
> different from those of the Fitzwilliam text (page 183ff in the
> Dover, volume 1). What score/MS was used as source?

With some difficulty I managed to find a midi file, one which
obviously is not too authentic in that it includes a part for celesta.
This wasn't actually something I found available somewhere for
download, but background music for viewing paintings.

> And, shouldn't we have a comma shift somewhere, either gradually or
> suddenly at several places (downbeat at time index 1:37?, but that's
> not where the score puts one)? This is analogous to crossing the
> International Date Line; the extra day or comma has to be accounted
> for somewhere.... Rather, it sounds to me as if in the MIDI source
> the distinctions between enharmonics were all discarded first (input
> in 12edo, perhaps?) and they haven't come back into the otherwise
> marvelous sound of 2/7.

The midi, as with most midis, was in 12 equal, and was notated simply
as integers. However if Bull wrote for a harpsichord with twelve keys
to the octave this can't matter, and if he didn't I'd like to know
about it.

> Methinks I'll go retune my virginal to be all sharps, and see what
> effect I get with it.

You might try it out with a circle of 2/7-comma fifths starting from
Eb and see what that seems to fit.

But even then, forcing the whole thing to stay
> in sharps instead of flats, I still think we'll need a B# and an Fx
> in the fifth go of the cantus firmus; C and G won't do. And on an
> instrument that really has only 12 notes per octave, even at slippery
> places like the 1:37 (maybe splicing together two recordings that
> were
> done in separate sets of notes...), there are still wolf major thirds
> (diminished fourths) to be dealt with.

Yes, but there are different ways to deal with these babies. 2/7 comma
makes the diminished fourth quite near to 9/7, and the wolf fifth even
nearer to 20/13, and it is possible this made a difference to how
people composed and played if they tuned to 2/7 comma. What if Bull
used 2/7 comma, and thought the wolves weren't really so bad? Do we
know anything which makes that unlikely or impossible?

> Do you know Alan Curtis' recording of 17th century Neapolitan
> chromatic music, on the "Nuova Era" label? He did it on a 12-key
> harpsichord but spliced together takes from different sessions tuned
> differently to simulate the presence of split keys, for extended
> regular 1/4 comma.

No, I've heard a lot of 1/4 comma but not extended 1/4 comma. I'll
check it out, thanks.

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "Brad Lehman" <bpl@u...> wrote:

> The piece doesn't modulate all the way around the circle of fifths,
> but it does use twelve different pitches as Ut, systematically.
> There's a comma shift to deal with: either when we go from B to Db as
> our "Ut", or (if we've lied and are really using C#, D#, E# there)
> going from E# to Ab. The Pythagorean comma either has to be handled
> stepwise somewhere in the piece, or we have to sprinkle little bits
> of it around so there's not such a noticeable single step of it.
> Furthermore, since melodically our cantus firmus starts on each of
> twelve different notes and rises and descends diatonically, there's
> simply nowhere to put a single complete Pythagorean comma step into
> some tone or semitone without it being noticeable.

The Pythagorean comma is a quartertone downwards in 2/7 comma, and
that is large enough to seem like a reasonable stepwise progression.
Hide in plain sight, perhaps. Incidentally, making the Pythagorean
comma *exactly* 50 cents down leads to a fifth of 695 and 5/6 cents,
and that makes the wolf almost a pure 20/13, 0.047 cents sharp.

🔗Brad Lehman <bpl@umich.edu>

> The midi, as with most midis, was in 12 equal, and was notated
simply
> as integers. However if Bull wrote for a harpsichord with twelve
keys
> to the octave this can't matter, and if he didn't I'd like to know
> about it.

I think that to hear this piece fairly in *any* regular variety, one
must go back to the notation and see what he put as sharps and what
as flats. There is an enharmonic shift in at least the places I
described.

Page 183ff in here:
http://store.yahoo.com/doverpublications/0486210685.html
...but see also the Musica Britannica edition of Bull.

>
> > Methinks I'll go retune my virginal to be all sharps, and see
what
> > effect I get with it.
>
> You might try it out with a circle of 2/7-comma fifths starting from
> Eb and see what that seems to fit.

Good idea. This discussion also puts me in the mood to try some of
the half-puppy layouts where one tunes all the naturals in some
regular scheme (might be 1/4 SC, might be Pythagorean, might be
something else...), and then sticks all five accidentals into mean
positions relative to other things. Been about 15 years since I
thought about it, but it would probably be something like this: C#/Db
midway in A-F; D#/Eb midway in B-G; G#/Ab midway in E-C; D-F#-Bb-D
400c each.

Of course, within each group of four one must parcel out the lesser
diesis (two syntonic commas less a schisma). So, if we start off
with pure F-A, G-B, and C-E, each of their tempered-accidental
bisectors (two averaged major thirds splitting the minor sixth) is
going to be half a schisma shy of a syntonic comma too sharp (i.e.
very slightly narrower than Pythagorean). That's quite a hot C#, Eb,
and G#. Even more so if you've started with major thirds that are
smaller than pure.

Brad Lehman

🔗Manuel Op de Coul <manuel.op.de.coul@eon-benelux.com>

Gene wrote:

> > No circle of fifths. According to Lindley this fantasia is for
> > 1/3-comma meantone with more than 12 tones/oct. So it requires a
> > keyboard with split semitone keys.
>
> Does Lindley document this view, or is he speculating?

I didn't remember it quite correctly. I looked it up and he said it
was most probably conceived for arcicembalo. So that means about
1/4-comma meantone and not 1/3. It's in "Temperaments", New Grove.
If you can find the score, it will be interesting to render a
version in Vicentino's tuning.

Manuel

🔗ideaofgod <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "Manuel Op de Coul"
<manuel.op.de.coul@e...> wrote:

> I didn't remember it quite correctly. I looked it up and he said it
> was most probably conceived for arcicembalo. So that means about
> 1/4-comma meantone and not 1/3. It's in "Temperaments", New Grove.
> If you can find the score, it will be interesting to render a
> version in Vicentino's tuning.

Do we know if Bull played the archicembalo? When would he have had a
chance to do so?

An extended meantone version, making use of the notations of Bull's
score, would indeed be interesting.

🔗Joseph Pehrson <jpehrson@rcn.com>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:

/tuning/topicId_55770.html#55770

> I've put up a version of this here:
>
> http://66.98.148.43/~xenharmo/ratwolfmus.html
>
> Persons with more knowledge of music history than I possess are
> invited to either shoot down or support my suggestion that Bull
could
> have used a tuning like this.

***Although this may be a lot of Bull, I agree that "Ratwolf" here
paints a pretty and intriguing pixture... (Especially with the "new"
Gene Ward Smith musical-sound ability...)

J. Pehrson

🔗wauchopek <WAUCHOPE@AIC.NRL.NAVY.MIL>

> --- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> /tuning/topicId_55770.html#55770
>
> > I've put up a version of this here:
> >
> > http://66.98.148.43/~xenharmo/ratwolfmus.html
> >
> > Persons with more knowledge of music history than I possess are
> > invited to either shoot down or support my suggestion that Bull
> could
> > have used a tuning like this.

I feel a bit like the boy who claimed the emperor has no clothes, but
I don't hear any meantone characteristics at all in this Ogg
rendition. It sounds exactly like 12-equal to me. Gene, are you sure
it got microtuned correctly? (If I'm the one who turns out to be
nekkid, I'll own up.) For comparison, I've put some MIDI harpsichord
versions in 2/7-comma MT, Werkmeister and Kirnberger in the tuning
group's Files section under Pucehawk/bull.zip.

--Ken W.

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "wauchopek" <WAUCHOPE@A...> wrote:

> I feel a bit like the boy who claimed the emperor has no clothes, but
> I don't hear any meantone characteristics at all in this Ogg
> rendition. It sounds exactly like 12-equal to me. Gene, are you sure
> it got microtuned correctly?

I was worried it didn't sound right too, actually, but I checked the
midi file and the changes were in it. However, maybe I'd better check
again.

(If I'm the one who turns out to be
> nekkid, I'll own up.) For comparison, I've put some MIDI harpsichord
> versions in 2/7-comma MT, Werkmeister and Kirnberger in the tuning
> group's Files section under Pucehawk/bull.zip.

I can't find it.

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
> --- In tuning@yahoogroups.com, "wauchopek" <WAUCHOPE@A...> wrote:

> > I feel a bit like the boy who claimed the emperor has no clothes, but
> > I don't hear any meantone characteristics at all in this Ogg
> > rendition. It sounds exactly like 12-equal to me. Gene, are you sure
> > it got microtuned correctly?
>
> I was worried it didn't sound right too, actually, but I checked the
> midi file and the changes were in it. However, maybe I'd better check
> again.

It occurs to me that what I checked may not be what I uploaded, so I
uploaded a correct version to make sure I got it right.

The full story of why I got worried it sounded wrong and had to check
is interesting and informative, and I think Manuel in particular might
be interested. I ran the Bull piece through the nytonyx stylizer,
which perversly added midi controller 1 (modulation) commands to the
midi file. Midi controller 1 in a file seems to prevent Scala from
retuning, and I think it would be a good idea for Scala to remove
these controller values and proceed anyway.

Howbeit, there they were. I had the same reaction--I listened, and
something seemed to be wrong; so I checked and I wasn't getting any
tuning data in the midi files from my Scala commands. If I had a text
editor which could remove any line which had a given expression on it,
I could have used that, but I don't know of one. What I did was edited
controller 1 to something which I hoped didn't do anything. I ended up
using controller 81, which seems to work, but I tried controller 70
first, and that also seemed to be a problem. The result was I had a
lot of versions lying around, some of which were, in fact, in 12
equal, since Scala didn't put in any tuning data when I asked it to.

This time I uploaded a pitch bend version of the ogg file (I can't
tell any difference between the pitch bend and the MTS versions, so
this shouldn't matter) and the pitch bended midi file which was
rendered. That midi file I put in

http://66.98.148.43/~xenharmo/scores/bullzar.mid

The new ogg file is in the same place as before

http://66.98.148.43/~xenharmo/ogg/ratwolf/bullzar.ogg

The supermajor triads should be heard without difficulty in a correct
version.

🔗wauchopek <WAUCHOPE@AIC.NRL.NAVY.MIL>

🔗Brad Lehman <bpl@umich.edu>

> This time I uploaded a pitch bend version of the ogg file (I can't
> tell any difference between the pitch bend and the MTS versions, so
> this shouldn't matter) and the pitch bended midi file which was
> rendered. That midi file I put in
>
> http://66.98.148.43/~xenharmo/scores/bullzar.mid
>
> The new ogg file is in the same place as before
>
> http://66.98.148.43/~xenharmo/ogg/ratwolf/bullzar.ogg
>
> The supermajor triads should be heard without difficulty in a
correct
> version.

There we go! Now your version is sounding a LOT more like I expected
it would, from my session of playing it on a real virginal in 2/7
comma. Your timbre choice is still hiding some things (it sounds
even
harsher in the virginal/harpsichord's plucked strings than it does
here)...due to the way the near-4/3 clash is being dodged. But, this
is much more like it already.

Why is there that little dynamic bulge at the end of the piece? :)

Brad Lehman

🔗Gene Ward Smith <gwsmith@svpal.org>

--- In tuning@yahoogroups.com, "Brad Lehman" <bpl@u...> wrote:

> There we go! Now your version is sounding a LOT more like I expected
> it would, from my session of playing it on a real virginal in 2/7
> comma. Your timbre choice is still hiding some things (it sounds
> even
> harsher in the virginal/harpsichord's plucked strings than it does
> here)...due to the way the near-4/3 clash is being dodged. But, this
> is much more like it already.

It's clear I must have uploaded a 12-equal version; sorry about that.

> Why is there that little dynamic bulge at the end of the piece? :)

This whole tale of woe started when I ran a preliminary midi file
through nytonyx; I haven't used it much but this seemed like a good
time. Nytonyx, which I think tends to go a bit overboard, added that.

Anyway, we are still left with the question of why these flattish
meantone systems seemed to have been favored at one time. Either
people must have been avoiding the extreme keys and sticking to the
diatonic region, or they must have found the harmonies acceptable for
some purposes.