Applications of serial pitch organisation in Urgynes (taken from another forum)
The numbers along the outside detail the Prime and Inverse rows, so when I say "P11" I'm referring to the 0 at the very start of the matrix, when I say "I25" I'm referring to the 7 which is the second interval in P5.
From that matrix, or grid, there are endless possibilities for generating material. What I did, in addition to simply following a row in a straightforward manner, was to apply various patterns and shapes and non-standard (e.g.: diagonal) directions to movements about the grid, sometimes I would even jump from one instance of a number to another somewhere else (e.g.: reaching the 8 at P12 and jumping to the 8 at P39 and continuing in any direction). Deriving material in this way became a game, and I was often devising different rules for getting from one end of the board to the other and seeing what the resulting melodies, harmonies, chords etc. were, and naturally I would alter or discard the results I was not pleased with.
One technique I used throughout the piece was to apply shapes to the matrix, and the portions of the matrix above highlighted in bold red resemble a particular division I used in the very first movement; two large isosceles triangles from P61 to P127 and I61 to I127. Within these triangles I used all my other techniques to generate more limited melodic material while I derived chords from the space in between them. In the final movement I used isosceles triangles again, this time to form eight equal divisions of the matrix which operated independently of each other.
Of course, the whole time I was combining all of this serially derived material with free writing and applying transformative techniques independently of the matrix. So ultimately my work was not serial in the strict sense, the matrix was only one tool of many used to reach the end result. I did not apply any complex mathematical processes to the matrix, certainly nothing like Set Theory, which I must confess I do not understand, so for me at least working with serialism was nothing close to an algorithmic kind of composition.
In response to further questions about construction and uses of rows/matrices in the piece
Each row was constructed differently, sometimes I wanted particular intervals to be emphasised, but some were almost created blindly. This row in particular is the most extreme example of doing it blind, I just asked friends in an IRC chatroom to call out numbers between 0 and 11 and wrote them in the order they came up, ignoring repeat numbers. If it had moved a little too predictably I would have scrapped it, but as it came out it seemed pretty interesting on paper. Initially I was not too happy working with it, however, so for most of the second movement I completely ignored it, but then I had something of an epiphany as I was working it back into the ending, then I went back and reset a lot of the material using the matrix as a guide and it sounded a lot better, more unified. So that one in particular was a case of having to get away from the row to write the music and then coming back to it later on. If I had rewritten the row, the movement would have become far too laborious a working process, and I think the end result would have suffered because of that.
The construction of the matrix itself is quite simple, all you need to do is invert the prime row to create the inverse row, then use each interval in the inverse row as the beginning of a transposed prime row. In that matrix I12 is 4, so P2 is the prime row transposed up two whole steps. The rest falls into place the same way: P3 is P1+9 half steps, P4 is P1+ 5 and so on until the entire thing is filled out. Every 12-tone matrix is crawling with patterns, whether intentional or accidental, just take a look at those two red triangles on the example I posted, notice how they are diagonal inversions of each other. P1-6 to P712 (10, 10, 11, 9, 10, 7, 3) is I61 to I127 (2, 2, 1, 3, 2, 5, 9) inverted, the same is true of all those left-to-right diagonal lines. The right-to-left diagonal lines offer up some interesting prospects as well: I8 to P8 is 2, 10, 7, 6 followed by its own retrograde inversion 6, 5, 2, 10, and the same is true of all diagonals in that direction. Simply put, using the left-to-right line of 0s as a dividing line, the left side is the inverse of the right. There are lots of other recurring figures, in this one the relationship between 7 and 3 is strongly emphasised, in most instances you can find a 3 right next to a 7, whether straight or diagonally. I think it's an exciting feature of the 12-tone matrix, the way patterns inevitably emerge, recur, invert and transpose each other etc.
Awareness of the results one will get from a matrix, that's something Milton Babbitt talked about, I think in the documentary Portrait of a Serial Composer, and he's lamenting composition students trying to use serial techniques without considering the musical outcome of the rows they create, their lack of understanding means they end up scrapping a lot of unsatisfactory pieces. Of course, Babbitt was very strict in his application of serial organisation, to the extent that the piece was determined by the rows before it was composed (if he was answering [the] question about patterns, I have no doubt he would talk about planning them out meticulously when he constructs a row), so when he talks about that awareness it is within the context of strict application, my applications are much looser and do not underpin the entire work so much as supplement it. Each movement begins with an exploration of the row but is soon enough suffused with free writing, so the construction of the row itself is not so important as the application from then on, but even in those initial explorations the vertical spacing and ordering of the notes makes all the difference, some sections will benefit from a more lyrical treatment while others will require large leaps from one register to another and so on.
Who actually wrote the Beatles music?
The person who actually wrote all the Beatles songs was Theodor Adorno, a music professor from Frankfurt University. And none of the songs were original, Adorno, a genius on the subject of theoretical music cleverly adapted well-known classical partitures, to create the Beatles songs.
Here are some examples...
Yellow Submarine is actually the theme from Verdi's Aida combined the Toreador song from Carmen by Bizet.
Can't buy me love is actually Aine Kleine Nacht Musik by Mozart, ingeniously modified.
Penny Lane is the Elvira Madigan Piano Concerto No. 21 by Mozart, modified.
From me to you is the Peer Gynt suite, Morning Mood, by E. Grieg
I want to hold your hand is a modified From me to you (listen carefully and compare the two songs)
Yesterday is a modified Neapolitan song, called "Piccere' Che Vene a Dicere"
Let us remember that the original J. Lennon/P. McCartney duo could neither write nor read music; in the period 1960-1962 they sang only cover songs, and manifested no music writing talent whatsoever
Got to get into my life is a modified Can't buy me love
I feel fine is actually Fire Dance by M. de Falla
Martha my Dear is a modified classical song, Martha by von Flotow (see
)
Something is nothing more than the theme from Spartacus by Khachaturian
For Hey Jude, Adorno pulled out all stops, he grouped into one song, masterfully, the Ride of the Walkiries by Wagner, the theme from the Piano Concerto no. 1 by Tchaikovsky, and the theme from Symphony no 9 by Beethoven
Blackbird is actually the Hungarian Fantasy by Liszt
Get Back is Obladi Oblada modified
Sgt. Pepper is clever combination of the Radetzky March and the Romanian rhapsody no 1 by Enescu
And Adorno reworked some of the Beatles songs to create others: She Loves You is a modified From Me to You, as is You're gonna lose that girl
A Hard Day's Night is a modified Mozart serenade
Ballad of John and Yoko is a modified And Your Bird can Sing
Theodor Adorno (seen here:
http://www.nndb.com/people/754/000026676/adorno.gif ) also wrote the entire British invasion: that is, the music of the Rolling Stones, Kinks, the Who, See Emily Play by Pink Floyd, and also Moody Blues' Days of Future Past (Nights in white satin is a modified theme from Swan Lake by Tchaikovsky), the songs for Mamas and the Papas, Doors, Jimi Hendrix, Crosby Stills and Nash, Iron Butterfly (Adorno wrote In a gadda da vida), Cream, Queen (We are the Champions, a modified Hey Jude, and Seaside Rendezvous, a modified Martha my Dear).
John Coleman actually discovered that Adorno owned the Beatles catalogue, from 1962 until his death in August 1969, and that he invented the heavy metal/punk styles of music.
The first five Led Zeppelin albums were also written by Adorno (he wrote music extensively, borrowing from Beatles songs and other, from 1964 to 1969); the Rain Song is a modified Something (that is the theme from Spartacus by Khachaturian), see the thieving magpies google search details.
The music for Jethro Tull (the early albums, including Aqualung and Thick as a Brick) were also written years ahead by Adorno, as was the Machine Head album by Deep Purple (Highway Star is a modified Magical Mystery Tour song).
The best B. Sabbath songs, Spiral Architect and She's Gone were also among the songs written for them by Adorno (copies of She's Leaving Home and the Rain Song).
Upon leaving the Featles project (1967-1969), Fohn Lennon was given some songs written also by Adorno to continue a possible solo carrier: Imagine, Bless You, Mind Games (a modified All You Need is Love).
F. McCartney was given more songs, but not enough to compare disasters like Ram to the Beatles albums: Another Day, Maybe Im Amazed (a modified Long and winding Road), My Love (a modified All my Loving), Live and Let Die (a modified Magical Mystery Tour), Admiral Holsy (the best post Beatles song by McCartney, that is, by Adorno) and some others.
F. Harrison was given Dark Horse (a modified Gallows Pole by Adorno, who was inspired from black soul music), What is Love (a modified Satisfaction), and What is Life, not to mention My Sweet Lord (which Adorno copied from some early sixties music, and got Harrison into plagiarism trouble).
The Rolling Stones music was written by Adorno, as I have mentioned already: Satisfaction is a modified Ticket to Ride, Lady Jane is a modified Norwegian Wood, Jumpin Jack Flash is a modified Satisfaction, and so on...
The Beach Boys were also created musically by Adorno, who wrote the entire Pet Sounds album, God only Knows (a modified Michelle), Sloop John B (a modified Eight Days a Week), and later California Girls...
Here is an interview with Adorno:
Adorno was a master at adapting classical music to suit his own purposes, that is, the institute which hired him to social engineer the entire 60s and 70s.
On the complexity of the Beatles songs:
http://www.icce.rug.nl/~soundscapes/VOLUME01/A_Beatles_Odyssey.shtmlhttp://www.icce.rug.nl/~soundscapes/DATABASES/AWP/awp-notes_on.shtmlAnd, all of the ABBA songs are nothing more than modified Beatles songs:
Dum Dum Diddle is a modified Obladi Oblada
Voulez Vous is Hello Goodbye all over again
Rock Me is actually a copied With a Little Help from My Friends
Dancing Queen is a modified Goodnight (from the White Album)
Mamma Mia is a modified Penny Lane
SOS is a modified Here Comes the Sun
Money Money Money is a modified Sgt. Pepper
Move on is a modified Blackbird
Take a chance on me is a modified We can Work it out (which is a modified Help)
Dance while the music still goes on is a modified I Saw Her Standing Her (borrowed by Adorno from one of Mozart's serenades)
Chiquitita is Michelle all over again
Eagle is a modified Maybe Im Amazed
Waterloo is a modified A Hard Days Night
Prior to 1972 both B. Anderson and B. Ulvaeus manifested no musical talent whatsoever (that is, at composing songs), all of a sudden, beginning with 1972, they came up, unexplicably, with a Mozart genius-like talent at writing songs, which expired suddenly in 1979.