TRIANGLEMETRE-THE MUSICAL MEASURE OF THE TRIANGLE-TROKUTOMETAR-GLAZBENA MJERA TROKUTA by Antun Toni Blazinovic

GLAZBENA MJERA TROKUTA TRIANGLEMETRE-TROKUTOMETAR

Glazbenu mjera trokuta sam postavio izmjenjivanjem više (2 ili 3) različitih mjera (polimetar=poly(više)+metron(mjera)grč.) i to načinom horizontalnog polimetra gdje promjene mjera slijede jedna za drugom (u omjeru svake dimenzije trokuta): a/n + b/n + c/n. Stranice trokuta (a, b, c), određuju broj dobi u taktu i pišu se u brojniku, a u nazivniku vrstu dobe (n). Kod onih trokuta gdje dimenzija hipotenuze nije cijeli broj, odredio sam dobe računalnim programiranjem te došao do manjeg odstupanja nego kod dirigiranja uživo neke "standardne glazbene mjere. Napomenuo bih da je trenutno najmanja doba 1/64, dok računalno možemo ići i do 1/128, 1/256, 1/512... Tri dimenzije trokuta mogu se sumirati i postaviti kao mjera u jednome taktu.

THE MUSICAL MEASURE OF THE TRIANGLE- TRIANGLEMETRE

During October 2004 the National and University Library in Zagreb (Croatia) was venue for an event called a musical measure of the triangle-Trianglemetre. This was a musical measure formed on the basis of the   dimensions of a right-angled triangle, the creation of Croatian composer Antun Toni Blažinović.

The triangle-meter was established by the alternation of several (two or three) different measures, in the manner of a horizontal polymeter in which changes of measures came one after another (in the ratio of each dimension of the triangle): a/n + b/n + c/n. The sides of the triangle (a, b, c) determine the number of beats in a bar and are written in the numerator, and in the denominator the kind of the beat (n). Each side of the triangle represents a single bar. The sides of the triangle can be aggregated and set up as the measure for a single bar.

In those triangles in which the dimension of the hypotenuse is not a whole number, he has determined the beat by computer programming and arrived at a smaller deviation than with the live conducting of some of the standard musical measures. Everything has been done on a computer, and accordingly the problem of the division of the measure into the smallest musical units – beats – did not constitute a problem, since with a computer it is possible to define beats of less than 1/64, for example, 1/128 or 1/512 and so on.
This measure can be classified as a mechanical measure attained with the use of technical devices, but there is also the triangle with 3-4-5 dimensions, which are whole numbers, and live performances thus become relatively easy. In live performance of the musical measures of triangles that are not integers, Blažinović mentions the use of monitors on which animation can be used to keep up with the adjustment of the measure per side.

Blažinović’s intention is to announce to the musical and cultural world his composing techniques and the musical measures that he has established according to the dimensions of the triangle. ©

Music genre: electronic/ minimalism/ contemporary

VIDEO SAMPLE-- TRIANGLE 3-4-5

THE MUSICAL MEASURE OF THE TRIANGLE-TRIANGLEMETRE

Musikalische Maßeinheit Dreieck – Trianglemeter- TRIANGLEMETRE

Das Dreieck als metrische Einheit in der Musik von Antun Toni Blažinović Im Oktober 2004 passierte in der National- und Universitätsbibliothek in Zagreb etwas, das sich die musikalische Maßeinheit Dreieck – Trianglemetre nennt. Es handelt sich hierbei um eine metrische Einheit, die auf den Dimensionen eines rechtwinkligen Dreiecks basiert und dessen Autor der kroatische Komponist Antun Toni Blažinović ist. Er stellte diese musikalische metrische Einheit auf, indem er mehrere (2 oder 3) unterschiedliche metrische Einheiten änderte,

und zwar nach dem Prinzip des horizontalen Polymeters, bei dem die Änderungen der metrischen Einheiten aufeinander folgen

( im Verhältnis zu jeder Dimension des Dreiecks): a/n+b/n+c/n. Die Seiten des Dreiecks (a, b, c) bestimmen die Anzahl der Zählzeiten in einem Takt und stehen im Zähler, während im Nenner die Art der Zählzeiten steht (n). Jede Seite des Dreiecks steht für einen Takt. Die Seiten des Dreiecks können addiert werden und als eine metrische Einheit innerhalb eines Taktes bestimmt werden. Bei den Dreiecken, bei denen die Dimension der Hypotenuse keine ganze Zahl beträgt, bestimmte Blažinović die Schläge durch Computerprogrammierung und kam zu kleineren Abweichungen als beim „lebendigen“ Dirigieren einer musikalischen „standardisierten“ metrischen Einheit. All dies wurde am Computer durchgeführt, so dass die Aufteilung der metrischen Einheit auf die kleinsten musikalischen metrischen Einheiten, die Zählzeiten, kein Problem darstellte, da man mit Hilfe des Computers kleinere Zählzeiten als 1/64 bestimmen kann, wie z.B. 1/128 oder 1/512 usw. Mit diesem Artikel bewegt sich Blažinović in die musikalische und kulturelle Welt, um seine Kompositionstechnik und seine musikalische metrischen Einheit bekannt zu geben, die er aufgrund der Dimensionen eines Dreiecks festgelegt hat. Kompositionen, die in dieser metrischen Einheit geschrieben werden, werden sich auf CD herausgegeben. Die Namen der Kompositionen enthalten die Dimensionen der Dreiecksseiten. Die Musikrichtung ist Elektronik/Minimalismus/Moderne.


SQUARE ROOT OF A NUMBER NOTE
In mid-August 2005, I recorded the process whereby I realized a note whose duration could be described in terms of the mathematical square root of a number. The duration of the note I achieved was equal to the root of the number 2. The starting point for this note was a triangle with the dimensions of 1-1-root of the number 2. The circumference of this triangle was supposed to be equal to the circumference of a circle – the “circle-instrument“ which I had made.

To this circle-instrument, I assigned arcs with the values of 1-1-root of the number 2. At the points that are the starting points of the arcs, I installed pins, which strike a bell when the circle-instrument is spinning. One rotation at a steady speed produces a note with the duration equal to 1-1-root of the number 2. If BPM=60, duration of the note is: 1,00 second- 1,00 second- 1,41…second= root of the number 2 The first public presentation of the note based on a root of a number was held on 29.11.2005.at the ZKM (Zagreb Youth Theater) -Zagreb, Croatia.

NOTA KORIJENA BROJA
Sredinom kolovoza 2005. snimio sam svoj postupak kojim sam dobio notu trajanja korijena broja. Nota koju sam dobio ima trajanje korijen iz dva(2). Trokut dimenzija 1-1-korijen iz 2 , je bio polazna tocka. Opseg tog trokuta trebao je biti i opseg kruga. „Instrument-kruga koji sam dao naciniti. „Instrument-krugu“ sam odredio duljine lukova 1-1-Korijen iz 2. U tockama gdje lukovi pocinju postavio sam klinove koji kada se „Instrument-krug“ vrti udaraju u zvonce. Tako u jednoj rotaciji pri istoj brzini vrtnje dobijemo note trajanja: 1-1-Korijen iz 2. Pri stalnoj brzini vrtnje i tempu=60, dobijemo note trajanja 1sekunda-1sekunda i 1,414… sekunda (korijen iz dva sekunde) Prva javna prezentacija note korijena broja se desila u ZeKaeM-Zagrebackom Kazalištu Mladih, (29/11/05-ZAGREB-CROATIA).

VIDEO CLIP-- "Square root of 2" duration note

A right triangle with the sides A=1, B=1, C=root of the number 2

A circle whose arcs have the lengths of 1-1-root of the number 2

the circumference of a triangle = the circumference of a circle


SQUARE ROOT OF A NUMBER NOTE- NOTA TRAJANJA KORIJENA BROJA

VIDEO CLIP-- TRIANGLE 3-3-k18

VIDEO CLIP-- DRUMFIRE

VIDEO CLIP-- "Square root of 2" duration note

Kronologija / Chronological

-Trianglemetre-prva javna prezentacija 23.10.2004. (18.10.2004.Press)

Antun Toni Blazinovic , Djurdjica Brezak Lugaric , Niksa Gligo

Press conference 18.10.2004.-National and University Library Zagreb

-Trianglemetre 1st public presentation 23.10.2004. (18.10.2004.Press)


-Nota trajanja korijen iz 2

Zagrebacko kazaliste Mladih 29.11.2005.

Duration of the note -equal to the root of the number 2

Zagreb Youth Theater 29/11/05-Zagreb, Croatia

-Plesna predstava-Studio za suvremeni ples-"Identitet dodira ili ritam matematike" (30.05.2006)

Contemporary Dance Studio: The identity of touch or the rhythm of mathemetics (30.05.2006)


-Kazališni performance"Trokuti" (07.12.2006.)

-Theatre performance"Triangles" (07.12.2006.)


-Izložba-Glazbena mjera trokuta-Nota korijena broja-Exhibition (06.11.2013.)


-Predstava-Theatre performance- Bife Titanic-Eurokaz 2015/16


IAKO ZNAM DA MOJE TRENUTNO OKRUŽENJE I ČITAVA ZAJEDNICA NEMA POTREBE ZA VRSTU GLAZBE KOJU SKLADAM U MJERAMA KOJE SU BAZIRANE NA GEOMETRIJI,

MENE NE ZANIMA NITI JEDNA DRUGA STVAR KAO TO, MOJA GLAZBA SE MORA MIJENJATI I IĆI U DRUGIM SMJEROVIMA.-ANTUN TONI BLAŽINOVIĆ

KONFUCIJE REČE: "AKO ŽELIŠ DOZNATI KAKVO JE STANJE U NEKOJ DRŽAVI, POSLUŠAJ NJEZINU GLAZBU."


ANTUN TONI BLAZINOVIC 2004© 2005© 2007© 2013© 2015©2017