Chirashi Gaki 

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The title of this text pays homage to Yuji Takahashi’s beautiful 2017 composition of the same name. His work renders into music three incredibly gorgeous examples of 11th century Japanese calligraphy. 

Chirashi Gaki has been defined in English as “scattered writing”; but I really do not care for that translation, as the word “scattered” implies a randomness, i.e. leaves are scattered on the forest floor (where they fell higgledy-piggledy); or sheets of music fall and are scattered on the ground; but there is nothing random in the calligraphy of these three poems. After some back and forth between us, Yuji decided on “Dispersed Calligraphy” as a better English approximation. 

The technique of Chirashi Gaki allowed the writer to “begin lines of the poem at different levels on the paper and portray the rhythm of the verse, or to write in darker and lighter shades of ink and give a sense of depth to the words, making the work look almost like a landscape painting” (from Yuji’s emails of March 4/5 2017). In short, instead of “looking” “scattered”, this calligraphy is a most extraordinary example of artifice!

Given my penchant for escaping from the musical bar-line, a take-away from these calligraphic “drawings” is how they escape some sort of “grid”; and this idea of escape gave me the solution for organizing a text I have been dreaming about for years.

This text returns to my obsession with variety in Haydn; but this time, unlike “pour un Haydn”, I wanted to concentrate not on larger form, but to compare all 32 “A” sections of the string quartet minuets that equal eight measures. Surely, an eight-measure grid must be too restrictive to allow for great variety? Nothing could be further from the truth.

Originally I intended to draw detailed comparisons between various versions of each minuet “A” section, but, given time constraints and health, it finally occurred to me to let each person fight with the problem on their own; so the project turned into a sort of solitaire which, when one gets good at it, can be played against two or more players (up to a total of four).


The “Game”

The text contains three versions of the 32 eight-bar minuet “A” sections. 

The first version is the original, only laid out in terms of equal time gets equal space i.e. throw out the old engraving rules, which allow less space for longer notes (assuming no fast stuff underneath or above); equal space = equal time layout will allow much simpler, more straightforward visual comparisons between minuets, one-on-one.

The second version is identical to the first version, except that all the bar lines have been removed.

The third version is identical to the second, but now minus the musical staves as well. Here we approach the world of pure graphics; close to the essence of Chirashi Gaki.

How to play the “Game”

The “game” may be played as follows: print copies of the second version (to start with); choose a part, preferably one you yourself would not play in a string quartet (so as to avoid as many preconceptions as possible); and without regard to the original version, but simply by evaluating, tasting and re-tasting the part, honestly pencil in where you think the bar-lines might go. Then, when you are feeling brave enough, go to version three (no bar-lines, no staves) and see if you would pencil in dividers (aka your putative bar-lines) more or less in the same place in your part. Eventually, do the same for a different part and compare parts. In how many places do your bar-lines coincide? Disagree? Conflict?  My guess is that if you are honest, and open-minded, to this process, you will find very often your sketched bar lines will not agree with Haydn’s original grid, which was purely a matter of convention, and not of real musical significance.

There are three major areas requiring careful consideration both before and during the playing of the game.

How to think about using your “revised” bar-lines

Do not think you must have a uniform meter throughout your chosen part i.e. there is no reason why an individual part can not change meters in the course of the 24 quarter-notes of the 8 measures. Of course you may have displaced 3/4 measures (i.e. the “downbeat” has been shifted to the left or right); but you may also suddenly find yourself in 4/4, or some other nominally “verboten” minuet meter. Just remain open to any and all possibilities; and of course this “rule” applies to each and every part, individually. Forget collective meters. For our game, they are there only because that was the notational convention of the time. True, there will be times when parts X and Y have identical meters, perhaps in contradistinction to parts W and Z, just as in a conversation amongst 4 people — sometimes 2 people speak against the other 2; or etc etc. But there will also be times when everything seems to be falling apart, with no controlling meter for all parts. Of course, do NOT get trapped in your new bar-lines. They are as rigid and bad as the old ones. All this is just means towards an end, the end being to better grasp the syntax; the stresses; the “thumps” (as Basil Bunting called them in poetry) of each individual part.

How to partition 8 measures; and Goldbach

Perhaps due to the geometric progression 2; 4; 8; 16; that we know so well, musicans and perhaps others tend to assume that the number 8 is most often (“best”???) partitioned 2 + 2 + 2 + 2; or perhaps 4 + 4; but there are many other partitions of 8; starting from 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1; and including 2 + 3 + 3 and their permutations  (3 + 2 + 3; &  3 + 3 + 2); as well as 5 + 3 ( and the reverse), and 7 + 1 ( also reversible). Essentially, we are in the world of the (as of this writing) still unproven 1742 Goldbach conjecture, which states that every integer greater than two can be expressed as the sum of two primes. The conjecture comes in two flavors, a strong, and weak one. Those details are not relevant here. What Goldbach does do is help get us out of our tendency to think that eight measures must equal 2 + 2 + 2 + 2, and this is a most important part of our game.

Which measure is really the “first”, or “primary”? The players are left to explore these and other questions.

Paul Zukofsky
Hong Kong
March 10, 2017

Note: Many thanks to Luke Bedford for preparing the musical example files.

In order to “move things along”, we employ a number of abbreviations throughout the text, viz:


H = Haydn
HSQM = Haydn String Quartet Minuets
SYM(s) = Symphony (ies)
SQ(s) = String Quartet(s)

We consider the data from two perspectives: either in terms of the components of the entire movement; or in terms of the juxtaposition, or opposition, of the three classic divisions of the entire movement, i.e. the minuet section, vs. the trio section, vs. the da Capo.

Any discussion of components involves quotation marks.

"A" = the first "section" of the "minuet" portion of the movement (i.e. up to the first repeat sign).

"B" = the second "section" of the "minuet" portion of the movement(i.e. from the first to the second repeat sign).

"C" = the first "section" of the "trio" portion of the movement (i.e. from the last repeat of the minuet to the first repeat sign of the trio).

"D" = the second "section" of the "trio" portion of the movement (i.e. from the first repeat sign of the trio to the last).

"E" & "F" = sections subsequent, and/or additional, to "A", "B", "C", "D".

The following are ways of thinking about the components, and are italicized.

"ML"(s) = Measure Length(s) (used in "A", "B", "C", etc.).

"S"(s) = Section(s); as in the total number of "A"s, "B"s etc. within an entire movement. These are usually "10-S" but there are also "7-S", "9-S", "11-S" and "14-S" .

"DL"(s) = Different Length(s); as in how many different lengths are used across "A", "B", "C", "D".

"W"(s) = Weight(s); a way to think about and to distinguish different arrangements of various "DL"s.


Any discussion of the juxtaposition of the major divisions involves BOLD.

M = the Minuet sections of the entire movement; i.e. normally "A" + "B".

T = the Trio sections of the entire movement; i.e. normally "C" + "D".

dC = the da Capo section.

TML = Total Measure Length (of an M or T).

PT = Partition Types i.e. how the total of an M (or a T) is partitioned.


A note of caution:

When refering to an entire movement, we say minuet movement, or more simply, movement. M ONLY refers to that part of the movement that occurs before the Trio.