EUKLIDISCHER RHYTHMUS – Part I – Theorie

Der euklidische Rhythmus bzw. Algorithmus gehört zu den Polyrhythmen. Er basiert auf einem Konzept des Mathematikers Euklid von Alexandria. Prinzipiell geht es dabei darum, den größten gemeinsamen Teiler zu finden. Hierzu gleich ein Klangbeispiel: 

Wouter Hisschemöller – Music Pattern Generator v2.1

Kurze Geschichte:

Schon vor 2300 Jahren hat der Mathematiker Euklid von Alexandria sein wichtigstes Werk „Elemente“ verfasst. In diesem beschreibt er auch das Konzept zur Findung des größten gemeinsamen Teilers zweier Zahlen. Dieses Konzept ist als Euklidischer Algorithmus bekannt.

Rhythmik und Mathematik:

Er ist im Jahr 2004 entdeckte der kanadische Informatiker Godfried T. Toussaint die Beziehung zwischen dem Euklidischen Algorithmus und Rhythmen in der Musik. Mit diesem lassen sich viele bekannte Rhythmen zum Beispiel aus dem Rock’n’Roll, der afrikanischen und der südamerikanischen Musik berechnen.

Was ist ein ‚guter‘ Rhythmus? Ein Algorithmus, der die Schläge in einem bestimmten Zeitintervall so gleichmäßig wie möglich verteilt.

Das interessante an euklidischen Rhythmen ist, dass es nicht ewig gleichbleibende Rhythmen sind, sondern abwechslungsreiche und so auch spannendere für die Zuhörer. Er bietet eine gute Balance zwischen eintönig und zu komplex und verteilt alle Schläge gleichmäßig.

Wie funktioniert der Euklidische Rhythmus?

Gegeben sind immer zwei Zahlen, z.b. 13 und 5. Dann wird immer die kleinere von er größeren Zahl abgezogen, bis kein Rest mehr bleibt.

Tipp: Der Euklidische Algorithmus funktioniert besonders gut, wenn man Primzahlen benutzt.

Für den Eukldischen Rhythmus ist sozusagen der Weg das Ziel. Aus den Zahlen können wir die Schläge (geschrieben als 1) und die Pausen (geschrieben als 0) herauslesen. Das funktioniert so:

13 – 5 = 8  [1 1 1 1 1]  [0 0 0 0 0 0 0 0]

8 – 5 = 3  [1 0]  [1 0]  [1 0]  [1 0]  [1 0]  [0 0 0] 5 Nullen werden nach vorne hinter die 1en gestellt, 3 bleiben hinten stehen

5 – 3 = 2  [1 0 0]  [1 0 0]  [1 0 0]  [1 0]  [1 0] 3 Nullen werden nach vorne hinter die 10 Sequenzen gesetzt

3 – 2 = 1  [1 0 0 1 0]  [1 0 0 1 0]  [1 00] 2x 10 Frequenz wird nach vorne hinter die 100 Frequenzen gesetzt. Nun haben wir den fertigen Ryhthmus

2 – 1 = 1 Da ein Rhythmus zyklisch ist würde es ab hier keinen Sinn mehr machen, nach vorne zu verschieben

1 – 1 = 0

Zum einfacheren Verständnis kann man auf dieser Seite visuell sehen und ausprobieren, wie die Schläge und Pausen verteilt werden: https://dbkaplun.github.io/euclidean-rhythm/

Zudem gibt es hier eine Liste mit Zahlenkombinationen und ihrem Rhythmusmuster: http://www.iniitu.net/Euclidian_Erd%C3%B6s_Deep_Aksak_rhythms.html

Abschließend noch zwei Beispiele zum reinhören:

Quellen:

Ableton AG. „Don’t DJ über polymetrische, polyrhythmische, zirkuläre Musik | Ableton“. Zugegriffen 15. Dezember 2021. https://www.ableton.com/de/blog/dont-dj-moving-in-circles/.

bettermarks. „Euklid von Alexandria“. Zugegriffen 15. Dezember 2021. https://de.bettermarks.com/mathe/euklid-von-alexandria/.

Toussaint, Godfried. „The Euclidean algorithm generates traditional musical rhythms“. In In Proceedings of BRIDGES: Mathematical Connections in Art, Music and Science, 47–56, 2005. https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.72.1340&rep=rep1&type=pdf.

W., Bernd. „Euklidische Rhythmen – Ist die Mathematik ein guter Percussionist?“ Tropone Sounds (blog), 18. Oktober 2018. http://tropone.de/2018/10/18/euklidische-rhythmen-ist-die-mathematik-ein-guter-percussionist/.

Birdman’s Soundtrack

In this blog post, I would like to write about a fairly unusual movie soundtrack to find, the Birdman soundtrack or (The Unexpected Virtue of Ignorance).

Birdman is a 2014 American comedy-drama directed by Alejandro G. Iñárritu.

Here is a small summary, just to know what it is:

“Riggan Thomson is an actor who played the famous and iconic superhero” Birdman “over 20 years ago. Now, in his middle age, he is directing his Broadway debut, a drama called “What We Talk About When We Talk About Love,” an adaptation from a Raymond Carver story. With the help of his assistant and daughter Sam, and his producer Jake, he will play premieres of the show, even when a talented actor he has hired, Mike Shiner, acts arbitrarily, the internal issues between him and the other cast, the his futile utmost efforts to critics and the unexpected voices of his old character, the Bird Man, pushing his sanity to the first debut show. [1]

Besides the movie itself, what I find really interesting is the soundtrack.

There are several classical music pieces, mainly from the 19th century (such as Mahler, Tchaikovsky, Rachmaninov, Ravel) and several jazz compositions by Victor Hernández Stumpfhauser and Joan Valent. But those are just “outlines” of the real thing.

Most of the score consists of a drum score composed entirely of solo jazz percussion performances by Antonio Sánchez.

It’s a rather unusual choice for a film, as the drums are just a percussion instrument, no harmony, (almost) no melody.

But why? As the director said:

“The drums, for me, were a great way to find the rhythm of the film … In comedy, rhythm is king, and not having the editing tools to determine time and space, I knew I needed something. that would help me find the internal rhythm of the film. “

When the director contacted Sánchez and offered him to work on the film, the composer felt a little unprepared and surprised, as he put it:

“It was a scary proposition because I had no benchmarks on how to achieve this. There is no other film that I know of with a soundtrack like this.” Sánchez hadn’t worked on a movie before either.

He first composed “rhythmic themes” for each of the characters, but Iñárritu preferred spontaneity and improvisation when he said, “Man, this is absolutely the opposite of what I was thinking. You’re a jazz musician. I want you to. you have a completely jazzy approach, which improvises, which has nothing too preprogrammed. I just want you to react to the story.” [2]

After Sánchez visited the set for a couple of days to get a better idea of ​​the film, he and Iñárritu went to a studio to record some demos. During these sessions the director first spoke to him through the scene, then as Sánchez improvised he guided him by raising his hand to indicate an event – such as a character opening a door – or describing the rhythm with verbal sounds. They recorded about seventy demos and, once they finished shooting, they put them in the rough cut.

He liked the way the soundtrack complemented the action, but not how the drums actually sounded. Having been recorded in a New York studio, the audio was extremely crisp and clear, not quite the mood they wanted for a film steeped in tension and dysfunction.

So Sánchez headed to Los Angeles to re-record the tracks.

They wanted “rusty, out of tune drums that hadn’t been played in years”. Also, Sanchez purposely degraded his kit. “I didn’t tune the drums, I used mismatched heads, stuck duct tape on the heads to make them weaker, and put things on the cymbals to make them sound a little broken. I also stacked two and three plates on top of each other, metal on metal. Instead of a sustained sound, you get a dry, trashy one. It worked a lot better.”

Iñárritu also pressured his sound design team.

In these scene they pass a drummer on the sidewalk outside the theater. The drum sounds change multiple times during the sequence — first when Keaton leaves the quiet of the theater and exits onto the New York City street, then again as he and Norton approach and move past Smith. Iñárritu wanted the volume level of the sidewalk drummer to rise and fall as Keaton and Norton walked by, but they did it in the most authentical way.

“We actually brought the drums out onto the street near the studio,” Sanchez recalls. “There were a couple of sound guys a block away with mics that had really, really long cables. I started playing, and they walked the whole block, right pass my drums, and kept walking to the next block. Then they came back. That’s how Alejandro approaches his work. Anybody else probably would have just turned the volume up and down.”

“The movie fed on the drums, and the drums fed on the imagery”.

The official soundtrack was released as a CD (77 min) in October 2014, and as an LP (69 min) in April 2015.

It won the Grammy Award for Best Score Soundtrack for Visual Media.

Resources

[1] Birdman Plot Summary https://www.imdb.com/title/tt2562232/plotsummary

[2] Neil Janowitz – “Birdman” composer drumming out the film’s soundtrack

[3] Wikipedia – Birdman

[4] Wikipedia – Birdman (film score)