一狂 Set analysis for intro

Although this is a contemporary piece of Chinese music, it is not written in an avant garde manner that makes it difficult for listeners to appreciate with few listening. It still contains aesthetic aspects which appeal to the masses, preserving folk and traditional elements and building upon them to create music that is new, yet not losing its sense of beauty – a philosophy held strongly by the composer.

1) Set analysis (concerned with unordered collection)

In this 1st erhu rhapsody, the composer draws upon tonal inflections from one of the minority race in Yunnan (or xi nan) to construct a 9-tone scale: C D Eb E F# G Ab Bb B (according to the writer 陈静), as well as various other elements from yunnan folk music instead of being constrained by the pentatonic scale, so as to depict the various musical imagery and a broader scope for expressiveness (i have not finished deducing all 9 notes yet).

The juxtaposition of a major and minor 3rd interval in a tetrachord seemed to be a characteristic of this piece (these four notes were introduced in the first set of notes played by the erhu right at the beginning and subsequently played at different inversions).

Normal form: [2, 5, 6, 9]
Inversional form: [3, 6, 7, 10]

This set of notes corresponds to the prime form [0, 3, 4, 7].
Looking at this prime form, I think we can derive 4 notes in the self-constructed scale, i.e. C, D#, E, G












~

As we can observe, this is a symmetrical set that maps onto itself at the axis between 3 & 4, 8 & 9.

The interval class vector (IcV) corresponding to this set is

So we can deduce that there is a wide palette of harmonic colours to work with, and the sonorities can consists of semitones, tones, minor 3rd, major 3rd, perfect 4th, perfect 5th, tritones, which is evident in both the linear and horizontal dimensions in this intro section. It also implies T3 and T4 give the most common tones.

Relationship within set class [0, 3, 4, 7] as it is transposed and altered in the intro section:
(the following collection of notes has been reordered to show the relationship)

~
As seen, materials are drawn from the set [0, 3, 4, 7] related inversionally, transpositionally and in terms of subset. In particular, notes G# and A# from the self-constructed scale is introduced in the 5th system.

There is also a strong sense of tonal center around D major and soon after, there is emphasis on ‘A’, which is the dominant of D, followed by a temporal return to tonic and back to dominant which served as a link to the key of A in the next section. Thus we can still observe functional harmony at work here.
The choice of key (D major) may be due to the nature of the instrument (open strings D, A), thus D major to erhu is similar to C major for the piano. Thus the plucking of strings technique in the 4th system using notes D and A would give more resonance.

I haven’t found a particular group of notes for the pc set in the Andante section, but there is a motive I picked up in bar 4 (beat 6) – bar 5 (beat 1), which is related to a subset of [0, 3, 4, 7] by T9.