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    Challenge 1:  The phrase is too simple to be a trademark of Mozart's music.



     The "trademark" aspect is not in the phrase itself, but rather what Mozart did with it.


While the basic phrase itself is fairly simple, what Mozart did with it is amazing

and unique. The sheer quantity and quality of its usage is surprising, as well as the

numerous ways in which he wove it into his music. To use a metaphor, Mozart

created "a forest of trees, all similar but slightly different, and all interesting".


Mozart seemed almost obsessed with it, re-shaping it in countless ways. He turned

a simple, 2-chord phrase into a study of musical creativity over the entire span of

his composing career - almost 30 years.


Additionally, there's the matter of the evidence.

The evidence says "it's almost everywhere". Disputing evidence seems like a pointless

thing to do. In this paper I've listed only a fraction of the "trademark phrase" occurrences.


But the challenge is often in finding the phrase. It's often "buried" in the music, and

it takes some detective work to find it.


It's likely that phrases which are difficult to locate exist because he was simply

continuing to create new versions of expressing the same thought, and the simpler

expressions had already been used.


And if he was using that phrase as a musical signature, he HAD to use it wherever possible.


With this phrase, the Devil is in the details. From a "complexity" standpoint, finding all the

phrases and documenting them would not only be difficult, it would be overwhelming.

But 18 citations, plus sound clips from 2 early pieces, and 7 general references in the FAQ

and elsewhere, is not a bad start.


Challenge 2:  There are very few notes in the trademark phrase.


The trademark phrase contains only 6 notes as 2 chords or phrases. The 6 notes represent

a reduction in the number of notes from the original music to the minimum necessary to

identify the phrase.



Challenge 3:  There are too few notes in the phrase to make it unique.


But it's not a unique phrase.

The uniqueness lies in the frequency, method, and variations used by Mozart,

(compared with other composers), not in the phrase itself.



Challenge 4:  There are sometimes intervening flourishes in the examples.


This is usually "Delayed Resolution" and is permitted.



Challenge 5:  This particular trademark phrase uses different chord names than you've listed.


The names of the chords are irrelevant to this "trademark phrase" concept since it deals

only with chord relationships.

Readers are free to use any chord names they wish.



Challenge 6:   Music is not numbers  (This pertains to the numeric definition, only).


But musical elements can be described with numbers.

A MIDI file is almost all numbers, yet it converts these numbers into audible and

listenable music - complete with "pedal events" for the piano, to "concert hall echo".

Numbers are used everywhere in music - from the meter (3/8, 4/4, etc) to scale definitions

(12-tone system, etc) to chord definitions (perfect 5th, dominant 7th, etc) to note pitches in

cycles per second (more numbers). If numbers can also describe note relationships, then there

is no rational case to be made using against them where useful and practical. Saying that "music

is not numbers" is like saying "medicine is not numbers", then proceeding to discuss a patient's

blood pressure numbers, his cholesterol numbers, his white cell count, etc. Medicine may not be

numbers, but numbers play an essential role in describing the patient's health.


Use of the numeric definition is optional since the trademark phrase is well-described by

using musical terms. The numeric definition may have applicability in computer analysis.



      Challenge 7:  The phrase is very common in the non-Mozartian musical literature.


     I'm talking about evidence that a single composer used the phrase to the degree that

     Mozart did, and with similar sophistication.

     In this paper, I provided 18 citations and 17 sound clips of the trademark phrase

     as used by Mozart. Let's see your evidence.

     Cite the piece, the movement, the measure, and the notes, and provide 20 examples

     from a single composer. Be sure the phrase is not simply expressed as 2 chords

     in all your examples, but with some creativity and nuance.


     Only a FEW other examples of its usage have  been  found to date:

     There is occasional usage by JS Bach, Gasparini, Mozart's composition students/assistants,

     a Chopin piano concerto (which doesn’t fully qualify), and certainly others.

     Mozart's composition students and assistants were probably copying their teacher,

     so counting such examples would be questionable. In any event, count them or not,

     none of them went on to become "great" composers with musical output performed

     regularly at concerts, and contributing to the popular, classical-music literature.


If some other composer used the phrase as often as Mozart did and in the way Mozart did,

complete with variations,  then so be it: It would qualify as that composer's musical

trademark, and we would have 2 composers who adopted that phrase: Mozart and

another composer.


Challenge 1 - Beethoven's 5th Symphony:


"In Beethoven's 5th Symphony in C minor, first movement, at measures 20 and 21,

an augmented 6th is followed by a major chord (G major). Both chords comply

with the requirements of the Trademark Phrase in terms of their note relationships,

 if you ignore some of the extra notes.

Therefore, this is an example of another composer using that phrase - right?".

(This is just prior to the repeat of the theme).


Response: It's not a valid example.


Analysis of Challenge 1:


 mm 20, 21

       Chord 0           Chord 1                  Chord 2           

    C--C--G--C--Eb    C--Eb--Ab--C--Gb--C  --->  G--D--B--G  


    --- = problem notes     --- = trademark notes


       Repeat of theme...

   (--> Ab-->Ab-->Ab-->lower F)




                          Click to hear sound clip



This challenge is close, but there are 2 problems:


1.  Wrong lowest notes.

There is a problem with the lowest notes in Chord 1 - the C-Eb.

Beethoven's use of a lower C and Eb emphasizes that we are not dealing with a

foundational Ab-C-Gb musical idea which would form the first chord of the

Trademark phrase. The lower C-Eb pair acts as a stress reliever on the chord and

disqualifies it.


If the lowest note had been an Ab (forming the bottom note of the augmented 6th),

the first chord would have qualified, as in:   Ab--C--Eb--Ab--C--Gb--C  before compression.


However, the 2nd chord would not have qualified. The upper C (the leading voice)

doesn't lead to a lower B in the 2nd chord, with the possibility of note interpolation,

as explained below.


2.  Wrong melody.

Consider the leading voice, shown below in green.


            Chord 0                                Chord 1                                       Chord 2           

  C--C--G--C--Eb    C--Eb--Ab--C--Gb--C  --->  G--D--B--G  



                         Click to hear sound clip



We have Eb, lower C, higher G.


Here the C has to jump up a 5th from Chord 1 to Chord 2, to continue as a G in the leading voice:

         C --->  G

(In a trademark phrase, the Gb in the first chord would normally be the leading voice - not the C).


Of course, in an "interpolation" situation, the C would be valid as the top note if the 2nd

chord contained a lower B as the top note. The following example would be a valid trademark

phrase, if Beethoven had written it this way:


            Chord 0                         Chord 1                                  Chord 2           

  C--C--G--C--Eb    Ab-----Gb--C  --->  G--D-----G--B   Beet5c.mid  before interpolation

  C--C--G--C--Eb    Ab-[C]-Gb     --->  G----[B]-G      Beet5d.mid  after  interpolation


This effectively puts the pairs of thirds Gb-C and G-B as the leading voices.

Interpolation validates the phrase and changes the leading voice to Gb--->G -

a note change up one step.


Valid leading voices in Chords 1 and 2 would have been either:

1.    Gb --->  G  (up   one step)    or

2.    C  --->  B  (down one step)   


But Beethoven didn't write it that way. His leading voice is  C ---> G (up one fifth), and there is no underlying

melody which progresses up one step from "Gb to G", or down one step from "(Gb)-C to (G)-B", to make it

a valid trademark phrase. It just doesn't qualify as a trademark phrase despite the augmented 6th and major chord.




What about the Mozart example A6 (K.594): The lowest note is correct (Db), but the leading voice in the

right hand jumps up a 5th from F to C (mm 5.3 to 6.1)? Doesn't it do the same thing as Beethoven's 5th

does with the leading voice?

Shouldn't the melody progress up by one step from B to C to be a trademark phrase?


The answer is Yes: It should, and it does progress up from B to C, but not as the leading voice.

This is because there are 2 additional melodies in that section of K.594 which progress from B to C:

    1. The secondary B-->C melody at mm 5.1 to 6.2 in the left hand - part of the trademark phrase.

    2. The tertiary melody in the pedals from mm 5.1 to 6.2 which includes B-->C.



               Example A6 (K.594)

        ------------>F---->C---->C     leading voice (highest melody), right hand

        B----->B---->B---->B---->C     left hand melody

        Db---->F---->B---->C---->C     pedal melody              

        5.1     5.2    5.3     6.1    6.2




The pedal melody also creates a 2nd layer of the trademark first chord in its first 3 notes.

In other words, the melody from 5.1 to 5.3 is the same as the notes of the first chord (Db-F-B),

followed by the top note of the 2nd chord (C) at 6.1.



        Db---->F---->B---->C---->C      pedal melody

        Db---->F---->B---->C---->C      pedal melody    

        5.1     5.2    5.3     6.1    6.2



        Click to hear sound clip of pedal melody







The pedal notes from 5.1 to 6.2:




                              A6 (K.594)


     m 4.3                m 5.1                m 6.2

    Chord 0              Chord 1              Chord 2  

   Bb---E---Bb --->    Db----F----B --->    C----E-----C    TM phrase in yellow

   Bb---E---Bb --->    Db----F----B --->    C----E-----C    TM melody in light green     

                                                             with Chord 0 added


                       Db--->F--->B---->    C   pedal melody with B->C highlighted

                                                (5.1, 5.2, 5.3, 6.1/6.2)


                Chords 0,1,2.                      Chords 0,1,2, plus pedal melody,

                                                   plus leading voice.


       Click to hear sound clip - Chords 0,1,2, then with additional harmony



     Click to hear sound clip of entire phrase with all notes and proper timings



While the leading voice in the right hand jumps up a 5th from F to C, the melody in the

trademark phrase and the melody in the pedals moves up from B to C as a normal, trademark

phrase would. In the Beethoven, there's no such underlying melodic progression.


Beethoven's music has its trademarks, but creative and consistent use of this phrase is probably

not one of them. It simply wasn't his style.



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