The end of the table is near

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. 

Civilization Exhaustion

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?

In news just to hand…

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!

Harry Potter 2 Here I Come

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.

Y and other things on my reading list

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?

Happenstance – Schillinger in Action

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)

 

On Symmetry

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…

Rhythm & Consonance

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

Ten Commandments for Classical Students

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. 

Schillinger – Part 3

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.

Schillinger – Part 2

THE SHILLINGER SYSTEM OF MUSICAL COMPOSITION

2.1 Overview

The origins of Schillinger’s ’system’ and his concept for it are unknown at this stage however; similarities are evident between the foundation of his system (the Theory of Rhythm) and Nikola Tesla’s theoretical work on the invention of alternating current electricity. As is widely known today, alternating current operates on the same principle as sound waves where the periodic motion moves through a 360º ‘phase’ and generates energy. That energy can be increased when the phases of two or more alternating currents are combined. While Schillinger doesn’t speak directly of a connection, he does write extensively of this type of periodic motion as being the scientific basis of all the arts. Furthermore, where phase interference between two cyclical currents generates electrical energy, Schillinger asserts that the ‘interference of periodicities’ (his term for phases or cycles) generates aesthetics.

Understanding Schillinger’s Theory of Rhythm is central to understanding his whole approach. For him, rhythm is not simply a matter of time-rhythm. Schillinger begins by applying rhythm to time durations and then extends it to all other stages of composition – the way in which block harmonies change, intervals in scales and melodies, entrances of counter-themes in counterpoint, distribution of parts through a score, and other processes of composition. These processes are broken down into twelve ‘books’ within the Schillinger System of Composition (hereafter referred to as the SSMC).

2.2 Book I – Theory of Rhythm

Schillinger states at the outset of chapter one of this book that the ‘customary method of musical notation…is inadequate for the analysis and study of rhythmic patterns.’ He then introduces three parallel systems of notation that he will use, initially for the notation of time-durations but ultimately for other components of music and composition in every other book within the SSMC. These are: (1) numbers, (2) graphs and (3) musical notes.

The use of musical notes is self-explanatory and numbers are used in their normal mathematical operations, such as the four actions of addition, subtraction, multiplication and division as well as raising to powers, extracting roots, and for the ease with which they can be used to create permutations of patterns.

However, it is the way in which Schillinger employs graphs that is the key to his system. The graph method he uses is the same used to record variations of components during a time period (stocks in finance; diseases in medicine, etc.). In Theory of Rhythm, Schillinger only deals with time (pitch, intensity and so on are dealt with later). The horizontal coordinate (the abscissa) read from left to right expresses time. The vertical coordinate (known as the ordinate) is used to express the recurrence of a phase, i.e., the moment of attack.

He then goes on with an explanation of basic wave motion and illustrates the way a sine wave is represented in his graph system as a square wave.2 This periodic motion is measured in phase units Schillinger calls periodicities of phases or simply, periodicity. The coincidence of two phases of two difference periodicities intensifies the attack. The recurrence of intensified attacks (“accents”) constitutes musical measures (“bars”). In Schillinger’s words, “The reality of bars depends actually on the placement of attacks, not on the placement of bar lines on music paper.”

Schillinger then illustrates various forms of continuous recurrence of attack groups – i.e., periodicity. The most basic form of periodicity in which all attack groups are identical is called uniform periodicity or monomial periodicity. Using numbers, these could be represented as:

1 + 1 + 1 + 1 + …
2 + 2 + 2 + 2 + …
3 + 3 + 3 + 3 + …
n + n + n + n + …

where each number represents a unit of graph measurement on the abscissa.

From here, Schillinger explains the way the numbers and graph representation can then be converted into musical notation simply by using those units to represent note durations. For example, “1″ could be said to represent a quarter note in which case “2″ represents a half note, “3″ a dotted-half note, “4″ a whole note and so on.

What follows after this is what Schillinger calls “generation of resultant rhythmic groups as produced by the interference of two monomial periodicities – that is to say, the way in which one monomial periodicity (say, 3, 3, 3, 3) may be combined with another (say, 4, 4, 4, 4) so as to produce another rhythm.” In its simplest form, the resultant of this type of interference is syncopation. The remainder of Book I is then given over to a thorough investigation of every possible type of interference and the way these resultant patterns (non-uniform periodicities) can themselves be combined to generate an infinite number of rhythmic patterns.

Ex. 1 below shows both rhythm and pitch relationships of Beethoven’s Minuet in G in graph form. The perceptual similarity to a city skyline should also be noted as Schillinger asserted his graph method worked both as an analytical tool and as one that could generate any musical component from anything with a pattern that could be represented in the two dimensions of his graph system. In other words, composers didn’t need to be limited to musical patterns when composing. He also asserted that the aesthetics of any pattern that was visually appealing could be directly translated into something of comparable aural appeal.

2.3 Book II – Theory of Scales

 The same universality of approach characterizes Schillinger’s Theory of Scales. He classifies any number of tonal units, beginning with a one-unit scale that represents a single note repeated. He also introduces the concept of symmetric scales based on the division of the octave into equal parts (2, 3, 4, 6, 12). Still more new groups are obtained by division of two octaves into three parts, three octaves into four parts, and so on. Interpolating passing notes to fill in gaps between pivotal tones can also create more new scales.

Familiar and unfamiliar scales can also be created by simple permutation of half-step combinations (2 + 2 + 1 + 2 etc.). Any scale can be created this way.

Schillinger then relates the resulting progressions to chordal structures derived from these scales. In other words, he explores modulation as a melodic event as well as a harmonic event. Example 4 shows how an octave divided symmetrically into three equal parts can generate a chordal root movement, as was done to great effect by John Coltrane in “Giant Steps”.

2.4 Book III – Variation by Means of Geometric Projection

This is the slimmest of all the books within the SSMC and perhaps for the non-mathematically minded, the most difficult to penetrate for meaning. The book is divided into two parts: (1) Geometrical Inversions and (2) Geometric Expansions.

In many respects, the processes of inversions that Schillinger explores have origins that date back at least as far as Bach. His graph method provides an easy to interpret visual guide to inversion. The second part with its mathematical permutations used to generate new scale and melodic material has all the hallmarks of pitch class set theory. However, Schillinger uses visual art references to illustrate the way ‘geometric rotation’ can be used to distort an image without losing the connection to the aesthetics of the original. This type of graphic manipulation we take for granted these days in computer applications such as Photoshop.

2.5 Book IV – Theory of Melody

In Schillinger’s conception, melody is the musical projection of a curve that thus can firstly be plotted using basic trigonometric operations and ultimately synthesized. Much of the introduction he writes to this book speaks of his most basic aesthetic that composition, particularly insofar as the composition of melodies is no different to the engineering involved in building a house. He is openly critical at this point about the lingering romantic-era notion of the composer as ‘divinely inspired genius’. It is perhaps this outspoken opinion, more than anything else Schillinger did, that led to music institutions of his time dismissing him and his theories out-of-hand.

Book IV then applies the graph method as a means to represent ‘axes’ of balance. The dynamic quality of a melodic line is determined by alternation of balancing and unbalancing axes, which are melodic fragments directed to and away from the axis of perfect balance. This latter represents the tone of maximum duration in a given melodic fragment. Schillinger further relates the arithmetical summation series with melodies in which each successive interval is the sum of two or more preceding intervals counted in semitone units. He also demonstrates how intervals can my permutated using multiplication so that a Bach fugue would sound like a piece by Debussy in whole tones if the intervals were multiplied by a factor of two, since all the semitones would vanish in the process of intervallic doubling.

2.6 Book V – Theory of Harmony

Schillinger includes an account here of orthodox procedures but its methodological value lies in the greatly generalized idea of stratified harmony in which single tones are formed into two-note, three-note and four-note combinations. These then serve in turn to form larger harmonic structures or, as Schillinger calls them, “pitch assemblages”. He also includes the concept of the voice leading ‘circle’ that produces motion between chords in a systematic manner (see Example 5). Ascending and descending root motion patterns are also described in mathematical (and therefore permutable) terms. Not only is the familiar cycle of fourths explored, but cycles of 2, 3, 5, 6 and 7 are also detailed.

2.7 Book VI – The Correlation of Harmony and Melody

Additional harmonic considerations are shown and exhaustively examined in numerous musical exercises both in this book and the one that follows. The material points out that the familiar Western European system of diatonic harmony is just the tip of the iceberg since, according to Schillinger, “any scale can form the basis of a diatonic or symmetric system from which characteristic intervals and chords may be derived.”

Other things explored here cover 7th, 9th, 11th and 13th chords and techniques for voice-leading upper structures (see Example 6) – hybrids and upper structure triads.

2.8 Book VII – Theory of Counterpoint

This book is sub-titled ‘The Technology of Correlated Melodies’ and it delves deeply into things such as correlation between two melodies, attack groups in two-part counterpoint, counterpoint with symmetric scales, canons and imitations, and so on. Harmonization of two-part counterpoint is also explored, as are melodic, harmonic and contrapuntal ostinato.

2.9 Book VIII – Instrumental Forms

Instrumental form for Schillinger means “a modification of the original melody and/or harmony which renders them fit for execution on an instrument.” Discussion of attack rhythms first explained in Book I is further explored here in instrumental forms. Further explanation is also given to the concepts of stratified harmony and counterpoint from preceding books.

2.10 Book IX – General Theory of Harmony

The focus on stratified harmony continues here. Schillinger begins with ‘one part harmony’ and ‘one stratum of one-part harmony’. From here he works through two-part harmony, starting with one stratum of two-part harmony, then two parts, then hybrids of those as well as diatonic and symmetric ‘limits’ of compound structures. Similarly, three-part and then four-part harmony is explored before he moves into the area of quartal harmony.

The second half of this book looks deeply into applications of the preceding. Schillinger addresses the issue of melodic and harmonic continuity, accompaniment, composition of canons from strata harmony as well as ‘density’ and its applications to strata.

2.11 Book X – Evolution of Pitch Families

This slim book is a summary of sorts of pitch scales, harmony and melodization of harmony.

2.12 Book XI – Theory of Composition

This book is perhaps the crowning achievement of Schillinger’s ’system’. Here, he methodically explores the components of a composition, beginning with thematic units, moving into thematic continuity and strategies for planning a composition, and finally into ‘Semantic (Connotative) Composition’.

It is in this section that Schillinger introduces what he calls the “psychological dial” – a representation of ‘quadrants’ analogous with the Myers-Briggs Personality Type indicator. A dozen or so chapters are devoted to the semantic basis of music, composition of sonic symbols and finally, the composition of semantic continuity.

2.13 Book XII – Theory of Orchestration

This final book in the SSMC addresses timbral considerations for all orchestral instruments as well as electronic instruments that Schillinger divides into two groups: (1) Varying Electro-Magnetic Field instruments such as the Theremin and (2) Conventional Sources of Sound such as an electrified piano and the Hammond Organ.

The second half of Book XII is devoted to ‘instrumental techniques’ (orchestral forms and so on) and then intensities, attack forms and pitch ranges as they relate to instrumental combinations.

In the final chapter of Book XII, is titled ‘Acoustical Basis of Orchestration’. It’s only a page long and the editors note the original manuscript didn’t finish at this point. However, the publisher decided the material that followed was incomplete and that much of the material on orchestration had already been presented in earlier books.

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2 It’s important not to confuse this square wave as representing a sound. It merely represents attack and intensity of a recurring phase cycle.

Schillinger – Part 1

INTRODUCTION

Joseph Schillinger (1895 – 1943) was arguably one of the most remarkable figures in the first half of the twentieth-century. As a young man, his interests ranged far and wide and encompassed many fields of learning from philosophy, literature and Slavic mythology, languages, mathematics, physics, electrical engineering, music, fine arts, dance and design. After graduating the St Petersburg Conservatory in 1918, where he studied composition and conducting under Nikolay Tcherepnin, he entered the newly formed USSR’s music academic world and quickly rose through its ranks to become an acknowledged authority on ‘modern music’ as well as administrator and musical consultant to the Soviet’s leading opera and ballet companies. He also organized and ran Russia’s first jazz orchestra in 1927.

As early as 1918, he published a paper about electricity and its potential applications in the development of a whole world of new musical instruments. In 1922, publication of a collection of his poetry in which he envisioned an artist in the future whose senses were fused anticipated art forms of today such as inter-media and virtual realities. Schillinger’s expertise in both music and electrical engineering enabled him to collaborate with Leon Theremin and bring the invention of the Thereminvox to fruition. Again with Theremin, he invented the Rhythmicon (a fore-runner of the electronic drum machine) as well as the world’s first electronic music synthesizer for the RCA-Victor Company. Schillinger’s name exists alongside that of Leon Theremin on the US Patents for these inventions.

Several years before he emigrated to the US, Schillinger made pioneering ethno-musicological field recordings of a number of Georgian tribes. After emigrating to the US in 1928, Schillinger (along with Charles Seeger, Henry Cowell and others) founded the New York Musicology Society.

Once in the US, Schillinger quickly established himself as a composition teacher of renown. His teaching methods were based on a system of his own invention (published posthumously as The Schillinger System of Composition) and attracted many of the most famous Broadway, radio, film and jazz composers of the 1930s. George Gershwin turned to Schillinger at a time when he believed he’d reached the peak of his creativity. During the four years Gershwin spent studying with Schillinger, he composed some of his finest works such as the Cuban Overture, Porgy and Bess, and I’ve Got Rhythm (Variations).

During the 1930s, Schillinger pioneered developments in the synchronization of music to film. His underlying belief of music and the arts as a scientific phenomenon ultimately led to the (posthumous) publication of his second major work, The Mathematical Basis of the Arts. At the time of its publication in 1947, various reviewers in academic journals cited the work as “the most systematic and exhaustive treatment of the subject ever written” and “a major landmark in the history of aesthetics”.1

In the years immediately following Schillinger’s premature death in 1943, aside from his two major books being published as well as several of his compositions from the early 1920s, Schillinger House was established in Boston to teach his ’system’. This later underwent a name change and is still known as the Berklee School of Music.

Despite all these successes in life, Schillinger’s name faded from memory to the point where it currently exists as a mere footnote to twentieth century music and arts history. It is outside the scope of this paper to scrutinize every one of Schillinger’s accomplishments and so it will focus on his major work on composition – The Schillinger System of Composition.

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1 Myhill, John, (1950), The Mathematical Basis of the Arts (Review), Philosophy and Phenomenological Research, Vol.11, No.1 (Sep. 1950), pp. 109 – 113.

The Computer As Musical Medium

Abstract

This paper examines the concept of computers as a musical medium. The word medium has many definitions. Among them is “a person thought to have the power to communicate with…agents of another world or dimension.”[1] Sceptics argue that such people are deluded or out of touch with reality. However, if disbelief is suspended and the computer considered as something that can channel fantasy into reality, then a case could be argued that a computer can actually act as this kind of medium.

Introduction

Christopher Longuet-Higgins in Musical Structure and Cognition (ed. Howell, Cross and West: xi)[2] describes music as “perhaps the most mysterious of all the arts, being at the same time so remote from reality and so faithful to experience.” To talk about reality at all is to talk about our perception of it. Perception is shaped by experiences, both real and imagined and these combine to create memories. Memories enable us to compare and contrast experiences, our perceptions of them, and thus define our reality. One of the prime characteristics of the computer as a medium is its ability to blur this reality and by extension, alter our state of consciousness.

Virtual Realities

Lewis Carroll’s stories of Alice’s Adventures in Wonderland and Through The Looking Glass both provide good illustrations of blurred realities created in the literary medium. They conjure worlds in which big is small, up is down, and so on. For a child, these stories challenge their perception of the world they know. It is the same challenge faced by the character of Neo in the Matrix films and the Virtual Reality world in which the films are set. It is a computer world where none of the usual laws of physics apply, just as Wonderland was for Alice. At a deeper, more philosophical level, both explore concepts of morality, choice, and a search for meaning.

Carroll’s Jabberwocky poem could also be a metaphor for today’s news media – a medium that presents to us a reality but which is filled with Orwellian double-speak and jibberish. Alice’s statement after reading Jabberwocky sums it up very eloquently:

“...it’s rather hard to understand!” (You see she didn’t like to confess, ever to herself, that she couldn’t make it out at all.) “Somehow it seems to fill my head with ideas – only I don’t know exactly what they are! However, somebody killed something: that’s clear, at any rate…”[3]

A Playground For Musical Fantasy

The references to Carroll have been used to highlight an important facet of the computer as a musical medium and in particular, the methods by which it can represent things that otherwise could only be imagined. When Alice first begins to read the Jabberwocky poem, it makes absolutely no sense to her at all because the typeface is all reversed. It dawns on her that the poem can only have meaning if its words are reflected in a mirror. If one was to make an audio recording of a reading of Jabberwocky using computer software, the medium is such that it can easily be played in reverse thus allowing the listener to hear the poem actually spoken as Carroll might have imagined. In a sense, it could be said that Carroll’s creative spirit is being channelled directly through the medium.

Similarly, the computer can act as a musical medium to channel any sound a person might be able to imagine from their thoughts and into a world where everybody can hear them. If there is any limitation to this, it’s unlikely the computer medium is at fault. Rather, the only possible limitation will be that of the human operator’s imagination and their ability to use the sonic manipulation capabilities of various music software programs.

Taboos, Invention and Creativity

In music, just as in life, there are many taboos. By definition, these are strong social prohibitions relating to human activity or social custom declared as sacred and forbidden; breaking of the taboo is usually considered objectionable or abhorrent by society.[4] What is particularly interesting, however, is that taboos are social conventions that exist in reality but not necessarily in the human mind. There seems to be a consensus among those who have studied creativity (Csikszentmihalyi et. al.) that creative individuals are aware of traditions but aren’t afraid to challenge and break from them.[5]

Throughout music history, various musical taboos have been broken. Perhaps the most significant break was when western music was liberated from its role as purely religious and devotional to become a secular entertainment. The tritone interval, once called diabolus in musica or the Devil’s interval in the early music era through to the Baroque, is now in common use across a range of musical styles.

In the past 100 years, many things once considered purely as noise and thus a taboo in music are now regarded as new and exciting timbres in the creation of new sounds. Technological advances have made this possible in music though there are many parallels in other fields of artistic expression as well. The invention of electricity not only paved the way for the capturing, storing, manipulation and dissemination of sounds. It made possible dozens of new forms of visual arts, from motion pictures to laser light sculptures and for the integration of these with sound and music. More than this, these combinations themselves – borne in the imaginations of creative people – can be channelled through the computer medium to form virtual worlds that are greater than the sum of their parts.

Conclusion

Sceptics might argue, just as they do about psychics, that the disembodiment of one sound from its traditional context to create another and the channelling of it into something labelled as “music” is the work of charlatans. It is certainly the case that the computer as a musical medium challenges traditional analysis and meaning of music but then, the very nature of music has eluded scholars for well over three thousand years.[6] As a phenomenon, music is ubiquitous and universal and yet its existence remains unexplained by any apparent practical purpose. Perhaps the best explanation might be simply that our entire perception of reality is flawed by the nihilism so prevalent in today’s culture. If the computer medium really is the conduit between some other world or dimension and this one, just as the rabbit hole was Alice’s portal into Wonderland, then the future as I see it looks as bright and meaningful as any I can imagine.

“Reality: a nice place to visit, but I wouldn’t want to live there.” (Anonymous)

References

1 Dictionary.com (2006), Medium, http://dictionary.reference.com/search?q=medium, Accessed 20 May, 2006.
2 Howell, P., Cross, I., and West, R. (Eds.), (1985) Musical Structure and Cognition, London: Academic Press.
3 Literature.org, (2005), Lewis Carroll: Through The Looking Glass, http://www.literature.org/authors/carroll-lewis/through-the-looking-glass/chapter-01.html, Accessed 20 May, 2006.
4 Wikipedia, (2006), Taboo, http://en.wikipedia.org/wiki/Taboo, Accessed 20 May, 2006.
5 Csikszentmihalyi, M., (1996) Creativity: Flow and the Psychology of Discovery and Invention, New York: Harper Collins.
6 Serafine, M. L., (1988) Music As Cognition: The Development of Thought in Sound, New York: Columbia University Press.

Writing About Music

Writing about music, as someone once wittily observed, is like dancing about architecture. Our language simply isn’t equipped to describe music – least of all with any empirical kind of certainty – in the same way it isn’t possible to fully describe what a person’s face looks like or even something less unique, like a chair. We can resort to the symbolic language of music to convey some meaning, but even this is almost as faulty a means of describing music as is writing about it. For example, take the following two snippets:

Even somebody untrained in reading music will be able to see that both snippets appear to be the same. Somebody trained in reading music should quickly also be able to identify them as being the opening motif of the tune Twinkle Twinkle Little Star. But are the two snippets really as similar as they appear? If you now imagine the first snippet as played on a trumpet and the second played by a violin, similarities would still exist, but only to a point. Aside from the different timbres of the two instruments and the different pitch transpositions, interpretation plays a very large part in how music ’symbols’ are converted into ‘meaning’ – arguably moreso than other written languages such as English and mathematics. Interpretation speaks to things such as tempo and dynamics as well as nuances that can’t be written, such as the performer’s existing knowledge and memory of how this tune is commonly played. In other words, traditional epistemologies of empirical and qualitative research aren’t enough to fully describe music.

This post isn’t really going anywhere, but that’s what’s in my head right now.

Music: It’s all Greek to me…

While Pythagoras is widely regarded as the founding father of ‘Musical Science’, it was Aristoxenus through his texts Harmonic Elements and Rhythmic Elements who sought to expand the boundaries of this science beyond the mere mathematical elements of the properties of sound.

It should be remembered that ‘Musical Art’ existed long before ‘Musical Science’ came onto the scene. This is to say that there already existed preferences of compositional style, performance methods for these, construction of instruments for this performance, and the habits formed by these preferences were passed on through instruction. Musical artists used diagrams and superficial generalizations in order to facilitate instruction and aid memory but they weren’t interested in principles for their own sake. It is with principles for their own sake that science begins and where Pythagoras and his disciples enter the picture. (The Harmonics of Aristoxenus – Macran: 1902) 

Pythagoras brought an empirical sensibility to the study of sound and a mathematical logic to the numerical relationships in the sensations of hearing pitch. The hypotheses of Pythagoras proved to be ‘good science’ and continue to underpin modern study and research of acoustical phenomena. However, as Macran goes on to note, “For if the artists were musicians without science, the physicists and mathematicians (Pythagoras et.al.) were men of science without music.” (p 88)

Where Aristoxenus differs from the Pythagorean school is he broadened the scope of musical science. He theorized musical science should include other elements of music beyond its purely physical acoustic properties – conceptions of voice, interval, high, low, concord, discord, etc. – and sought to reduce the complex phenomena of music to these simple forms and to ascertain general laws with regards to their interconnectedness. In short, what Aristoxenus could see (and what the Pythagoreans failed to see) was that the essense of musical sounds lies in their dynamic relationship to each other. Furthermore, Aristoxenus conceived a notion of music as a system or organic whole of sounds, each member of which is essentially what it does, and that no sound can be a part of that system simply because there’s room for it, but only if there’s a function it can discharge.

The conception then of a science of music which will accept its material from the ear, and carry its analysis no further than the ear can follow; and the conception of a system of sound functions, such and so many as the musical understanding may determine them to be, are the two principle contributions of Aristoxenus to the philosophy of music.

Aristoxenus was concerned with the philosophical definitions and categories necessary to establish a complete and correct view of the musical reality of scales and tonoi (accent), two primary elements of musical composition. In Harmonic Elements he defines seven “technical” categories (not necessarily in this order) in his theoretical system:

Notes. Aristoxenus’s definition is both economical and sophisticated: “a falling of the voice on one pitch is a note; then, it appears to be a note as such because it is ordered in a melos and stands harmonically on a single pitch.” This subtle definition destinguishes among a voice, which is articulate sound; a single pitch, which is the position of a voice; and a note, which is a production of sound at a single relative ordered position within a musical composition, a melos.

Intervals. Intervals are defined as bounded by two notes of differing pitch, distinguished by magnitude, by consonance or dissonance, as rational or irrational, by genus, and as simple or compound (the first four distinctions also apply to scales). For Aristoxenus, the fourth and the fifth, not the octave, were the primary scalar components of music and music theory.

Genera. Aristoxenus recognized three basic genera of tetrachords: the enharmonic (also known as harmonia), the chromatic (also known as color), and the diatonic; the last two of which exhibited various shades. The intonations were created by the two middle notes of the tetrachord, which were “movable”, in relation to the two outer notes of the tetrachord, which were “immovable”.

Scales. Aristoxenus rejected the closely packed scales of the Harmonicists (Pythagoreans) because by ignoring the principles of synthesis and continuity and consecution, they failed to accord with musical logic. Scales, Aristoxenus asserts, must always follow “the nature of melos“: an infinite number of notes cannot simply be strung together; and if a melos ascends or descends, the intervals formed by notes separated by four or five consecutive degrees in the scale must form the consonant intervals of a fourth or fifth. Scales larger than the tetrachord are assembled by combining tetrachords, either by conjunction (eg., E F G A and A B C D) or disjunction (eg., E F G A and B C D E). Relying on the aforestated principles, Aristoxenus formulates a detailed set of possible progressions.

Tonoi and harmoniai. This section of Harmonic Elements hasn’t survived, but it’s clear from other sections of the treatise that Aristoxenus associated the tonoi with “position of the voice.” Harmoniai is the collective name given to the seven Greek modes (not to be confused with the seven Church modes of the Middle Ages). Both Plato and Aristotle considered that the harmoniai could have an impact on human character, but in their use of the term, they almost certainly are referring to a full complex of musical elements, including register, characteristic rhythmic pattern, textual subject, etc.

Modulation. Since the functions of the notes in a scale would change in the course of a modulation, a full comprehension of musical logic would be impossible without determining the nature of a modulation. This section of Aristoxenus’s treatise hasn’t survived, but Cleonides articulates four types of modulation: in scale, genus, tonos, and melic composition.

Melic composition. This subject, Aristoxenus’s final category, remains obscure in the surviving treatises. Aristides Quintilianus refers to choice, mixing, and usage as three parts of melic (and rhythmic) composition. He goes on to remark that the particular notes used will indicate the ethos of the composition. Cleonides identified three types: diastalic, or elevating, which conveyed a sense of magnificance (mainly elevation of the soul, and heroic deeds, especially appropriate to tragedy); systaltic, or depressing, which expressed dejection and unmanliness, suitable to lamentation and eroticism; and hesychastic, or soothing, which evoked quietude and peacefulness, suitable to hymns and paens.

Because the Aristoxian tradition lent itself to the construction of musical “rules”, it came to be viewed as a practical tradition, distinct from the ideal or purely theoretical traditions of the Pythagoreans and the Harmonicists. Yet this is a misleading and simplistic dichotomy. While Aristoxenus’s followers may often have failed to grasp his larger epistemological concerns, it is clear that he was trying to develop an idealized phenomenology of music, based not on the abstraction of number but rather on a careful definition of the separable elements of musical sound that became music only when they combined to create something the intellect would comprehend. It is one of the ironies of history that the Aristoxian tradition, especially as it was adopted and adapted by later Western theorists, forgot the interests of its founder and instead became mired in fruitless practical controversies, especially in the areas of tuning.

THE PAN!

The show was called The Pan. It looks like it is dead now.

That had been driving me nuts.

Your Fred fix

Satiate your fundamental human need for strange independent toons with Channel Frederator. Anyone can submit stuff to them, in any style, serious, funny, or just weird (as long as it’s animated), and actually more of it is at least interesting than is total crap. Occasionally brilliant. One short that I really like is “Missionary”, the second one in episode 63 (above), starting just before 6:00. Dig that ominous bass line every time the repressive tyrant returns — he of course represents me, Rodney Toady, lording over the other writers on this blog. Bwahahaha.

What Is Music?

I woke with the answer to this in the middle of the night last night. Well, not the complete answer, but a brainwave of sorts that I’ll likely pursue in my research. The actual wording of the answer is still sketchy, but it goes something like this.

Beethoven apparently once answered this question by saying, “Music is a metaphor – life provides its analogies”. I think it’s more true to say life is its analogy. The origins of the question of ‘what is’ anything can be traced back to antiquity and it remains a cornerstone of philosophical thought. ‘What is music?’ is a question that boggled the minds of the ancients and its answer continues to remain ellusive. Throughout the history of Western knowledge, music has at various times been placed on a singular polarity with science at one end and the Divine or supernatural at the other.

Pythagoras certainly did much to create an empirical scientific basis for music, although his findings related more to the acoustic properties of musical sounds than to the art of creating music. Aristoxenus (a pupil of Aristotle) advanced a theory that the acoustic properties of musical sounds (the ratios of the harmonic overtone series) were at the heart of musical rhythms. In effect, Aristoxenus took a step closer to defining music composition as a natural phenomena that could be explained by science. This relationship between pitch and rhythm theorized by Aristoxenus was confirmed by the experiments of Hermann von Helmholtz in the 19th century. (See his book On the Sensations of Tone as a Psychological Basis for the Theory of Music first published in 1863.)

Before leaping forward in history from Aristoxenus, it’s important to note how philosophy in general has slowly disolved into a multitude of ’sciences’. Put very simply, as philosophers arrived at answers to the questions they asked, branches of science were founded. These branches themselves subsequently, through questions of problems that arose within them, formed branches of their own leaving philosophers with less and less to ponder beyond ‘does any of this really exist at all (and what does it matter anyway)?’

If Beethoven’s statement above is true, let’s look at some of the common analogies people have used to describe music. The two most common are ‘music is like mathematics’ and ‘music is like language’. While it’s true that music embodies many of the characteristics of both of these, neither in itself seems able to fully describe music nor explain what it actually is. I’m of the opinion that music is most like mathematical theories that posit the idea that numbers exist a priori. In other words, music already exists and composers (as creators of music) simply ‘discover’ things about it and these discoveries are called music. Following on from this, the variety of musical styles across cultures and epochs is analogous to arithmetic, algebra, geometry and a raft of other things that could be classed under the umbrella term of mathematics.

That said, music shares a lot of the attributes of language. Theories of the origins of human speech and language point to the possibility it evolved from involuntary verbal expressions of basic emotions (fear, fright, joy, etc.) This sounds entirely plausible though it’s worth noting that the evolution of language – meaning, its development into a variety of sophisticated verbal and written forms – occured much more rapidly than the evolution of music. For example, if Indigenous Australians are taken as the earliest evidence of human civilization, we can assume language has its origins somewhere between 40,000 and 70,000 years ago. Similarly, the origins of music can be said to have the same time frame.

Indigenous Australian music, recent research has shown, is not only closely intertwined with its language; songs contain all the knowledge know of the world to its people. This is interesting in itself, though outside the scope of the point I want to make. My point is twofold: that music’s origins were born in rhythm and that it then took thousands of millenia for the ‘unison’ (two people or instruments performing the same pitch together) to evolve. Language by this time was likely much more advanced from its involuntary vocalizations.

After the development of the concept of the unison, it then took several more millenia before basic harmony was conceived and developed. In the parallel world of language, the printing press had already been invented by the time triadic harmony (as well as matters of tuning and temperaments) started to be refined. Put simply, language has evolved in slow and subtle ways over the past 300 or so years while music has evolved more in the same number of years than in the past 70 millenia.

Of course, all of this hinges on the notion that ‘music’ is an evolutionary process. Charles Darwin didn’t believe this (specifically that ‘knowledge’ and ‘ideas’ weren’t subject to evolutionary principles) and more recently, Thomas S. Kuhn in his book ‘The Structure of Scientific Revolutions’ (1962) agreed. On the other hand, the music theorist Joseph Schillinger was of the opinion that music was an evolutionary process and thus bound by the same kind of laws that govern the evolution of biological organisms. His explanations of this can be found in his book ‘The Mathematical Basis of the Arts’ and these essentially expand on the language evolution idea written about above.

In Schillinger’s time (1895 – 1943) modernists (and ultra-modernists as Schillinger and many of his contemporaries in New York called themselves) were strongly attracted to the idea of music being an empirical science and that it could be composed to ’scientific’ principles. He, probably even moreso than other theorists he mixed with (Henry Cowell, Joseph Yasser, Henry Cowell in particular), was strong in his conviction about the existence of a ‘unifying theory’ for music. Unfortunately his theories were presented in a mathematical language of his own invention and thus were rejected by many mathematicians as being ‘pseudo-science’ and by many composers in the academic tradition who, by the time Schillinger’s theories were published (1947 – 1948), were strongly under the influence of John Cage’s aleatoric compositional methods or the strict serialism of composers such as Schoenberg.

I say ‘unfortunate’ because I believe Schillinger was on the right track. It must be remembered that in his time, the ‘hard sciences’ such as mathematics and physics were the only ones deemed worthy of academic study. ‘Soft sciences’ such as psychology and sociology were in their infancy – in other words – a sharp divide between science and the humanities. Music didn’t properly enter the American academic world until 1915 and even then, its focus was primarily toward performance practices. Schillinger was in the vangard of early 20th century thinkers that introduced ‘musicology’ to the American academic world.

Musicology – a broad discipline that encompasses performance as well as history, composition, pedagogy, analysis, cultural, sociological and psychological aspects, ethnomusicology and more recently, bio-musicology and the neuro-sciences – first started in Europe in the late 19th century but didn’t take root in America until the 1920s. Even so, it took another 40 or so years before musicology gained any real acceptance in academia and another 20 before the fruits of its labors started to be taken seriously. It’s worth nothing at this point that there were only four ‘new’ theories of music written and published in America between 1900 and 1950: Henry Cowell’s ‘New Musical Resources’, Joseph Yasser’s ‘An Evolving Theory of Tonality’, Harry Partch’s ‘Genesis of a Music’, and Joseph Schillinger’s “The Mathematical Basis of the Arts’ (and by extension, ‘The Schillinger System of Composition’). All four theories spoke to a mathematical basis for the creation of music. All four men were among the founding members of the New York Musicology Society in 1932 (later to become the American Musicology Society – the name by which is it still known to this day).

Terms such as ‘musico-scientific experiments’ were much in vogue as well, undoubtedly due to two factors: the invention of electricity in the late 19th century (and the creation of new musical instruments that resulted from this invention) and Albert (not to be confused with Alfred, the musicologist) Einstein’s ‘Special Theory of Relativity’ in 1905. Schillinger frequently draws on Einstein’s terminology where he writes of ‘Special Theory of Harmony’ etc. in his books. It’s also quite possibly the case that Einstein’s theories toward a ‘General Theory of Relativity’ (and the quest it created in the physics world) were at the heart of Schillinger’s quest for a ‘General Theory of Music’ that would explain all music (in his words) ‘from any culture or epoch, past, present and future.’

There is precedence for such a quest going right back to Pythagoras that science could conclusively prove a general and unifying theory of music. Composer-theorists such as Jean-Philippe Rameau had similar ideas – ideas considered radical in 1722 when they were published in his ‘Treatise on Harmony’. Rameau was later dismissed as a crackpot by Jean-Jacques Rousseau who firmly held the view of Plato that the creation of music is something Divine. Rousseau coincidentally was possibly the first writer to use the word ‘genius’ in its modern meaning. Doing so created the backdrop for the romantic-era notion of the ‘musical genius’ as ‘madman inspired by God’. It was a notion staunchly rejected by the modernists and ultra-modernists, particularly Schillinger who was himself declared to be a crackpot by the academic establishment in his time (and for some years after his death).

Schillinger, Cowell, and other modernists/ultra-modernists were considered radical in their time for attempting to subvert the 19th century thinking that still held sway in the academic world well into the 20th century. While some intellectual ground was surrendered by traditionalist thinkers, it was only in matters of harmonic progressions (as something that can be reduced to formulas) and acceptance of Schenkerian analysis as a legitimate tool for understanding (retrospectively) the basic details underlying compositions of the pre-twentieth century European classical canon. However, to this day, the romantic notion of melody creation as being something exclusively the preserve of intuitive genius remains as strong now (ask most rock guitarists if they think music ‘theory’ is of any value to them, for example) as it was in the late 18th and 19th centuries. Until very recently (with the advent of computers and their applications in the composition of music) music and ’science’ were uneasy bedfellows.

So, where is all this going? As mentioned at the outset, my theory is still in its infancy and there is a lot of reading yet to be done. At the core of my theory is an idea that Schillinger limited his ’scientific’ scope to mathematics (simple arithmetic mostly) and projective geometry. As already mentioned, the academic zietgeist of his time held the view that humanities were ‘inferior’ as a science discipline. Through the adoption of qualitative (as opposed to traditional quantitative) research methodologies, ’soft sciences’ such as psychology and sociology have grown in academic stature. My theory – the one that woke me last night – is Schillinger’s theories might have a better chance to be proved correct if studied from a variety of modern scientific perspectives. It should be acknowledged that Schillinger theorized about the psychological dimension of music but such thinking was so radical at the time he couldn’t prove anything using existing scientific tools and methods. Much more is known now, but it’s still a relatively new field of enquiry.

If we step back for a moment and again look at the question, ‘what is music?’

Let’s assume that music, whatever it is, exists a priori. This philosophical viewpoint could be compared to John Cage’s view of ‘music’ existing in all the sounds we hear around us, whether organized by a composer or not. From a practical viewpoint, we now have, in the 21st century, the musical composition tools available to create, analyze and synthesize any imaginable musical structure. These tools enable us to perform the ‘hard science’ of answering our question through describing its physical properties, but the answer isn’t complete. Neuro-science tools enable us to map the effects of music in the human brain. Thus we’re able to describe more music properties through the physiological dimension. These two descriptions may even be synthesized to generate a more complete understanding of the properties inherent in music, but it still doesn’t necessarily answer things fully. In fact, it may even point to a case of there being more than one answer and not any ‘universal principle’ at play.

So, perhaps a better question to ask is not only what properties music possesses, but how does it behave? In other words, if we’re to assume that music is an evolutionary system governed by the same rules as biological systems as suggested by Schillinger, then as well as the microscopic (measurable) levels in music – where sound frequencies are analogous with atoms; harmonic and rhythmic combinations (patterns) are analogous with cells – we need to take into account the macroscopic (also measurable using qualitative methodologies) levels. Schillinger believed projective geometry could be adapted to suit the task of measuring, analysing and synthesizing the macroscopic dimentions of music – macroscopic here meaning the whole aesthetic experience of music.

Projective geometry goes some of the way to describing the emotional effect as it provides a scientific explanation of how perception works. However, if we extend Schillinger’s original concept of music as a biological entity and fully anthropomorphize it, it can be assigned a ‘personality’ that may be analysed using traditional psychological tools. Through understanding how it (music) behaves, a set of rules may be devised that don’t govern what it should be but simply what music is.

That’s all for now. My brain hurts…

Baha’i-hi-hi

The Baha’i message is unity among faiths, races, nations.

My name is not Joe Butcher. I do, however, fry eggs with my mind.

Google Trends

The ‘hot 100′ (http://www.google.com/trends/hottrends?sa=X) is headed by Susie Sprague Feldman. I’ve never heard of her, and her name makes me think of a Russian space-aeronautics agency.

Number three on the list is ‘harry potter missing pages’. Given the many thousands of pages in all the tomes, who would notice if a few were missing?

Beverly d’Angelo turns up twice on the list: ‘beverly deangelo’ at #48 and ‘beverly d angelo’ at #53. As far as any reading of the trend here goes, it appears as if people who can’t spell her name are in the majority.

The only politician name I recognize on the list is John Ashcroft at #49. Politicians take note: nobody is interested in you.