This blog will self destruct at 7:06 PM EDT on Friday, September 14, 2007.

Unless it miraculously gets good sometime before then.

Thank you to everybody who made this lunch table so popular!

Update 9/16/07: I am officially handing this blog over to Ken, since he’s the one that has written 99% of what’s on here so far.  Hopefully it will now acquire a name and a direction.  Everyone say hello to your new overlord, Ken, aka Altered 7th, aka Mr. Pervert, aka Mrs. Babymash.  I look forward to reading it without feeling responsible for it. 

Well, I tried to write this in the wee hours of the morning, but WordPress was down. At 4:30 AM this morning I completed a 9-hour Civilization: the Boardgame game. And lost. Damn! But it was fun, I guess. Has anyone else played this game?

Well, it’s official: I’ve been accepted into a PhD (Music) program. Better still, the 6 months spent earlier this year working on a Masters is being credited so, it’s conceivable I can complete the PhD by the end of next year. Not bad going considering I started last year in a Post-grad certificate and had planned to spend as many as 8 years to get a PhD. Go me!

So, we just finished Harry Potter 1. It was pretty good. I liked it a lot more than I thought I would.

Also, I finished the Gunslinger only to realize that there is an expanded and revised edition available, so I think I’m going to read that next.

Super-Exciting: I’m pretty sure I’m getting an iPhone today. !! I had been planning on getting one at the end of this month or in September, but I lost my phone the other day, so I’m going to step up the schedule. Yay!

Also, I’m starting up a literary/arts magazine with a friend, so if you’re a writer at all, start polishing up your pieces, we’ll begin accepting submissions for our Winter issue in September once the web site is built.

Just saw Maria Full of Grace. It was really good, but it made me uncomfortable in the way that Thirteen did (I couldn’t even finish Thirteen). However, Catalina Sandino Moreno was amazing in it.

OK. Enough random ramblings for one morning.

Hey all—

So, I’ve been getting back into reading lately and thought I would just give a brief shout out to things on my list, recent past and present.

Gene Wolfe: Book of the New Sun and Latro.

Y: The Last Man

The Dark Tower (only on book 1. Don’t spoil anything for me)

Harry Potter (also only on book 1. Please no spoilers, I’ve stayed away from most everything.)

Anyone else?

This essay was written as an assignment for a composition class I took at college last year. It refers to music (Happenstance-Full-Mix.mp3) and the score (Happenstance-Score.pdf) that can be downloaded from here:

http://www.4shared.com/dir/2043046/e1b852b5/schillinger.html

Happenstance: Analysis

The Concept

Happenstance, as the title suggests[1], was composed from a few simple musical ingredients to yield a rhythmically complex and surprising score. A single scale source, namely an 8 note diminished scale formed from C, provides the tonal basis. The rhythmic organizational structure was initially determined by a technique Joseph Schillinger[2] called fractioning. As the composition grew from this, certain aesthetic considerations were imposed to create some regularity and simplicity of overall form from the irregularity and complexity generated by the fractioning technique.

The Rhythmic Sketch

Eleven MIDI sequencer tracks were each assigned a single note from the scale source to play one quarter-note duration on beat 1. Each of these tracks was then set to loop periodically according to the following table:

These loops were then rendered by multiplying each periodicity by a factor of 150, thus creating 11 tracks of varying lengths. Track 1, for example, became 600 beats long (150 bars of 4/4 time) while Track 11 rendered to 2100 beats (14 x 150) or 525 bars of 4/4 time. In order to keep the whole piece within the specified time limit[3], it was decided at this stage to “double time” all the tracks – a process that halved the durations of notes and the total number of bars.
Concept Draft

Once the sketch had been created, the tracks were mixed down into one so that the rhythmic regularities and irregularities, such as accents caused by the incidence of chord clusters, could more easily be extrapolated. When played back on a piano, the piece at this stage sounded rhythmically interesting. The algorithmic nature of its creation yielded significant amounts of syncopation and rhythmic complexity within the 4/4 metric framework. This, when combined with the ambiguous tonalities of the four diminished seventh chords inherent in the scale source, proved to be aesthetically pleasing, albeit in a sterile and inorganic way. The aim from this point on was to rearrange and orchestrate the draft to make it sound more rhythmically organic.

Ironically, this was achieved by refining seemingly irrational asymmetrical elements of the draft. An 8 bar section was excerpted from bars 187 to 195 of the concept draft and used to create a bass part cell that would form the basis for the arrangement.

Imposing A Form

The method used to determine the bass line in all sections was simple and arbitrary: use the lowest notes of any section excerpted and, where chords occur, delete all notes above the lowest.[4] Transpose to suit the range of an electric bass guitar. The bass figure mentioned above was created this way and used to form an introduction. This 8 bar cell is then repeated four times to create an “A” section. The piano part, when it enters, simply doubles the bass. The opening 16 bars lead the listener to believe there isn’t any regular pulse to the piece. The drums enter to establish the underlying pulse and even a 4/4 beat, though only briefly. This is discussed separately below.

The “B” section (beginning at bar 33) is essentially the bass part created from the beginning (bar 1) of the concept draft score. The zither and zampona parts are the same as the bass line transposed up (an octave and an octave + minor third respectively) however; their entrances have been delayed to create stratified sections like a musical round. These two parts have also been processed with an FX device that causes the zither and zampona notes to echo an 8th note delay an octave below and above respectively.

The piano part that enters at bar 33 is actually the part created for the concept draft reversed and rhythmically displaced so that it begins on the downbeat of bar 33. Specifics of this serendipitous melody will be addressed below.

The Lead Voice that enters at bar 39 was recorded live and in time with the underlying 4/4 metric structure. The durations are irregular although it is the random oscillations of the sound itself that really give it its organic rhythmic quality.

Section “C” marks a point where the periodicity of Track 1 from the original rhythmic sketch (C1 recurring on beats 1 and 3 every bar) ends. In effect, its end creates a tonal shift up a half step to C# and thus a new rhythmic texture – the fractioning of ten periodicities rather than the original eleven. Considerations of the overall length of the composition forced the abridging of this section though similar rhythmic tonal shifts would have resulted if all of the original periodicities had been allowed to play out their full cycle durations.

Section “D” is a recapitulation of the bass and drums from section “A” but with the piano, zither and zampona parts continuing unchanged from section “C”. Doing this created an overall sense of symmetry to the composition through the use of repetition of the “A” section’s rhythmic theme. All parts have been edited in bar 145 to create a definitive end to the composition.

The Drums

This part was created as a 16 bar cell, introduced at bar 17 and then repeated regularly throughout. The first 8 bars of it follow the bass part’s rhythmic displacements of the beat while the syncopated 8th notes played on the ride cymbal bell (bars 7 and 8 of the cell) create a transition to resolve the rhythmic dissonance at the beginning of bar 9 of the cell. The remainder of the drum cell is a (relatively) simple and definite 4/4 funk beat. Like the melodic rhythmic textures, this beat could have been created using fractioning techniques but it was decided to keep it simple so that an underlying sense of recurring rhythmic symmetry could be established and maintained throughout the composition.

Serendipity

The idea to add the reverse piano part came late in the composition process. It wasn’t anticipated that it might sound quite as developed as it does. It begins with a very sparse rhythmic texture in much the same way as an improvised piano solo by Thelonious Monk5 might sound. As it becomes denser, both rhythmically and harmonically, it develops into a type of rhythmic call-response dialog with the bass and drums that is at its most recognizable and musical in the brief exchange that occurs between bars 113 and 119 in the finished score.

Conclusion

The processes used to organize rhythmic texture and timbres in this composition are, in my opinion, a lot like ink blocks are for a painter. They enable a composer to very quickly generate ideas and a framework in which to work with those ideas. More than this, they are processes that can expand the rhythmic vocabulary of composer and improvising performer alike, not just for ensemble or comping rhythms, but for phrasing of bass, melody and other solo instrument lines.

Bibliography

Schillinger, J., The Schillinger System of Musical Composition: Book 1 – Theory of Rhythm. New York, Da Capo Press, 1973.

Vella, R. and A. Arthurs, Musical Environments: A manual for listening, improvising and composing. Sydney, Currency Press, 2000.
1 Happenstance n : an event that might have been arranged although it was really accidental. (www.dictionary.com)
2 Schillinger, J., (1973) The Schillinger System of Musical Composition: Book 1 – Theory of Rhythm. New York, Da Capo Press.

3 The original tempo was 185 BPM. This was later revised to 165 while a few improvised piano solos were recorded. These solos were ultimately discarded but the tempo remained unchanged, thus the recording runs slightly longer than 3 minutes.

4 One notable exception occurs in bars 33 – 34 to allow the statement of all 11 notes of the original scale to unfold in sequence, thus establishing the tonality of all that follows.
5 Specifically Monk’s solos on Bags’ Groove (Miles Davis, Bags’ Groove, Original Jazz Classics OJC 245 CD, 1954)

I won’t speak directly to his ideas as I haven’t fully grasped them yet, but M-base has a great essay on this topic at his website. What I was reminded of, however, was how one aspect of symmetry was covered by Schillinger. Take for example a C major scale expressed in the numbers of its half-step intervals:

 2+2+1+2+2+1

That’s C major ascending but if we use that same interval sequence and descend from C it yields the notes:

C Bb Ab G F Eb Db C

In other words, the symmetrical inversion creates the C phyrigian mode or conceived another way, the key of Ab major as being the “symmetrical relative” of C major.

Similarly C harmonic minor:

2+1+2+2+1+3+1

When symmetrically inverted:

C Bb A G F E Db C

Reversed:

C Db E F G A Bb C

As a basis for creating new melodic material, using symmetry in this way yields some tasty results. The above scale, for example, being one that would form a colorful base for improvising around C7, Eb7, Gb7 or A7. In other words, the symmetric inversion of a harmonic scale generates a dominant scale for its parent note and the notes of a diminished 7th chord built on that note. Why? The new scale contains the tritone intervals of Db – G (hence Eb7 or A7) and E – Bb (hence C7 or Gb7)

I’m not sure how any of that relates to the Ancient Greek modes and their manipulation – more reading to do…

The coincidence of two periodic frequencies where the ratios are 1:1, 2:1, 3:1, etc. produce the unison and unison octaves. These are said to be the intervals of most consonance because the human ear is most sensitive to slight variation. For example, if you start with two sine waves tuned exactly together (a 1:1 ratio) and then slowly detune one, you will hear a slight ‘beating’ effect introduced as the ratio relationship drifts away from the perfectly consonant 1:1.

In the harmonic overtone series, the ratios of the first two partials (the fundamental tone and the 1st overtone) are 1:1 and then 2:1 – intervals of the unison and the unison octave. The ratio of the third partial is 3:2 and produces the interval of a fifth. Helmholtz conducted experiments using two sirens that spun at the rate of 3:2 and found if the frequency was decreased sufficiently, the pitch relationship remained the same but eventually all that is heard is the rhythmic beating of 3 against two.

If we skip over the fourth partial (3:1 – a unison two octaves above the fundamental) to the fifth partial, we find a ratio relationship of 5:4 – a ‘pure’ major third.

Henry Cowell, following from Helmholtz’s experiments, combined these intervals not just harmonically but rhythmically. Thus, a simple C major triad could become a rhythmically interesting composition from the simple materials of three notes regarded as consonantly related to each other and the polyrhymic nature that arises when combining their respective ratios. Example:

An audio example can be heard here: http://www.4shared.com/file/21153861/8befbb2f/Cowell1.html

1. Thou shalt have no other gods before Syntax.

2. Thou shalt not set up unto thyself modern authorities: thou shalt bow thyself down before the original sources, and them only shalt they serve.

3. Thou shalt not take the name of the latest German in vain; for the reviewers will not hold him guiltless that taketh the name of a German in vain.

4. Remember thine author: peradventure he is not spurious.

5. Honor prose composition, when thou teachest: that thy pupils may rejoice and thy pile of exercise books increase before thine eyes.

6. Thou shalt not murder thy native language.

7. Thou shalt read the journals.

8. Thou shalt pronounce proper nouns: moreover, thou shalt pronounce them fluently.

9. Thou shalt not bear false witness against the text of a poet by filling up the lacunae therein, until thou shalt have transposed the verses and turned them end for end.

10. Thou shalt not covet thy neighbor’s horse. 

3.0  ANALYSIS OF SCHILLINGER’S Op.12, No.1

3.1 Introduction to Schillinger’s Compositions

There are believed to be thirty-three complete works and eight to ten fragmentary (or abandoned) works.3 Works Op. 1 to Op. 19 were all composed in Russia. Op. 20 was composed either while in transit to the United States4 or shortly after arriving there. Only eight of his works were ever published, all of which were composed prior to Op. 20. Of the ten works composed in the US, four employed the Theremin.

Due to Schillinger’s fame as a music theorist and teacher throughout the 1930s, it’s easy to overlook the fact he was widely regarded as a composer of renown prior to his leaving Russia. Contemporaries such as Dimitri Shostokovich and Vladimir Horowitz hailed Schillinger as ‘the next Beethoven’. His compositions were performed often and by some of the finest orchestras, both in the USSR and abroad in Europe and the United States. In fact, such was the regard for Schillinger as a composer; he was commissioned to compose a piece in celebration of the 1927 tenth anniversary of the formation of the Soviet Union. The official concert to mark this date exclusively featured just two composers: Beethoven and Schillinger.

3.2 Review by Henry Cowell

In 1947, the Schillinger Society5 oversaw the publication (by Russian-American Music Publishers: New York) of Schillinger’s Op. 12 Five Pieces for Piano; Op. 14 Excentriade – Three Pieces for Piano; and Little Waltz (Valse for Piano – 1926). Complete transcriptions made by me from the original sheet music for all of these are included in section 5.0 (Appendix I) of this paper. After their original publication, Henry Cowell had this to say about them in a review:6

“Discussion of the Schillinger System of Composition7 has made Schillinger famous as a theorist, and one is apt to forget he was a skilled and interesting composer. Since the System was a work of his maturity, he did not use it in creating his earlier works.“

The emphasis is mine because I intend to prove in this analysis where Cowell is mistaken. His review continues:

“All the piano works in the two sets under discussion here fall into the same general category. They were written at a time when Scriabin’s was the greatest influence among most young Russians; Scriabin was felt to be the great new force creating fresh musical materials. A casual look at the pages of these piano pieces suggests that Schillinger works are no more than the imitation of Scriabin’s chords and general style, but closer examination reveals that while Schillinger has adopted Scriabin’s form, his chord spacing, and his idea of exploring new sounds, the actual chords are not Scriabin’s famous ‘chord of nature’, but are Schillinger’s own. Moreover the tonal relations are far more daring than those of Scriabin; there is more counterpoint, and there are excursions into unheard-of keys.”
 

3.3 Where Cowell is Mistaken

First impressions of Op. 12 (and the other pieces published) do agree with Cowell and his reference to Scriabin. Initial probing of analysis in which questions were asked about the extensive use of double-sharps (a hallmark of Scriabin) led to considerations that perhaps their use had some kind of symbolic meaning.

This was particularly so in Op.12, No. 1 titled Poème Héroïque where it might be possible to interpret the use of double-sharps (most notably in the octave run down in bar 7) could allude to something higher than is able to be expressed fully in notation. This conclusion was drawn from knowledge that Schillinger was known to have been interested in ancient Greek and Slavic mythology and the possible connection between this and the ‘Homer epic’ suggested by the title. This hypothesis may still be true however, the simplest explanation can actually be found in Schillinger’s own system.

In Book II (Theory of Scales) Schillinger extensively explores the music materials that can be developed out of symmetrical divisions of the octave. In particular, if one looks at the recurrence of tonal resting points of Eb (bar 2), G (bar 3) and B (toward the end of bar 4) we see an augmented triad or, the symmetric division of the octave into three parts.

This still didn’t explain the use of the double-sharps in the melody (e.g., the melodic phrase at the end of bar 2). However, once it was realized that the scale source that would produce those alterations was D# major, this then made convincing evidence that Schillinger had indeed used his symmetry theories from Book II of his System. The Eb – D# octave relationship is thus explained by the symmetry of an expanded scale built entirely of major third intervals: Eb – G – B – D#.

This enharmonic spelling difference, aside from being evidentiary of Schillinger’s theories from Book II is again confirmed in Book IV (Theory of Melody). Here, Schillinger devotes several pages to thoughts about twelve-tone equal temperament tuning and to other systems in which enharmonic differences produce different pitch frequencies. It could be deduced from this that, while Schillinger’s pieces in Op. 12 were composed for performance on a piano of twelve-tone equal temperament, he could well have conceived the piece in another tuning, such as Meantone. This hypothesis is based on notion that Meantone tuning (like Pythagorean) is such that it makes intervals such as the major third closer to their ideal just rations. In doing so, it slightly flattens all the fifth intervals and sharpens fourths in such a way as to produce the octave relationship of Eb to D#.

Another pointer to evidence of Schillinger using his System in the composition of Op. 12, No. 1 is actually pointed out by Cowell himself where he says, “there is more counterpoint (than in Scriabin)”. This isn’t any surprise after one sees Schillinger devote very large sections of the SSMC to counterpoint (Book VII – Theory of Counterpoint is written entirely to the subject, but it recurs in each of the books that follow).

Another less obvious sign of Schillinger’s System in action is his use of stratified harmony. This compositional technique also is extensively discussed in the SSMC. In fact, the notion of stratification is fundamental to the Schillinger System and is first introduced at the beginning of Book I in Theory of Rhythm (the coincidence of two periodicities to generate a resultant third periodicity). However, even without this evidence, one only need look as any of the Books from V onward to see various types of stratification in Op. 12 No. 1.

If one breaks down the polyphony of this tune, what can be seen is the way Schillinger has conceived it in four voices and that each voice is in a different (major) key: D# – B – G – Eb respectively for voices one through four. There is, as Cowell noted, much use of counterpoint in the form of phrases that cascade in canonic form through the voices. However, once the polyphony is separated into individual voices – as four separate strata – it also explains things that might otherwise seem anomalous, such as the use of D# and Eb to spell ‘the same’ note in the treble of bar 4. It also explains various vertical amalgamations (e.g., the altered G7 chord that occurs in bar 3) that Schillinger discusses in Book V and calls ‘pitch assemblages’ (the coming together of different strata).

Perhaps the reason why Cowell didn’t believe Schillinger’s System is evident in this piece is the fact it doesn’t appear to be particularly sophisticated rhythmically. More analysis needs to be done however; I suspect each strata of polyphony is operating in a different time signature and this too would be in accord with Schillinger’s most basic underlying principles outlined in Book I – Theory of Rhythm.

–

3 Quist, Ned, (2002), Toward A Reconstruction of the Legacy of Joseph Schillinger, Notes, June 2002, Vol. 58 Issue 4, p765.
4 Schillinger in West Germany for some months in 1928 before finally settling in the US.
5 A group founded posthumously by Schillinger’s widow, Frances, and several of his students to promote his teachings.
6 Cowell, Henry, (1947), Review: Five Pieces for Piano, Op. 12; Excentriade, Three Pieces for Piano, Op.14, Notes, 2nd Ser., Vol. 5, No. 1. (Dec. 1947), pp. 128 – 129.
7 First published in 1945.