What do these many alternatives imply for the work’s existence ?
These ‘versions’ create within the score ‘blind holes’ as I’d like to call them – dead ends in the text, suggestions that cannot lead anywhere on a musical, developmental level – as well as creating through holes, or the insertion of musical ideas which can be and are developed throughout a movement. We are voluntarily using the lexicon of the field of topology for this text study, since our goal is to pinpoint the transformations operated by Beethoven and by the performer in the score during the whole creative process. It is indeed possible for the performer to inform this piece with through holes – by way of, for example, using a certain type of articulation – and many 19th century editions (specifically F. David) use this device to render the text readable and understandable to the performer on a micro level (every note being accounted for).
Another small disclaimer.
The textual history of the violin concerto is very, very messy. I would in fact be ready to consider it an unfinished work, were it not for the great richness of the text and especially the original manuscript. Discussion on these sources (with what I believe to be the main work on the topic: "the textual problems of Beethoven's violin concerto" by Alan Tyson (the Musical Quarterly 1967), while being taken into account, will not be opened in these pages, since a historical approach is not the goal of this research – therefore one must be careful when drawing conclusions. Taking faith in the fact that the violin text of the Bärenreiter edition is correct, we will however look and compare the many versions Beethoven appended to the manuscript, and see how those various versions actually change the nature of the work, that we have a work in progress at our grasp, while the very fabric of the work shows a new manner of processing musical material - a new style of evolving musical material. For each of those characteristics (excess and lack of information on the manuscript, as well as new style of orchestral composition), we will use a scientific tool.
, instead of his own written down development of this part of the score). I would regard these musical objects as the latent first products of the score – like slurs would be in Bach’s diatonic homorhythmic writing – they being in the mind of the composer when figuring out the work, therefore not byproducts. This use of ‘informing figures’ brought by the performance, which can be called ‘tropes ’, (R. Hatten, Musical Meaning in Beethoven) generate within the work, and sonata form in general, a sort of homeomorphism.
Morphosonic, sonomorph and antagonism.
Of Homeomorphism, this is WolframMathworld’s definition : « A homeomorphism, also called a continuous transformation, is an equivalence relation and one-to-one correspondence between points in two geometric figures or topological spaces that is continuous in both directions. A homeomorphism which also preserves distances is called an isometry. Affine transformations are another type of common geometric homeomorphism. » Transported into the field of music, I wouldn’t like to define what I’m trying to say as a simple transposition – that would mean affine transformation in the mathematical field (identity of lines and distances between iterations) – but as a process within which it is even difficult to distinguish iterations, due to the activity and multiplicity of simple musical transformations taking place. And I think that the concerto’s material and its working out in a clear, economical manner (compared to Beethoven’s piano concerti) serves a good example to this theory.
Especially the first movement of the concerto is a unique opportunity to analyse music through this lens, given the continuous quality of the solo part in its ornamental relationship to the orchestral part which carries rhythms and harmonies.
Homeomorphism might help us understand how and when the ‘map’ of the solo part preserves the topological (read harmonic/dynamic/rhythmic) properties of the work. Therefore, we will only have a look at the first movement of the concerto. But before understanding how the properties of the work relate to one another from the violin and the orchestra perspective, we must observe that the very properties of the work have been gravely misunderstood, through the dilemma of the excess of material for the solo part, and lack of signs on individual ideas.
a surface for the published work/ surface work done by editors
Here is Jenő Hubay’s 1918 edition of the solo part.
We know that this additive method is also the one Mozart used in his relationship as performer to his own piano concerto (with the famous example of the 24th concerto in c minor rarely having more than a bass line in the left hand
