Bartok'S Use Of A Row In Bulgarian Rhythm (Mikrokosmos #115) printable pdf download

Bartok’s Use of a Row in Bulgarian Rhythm (Mikrokosmos #115)

The 6 note row is “scalar” – a grouping of whole and half-step motion stretched between a

tritone. Each Row is, hence, very linear, very “oriented” contrapuntally – moving towards a goal

note which is harmonically unstable i.e. needs completion, resolution. Note that the C# cadence in

the melody at Bar 4 (the final note of T0) moves up by ½ step to the D in bar 5 (a “traditional”

resolution). Bartok selects the next row (R1) because, among other considerations, the first note, D,

“satisfies” the linear energy generated by the previous row. Similarly the Eb Cadence in Bar 16

(which follows a Cantus Firmus descent in half steps from F#) resolves down to the D of Bar 17.

Bartok uses the traditional tensions associated with horizontal and vertical intervals to give

an underlying harmonic order and direction to his music. He makes decisions as to which rows

should be used with these tensions in mind. His melodic figuration (the “row”) provides a tight web

of recurring shapes (related by transposition, retrograde, inversion, and retrograde inversion) which

give an ordered, logical, quasi-geometrical surface to the harmony underneath.

This work is a 2 voice contrapuntal composition which adds a 3rd voice for the cadential

section. The third voice, in fact, allows Bartok to suggest a triadic tonal interpretation for the

conclusion. Overall this is a “hybrid” work which very clearly mixes aspects of traditional tonality

with use of a row.

An examination of the Row Chart which has been provided reveals a number of

relationships which Bartok exploits:

1. The G-C# outline of Hexachord T0 is found also in Hexachord I0 and reversed in the C#-G

outline of the Hexachords of T6 and I6. This means these hexachords share common departure and

arrival points. The note C# (the conclusion of T0), for example, can provide a common tone (a

“link”) for connecting T0 “naturally” with T6, I6 and RI0 which, in turn, will bring the line back to

In Bars 1-2, Bartok selects the T0-I6 pairing where I6 has 5 tones in common with T0, allowing

him to “return home” to the G – the functioning center for this work- by “retracing” his steps. He

literally returns with the same step pattern: 2 whole steps down, 1 half step up, 1 whole step and 1

half step down and, in so doing, he touches almost all of the same “steps” – common tones - only in

a different order.) This creates a very convincing unit of departure and return (Bar1-2) and can be

seen as a prolongation of the central note G. He uses the same relationship in Bars 17-18, but

transposed up a 5th to prolong D – the “dominant” of G.

Later he also uses another of the possible pairings suggested by the Row chart by using a

transposition of the T0-T6 relationship: T7 followed by T1 – Bars 19-22 in the soprano. This

pairing allows him to continue prolonging the note D (first note of T7 and final note of T1 - the

“dominant”), but in this case the second hexachord (T1) offers 4 new “fresh” notes which are

complementary to the previous hexachord (T7) and, since it is the identical contour of that

hexachord (i.e. one is the identical transposition of the other), it continues the ascending line (begun

in bar 19) sequentially.

2. In Bar 5, since Hexachord T0 has cadenced on C# in bar 4 (see earlier reference) and requires

resolution, Bartok uses the Retrograde R1 which begins on D. In the next bar this is followed by

R11 which begins on C - hence is a sequence. Both hexachords R1 and R11 have 4 common tones

with T0 (see the interval class vector) so both share common territory. Bartok furthers this process

of identification by omitting the final note of Hexachord R11 (a process which is naturally

supported by the 5 beat meter vs. the 6 note row) and substituting the final 2 notes of Hexachord R1

with a G for cadence. Among other points, this latter modification means that the pitch collection of

Bar 8 and Bar 1 is identical (GABbBC) hence bars 6 and 8 feel like points of return. Note also that

this form (5 notes instead of 6) excludes the tritone so the collection is harmonically stable.

Bartok'S Use Of A Row In Bulgarian Rhythm (Mikrokosmos #115)

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