Dead caviar

If you want to see what messing about with the tuning of Shostakovich
can lead to, follow the link below. If you have the patience to
download and listen to an actual symphony, you can do that.
Otherwise, the second movement is short.
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http://66.246.86.148/~xenharmo/asbrumus.html

i wrote:

/tuning/topicId_44573.html#44784

> From: "monz" <monz@a...>
> Date: Tue Jun 17, 2003 5:54 pm
> Subject: Re: [tuning] Re: Mozart 31-equal??
>
>
> <snip>
>
> ... right now i'm busy tracking down a copy of
> the Attwood studies to see what W.A. Mozart himself
> wrote about intonation.

and now i've gotten it, and can share what i found.
(thank the gods for interlibrary loan!)

basically there's nothing new that i didn't already
glean from Chesnut's article, and which i've already
included on my 55edo webpage:

http://sonic-arts.org/monzo/55edo/55edo.htm

The largest set of pitches actually written in
Mozart's handwriting is a 21-tone meantone chain
of 5ths Ebb ... A#, but without Cb :

Ebb Bbb Fb [Cb] Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A#

Attwood apparently understood Italian better than German,
because Mozart wrote in Italian for his benefit. It is
clearly stated several times in both of their handwritings
that the 8ve contains 5 tones and 2 large semitones.

The notes begin with ascending and descending (one 8ve)
C-major and A-melodic-minor scales, in Mozart's handwriting,
with notes explaining where the semitones occur.

then (p I/1 and I/2) Mozart wrote the first note of several
other major scales and their relative minors, and Attwood
filled in all the other notes correctly, except for the
leading-tone of G#-minor, which he wrote as F# ascending
(corrected by Mozart to Fx) and F-natural descending
(corrected by Mozart to F#). the list of major scales
is, in Mozart's order, C F Bb Eb Ab Db Gb B E A.
the relative minors are thus A D G C F Bb Eb G# C# F#.

the 21-note meantone chain of 5ths which contains all
the notes included in these scales is thus:

Cb Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A# E# B# Fx

page I/4, entirely in Mozart's handwriting except for
one sentence by Attwood, is a list of large and small
semitones and then a table of intervals arranged in
8ve-complementary pairs (and continued on page I/5).
Mozart's list of semitones is:

large semitones: C-Db, C#-D, D-Eb, D#-E, E-F, F-Gb, F#-G
small semitones: C-C#, Db-D, D-D#, Eb-E, E-E#, F-F#, Gb-G

(the complete text is quoted below)

page I/10 contains Attwood's attempt at making a table
of all the meantone intervals from a reference pitch of A#,
and it is remarkable for the number of errors in what is
otherwise a rather well-done set of studies -- i have marked
them all and indicated the corrections, which Mozart didn't
even bother to do. Mozart instead preferred to write a
new table of intervals on the next page, again using a
reference pitch of C, as on pages I/4-5, giving Attwood only
one of each pair of 8ve-complementary intervals and having
Attwood write the complement.

Attwood finally got all of information for semitone
sizes correct on page I/25, and the interval sizes on
pages I/26 and I/27, none of which i have included
as they simply recap what Mozart wrote. however, he
does note that in the cases of Ebb, Fb, and Bbb,
"these tones the Harpsichord has not, but all other
Instruments have ---".

the numerous other pages of the book contain harmony
and counterpoint exercises.

now, it is true that the relative sizes of the two
different semitones it is not stated anywhere in this book.
however, we know that Mozart's father Leopold taught
that the flats were a comma higher than the sharps,
which indicates 55edo or another meantone similar to it.

------- begin pages quoted from Attwood's notes ----------

* I/1, p. 3 *

Nella scala maggiore il 1mo mezzo tuono �
dalla terza alla quarta. ed il 2do dalla 7ma all' octava.

il lmo dall' octava all 7ma ed il 2do dalla
quarta alla terza.

* I/4, p. 6 * [see I/10, p. 10]

[in Attwood's hand:] A tone ought to have a little tone & half a great one

[Attwood mangled this: he meant to say "A tone ought to have
one little half-tone and one great one".]

[all music examples on this page and the next in Mozart's hand:]

Mezzi tuoni grandi
C-Db, C#-D, D-Eb, D#-E, E-F, F-Gb, F#-G

mezzi tuoni piccoli.
C-c#, Db-D, D-D#, Eb-E, E-E#, F-F#, Gb-G

unisono C-C

mezzo tuono piccolo.
unisono superfluo C-C#
8tava diminiuta C#-C

mezzo tuono grande.
seconda minore C-Db
7ma maggiore Db-C

un tuono.
seconda maggiore C-D
7ma minore D-C

1 tuono ed un mezzo tuono piccolo.
seconda superflua C-D#
7ma diminuta D#-C

1 tuono, ed un mezzo tuono gr.
terza min: C-Eb
6ta mag: Eb-C

2 tuoni
terza mag: C-E
6ta min: E-C

1 tuono, e 2 mezzi tuoni gr:
quarta diminuta C-Fb
5ta superflua Fb-C

2 tuoni, ed un semitonio gr:
quarta minore C-F
5ta reale F-C

3 tuoni
quarta mag: C-F#
5ta falsa: F#-C

2 tuoni, e 2 mezzi tuoni gr:
quinta falsa C-Gb
4ta mag: Gb-C

3 tuoni, ed un semit: gr:
quinta vera o 5ta reale C-G
4ta minore G-C

3 tuoni, un semit: gr. ed uno pic:
quinta superflua C-G#
4ta diminuta: G#-C

* I/5, p. 7 *

...

3 tuoni, e 2 semit: gr:
sesta minore C-Ab
terza mag: Ab-C

4 tuoni, ed un semit: gr:
sesta mag: C-A
terza min: A-C

4 tuoni, un semit: gr: ed uno pic:
sesta superflua C-A#
terza diminuta: A#-C

4 tuoni, e 2 semit: gr:
septima min: C-Bb
2da mag: Bb-C

5 tuoni, ed un semit: gr:
septima mag: C-B
2da min: B-C

5 tuoni, e 2 semit: grandi
8tava C-C (high)
unisono: C-C

[in Attwood's hand:] An Octave must have 5 tones & two Great half tones.

* I/6, p. 8 *

C C#,Db D D#,Eb E E#,F F#,Gb G G#,Ab A A#,Bb B B# c

[meantone chain: Gb Db Ab Eb Bb F C G D A E B F# C# G# D# A# E# B#]

* I/10, P. 10 * [see I/4, p. 6]

[entire page in Attwood's hand, and filled with errors:]

Unis: Mez. t Gr
A#-B, B-C, B#-C#, C#-D, Cx-D#, D#-E, Dx-E#, E#-F#, Ex-Fx, Fx-G#

Mez. t p:
A#-Ax, B-B#, C-C#, C#-Cx, D-D#, D#-Dx, E-E#, E#-Ex, F#-Fx, G-G#

[meantone chain: C G D [A] E B F# C# G# D# A# E# B# Fx Cx [Gx] Dx Ax Ex]

Antonio Sdadler [?}

Unis A#-A#
8tava A#(low)-A#

mez t pic.
unis sup: A#-Ax
8ta diminuta Ax-A#

mez Gr:
2do Minore A#-B
7ma Mag: Bb-A# [incorrect: should be B-A#]

1 t.
2da Mag: A#-B#
7ma min. B-A# [incorrect: should be B#-A#]

1 t e un mez p:
2 sup: A#-Bx
7ma dim: B#-A# [incorrect: should be Bx-A#]

2 mag gr
3za dimi: A#-C [Cbb crossed out]
6ta Super Cbb-A# [incorrect: should be C-A#]

1 t e mag gr
3za Minore A#-C#
6ta Mag. Cb-A# [incorrect: should be C#-A#]

2 t p:
3 Mag: A#-Cx
6ta Min C-A# [incorrect: should be Cx-A#]

1 t: e dui mez. gr:
4ta dimi A#-D [Dbb crossed out]
5ta Super Dbb-A# [incorrect: should be D-A#]

2 t e mez Gr
4 Minore A#-D# [Db crossed out]
5ta Mag Db-A# [incorrect: should be D#-A#]

why can't the fourth have a Superflua [Attwood's marginal note]

3 t:
4ta Mag: A#-D [natural sign crossed out] [incorrect: should be A#-Dx]
5 Mag. D-A# [incorrect: should be Dx-A#]

2 t e 2 mez Gr
5ta falsa A#-Ebb [incorrect: should be A#-E]
4 Mag Ebb-A# [incorrect: should be E-A#]

3 t e mez Gr
5ta vera A#-Eb [incorrect: should be A#-E#]
4 Minore Eb-A# [incorrect: should be E#-A#]

3 t e mag Gr e mez p:
5ta Super A#-E [incorrect: should be A#-Ex]
4ta dimi E-A# [incorrect: should be Ex-A#]

3 t e 2 mag Gr
6ta minore A#-Fb [incorrect: should be A#-F#]
3za Mag: Fb-A# [incorrect: should be F#-A#]

4 t e mez Gr
6ta Mag. A#-F [incorrect: should be A#-Fx]
3za Minore F-A# [incorrect: should be Fx-A#]

4 t e 2 Gr mag p: [incorrect: should be 4 t e mez Gr: e mez p:]
6ta Super A#-F# [incorrect: should be A#-FX#]
3za dimi F#-A# [incorrect: should be Fx#-A#]

4 t e mez Gr: [incorrect: should be 3 t e 3 mez Gr:]
7ma dim: A#-Gbb [incorrect: should be A#-G]
2 Super Gbb-A# [incorrect: should be G-A#]

4 t e dui Mez Gr.
7 minore A#-Gb [incorrect: should be A#-G#]
2 Mag Gb-A# [incorrect: should be G#-A#]

5ta e mez Gr
7ma Mag. A#-G [incorrect: should be A#-Gx]
2 Super G-A# [incorrect: should be Gx-A#]

5ta e 2 mez Gr
8tava A#-G# [incorrect: should be A#-A#(high)]
unis. G#-A# [incorrect: should be A#-A#]

[meantone chain for Attwood's incorrect notes:
Cbb Gbb Dbb [Abb] Ebb [Bbb] Fb Cb Gb Db [Ab] Eb Bb F C G D [A] E B F# C# G#
D# A# [E#] B# [Fx] Cx [Gx] [Dx] Ax [Ex] Bx - clearly incorrect, no
corrections given by Mozart -- Mozart wrote out a new example on next page.]

[the correct meantone chain for the intervals given by Attwood from A# is:
C G D [A] E B F# C# G# D# A# E# B# Fx Cx Gx Dx Ax Ex Bx Fx#]

* I/11, p. 11 *

[all top intervals in Mozart's hand, all bottom intervals in Attwood's:]

unis: C-C [Mozart]
otava C(low)-C [Attwood, etc.]

unis: superfl: C-C#
8tava diminuta C#-C

2da min: C-Db
7 mag: Db-C

2da mag: C-D
7ma minore D-C

2da sup: C-D#
7ma diminuta D#-C

3: dim: C-Ebb
6ta super: Ebb-C

3: min: C-Eb
6ta mag: Eb-C

3 mag: C-E
6ta minore E-C

4: dim: C-Fb
5ta super: Fb-C

4ta min: C-F
5ta vera F-C

4: mag: C-F#
5ta falsa F#-C

5: falsa C-Gb
4 mag: Gb-C

5: vera C-G
4 minore G-C

5: sup: C-G#
4 diminuta G#-C

6: min: C-Ab
3za mag: Ab-C

6: mag: C-A
3 minore A-C

6: sup: C-A#
3za dim: A#-C

7ma dim: C-Bbb
2da super Bbb-C

7: min: C-Bb
2 Mag: Bb-C

7: mag: C-B
2 minore B-C

Octava C-C (high)
unis C-C

[i.e., thus this is the same as I/4-5, except that it also adds
diminished-3rd/superfluous-6th and diminished-7th/superfluous-2nd pairs.]

[meantone chain: Ebb Bbb Fb [Cb] Gb Db Ab Eb Bb F C G D A E B F# C# G# D#
A#]

[on I/26,p.28 and I/27,p.29, Attwood rewrites exactly this same
diagram, with English names for the intervals.]

----- end pages quoted from Attwood's notes --------

REFERENCE
---------

Heartz, Daniel; Mann, Alfred; Oldman, Cecil B.; Hertzmann, Erich. 1965.
_Thomas Attwoods Theorie- und Kompositionsstudien bei Mozart_.
Wolfgang Amadeus Mozart: Neue Ausgabe s�mtlicher Werke,
Ser. X, Werkgruppe 30, Bd. 1.
Kassel.

-monz