Tintinnabuli Mathematica is an experiment in programming Arvo Pärt’s tintinnabuli method of composition. The process has two stages. Firstly, a melodic part (or M-voice) is created by generating a string of notes and timings. Then harmonic tintinnabuli parts (T-voices) are generated by applying transformation rules to the melody.
To generate a melody, a program was written to select notes from a scale, which in this case is A natural minor, i.e. all the white notes on a piano starting from A. Two types of generative method are used: random selection and series based on integer sequences (e.g. the Fibonacci sequence or the series of prime numbers). The random methods include equal-weighted choice of pitch and duration which generates notes scattered all over the scale, and a random walk method which produces wandering melodies of close pitches, varying in closeness depending on the maximum size of interval. In the random walk method…
“The Avant Garde Project is a series of recordings of 20th-century classical, experimental, and electroacoustic music digitized from LPs whose music has in most cases never been released on CD, and so is effectively inaccessible to the vast majority of music listeners today.”
“The scores and libretti in this Virtual Collection include first and early editions and manuscript copies of music from the eighteenth and early nineteenth centuries by J.S. Bach and Bach family members, Mozart, Schubert and other composers, as well as multiple versions of nineteenth century opera scores, seminal works of musical modernism, and music of the Second Viennese School. Many, such as variant editions of nineteenth century operas and related libretti, fall into intellectually related sets that are meant to be seen and used together. As a group, they give scholars a window into the study of historical performance practice that cannot be duplicated using the holdings of any one other library.”
“The Rest Is Noise: Listening to the Twentieth Century is a voyage into the labyrinth of modern music, which remains an obscure world for most people. While paintings of Picasso and Jackson Pollock sell for a hundred million dollars or more, and lines from T. S. Eliot are quoted on the yearbook pages of alienated teenagers across the land, twentieth-century classical music still sends ripples of unease through audiences. At the same time, its influence can be felt everywhere. Atonal chords crop up in jazz. Avant-garde sounds populate the soundtracks of Hollywood thrillers. Minimalism has had a huge effect on rock, pop, and dance music from the Velvet Underground onward.” Press Here To Enter Alex Ross:The Rest Is Noise
The Well-Tempered Clavier (Das Wohltemperierte Klavier in the original German), BWV 846–893, is a collection of solo keyboard music composed by Johann Sebastian Bach. He first gave the title to a book of preludes and fugues in all 24 major and minorkeys, dated 1722, composed “for the profit and use of musical youth desirous of learning, and especially for the pastime of those already skilled in this study.” Bach later compiled a second book of the same kind, dated 1742, but titled it only “Twenty-four Preludes and Fugues.” The two works are now usually considered to comprise the Well-Tempered Clavier and are referred to respectively as Books I and II. The Well-Tempered Clavier is generally regarded as one of the most influential works in the history of Western classical music.”
Title Page Of The Well Tempered Clavier
Bach WTC Book 1 Prelude and Fugue 01 in C BWV 846 SDRodrian