Tropical technology
Tropical technique is a special, generally very complex tool within twelve-tone composition . In general, it describes the conscious application of knowledge of the 44 tropics . As a fundamental ordering and overview system for all possible tone relationships in the twelve-tone space, the tropics allow total control over the system of twelve tones and its structure. However, one must first extract methodical "implementation strategies" from the tropics and develop constructive processes that a composer can apply in practice. The entirety of these processes can be summarized under the term tropical technology. Tropical technology is a practical tool for composition and is not designed for the analysis of twelve-tone pieces of music, although the tropics are often misunderstood and used as a means of analysis.
application
Tropical system none of composition in itself technology and a style, but it is a tool, how certain compositional problems constructively with the help of the tropics can solve. The areas of application can be:
- the formation of highly complex twelve-tone rows
- the construction of a formal arrangement of the composition from the form properties of a row or trope
- the mixing or integration of different traditional musical components in a (twelve-tone) composition, e.g. B. an existing cantus firmus , certain harmony sequences, the creation of certain tonal or modal fields
- the creation of a form structure in which classical counterpoint can be used
- Symmetry of any kind, such as B. the formation of arbitrarily complex canons , fugues, etc.
- any combination of all of the above areas, provided the twelve-tone structure allows this at all
Curiously, tropical technique can also be used outside of a twelve-tone composition for creating tonal or modal compositions; it is not tied to the use of the totality of the twelve tones. The existing methods of tropical technology are demanding in different ways. Almost everyone will be able to create a large number of equally symmetrical twelve-tone rows from a symmetrical tropical image relatively quickly. But only a few will be able to construct a harmonious sounding, four-part canon from a trope, in which the individual voices are at the same time in the mirror , cancer and mirror cancer .
Today tropical technology is primarily used and maintained in the context of composing sound series .
example
In order to get an adequate impression of tropical technology, it is necessary to familiarize oneself with the available possibilities that the tropics offer from a compositional point of view. The following example illustrates some possible applications based on a few selected tropical properties: If, for example, one falls back on tropics 3, then the theory of the tropics says that the interval relationships between the two hexachords are reversed there (tropics 3 is a mirror-inverted tropics ). This enables, for example, the creation of twelve-tone rows, the second half of which is in the mirror or in the mirror cancer. The first tropical half of trope 3 also contains the trichord (0,2,6) twice in the respective semitone spacing (e.g. FGH and Ges-As-C), the second half therefore contains its mirror (0,4,6), for example BDE and A-Cis-Dis. The fourth and fifth permutations of all twelve-tone rows formed from trope 3 always lead to trope 30. In addition, the present trope allows the formation of two interlocking six-tone structures in cancer and whole tone spacing, or in the interval of a minor seventh. The theory of the tropics basically states that a transposition of complementary hexachords in a whole tone or a small seventh interval is only possible on the basis of the contradicting trope 17. Consequently, the said hexachordal cancer guidance within trope 3 requires a projection of trope 17 in trope 3 (something like this: G-As-CH -F-Fis- | - E-Es -Cis-DBA → The bold notes indicate a hexachord of trope 17). A simpler option would be to create a twelve-tone row from trope 3 with two separate halves that are mirrored to each other (e.g. G-A-flat-CHF-F sharp | -D-C sharp-ABE-D flat). Using a four-part [3-3-3-3] harmonization, as practiced many times by Hauer, one would then obtain a harmonic band, the second half of which represents the exact mirror of the first:
Such a chord progression would, for example, be suitable as a basis for composing works with mirror guides that start offset by a few bars (following illustration).
Other harmonization methods can change the composition e.g. B. of works (or only of individual sections) in Spiegelkrebs or with multiple symmetries, for example with regard to permutations of the three-tone cells mentioned (0,2,6) and (0,4,6). Other conceivable variants would be, for example, reinterpretations of the existing interval relationships to gradually transfer them to the aforementioned Krebs: Since the two twelve-tone rows listed above have the same first half, cross-connections and expansion options in the tone and interval material can be established very easily.
The question of the choice of the musical style of such a composition is, however, largely independent of these considerations. For example, using Steinbauer's sound series techniques , this could extend to a twelve-tone series of largely tonal seeming homophony or a harmonious counterpoint through to strict series technique. As a demonstration, the canon in the figure above was written in such a way that a twelve-tone row can no longer be imagined as a formal basis. In fact, however, this piece makes use of the chord progression ( note example ) relatively strictly and mechanically : Each chord represents the harmonic material of half a bar in the mirror canon, from the seventh and thirteenth bar the sound sequence repeats.
history
The history of tropical engineering is riddled with difficulties, but also with myths. The beginning of Tropentechnik coincides with the formulation of the 44 tropes by the Austrian composer and music theorist Josef Matthias Hauer in 1921. Hauer was also the first to develop and apply tropical engineering methods. Although Hauer has also published on the subject, there is almost no really useful information to be found in his writings.
Even in posthumous texts by Hauer, there are no concrete findings on tropical technology. The composer himself once stated the reason for this in a letter: “My students only understand the twelve-tone theory as much as they have learned from me. The literary publications that I have published in the course of my development are more misleading than instructive, because I have always kept the main things secret and reserved for personal instruction. I had to protect myself against plagiarism, against everything that could have discredited my peculiar, much vilified music in front of the public. ”The fact that Hauer knew more about the application of the tropics than he left behind in texts can be seen from his own tropical tables ( especially on the basis of those from 1948) in which the tones are arranged according to certain symmetries, which he never wrote about.
On the other hand, there are texts by Hauer's students that are somewhat more illuminating for an understanding of the tropics and their possible applications. In addition to Hermann Heiss and Heinrich Simbriger , whose complementary harmony is essentially based on the tropics, Othmar Steinbauer should be mentioned primarily . Steinbauer's posthumous documents prove an intensive occupation with the tropics from the early 1930s. In the textbook on the composition of the sound series , Steinbauer goes into concrete tropical technology processes for the first time. To what extent he had taken these partly from Hauer and partly derived them himself remains unclear. It is likely that Steinbauer, at best following Hauer's advice, developed his tropical technical knowledge himself. As early as 1932, Steinbauer pointed out the special symmetrical properties of those six tropes, which correspond to the all-combinatorial sets discovered much later by Milton Babbitt . Steinbauer also constructed tropical variants at this time, in which he cataloged certain cases of permutation possibilities of 3 groups of 4 tones each ("four-tone groups") and of 4 groups of 3 tones each ("three-tone groups"). However, these investigations remained incomplete and were only brought forward much later by Heinrich Simbriger.
As a result, the stone farmer student Johann Sengstschmid should be mentioned, who tried to draw conclusions about the tropics in his writings on Hauer's composition techniques.
Problems
To this day, tropical technology has the character of a "secret doctrine". On the one hand, this is due to the extremely high complexity of the subject, which can cause problems even for experts. You can only become familiar with tropical technique if you already have in-depth knowledge of the tropics themselves and of compositional methods (e.g. various forms of twelve-tone composition , contrapuntal genres, etc.). Most of the more complex (and more powerful) tropical engineering techniques currently in existence also require a deeper understanding of sound series composition and its methods. This does not mean that tropical technology cannot exist outside of the methods of sound series theory, but it only shows that hardly anyone outside of it has ever formulated tropical technology processes.
Another serious problem is that there is almost no literature on the subject. The historical "veil" caused by Hauer's bad information policy over decades not only did not contribute to the general understanding of tropical technology, it also blocked it in the long term and hindered the existing interest in it. On the other hand, tropical technique received the reputation of a hidden "supreme discipline" within twelve-tone techniques, even among specialists, since the methods of twelve-tone composition are directly connected with the techniques of late counterpoint art in the 18th century. And there has been a lot of speculation about the possibilities of tropical technology, since only a few people know and can assess them in detail.
See also
literature
- Josef Matthias Hauer : From the melos to the kettledrum. An introduction to twelve-tone music . Universal-Edition, Vienna a. a. 1925, (Josef Matthias Hauer: Theoretical Writings 1).
- Josef Matthias Hauer: twelve-tone technique . Universal-Edition, Vienna a. a. 1926, (Josef Matthias Hauer: Theoretical Writings 2).
- Helmut Neumann : The theory of sound series composition according to Othmar Steinbauer (1895–1962) . Lang, Frankfurt a. a. 2001, ISBN 3-631-35490-8 , pp. 192-197 and pp. 220-225.
- Dominik Sedivy: Serial Composition and Tonality. An Introduction to the Music of Hauer and Steinbauer . edition mono, Vienna 2011, pp. 82–159.
- Dominik Sedivy: Tropical technology. Their application and their possibilities . Königshausen & Neumann, Würzburg 2012.
- Johann Sengstschmid : Between trope and twelve-tone play. JM Hauer's twelve-tone technique in selected examples . Bosse, Regensburg 1980, ISBN 3-7649-2219-2 ( research contributions to musicology 28).
- Heinrich Simbriger : Complementary Harmonics . The artists' guild, Esslingen 1980.
References and comments
- ↑ Especially in Vom Melos zur Pauke (Vienna 1925) and in twelve-tone technique (Vienna 1926)
- ^ Josef Matthias Hauer in a letter to Paul von Klenau dated October 6, 1933
- ↑ So z. B. Othmar Steinbauer's unpublished and incomplete typescript Klang- und Meloslehre , Vienna 1932/34, pp. 56–68 and the accompanying handwritten notes; Estate of Othmar Steinbauer, Society for Sound Series Music, Vienna
- ↑ Helmut Neumann (ed.): The sound series composition theory according to Othmar Steinbauer (1895–1962) . Frankfurt / Wien 2001, Volume 1, pp. 192–197 and pp. 220–225
- ↑ Othmar Steinbauer: Handwritten notes on the theory of sound and melos , unpublished. Typescript, Vienna 1932/34; Estate of Othmar Steinbauer, Society for Sound Series Music, Vienna
- ^ Heinrich Simbriger: Complementary Harmonics . 2nd Edition. The artists' guild, Esslingen 1980