Mozart K516 enharmonics

The progression in question is in the 3rd movement, bars 63-65.

The first violin and viola hold the notes Gb and An continuously over
the whole progression. This is what it makes it impossible to write
the chords as normal aug 6, dim 7, minor or dominant 7th chords.

From my pocket score, we start in the tonality of Cb major. Then here
are the chords:

Bn An An Eb Gb

B# D# An Eb Gb

C# () An Db Gb

Dn Cn An Cn Gb

Eb F# An Bn Gb

C# () An Db Gb

Cn Dn An Dn Gb

Cb () An Eb Gb -> Cb Ger 6

and from then on we are in a standard aug 6 progression in E flat
major. Clearly this cannot be interpreted literally within meantone.

If we then try to rejig enharmonics to respect the E flat minor
tonality with aug 4th degree we get

Cb An An Eb Gb -> Cb Ger 6

Cn Eb An Eb Gb -> An dim 7

Db () An Db Gb -> * Gb 'wolf minor' chord with An not Bbb

Dn Cn An Cn Gb -> * D 'wolf dominant 7' chord with Gb not F#

Eb Gb An Cb Gb -> Cb Ger 6

Dn Cn An Cn Gb -> * D 'wolf dominant 7'

Db () An Db Gb -> * Gb 'wolf minor'

Cn Dn An Dn Gb -> * D 'wolf dominant 7'

Cb () An Eb Gb -> Cb Ger 7

So, it seems that in this passage, unless the viola and violin
actually change pitch back and forth during their sustained notes,
Mozart does use the wolf enharmonically 'wrong' intervals for
expressive effect.

~~~T~~~

In a message dated 4/26/2005 6:41:58 AM Eastern Standard Time, tdent@auth.gr
writes:
So, it seems that in this passage, unless the viola and violin
actually change pitch back and forth during their sustained notes,
Mozart does use the wolf enharmonically 'wrong' intervals for
expressive effect.
Ah, yes. C.P.E. Bach speaks some where in his book about a drone moving on
an enharmonic note...and back. This was done, although it doesn't guarantee
that Mozart had this mind. Johnny

--- In tuning@yahoogroups.com, "Tom Dent" <tdent@a...> wrote:
>
>
> The progression in question is in the 3rd movement, bars 63-65.
>
> The first violin and viola hold the notes Gb and An continuously over
> the whole progression. This is what it makes it impossible to write
> the chords as normal aug 6, dim 7, minor or dominant 7th chords.
>
> From my pocket score, we start in the tonality of Cb major. Then here
> are the chords:
>
> Bn An An Eb Gb
>
> B# D# An Eb Gb
>
> C# () An Db Gb
>
> Dn Cn An Cn Gb
>
> Eb F# An Bn Gb
>
> C# () An Db Gb
>
> Cn Dn An Dn Gb
>
> Cb () An Eb Gb -> Cb Ger 6
>
> and from then on we are in a standard aug 6 progression in E flat
> major. Clearly this cannot be interpreted literally within meantone.

It's hard to believe this is really supposed to be played as scored,
however. You are in the key of Cb; hence, the first chord of
B A A Eb Gb is already hard to believe; it would seem it ought to be
Cb A A Eb Gb, solidly planted in the tonic. These are 18th century
string players; they aren't actually going to play the Cb root a
diesis higher as a B, fighting off the rest of the chord and the key
as well. They are not the Kronos Quartet plus a violist. If you assume
we start out with a Cb, not a B, which almost seems required, then
passing from there to B# makes even less sense. The second chord not
only has the indigestible B#, it has a D# fighting with an Eb. Again,
the Kronos would not be playing this, so it is hard to see that this
could really be anything other than C-Eb-A-Eb-Gb. It looks like
replacing all the anomalous sharps with flats in the rest of it sorts
it all out nicely: we don't want a C# and a Db in the same chord, nor
an F# with a Gb.

Why is this a problem?

> If we then try to rejig enharmonics to respect the E flat minor
> tonality with aug 4th degree we get
>
> Cb An An Eb Gb -> Cb Ger 6
>
> Cn Eb An Eb Gb -> An dim 7
>
> Db () An Db Gb -> * Gb 'wolf minor' chord with An not Bbb

This is not a "wolf" anything chord. This is a perfectly nice and
acceptable chord as it is written, since the augmented second in
meantone from Gb to A is not a "discordance" or whatever we are
calling it today in meantone, but a nice, pleasing interval which
makes a nice sounding chord.

> Dn Cn An Cn Gb -> * D 'wolf dominant 7' chord with Gb not F#

Again, this is NOT a wolf! A wolf is the fifth you get with a
diminished sixth in place of a perfect fifth. This chord is
one I'm quite familiar with and have often used; it is the meantone
approximation to a 1-9/7-3/2-9/5 chord, which in meantone translates
to D-Gb-A-C. It works even better with a flatter fifth that 1/6 comma,
but these are string players and if they have the ears to hear it,
they can find this chord. It has a distinctive sound and it would be
interesting to know other examples in the 18th century literature
where it appears to be used.

> Eb Gb An Cb Gb -> Cb Ger 6
>
> Dn Cn An Cn Gb -> * D 'wolf dominant 7'
>
> Db () An Db Gb -> * Gb 'wolf minor'
>
> Cn Dn An Dn Gb -> * D 'wolf dominant 7'
>
> Cb () An Eb Gb -> Cb Ger 7
>
> So, it seems that in this passage, unless the viola and violin
> actually change pitch back and forth during their sustained notes,
> Mozart does use the wolf enharmonically 'wrong' intervals for
> expressive effect.

I think you could use this passage as evidence that Mozart sometimes
uses septimal chords aside from the German sixth. Once you get rid of
the clearly anomalous sharps and replace them with the flats
appropriate to the key of Cb, there is no problem with the tuning and
no problem with the harmony, unless being interesting and intelligent
is a problem. This is a very illuminating example; thanks for this,
Tom. It suggests to me that the septimal resources of meantone, which
Mozart was writing in when he wrote string music, were being explored
pretty fully in the 18th century. Again, by not using meantone as a
tuning basis I think we've destroyed the music and any hope of
understanding what it actually is doing.

hi Gene and Tom,

--- In tuning@yahoogroups.com, "Gene Ward Smith" <gwsmith@s...> wrote:
>
> --- In tuning@yahoogroups.com, "Tom Dent" <tdent@a...> wrote:
> >
> >
> > The progression in question is in the 3rd movement, bars 63-65.
> >
> > <snip>
>
> It's hard to believe this is really supposed to be played
> as scored, however.

i appreciate the effort that both of you have put into
analyzing this. however, knowing that Mozart himself taught
his students that musical intervals should be tuned
according to 55-edo / 1/6-comma meantone, i think it's
important to recognize and preserve his own notation of
pitches in his compositions.

if he taught his students that there is a comma difference
between D# and Eb, and he put them both into a chord
played by unfretted strings, then i can only assume that
he *wanted* that comma to be part of the chord.

in fact, i can see that Mozart was probably guided by
melodic movement in this passage:

the 2nd violin has: Eb - Db - C - B - C - Db - D - Eb

the cello has, in between the F# - A:
B - B# - C# - D - Eb - D - C# - C - Cb

i made a version of it in 55-edo in my Musica software,
using exactly the pitches notated by Mozart, and it sounds
fine -- in fact, quite like what a real string quintet
might play.

(unfortunately, i can't share it yet with anyone except
our small handful of Alpha testers. hopefully soon we'll
be able to export Musica .piece files as MIDI files, then
i can post them here.)

-monz

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

> i appreciate the effort that both of you have put into
> analyzing this. however, knowing that Mozart himself taught
> his students that musical intervals should be tuned
> according to 55-edo / 1/6-comma meantone, i think it's
> important to recognize and preserve his own notation of
> pitches in his compositions.

In 55 meantone, the diesis is just a comma, and hence you have chords
with a comma's worth of difference in them. I don't think string
players would actually *play* such chords, and I think Mozart knew
that, so I don't think this is a very viable theory.

> if he taught his students that there is a comma difference
> between D# and Eb, and he put them both into a chord
> played by unfretted strings, then i can only assume that
> he *wanted* that comma to be part of the chord.

Good luck in the 18th century if Mozart was trying to be a
microtonalist, but it hardly seems likely.

> i made a version of it in 55-edo in my Musica software,
> using exactly the pitches notated by Mozart, and it sounds
> fine -- in fact, quite like what a real string quintet
> might play.

A midi version, and then a comparison version, also in 55, with the B
lowered to Cb and the sharps to flats would be nice.

In a message dated 4/26/2005 4:16:59 PM Eastern Standard Time,
gwsmith@svpal.org writes:
Good luck in the 18th century if Mozart was trying to be a
microtonalist, but it hardly seems likely.
Why not? Frederick The Great had Quantz make him many beautiful flutes and
the latter examples have a different key for the Eb than used for the D#. This
difference is specifically to distinguish a music reality that Quantz
describes in great detail in his book on Playing The Flute.

I've read a Mozart letter where Wolfgang is remarking that a soprano he just
heard was intentionally singing a full comma above the orchestra. He
suggested this may be why she pulls in the big money.

all best, Johnny Reinhard

--- In tuning@yahoogroups.com, Afmmjr@a... wrote:

> In a message dated 4/26/2005 4:16:59 PM Eastern Standard Time,
> gwsmith@s... writes:
> Good luck in the 18th century if Mozart was trying to be a
> microtonalist, but it hardly seems likely.

> Why not? Frederick The Great had Quantz make him many beautiful
flutes and
> the latter examples have a different key for the Eb than used for
the D#. This
> difference is specifically to distinguish a music reality that Quantz
> describes in great detail in his book on Playing The Flute.

It's a pretty big leap to assume Fredrick the great wanted these
flutes so he could play D# while someone else was playing Eb.

> I've read a Mozart letter where Wolfgang is remarking that a soprano
he just
> heard was intentionally singing a full comma above the orchestra. He
> suggested this may be why she pulls in the big money.

That's pretty funny, and it sounds to me that Mozart is being ironic.

In a message dated 4/26/2005 5:03:14 PM Eastern Standard Time,
gwsmith@svpal.org writes:
That's pretty funny, and it sounds to me that Mozart is being ironic.
Yes, he was ironic. But only after seriously establishing that the soprano
was indeed singing a comma high.

Solo violinists have commonly played sharp to their accompanying orchestras.
Once they latch on to a pitch level above the concerting musicians, I'll bet
they keep their distance (figuratively etc.)

As for a bass drone tone riding up in pitch because its notation has changed:
I've had this experience many times. I remember it in Gershwin's Rhapsondy
in Blue. Are there any other orchestral experiences that bespeak remarks to be
made concerning the playing of drones?

all best, Johnny

Back on April 23, Tom Dent started an interesting
discussion about Mozart's use of simultaneous
enharmonically equivalent pairs of notes, in the
slow movement of his String Quintet K.516:

/tuning/topicId_58168.html#58174

Gene Ward Smith followed up with some comments on this:

/tuning/topicId_58168.html#58175

A few days later Tom wrote a post describing the section
in question in detail, expressing the probability that
"... Mozart does use the wolf enharmonically 'wrong'
intervals for expressive effect."

/tuning/topicId_58260.html#58260

Gene replied in agreement with Tom that Mozart probably
intended a meantone, because this passage has augmented-6th
chords, which in a meantone tuning gives a strong 7-limit JI
effect ... however, he assumed that the enharmonically
equivalent pairs of notes would be "normalized" into
the single note which best fit the chord.

/tuning/topicId_58260.html#58271

Then i made a version of that excerpt using Tonalsoft Tonescape,
tuned in a subset of 55-edo, and posted a comment here
that, in my opinion, the clashing enharmonics (a "comma"
apart) in 55-edo sounded fine ... in fact, quite like
what a real string quartet might sound like.

/tuning/topicId_58260.html#58276

The latest version of Tonescape (still pre-release, in
alpha test phase) now allows the user to export Tonescape
files to MIDI files. The disadvantage of using MIDI instead
of Tonescape is that you lose all the Pitch-Height and
Lattice data, but the advantage gained is that now any
piece composed with Tonescape can be shared with anyone
in cyberspace with a simple MIDI file.

So, i've uploaded the MIDI file of my 55-edo version of
the Mozart excerpt to the Files section of the
tuning_files group:

mozart_quintet_k516_55-edo.mid

or delete the line-break from this link:

/tuning/files/monz/mozart_q
uintet_k516_55-edo.mid

-monz

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
> Back on April 23, Tom Dent started an interesting
> discussion about Mozart's use of simultaneous
> enharmonically equivalent pairs of notes, in the
> slow movement of his String Quintet K.516:
>
> /tuning/topicId_58168.html#58174
>
> Gene Ward Smith followed up with some comments on this:
>
> /tuning/topicId_58168.html#58175
>
>
> A few days later Tom wrote a post describing the section
> in question in detail, expressing the probability that
> "... Mozart does use the wolf enharmonically 'wrong'
> intervals for expressive effect."
>
> /tuning/topicId_58260.html#58260
>
>
> Gene replied in agreement with Tom that Mozart probably
> intended a meantone, because this passage has augmented-6th
> chords, which in a meantone tuning gives a strong 7-limit JI
> effect ... however, he assumed that the enharmonically
> equivalent pairs of notes would be "normalized" into
> the single note which best fit the chord.
>
> /tuning/topicId_58260.html#58271
>
> (...)
>
> So, i've uploaded the MIDI file of my 55-edo version of
> the Mozart excerpt to the Files section of the
> tuning_files group:
>
> mozart_quintet_k516_55-edo.mid
>
> or delete the line-break from this link:
>
/tuning/files/monz/mozart_q
> uintet_k516_55-edo.mid
>
> -monz

By strange coincidence I thought just now 'wonder what they're up to
at "tuning"'. After having more or less disappeared for weeks.

Anyway, that Mozart ought to be good. BUT... I have to join another
group to get the file?

Oh well,

~~~T~~~

Alas, what I hear is a string quintet with a deaf cellist - K516
never sounded like that in performances I heard.

We'd have to go back to the real Urtext to reach any definite
conclusion on the C-flat/B-natural problem. Perhaps Mozart just
thought the players would find naturally whatever pitch sounded most
consonant.

Now the other place was K515 (3/4 of way through first movement)
where there is a complete harmonic cycle in the flat direction, but
Mozart makes an enharmonic shift just before it, when there is only
one instrument playing, so it doesn't create any real clashes.

~~~T~~~

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
(...)
>
> Then i made a version of that excerpt using Tonalsoft Tonescape,
> tuned in a subset of 55-edo, and posted a comment here
> that, in my opinion, the clashing enharmonics (a "comma"
> apart) in 55-edo sounded fine ... in fact, quite like
> what a real string quartet might sound like.
>
> /tuning/topicId_58260.html#58276
>
> The latest version of Tonescape (still pre-release, in
> alpha test phase) now allows the user to export Tonescape
> files to MIDI files. The disadvantage of using MIDI instead
> of Tonescape is that you lose all the Pitch-Height and
> Lattice data, but the advantage gained is that now any
> piece composed with Tonescape can be shared with anyone
> in cyberspace with a simple MIDI file.
>
> So, i've uploaded the MIDI file of my 55-edo version of
> the Mozart excerpt to the Files section of the
> tuning_files group:
>
> mozart_quintet_k516_55-edo.mid
>
> -monz

Ditto.

-Carl

--- In tuning@yahoogroups.com, "Tom Dent" <tdent@a...> wrote:
> Alas, what I hear is a string quintet with a deaf cellist - K516
> never sounded like that in performances I heard.
//
> ~~~T~~~
>
> --- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
> (...)
> >
> > Then i made a version of that excerpt using Tonalsoft Tonescape,
> > tuned in a subset of 55-edo, and posted a comment here
> > that, in my opinion, the clashing enharmonics (a "comma"
> > apart) in 55-edo sounded fine ... in fact, quite like
> > what a real string quartet might sound like.
> >
> > /tuning/topicId_58260.html#58276
> >
> > The latest version of Tonescape (still pre-release, in
> > alpha test phase) now allows the user to export Tonescape
> > files to MIDI files. The disadvantage of using MIDI instead
> > of Tonescape is that you lose all the Pitch-Height and
> > Lattice data, but the advantage gained is that now any
> > piece composed with Tonescape can be shared with anyone
> > in cyberspace with a simple MIDI file.
> >
> > So, i've uploaded the MIDI file of my 55-edo version of
> > the Mozart excerpt to the Files section of the
> > tuning_files group:
> >
> > mozart_quintet_k516_55-edo.mid
> >
> > -monz