BAIN Atonal Assistant. Rhythm and Mathematics. Rhythm and Mathematics. Euclidean rhythms at free variable. Banff. Mathematics and Music. Here are some collections of information about the interplay between music and mathematics. I have collected a bibliography of such items as they float past me in cyberspace, and I went hunting for references in the reviewing journal Mathematical Reviews for mentions of music. In addition I am interested in a few other specific topics. Special note to students: I am delighted that so many people seem to find this page when they are considering illustrating the connections between music and mathematics. Evidently this relationship has been explored in quite a few Science Fair projects; it is the basis for a number of classroom modules prepared by student teachers; it is the theme for essays in many general-studies courses in music or mathematics departments. At least, so I must surmise from the flow of mail!
Yes, I am pleased that so many people find this topic interesting and I hope to hear about novel angles from which you will study it. Tunings Odds and ends about tunings: This page is. John cage: some rules for students and teachers. RULE ONE: Find a place you trust, and then try trusting it for awhile. RULE TWO: General duties of a student - pull everything out of your teacher; pull everything out of your fellow students. RULE THREE: General duties of a teacher - pull everything out of your students. RULE FOUR: Consider everything an experiment. RULE FIVE: be self-disciplined - this means finding someone wise or smart and choosing to follow them. To be disciplined is to follow in a good way.
To be self-disciplined is to follow in a better way. RULE SIX: Nothing is a mistake. RULE SEVEN: The only rule is work. RULE EIGHT: Don't try to create and analyze at the same time. RULE NINE: Be happy whenever you can manage it. RULE TEN: "We're breaking all the rules. HINTS: Always be around. Rhythm Patterns In Carnatic Music | A collection of Korvais that are frequently heard in Carnatic Music. Hexachord. In music, a hexachord (also hexachordon) is a six-note series, as exhibited in a scale or tone row. The term was adopted in this sense during the Middle Ages and adapted in the 20th century in Milton Babbitt's serial theory. The word is taken from the Greek: ἑξάχορδος, compounded from ἕξ (hex, six) and χορδή (chordē, string [of the lyre], whence "note"), and was also the term used in music theory up to the 18th century for the interval of a sixth ("hexachord major" being the major sixth and "hexachord minor" the minor sixth).[2][3] Middle Ages[edit] The hexachord as a mnemonic device was first described by Guido of Arezzo, in his Epistola de ignoto cantu.[4] In each hexachord, all adjacent pitches are a whole tone apart, except for the middle two, which are separated by a semitone.
These six pitches are named ut, re, mi, fa, sol, and la, with the semitone between mi and fa. 20th century[edit] See also[edit] Sources[edit] Further reading[edit] External links[edit] Les logiques musicales du rythme. Les lLogiquess musicaless du rythme François Nicolas À Geneviève Mathon et Éric Dufour 1. Première dimension logique : les durées au principe du rythme 2 1.1 La lettre de durée 2 1.2 Le rythme, comme groupe de durées 3 1.3 Rythmer un objet sonore, c’est le musicaliser 4 2. 2.1 D’un tournant géométrique de la pensée 4 2.2 Conjonctions et enveloppes rythmiques 5 2.3 Sommes et produits rythmiques 6 3. 3.1 Modulations métriques d’Elliott Carter 6 3.2 Cribles rythmiques Brian Ferneyhough 6 3.3 Les enjeux stratégiques 6 4. 4.1 Remarque préliminaire 6 4.2 Trois sens comptables-pour-un ?
Entreprenons ici de thématiser les logiques musicales du rythme, i.e. lesa dimensions proprement logiques des opérations rythmiques dans laen musique. « Logique musicale » ne désignera pas une sorteici un ersatz de grammaire d’un supposé « langage musical » mais le principe immanent rendant raison des consistances propres à la musique. · comment le rythme participe-t-il en propre à la cohésion structurale du monde-Musique ? Composition dodécaphonique Initiation au sérialisme. Avant-propos : Ce texte constitue un résumé succint des principes de composition exposés dans l'ouvrage de René Leibowitz : "Introduction à la musique de 12 sons" (Editions de l'Arche, Paris, 1949).
Nous conseillons au lecteur désireux d'approfondir sa connaissance de s'y référer. 1. De l'atonalité au sérialisme : Des modulations audacieuses de Wagner aux nouveautés polytonales de Debussy, la fin du XIXème siècle se caractérise par une recherche constante d'une nouvelle liberté pour le compositeur, signe d'une nouvelle expression. Cette recherche aboutit à l'abolition des règles du système tonal, pour une liberté contrapuntique sans limite. "Le contrepoint est la conduite simultanée de lignes mélodiques indépendantes. Ce nouvel espace ouvert au compositeur semble dénué de règles. 2. La technique sérielle impose une organisation particulière des notes et un principe de conduite des voix. 2.1. 2.1.1.
L'ordre des 12 demi-tons est libre. 2.1.2. 2.2. 2.2.1. Cependant, 2.2.2. 2.2.3. 3. 3.1. 3.2. Twelve Tone Row - Matrix Calculator. Music Harmony and Donuts. George Russell's Lydian Chromatic Concept of Tonal Organization. Musique contemporaine : de Pythagore à Boulez. Il est frappant de voir que la musique par l'équerre et le compas est associée à la Géométrie.
Dans le Rite Écossais Ancien et Accepté, elle fait parti des 4 arts dits des nombres (quatrivium) permettant d’accéder à l'harmonie cosmique. En effet Pythagore dont je parlerai plus loin, fut le premier théoricien de la musique à associer le nombre à la musique. Il affirma que les lois de l'harmonie se déduisent des lois mathématiques.
La musique contemporaine est en cela la meilleur illustration avec des œuvres abstraites purement « mathématiques ». J'ai intitulé cette planche symbolique « Musique contemporaine : de Pythagore à Boulez ». Pythagore, figure centrale du symbolisme et qui a inspiré une partie du rituel maçonnique. Je vais d'abord donner une brève histoire de la musique commençant par Pythagore et l'école pythagoricienne et terminant par ce qu'on appelle la musique savante du 20eme siècle la musique contemporaine. Pythagore fut le premier à théoriser la musique. Je cite ici I. Variationen für Orchester [Variations for orchestra] op. 31. Schönberg was appointed to chair a master class in composition at Berlin’s Preussische Akademie der Künste in October 1925, succeeding Ferruccio Busoni, who had died the previous year.
Leo Kestenberg, a lecturer of the Prussian Ministry of Culture, had called for Schönberg’s appointment, and he found the job quite aggravating; he was an alien disturber whom the conservatives held to be contemptuous of tradition, while the younger generation thought he was an out-of-date dogmatic. Apart from teaching composition, Schönberg’s duties at the academy included sitting on the senate, which was charged to advise the Ministry of Culture on musical issues.Schönberg, the founder of the Vienna School and mentor of the twelve-tone method, moved to Berlin in late 1925 (for the third time in his pedagogical career), but his health did not permit him to begin his work at the academy until January 1926. Therese Muxeneder© Arnold Schönberg Center.