How To Make A Serialism Matrix

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Durations, dynamics and other aspects of music other than the pitch can be freely chosen by the composer, and there are also no general rules about which tone rows should be used at which time (beyond their all being derived from the prime series, as already explained). However, individual composers have constructed more detailed systems in which matters such as these are also governed by systematic rules (see serialism).
On the other hand, consider the matrix that rotates the coordinate system through a counterclockwise angle . The coordinates of the fixed vector in the rotated coordinate system are now given by a rotation matrix which is the transpose of the fixed-axis matrix and, as can be seen in the above diagram, is equivalent to rotating the vector by a counterclockwise angle of relative to a fixed set of axes, giving
where is the transpose and is the identity matrix. Equation (15) is the identity which gives the orthogonal matrix its name. Orthogonal matrices have special properties which allow them to be manipulated and identified with particular ease.
Any twelve-tone composition is based on several forms of a row.One can easily create and refer to a table of row forms when analyzingor composing a serial composition. This table is called variously atwelve-tone matrix, twelve-by-twelve array, or magicsquare.
To complete the matrix in columns instead or rows, add the number inthe first column to each pitch class number in the first column. Thenumber at the top of each column serves as the reference pitch for eachtransposition of the inversion.
When the matrix is complete, one can find any retrograde form byreading a row backwards (right to left). One can find any retrogradeinversion form by reading an inversion backwards (bottom to top). Thereference pitch of the prime and retrograde forms is always in thefirst column. The reference pitch of the inversion and theretrograde inversion is always in the top row.
As one final piece of technical, terminological preamble, we introduce the matrix (plural: matrices). This is a neat, compact way of setting out all of the 48 rows in a row class on one 12-by-12 grid. By convention:
Thus my question: under what stipulations will a twelve-tone matrix have both of these diagonals using only their own pitch? (By "twelve tone" I mean a row that uses all twelve pitch classes once and only once.) Does this occur only when the row form is completely symmetrical, or are there outside possibilities that would also create such a matrix?
It's starts out ugly, but the general strategy is to figure out relations between these intervals to try to reduce them down. From this first row we can construct a full matrix. Here it is (with only 1st row, 1st column, and diagonals completed).
Where we are now is very close to the end. These are the minimum required conditions to find a 12-TET matrix with a both diagonals constant. The goal from here is to construct a row such that each tone only appears once, and the intervalic relationships provided are observed. So long as the first interval is, for example, a=7, then the second last row element must be 6+7=1, and so on.
This grid is a called a matrix. We could then fill in each row of our matrix with the transpositions of the original pc set and each column with inversions. For example, where would the other two pc sets that we figured out in our original example, T1 and T1I, fit in this grid?
The great thing about this system is that once each of the transpositions (rows) are filled in correctly, each column will be a correctly transposed version of the inverted tone rows. Once filled in, a matrix such as this shows every transposition and inversion of any aggregate pc set.
Using our terminology of P, R, I, and RI, complete the tone row matrix above by filling in each row and then labeling. Is it necessary to go in a particular order? What is the e

How To Make A Serialism Matrix

Serialism 1 - Space Counterpoint is one of my first approaches to the incorporation of serialism into my music. 

You can find the sheet music and explanation in my website juanigcatalano.wixsite.com/portfolio

Serialism N. 1

Apocrypha

Apocrypha III

Apocrypha II

Apocrypha I

low season

low season I

Full album in free download here https://yoshiwaku.bandcamp.com/album/remembering-the-comet
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Remember The Comet [Full Album in Free Download in The Description]

A bewitching and disturbing picture, created under the influence of the laws of nature, a swift continuous stream destroying and creating a beautiful new.
The shaping of the sound on this album is like the shaping of a volcanic coast. A stream of sound containing in every moment a mixture of the hormonal spectrum, like magma containing a melt of all elements under the earth's crust, bursting outward as a stream of lava, solidifying when it reaches the coast and cooling down.

Opus Magma

Opus Magma III

Opus Magma II

Opus Magma I

Matrix

Luke Moran composition, recorded in the van on location somewhere in Nedlands. Performed by Luke Moran, Produced by Alon Shimon Shai-Kaspi.

Peanuts Tuesday

OM-EИ (2011/2023)
for solo piano

This piece was my first experiment using the twelve-tone technique (also known as dodecaphony), an influential compositional approach that rose to great prominence throughout the twentieth century but has largely been set aside by modern composers. By only using all twelve pitches of the chromatic scale (all the notes within an octave) in a fixed order and not repeating any pitches before the full list has been expended, practitioners of the technique attempted to forge new musical grammars and cast off the hierarchies of common-practice harmonic syntax they had inherited from centuries of composers that came before. This often-rigid ordering of pitches in “tone rows” still provided room for permutation (and therefore, intellectual complexity), through presenting rows in reverse, inverting the intervals within (making all upward movement go down, for example), or transposing the row to start on a different pitch but still proceeding through the same order of intervals. The rules of counterpoint, tonal centres, and conventional chord relationships that defined Western art music from the Baroque period to that point were intentionally being cast aside, the culturally accumulated standards of consonance and dissonance being flattened. This initial framework spawned many streams of compositional practice from the mid-century on, known widely now as “serialism.”

The prompt that generated this specific piece was to write a short solo work for piano using said twelve-tone technique. We were permitted to choose our own tone row and employ its permutations how we saw fit. My personal intent was to explore how a conventional tune (often birthed from a traditional harmonic framework) could still be expressed within the twelve-tone idiom. From my limited understanding of what was possible in this system at the time, I set forth interweaving rows – some inverted, transposed, and/or presented in retrograde – with the goal of perserving a traditional melody throughout and allowing new harmonies to emerge from this tapestry. As with the turbulence I experienced with my preceding microtonal violin piece, my challenges to bring this idea to fruition resulted in what was ostensibly just a plan for the arrangement of the tone rows, without much attention to other musical dimensions. The main criticism I received on my submitted draft was that I used a very restricted range of the instrument. It was left as mostly a sketch, and I never made it to the class where we got to hear these compositions read through by an actual pianist. 

On revisiting this piece recently, I finally fleshed out the texture and character that I had always intended, indicated primarily by my original marking of a “moderate rag” tempo and style. With the familiar tune still present throughout, the composition has become a bit of a piano showpiece, perhaps a fun encore to a recital. 

As for my relationship to twelve-tone composition: like many, I now appreciate that its framework for organizing pitch and the manipulations used to elaborate within that system suffer from being opaque to perception by the listener, especially those not versed in the theoretical underpinnings of the style or the particular work at hand. Most people cannot identify that a tone row has been repeated – let alone in reverse or with its intervals flipped upside down – and the complexity of how these processes are then superimposed and woven together cannot be casually appreciated without that foundation, especially on first hearing (assuming a listener might grant a second). Expect an upcoming follow-up that will explore this a little further. With that in mind, the sonic palette that twelve-tone composition can create remains fruitful and still free of the trappings of classical harmony that permeate much of modern music today – it is yet another tool of expression, to be kept in the back pocket for when the need arises.

OM–EИ (2011/2023)

Confugion: a 12-tone double fugue.

Score available here: https://musescore.com/user/57635814/scores/10988335

Confugion

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Sacha Kwach's music is an immersion in serial music to the level of fractal elements, rendered with a brush of spectral synthesis. Searching for new ways of extracting and shaping sound, using effects and recording methods as part of the composing process. The result is a seething mixture of contemporary classics and experimental electronics. Sounds created from noise and drone by the natural laws of physics create a unique ambient, which, like a living organism, is constantly changing while remaining unchanged. Each time you listen, new nuances are revealed, what felt like percussion becomes shush, what was a rumble turns into singing or melody.

Australian in the Netherlands.
Latest release: Atlas 3 EP (2023). 
Alternative in style blending semi/acoustic guitars, fretless bass and sequenced synth. 
Self-produced, building on past experiences with Melbourne band Musquito.

Toronto-based multi-instrumentalist, composer and music educator with diverse roots in classical, jazz and contemporary art music, as well as street performance and musical theatre. Frequently juggling a unique array of saxophones, bassoons, and clarinets (even cello) within a single performance, he has performed alongside ensembles from across southern British Columbia, including the Victoria Symphony, Theatre Under the Stars Vancouver, and as a founding member of the BT Williams Quartet. Whitehorne earned a Bachelor of Music from the University of Victoria in 2018 and currently pursues academic research into music, language, and the brain, as part of graduate studies in psychology. As a composer, his output includes works for solo musicians, chamber ensemble and larger forces. Whitehorne has often been heard in an eclectic mix of venues around Victoria, from the Royal Theatre to the Inner Harbour causeway, passionate about sharing fresh, engaging music with new audiences.

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