© Guido Kramann

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© Guido Kramann

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The combined use of Kaleidophone and AOGdogma in the composition algorave2sleep#56

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algorave2sleep#56 on youtube:

With the series of music pieces that I publish on the youtube channel algorave2sleep, my aim is to explore and also demonstrate the potential of AOG itself. The name of the channel comes from the idea to publish there long, meditative pieces of music, which are characterized by being calm and sonically appealing in their metamorphosing progression, while remaining musically interesting over long stretches. They are intended to convey a pleasant feeling and to stimulate the imagination while listening. The composition algorave2sleep#56 represents one in this series, in which this self-imposed claim is fulfilled quite well, I think. And this, although the composition can be represented in the script language of AOGdogma very compactly, in few lines (compare further below). That's the point, to show that actually usable music is created, if the progressive sequence of natural numbers, respectively their inner divisor structure is the basis of the compositions. The hypothesis is that the music is, so to speak, in the natural numbers, that the natural numbers are a very deep-lying basis of everything and via many detours also for our musical feeling. But how was the composition algorave2sleep#56 made? - This will be described in the following.

algorave2sleep#56 was created using two interfaces for AOG (Arithmetic Operation Grammar). First I experimented with Kaleidophone and found there two formulas whose musical production I liked very much and which can easily be converted into each other:

  • Formula 1: 30240 // (t*22%12)
  • Formula 2: 40320 // (t*34/2)
Screenshot, how in Kaleidophone Formula 1: 30240 // (t*22%12) is retreived.

Bild 0-1: Screenshot, how in Kaleidophone Formula 1: 30240 // (t*22%12) is retreived.

Screenshot, how in Kaleidophone Formula 2: 40320 // (t*34/2) is retreived.

Bild 0-2: Screenshot, how in Kaleidophone Formula 2: 40320 // (t*34/2) is retreived.

This way of experimenting with Kaleidophone can be tried by each person for himself, since it is a web-based program written in Javascript. In fact, several people can even work together over the web on a musical performance with Kaleidophone. The web link for this is:


With Kaleidophone, spheres of equal size in the colors blue, red, green, yellow, gray and black can be inserted into a 5x5x5 grid. The resulting spatial figure is then projected in two planes. The two projections are in turn used to generate two AOG formulas from them in an unambiguous manner, each of which controls a musical instrument.

The transfer of the projection runs roughly in the following way: First, contiguous colored areas are segmented, separated from each other by a black background. In these separated areas, again areas can be segmented, which consist of exactly one color. The colors are assigned prime numbers: blue=2, red=3, green=5, yellow=7. By counting the number of contiguous areas of one color within the separated large areas and adding up their numerical correspondence, one obtains a number for each separated area. An associated operator results again from the number of the existing gray areas. A possible operator is: + - * / %, where % stands for modulo. If there is no gray patch in an area, it is inactive. Furthermore, the assignment to the operator runs cyclically according to the number of gray patches. "*22", "%12", "*34", "/2" are operations in the above examples. The operations are arranged in their natural order in the projection (left to right, top to bottom). The first one is applied to t, i.e. the natural numbers passing through with a fixed time interval. The second is applied to the previously resulting result, and so on. For each intermediate result it is checked whether it divides the base number on the left without remainder. The result is interpreted as a frequency, multiplied by a factor FACTOR (default: 0.07) and converted to a midi pitch and played, if this is possible for the musical instrument used. The base number is initially fixed in Kaleidophone (BASENUMBER=2*2*2*3*5*7=10080), but is changed according to the number of isolated monochromatic areas in the projections.

After identifying the two formulas above, they were in turn brought into another software tool linked to AOG, AOGdogma. The basic idea with AOGdogma is to provide a scripting language that can interpret AOG formulas, and where one can replace any number with a time-varying variable as needed to arrive at metamorphosing formulas. This is exactly what has now been done.

Formula 1: 30240 // (t*22%12) ... can be represented in AOGdogma as follows:

9000 268 ! t
5 3 1 1 1 7 24 53 89 : xy
t *22%12 ~ xy

Code 0-1: Essential parts in AOGdogma-script, which represent the formula 30240 // (t*22%12).

The first line specifies that t starts at 9000 and is incremented every 268 milliseconds. The leading numbers of the second line stand for: BASENUMBER = 2^5*3^3*5^1*7^1 = 3240. The 7 stands for a value of FACTOR of 7/100, which is the desired value of 0.07. Finally, the third line describes the essential part of the formula. The comparison with the base number and the tonal conversion are implicit. Analogous can be proceeded with the second formula.

The special thing about the used base numbers is that the following applies: 40320 = 30240 / 3 * 4 This means that both base numbers are in the ratio of a fourth to each other. This probably causes that again with the formation of the played frequencies the connection of a fifth case forms with the change between the base numbers. This principle was then extended in the composition created in AOGdogma to the running through of five base numbers, which stand in this relation to each other.

In addition, a third voice was inserted, corresponding to a recombination of the formulas of the first two, and the formulas were in turn subjected to a slow metamorphosing change.

The overall script that generates the composition published on youtube now looks like this:

240 ~ DT
9000 ~ T0
# 120 ~ PT
# 1440 ~ PQ
30 ~ PT
180 ~ PQ

T0 DT ! t

t -T0 /PT %5 ~ MM
MM *2 ~ NN
9 - NN ~ PP
MM + 1 ~ QQ

t -T0 /PQ %11 ~ UU
t -T0 /PQ %13 ~ VV

25 - UU ~ WW
25 + UU ~ XX
2 + VV ~ YY

# 2er 3er
#  1  5
#  3  4
#  5  3
#  7  2
#  9  1

PP QQ 1 1 1 7 24 53 89 0 70 30 : xy
PP QQ 1 1 1 7 12 28 102 1 60 40 : vl
PP QQ 1 1 1 7  0 24 108 2 30 70 : vb

t *34/YY  ~ xy
t *22%WW  ~ vl
t *34%XX  ~ vb

16 -DD /2 +CC /4 %3  xy
16 -DD /2 +CC /4 %3  vl
16 -DD /2 +CC /4 %3  vb

Code 0-2: Entire script generating algorave2sleep#56 in infinite length, whereas the duration of half an hour in the video was set by random.

Also with AOGdogma every person can experiment by himself. A slightly reduced version of the possibilities is also available here as a web application:

There is also a detailed description of the syntax of AOGdogma and some examples here:

To achieve a musically appealing sound of the instruments, physical modeling instruments from Pianoteq were used: Vibraphone, Harp and Church Organ.