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 musical 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 in the actual score of the 3rd Symphony 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 which represent an Eb M/m triad in 2nd inversion (cf. m.25): 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, with pitch set 1 occuring inverted on the dominant as C sharp-D in the antecedent phrase, the C natural appearing as an outlier 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, exemplifying the higher order systemic logic, musico-mathematical thinking, and lateral reasoning that drives Beethoven's creative process.
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 (g-f-e flat-d-c-b flat), 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, as a temporally expanded mosaic paraphrase of it:
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 intrinsic structural determinants 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!)
(Note the consistent presence of outliers, as in Theme I: C# - D ————C natural)
For further details, see EROICA DECODED: A Study in Beethovenian Logic through another look at the 1st movement, Opus 55 on this website.
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 as implied functions in the Dominant (BbM/m/gm, the m3 of B flat minor notated enharmonically as C#)
mm. 15-24 sequential bridge defines transpositions of pitch set 2 to Db C F, mm. 18-19, and Cb Bb Eb, mm.22-25.
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 via a temporally expanded mosaic paraphrase of the downscale G-F-E flat-D-C-B flat in mm. 55-57 and mm. 90-91
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 of transformational bridge and macrocosmic completion of pitch set 2 on Bb-A-D in m. 117, Eroica Decoded, ex. 35a &b)
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 (cf. d5th C# - G in Theme I)
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 (Db-B-C, Eb-C#-D, Cb-A-Bb) using pitch set 2 Cb-Bb-Eb to repeat back to m. 5 (digital root of Bach) from 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 an expansion of pitch set 1 on F/C: Ab-G-A natural, which is therefore omitted at the end of the transformational bridge on C. Its inversion G#-A-G natural (m.252-278) becomes the counterpoint for the synthesis of G parallel M/m in the climactic stretto (Bassline: d c B A# A G, A# for Bb notated enharmonically cognate to the c# in theme I - Eroica Decoded, ex. 32 c), which acts as a crucible/forge/prism to complete the transformation of the elements of the development theme (the 3rd subject) and its countersubject. 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 on Ab juxtaposed in reverse order which explains WHY there are differences in the recapitulation, as well as the need for the 140 measure extension (ex. 34 a&b, Eroica Decoded)
mm. 555-695 completion of elements of theme II on Ab (60 measures), recursive completion of elements of the transformational bridge in Bb (omitted in the working through of the piece, Eroica Decoded, ex. 35a & b) in m. 617 (6+1+7=14=Bach; remember the largest macrocosmic expression of pitch set 2 on the dominant Bb-A-D was 102 measures? 102 = 6x17!) 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! With the two measure introduction the entire movement has 842 measures: 8+4+2 = 14!
(The exposition has 155 measures. The repeat from the 1st ending back to m. 5 (digital root of BACH!)
means 8 measures are not included in the repeat: the 1st 4 measures and the 4 measures of the 1st ending. 155 - 8 = 147. The 1st movement has 695 mm. 695 + 147 = 842. Why 842 measures? 8+4+2= 14 AND (1+7) 1+7 and 42 i.e. 1742, the year the first edition of Bach's Kunst der Fuge was published, and internal evidence in the first movement of op. 55 has strong links to Contrapunctus 14, as shown in Eroica Decoded: A Study in Beethovenian Logic through another look at the First Movement of Opus 55, Appendix A/example 30 on this website, or see Exploding the Beethoven Mythology on this website.)
So many silly things have been written about Josquin's masterful frottola El Grillo. It serves as a perfect example why historical context is so important for accurately analyzing and understanding music of different time periods, not to mention an historically accurate translation!
Josquin’s EL GRILLO1: When is a cricket NOT a cricket?
A brief analysis
Macrocosm: a complex musical structure existing as a larger systemic entity consisting of smaller entities of similar structure (microcosms) contained within it.
Microcosm: a smaller musical structure existing as an entity of lesser duration within a larger similar musical structure (macrocosm).
Microcosm: First four triads: F – G – dm – C( first 2 and a half measures) Josquin’s strategic plan
Motivic Cell: dotted quarter – eighth- half (cf. mm. 2 to db. 3)
Modulatory functions:
D Major (cf. measure 4, 2nd beat), V/V
A Major (cf. mm. 31 – 35), V/ii
Concrete word painting: Longo Verso mm. 7 -8 – 9 outer voices are tied whole notes Abstract text painting: inner voices exchange motivic cell in canon mm. 7 - 8 - 9 to represent everlasting (canon=round=circle=no end)
Love should be long-lasting and eternal (like cricket’s song)
F Major (temporal expansion of F triad from m. 1) mm. 11 – 16
G Major/Mixolydian mm. 22 – 27 (starts on subdominant C, cf. F major m. 1)(temporal expansion of G triad, 1st beat m. 2)
d minor mm. 28 – 37 (starts on subdominant G, cf. m. 28)
(temporal expansion of dm triad, 2nd beat m. 2)
C Major mm. 6 - 10 (the piece begins on subdominant(IV-F); this is why the other sections begin with their respective subdominants) (temporal expansion of C triad, 1st beat m. 3)
Dalle flirt (this word came into English via Norman French; it is the root of the word dalliance and still survives and is cognate to the slang terms Don't dally and dilly-dally.
Beve drink
Canta sing
Text Painting: Pairs of voices alternate treble to bass to represent hopping
Word Painting: All voices in rapid eighth notes represent “singing” (i.e. chirping)
Love should be happy and joyful
Texture: mostly homophonic; exceptions are the canon mm. 6-10 and the climactic dm section mm. 28 – 37 (culminating on the word amore) which are polyphonic.
declamation: mostly syllabic, except for the polyphonic sections which are melismatic
Harmonic Structure: all triads are in root position. Yet another way Josquin represents the steadfastness of idealized love as exemplified by the cricket
Unlike the “other birds “(altri uccelli) 2 who have sung a little bit and then go off to somewhere else,
Love should NOT be flighty, fickle and unfaithful
the cricket remains “pur saldo” STEADFAST (cf. Florio’s Renaissance Italian Dictionary)
Love should be steadfast, faithful and true
La Maggiore the month of May, i.e. the month of courtship (Maypoles, etc.) When the (month of) May is warm, he only sings for Love
The path to true love never runs smoothly: use of minor tonality for affective quality that represents the sometimes bittersweet aspect of love, coupled with the use of polyphonic texture and melismatic declamation to represent the “bumpy” nature of love as the piece climaxes on the word “AMORE.” This is Josquin affirming that the piece is in fact about LOVE.
When is a cricket not a cricket?
When it is a Metaphor for true and everlasting LOVE, set to the most masterful music imaginable by one of the greatest composers of all time.
____________________________ 1 sometimes Josquin Des Prez’ authorship has been questioned because of an attribution to “Josquin d’Ascanio” despite the overwhelming presence of Josquin’s characteristic compositional details. In the Renaissance musicians were considered to be servants, and since Josquin spent a significant part of his creative life in the service of Ascanio Sforza, it is no wonder he was frequently referred to as “Ascanio’s Josquin.”
2 often deliberately mistranslated due to a lack of understanding that according to the Aristotelian classification of animals in use well into the 17th century, birds and crickets belonged in the same broad classification.
VUMP
noun
Useful term to describe great composers
origin: I made it up. Acronym consisting of the first letter of each of the attributes that distinguish the greatest composers: Visionary, Unique, Masterful, Prolific. It is genuinely useful when illustrating the differences between composers. Compare Telemann and Bach, Salieri and Mozart, Danzi and Beethoven for example. Telemann, Salieri and Danzi were all reasonably masterful and prolific, but none of their works exhibit visionary qualities and were certainly not unique; their works were the typical generic output of many composers of their respective eras, whereas Bach, Mozart, and Beethoven composed music of far-reaching influence that transcends historical, cultural, geographical, linguistic and generational barriers. In short, they are VUMPS, and the other three are not. This is why efforts to revive the music of lesser composers is often short-lived and doomed to failure. Telemann, for example, was even more prolific than his famous contemporary, J.S. Bach. Although Telemann composed nearly 5 times as many motets as Bach, it has been said that all of them put together do not equal even one of Bach’s, the important question being, WHY? Similarly, it has been said there is more music in a single Chopin Prelude than in “all the trumpetings of Myerbeer!” But what exactly does that mean, and if true, WHY? The answers to this are important because they are an antidote to superficial websites like Mozart or Salieri? that claims to be a “scientific” comparison between the music of these two composers, and draws the rather remarkable conclusion that Mozart’s greatness is a “superstition of our age!” This is exactly the type of nonsense that proliferates when singular works of high musical art are trivialized, poorly understood, incorrectly interpreted, and misrepresented, based upon superficial criteria.
Bach sollte nicht Bach sondern Meer heissen
(Side note: recursive used here in its linguistic /grammatical sense i.e ideas embedded within other ideas. Music is also a language in and of itself. To put it another way, by adding to Bach’s definition of music: Kunst, Wissenschaft und Sprache (Art, Science AND Language).
(Side note: This demonstrates why there are temporally expanded episodes in d minor and g minor in mm. 190 and 202 respectively. See below)
Pitch set 2 on V: B flat-A-D
B Flat m. 14 to A natural m. 65 51 measures
A natural m. 66 to D m. 117 51 measures
Macrocosmic expression of Pitch set 2 on V
2*51 = 102 = 6*17, 6+1+7= 14 (BACH)
Why 51 measures?: E R O I C A
5+18+15+9+3+1= 51
(See Below)
EVERYTHING in the entire movement is foreshadowed in the first 14 measures!
This is consistent with the first of Beethoven’s characteristic compositional details: Foreshadow EVERYTHING!
The three pitch sets that Beethoven uses to create the entire movement:
Gb-F-G, 2. Eb-D-G, 3. Bb-C-Ab
They appear both microcosmically and macrocosmically as structural and generative compositional determinants throughout the movement creating patterns within patterns, i.e. Fractals. In fact it can be convincingly shown that the entire movement demonstrates the processes of Fractal Geometry and Set Theory in sound. This is made all the more remarkable when it is understood that Set Theory, the study of mathematical logic concerning sets of objects, is not even defined in Mathematics until the 1870’s with the work of Georg Cantor in Germany and Kurt Godel in the early to mid 20th Century. Which leads to the next point: Beethoven never “Breaks the Rules.” The very places most often cited as examples of Beethoven’s “Rule Breaking” are the very places where he is most obsessively following them:
Example: the infamous French Horn entrance in M. 398 serves two purposes: 1. it is the microcosmic completion of Pitch set 2 on Cb -Bb-Eb, and 2. simultaneously creates the Bb7sus4 chord to Bb7 needed to end the macrocosmic expression of Theme II on C (the second member of pitch set 3) i.e. the underlying structure of the Development section. (see below)
Why multiples of 6? EROICA has 6 letters AND a digital root of 6.
(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: Op. 13, mm. 11-13
Transposed to V, paraphrased and embedded in mm. 1-4:
Note the inversion of pitch set 1 that appears in Mvt. 1 of the Eroica Symphony in mm. 65-70
Transpositions and permutations of the 3 pitch sets. Assigning the pitch set numbers isn't arbitrary: Pitch set 1 - G-flat/F/G natural represents the thirds of E-flat Major/minor; Pitch set 2 - E-flat/D/G represents the root of the E-flat triad; Pitch set 3 - B-flat/C/A-flat represents the fifth of the E-flat triad. This places them in the order from top to bottom as a second inversion E-flat triad (cf. m. 25). Second inversion triads are used extensively as a significant compositional detail in strategic positions throughout the movement.
Pitch set 2 on the dominant is B flat-A-D. It is macrocosmically expressed over time with B flat in m. 14, A in mm. 65-66 on the middle of the measures, and D in m. 117. The gematria of Eroica is 51: 14+51=65; 66+51=117. Mm. 14 to 117 is 102 measures (2x51). (5+18+15+9+3+1=51)
This demonstrates that Beethoven not only foreshadows what he is going to do, but also the process he will use to realize his artistic vision, i.e. how he will do it!
Process: separate into subsets, paraphrase emphasizing main pitches on middle of each measure with durational weight and transfers of register, recombine by merging the subsets back together. This foreshadows the merging together of parallel major/minor that occurs in the climactic stretto of the development to forge the countersubject of the development theme in m. 288, and the merging together of Theme I and Theme II at the beginning of the recapitulation:
E flat - F - D flat (Pitch set 3 Bb-C-Ab on Tonic).
Many analysts have tried to make a case for Theme II being the passage beginning at m. 45, not the actual Theme II beginning at m. 83, claiming that the passage at m. 83 is not developed or even appears in the development section - not only is m. 83 aka Theme II EVERYWHERE - it IS the development section and the recapitulation (see below)
The passage mm. 45-57 is a temporally expanded mosaic paraphrase of the downscale that foreshadows the descending downscale in the climax of theme II: IT IS NOT THEME II!
Pitch Set 1: G flat-F-G natural DOWN a M2
F flat(E natural) - E flat - F natural =Macrocosmic expression of Pitch set 1 using the development theme as another structural and generative compositional determinant in the overall form
(Note the consistent presence of outliers just as incorporated in Theme I:C#-D______________C, and Theme II: B-flat - C ____________A-flat, and at the end of the codetta, mm. 136-155, D-flat, E-flat with the third member of pitch set 3, C-flat, as an outlier in the 1st and 2nd endings. Ex. 13, pg.10, Eroica Decoded on this website)
Why 2 chord intro? 2+12 mm. of Th. I = 14(Bach!)
f#-g-f natural is the climax of Theme II
it is preceded by the downscale that follows it
i.e. reverse order in the foreshadowing
Why F# instead of Gb in the inversion? Voice leading: F# resolves upward to G, Gb resolves downward to F; Beethoven does NOT "break the rules!"
Th.II: Bb Cm F#-G-F BbM/m Ab7sus4 - Ab7
on C: C Dm G#-A-G CM/m Bb7sus4 - Bb7
The first C''' in m. 98 should be a Db'''; cf m. 505 in the recapitulation where it is Gb to F. See Beethoven Errata in the Journal of this website or consult Eroica Decoded, p.13,on this website
(The temporally expanded episodes on d minor and g minor which represent the macrocosmic completion of pitch set 2, E-flat-D-G, occur in mm. 190 and 202 respectively. 1+9+2+2 = 14. The Eb M/m in m. 25 to the end of the gm episode with the G Major triad on the downbeat of m. 210
comprises the macrocosmic expression of Pitch Set 2 on tonic; it is 185 measures: 1+8+5=14.
The stretto is mm. 236 - 287. It contains the final foreshadowing of the development theme through paraphrase in gm (Eroica Decoded, ex. 19) and is 51 measures long.
C Major m.170
dm m.190
(G# - A - G natural mm.252-278)
C Major/minor m.304
Bb7sus4 -Bb7 m.398
(side note: The exposition with the repeat has 302 measures 155+147=302; the rest of the movement has 540 measures. Bach permeates everything in this piece: 3+2+5+4=14! Beethoven was NOT “bad at math!”)
Patterns within Patterns:
Exposition Development Recapitulation
B flat C A Flat
Bridge (successive iterations)
Bb m. 45 C m. 170 Ab m. 224
Theme II (pitch set 3)
Bb Cm Ab
m. 14 foreshadowing pitch set 3)
Bb - C - Ab
Mozart employs an algorithmic (if-then) process to create mathematically perfect intervallic/musical relationships.
Algorithm for the creation of the antecedent phrase of the menuetto:
1. 1st 4 pitches: d-g-a-b
2. retrograde: b-a-g-d
3. transfer of register to cello
4. temporal expansion through placement on downbeats of 1st 4 measures - the "d" bassline m. 4 cognate to the anacrusis preceded by V/V foreshadowing the modulatory bridge in trio
Algorithm for the creation of the trio:
1. select main melodic pitches in antecedent phrase
2. transpose them to the dominant
3. place them on the downbeats of each of the 8 measures creating a musical period
4. paraphrase using permutations of the melodic sequences from contrasting phrase of the menuetto (derived from m. 4)
5. transpose the g-e-c# from m. 3 to the dominant d-b-g#
6. retrograde to g#-b-d
7. transfer of register to violin 1 w/diminution from quarter notes to eighth notes
8. interpolate between the repetitions of the single musical period
(Side note: Dalle existed as a cognate in Renaissance Italian, Spanish, and French.
Over time, it has evolved different meanings in the parent languages, and it is a linguistic irony that it has preserved something of its original meaning as a borrowing through English slang.)