Yahoo Tuning Groups Ultimate Backup tuning harmonic analysis of Mahler's 9th/4, m. 49-56

Here's part of something I sent to the Mahler-List that
makes a point about tuning at the end, so I thought some
folks here might be interested:

--------------

On Wed, 27 Oct 1999 21:29:00 -0700 Nolan Stolz <nolanstolz@HOTMAIL.COM>
writes:

> Ive read several books on Mahler, even a book just on his sixth
> symphony, but I haven't found any roman numeral analyzations of
> his work. Ive seen plenty of excerpts of Mozart or Schubert
> symphonies with little N6s, and V7s, viio/iis, and such written
> everywhere---this is what I need....
>
> I'm to write a 10 page paper(with a 20 minute class presentation)
> for theory class, my topic of choice: Mahler's Adagios..... his
> harmonic movement is just incredible. Well to analyze hundreds
> of bars, which only a few I will discuss, is quite a project.
> Where can I find someone else's work to use as bibliography and
> such?

Hmmm... interesting point you make about the dearth of
'Roman-numeral' (which would be called _Stufen_ in German
theory) analysis of Mahler's harmony. Mahler himself
said that his music was basically diatonic, which would
indicate the value of this type of analytical approach.

Part of the reason is that his work cannot always be analyzed
in this manner in such a straightforward way, because of
his pervasive use of chromaticism and mediant-relationships.
<snip...>

I've also done a 'Roman-numeral' analysis of m. 49-56 of the
last movement of the 9th - it's only 8 bars (one variation),
but since you're working on adagios specifically, you way
want it. (Just quote this posting with the date and time
in your bibliography if you use it).

Preface on the notation:

- The Arabic numerals should be superscript, and indicate
movement in upper voices - in other words, '6 5' means a
major 6th or 13th moving to the perfect 5th; the notes
represented by the Arabic numerals are tuned according to
the key indicated by the Roman numeral: for instance, '7'
with 'V' means a minor-7th, but '7' with 'IV' means a
major-7th; plus and minus signs indicate sharpening or
flattening (respectively) according to these rules.

- Parentheses are used to help clarify the intonation
of certain intervals where confusion may be a result
of chromatic alteration of the root of the chord. A
chord is considered to be a major, minor, or dominant
type depending on its Roman numeral in the key of Db-major.
Thus, I and IV are normally major, V is normally a
dominant-7th, and II, III, and VI are normally minor.

- Commas separate simultaneous events - these numerals should
really be written one over the other: so '6,5' means the first inversion;
the successions of Arabic numerals from left to
right indicate the moving voices from top to bottom.

- A slash after the Roman numeral indicates inversion of a chord

- Ellipsis [...] indicates a tie (as from 3rd beat to 4th beat
of m. 49. in the lead voice, which at this point is second
from the top.)

Key: Db major

m.
49:
I 3 4
V 6 5, 9 8 +7 8
bVI +4 +3...
III 7, ...+5 5, +3

50:
IV 5..., +4 3 +2 3
V 7 6 5, ...4 3 2 3, 7
IV/6,4 6 5 4, 4 3 2
I 8 7 6

51:
V -3
II/6 7 6 +5 6
#I 9 8 7 6, 8 9 8 7 8

52:
VI 6 5
III/6 +5 6, 4 3 +2 3
bIII +3
V 6 +5 5 +5

53:
I 4 3...
V/4,3 4 3, ...9 8, 7 6 5 6
bVI/4,3 7 6 5 6, 3, 6
bIII +10 (+)9 8 7, 7, +3, 1 (+)2 [i.e., V of bVI]

54:
IV +5 5 (+)4 5, 8 -9 8 (+)7 8
II/6 +2 +3 +2 2 +2, -9 [+1 bass] OR bVI/2 +5, 2 3 2 +1 2, 6

55:
V 13, 7
VI 8 7
II 11, 9 8 7 5
V 7 5 2 3

56:
I
etc.

The third beat of m. 54 is most interesting. This chord
utilizes the kind of tritone-substitution common in jazz
from bebop and later: it can be analyzed as an inverted
dominant-7th with sharp 11th with a root of either A (= Bbb)
or Eb. The progression to the Ab dominant-7th is thus
either by semitone (from A) or by dominant relationship
(from Eb); in either case, a strong step in the cadential
formula according to jazz theory. The rest of the cadence
couldn't be more conventional, from either a jazz or romantic
standpoint: an evaded cadence from V to VI, then a
series of dominants VI - II - V - I, without any chromatically
altered chord-tones, that is, respecting the harmonies
resulting from a strict observance of the key-signature.

After sliding into the key of Bbb-minor momentarily in m. 53,
as in every statement of the theme or one of its variations,
the following Gb chord can be explained as both a submediant
to Bbb and a subdominant to Db, which sounds to me like a
tendency to move back into the tonic Db. But the chord after
that (the one with the tritone double-meaning) has a tritone
interval within it, thus totally confusing the listener's
expectations as to where the harmony is going. Analyzed
as an Eb -9 +11, it is a sort of altered II in Db, but
the notes in the 'turnaround' melodic figure imply an
interpretation with a root of Bbb much more strongly than Eb.

Interestingly, this Bbb chord can thus be interpreted as a
dominant-7th-type chord on A, which is V in the key of D,
the key of the opening movement of the symphony. Mahler
is generally supposed in this movement to be expressing
resignation in the sliding-down of the tonic of the symphony
from D in the first movement to Db in the last. Perhaps
the hint of A-minor (i.e., Bbb-minor) in m. 53, and of
a dominant of D in m. 54, is a sort of struggle to regain
D-major as a tonic, which is unsuccessful as the harmony
goes firmly back into Db-major at m. 55.

Perhaps the most interesting thing of all about this chord
is that it lacks the important note Db, which would be
simultaneously both the major 3rd of Bbb and the 7th of Eb
(chord tones which are *necessary* for either of the harmonic
interpretations I've given), as well as the general tonic
of the entire passage and movement.

But immediately at the first beat of m. 55, this listener
feels right back home in Db again. This amazing artistry
is the result of Mahler's voice-leading, where the intervals
of the different melodic lines clash vertically but make
total sense horizontally.

This foreshadowing of jazz harmonic usage in Mahler is
something that can also be seen in Schoenberg's theories
as presented in his _Harmonielehre_ of 1911. To a great
extent, it depends on acceptance of the 12-tone equal-
tempered scale as the basic intonational resource, which
I find unusual for Mahler, as his self-stated grounding in
diatonic harmony would imply a form of meantone tuning
in his conception of harmony. This is one of the reasons
why I find his 9th Symphony to be a kind of new territory
for him.

BTW, m. 55 is almost a quotation of m. 337 of the first
movement of the 7th.

-monz

Joseph L. Monzo Philadelphia monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
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harmonic analysis of Mahler's 9th/4, m. 49-56

🔗Joe Monzo <monz@xxxx.xxxx>