Ludus tonalis

Ludus tonalis ( Latin for “ tonal play”) is a piano cycle by Paul Hindemith from 1942 , which consists of twelve fugues , eleven interludes , as well as an opening prelude (prelude) and a final postlude (epilogue).

The work is considered a modern counterpart to the Well-Tempered Clavier by JS Bach . While the well -tempered piano was intended as an application example for the achievement of the well -tempered tuning , Hindemith's Ludus tonalis is a musical example of the tonal structure of the chromatic scale that he himself discovered .

Bach arranges his preludes and fugues in ascending chromatic order and thus demonstrates the new possibility at the time of being able to play cleanly in all keys. In the arrangement of his pieces, Hindemith follows the so-called "series 1", which, as one of the results of his theoretical investigations, establishes a new system of tone relationships which, according to Hindemith, could replace the traditional circle of fifths.

Theoretical background

row 1

In the theoretical part of his instruction in composition , published in 1940 , Hindemith deals in detail with the fundamental properties of the musical material. He starts from the knowledge that there is something - from his point of view - attached to the previous ways of creating scales that is unsatisfactory. So he sees z. B. in the equal chromatic scale, i.e. the division of the octave into twelve equal intervals, an unnatural artifact. He contrasts this with a new proposal and develops a method to derive the chromatic scale in an organic way from the natural starting material of the overtone series . This somewhat complicated procedure cannot be described in detail here (Hindemith needs more than 10 pages for this!). In principle, it is a kind of "journey of discovery" in the realm of overtones. The order in which the individual tones are "discovered" results in "Row 1", which - in relation to the starting tone C - looks like this:

CGFAE Eb As DB Des B F sharp (= G flat)

This series describes the (decreasing) degree of relationship of the tones in relation to the keynote C. In Hindemith's system of free tonality , it replaces the traditional circle of fifths, so to speak .

Free tonality

Corresponding to row 1, the chromatic scale no longer appears as an extension of the diatonic major or minor scale, but is an autonomous structure independent of the gender of the pitches with graded degrees of relationship that do not necessarily always correspond to the traditionally assumed relationship of the keys.

The emancipation from the major-minor tonality consequently leads to the so-called free tonality , the basis of which is the entire twelve-tone chromatic scale. Despite superficial similarities, Hindemith attaches great importance to a sharp demarcation from the atonal twelve-tone music of Schönberg and the Vienna School . Hindemith even straightforwardly claims that atonality in the strict sense is impossible because one tone always asserts itself over the other as the basic tone (“tonal center”). In the last chapter of his instruction in composition, which deals with the analytical application of his theories to musical examples, he even scrutinizes a twelve-tone composition by Schönberg and shows that tonal centers can be identified even here.

Explanations of the work structure

Prelude and Postlude

The Prelude is a freely designed piece in the style of a fantasy , which in parts also takes on toccata-like features. Characteristic are the seemingly improvisational passages in free tempo ( a piacere ) and the loose sequence of several parts of different imprints.

The piece begins unanimously with a (three-stroke) c ³ , the last note struck is a (double) F sharp ₁ . The prelude is "framed" by the beginning and ending notes of row 1 . However, Hindemith notates the (major) C sharp that has already been played in such a way that it is sustained longer than the F sharp ₁ and thus becomes the actual final note .

This fact, which at first seems strange, is explained in the postlude. This is namely an exact reversal of the Cancer Prelude, that is, the latter is now notated tone for tone backwards with simultaneous mirroring ( reversal ). Since the first auxiliary line above the bass clef or (with the same meaning) below the treble clef system was chosen as the mirror axis, the C sharp notated on the second auxiliary line below the bass system becomes a c sharp ³ notated on the second auxiliary line above the treble system . Thus, the correspondence between the last note of the Prelude and the first of the Postludiums also aural and not only optical in nature as in the Fis ₁ , which in the reflection for gis ³ is.

The last note of the postlude, which corresponds to the first of the prelude, is followed by a full-bodied C major triad, which concludes the entire cycle with a reminder of the pure overtone sound (from which the whole theory started).

The interludes

In the interludes, Hindemith exploits the sonic possibilities of the piano in a variety of ways. They all have a very playful nature and are usually characterized by a distinctive character: Here a tender pastoral, there a strangely unreal waltz, then a strangely jagged aria, a lively "perpetual motion machine", a lively Scherzino or even pieces of strong virtuosity Character like the interlude, which leads from D to B, with its interlocking chord chains of the two hands. Of course, Hindemith's favorite “Marcia” should not be missing either.

The joint

The fugues, in which no consideration is given to the tonal effect, are in deliberate contrast to the cheerful interludes. The composer recorded them in three-part nudity, without doubling the sound, without broadening the cadence. To do this, he works with the entire arsenal of contrapuntal complications, such as: narrowing , cancer , inversion , cancer inversion , augmentation and diminution .

One can distinguish between two types of joints: those who enjoy playing and are predominantly constructive, in other words: wide-meshed and strictly thematic. The constructive pieces are in close succession at the beginning and at the end of the cycle, while the cheerful ones make up the middle (E, Eb, A flat, D).

An increase can be observed within the absolutely constructive pieces. One thinks that the fugue in F, the second half of which is the exact crab shape of the first, already represents a pinnacle of compositional compression. The next piece is a three-part double fugue (A, C sharp, A), in the third part of which the themes, which were initially carried out separately in the first two parts, are contrasted with one another in contrapuntal terms. And towards the end we find the fugue in Db, which is reversed note by note, and then the fugue in B, which is designed as a two-part canon over an unsubstantial bass.

The omission of the so-called “tonal answer” is characteristic of the compositional design of the joints . This was a concession to the tonic - dominant - tension of the major and minor tonality. It is superfluous in the free tonality of the twelve-tone chromatic ladder. The thematic answers are given first in the fourth, then in the third and sixth, and only from the fugue in A flat onwards in the fifth. The last fugue (F sharp) returns to the fourth answer. The third use is always in the tonic.

With the exception of the double fugue in A with two themes, all fugues have one theme. In this regard, the first fugue in C occupies a special position: it has three themes, which are only used in their original form.

The harmony

The chord theory developed by Hindemith abandons the basic principle of the layering of thirds prevailing in traditional harmony theory and no longer differentiates between "actual" chords and " lead chords ". He also throws the principle of the reversibility of sounds overboard. This means that all conceivable sounds can be used musically with the same degree of certainty.

The harmonic freedom established here (in principle unlimited) allows Hindemith in the fugues a downright “merciless” consistency of counterpoint, which takes no account of tonal hardship. The sometimes extremely harsh interrelationships, however, always seem to be justified by the logic of the voice leading and no longer appear disturbing after a certain period of familiarization.

The harmony that is typical for Hindemith differs from the emotionally charged “tension harmony” prevailing in Romanticism in that it is more cool, austere and even brittle. One of the reasons for this is that Hindemith shows a certain tendency towards the preferred use of tritone-free dissonance chords.

Compared to the early Hindemith, which with its sometimes brutally provocative sounds earned the reputation of being frightened by the citizens, the later Hindemith of the Ludus tonalis appears neoclassical . While he used to have no inhibitions about slapping the listener with a five-part dissonance chord con tutta forza at the end of the “Shimmy ??” in the “Suite 1922” , in the Ludus tonalis he appears almost puristically clarified when it comes to closing sounds.

No matter how dissonant the previous sounds may have been, there is always a consonance at the end of the pieces. Of the 25 pieces in the Ludus tonalis , eight end with a major triad, four with a major third, one with a major sixth, four with an empty fifth and six even with just an octave sound or a single note. The minor triad does not appear as the final sound, which raises the question of whether Hindemith might revive the early Baroque doubts about the real finality of the minor chord. After all, he explains in his instruction in the composition of the minor the minor chord as a "clouding" of the major triad naturally occurring in the overtone series.

Although Hindemith avoids the minor triad, which is completely accepted and common as the final chord in classical music, in two pieces he uses a final chord that would have been inconceivable as such in classical music, namely the second inversion of the major triad: the fourth chord . He is aware of the traditional interpretation of this chord from that rather saw an unstable, resolution needy entity in him and him close to a dissonance sound ( " believes dissonance moved"). The tension inherent in the sixth-fourth chord was felt to be so strong in classical music that it was even used as a standard drum-roll-like tension in instrumental concerts before the solo cadenza. According to the results of Hindemith's acoustical-theoretical considerations, the sixth fourth chord is a completely unproblematic consonance sound, whose value compared to the basic form of the major triad is only slightly weakened because its root is not the bass note.

List of unique pieces

The titles and performance names of the individual pieces are given below. The information marked in italics is not - like the others - large above, but small in or below the notes. The tonality designations are given here with the German nomenclature, while the English designations are used in the original.

Prelude: a piacere - largamente - Arioso, tranquillo - a piacere - Lento - Solenne, largo
- Fuga prima in C: Lento
Interlude: Moderato con energico
- Fuga secunda in G: Allegro
Interlude: pastoral, moderato
- Fuga tertia in F: Andante
Interlude: Scherzando
- Fuga quarta in A: Con energica - Lento, grazioso - Tempo primo
Interlude: Vivace
- Fuga quinta in E: Vivace
Interlude: Moderato
- Fuga sexta in Eb: Tranquillo
Interlude: Marcia
- Fuga septima in As: Moderato
Interlude: Molto largo
- Fuga octava in D: Con forza
Interlude: Allegro molto
- Fuga nona in Bb: Moderato, scherzando
Interlude: Molto tranquillo
- Fuga decima in Db: Allegro moderato, grazioso
Interlude: Allegro pesante
- Fuga undecima in H (Canon): Lento
Interlude: Valse
- Fuga duodecima in F sharp: Molto tranquillo
Postludium: Solenne, largo - largamente - Arioso tranquillo - Moderato - largamente - a piacere

literature

Paul Hindemith: Instruction in composition , theoretical part, B. Schotts Sons, Mainz 1940
Heinrich Strobel: Paul Hindemith , B. Schotts Sons, Mainz 1948
Torok, Debra: Paul Hindemith's “Ludus Tonalis”: Harmonic Fluctuation Analysis and Its Performance Implications . Ann Arbor: UMI, 1993. Zugl .: New York University, Ph.D. 1993

Remarks

↑ Hindemith uses the spelling “Praeludium” (not “Präludium”).
↑ There is also a "series 2", which refers to the degree of consonance or sound value of the intervals arranged in descending order and is of great importance for Hindemith's chord theory, but is of secondary importance in the present context.
↑ Of course, the derivation could also start from any other fundamental tone and would then result in a correspondingly transposed variant of the series.
↑ The analytical method that Hindemith uses here is based primarily on the findings that emerge from "Series 2". In particular, the fact that intervals and chords have physically detectable fundamental tones plays a role here.

[1] Hindemith uses the spelling “Praeludium” (not “Präludium”).

[2] There is also a "series 2", which refers to the degree of consonance or sound value of the intervals arranged in descending order and is of great importance for Hindemith's chord theory, but is of secondary importance in the present context.

[3] Of course, the derivation could also start from any other fundamental tone and would then result in a correspondingly transposed variant of the series.

[4] The analytical method that Hindemith uses here is based primarily on the findings that emerge from "Series 2". In particular, the fact that intervals and chords have physically detectable fundamental tones plays a role here.