The key to understanding 20th century music: On Hemitonicism and Webern's Op. 11, No. 2 & No. 3, Marco Alejandro Gutierrez

Marco Alejandro Gutierrez

        Hemitonicism is a system characterized by a combination of the semitone and chromaticism. It is the key to understanding the structure of Anton Webern’s music and his compositional process.

 
        It is an independent pitch system and self-sufficient. As can be said of twelve tone technique, or traditional tonal music with its characteristic management of Tonic, Dominant, and Subdominant.

 
        Harmony always develops faster than form. Despite Johann Sebastian Bach’s advances in the field of harmony, his musical compositions are in older genres and styles***. It was until Ludwig van Beethoven that these advances in harmony met their match in musical form. The same can be said of the advances in harmony made by Arnold Schoenberg at the very beginning of the XX century. Much like Bach (who Schoenberg referred to as the very first twelve tone composer), despite his advances in harmony, Schoenberg still composed in genres of a previous era. His pupil, Anton Webern went much further in the development of musical form, fitting to Schoenberg's advances in harmony. This composition, Op. 11 is a clear example of Webern’s experimental steps to this goal.

 
        Three small pieces for cello and piano Op. 11 can be performed in under two and a half minutes in their entirety with the first and last pieces being calm and slow, with an energetic middle piece in between. They are surprisingly short by most people’s perception of a piece of music of any genre. Being nine, thirteen, and ten measures long respectively, it begs the question: Why are they so short and how is this accomplished? Hemitonicism provides an answer to this. The pieces are short due to the dense synthesis of musical ideas contained within them. It is a necessity for them to be the length they are.

 
        It is important to mention that I am not aware of the original proponent of the term hemitonicism. Webern did not speak of his system using this word, but rather he used the term “chromaticism”, adding to an already unclear musical vocabulary the potential for further confusion. Yet, as his system is something new and unique, it deserves another name. Hemitonicism therefore has been adopted from a Russian term found in the writings of Yuri Kholopov and Valentina Kholopova.

 
        Hemitonicism is the combination of a semitone and an interval. It is characterized by hemitonic groups and fields. Hemitonic groups are composed of three to four notes connecting an interval and a semitone or two. Hemitonic fields are notes who continuously fill in a portion of the chromatic scale by the use of the semitone regardless of the order in which they appear in a particular section of the piece. In hemitonicism, it does not matter the order, octave, or direction of the notes in a particular group. In this regard it is similar to the P, I, R, and RI forms of twelve tone music.

 
        There exist five trichordal hemitonic groups and five tetrachordal hemitonic groups and are named by the number of semitones present in their respective interval.

        It is important to note that generally speaking in Webern’s music and in the hemitonicism technique, it does not truly matter whether the same note is called Db or C# for example, as it would be traditionally characterized by a slightly different tuning in tonal music. A quick review of the naming of intervals leaves us without augmented 2nds for example, due to their redundancy, amongst other conflicting names for the same interval. According to the Kholopovs, this music should be played by tuning all instruments as close to equal temperament as possible. Adding to this, my teacher Semyon Vekshtein, states that in chords the notes should be played more or less equally in volume. Corresponding to the marked dynamic (no highlighting of a specific note in a chord). Webern’s melodies are characterized by the linking of hemitonic groups.

 
        In the analysis of these pieces, it is interesting that hemitonic fields often line up well with what could be called phrases in the music. Also important to note is the fact that the last note of a field is usually marked or highlighted in some manner.

 
The following is Op. 11 No. 2 in its entirety, with hemitonic group and field analysis:

 

        For sake of a cleaner view of the piece, I have chosen to only mark the least possible amount of hemitonic groups. This means that every note is included in at least one group, yet it can form part of several more. There are many more relationships by various hemitonic groups in every beat of this piece. A piece characterized by densely packed interrelations between every note is part of the reason and justification of its length. No note is left out of a group, and from this fact we can call Webern’s technique here as strict hemitonicism.

 
        The piece is divided into 5 hemitonic fields. All corresponding to phrases and all characterized by the note finishing the field being marked in some way.

 
        The first field is from measure one to the first half of measure two and runs from D to B♮ continuously with the exception of the note A which is missing. The ending note of the field, f#, has a diminuendo.

Field #1 fills in the chromatic scale as follows:

 

        The second field appears from the second half of measure two to measure five and runs from C to B♮. This field uses all 12 tones and can be described as a field with “total hemitonicism”. Only C#, F, and A are repeated. The note A, which was missing in the previous field, is repeated here. F, being the last note of the field and marked with a tenuto.

Field #2 fills in the chromatic scale as follows:

 

 
        The third field goes from measure six to measure 9 and runs from C to B♮ and can also be considered to contain “total hemitonicism”. The notes C, C#, Eb, and E, are repeated and C is the closing note of the field, marked with a diminuendo.

Field #3 fills in the chromatic scale as follows:

 

 
        The fourth field appears from measure ten to measure eleven and runs from Ab to F# with notably the notes Eb, and E missing from the continuous chromatic scale. These notes were repeated in the previous field. The last note of this field is Db and is marked by crescendo.

Field #4 fills in the chromatic scale as follows:

 

        The last hemitonic field goes from the pickup to measure twelve to the end of the piece. It runs from F to Eb. The last note of the field is B♮ and is marked with an accent.

Field #5 fills in the chromatic scale as follows:

 
        It is curious how “wave like” Webern’s piece is. The shape and line of Op. 11 No. 2, can be seen from a distance as a series of waves with peaks in measures 1,4,7,11, and 12 in the cello part, and troughs in measures 3, 5, 9, 12, and 13 in the piano part. All three pieces are characterized by this: when the piano stops playing, the cello plays and vice versa. Both instruments' interconnectedness makes it a challenge for any performer. In my own experience, I have found them to require an exquisitely robust palette of colors from the cello, following closely what the Second Vienna School calls “Klangfarbenmelodie” and making the cello sound like a small, variedly orchestrated ensemble. The same demands of course goes to the piano.

 
        Moving on to the third piece, the following is Op. 11 No. 3 in its entirety, with hemitonic group and field analysis.

        It could be observed, despite its short size, that this piece has a period-like structure at the beginning. With the first two phrases (m.1-3 & 4-6 respectively) behaving somewhat like antecedent and consequent, or maybe more appropriately as proposta and risposta due to the arguable lack of the two cadences that characterize a period. The two phrases are related as well by their common tones, with the initial two notes of the cello: Eb and Fb, being repeated by the piano at the end of the second phrase. Also by the lowest note in the piano in the first phrase, being repeated this time as the highest note in the cello at the end of the second phrase. The second phrase can be described as being climactic in a way, with the presence of both the lowest and longest note in the piece played together with the highest. George Perle, observes the third phrase as a kind of coda from this point of view and notes how the repeated notes of the first two phrases are missing in the third. It is also important to notice that the note A is played for the very first time in the piece by the cello until the third and final phrase.

 
        The piece is divided into two hemitonic fields, and as before, they mostly coincide with phrases. Every field is characterized by the note finishing the field being marked in some way.

 
        The initial hemitonic field appears in the first three measures, ending in the first half of the 3rd measure. It runs from Bb to F. Its last note is the Bb played by the cello and is marked by diminuendo to ppp.

 
Field #1 fills in the chromatic scale as follows:

 

        The second hemitonic field goes from the pickup to measure four to the end of the piece. It runs from F# to F containing all twelve notes and fulfilling the requirements of “total hemitonicism”. Only the note F# is repeated. The note closing the field and the piece, is marked by a fermata and a diminuendo to pp.

 
Field #2 fills in the chromatic scale as follows:

 

        In the first six measures there is an interesting pattern worth calling attention to. The notes Eb, E, B, and C in the opening cello line form the hemitonic group 3b. This pattern becomes a kind of tone row and is repeated twice more by the piano. The first time is in measures 2-3 with the notes C#, D, F, and F# forming the same hemitonic group, and the second time is in measures 3-6 with the notes G, G#, Eb, and E.

        Hemitonic groups 3a and 3b are the most favored by Webern due to their intervallic composition. Such is the preference that these groups have come to bear his name as the “Webern hemitonic group” due to them being closely associated with him. From the various examples of hemitonic group analysis in this text, it is easy to see how common hemitonic group 3 is.

 
        Composed in 1914, before twelve tone technique was fully developed, Op. 11 shows Webern’s natural feeling for tonal balance. When the hemitonic field is completed, the phrase ends. And often, when all notes are played, the piece ends.

 
        An experiment in musical form and written in strict hemitonicism, it is a piece full of "expression" despite its size. Though I must admit that I dislike this word. Maybe, due to their length, Webern opted not to attend the premiere.

 
        This analysis is based on my studies following the New Vienna School tradition with my teachers, Vladislav Soyfer and Semyon Vekshtein, and on the information obtained from the works of George Perle, Philip Herschkowitz, Anton Webern, Arnold Schoenberg, Valentina Kholopova, and Yuri Kholopov. I would also like to thank my colleagues and friends Varvara Soyfer and Giuseppe Gil for lending me their ears in a lecture of an initial draft of this article and for their observations and advice.

If you are interested in learning more about music, you are welcome to visit my personal website https://www.learningmusicasalanguage.com where you can obtain more information about my courses and approach to music and arts education.

Footnotes:

***Here we encounter one of the biggest problems in the teaching and understanding of music: its vocabulary! Some concepts have relatively solid meanings in their name, and others might as well be parables or riddles. Here I stated that J. S. Bach composed in older genres and styles. I chose these two words to avoid using the word "form". By genres and styles I would like to point to his Allemandes, Sarabandes, Lourees, amongst many others. This is regardless of the fact that many of these are composed in what is known as Baroque Binary Form. Which is certainly worth mentioning, is not a form at all... Form is the underlying structure of the piece, which despite being in this Baroque Binary form, can have elements reminiscent of later developments in musical form such as Sonata Form (period, main theme, fragmentation) or something else altogether. At no point do I wish to misstate that Bach's pieces have no form either as this is obviously not the case. In German language, Arnold Schoenberg invented new terms to differentiate these and many other concepts. In English I will try to differentiate between form/underlying structure (Sonata Form, period, main theme, modulatory section, etc...) from genre (Louree, Bacarole), and superficial structural descriptions (Baroque Binary Form). I am open to any suggestions or comments in this regard.