Some perspectives on specific musical compositions that reflect a belief that there is a profound, demonstrable and quantifiable difference in the music of the universally acknowledged greatest composers. Analyses often focus on what makes music the same: harmonic analysis, generic stereotyped analyses of form, graphic representations that in the end all look similar because they essentially ignore and downplay the details that distinguish singular works of high art, and highly subjective programmatic scenarios that often reflect the biases and preconceived ideas of the analysts rather than the true intent of the composer. The genius is in the details!
Evidence exists that Bach, not Napoleon was Beethoven's true hero (carwn ddiolch i Drefor Van de Velde am y darlun ardderchog hwn)
The 1st movement of Beethoven's 3rd symphony is an algorithmic structurally and generatively recursive system based on multiples of 6, the gematrias of the words EROICA (51) and BACH (14) and transpositions and permutations of three pitch sets: G flat-F-G natural(pitch set 1), E flat-D-G(pitch set 2), and B flat-C-A flat (pitch set 3). All 3 pitch sets are present in the first 14 measures of the piece. Pitch sets 2 & 3 are unaltered, and pitch set 1 occurs inverted on the dominant as C sharp-D in the antecedent phrase, the C natural appearing recursively in the consequent phrase ( G flat-F-G natural inverted to F sharp-G-F natural, cf. bassline mm. 65-70, transposed to V: C sharp-D-C natural). The above table details Beethoven's use of pitch sets 2 and 3 in the structure of the exposition and provides the answer to why the development contains temporally expanded episodes in d minor (mm. 190 - 201) and g minor (beginning in m. 202). The realization of theme I above shows the multi-dimensional overlays of musical ideas that account for everything in the entire movement.
The passage from measures 45-57, claimed by some analysts to be "theme II" is actually a transformational passage in which the pitches from the 3rd beat of m. 12 through m. 13 (c-b flat-a flat-g-f-e flat) are transposed to the dominant, separated into subsets, given durational weight as dotted quarter notes, and ultimately rhythmically metamorphosed into the climax of theme II through diminution in measure 89-90. The importance of the middle beats of measures in the unfolding of the movement is also emphasized as well:
That this musical idea appears in the first movement of the 9th Symphony attests to the fact that Beethoven was fully cognizant of what he did in this passage of the 3rd symphony by restating and temporally compressing it in the 9th:
Macrocosmic expression of the 3 pitch sets used as an intrinsic structural determinant in the overall form, with pitch sets 2 and 3 used as they were foreshadowed in theme I, the mutable pitch set 1 transposed to the subdominant as F flat-E flat-F natural (its inversion, E natural-F-E flat, explains the WHY for the use of e minor for the development theme in m. 288). But of course, Beethoven doesn't think like this (no composer does!)
For further details, see EROICA DECODED: A Study in Beethovenian Logic through another look at the 1st movement, Opus 55 at Academia.edu.
The first movement of the Eroica Symphony at a glance:
mm. 1-14 Two tonic triads and Theme I containing tight temporal compression of parallel M/m/relative minor in the Dominant (BbM/m/gm)
mm. 15-24 sequential bridge defines transpositions of pitch set 2 to Db and Cb
mm. 25 - 44 temporal expansion and juxtapositioning of ideas on V in Theme I to Tonic Eb (EbM/m in m. 25, EbM/cm in mm. 37-42
mm. 45 - 64 transitional bridge transforms and presents elements of Theme II
mm. 65 - 70 inversion of pitch set 1 F#-G-F natural in the bass with inversion of Pitch set 3 down a m2 A-G-B as its counterpoint on middle of measures
mm. 71 - 82 modulatory bridge continues foreshadowing elements of Theme II in reverse order
mm. 83 - 94 Theme II (pitch set 3 Bb-C-Ab) incorporating BbM/m in m. 91
mm. 95 - 108 pitch set 2 Db-C-F and connecting bridge to codetta
mm. 109 - 117 codetta theme (reverse order of pitch pairs from transformational bridge and macrocosmic completion of pitch set 2 on Bb-A-D in m. 117
mm. 118 - 122 sequential canon @ the 5th incorporating retrograde of pitch set 3 on D-F#-E
mm. 123 - 131 retrograde inversions of pitch set 3 C-Ab-Bb treble/ F#-D-E bass on middle of measures create d5ths as the outer intervals
mm. 133-135 pitch set 1 distilled to its essence in the bass
mm. 136-155 retrograde of pitch set 1 on each member of pitch set 3 transposed to Db, using pitch set 2 Cb-Bb-Eb to repeat back to m. 5 in the 1st ending
mm. 156-401 development section: temporal expansion of Theme II on C, the second member of pitch set 3 (Bb-C-Ab) beginning with a prolongation of pitch set 1 on C: Ab-G-A natural, which is therefore omitted at the end of the transformational bridge on C. Its inversion G#-A-G natural becomes the counterpoint for the synthesis of G parallel M/m in the climactic stretto. The development ends predictably with a Bb7sus4 to Bb7 thus validating that Theme II on C is its underlying structural plan.
mm. 402-555 recapitulation opens with statements of the arpeggio of theme I stated on each member of pitch set 3 on tonic: Eb-F-Db and proceeds incorporating the elements of theme II as it would occur in Ab juxtaposed in reverse order which explains WHY there are differences in the recapitulation, as well as the need for the 140 measure extension
mm. 555-695 completion of elements of theme II in Ab (60 measures), recursive completion of elements of the transformational bridge in Bb (omitted in the working through of the piece) in m. 617 (6+1+7=14=Bach) as part of the interpolated 20 measure passage between the first 60 measures and the 60 measure TAG CODA which begins in m. 635 (6+3+5=14=Bach). WHY a 20 measure interpolation? Two reasons: first, the entire extension must equal 140 measures, i.e. one sixth of the 840 measures (less the two chord intro)of the piece, and second it is the final validation that it is Bach who equals Beethoven's heroic ideal. 14(Bach) and 51(Eroica) add up to 20: 14+(5+1)= 20!
(side note: this isn't the first time Beethoven foreshadows a main thematic element on the dominant. He does this in the introduction of op. 13 as well):
Theme I transposed to V
Theme I on V paraphrased and embedded mm. 1-4
