Probably no other country in the world has undergone a more profound metamorphosis in the twentieth-century than Japan. Despite the current massive influx of Western influences at every level, however, Japanese society for the most part remains uniquely 'Japanese.' In the world of contemporary music this same quality of 'Japaneseness' is often attributed to the work of Toru Takemitsu. This paper identifies particular influences of the Togaku tradition of Japanese Gagaku in several of Takemitsu's works in order to give a clearer idea of just what might be said to be 'Japanese' about his music.
The chords produced by the sho, the only traditional Japanese instrument capable of producing all nine notes of the Togaku system, are the basis for my study and are shown to be a possible source of inspiration for many facets of Takemitsu's own harmonic language and process.
Specifically, this analysis will discuss:
1) various points of contact between certain aspects of Takemitsu's musical language and that of Togaku
2) the special treatment of register in Takemitsu's harmonies in ways that highlight Togaku harmonies.
3) the frequent occurrence in Takemitsu's music of harmonic and melodic material pitch-identical to harmonic and scalar features of the sho.
My discussion will refer to passages from Garden Rain, A flock descends into the pentagonal garden, November Steps, and other works, as well as to my unpublished translation of passages from Takemitsu's book, Yume to Kasu (Dream and Number).
A native of Wisconsin, Steven Nuss received his Bachelors and Masters degrees from the University of Wisconsin at Madison. From 1985-90 he was on the faculty of the Seishin International School and University and was a conducting fellow of the Aspen Music Festival. Mr. Nuss is currently teaching at Queens College and is a Gilleece Fellow in the doctoral program in music theory at the Graduate Center of the City University of New York where his principal areas of research are atonal theory and the traditional and contemporary music of Japan.
Because this presentation will deal a great amount with the terms gagaku and sho, I need to play some examples of gagaki music and the particular sounds of the sho. The sho is a traditional Japanese harmonic instrument - as mentioned in a previous presentation. It is a mouth organ which produces different complex chords. I have three short examples to play to set a frame of reference for what I'll be talking about. The first example is of the sho playing alone. It is essentially playing an excerpt from the gagaku composition Zengatsu - probably the most famous gagaku composition. I was also reminded very strongly when Matsuo-san's piece for shakuhachi and organ (first movement) was played - the organ sonorities reminded me very much of the sho.
TAPE - sho alone
The crescendo-decrescendo is a normal part of the performance practice. This instrument has the unique quality of producing sound whether the player is exhaling or inhaling.
The second example is the complex chord progression that the sho just played, in the context of the whole gagaku orchestra - just the short opening. We hear the normal introduction for percussion and fue (Japanese flute), and then the entire ensemble comes in, including the sho.
TAPE - gagaku excerpt
The sho provides harmonic background to these melodic lines. The third example is a piece by Takemitsu which first got me thinking of this music in the way that I will talk about - the piece is Garden Rain for brass ensemble. I think just on the superficial level you can hear the connections in styles and approach in this particular piece.
TAPE - Garden Rain excerpt
Again, this collection of complex chords I think are very similar to the sho itself.
Toru Takemitsu is without question one of the foremost modern Japanese composers. His compositions are widely performed throughout the world and have come to be increasingly popular subjects for musical analysis. Scholarly attempts at describing structure in Takemitsu's music, however, have been almost exclusively based on Western conceptual models. This talk will examine Takemitsu's music with an approach that combines elements of traditional Japanese music theory with twentieth-century set theoretical techniques and original analytical methods in order to present a view of this music that does not ignore its cultural origins. I will demonstrate that elements of Takemitsu's musical language have certain striking similarities to the musical tradition of gagaku, the ancient court music of Japan. Harmonies of gagaku are performed by the sho, the only harmonic instrument used in traditional Japanese music. This ancient brand of mouth organ produces eleven chords, which I will use as a basis for discussion of various aspects of Takemitsu's music. I will demonstrate that a high percentage of Takemitsu's harmonic structures, as well as their voicings within the musical texture, have parallels in the sho chords. In addition, the exploration and development of these relationships will demonstrate the logic and consistency of Takemitsu's compositional choices within an analytical framework derived from Japanese models.
I will begin by discussing the harmonies of the sho in detail and discuss how they relate directly and through various derived applications of Takemitsu's own harmonic language. The sho chords, along with their Japanese names, are shown on the handout as Example 1. Each of these chords contains five or six pitches with varying degrees of internal doubling. For those conversant in set theoretical jargon, below each chord I've also given numerical labels commonly used in current pitch class set theory, and the prime form for each of the sho set classes. For those unfamiliar with this type of numerical representation, each set number simply represents unique intervallic collections, and thus unique sounds. In the same way that a dominant seventh or augmented sixth label operates in tonal music, set class numbers work in the same way by labelling the particular sound of the chord, regardless of inversion, which occurs in a non-tonal setting where major and minor labels are no longer analytically applicable. Thus, we can think of each unique set number as a particular sound type - the 5-25 sound, or the 4-23 sound. The 5-35 sound, which appears four times in the sho chords, represents a harmonic presentation of the pentatonic scale. I'll also frequently use the term pitch class, which is a general term that disregards range, and identifies only the particular spelling of a pitch - pitch class C, for example, refers to all C's in any range.
These sho harmonies are pitch specific. These chords and their respective voicings cannot be transposed or inverted in gagaku practice. Because of this static arrangement, I've taken the liberty of breaking each of them up into what I will term boundary partitions. By a boundary partition, I mean a division of a chord into smaller segments of equal size. These smaller segments each, in turn, again identifiable by unique set class memberships and thus unique sound quality, are formed by counting successive unique pitch classes from both the highest and lowest note of the chord. Thus, each sho harmony will be regarded as consisting of two intersecting harmonies, upper and lower, in the same way that we might view a dominant seventh chord in simple position as a union of an upper diminished triad and a lower major triad, for example. Example 2 shows this concept of boundary partition applied to the chord ku, a member of set class 6-25. Because of its size of six pitches, the chord can be partitioned into two trichords, two tetrachords, or two pentachords. The example shows the partition process for tetrachords. The upper tetrachord partition of ku comprises B-A-G#-E - that is, four unique successive pitch classes down from B, yielding a sonority labeled 4-14. By the same logic, the lower tetrachordal partition of ku comprises C#-D-E and G# - four successive pitch classes counting up from the lower boundary pitch, resulting in a different sound quality - namely that of set class 4-29. And so these sho chords can also be viewed as the union of these two tetrachordal partitions.
What I'm proposing is that each of the sho chords be viewed then not as a single entity, but a composite of smaller harmonic units each having their own personality and, as I will show, their own role in Takemitsu's music. This is a view not at all out of keeping with many facets of theory and practice in all genres of Japanese traditional music. It also is very striking that quite often Takemitsu, in his compositions, will divide the performing body into two groups in which these sho harmonies, I believe, are split up - he'll put half of a chord here and half of a chord there and the chords are used not as a unified texture, but are indeed split up in this partitioned way. All upper partitions for any chord will be referred to here as an alpha partition - the lower partition will be called a beta partition. In this presentation, I place special emphasis on trichordal and tetrachordal partitions.
If you look at Example 3, it is a sort of extraordinary table showing the results of applying this idea of partitioning to all the sho harmonies. Each resultant set class is again shown with its prime form below. Row W contains the eleven sho harmonies. Row X shows tetrachordal partitioning, and Row Z shows pentachordal partitioning. As mentioned, the set class numbers refer to particular sound qualities, and thus each sho chord is expressed in this chart as a union of two separate harmonies. It must be added that while the sho chords can be partitioned in Example 3, they represent pitch specific entities - that is, they are played on those notes and no other. It is the individual set classes and their sound qualities in their abstract forms, as derived from this partitioning, that are of interest at this point in my analysis. To use a tonal analogy, I'm concerned with the particular sound, for example, of a major triad - not the fact that it's a C major triad, or an F major triad. I'm concerned with the sonority "major." In the case of the sho chords, I'm concerned with the sonority of 4-23 or the sonority of 4-22.
The table of partitions for the sho harmonies reveals a family of related set classes, so not only are we talking about just the sho chords, but we are talking about smaller groups - these subsets of sho chords. I will use these as a basis for comparison with Takemitsu's own harmonic language. Any of the individual sets on this chart, and their alpha and beta partitions, can be employed in a transposed and/or inverted form without losing their identity as sho partitions or chords. In Example 4, I have given a reduced list of sho partitions by pulling out those that occur most frequently in Example 3. The examples which follow will demonstrate Takemitsu's particular preference for these set classes and sonorities. For ease of reference, I will use three chord categories to refer to the sho chords and partitions. By Category 1, I refer to the minimal sho harmonies - what the sho actually plays. Category 2 will contain the most frequent partitions for the sho chords which are in Example 4, and Category 3 are the less frequent partitions - those that don't make it into Category 1 or Category 2, but that nonetheless are in Table 3. So Example 3 is basically a repertory of harmonies which I believe Takemitsu utilizes and that are derived from the sho harmonies.
Example 5 will show how Takemitsu makes use of this chordal partitioning. In this passage from Garden Rain for brass ensemble, the Category 2 set classes, the frequent partitions of Example 4, are prominently featured - this is the opening. The set class for each distinct chord (verticality - it's a very homophonic piece) and its respective partitions are given below the score and are enclosed in square brackets. Sets marked with rounded brackets are from Category 3 - the less frequent partitions. Below each partition, its pitch class content is given in letters, and, as you can see, the frequency of appearance is used as a criterion to pull sets out in Example 4 - the frequency of appearance in that table is also reflected in this passage. Takemitsu concentrates on those particular sonorities. Although the tetrachordal set classes in this example (4-15 and 4-20) do not appear anywhere in the chart in Example 3, and thus are not sho chords or sho partitions, notice that the trichordal partitioning of 4-15 maintains a Category 2 3-7, which is on Example 3 (beta partition), while the trichordal partitioning of 4-20 retains a Category 3 3-11 trichord as its lower partition. And these two chords, as I have said, are literal subsets of sho harmonies. So, even though these particular chords are not sho chords or sho partitions, Takemitsu voices them in such a way that in dividing the harmony those particular set classes are highlighted - so still the sho sonority is there, but yet a different environment.
Another interesting feature of this passage is the timbrely distinguished melodic presentation in the horn of the Category 2 partition 4-22, indicated by the circled pitches in the score. The significant harmonic features of this passage can be discussed almost entirely in terms of chord Categories 2 and 3, which are taken directly from the sho harmonies. The point to be re-emphasized is that even though a particular overall harmony may not be a sho chord or partition, Takemitsu frequently uses voicings which stress sho harmonies as upper or lower partitions or indeed, in some cases, both. While this direct and predominant use of sho set classes and partitions can be seen with great frequency in all of his music spanning the Requiem to some of his latest works (a period of more than thirty years), Takemitsu in no way limits himself to these sonorities.
What I will show now is a method of broadening the three sho-based chord categories, in order to account for Takemitsu's use of harmonies and partitions that lie outside Categories 1-3. I'm interested at this point, when sets come out that don't fit in Example 3 - why is he using this chord? How is he deriving these sets? The 1 function, abbreviated as 1f, will be used to account for this expansion of Takemitsu's harmonic vocabulary, and it works in the following way. Given any pitch class set collection of notes, transpose or inverted transpose all but one of its pitches by a given number of semitones - then apply the same procedure to the one remaining pitch class, except alter the interval of transposition for that one pitch by a semitone higher or lower than that used for the large collection. If this process is carried out in a thorough and systematic way, realizing all the possibilities for the pitch class set, an additional family of sets will be created from the original parent set that will be regarded here as being related to the parent set and a member of the 1f family of that particular set.
In Example 6, I've shown the 1f process carried out on the spelling of Category 2 tetrachord 4-22 and the Category 1 tetrachord 4-23 - Category 1 tetrachord 4-23 is in literal sho sonorities. For ease of presentation I have not used any inversion here, and I've kept the interval of transposition for each internal trichord constant at 0, and have used plus or minus one semitone as an interval of transposition for one remaining set or pitch class in each instance. Takemitsu only varies one pitch of the set by a semitone - the others still form the sho pitch set. He's only changing one element by a set degree. I'm basically saying that Takemitsu takes the sho harmonies, develops a new harmonic vocabulary from them - in addition to them - and appoints them in his music as well, and the harmonies that don't belong to Example 3 quite often can be accounted for in this fashion - particularly from the sets in Example 4 (the most frequent partitions of sho chords). By applying the 1f he derives a new harmonic vocabulary which is very prevalent in his music.
The expanded harmonic vocabulary produced by the application of this 1f relation to the sho chords and their partitions plays a vital role in all of Takemitsu's music, and allows him to create a harmonic and melodic vocabulary derived from the original harmonies of gagaku. These harmonies and their partitions will be used in combination with their 1f related families in the example that follows in order to establish models of harmonic construction and of logical harmonic succession. This will allow us to understand the reasons behind many of Takemitsu's harmonic choices and enables him to maintain the traditional Japanese harmonies of the sho as the basis of my analysis.
I will illustrate with a passage from November Steps - specifically, measures 5-7. The orchestra is divided into two main sections which are clearly marked in the score. The viola, cello, and bass parts are groups 1 and 2 from this passage, and have been extracted with only minor rhythmic alterations. I show them in Example 7 with their corresponding set classes and tetrachordal and pentachordal partitions from the score. The pitch class content of all these partitions is given beneath the partition there - the letter notation simply means an elaboration of the simple set class labels (so, I've given you the actual pitches that are in these set classes). Because of the near identity of the music of groups 1 and 2 in measure 5, the two groups will be regarded as a single performing body, at this point.
In measures 6 to 7, however, there is a drastic change in orchestral texture, combined with rhythmic contrasts between the two groups, and thus their resulting harmonies at that point will be considered separately. As in the previous example, the most interesting partitioning occurs at the tetrachordal level, and it is from these tetrachords that I will examine Takemitsu's patterns of harmonic succession. Again, you can see that there are a number of set classes in this passage (check with Example 3) that are not literal sho chords or partitions, but I believe the 1 function can demonstrate how these other chords are derived from the actual sho harmonies and partitions.
Example 8 shows the successive transformations of each tetrachordal partition's set class of Example 7. The final alpha partition of the example on the far right contains only three notes - shown as trichord 3-8. Successive chords related by 1f are connected by a solid line. Non-consecutive 1f related tetrachords are connected by an arrow. Consecutive tetrachords no related by 1f are shown with an X between them - each simultaneity is numbered 1 through 4. For instance, in the bottom row 4-23 and 4-27 - 4-23 is a literal sho harmony or partition; 4-27 is not. But by applying the 1f to 4-23, you can create a 4-27. On the upper rung of the harmonic presentation (Example 8) 4-21 is not related to 4-26, nor is 4-26 related to 4-23, but all of the upper row is related to 4-22 and it is the only set class in the traditional sho harmonic partitions which can generate all four of those sets. The alpha partitions demonstrate a non-successive application of 1f - none of the alpha partitions are 1f related to any of their neighbors. Instead, all the alpha partitions in this example belong to the 1f family of 4-22 which we saw derived in Example 6. Anyone looking at Takemitsu's music a great deal will eventually notice that 4-22 really does seem to be a part of his musical signature. Indeed, 4-22 is the only set class within the group of sho partitions which account for all of the alpha partitions of this passage, and thus we might even imagine a type of implication of the Category 2 4-22 sonority throughout the passage. In effect, maybe the 4-22 is really there in a way, but he's giving you all these analogous chords on top. Later on in the piece, 4-22 will assert itself most profoundly, and so I think that this passage is a particular inference of that set class.
In contrast to the alpha partitions of this example, all the beta partitions are generated by successive application of the 1 function. That is, each consecutive chord is 1f related to its neighbor. The successive 1 application shown to these partitions will also serve to show, in a less abstract way, exactly how the 1 function operates in generating harmonies. Example 9 shows only the beta partitions - the lower partitions. Letter names are given below the score, and below this I've shown the respective transposition and/or inversion operations that transforms each chord into its neighbor. The operation marked with the * refers to the operation applied to the three notes connected by solid lines - to their transformations in the following chords. The operator without the * below has been applied to the one remaining note and is connected to its transformation in the following chord by a dotted line As defined by the 1 function, the interval of transposition for the upper and lower operations always differs by a value of plus or minus one semitone. Thus, even though only the first chord 4-23 is a literal sho chord, the appearance of the remaining three harmonies in the music can be viewed with the help of the 1 function as a direct transformation of, or derivation from, the traditional Japanese harmonies of the sho.
In summary, I've shown that Takemitsu's harmonic language bears a strong resemblance to that of the centuries-old Japanese musical tradition of gagaku. The harmonies, as performed by the sho, can be compared to passages from two of his works. The harmonies are employed analytically in their original form as pairs of boundary partitions and as an inspiration for a technique of set generation. Though Takemitsu makes no explicit mention in his theoretical writings of compositional models based on elements of gagaku, the approach adopted here makes an attempt at explaining the quality of Japaneseness so often attributed to his music by basing its analytical procedures on traditional Japanese harmony. Whether or not a composer claims particular cultural models as a basis for his work, our understanding of his musical message can only be enriched by deepening our understanding of his cultural origins. I believe that this discussion is a step in that direction.
Thank you.
[transcribed and edited by E. Michael Richards]