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

The Eyes Around

Video Link: https://www.youtube.com/watch?v=WJRhc5D4uTA

The Swan & The Fox Part II

The Swan & The Fox Part II & Video Link

Having a little play with this new track experimenting and expanding. I will be developing this much further. 

Please feel free to leave a comment as your feedback is really useful and valuable to me.

Exploration (Instrumental)

The third movement of the Symphony for String Orchestra (2025).

Pawel Strzelecki: 3. Adagio [Symphony for String Orchestra (2025)].

The secret laboratory of Dr. Hindenburg

Photo by <a href="https://stockcake.com/i/light-meets-shadow_1589714_1178267">Stockcake</a>

2025-09-18

very long shadows

Cozy Cottage

TRAMPELFÂD
Laboratory for Contemporary Electronic Experimental Music

Rec.name : " VST Plugs V "
credit :

date : 22-09-2025

PLEASE VISIT OUR MAIN PAGE :

trampelfad.bandcamp.com
and
maxelzholz.bandcamp.com

Live 2024
https://www.youtube.com/watch?v=Y52VDBHP-cc

gFLIE2ATree

a project created in december 2020 found from the archive 

Procedure:
A MIDI sequence was created with Elektron Octatrack,
which drives a piano track in Ableton.
The sequence was then broken down into four melodic lines.
The first line were transposed by +7 semintones
the second by +11 semitones
the third -13 semitones
the fourth line remains in the same pitch
then the harmony was extracted from each melodic line.
For each track, the ghost plays its part and sings as it pleases.
Next, for the sake of musicality, each ghost decides which notes to play and which to omit from its part.
During the performance the Time increase and the ensemble takes place
second take with the "singing ghost" track add

work in progress

cover art is a waterpaint made by me in 1999

ghost III *take two

decaying flowers

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

Please don't spam this account!

High Phi, for drums and piano obbligato

David Victor Feldman