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I happened to hear Mahler's Symphony no 6 in A minor Tragic, 3rd Movement, Andante Moderato this week for the first time and was surprised to hear what sounded like the primary theme from Joaquín Rodrigo's Concierto de Aranjuez, Second Movement, Andante Moderato.

I looked at the dates on both works and found Mahler composed his 6th Symphony in 1903-1904. Rodgrigo composed Concierto de Aranjuez in 1939.

Here is the theme from Rodrigo's Andante Moderato: Andante Moderato theme

Here is the theme from Mahler's 6th, 3d Movement: Mahler's 6th 3d Movement

There are a few technical questions, some of law and some of music theory (which I trust will justify presenting the matter in this forum), which are pertinent. Is there substantial similarity in the relevant musical phrase in question? Is the phrase so common that one might claim scenes a faire, i.e., in common use in the genre?

As a matter of legal distinction, but this also pertains to attempting to understand the similarity of the similar phrase here, did Rodrigo have access to Mahler's work, i.e., was it possible that Rodrigo heard Mahler's work before composing his?

Interestingly, Rodgrigo studied music in Paris sometime after 1917, first at Ecole Normale de Musique and then with Maurice Emmanuel and Andre Pirro (in Paris). Rodrigo subsequently composed Concierto de Aranjuez in Paris in 1939. He recalls "...I heard a voice inside me singing the entire theme of the Adagio [his Second Movement] at one go, without hesitation...born of an irresistable and supernatural inspiration.."

At the time of his death in 1911, Mahler was "...a major musical figure in Europe...his music performed in St. Petersburg in the east, Helsinki in the north, and in Paris in the west."

May we conclude that that Rodrigo probably unconsciously used Mahler's phrase in his own work in 1939?

  • Wow. I've known both of these pieces for years and never heard any connection, but I definitely hear it once you point it out. Great question! – Richard Feb 2 '17 at 0:02
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    @Richard I'm glad someone else hears a connection (and that it is not well-known). Last week I "discovered" Eric Carmen borrowed most of the melody for his 1975 hit "All by Myself" (not one of my favorites) from Rachmaninoff's Piano Concerto No. 2 (2nd movement), only to find that Carmen had acknowledged it and even paid 12% royalty to the Rachmaninoff estate. – Dalton Bentley Feb 2 '17 at 3:07
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To recap, we are considering the question of whether the minor key theme in Mahler's Sixth Symphony, Andante Moderato movement, is similar to the subsequent composition of either or both of the two melodic themes in Rodrigo's Concierto de Aranjuez, Adagio (the second movement in this work), so similar as to support a hypothesis that Rodrigo unconsciously relied on Mahler's 1903 phrase in his 1939 composition.

Can an average listener hear so much similarity as to suggest these segments reflect copying of some kind? Stripping the compositions under consideration down to just the bare primary melody sequences and transposing Rodrigo from D/Bm to Eb/Cm to facilitate comparison with Mahler's theme in the same key (and adjusting the timing to put them in about the same rhythm) we can display the musical score and highlight the notes as they are sounded in the following videos. In the first YouTube video we present the minor theme from Mahler's Sixth (“MAH”) followed by Rodrigo's first theme (“ROD-I”), followed by Mahler again as it seems most people immediately want a second hearing:

MAH V ROD-I youtube comparison

In the second video we present the same minor theme from Mahler's Sixth (“MAH”) followed by Rodrigo's second theme (“ROD-II”), followed by Mahler again:

MAH V ROD-II youtube comparison

Many people will probably hear some similarity in these segments, musically and in the emotion they invoke, but can we make a more objective comparison? For cases of outright replication of one song by another it is enough to present them in the fashion above (or running concurrently, when there is literal copying), but this is not the case here.

As a first step in a more technical analysis, it might be useful to examine the way the two composers developed their melodies, i.e., did the notes leap large pitch distances between successive notes, did they use similar transitions, etc. In music theory you will be familiar with the distance between two successive pitches (notes) as intervals in the diatonic scale and they will be defined by the number of semitones in the step. I assume the reader has a basic education in music theory, but if not (or if you want to check definitions, I found the 1914 textbook by Gehrkens to be an excellent resource; freely available at Project Gutenberg) Gehrkens Music Notation and Terminology

I used Matplotlib, an open source Python-based plotting library widely used in the scientific computing community (see the interesting article by the creators of Matplotlib at article by the creators of Matplotlib to create a stacked histogram (a bar chart) with bins equal to the intervals appearing in the melodies under examination and the frequencies the number of occurrences of that particular interval, e.g., -3 semitones on the x-axis is a falling minor 3rd interval. The three melody sequences are color coded and the respective frequency of occurrence in their melodies is stacked (so the length of a particular color segment within a histogram bar indicates the number of occurrences of that interval in the melody coded with that color): Histogram

Looking at that stacked histogram of the frequency of occurrence of ascending and descending melodic intervals in MAH and ROD-I and ROD-II it appears that if you discard the repetitive notes (the “0” bin which indicates repeated notes, which are used only by Rodrigo) there is a close correspondence between Mahler and Rodrigo, closer perhaps between Mahler and ROD-II where they each have added a unique outlier, otherwise making similar use of interval motion.

But interval motion presented in a histogram doesn't give a gestalt impression of the actual flow of the melody, so let us look at a contour graph, a line plot of the actual notes of these melody segments as they appear one after another in time. This can be done by hand, sketching up and down line segments above the musical score to show the rough contour of the melody, but I will instead use Matplotlib again.

Here is the line plot of MAH, which gives you an idea of the shape of the melody, the types of changes in slope sign (up or down movement of the notes) and whether the notes leap or make step-wise movement to the next note: MAHIb note seq you can see more or less a descent of the melody in several groups to the terminating note. This helps me somewhat to understand the emotion associated with this segment (the affect), somewhat of a continuing descending lament, being notes from the melodic minor scale. The sequence begins on the dominant and briefly touches the tonic once before sinking in melancholy musing to the dominant again, leaving an unsettled feeling (of not resolving to the tonic). Mahler (I note that I have only studied Mahler's Andante of the Sixth, the Adagietto of the Fifth and the First movement of his unfinished Tenth) seems often to communicate through his music that we savor the peaks in human existence only to the extent we must climb from the dark valleys and that there eventually will come to us all a time when we are unable to make the ascent again.

Looking at ROD-I: ROI-I note sequence and ROD-II: ROD-II note sequence We immediately find the same pattern of stepped descent we saw in the Mahler segment, perhaps more so in ROD-II. Rodrigo stays within the Primitive/Aeolian minor scale, not using the natural on the sixth that Mahler adds (Mahler freely using this feature of the melodic minor scale on ascent and descent and otherwise mixes from the primitive/aeolian scale). However, this does not distinguish the emotional effect of the segments appreciably to my hearing. Unlike Mahler, Rodrigo closes his descending melancholy introspection on the tonic, providing somewhat more of a termination to the feeling (one still has the impression that there was some resistance to that final descent though).

I wondered what another theme in a minor key might look like in comparison to these three, i.e., is this a relatively distinctive shape (the continued descent), so I graphed the basic theme of Mozart's Requiem Aeternam (transposed to Eb/Cm): Mozart Requiem note seq

Quite a difference in shape! Mozart's theme climbs in sad majesty as befitting one leaving this life and ascending to eternity.

One could examine the relationship of notes of a melody with the accompanying chords, i.e., harmonic analysis, but I don't believe that is necessary in the present context. Mahler's and Rodrigo's themes here seem to suggest harmony to me rather than to acquire essential character from it (an opinion I arrived at after doing this work).

There has been an ongoing effort for some years now, driven in large part by the business of content-based music retrieval (or the possibilities of that capability), to define similarity measures between pieces of music. A simple approach to computing melodic similarity might be to represent the melodic profile of pieces using three classes of pitch intervals, i.e., ascending, descending, and same, much as we did earlier by constructing a histogram based on this data structure.

More complex representations may use finer quantization of the intervals, add analysis of the relationship of harmony (melody note relation to accompanying chord) and metric weight (position and duration of the note in the sequence). Software implementing melodic similarity analysis may use a sliding window, looking for the best match between successive portions of one melody while holding the query segment constant, aligning elements of one sequence with an element of another (or with a gap). [see A Measure Of Melodic Similarity Based On A Graph Representation Of The Music Structure; Orio and Roda 2009 ] The implication/realization model looks at three note sequences constituting two intervals, categorizing experimentally determined expectations by listeners on how the melody will continue. Once categorized as sequential data, general methods for comparing sequential data, e.g., edit distance, can be used to evaluate similarity of one sequence with another. [see Melody Retrieval using the Implication/Realization Model; Grachten, Arcos and Mantaras].

The Répertoire International des Sources Musicales or RISM maintains a comprehensive database of music, including a music incipit search, which makes it possible to search (using melodic similarity software) a database of about one million incipits for works that are musically similar, based on the progression of the beginning notes of a composition (the note names can be typed or entered with an onscreen piano keyboard). These seem to be primarily works prior to 1800, however, this is still a valuable database for testing melody similarity software, among other purposes. I found the online search provided by Ultrecht University at Online RISM incipit search to be more useful as a hook into the RISM incipits. With that facility I found incipits by Domenico Gallo "Dixit Dominus" (18th century) that were considered to be most similar to Rodrigo in part and Antonio Cesti "Bella Clori" (17th century) most similar to a portion of Mahler (keep in mind that this simply means for the million or so incipits, the returned segments had the highest computed similarity scores, i.e., it doesn't mean that they matched exactly the query, but I could hear brief similarity of significance).

I thought it might be interesting to use melody similarity software, MelodyShape, developed by Julian Urbano [available atUrbano MelodyShape program using algorithms he achieved best results with in the MIREX Symbolic Melodic Similarity task competition 2010 – 2015, to run some comparisons on the Mahler and Rodrigo segments, as well as incidental pieces for comparison. Urbano's MelodyShape Java software accepts MIDI files for comparison and “transforms note trigrams to a series of B-spline interpolations, which are curves fitted to the contours of the note trigrams. The resulting series of B-splines of two melodies are then compared through alignment,” quoting from A Comparison Of Symbolic Similarity Measures For Finding Occurrences Of Melodic Segments; Janssen et al, 16th International Society for Music Information Retrieval Conference 2015. In other words, MelodyShape does something similar to what we did earlier in plotting lines connecting the notes of the melodies in order to get a feel for the shape of the resulting contour. Each group of three notes in succession has a smooth curve calculated to connect them; that mathematical function is then a “spline” defined for that section. Another spline is calculated for the next group of three notes, designed to connect smoothly with the previous spline also. In this way a piecewise smooth numerical characterization of the shape of each melody segment is obtained and then compared in successive alignment to find the areas where the shape matches in the two melodies under comparison. Good matches should return a high value, bad matches a low, possibly negative value. Running MelodyShape (installed locally on my computer) with Mahler as the query I obtained the following results:

Mahler compared to itself: 6.55140000
compared to Antonio Cesti "Bella Clori" (17th century): 3.54120893 compared to Domenico Gallo "Dixit Dominus" (18th century) -0.14140608 compared to Rodrigo's second theme: -0.16697577
compared to Rodrigo's first theme: -0.16697577

Running MelodyShape with Rodrigo's first theme as the query gave: compared to itself: 6.55140000
compared to Rodrigo's second theme: 0.34103238
compared to Domenico Gallo "Dixit Dominus" (18th century): 0.17138156 compared to Mahler theme: -0.16697577
compared to Antonio Cesti "Bella Clori" (17th century): -0.38888889

Running MelodyShape with Mozart's Requiem Aeternum theme as the query: compared to Antonio Cesti "Bella Clori" (17th century): 0.87988889 compared to Mahler theme: 0.23808437
compared to Domenico Gallo "Dixit Dominus" (18th century): -0.02564103 compared to Rodrigo's second theme: -0.04861111
compared to Rodrigo's first theme: -0.04861111

MelodyShape rightly suggests Rodrigo's themes I and II are somewhat similar, agrees with the RISM incipits similarity (Dixit Dominus somewhat similar to Rodrigo themes; Bella Clori very similar to Mahler's theme), suggests Mahler is not very similar to either Rodrigo theme, and Mozart is not similar to any of them.

My work here suggests that we may not conclude that Rodrigo unconsciously (or otherwise) used Mahler's phrase in the composition of his own work, though we see technical reasons why these three melodic segments feel similar, e.g., melody shape/contour, use of same melodic interval motion. It is only possible that Rodrigo had Mahler's work in his mind on the level of musical memory (whatever level that is), a tantalizing hint being Rodrigo's long silence on where he got his inspiration for the Adagio, finally commenting that he heard a voice singing it inside him.

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I love your question and the research you put into.

I am not a lawyer so this is purely my opinion here. In the example you give, I really do not hear enough resemblance to raise the question of copyright infringement. Some subtle music appropriation, which has been common in the history of music, possibly.

I would guess that to claim a composer infringed on someone else's work, there would need to be at least one element that is distinctive enough from the original piece that finds its way in the "remake". The distinctive element could be melody, rhythm, texture, etc.

When you mention the Aranjuez concerto, I think people will easily hum the part you pointed us to in the video. Reversely, you hum that air and many people will identify it as from Rodrigo: it just has a melody and rhythm that stick. I am pretty sure this wouldn't be the case with Malher's symphony.

It could very well be that Rodrigo wouldn't have composed this piece in this exact way if he had never heard Malher before, we will never know--and from what you quote, it might be that even Rodrigo himself wouldn't know--but I don't see/hear the identity of Malher's piece in what Rodrigo created.

Now, with respect to what legal experts say, I poked around and found some cases that provided some insights into what is or is not acceptable in terms of reusing earlier work.

Here for example, they say

If the said musical composition was borrowed altogether from a former one, or was made up of different parts, copied from older musical compositions, without any material change, and put together into one tune, with only slight and unimportant alterations or additions, then Russell was not the author within the meaning of the law; but the circumstance of its corresponding with older musical compositions, and belonging to the same style of music, does not constitute it a plagiarism, provided the air in question was, in the main design, and in its material and important parts, the effort of his own mind.

To me, that means that "if you worked hard enough on the piece to bring clearly new distinctive elements to it, it's yours". That's a much stricter definition of infringement than I would have instinctively used. For example in the lawyers who wrote that decision, I expect that they would find the work from Jacques Loussier like here a new work on its own right and thus not an infringement. And same would go with Rodrigo's work.

  • I found your answer very creative, but you could make a similar argument in favor of Eric Carmen's use of Rachmaninoff's Piano Concerto No. 2 (2nd Movement), i.e., most people would now identify the melody in question as Carmen's though he admits taking it from Rachmaninoff. By analogy, if someone moved into your home while you were away it might be argued that they had been there long enough to displace your ownership. If you consider that the Mahler sequence is not only reproduced melodically but with the critical harmony that makes it so distinctive, it cannot be coincidence by Rodrigo. – Dalton Bentley Feb 17 '17 at 19:24
  • Hard to respond in few words! 1. I do see the law as more lenient to the reuse of material than what my intuition would have been. 2. Whether it is due to my familiarity with the piece or something else, I find Rodrigo far enough from Malher to not even see his work as a make over of Malher's symphony, left alone an infringement. 3. Whereas Carmen's piece is clearly building on Rachmaninov's concerto, keeping enough of the original to leave no ambiguity. – Lolo Feb 23 '17 at 13:53
  • 4. Back to "personal" position here, which wasn't your question, I have no issue with what Carmen does: he quotes his inspiration (hard to hide anyway!) and uses it to convey something different enough while still touching millions, some likely not overlapping with the Rachmaninov admirers by lack of exposure. Rather than kicking Rachmaninov out of his house, I think he built him a nice extension. – Lolo Feb 23 '17 at 13:54
  • There is an excellent resource for looking at the law regarding music copyright infringement sponsored by Colombia Univ. and USC mcir.usc.edu/purpose/Pages/default.html. I have been conducting a formal musical analysis and will post that soon. I am leaning towards agreeing that the Mahler segment and Rodrigo are not significantly related, but want to present that in more objective terms. Interestingly, I did find a segment by Domenico Gallo "Dixit Dominus" 18th century that does match Rodrigo in part and Antonio Cesti "Bella Clori" 17th century matches Mahler. – Dalton Bentley Feb 24 '17 at 17:02
  • Please keep us posted when you post your analysis! Is your analysis about classical composers reusing other's work or is it more general? – Lolo Feb 24 '17 at 21:49

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