Arabic : Bach : Change

"The game began with a rhythmic analysis of a fugal theme and in the centre of it was a sentence attributed to Confucius. " The Glass Bead Game, Hermann Hesse

This short game fragment was directly inspired by the above passage from the Glass Bead Game novel, where Hesse sketches the outline of an actual game, without giving specific details. It starts by focusing on the rhythm of a fugal theme from Bach, which is then compared to a metrical pattern from classical Arabic poetry, and then linked to a hexagram in the ancient Chinese classic, the I Ching. It is presented in the form of a proportion (A is to B as C is to D as E is to F), which is the basic building block of the Glass Bead Game variant proposed in 2010.

Five whole quantities and two halves are to the rhythm of Fuga I of Bach’s Art of Fugue

(60 - 40 – 50 – 60 – 64 – 60 55 - see note below on this mathematical notation of the musical theme, and here for Glenn Gould's rendition of the fugue http://www.youtube.com/watch?v=vhU9Ld1NNZg)

As

Five whole quantities and two short quantities are to the Arabic Tawiil metre (the rhythm of the line is anglicised as faa-9oo-lun maa-faa-9ilun)

And as

Five whole quantities and 2 halves are to the I Ching Hexagram 43 (Kuai)

N.B. Following the Sumerians (as interpreted by Ernest McClain in The Myth of Invariance), if a number is fixed as a reference point, fractions can be implied from it. For example the sequence 60 - 40 – 50 – 60 – 64 – 60 55 is the Bach theme d-a-f-d-c#-de with 60 representing the tonic D, and all the other notes defined by reference to it (e.g. 40:60 is 2:3 representing a, 50:60 is 5:6 which represents f).

Further play from this comparison may involve the following considerations:

• Close analysis of the musical theme itself:

o The intervals between the first few notes of the fugue (30-40-50-60 after allowing for ‘octave equivalence’ represented by a factor of 2) are 4/3, 5/4, 6/5, which are successive ratios of the form (n+1)/n, the Greek theorists’ epimoric ratios, and as such represent successive intervals between notes in the harmonic series; The next three intervals in the theme are 16/15, 9/8 and 10/9, meaning that the full set of epimoric ratios in the diatonic scale are contained in this single theme (allowing the presence of 3/2 as the inverse of 4/3);

o The counter-theme to Fugue I in the Art of Fugue has a different melody but the same rhythmic structure, doubled in speed;

o The first four notes of the counter-theme exactly echo the pitches at the end of the theme, so that the melodic seed for the counter-theme is contained in the theme, as is the rhythmic seed;

o Bach’s Fugue VI from the Well-Tempered Clavier also has the same rhythm;

• Any cross-interpretation of the texts associated with the I Ching Hexagram with other positions played. For example, using the Eranos Edition:

o “Persisting and stimulating” and “Breaking up and harmonising” might be taken to echo the harmonising counterpoint of theme and counter-theme of the fugue, and the persistent presence of the seeds of the counter-theme in the abstracted elements of the theme itself;

o The suggestion of “unwearied heavenly bodies in their orbits” in the Chinese ideogram for “persisting” echoes the successive intervals from the harmonic series which appear in the fugue’s melody;

• Tawiil is a common metre in Classical Arabic poetry, so there is a wealth of choices from that source. The choice of text might develop other variations (e.g. the themes of “doubling”, “the self containing the seeds of the other”, “succession of musical notes and planets”), and could be from any language. Staying with classical Arabic, for example, the following beautiful fragment in the tawiil metre from the Arabic poet Thabet ibn al Haaris ibn Rabi’a contains the themes of doubling and the self containing the other:

taDaa’fa nabD ul kalbu hiina ‘ashiqtuha

wa Surna fu’adiini bi jismin huwa llibsu.

which translates into English as:

My heart beats double when I meet her

and we become two hearts wearing one body.

By convention, mightn’t the Chinese character Kuai, written on an axis concerned with music or Arabic, come to represent this rhythm and metre?