Jo Kondo’s Still Life (1981), for 8 violins, is 105 measures (meas.) in length. Each meas. contains an “aggregate” (“agg”(s)) of one to eight pitches (“P”s).1 Other than for the last two,
all “agg”s are nominally identical in duration, dynamic, and attack.
Example 1 shows the 105 “agg”s, denatured.
What “P”s are used, and in what order do they appear?
Ex. 2 shows 34 (41, counting enharmonics) “P”s.
One senses the pace of entries -- sometimes individual; sometimes simultaneous; sometimes in consecutive meas.; sometimes intermittently. Entries terminate by meas. 57 (81, counting enharmonics). “P”s (and/or spellings) that are never used appear on the last line, in a faint shade.
Some “P”s are used more than others. Which?
One answer would count the total number of times a specific “P” is played by all violinists, in all meas.. Ex. 3 presents this data. “D4” appears most often; followed by “A3”, “F6”, etc.; but the total number of times a specific “P” is played by every violinist may not be apposite. It may matter (far) more in HOW MANY meas., “D4”, “A3”, etc, appear.
To clarify: within any meas., all violinists can play the same “P”. Therefore, arithmetically, 12.25 meas. with everyone playing “D4” satisfies the 98 appearances of Ex. 3 (as 12.25 x 8 = 98); but how would “12.25” unison meas.s of “D4”s shape our “perception”, perhaps “understanding”, of the work, as opposed to the presence, in each of 98 meas., of a single “D4” played by one violin only?
To answer this, ex. 4 rank-orders “P” by the total number of meas. in which a specific “P” appears, no matter the number of violins playing. “D4” is again first, but thereafter the order diverges from ex. 3; but as shown in ex. 5 (which compares ex. 3 & ex. 4), the first twelve “P”s are, with one exception, identical; and both lines of ex. 5 contain the same 7 “PC”s (pitch class(es)) i.e. D, F, G, A, E, C and F#.2 We therefore posit no schism in information received when comparing played-by-total-number-of-violinists vs appears-in-how-many-meas.. The primary difference is
that ex. 3 tells about color more than structure; whereas ex. 4 primarily tells about “attractants”.
Which “PC”s repeat continuously across the most measures?
Ex. 6 shows that the longest continuous length (13 consecutive meas.) is “PC" = F. "PC" = D (12 meas.) is next. G follows, etc., ending with "PC"s = C#/D♭ & A#/B♭, that never exceed three consecutive meas. The
six “PC”s with the most consecutive meas. are identical to the “PC”s of ex. 5. i.e., these “PC”s are prominent in three ways: “played by how many”; “appearing in how many meas.”; and most continuous.
Why do we care about the most continuous “PC”s?
Any "PC" appearing in two consecutive “agg”s conjoins them. The greater the number of consecutive reps, the more likely the repeated "PC" provides a woof to the warp of vertical progression.3
How can the above infuse a performance of the work?
Ex. 7 shows the outer contour of the “agg”s.
The lower bound changes “P” 72 times; has many two- meas. reps; and a max. rep length of 4 meas..
The upper bound changes “P” 59 times; has fewer two-meas. reps; and more long lengths.
That the lower bound wobbles more than the upper is NOT a function of the number of different “P”s used. Total meas. for the three most used “P”s (upper bound F6 = 23, G#6 = 13 & F#6 = 11; vs. lower D4 & A3 = 20 each & G3 = 11) are roughly comparable. The range between bounds varies greatly.
Ex. 8 adds (to ex. 7) any internal “P”s or “PC”s that repeat for at least 5 consecutive measures.4 Red and blue horizontals are not constant thruout, with six gaps of 1 - 5 meas. in length; plus a 16 meas. gap from meas. 73 - 88.
There are three single horizontals i.e. meas. 67 - 72 & 98 - 103, (each 6-meas. long; both “PC” = A); and meas. 51 - 55, (“PC” = F), which connects two fields of compound-horizontals.
The six compound-horizontals are found in: meas. 1 - 12; 18 - 28; 30 - 37; 43 - 48; 56 - 60; & 89 - 95.5
“PC” = A appears in all compound fields.
“PC”s = F, D, G, E, C, F# each appear in 2 fields.
“PC”s = E♭ and G# are in 1 field each.
The two longest lines are “PC”s = D & F.
Within some of the above, octaves reinforce the “weight” of various “PC”s.6
Ex. 9 applies the red and blue horizontals of ex. 8 to the “agg”s of ex. 1. Meas. 73 - 88, bare of horizontals, is disparate. Would a shorter rep.length change that?
Assume a 4-bar rep. rate.
Ex. 6 showed 14 rep lengths of 4 meas. each.7
Only three of these occur in meas. 73 - 88, i.e.
A (meas. 74-77);
F (meas. 85-88);
C (meas. 76-79);
and meas. 73 - 88 maintains its disquietude.
But much as we wish to emphasize the horizontal, Still Life remains a procession of verticals. How can we address them?
Distributions of and within “agg”s.
For a sort of “agg”s as a function of “agg” sizes 1 - 8; distributions of “P”s within “agg” sizes; and a graphical “PC” plot of the work, see App. i, &. exs. 19, 20 & 21.
What "agg”s repeat, and where?
The 105 meas. contain 80 different “agg”s.
Ex. 10 shows all “agg”s, some now in different colors.
“Agg”s that repeat five times each (meas. 1, 12, 17, 40 & 89; and 15, 38, 61, 76 and 101), are colored red.
"Agg”s that repeat four times (on a "PC" basis) (meas. 16, 39, 62 and 78; 5, 6, 65 and 66; and 18, 19, 41 and 51) are colored green.
The 16 "agg”s appearing twice each are colored blue, and are labeled A–P.8 Three letter-pairs repeat contiguously (“AA”; “KK”; “PP”). “KK” is as close to the midpoint (meas. 52 & 53) as possible. “AA” appears at the start. “PP” closes the work. The adjacent letters “CD” (meas. 10 & 11 & 94 & 95) repeat almost equidistantly from the start and end of the work. The remaining letters seem jumbled. There is no evidence of retrograde order. Letters are not distributed evenly. Patterning is not evident; but for a reading that shows how repeating “agg”s agglutinate, see App. ii & exs. 22 & 23.
How “agg”s may be created.
Kondo often organizes “agg”s by superimposing P5ths or P4ths. The process may be seen below, where archetypes are formed using D4 as the kernel:9
All of the above “PC”s appear within the first eight ranks of ex. 5; and the interval archetypes permeate the composition.
The four “PC”s (D, C, A, F) appearing singly (i.e. “agg” size = 1), are among the most frequently used “PC”s.
P5ths and P4ths never appear unclad, but one or more P5ths or P4ths may be found in 71 meas., and are present in every “agg” size of 5 “P”s or greater.
Major 2nds may be found in 87 meas., and are present in all “agg”s of 4 “P”s or greater. However, major 2nds (both singly, and paired) can not be properly tuned without a context, and for that, we turn to triads, and ex. 11, which shows 51 meas. with purple letters (above the staff), each letter labeling the embedded MAJOR and/or minor triad(s) (eschewing chimeras such as the
B/F#/E♭ of meas. 84).10
Twenty-six meas. have “single” triads: “a minor” and “F Major” appearing 5 times each; “d#”, “E♭”, “b” and “G♭”11 appearing twice each; and “d”, “D”, “c”, “e”, “E”, “f#”,
“g”, “B♭” once each. Seventeen meas. have “paired” triads: “D, d” appears 8X. “F, d” and “G,e” appear twice
each. “G♭, a”, “C, c”, “C, a”, “F, a”, and “F#, c#” appear
once each. Eight meas. have multiples of 3 - 7 triads. Triads are more prevalent (i.e. 32 vs. 19 meas.) among “agg”s that do NOT repeat.
“PC” semitone dyads (27 meas.) and triunes (36 meas.), as well as more complex “clusters” of four (5 meas.),
five (7 meas.) or seven (1 meas.) adjacent “PC” semitones (there are no 6-adjacent “PC” semitone clusters), provide a “most loyal opposition” to the triads, sometimes cooperating, sometimes disputatious, sometimes governing. Ex. 12 uses (single or double) purple triangles to blazon the triunes; (single or crossed) bilious slashes for the dyads; and green ovals to show larger “clusters”.12 Triunes are of especial importance, as that is the first cluster one hears, just as a triad is the last sound.
As regards “intonation”, a non-equal temperament is imperative. Only by emphasizing the “beating” vs. non- beating intervals will one surely savor the piquancy of, and within, “agg”s.13
Vacuously sawing thru 105 “agg”s is not an option. How may we shape our rhetoric?
An obvious solution is to “aim” for the five repeated solo “D4”s of meas. 1, 12, 17, 40 & 89, demarcated in Ex. 13 by large red pillars. These are, with one exception, distant from each other by prime numbers i.e. 11, 5, 23, , + 17 to the double-bar. This division in to five large sections provides great variety of section-lengths; but the 49-measure length is difficult to sustain.
An almost equally obvious possibility affirms the repeated group that reminds of an “amen”, or refrain. The red brackets of ex. 14 show five such. Meas. 15 - 19/20 is four measures in length, plus a fifth-measure prolongation. Meas. 38 - 41, a “PC” repeat of meas. 15 - 19, but embedded in an entirely different context, lacks the last measure prolongation, allowing one to pass more freely on to meas. 42. Meas. 61 - 64 retains the four-meas. form, but the primary stress of the phrase has been shifted to the third bar. Splayed across 14 bars (meas. 76 - 89), the fourth is so dispersed as to be only the reminiscence of a faint perfume; and meas. 101 - 103 is the briefest of truncations. From start to start, three of these groups are almost equidistant from one another i.e. the distance from meas. 15 - 38, and 38 - 61 are both 23 bars. Meas. 76 - 101 is 25 bars. The 15 bars from meas. 61 - 76 is the exception.
A (perhaps) less obvious parsing may be found in ex. 15. Nine grey pillars articulate those places where no “PC”s carry thru to the next measure. This results in 10 lengths (of 12 + 4+ 12 + 11 + 33 + 1 + 11 + 4 + 15 + 2 meas.). Also enclosed are those measures where “P”s (encased in solid quadrangles), or “PC”s (corralled using
dashed quads), repeat consecutively. These moments of stasis complement the points of total “PC” change. The quadrangles have some interesting properties, as may be seen in the extraction below (showing only the first meas. of each quad):
i.e. the quadrangles may serve as a cantilever upon which the work suspends. Note the “harmonic” tension-relaxation-tension-relaxation “agg” progression.14
Ex. 16 combines all previous parsings. These sometimes reinforce, sometimes contradict, each other i.e. the order of grey and red pillars before meas. 13, 17, 40 & 89, clarifies if the “D4”s are terminations, or beginnings; red pillars and red brackets may interact; black quads do not seem to interact with the other elements; etc.
The green ovals of ex. 17 (now filled in) highlight “crunches”, i.e. clusters of 4 or more adjacent “PC” semitones. These “crunches” may be points of maximal expressivity, or perhaps dissonance (if one regards such clusters as more dissonant than triunes etc.) and these points could function as an additional “parsing”. The spacing of these “crunches” i.e. expanding pairs (until the final three), is of interest, and helps to fill some of the interstices of the previous parsings.
Discussion of how first entries (small orange circles) may add to all of the above is omitted; but ex. 18, showing six horizontal ochre ovals vs. areas of blank meas., can not be so easily dismissed. Ochre ovals yoke “agg”s that will repeat, or have been heard before. Empty meas. signify “agg”s appearing once only. Horizontal blue lines substitute for the red and blue lengths of ex. 9. There are few congruences between the horizontal ovals of ex.18 and the earlier parsings.15
The salient finding is that “agg”s that repeat tend to “clump”. “Agg”s that do NOT repeat also tend to “clump”; and the repeated/non-repeated “clumps” are dichotomous, at least temporally. If the midline pink swath has any meaning, it has little to do with our parsings. Rather, the swath may serve as a signal (which one can, or can not, acknowledge) of an equilibrium point between repeated and non-repeated “agg”s.16 This allows one to think of the composition as a paired set of “nested” mutations, i.e. there are red “agg”s that repeat 5 times, enveloped amongst “agg”s that either have already repeated, or will repeat. These form the ochre oval areas that are similar to each other, yet are “different”. The ochre ovals tug against areas of “agg”s appearing only once, areas so varied as to lapse in to “sameness” i.e. their constant changes overwhelm our sensibilities; and our disorientation between “sames” sounding “different” vs. “differents” sounding “same” beclouds us, and is representative of the ambiguity so inherent in Kondo’s music.
The above parsings are hardly exhaustive. Starts and terminations of red and blue horizontals (first seen in ex. 8) could provide an articulation. For numerologists, 105 (the 14th triangular number), is the sum of the numbers
1 thru 15. One might wonder if there could exist a parsing of 15 phrases, of 15 different meas. lengths.17 Alternate possibilities are manifold. One need only “let your rambles be sweet, and your reveries spacious”.
That is the wrong path.
Despite the renunciation of rhythm, dynamics, timbre, motifs, second themes, development sections, and most of the rest of the panoply, Still Life is NOT unidimensional, but rather operates on an astonishing number of levels imbued with classical concerns. The simplest rhythmic patterns can possess counterpoint. Mr. Tinctoris, or Herr Dr. Fux, would immediately recognize the methodology of note against note; of sustained horizontals vs. shorter lengths; no matter how askance they might look at the specific “PC” selection.18 The diverse interactions between sustained “PC”s vs. embedded triads vs. clusters; if certain "PC"s act as attractants, or not; how one “paces” the work; how one “sets-off” repeated vs. non-repeated sections; these, and many many other questions, are all food for thought, consideration, and --- “interpretation”! That a notated score may seem devoid of all “emotional” cues is not, and must not be used as, an excuse to abjure opinion. The introduction of a heretofore unused “P”; the change of an inversion; the sudden massing of 8 violins on a single “P”; a change from dissonance to consonance, or the reverse; the exact repeat of an “agg”; these, and a myriad of others, are events that one might wish to “point out”. Today’s counterfeit emotionalism (so very common) of today’s “knockoff” fartistes, with their seizures, is anathema; but such vileness is a far cry from a performer knowing that something new has occurred, and from making a “Suprematist” shade gradation so as to better inform perceivers; and for the do-nothing “plus- royaliste-que- le-roi” crowd, I assure you that the composer would be MOST pleased with such subtlety.