Introduction

2.1      Messiaen’s coloured hearing     

Son-couleur

Bidirectional synaesthesia

Triads and colours

Keys and colours

Questioning Messiaen's synaesthesia

Colours in Choral de la Sainte Montagne

2.2      Michaely: modal and chordal analysis of the two chorales in La Transfiguration

2.3      Forte: Pitch-class set theory and Messiaen’s chords

Pitch-class set theory

Messiaen's chords

2.4      Beckman: Harmonic Complexity Index

2.5      Bernard: spacing of Messiaen’s chords     

Colours

Spacing

Voice leading

2.6      Neidhöfer: counterpoint, harmony and voice leading in the music of Messiaen

Conclusion

Introduction

In order to determine common approaches to the analysis of harmony and voice leading in the music of Messiaen, a search for theories, ideas, thesis and articles has been done. To my knowledge, this chapter includes the most important approaches in current literature. A short overview:

For Messiaen, the notion of son-couleur is an important way to describe his music. What could this concept contribute to our understanding of his music?

In the two chorales in La Transfiguration, Messiaen uses his modes and accords spéciaux. German musicologist Aloyse Michaely analysed these chorales.³⁷ What are the aims of a modal and chordal analysis?

The pitch-class set analysis of Forte is a well-known approach to the analysis of atonal, 12-tone and serial music. Can this theory also be useful for analysing the music of Messiaen?

Musicologist Krista Beckman developed a system to classify the complexity of Messiaen’s chords.³⁸ This system (she named it Harmonic Complexity Index) is based on a multiplication of the number of different types of intervals within a chord. In what way does an (abstract) number give information about the complexity of a chord?

In order to describe those chords which are not identified by Messiaen as 'coloured' chords, Jonathan W. Bernard, an American theorist, discusses the spacing of chords.³⁹ In what way could spacing influence the colour of a chord?

Neidhöfer, a Swiss theorist, developed a theory about Messiaen’s harmony and voice leading, focussing on Messiaen’s modal compositions. What does this theory make clear about analysing Messiaen’s harmony and voice leading?

2.1      Messiaen’s coloured hearing

Son-couleur

As mentioned by Bernard,⁴⁰ Messiaen had coloured hearing synaesthesia: son-couleur. In Technique (1944) Messiaen writes about the relationship between colour and sound for the first time. In chapter 14 in Technique⁴¹ a succession of chords in the 2^nd movement of Quatuor pour la fin du temps is described as a:⁴² “cascade douce d’accords bleu-orange (…)”.⁴³ In conversations with the French journalist Claude Samuel (1967), Messiaen explains his understanding of son-couleur:⁴⁴

“C.S.: Voyez-vous ces couleurs ou les imaginez-vous?

O.M.: Je les vois intérieurement; ce n’est pas de l’imagination, ce n’est pas non plus un phénomène physique, c’est une réalité intérieure.”⁴⁵

It is unclear what the difference between a ‘physical phenomenon’ and an ‘inward reality’ is, but for Messiaen, son-couleur seems to be an unignorable perception.

Belgian musicologist Harry Halbreich pointed out⁴⁶ in 1980 that Messiaen describes the colours of the modes in detail in Tome VII of Traité. The colours that are called the ‘dominant colours’ in Traité, were already in the book by Halbreich. For each mode, Messiaen gives a Couleur Générale as well as a progression of parallel chords (with mode 2, each chord has five different notes; with mode 3 six) that specifically correspond to the dominant colour. To show that Messiaen’s colours are his own individual perception, I asked two other musicians with coloured hearing synaesthesia to listen to Messiaen's modes and their transpositions. Both musicians are female string players and in their twenties. Examples 2.1 and 2.2 will present modes 2 and 3 with the colours. The paintings were specially made for this research by my wife Suzanne Taylor.

At Conférence de Kyoto (1985), one of the topics is son-couleur. Messiaen talks about his modes, some accords spéciaux and the way he experiences colours with sound.⁴⁷ 

In Traité, Tome VII (published in 2002) Messiaen provides lists of modes, their transpositions and colours, as well as accords spéciaux with their colours.

Bidirectional synaesthesia

It seems that Messiaen’s synaesthesia was bidirectional: sound to colour and colour to sound, something that is also mentioned by neurologist Richard Cytowic.⁴⁸

What is the reason for concluding that Messiaen’s synaesthesia was bidirectional? The colours associated with Messiaen's modes and accords spéciaux are clear, but does Messiaen also perceive sound with colour? In conversations with Samuel, Messiaen talks about the 7^th movement of Des canyons aux étoiles: Bryce Canyon et les rochers rouge-orange. For Messiaen, the general colour of the piece is expressed in the title. Samuel asks:⁴⁹

“Ce rouge primordial de Bryce Canyon, avec quel type d’harmonie ou d’instrumentation avez-vous tenté de le traduire?”⁵⁰

Messiaen’s answer is interesting:⁵¹

“Il m’est difficile de vous répondre. Je vous indiquerai néanmoins que la pièce est écrite autour du ton de mi majeur, que représente, pour moi, la couleur rouge. Mais je ne crois pas à une correspondence exacte entre telle note, telle tonalité et telle couleur.”⁵²

The only thing Messiaen mentions is the colour of the key. For a coloured hearing composer the ‘translation’ of a colour into music is possible when using compositional material that will create the required colour. In other words: if Messiaen would have wanted to create a ‘red composition’, he would have used E major chords, certain modes or specific accords spéciaux that appear red to him.

In Messiaen’s synaesthesia Jörg Jewanski,⁵³ a German guitarist and musicologist, claims that synaesthesia can only work in one direction.⁵⁴ Sean Day however, the current president of the American Synaesthesia Association, makes it clear that this is not always the case:⁵⁵

“Synästhesie verläuft in einer Richtung. (…) Es gibt jedoch ein paar seltene Fälle von Synästhesien in beiden Richtungen verlaufen, bei denen also z. B. Musik synästhetisch Farben und auch Farben synästhetisch Töne hervorrufen (…).”⁵⁶

Could Messiaen have been one of these rare examples of persons with bidirectional synaesthesia?

Triads and colours

Messiaen describes the colours of modes and accords spéciaux, but he doesn’t write much about the colours of (simple) major or minor triads. Michaely⁵⁷ made a short list of major triads mentioned by Messiaen in a conversation with organist Almut Roßler in 1983:⁵⁸

• C major: white
• E major: red
• A major: blue
• G major: yellow
• F♯ major: all different colours (as the equivalent of C major)

It is interesting that only these specific major triads are mentioned by Messiaen.  Are these the only triads that generate colour for Messiaen?

In some cases, Messiaen divides more complex chords into different sections and connects separate colours to each of these sections. Table 2.1 shows both the modes and accords spéciaux as well as the way in which Messiaen connects colours to sections of these chords. If those separate sections are (major or minor) triads, one could perhaps see what colours are connected. Musicologist Stefan Keym attempted to discover which colours are connected to every one of the major triads that are part of Messiaen’s accords spéciaux.⁵⁹ The result is not entirely convincing, however, since with certain triads there is still some small variation in colour, perhaps due to the fact that those triads are only part of a bigger constellation. Pianist Håkon Austbø made a list of the colours associated with Messiaen’s major and minor triads.⁶⁰ Table 2.2 shows Messiaen’s colours of the major triads according to Keym and Austbø. The colours that match exactly, appear in bold. In general, Keym's and Austbø's interpretations of Messiaen's colours tend to correspond.

Keys and colours

Kenneth Peacock, a Canadian composer and pianist, describes Scriabin’s coloured hearing⁶¹ and compares the relationships between the keys and colours of Alexander Scriabin with those of Nikolai Rimsky-Korsakov. While certain similarities could be seen, the majority of the colours were totally different.⁶² Messiaen himself didn’t mention the relationships between keys and colour at all. The following exchange is documented in his conversations with Samuel:⁶³

“C. S.: – Quelle est la tonalité que se marie le mieux avec le violet?

O.M.: – A vrai dire, on ne peut pas parler de correspondence exacte entre une tonalité et une couleur; ce serait une façon un peu naïve de s’exprimer parce que, je le répéte, les couleurs sont complexes et sont liées à des accords et à des sonorités également complexes.”⁶⁴

When Messiaen writes about tonality, it is in connection to his modes, not to colours.

Questioning Messiaen’s synaesthesia

Many questions could be asked about the synaesthesia of Messiaen. Above all, Messiaen’s coloured hearing is a very personal perception. When Messiaen writes about his first experiences with son-couleur,⁶⁵ he concludes by saying:⁶⁶

“Tout ces exemples m’ont fortifié dans ma recherche du son-couleur.”⁶⁷

Why does Messiaen talk about a ‘search’ for son-couleur? A person with coloured hearing synaesthesia does not search for a connection between sound and colour, it is a permanent and constant experience. Messiaen also wrote the following about his synaesthesia:⁶⁸

“Existe-il des synoptiques? Tous les hommes et toutes les femmes sont-ils synoptiques? Je pense qu’on peut répondre oui sur tout la ligne. En ajoutant qu’il s’agit (pour l’heure) d’un rapport mal contrôlé, variable suivant les individus, et entièrement subjectif.”⁶⁹

In conversations with Rößler:⁷⁰

“Ich glaube, daß die meisten Menschen eine Art sechsten Sinn haben und die Beziehung Klang – Farbe empfinden, nur ist es ihnen nicht bewußt und verständlig. Sie müssen ja auch gar nicht die gleichen Farben sehen wie ich.”⁷¹

If we as listeners don’t have to see the same colours as Messiaen, then why does he consider them to be so important? British pianist and writer Peter Hill made the following point in an interview (Video 2.1) with the London Philharmonia:⁷²

“When we talk about colour in music in a rather loose kind of way, and we talk about it in all music, but with Messiaen it was different: he actually really did, as it were, see these colours when he heard musical sounds, and in a way that's a sort of difficulty with Messiaen’s music, because [what] one feels here is a whole kind of private world that we can’t have access to, because we don’t have Messiaen’s private colour-language.”

Bernard asks “why we should be interested in Messiaen’s synaesthetic responses”;⁷³ Robert Johnson says the following on the topic: “the whole question of colour association, of course, is a highly personal affair.”⁷⁴ Messiaen’s students have already made it clear that it is difficult to understand his ‘private world’. Messiaen makes the following statement in an interview with Rößler:⁷⁵

“O.M.: (…) ich habe diese Leidenschaft für die Beziehung Ton – Farbe (“son-couleur”), von der ich schon so viel gesprochen habe und niemand verstanden hat, und ich glaube, ich bin der einzige in meiner Epoche, der sich dafür interessiert. Ich habe oft in meiner Klasse den Schülern Akkorde vorgespielt und sie gefragt: “Welche Farbe ist das?” – sie haben überhaupt nichts gesehen, oder sie sahen etwas, um mich zu erfreuen.”⁷⁶

How does Messiaen know that his students are not able to see colours at all? And if they did mention some colours, it is almost impossible that these were exactly the same as Messiaen’s.

Conversely, it’s not even entirely sure that Messiaen had synaesthesia at all. In an interview with Dutch pianist and conductor Reinbert de Leeuw⁷⁷ Messiaen gives the following answer (Video 2.2) to a question on whether “both chorales in La Transfiguration are in E major”:⁷⁸

“(…), et je voyais exactement des couleurs correspondant aux complexes de sons. Et c’étaient toujours les mêmes couleurs. Le même complexe de sons faisait toujours la même couleur. Alors ça m’a intéressé beaucoup, j’ai moi-même écrit ce que je voyais intérieurement, je me suis fait un petit dictionnaire auquel je me reporte quand je travaille, pour être sûr de ne pas me tromper. Parce que j’avais beaucoup de mal à savoir ce que je voyais, ce que je sentais intérieurement. J’étais mon propre médecin, n’est-ce pas, c’était très difficile.”⁷⁹

A person with colour-sound synaesthesia could hardly understand the last part of this quote: when experiencing a particular colour-sound relation, there’s no way to make a mistake: it will always be the same colour-sound relation.⁸⁰ Dutch organist Peter Ouwerkerk has also doubts about Messiaen’s synaesthesia⁸¹ and refers to his French colleague Thomas Lacôte who questions Messiaen’s coloured hearing too.⁸² Through connecting colour to sound, Lacôte thinks Messiaen has created a way to describe his harmonies.

If some elements of Messiaen’s son-couleur are doubtful, how does this influence one’s evaluation of his texts on the subject? Are Messiaen’s observations ‘true’? To a person with synaesthesia, such observations are unquestionable – there is no other observation possible since it is a permanent and constant phenomenon. However, Messiaen realises that his son-couleur is a very personal observation, as mentioned earlier. Is it possible that Messiaen repeatedly mentions his sound-coloured synaesthesia simply because he is interested in coloured hearing? Or is it – as Lacôte states – a way to describe his extraordinary harmonies?

Colours in Choral de la Sainte Montagne

In Musique et couleur Messiaen mentions the colours of the chords in the two chorales in La Transfiguration:⁸³

“Les couleurs étant ici très nettes, à cause du mouvement très lent (…)”.⁸⁴

In an interview with Samuel⁸⁵ (1986) and in Traité, Tome VII⁸⁶ (2002), Messiaen gives a detailed chord-by-chord colour analysis of Chorale de la Sainte Montagne. The 2^nd chorale in La Transfiguration, Choral de la Lumière de Gloire is not analysed by Messiaen, but is mentioned in his analysis of La Transfiguration in Musique et couleur:⁸⁷

“(…) C’est un long tutti du choeur et de l’orchestre, extrêmement lent, et fortissimo. Il comporte de nombreux changements de couleurs d’accords.”⁸⁸

Example 2.3 shows my reduction of Choral de la Sainte Montagne; Example 2.4 is this reduction and the translation of Messiaen’s colours. Those colours show varying degrees of complexity: the E major triad is simply ‘red’; a chord with higher complexity also shows a complex or combinations of colours.  Some remarks:

• simple (consonant) chords have a simple, mostly single colour
• more complex chords (with a higher cardinality) have a more complex colour
• repeated chords have the same colour and are not mentioned by Messiaen again, except for when the intensity of the colour changes

To prove that Messiaen’s perception of these colours is entirely subjective, the two other musicians with coloured hearing synaesthesia made their colour analysis of Chorale de Sainte Montagne. The results are shown in Example 2.5: the colours are shown in my translation from the original Dutch. Video-fragments 2.3-2.5 present Choral de la Sainte Montagne with Messiaen's colours and the colours of the two other musicians with synaesthesia. The paintings in the videos were specially made for this research by Suzanne Taylor.

The paintings shown in the videos are certainly not precisely those colours perceived by the synaesthetes: they are instead an interpretation by the painter of the colours described by the synaesthetes – one could imagine that a colour expressed in words could mean slightly different colours for different people. A direct translation of the colours described by a synaesthete is impossible because the colours themselves exist only in the minds of persons with synaesthesia.

As one can see, the colours per chord differ for each analysis. Some examples:

• chord 4: Messiaen, red; person 1, green; person 2, blue. Person 1 is not entirely consistent with the colour for this chord: when it returns (nos. 34 and 35), the colour is described as orange, probably because of the register
• more complex chords have – with all three analyses – a more complex colour, or a combination of different colours

Messiaen is consistent in his colour analysis: repeated chords are always described as having the same colour. The 2^nd analyst is not always consistent: repeated chords are sometimes described as being slightly different in colour. The last musician explained that repeated chords could be different in colour because of the context: a chord with a certain colour could influence the colour of the next chord and could possibly change the colour. This makes it clear that the process could work differently for each individual.

In order to compare Messiaen’s colour analysis with other coloured hearing synesthetes and to draw conclusions from it, a more extensive study should be done. This is beyond the scope of this research.

2.2     Michaely: modal and chordal analysis of the two chorales in La Transfiguration

In the two chorales in La Transfiguration, Messiaen uses his modes and accords spéciaux. Michaely describes those chorales as:⁸⁹

“Modal-tonaler Satz (Mode 3; E-dur), angereichert (vor allem im umfangreicheren XIV. Satz) mit accords spéciaux.”⁹⁰

He continues with his analysis of Choral de Sainte Montagne:⁹¹

“Der tonikale E-Dur-Dreiklang erscheint dreizehnmal (…). Driemal klinkt der tritonische Komplementärfarbe B-dur: immer mit hinzugefügten Tönen (…); einmal (…) der subdominantische A-Dur-Akkord mit sixte ajoutée.”⁹²

Michaely doesn’t explain his ideas on the chorale as a ‘Modal-tonaler Satz’, but suggests a mix of modality (Messiaen’s modes) and tonality. His qualification of the E major chord being a ‘tonikaler Dreiklang’ and the A major as ‘subdominantisch’, confirms this way of thinking.⁹³ A question could be: where is the ‘dominant’ in Michaely’s analysis? In Messiaen’s own analysis of the chorale there’s no clear indication that he considers E major to be the main tonality. However, he does at one point name ‘Mi’ as the tonic:⁹⁴

“cluster fait de toutes les notes du mode 3¹, (…) avec doublure du Mi (tonique) (…).”⁹⁵

Messiaen writes about the last chord in bar 23, a 12 tone chord:⁹⁶

“Le troisième accord contient Si, La, Ré diése: ces 3 notes appartiennent à la septième de dominante de Mi majeur, et le Ré dièse est la « sensible » de Mi majeur.”⁹⁷

Example 2.6 shows this 12 tone chord with resolution (chord nos. 42 and 43 in my reduction of Choral de la Sainte Montagne). It is remarkable that Messiaen analyses chord no. 42 as a dominant 7 chord and ignores the bass line (which has a C that is not part of the dominant 7 chord) in this analysis, although he wrote about the bassline moving chromatically in downwards motion.⁹⁸ In this quote Messiaen suggests that E major is the tonic by using the terms ‘dominante’ and ‘sensible’ ‘de Mi-majeur’, although he doesn’t explicitly qualify the E major chords as tonic in his analysis. However, each E major chord is described⁹⁹ as “rouge”.¹⁰⁰

The 12-tone chord in bar 23 is analysed by Messiaen as a dominant 7-chord on B: he doesn’t even mention that this chord is a 12-tone chord. Michaely analyses this chord as being part of mode 2³ finally becoming a full 12-tone chord because of the 4 added notes. Michaely names¹⁰¹ these notes ‘Komplementärtöne’¹⁰² and explains this as:¹⁰³

“zu den vielstimmigen “accords spéciaux” – aber auch zu den modalen Klängen – treten regelmäßig (als untere und/oder obere Resonanz) ihre Komplementärtöne (= Komplementärfarben) (…).”¹⁰⁴

Messiaen writes in Technique about his modes:¹⁰⁵

“(…) mélodie et harmonies ne sortant jamais des notes du mode.”¹⁰⁶

This suggests that – when using a mode – Messiaen does not allow himself to use ‘non-mode-tones’ either melodically or harmonically. Michealy deviates from this by using ‘Komplementärtöne’ in his analysis: he analyses a chord as being modal with added non-modal notes. Messiaen does add notes to chords to create his accords à resonance contractée and accord du total chromatique,¹⁰⁷ but does not identify those chords as modal chords with non-modal added notes.¹⁰⁸ The full 12-tone chord in Choral de la Sainte Montange could probably be described as one of Messiaen’s accord de total chromatique, but this chord is not part of the list that Messiaen provides in Traité.¹⁰⁹

In Messiaen’s own analysis of Choral de la Sainte Montagne, he analyses all accords spéciaux as well as certain modes. ¹¹⁰ Michaely has also made a detailed analysis of the modes and chord types in the two chorales.¹¹¹ Table 2.3 shows the analysis of the modes and accords spéciaux in Choral de la Sainte Montagne by both Messiaen and Michaely.

In general, Messiaen’s and Michaely’s analyses are similar. Some differences:

• the first two chords (also appearing in bars 1, 4, 9 and 21) are in mode 3³, according to Michaely; Messiaen does not connect a mode to these chords
• Michealy’s numbering of the accord tournant is different: the type that is numbered ‘No. 4’ according to Messiaen is ‘II’ in the analysis of Michealy¹¹²
• Messiaen’s analysis of bars 6, 8 and 25-26 is mode 2²; Michealy analyses the E major chord not being part of a mode¹¹³

How to explain the differences between the two analyses? Some ideas:

• perhaps the first two chords have characteristics for Messiaen that are more important than a modal analysis: in his analysis in Traité he describes these chords as being a two-layer chord – F♯ minor and F minor (with their corresponding colours)
• the different numbering of the accord tournant could be explained by the fact that the numbering of Messiaen was published later than the work of Michaely
• in contrast to the analysis of the first two chords, the E major chord is analysed modally by Messiaen; Michaely analysed this chord simply as an E major chord without any connection to a mode

In chapter XVI of Technique, the Modes à transpositions limitées are discussed by Messiaen:¹¹⁴

“Tous les “modes à transpositions limitées” peuvent être utilisés mélodiquement – et surtout harmoniquement, mélodie et harmonies ne sortant jamais des notes du mode. Nous parlions (…) du charme des impossibilités: leur impossibilité de transposition fait leur charme étrange. Ils sont dans l’atmosphère de plusieurs tonalités à la fois, sans polytonalité – le compositeur étant libre de donner la prédominance à l’une des tonalités, ou de laisser l’impression tonale flottante.”¹¹⁵

Messiaen uses his modes both as ‘a source’ for creating melodies, but primarily for creating harmonies. How important is a modal analysis to the understanding of Messiaen’s music? What does the identification of accords spéciaux contribute to an analysis? Perhaps an analysis which identifies the mode and the accords spéciaux makes clear the ‘ingredients’ used by the composer, but what does it actually tell us?

2.3      Forte: Pitch-class set theory and Messiaen’s chords

Pitch-class set theory

The pitch-class set theory of Forte is a theory developed for analysing atonal music.¹¹⁶ In his article Messiaen’s chords, Forte writes:¹¹⁷

“(…) I have used pitch-class set-class labels (…) in order to reveal certain regularities perhaps otherwise not evident.”

Forte’s pitch-class sets¹¹⁸ are also used by theorists Wai Ling Cheong, Bernard and Neidhöfer as an approach to the music of Messiaen and are mainly used by theorists outside of Europe. Dutch musicologist Michiel Schuijer refers to a session during a European conference on analysis where a ‘clash’ between the American and European traditions of analysis became clear when an American visitor asks:¹¹⁹

“You guys are discussing methods of analyzing twentieth-century music. Why don’t you talk about pitch-class sets?”

The chairman from Sorbonne answered:

“We do not talk about pitch-class sets, because we do not hear them!”

Whether one 'hears' pitch-class sets or not, pitch-class set theory is frequently used as an approach to Messiaen’s music. To make clear how an analysis with Forte’s pitch-class sets works, a full Forte-analysis of Choral de la Sainte Montagne chorales is given in Table 2.4; Table 2.5 shows this analysis of Choral de la Lumière de Gloire. Example 2.7 shows the reduction of Choral de la Lumiere de Gloire.

Some remarks:

• with Forte numbers, the cardinality of each chord is made clear easily
• chords with the same pitch classes have the same Forte number, although they could be in a different position (or renversement according to Messiaen)
• strict transpositions of a chord will create similar Forte numbers
• dividing Messiaen’s chords in subsets clarifies when a chord consists of two or three different chords: by dividing chords in subsets, some preferences for certain sets could be made clear

Messiaen’s chords

In the article Messiaen’s chords¹²⁰ Forte discusses certain aspects of Messiaen’s chords. Forte analyses Messiaen’s chords with pitch-class set numbers including subsets, intervallic equivalence and pitch-class equivalence. Forte also searches for voice leading patterns. Discussing the opening bars of Les Mains de l’abîme from Livre d’orgue, Forte uses pitch-class set numbers, but concludes with:¹²¹

“I do not believe that Messiaen actually constructed these chords following the traditional Rameauian root-oriented formulae, but simply described the chords using a symbolism that would have been understood by his students, following the venerable traditions of the Paris Conservatoire. Nor do I believe that he constructed his chords with pitch-class sets in mind! But I do feel that consideration of voice-leading patterns, subsets and overall sonority came directly from his compositional improvisations and his intuitive musicianship. Moreover, his writings – especially in the Traité – substantiate this conviction.”

This quote makes clear that Forte doesn’t only use his pitch-class sets to approach Messiaen’s harmony. However, no further explanation of the other observations is given by Forte, although they are most valuable.

Another progression of chords discussed by Forte is the succession of 29 chords from Liturgie de cristal. Forte analyses pitch-class sets, modes and octatonic sets but also common-note connections:¹²²

“Further consideration of common-note connections between successive      chords offer yet another view of voice-leading (…).”

Dividing chords in subsets is a meaningful approach since Messiaen also divides the chords in two or three different sections. Forte argued that dividing non-modal chords into subsets could be useful if the subsets are part of the Messiaen modes:

“(…) subsets that are members of one of the distinctive modes. In such instances one could say that the parts are greater than the whole.”

2.4       Beckman: Harmonic Complexity Index (HCI)

Beckman developed a method for analysing the complexity of the harmonies of Messiaen: the ‘Harmonic Complexity Index’ (HCI) as explained in her article on the analysis of three early works of Messiaen.¹²³ This index is based on the interval class vector (ic-vector) of a set. The ic-vector is also part of the pitch class set theory of Forte. The interval classes used in the pitch-class set theory are:

1 (m2), 2 (M2), 3 (m3), 4 (M3), 5 (p4), 6 (A4).

The ic-vector also uses this order of intervals. Beckman ‘ranks’ these intervals and multiplies each member of the ic-vector the ‘ranking-number’. Table 2.6 shows the ranking of the intervals.

Taking the normal appearance of intervals within the ic-vector, the multiplication number is 532214. Thus, ic1 is multiplied by 5, ic2 by 3, ic3 and ic4 by 2, ic5 by 1, ic 6 by 4.

Beckman says the following about this ‘ranking’: ¹²⁴

“the factors of the {532214} formula have been determined broadly from commonly accepted tonal categorizations of consonant and dissonant intervals, which have their own origins in the harmonic series. (…) More specifically, the HCI factors break down as follows, from least to most dissonant: ic5(1), ic3 and ic4 (2), ic2 (3), ic6 (4) and ic1(5).”

It is unclear from what sources Beckman concludes that it is a ‘commonly accepted’ categorisation of intervals. However, one could agree this ranking is – in general – an acceptable categorisation of the given intervals from consonant to most dissonant, from a (general) tonal perspective.¹²⁵

After multiplying each ic-vector member with the correct number of the formula, the sum is the HCI. Examples of calculating the HCI are shown in Table 2.7. What is the result of calculating the HCI? Since the HCI is based on the ic-vector, the HCI is closely related to the cardinality: a higher cardinality number means a high number of different pitch-classes that results in a higher number of different interval-classes. To show this relation, Table 2.8 presents a Forte analysis with HCI of Choral de la Sainte Montagne; Figure 2.1 shows the cardinality and HCI in a graph. Comparing the diagram of the cardinality and the HCI, one sees they are quite similar, although the HCI differentiates between chords of the same cardinality: chords nos. 8-10, 16-18, 20-24, 30-33, 49-50 have the same cardinality but a different ic-vector which results in a slightly different HCI.

2.5      Bernard: spacing of Messiaen’s chords            

Colours

In his article on Messiaen’s synaesthesia, Bernard writes about the colours of Messiaen’s modes. Bernard points out the following issues:¹²⁶

“However, there are certain inherent limits upon both the scope and precision of the information provided by pc-set identity.”

Those limitations are:

• Messiaen’s modes have several subsets in common (those subsets could have different colours because they belong to different modes)
• for Messiaen, the colour of a chord changes when transposed (in connection to his modes)

The limitations of the pitch-class set analysis in connection to Messiaen’s chords are important and address a problem that is – unfortunately – hardly mentioned.

Bernard writes about spacing being “an important factor in drawing distinctions between colors” and analyses the “vertically adjacent interval content, expressed in numbers of semitones.”¹²⁷

Spacing

Bernard searches for other elements that could influence the colours of a chord. For some fragments, Messiaen doesn’t use a mode or accords spéciaux, but is indicating a colour. In these cases, Bernard analyses the spacing of chords by giving numbers which indicate the number of semitones between the successive notes. In a limited number of fragments from Messiaen’s piano repertoire, he finds certain chords – as part of a mode – that are frequently used with a certain spacing. The way Bernard analyses spacing is by using numbers of semitones for each of the intervals. He mentions 4-Z29 as being used with the 9,2,6,6-spacing (in semitones from bottom to top); 5-25 in 7,3,6,5-spacing. These two pitch-class sets are also used in Messiaen’s chorales, but show completely different spacing.

Bernard concludes that connecting pitch-class set to colour could be difficult because different spacings of the same set may create a different colour; two different sets may ‘by virtue of superimposition’¹²⁸ be connected to the same colour. This conclusion completely disregards the notion of the transposition of sets: for Messiaen a complex of notes belongs to a certain colour – a transposition of the same complex creates a totally different colour. Another element not mentioned by Bernard is the connection with the keyboard: one could imagine that the spacing of chords could be guided by the physical element of the hands at the keyboard, in particular with the piano and organ repertoire. When playing Messiaen’s music for piano and organ, the physical connection between the hands and the keyboard seems very strong. On paper, chords may look complicated but while playing, one feels that they ‘are composed at the keyboard’. An analysis of the spacing of Messiaen chords by using numbers to indicate the distance between consecutive notes could make clear preferences in spacing of chords from the same set, but also adds another ‘abstract’ piece of data to a pitch class set analysis, while leaving out the physical aspect of chord spacing.

Voice leading

Bernard says the following on the subject of voice leading:

“By and large this is entirely ancillary to color definition; much more important are the qualities of the individual chords.” ¹²⁹

For Bernard, aspects of voice leading are less important than Messiaen’s colours or ‘qualities’ of chords, although it is unclear what Bernard means by these qualities. However, he analysed examples which use chords in a series and concludes that “the voice leading simply corresponds to the scalar order of the mode.”¹³⁰

2.6      Neidhöfer: counterpoint, harmony and voice leading in the music of Messiaen

The literature on Messiaen often avoids the aspect of voice leading and counterpoint. Michaely analysed aspects of voice leading in Messiaen’s chord progressions using accords tournants and discovered that all voices either move by small intervals, stay on the same pitch or move in parallel motion with the other voices.¹³¹ Neidhöfer is the only scholar addressing this topic extensively in his writings. In his article on harmony and voice leading, Neidhöfer focuses on ‘voice-leading patterns and harmonic materials commonly found in Messiaen’s music, paying particular attention to multi-voiced note-against-note textures’.¹³² In part II of his article,¹³³ Neidhöfer discusses ‘contrapuntal patterns and their harmonic implications’ and distinguishes between:

• parallel voice leading (progressions of chords which move parallel within the mode)
• canonic voice leading and harmonic sequences (a set of voices which makes a canon based on step classes¹³⁴ which may create a harmonic sequence)
• inverted and double counterpoint (invertible counterpoint in the traditional way; with double counterpoint Neidhöfer means that both lines are shifted in an inward or outward direction – after the shift, both lines still have the same relationship: upper and lower line)

The fragments discussed by Neidhöfer are all based on Messiaen’s modes and are from either Technique or early piano (and voice) repertoire.¹³⁵ All fragments have a clear (mostly four-part) texture, related to the 'note-against-note' textures mentioned by Neidhöfer. Some fragments use sequences and subsequently create (repetitive) patterns of voice leading. Since the examples are all composed for piano, a connection with the playability at the keyboard could be seen. However, Neidhöfer does not mention any connection to this physical aspect. In his article on Messiaen’s counterpoint,¹³⁶ Neidhöfer emphasises Messiaen’s skill in improvising:¹³⁷

“Given Messiaen’s improvisation skills, we can easily imagine him developing modal harmonic progressions and contrapuntal passages (…) through improvisation”

The examples cited in this article are from Messiaen’s entire oeuvre.¹³⁸  Essentially, Neidhöfer discusses the same ‘voice leading patterns in note-against-note’ settings¹³⁹ as in his first article, although he develops some new ideas on:¹⁴⁰

• vertical shifting counterpoint (the vertical distance between blocks of chords is changed)
• rotational array (a series is repeated in different transpositions in different voices)
• counterpoint and contrapuntal transformation (divided into five different principles: 1. a string of parallel chords is attached to a contrapuntal combination; 2. layers are superimposed on different types of texture; 3. chord progressions are constructed from intricate voice leading patterns; 4. different contrapuntal techniques are applied to certain passages; 5. contrapuntal patterns are expanded into larger groups)

Neidhöfer finishes this article with the comment that:¹⁴¹

“Most of these techniques go back to traditional contrapuntal concepts. But rejecting a more literal, neoclassical use of historical contrapuntal models, Messiaen takes their principles and applies them in new ways, transforming counterpoint into something distinctively his own.”

Conclusion

Existing analytical approaches of Messiaen’s harmony and voice leading are very much focused on the vertical aspect of the chords: Messiaen’s son-couleur, analysing modes and accords spéciaux, using pitch-class sets, the harmonic complexity index and describing the spacing of chords. This could potentially be explained by the fact that Messiaen’s own focus is primarily on the vertical aspects. Forte and Bernard write about certain voice leading features of the music of Messiaen, but both show a primarily vertical approach. Forte emphasises the importance of voice leading, but only considered the existence of a common tone between consecutive chords to be important to voice leading.

Neidhöfer’s approach is more horizontal: he discusses certain voice leading patterns in Messiaen’s music using the modes. However, these patterns are primarily found in homorhythmic excerpts in piano repertoire with the use of sequential harmonies. Those multi-voiced situations use a strict number of voices.

Sub question 2: In which ways have Messiaen's harmony and voice leading been analysed over the past decades?

Table 2.8: Analysis Choral de la Sainte Montagne with pitch-class sets and HCI

Table 2.6: HCI formula connected to ic-vector

Video 2.5: E.R.'s colours in Choral de la Sainte Montagne.

Painted by Suzanne Taylor. Recording: La Transfiguration de Notre Seigneur Jésus-Christ, Choeur de Radio France, Orchestre Philharmonique de Radio France, Myung-Whun Chung. Deutsche Grammophon, 2001.

Table 2.7: examples of calculating the HCI

Figure 2.1: Choral de la Sainte Montagne: cardinality and HCI

Video 2.1: Philharmonia Orchestra (London, UK):

Olivier Messiaen 1908-1992: Messiaen and Synaesthesia.

https://www.youtube.com/watch?v=qM4WvF_PikI

Video 2.4: LvR's colours in Choral de la Sainte Montagne

Painted by Suzanne Taylor. Recording: La Transfiguration de Notre Seigneur Jésus-Christ, Choeur de Radio France, Orchestre Philharmonique de Radio France, Myung-Whun Chung. Deutsche Grammophon, 2001.

Video 2.2: Reinbert de Leeuw and Cherry Duyns:

Toonmeesters, Messiaen.

VPRO - VD 13138. 0:25:23-0:25:53

Video 2.3: Messiaen's colours in Choral de la Sainte Montagne.

Colours after Messiaen's analysis in Traité, Tome VII, painted by Suzanne Taylor. Recording: La Transfiguration de Notre Seigneur Jésus-Christ, Choeur de Radio France, Orchestre Philharmonique de Radio France, Myung-Whun Chung. Deutsche Grammophon, 2001.

Example 2.2: Messiaen's mode 3 with colours. Paintings by Suzanne Taylor.

Table 2.1: modes, accords spéciaux and colours per section

Table 2.2: Messiaen’s colours of major triads, Keym and Austbø

Table 2.3: Messiaen and Michealy: modes and accords spéciaux in Choral de la Sainte Montagne

Example 2.1: Messiaen's mode 2 with colours

Example 2.6: chord nos. 42-43, Choral de la Sainte Montagne

Example 2.3: Reduction Choral de la Sainte Montagne

Example 2.7: reduction Choral de la Lumière de Gloire