LEAVE ON A GOOD NOTE

Said the poet: "Euclid alone has looked on Beauty bare."

Push back on "alone" if you like, but beauty may dwell in the immaterial, and from thus the possibility of art formed purely out of ideas. Or not purely: a sensual experience may, by its structure, simultaneously carry ideas. Two art objects, one immersive, the other cognitive, can simultaneously inhabit the same experience.

Varèse framed music as "structured sound," and I would add, alternatively, "sonified structure." Mathematics is the science of structure, so, if you like, the part of music theory robust (to some extent) against the contingencies of sonic materials. I have a long interest both in bringing to my composition ready-made mathematical objects and mathematical phenomena, and in letting the same emerge from sonic considerations themselves. But truly to infuse music with at least the ghost of "Beauty bare" requires evoking mathematical argument.

So consider communicating something by drumming. Fix a small unit of time. Now say you decide to work with only two durations between strikes, namely 2 units and 3 units. Even with the best coding, that choice limits your bandwidth—limits the rate at which you can transmit information.  Now one can quantify this in a sophisticated way with information theory, but we don't need to get into that now. But here's an interesting and not quite trivial fact: if your durations are 1 unit and 5 units, then you have exactly the same bandwidth as with 2 and 3 units! 

A long and short duration might remind you of Morse code. Well, if you "glue" the "dash", the long duration, of the 2–3 system to the following duration, you will get a drumming pattern in a 2–5–6 system. And that translation is reversible. But if you glue the "dot" of the 1–5 system to the following duration, then you also get a pattern in the 2–5–6 system, and also in a reversible way. So you can get from 2–3 to 1–5 via the trick of interpolating between them with another system you might not originally have thought to consider. There's an episode in the piece that makes precisely this transition/translation audible.

But it doesn't stop there! All the following systems also have the same bandwidth as the three mentioned above:
                                                                1–6–11–16–20, 
                                                                1–6–10, 
                                                                1–7–10–12–16, 
                                                                2–6–7–10–11, 
                                                                3–4–5, 
                                                                3–4–8–9–10, 
                                                                3–5–7–8–9, 
                                                                4–5–6–7–8.
Now hopefully the required "bridge" between, say, 1–6–11–16–20 and 3–4–8–9–10 doesn't seem obvious at all! Nevertheless one will experience it if one attends very closely to the sonic details of the piece.

Yes, you can forget all this and you still have an intense experience reminiscent of ritual drumming, albeit without any periodic underpinning. By the way, he piano part works just as the drums do, but also correlates pitches to the durations.

The title: if you wish to transmit a long random "message" in the 2-3-system, a certain ratio between the frequency of 2's and 3's will emerge.  The famous golden ratio would emerge from the 1-2-system and goes by the name "phi."  Hence "high phi" as one old and mostly forgotten proposal for a name of our ratio here.

High Phi, for drums and piano obbligato

4-track recording, performed by Zach Wilson 2024
The canon is a technique in which polyphony is gained by phase-shifting a single part. This technique can be applied not only to melodies, but in principle to any sonic form process: phase-shifted acceleration and deceleration creates polyrhythmic interference; phase-shifted increase and decrease in volume creates perspective depth. To observe these phenomena, I have developed the form of the four-stroke. 
The sonic progression here takes place in four phases of a permanent rotational movement, each of which involves an increase or decrease in dynamics and tempo, so that in cross-section each part is always executed in different levels. Through the overlapping of accelerations and decelerations, the sound comes to a standstill, and the listener can explore the depth of the sound space instead of following a timeline. The source material is kept as purpositive as possible not to distract the attention from the plastic process of modulating the sound mass.

4 Canons for Vibraphone II

The boss (not like “final boss”, just boss) of Carpet & Snares label, Jorge Caiado, brings his new Caiado LDA alias to deliver us two great pieces on Carpet/Patterns sublabel. [continue reading at...https://trommelmusic.com/music/premiere-a1-caiado-lda-process-carpet-patterns04/]

BUY CARPETPATTERNS04

Premiere: A1 - Caiado LDA - Process [CARPET/PATTERNS04]

The Great Wide Open

Escape

The Hufflebump Journey

TRUST!

In both movements of this quartet, each instrument gets assigned a repeating rhythmic pattern—sequences of notes and rests of equal length (say, all eighth notes). 

The first violin plays a pattern of 11 beats (6 notes, 5 rests), the second violin a 7-beat pattern (4 notes, 3 rests), the viola 6 (3+3), and the cello 5 (3+2). These patterns cycle independently.

One full cycle  takes 2310 beats—the least common multiple of 11, 7, 6, and 5.

But—crucially—beat durations vary.

Indeed, the duration of a beat depends on its density—meaning how many instruments are sounding at that moment (0 through 4). Each density appears a fixed number of times within the full cycle, independent of pattern contents assuming the constraints above. 

The twist: beat durations get adjusted so that each density—whether a silence, solo, duo, trio, or a full quartet—occupies exactly one-fifth of the total time of the movement. Rare textures are stretched, common ones compressed.

Thus the interaction of the parts effects an emergent large-scale rhythm.

Out of millions of possible combinations of patterns, one movement employs the set that yields the most unpredictable overall rhythm (in a precisely defined mathematical sense). The other, the most predictable.

As for pitch: each instrument traces a fragment of the cycle of fifths—in near standard tuning. The quartet plays 17TET, so with the octave divided into 17 equal steps, which makes a "perfect" fifth span 10 steps. Each instrument repeatedly travels through this cycle fragment, alternating between octaves. Individually, the lines sound diatonic; together, they form unfamiliar and highly dissonant verticalities—often stranger than even the most dissonant music in 12-tone systems.

Despite this microtonality, no specialized technique is required. If each player tunes their instrument to a slightly different “A,” then standard fingerings suffice—as long as they resist the instinct to tune to one another.

Composer, mathematician, visual artist. 
Seeks collaboration with performers and choreographers.

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Collaborative Work by Artist's Record Label / Experimental Vibes

'A Space to Dream and Dive into coffee and music'

Images by BananaFish : https://www.instagram.com/bananafish_i/

Events & Multi-Versial Content @ Station Caffeination
https://www.youtube.com/channel/UCyt2Dc8DC4Ihq13DoTcwMHg

The Xyphoid Process is an Entity Formed on Bass and Drums. We go where it is needed and bring the Strange with us. we do whatever sounds right, that may be Experimental Trance Rock or Blues, we are the muse.

Nikolaus Gerszewski is a trained visual artist and self-trained composer of experimental music, born 1964 in Hamburg, currently living in Budapest, Hungary, where he has been teaching experimental soundproduction at the university of fine arts, since 2014. 

"The term ‘experimental music‘ means to my understanding, music that results from an experimental arrangement. The notation follows a procedure model, which substitutes the compositional decision making process. Depending on the listener’s mindset the sounding result may be found intersting or boring, beautiful or annoying. I have never been very much interested in sound as such, or even beauty as such, whatever that means. The sound of music is the trace of a thought process, and all that matters, is that the idea takes shape as clearly as possible." Since 2021 Nikolaus is a member of the composer's collective Frog Peak Music

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