Modes with limited transposition options
The seven modes with limited transposition possibilities by the composer Olivier Messiaen systematize the distant octave divisions known since Franz Liszt , Claude Debussy , Maurice Ravel , Alexander Scriabin and Béla Bartók (equal or periodically alternating interval chains) and already use these as “comprehensive” scale material for long harmonic distances. Messiaen regards the chromatic scale (an octave 12-EDO divided into 12 equal pitch steps) as "our current chromatic system" (p. 56) and therefore as a superset and not as a mode of its own. Messiaen already explained these modes in the foreword to his organ cycle La Nativité du Seigneur (1935) and in his book Technique de mon langage musical (1944).
The modes
1st mode
The first mode, which is equal, is the whole tone scale and thus divides the octave into six equal intervals. It is therefore only transposable once , because every further transposition would coincide with one of the shapes that were already used. In Olivier Messiaen's linguistic regulation, the shape starting with C ("basic shape") is already the 1st transposition. As a numerical form, this mode looks like this: 222222 and therefore has no inversion analogous to chords. (2 = whole step)
2nd mode
The second mode is based on the subdivision of the octave and corresponds to the alternating eight steps (also known as octatony), known since the 19th century and often used since then , i.e. a scale of eight tones, each consisting of semitone and whole tone steps in periodic alternation . This mode divides the minor third as a nucleus into a semitone step and a whole step, it can be transposed three times, because from a fourth transposition onwards there would only be repetitions of the previously used scales. In Olivier Messiaen's linguistic regulation, the shape starting from C with the semitone step ("basic shape") is already the 1st transposition. In terms of numbers, this mode looks like this: 12121212 and has an inversion (21212121). (1 = semitone step, 2 = whole step)
In jazz harmony theory, this scale is also known as the HTGT scale (semitone whole tone) and is mainly used over dominants. Another name is diminished scale .
3rd mode
The third mode is based on the major third division of the octave and divides the major third as the nucleus of the mode into a whole tone and two semitones; it can be transposed four times. In the language used by Olivier Messiaens, the figure starting from C with the whole step is already the 1st transposition. As a number, this mode looks like this: 211211211 and has two inversions (112112112 and 121121121)
4th-7th mode
Modes 4th to 7th are based on the semi-octave ( tritone ) and can therefore be transposed six times. As a numerical form they look clearly like this (3 = minor third, 4 = major third):
4th mode: 11311131 with three inversions (13111311, 31113111 and 11131113)
5th mode: 141141 with two inversions (411411 and 114114)
6.Mode: 22112211 with three inversions (21122112, 11221122 and 12211221)
7.Mode: 1112111121 with four inversions (1121111211, 1211112111, 2111121111 and 1111211112)
Use and characteristics
The modes serve - just as is the case with the various keys or church keys in the traditional diatonic tonality of past centuries - not only as the basis of the melodic material, but of course also as the basis for the accompanying chords . The accompanying chords in the 2nd mode are, for example, mostly either major and minor triads on the root-carrier axis that results from the current transposition of the octave's underlying minor division (e.g. in the so-called 1st transposition of the 2nd mode is the Root-carrier axis c -e-flat -f sharp-a ) or also four-note chords, which for example consist of a major sixth chord with added tritone or # 11 or with added major sixth or treble or from the combination of a fifth-less dominant seventh chord with added major Sixths or tredezimes exist.
Messiaen speaks of “limited transposable” modes because the traditional diatonic scales (e.g. the church tonic modes or also major and minor) are known to be transposable eleven times before the starting position (original shape) is reached again. Note: Even the traditional diatonic scales cannot be transposed indefinitely. Measured against a total of twelve manifestations, the fact that they can be transposed twice, three times, four times or six times, can of course be regarded as “limited”.
An eighth mode
The American musicologist John Schuster-Craig published an article in No. 51 of the journal The Music Review (BlackBearPress Ltd., Ed. Geoffrey Sharp) in 1990 , in which he proves that there is actually another, eighth mode that is not Is transposable 12 times, but Messiaen neither discovered nor forgot. It has the following structure (see above): 131313 or 313131 and would be transposable four times (C = 1st transposition analogous to Messiaen's usage). This is formed from alternating a minor second and a minor third and prominent composers of the 19th century used it intuitively: Franz Liszt in his Faust symphony , Rimski-Korsakow in his symphonic poem Sadko and his opera Der goldene Hahn and finally even Béla Bartók very exposed in the third movement of his concerto for orchestra (bars 10–11 + bars 23–27).
Mathematical analysis of the modes
Messiaen postulates a mathematical completeness for his modes, which was already falsified with the mentioned, later discovered eighth mode. If one looks at the modes as a translation-invariant scale structure with the ambitus of an octave, the number of all modes can be determined by counting the ordered partitions of the numbers 6 and 4. In other words: we are looking for all the possible ways of using natural numbers to achieve the sum of 12. (1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1 = 12 = 6 + 6 the two extreme examples) If one summarizes from the 38 resulting ladders those that are merely inversions of each other , you get 16 scales that meet the given conditions. Of these, Messiaen counts seven among his modes, of seven others he explains why he does not count them among his modes. However, he does not mention two more; one of these two is the eighth mode mentioned above, the ninth mode has the following structure: 2424 or 4242 and, analogous to modes 4–7, could be transposed six times.
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swell
- ↑ German: Technique of my musical language. Paris 1966
literature
- Gárdonyi-Nordhoff: Harmonik , Wolfenbüttel: Möseler Verlag 2002, chapters 15 and 16
- Koepf, Siegfried: On Messiaen's "Modes with Limited Transposition Options". In: " Organ - Journal for the Organ ", issue 4/2008
- Messiaen, Olivier: Technique de mon langage musical : Leduc, Paris 1944