The mode of limited transposition presented in the spreadsheet below can be thought of as the third of Messiaen’s Mode of Limited Transpositions (MLT).  As usual my preference is simplicity, and some of the potential uses of harmony and melody are given without further comment.

The point of greatest reduction in the mode is the interval pattern 2,1,1  (and the full interval pattern of the scale can be rotated three times). In terms of melodic invention this pattern is less useful than the wealth of harmony available.  To provide examples of its melodic use three short commentaries on British masterworks will be given.  These are the final movement from the Planets, a melody from Bax’s third symphony and the final movement of R.V. Williams’ 6^th symphony (also featured in a recent blog).

If the Banquet Celeste is taken as one of the first published works by Messiaen to use MLT then we can safely say that he was working with MLT in general in the 1920’s (Banquet Celeste uses the 8 note mode, interval pattern 1,2,1,2,1,2,1).  The Holst movement Neptune had been completed by 1916. This is not to say that this is the earliest use of MLT, the date is given as a point of interest which relates to another of our blogs concerning the voice of British music.

The first commentary is on the Williams 6^th symphony epilogue.  Having already made comments on this movement I shall immediately move to the use of the MLT.  

The opening of the movement uses two of the transpositions, sometimes sharing a note as a pivot between the modes.  

To develop the argument I have taken a later section (rehearsal mark 1) where all three versions are used and marked: those in ink red (1) , green (2) and blue (3). While the linear argument is clear the resultant harmonies are complex ranging from 5/3 triads to diminished and augmented triads and dissonant collections, all of which can be found in this short extract.

In our e-mail discussions on the British voice Nurtan commented on the Neptune movement:

The 7^th movement of The Planets by Gustav Holst starts out with limited application of MLT, mainly in defining chords with similar instruments (e.g. Oboe and English Horn b. 12 & 13 followed by flute & bass flute b.14 & 15) and in the woodwind family both vertically and horizontally and in both modes  (b.18-21). The seventh movement of the Planets, Neptune the mystic is played pp by the orchestra throughout the movement. At that dynamic, the texture produced by the repeated application of 211 MLT provides "pockets" of richly dissonant sounds that dissolve into the background. 

This extract uses the first MLT throughout.

The earnest application of MLT starts with 2 harps, 1^st and 2^nd violins and violas, to be joined by the celesta in b.26. With some breaks this continues until b 31. This treatment recurs regularly throughout the Neptune movement. Even in this short passage of music there is sufficient evidence to confirm the use of the MLT within highly dramatic passages.

The question is bound to arise that even if we change the starting pitches, the MLT only based on 211 interval relationship would be of limited use. In fact there are criticisms of the use of recursive 9 note relationships. Fortunately, by a simple set of rules, the MLT can be extended to a very large number of configurations of the initial interval structure, and this extension would provide a rich resource for melodic invention.

 The statement “the texture produced by the repeated application of 211 MLT provides "pockets" of richly dissonant sounds that dissolve into the background”, could equally well be given to the RVW epilogue.  

The third example is from the opening of Bax’s third symphony where the bassoon provides the melody.  At first the treatment seems akin to the other examples with clarinet and flute imitations of the opening theme, but where the mood of the Holst and Williams’ movements are uniform the Bax quickly moves into a rich Impressionistic landscape.  The intention is to explore this work in greater detail in a later blog, but the connection to the MLT is clear.

As Nurtan says the MLT is a rich resource and capable of extensive use for contemporary composers.

I hope this blog has also illustrated in part the range of material used by English composers who may these days be passed over as less audacious and bold.