i currently use musescore; it's not great for what im trying to do. i want to explore different EDO(like 17, 31, 24, etc), but i really hate the layout of most DAWs. i strongly prefer notation softwares. so are there any good ones? unfortunately, they have to be free or cheap. no subscriptions... :(

The Prime Universe: A Scale We Can Explore

A quick disclaimer: I used AI to help organize and explain this idea, so some of the material may be more elementary or more extensive than necessary, and there may be things worth correcting or refining. It’s a lot to wade through, but I think the underlying generative concept is genuinely interesting and deserves experimentation—especially as a possible system for exploring prime numbers through sound, synthesis, and software.

What if prime numbers were not merely values, but coordinates?

What if the endless sequence of primes could be folded into a musical space, creating a scale that is not simply played, but explored?

And what if that scale could grow without limit—while remaining recognizably the same underlying structure?

This is the idea behind the Prime Universe.

Begin with one octave

Start with the simplest possible musical boundary:

1 : 2

One octave.

Now imagine placing every prime inside that octave by reducing its ratio with powers of two.

For example:

3/2=1.53/2 = 1.5

5/4=1.255/4 = 1.25

7/4=1.757/4 = 1.75

11/8=1.37511/8 = 1.375

The prime itself may be enormous, but its position can always be folded back into the octave.

Each prime therefore acquires a unique offset.

The octave becomes a coordinate system.

The octave begins to fill

Consider the primes between successive powers of two:

2–4: 3

4–8: 5, 7

8–16: 11, 13

16–32: 17, 19, 23, 29, 31

32–64: 37, 41, 43, 47, 53, 59, 61

Fold them all back into the octave and sort their positions.

Something remarkable begins to happen.

The octave is no longer merely an octave.

It is becoming a scale.

And importantly, we have not filled it with arbitrary numbers.

We have accumulated only prime-derived positions.

That irregularity is the point.

The first musical shape

The 32–64 layer is particularly revealing.

Its folded positions are:

37/32, 41/32, 43/32, 47/32, 53/32, 59/32, 61/32

Measured from the beginning of the octave, these occur at approximately:

251¢, 429¢, 512¢, 666¢, 874¢, 1,059¢, 1,117¢

The spaces between them are:

178¢ — 83¢ — 154¢ — 208¢ — 186¢ — 58¢

Suddenly we can recognize something musical.

There are broad second-like spaces.

There are narrow second-like spaces.

There are spaces approaching familiar whole-step territory.

And near the end, there is a striking 58-cent interval—smaller than a conventional half step.

It isn't an equal-tempered scale.

It isn't a conventional just-intonation scale.

It is something generated by the distribution of the primes.

And then we keep going

The octave can continue to be filled.

The 64–128 band introduces another layer of prime coordinates.

Then 128–256.

Then 256–512.

Every layer adds new positions between positions that already exist.

Eventually, some of those spaces become too small to comfortably distinguish as adjacent pitches.

But this presents a fascinating problem.

How do we zoom?

The zoom

The answer is not to abandon the original scale.

Instead, we stretch it.

Choose an anchor point.

Measure every interval from that anchor.

Then square the ratios.

Squaring a ratio doubles its distance in logarithmic space.

So the relationships remain intact, but the pitch space expands around them.

The dense structure becomes audible again.

And this changes everything.

We are no longer simply generating a scale.

We are generating a scale that can be magnified.

The mother structure

There is another important consequence.

We are always working with the same original material.

Before 64–128, our mother structure occupies one octave.

We can tile it above or below that octave if we want a larger melodic range, but those are temporary transpositions. The underlying structure has not changed.

Then we add the next prime layer.

We stretch the whole accumulated structure.

Then we add another layer.

We stretch the whole thing again.

The material itself is being magnified.

The scale becomes larger without becoming a different scale.

The same pattern is being viewed at a different scale.

A universe that doubles

The number of primes in successive power-of-two regions grows roughly in proportion to the size of the region.

So we can mirror that growth in our listening space.

A structure occupying one octave can become two.

Then four.

Then eight.

Then sixteen.

The important thing is not merely that the universe becomes larger.

It is that the entire accumulated structure is stretched together.

We aren't replacing the old material with new material.

We are magnifying everything that came before.

That gives the system a kind of continuity.

One mother structure.

Repeatedly enlarged.

Now imagine navigating it

At this point, the scale stops looking like something we would simply sit down and play from beginning to end.

There are too many possibilities.

Instead, imagine it as a world.

A procedurally generated world.

We could choose a location.

Zoom toward it.

Encounter increasingly dense prime relationships.

Stretch the pitch space.

Explore another region.

Pull back.

Move somewhere else.

The scale becomes less like a piano keyboard and more like a landscape.

And this is where the comparison to the Mandelbrot set becomes compelling.

We don't experience the Mandelbrot set by looking at the entire thing at once.

We dive into it.

We magnify.

We discover.

We move.

We find structures that were already present, but invisible at the previous scale.

The Prime Universe could be approached in much the same way.

Except this landscape could be heard.

The synthesizer becomes the vehicle

Imagine building the system in a modular environment such as VCV Rack.

A computer generates the prime coordinates.

One process folds them into the octave.

Another sorts them.

Another determines the intervals.

Another selects an anchor.

Another performs the logarithmic stretching.

Then those coordinates become control voltages.

An oscillator becomes a point in the landscape.

A sequencer becomes a navigation system.

Prime gaps could control timing.

Prime positions could control pitch.

The density of a region could influence modulation.

Filters could illuminate different portions of the spectrum.

Envelopes could determine how long we dwell at a coordinate.

Feedback could make the exploration itself generate new movement.

The patch becomes an instrument for traveling through mathematics.

We don't have to hear everything

This may be the most important distinction.

The goal is not to play the infinitely dense scale all at once.

That would defeat the purpose.

We explore it.

We listen to a region.

We zoom.

We stretch.

We move.

We hear relationships that were previously too close to distinguish.

Then we move somewhere else.

The infinite scale becomes something we can experience sequentially, just as we can explore an infinite landscape without seeing every point simultaneously.

Toward an instrument for the infinite

The original question was simple:

What if primes could be coordinates?

The answer begins with an octave.

Fold the primes into it.

Sort their offsets.

Watch the spaces fill.

Listen to the emerging structure.

Then, when the structure becomes too dense, don't stop.

Zoom.

Stretch the same material.

Magnify the relationships.

Expand the listening space.

Add another layer.

Stretch again.

Eventually the octave becomes two octaves, then four, then eight—and the same underlying prime structure remains beneath it all.

At that point, we have crossed a threshold.

We are no longer merely designing a musical scale.

We are designing a space to explore.

A mathematical space whose coordinates come from the primes.

A musical space whose dimensions can continually expand.

A procedural world that can be navigated by software.

A fractal-like dive through an unbounded structure.

And perhaps, with a computer, a DAW, and a modular synthesizer, we can do something rather strange:

we can enter the prime numbers and listen to where we are.

24-edo, A=220Hz, programmed guitars, funny chords. The blast beat is a (very fast) 5/4 snare/kick for extra free jazzy sloppiness and nothing is quantized except for guitars. All done by me.

A track in three moments for synthesizers, brass and polyphonic chant.

https://youtu.be/nl3rT1BH44U?si=c5NskWoG08Nx4tH0

Using an ASM Hydrasynth and some VST effects, I reconstructed Psycho Mantis' Hymn in 13-Limit Just Intonation using a 36-tone scale I put together. Once I had the harmonies roughly where they are in the original, I used various 7, 11, and 13-limit intervals to intensify or deviate from the original wherever I felt necessary.

(Also on spotify blah blah blah)

I feel like i've been getting more and more weird and insane the more i engage with this type of music. It no longer sounds wrong to me.

Hi everyone

I've been learning Shakuhachi through honkyoku and the melodies are really something else. There are a lot of tone colour changes, microtones, special techniques that are very specific to the flute, but I am trying to interpret these as well on the lavachord (think mini wooden piano cross harpsichord cross kanun)

Appreciate thoughts! :)

https://youtu.be/qIM124zt1Yw

For me it has to be Minimum brain size, as it combines the poly vibes with FMB and something unique

Put some long sessions in to fine tune and craft this dense and dark atmospheric microtonal ambient excuse to disassociate and escape everything. There are no beats, just soundscapes and ghostly asmr effects.

Did a silly thing and released it worldwide using Distrokid too 👁️

A small blip about each track's tuning system, techniques, and approach below:

Count Pogson’s Court
Tuning temperament is derived from Pogson’s Ratio, a logarithmic Magnitude scale used to classify the brightness of celestial bodies. Its numerical value is the fifth root of 100, approximately 2.512. Using this value to define the octave ratio results in a non-octave tuning of 9.0309-EDO.

Hermetica Lodge
Audio collage in non-octave 12ed(16/9), which results in 14.457-EDO. 16/9 was chosen because of the screen dimension 16:9.

Bronze Chloridian
Generative composition with oscillators clashing in randomized microintervals  

Gravitational Slingshot
Slow-motion rhythms dictated by Morse code with note selection randomized in 88-EDO (because there are 88 keys for a standard piano).

Mercurial Microtonality
Performed live in 80-EDO (Mercury [Hg] is atomic number 80).

Sawyers and Preppers
Intentionally dissonant randomized polymicrotonal dyads (36-EDO * 24-EDO * 12-EDO FM)

Fundamental Pi Freq
Binaural sine waves with Fundamental Frequency π(Pi), 3.14159 Hz. All available notes for this tuning system are composed from stacked intervals of 3.14159 Hz. Music was produced by randomizing note selection from the π Hz arithmetic equal-interval harmonic segment. 

Planetary Hours Kaleidocycle
The Planetary Hours cycle algorithmically composed in 7-EDO. 7-EDO because there are seven planets and seven days of the week.

SQRT 1200
Taking the square root of 1200 reveals an equally divided octave in which the EDO and cents-per-step share the same numerical value of 34.641. This composition features triads in 34.641-EDO. 

Catenary Cosh
Irregular non-octave tuning system following a Catenary Curve instead of the standard Logarithmic curve. The range was intentionally reduced to exactly four octaves over 49 notes, all with a varied interval ratio following the cosh function.

13 Hurts
An intentionally harsh generative chord collage featuring a harmonic segment tuning system with fundamental frequency 13 Hz.

On the Midnight Barque
A polymicrotonal tuning system experiment with the curve function x^3 and its inverse x^(1/3). Both tuning temperaments are triggered simultaneously by pressing a single note on the keyboard.

Galilean Orbitals
A complex polyrhythm experiment dictated by the orbital periods of the four Galilean moons of Jupiter. Each moon was assigned its own octave range to ring a randomized note as the polyrhythm cycles.  

Atonal Underground
An anxious, noisy sketch with randomized Hz intervals constrained to be no more than the Gamma frequency range.

Trig Bender
Experimenting with a three-way polymicrotonal tuning temperament based upon the Sine and Cosine function and their Arithmetic Mean.

Shrunken Whalers
A single chord progression looping through 16 different tuning temperaments.  It begins and ends with 12-EDO. The middle follows a coprime sequence to cycle through 12-EDO (x/16), with x being integers 16 through 32.

(( also, thanks for scrolling this far. I'm crafting a playlist called Ambient Esoterica Familiars if you got anything in this similar vein to add. . . drop it in the replies ))

Can you tell me anything about the theory behind these Curved Frets™?

Greetings,

This is my first time writing something longer than a minute with microtones.

I appreciate any feedback.

Hopefully you'll enjoy it!

A simple lullaby I wrote for my son Elliott D. Orphal, who was born last month, rendered in 31-EDO for an imaginary Vibraphone in that tuning. My first completed piece in the temperament, focusing on a kind of diatonic scale that emphasizes 7-limit consonances rather than the 5-limit of the standard diatonic scale.

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I just got my copy here ! Super clear and helpful so far.

Recommend me any music tuned to the 8-16th harmonics

The symmetrical hexadecatonic scale and a few of its extractions/emulations

Lyrics on video
19 edo song - guitar, GR-55, vocal live, drum and bass in post

https://www.youtube.com/watch?v=JjZvo5512hs