Composers on Mathematical Music
A Subtext Poem

by John Greschak

April 21, 2005



  ...the overtone series as a compositional resource...the art of science and the science of art...pitch classes and the gesture of a melody...electronic music...Time: the most common denominator of music...<Indeterminate>...tape music: continuous versus discrete......the historical relationship between music and other fields......music theory and the scientific method......his piece messagesquisses and the name paul sacher......National art and national science......The ratio between successive tempi...randomly generated tempi and his work music of changes......Early works he wrote using mathematics...his twenty-five tone compositions...his twenty-five tone compositions...the mathematical nature of the term counterpoint...Twelve-tone improvisation......music theory...Music based on geometrical schemata...The organic effect of the fibonacci series on a listener......new mathematics from music......(novel ideas and) magic squares for composition......Pitch-class numbers...on the scientific basis for major triads and seventh chords......Physics and atonal music...Music from numbers...The scientific element of music......Computers, mathematics and composition...articles on the relationship between music and mathematics......The term counterpoint in mathematical terms...quasi-"geometric" music......The notion of mathematical music......Music as geometry in time...the performing computer...machine-made music...The coin oracle of composition...unbounded music......Mathematics as a compositional prescriptive...His use of proportional notation...An axiomatic basis for music theory...Schoenberg and his school...arithmetic art......is musical form "mathematical"?...music for engineers...his rhythmic structures based on perfect squares...bucky fuller's vision of music...the heart and the brain...A scientific basis for discourse on music......the number series for his the seasons......How do you think the development of information theory in music might affect your art?...the word elegant...A mathematical universe and twelve-tone minds......The musicians' take on science and math......rameau and the "arithmetic of sound"...the notion of abstract music...random music...his 31 sections with 31 measures...automatic mechanisms for composition......A critical comment on new music by a mathematician......A subroutine for change-ringing permutations......Computer-assisted composition...the internal environment of a musical work...nested (his) and symmetric (satie's) rhythmic structures...open questions in music psychology......Mathematics at black mountain college...bach on math...Biological structure and the gestures of music......The music of nature...three modes of art: inference, experiment and revelation...the transformation of nature in art......how do you use the chance operations?......the twelve-tone axiomatic system...Is bach's music mathematical?...<Indeterminate>...perceptual and formal characteristics of the twelve-tone system......Changes in science; changes in art......interval ratios and dissonance...The points and curves of his fontana mix...Ratios, square roots and john cage...The "style-bound" artist...to promote science and art......piano technique: geometry and coordination......random answers to composed questions...The primary axis of a melody...music and the imagination...Mathematics and the art of composition...the quantification of art...musical expressions are associative...on scientific explanations of beauty......Square-root dance music...Music theory and the art of composition...his calculated compositions......Math geniuses, blindfolded chess players and musical minds......musicae formulae...the quadrivium...Scientific music...university music and math: historically retarded parallels...variations i: points, lines and perpendiculars......Electronic music in europe: permutations and logarithms, and homemade hieroglyphics...art as an imitation of nature......metrical harmonies......the schillinger system of musical composition...Symmetric chords and geometrical metaphors...the performance of irrational rhythms...on calculated twelve-tone music......the business of science; the spirituality of art......mathematically computed "paper rhythms"...Composing new abstract forms...physicomathematomusicology...the unexpected pleasure of randomly generated music...languages of words, numbers and sounds...music as a science of measurement...The unity of science; the multiplicity of art...A score of numbers...logical music...a magic square of sound aggregates...Inedibles......thought and mathematics in composition...Numbers written by satie......pure and applied music...graphs for music notation...formulist composers...his use of the i ching and the computer...the science-in-music ideal......harmonic harmony...The center of experimental music......Mathematics and composition by computer...Mechanical music...Disproportionate pieces and the avant-gardes......The durational row...research directions at institut de recherche et coordination acoustique/musique (ircam)......Musical vectors......Infinities of music...scientific musical minds...music for moving squares, triangles and circles......i'd like to know if you ever think in images and if so if you ever use visual thinking as a source for your work with sound or words...The higher mathematics of music...musical (and mathematical) perception...Serial music, aleatory music and number games......Mirror forms and unity......the mathematics and music of intellectual learning...His use of the i ching as a computer......all things are related......numbers, exact fantasies and musical invention......polygonal templates for music...on formula and arithmetic in schoenberg's fourth quartet......operation art......The contextuality of twelve-tone compositions...the definition of music......His music walk: plastic rectangles with lines over points...Serial music numbers......Advanced music......Hpschd: a progress report......Composers influenced by science...chess, math and art for all...the composer as mathematician...Self-similar rhythmic structures......composition by numerology...The arca musarithmica......tracing melodic lines...scientific composition plans...geometric designs in notation......The consequences of total serialism......Irregularity in musical form......evocative music (and mathematics)......mapping a composition's title to melody and rhythm...spiraled music...universes of music and math...ratios in sound...Scientific music theory...original repetition......zen, magic squares and chance music......Mathematics in the context of music, and vice versa...his kaleidophone and mathematical basis of the arts...The nonexistence of all-trichordal, all-interval sets......The universal nature of science and art...Music, to a mathematician......<indeterminate>......Mathematical ways to suppress composer preferences...rhythm and arithmetic...proportional art (and the unkempt forest)...Computer cantata...the square of a rhythmic structure...What was your first music like?...compositional questions; numerical answers......The quadratic monomial of artistic beauty......A mathematical path to new scales and chords......A common mathematical basis of time and tone......Extra-musical criteria......(graphemic musical compositions (and thought experiments))......Electronic sound: possibilities and choice...a score with points, curves, a graph and a straight line...a mathematical excerpt selected by a composer...Random responses to conventional phrases...parametric music...Combinatorial chord progressions...Tonal equations...The application of scientific methods for creating art...The language of music; the language of science......the terms row, series and set......engineering art......Symmetry in twelve-tone music...mathematics and machines for composition......(The germ of creativity)......From nature to art, through science...the measurability of chords and harmony...the mathematical synthesis of musical patterns......<indeterminate>...Cartridge music: points, circles, a curve, a chronometer and biomorphic shapes...A function common to science and art......temporal fractals......The rhythms of a summation series...quasi-mathematical compositions...From nature to music, through geometry and numbers......The numerology of bach...the translation of geometric shapes into musical structures......rhythmic recursion...The music of tossed coins...Perceptual capacities and the limits of science and music......on the mechanical nature of twelve-tone composition...popular music; popular math...mapping stars to music...the origin of his stochastic music......The combinatorial mathematics of form......Clear and candid perceptions in composition and scientific discovery......The method of engineering musical melodies...consequences of using computers for composition...<Indeterminate>...music as an emotional science...Magic squares for nonintentional music......Their illiac suite for string quartet......(mathematical formulae for short pieces)...What is academicism in music?...all-interval twelve-tone rows  


Auxiliary Notes
   
For a description of how this poem was written, see Method.   For a list of works from which excerpts were taken, see Bibliography.
   
The number of dots in an ellipsis indicates the duration of the pause between consecutive phrases. A 3-ellipsis (i.e. an ellipsis consisting of three dots) indicates a short pause. A 6-ellipsis (i.e. an ellipsis of six dots) indicates a longer pause. The pause for a 3-ellipsis should be longer than that of a comma, colon or semicolon.   Italicized words should be spoken a bit louder and slower than other words. Words in parentheses should be spoken a bit softer and faster than other words.
   
For the phrases that are "<indeterminate>", the word indeterminate should not be spoken. Instead, a collection of one to eleven words should be selected from the associated subtext page. To select these words, one should devise some method that involves tossing a coin.   For a discussion of the term mathematical music, as it is used here, see the article What is Mathematical Music?
   
The case of the first letter of a given phrase is significant. A lowercase letter indicates that the phrase is a continuation of the current thought. An uppercase letter indicates the beginning of a new thought.   This poem consists of a sequence of phrases delimited by ellipses. Each phrase is a clickable link to a subtext page, which contains an excerpt of writings by a particular composer on mathematical music.


 

Other Work by John Greschak

Public Domain