this is where people get wood straightened and bent

Title:
Tetration

Dates:
20-Jul-2024 (inception), 21-Jul-2024 (finalised), 25-Aug-2024 (released)

Artists:
Music composed, performed, produced by Norman Freund
Artwork by Norman Freund

BandCamp Purchase:
https://normanfreund.bandcamp.com/track/tetration

Description:
(cut down description, SoundCloud limits, see my BandCamp or FaceBook page full details)
Inspired by a Tetration tuning question on the "Microtonal Music and Tuning Theory" FaceBook group by Steven Socha (18 July 2024).

A simple description of tetration, is to recursively exponentiate a number. For each tetration operation (or iteration) yields another level of tetration. For example the tetration of 2.3 to three levels is:

(2.3^((2.3^2.3))) = 286.234

and the tetration of 2.3 to two levels is:
2.3^2.3=6.792

So there are two components or inputs to a tetration operation, the base number (in the above example 2.3) and the number of integer levels (in the above examples (3 and 2 respectively).

So what base to choose? I felt in a Just Intonation (JI) mood (is that a thing?), so decided to use a base of 3/2. 

Now for a formal definition of the tetration process:

The tetration notation used here is that of:
T=i:R
where
T = the tetraion result (floating point number)
i = the number of tetrations or tetration level (positive integer number)
R = the base of tetration (floating point or integer number, *(1) )
: = tetration symbol (or authors may us a different symbol, convenient to use here)

In general R can be a real or complex number, here I chose to use real positive numbers.

for example
2:R = R^R
3:R = R^(R^R)
4:R = R^(R^(R^R))
5:R = R^(R^(R^(R^R)))
...

The tetration tuning ratio T, for steps i=0,1,2 ... 8 here were:
0	1/1 = 1. = 0 c
1	(3/2)^(3/2) = 1.837 = 1052 c
2	(3/2)^((3/2)^(3/2)) = 2.106 = 1290 c
3	(3/2^((3/2)^((3/2)^(3/2))) = 2.349 = 1478 c
4	(3/2)^((3/2^((3/2)^((3/2)^(3/2)))) = 2.592 = 1659 c
5	(3/2)^((3/2)^((3/2^((3/2)^((3/2)^(3/2))))) = 2.860 = 1819 c
6	(3/2)^((3/2)^((3/2)^((3/2^((3/2)^((3/2)^(3/2)))))) = 3.189 = 2008 c
7	(3/2)^((3/2)^((3/2)^((3/2)^((3/2^((3/2)^((3/2)^(3/2))))))) = 3.644 = 2239 c
8	(3/2)^((3/2)^((3/2)^((3/2)^((3/2)^((3/2^((3/2)^((3/2)^(3/2)))))))) = 4.383 = 2558c 

Above is the whole scale, which shows the tuning frame was not an octave ratio of 2/1=2.,
instead a ratio of 4.383 or 2.132 octaves, so made for some interesting improvisations.

This tuning was placed in a Ableton Live (release 12) scala file along with meta definitions to give:
! Tetration_01-1.ascl
!
Tetration_of_3 divided_by_2 for a 8_note_scale_with_an_offset_of_1
 8
!
 1052.93250 cents
 1289.57373 cents
 1478.45996 cents
 1648.89600 cents
 1819.48535 cents
 2007.90125 cents
 2238.76245 cents
 2558.12329 cents
!
! @ABL REFERENCE_PITCH 3 0 440
! @ABL NOTE_RANGE_BY_INDEX -5 0 10 7

Harmonic, melodic and rhythmic ideas were developed in tandem. The master time signatures were 4/4 and 5/4, however the recorded clips used a variety of time signatures:

Time signatures used:
	Master time signatures: 4/4 and 5/4
	Clip Time signatures:
		Percussion: 4/4, 47/32, 5/4, 17/16, 5/16
		Rhythmic melodic: 41/16, 5/4, 
		Melodic and Harmony: 4/4, 5/4

Instrument choice was simple:
* Two drum tracks using the same drum kit.
* One bell sound track
* One bass sound track (very wide range used)
* Four pad sound tracks using the same pad instrument

The primary role of the drums were to provide rhythmic interest and to provide variety of time signatures.

The bells took on the role of a cross between melody and rhythm, and in particular contrasting to the rhythm of the drums, the drum and bells not necessarily having simultaneously the same time signatures. 

The bass took on the roles of from a spanner in the works to it's own melodic content. Hey it's a wacky tuning, so a wacky bass line felt in order!

The pads took on the role to establish the harmony as it exists in this tetration tuning system, long sustain chords, drones and at times playing it's own melody.

Buy Tetration

Tetration

here's the tuning

https://sw3.lumipakkanen.com/scale/Rtk5-NVtu

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retro (2012)

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2hollis - nerve (remix)

HOORAY FOR ONE YEAR! The amount of support in that time is so amazing, and we're so grateful for all of you. This isn't the craziest song in the world, but I thought we could put something out for you guys for this milestone.
Direct DL is on <3
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charli xcx - talk talk
bladee - be nice to me
[ rave tool 41 / HAPPYMAKER ]
ellie goulding - burn
1 single "op" from gangnam style
bladee - be nice to me (miku cover)
tsubi club - burbank house
p*rter r*binson - sad machine
p*rter r*binson - clarity
soulja boy - crank that

puppytalk

We are beyond excited to unveil the debut album and unlock the blueprint of consciousness with this mind-bending transmission from one of South Africa's most visionary producers, Solus!

Each track unfolds like an encrypted page of ancient knowledge, driven by hypnotic rhythms, crystalline synths, and otherworldly textures. Designed for both the dancefloor and the deep dreamer, this album is a sonic gateway to inner realms and cosmic truths.

Whether you're journeying through sound or igniting a dancefloor — Codex is your map to the unknown.

01 :: Solus - Best Test in the West
02 :: Solus - Mind Control
03 :: Solus - Codex
04 :: Solus & Mutaliens - Luminox
05 :: Synthetik Chaos - Peter les Boolons (Solus Remix)
06 :: Solus & Bandicoot - Spellbound
07 :: Solus - Momento
08 :: Solus - Mirror

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Codex

Solus (SA) - Codex

Title:
Harmonic 12

Dates:
25-Jun-2025 (inception), 25-Jun-2025 (finalised), 30-Jun-2025 (released)

Artists:
Music composed, performed, produced by Norman Freund
Artwork by Norman Freund

BandCamp Purchase:
https://normanfreund.bandcamp.com/track/harmonic-12

Description:
This is inspired from Antonije Tot's posting Ref. [1], where he discussed a "the Isfahan Tetrachord as (a) Modal Interchange in Ottoman Music". He described a Just Intonation (JI) tuning system with a fixed denominator of 12 with the numerator also starting with 12. 

This forms the following frequency ratios:
12/12=1/1
13/12
14/12=7/6
15/12=5/4
16/12=4/3

I then took this basic theme of a JI tuning system based on an ascending harmonic series with the number of 12, then experimented some more.

At the time, I was experimenting with constructing tuning scales based on a combination of two JI vectors. The second vector would be the harmonic series starting from 1 with a numerator of unity.

So the underlying frequency ratio vectors were:

First frequency ratio vector:
i,R
0, 12/12=1/1
1, 15/12=5/4
2, 16/12=4/3
3, 17/12=17/12
4, 18/12=3/2
5, 19/12=19/12
6, 20/12=5/3
7, 21/12=7/4

i = vector index
R = frequency ratio

Second frequency ratio vector:
i,R
0, 1/1
1, 2/1
2, 3/1
3, 4/1
4, 5/1
5, 6/1
6, 7/1
7, 8/1

And if you are interested, when these were combined gave this final tuning of frequency ratios:
i,R,colour
0, 1 16;
1, 1.25 0;
2, 1.33333333 0;
3, 1.41666667 0;
4, 1.5 0;
5, 1.58333333 0;
6, 1.66666667 0;
7, 1.75 0;
8, 2 2;
9, 2.5 0;
10, 2.66666667 0;
11, 2.83333333 0;
12, 3 0;
13, 3.16666667 0;
14, 3.33333333 0;
15, 3.5 0;
16, 3 2;
17, 3.75 0;
18, 4 0;
19, 4.25 0;
20, 4.5 0;
21, 4.75 0;
22, 5 0;
23, 5.25 0;
24, 4 2;
25, 5 0;
26, 5.33333333 0;
27, 5.66666667 0;
28, 6 0;
29, 6.33333333 0;
30, 6.66666667 0;
31, 7 0;
32, 5 2;
33, 6.25 0;
34, 6.66666667 0;
35, 7.08333333 0;
36, 7.5 0;
37, 7.91666667 0;
38, 8.33333333 0;
39, 8.75 0;
40, 6 2;
41, 7.5 0;
42, 8 0;
43, 8.5 0;
44, 9 0;
45, 9.5 0;
46, 10 0;
47, 10.5 0;
48, 7 2;
49, 8.75 0;
50, 9.33333333 0;
51, 9.91666667 0;
52, 10.5 0;
53, 11.08333333 0;
54, 11.66666667 0;
55, 12.25 0;
56, 8 9;
57, 10 0;
58, 10.66666667 0;
59, 11.33333333 0;
60, 12 0;
61, 12.66666667 0;
62, 13.33333333 0;
63, 14 0;
64, 16 2;
65, 20 0;
66, 21.33333333 0;
67, 22.66666667 0;
68, 24 0;
69, 25.33333333 0;
70, 26.66666667 0;
71, 28 0;
72, 24 2;
73, 30 0;
74, 32 0;
75, 34 0;
76, 36 0;
77, 38 0;
78, 40 0;
79, 42 0;
80, 32 2;
81, 40 0;
82, 42.66666667 0;
83, 45.33333333 0;
84, 48 0;
85, 50.66666667 0;
86, 53.33333333 0;
87, 56 0;
88, 40 2;
89, 50 0;
90, 53.33333333 0;
91, 56.66666667 0;
92, 60 0;
93, 63.33333333 0;
94, 66.66666667 0;
95, 70 0;
96, 48 2;
97, 60 0;
98, 64 0;
99, 68 0;
100, 72 0;
101, 76 0;
102, 80 0;
103, 84 0;
104, 56 2;
105, 70 0;
106, 74.66666667 0;
107, 79.33333333 0;
108, 84 0;
109, 88.66666667 0;
110, 93.33333333 0;
111, 98 0;
112, 64 9;
113, 80 0;
114, 85.33333333 0;
115, 90.66666667 0;
116, 96 0;
117, 101.33333333 0;
118, 106.66666667 0;
119, 112 0;
120, 128 2;
121, 160 0;
122, 170.66666667 0;
123, 181.33333333 0;
124, 192 0;
125, 202.66666667 0;
126, 213.33333333 0;
127, 224 0;

the colour is simply an integer between 0 and 127 which I used to colour code the scale as applied to my Ableton Push2 midi controller.

That evening after seeing this post (Ref. [1]) and experimenting with the tuning, I switched on my synthesiser (PulseRectOsc) with this tuning and began to explore the tuning system, improvised and recorded. I then added some more layers with a freely tuned hardware synthesiser, the Soma Enner for melodic ideas and percussive ideas.

Perhaps not true to the original Ottoman music, but inspired by it.


References:
[1] Antonije Tot, 24-Jun-2025, "The Isfahan Tetrachord as Modal Interchange in Ottoman Music", FaceBook Group "Microtonal Music and Tuning Theory", link: https://www.facebook.com/share/p/16s1WsugHJ/


Harmonic 12

Field of Action - empathy // cassette 

by Eric Wubbels 
in collaboration with Charmaine Lee

score: http://wubbelsmusic.com/ec_score.html

text and documentation about the project: http://wubbelsmusic.com/pieces_FieldofAction.html

Charmaine Lee: voice, microphones
Eric Wubbels: prepared piano, composition

Full piece / album here:
https://ericwubbels.bandcamp.com/album/field-of-action-contraposition-2






empathy // cassette [2020] (w/ score)

I like messing with tuning and rhythm, occasionally I might even make actual music.

Bandcamp, which has a lot of my older stuff: https://guessw3rk.bandcamp.com/

youtube: https://www.youtube.com/channel/UCLHHDTjGCsETTIrbGTrL6Mw

got a freesound page, where I upload glitchy sound textures and such : https://freesound.org/people/dudebroman2/

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