TMS
Musinum legacy
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I. Musinum in Plugdata
– Musinum out is by default routed to PD synths.
– of course any Manual is just a pure fantasy…))
– one can see, that in Arch version – tp, rg, c/div par. plus Rise, Fall, Fitsm and Swing are missing, while it has some extra par. for velocity.
L – Pure Data (for comparison next is Arch Musinum.
II. Musinum in Architect
As mentioned in intro, concept is loosely built on TMS applying self-similarity principal and AZZIN also show it use in Matlab/ Octave.
% example initialization
N = 1000;
start = 0;
step =1;
base = 2;
% main loop
for i = 1:N
num = start + i*step;
D = dec2base(num,base);
L = length(D);
temp = 0;
for j = 1:L
temp = temp + str2num(D(j));
end
out(i) = temp;
end
W/ Matlab/Octave on your computer try the following:
% in case of base 2
out(1:20)
out(2:2:40)
out(4:4:80)
% in case of base 3
out(1:20)
out(3:3:90)
out(9:9:180)
and you have identical sequences, i.e. self-similar as are 2nd and 4th tones in Lpic bellow:
Intro to binary number and base (base number)
– Base2 – binary number (only 0 and 1) is counting same like in decimal (base10) just 1 not 9 is last number.
In base-ten-system 10 is 1ten 0ones.
Way the binary numbers in left column are created (to 16)
– as one can see u start on 0s and adding successively 1s from right to left (Rmost-pic).
0. step – 0
1. step – just add 1 – finished
2. 1 is on second row
3 last row is also changed to 1 – finished
4.. 1 is on 3. row
5. last row is also changed to 1
6. next to last row is also changed to 1 while last keep 0
7. ……………………………………………………………………….last keep 1 – finished
Way the numbers are interpreted – right column – for Thue Morse sequence
– if binary expansion is odd – than it equal 1, if even it equal 0 (very complicated)).
Odd numbers are here also called oddius)) – 1, 2, 4, 7, 8, 11, 13, 14, 16, 19, 21, 22, 25, 26, 28, 31, 32, 35, 37, 38 – odd parity
Even are called evils)) – have even parity – 0, 3, 5, 6, 9, 10, 12, 15, 17, 18, 20, 23, 24, 27, 29, 30, 33, 34, 36, 39
Binary numbers to 32 – warning in progress in hazy state..
Binary number are number with base2.
– as Liebnitz and others even before pointed out: 2^0=0 – ^1=2 – ^2=4 – ^3=8 – ^4=16 – ^5=32 – 6-64 – 7-128 (8bits)) – and here 1 stays on first position following w/ just zeros – so sum of digits is 1.
In processors (CPU – central processing unit) construction bit slicing arithmetic logic unit (ALU) goes to 8 or 16 bits (that creates on bytes)).
In RGB color processing it is typical to combine 3x 256bits – that is three times 2^256=1.1579 x 10^77
2^4=16 possible values – 4bits/4digits – in 16 as single numeric value (16 + 0) 1 will be on the beginning in row of 5 digits following w/ just 0s – so digit sum is 1/, but total value (w/ counting 0) will be 17 (so it will be first number require increase from 4 to 5th bit), while last chain of 4 bit will consist of 4×1 – so sum value is 4.
2^5-32 – 5bits – in 32 1 will be on the beginning in row of 6 digits following w/ just0 – so digit sum 1/, but total value w/ counting 0 will be 32.
2^6-64
2^7-128
2^8=256
2^9=512
2^10=1024
2^11=2048
2^12=4096
2^13=8192 – 13bits – in 4096 1 will be on the beginning in row of 13 digits following w/ just0 – so digit sum 1/, but total value w/ counting 0 will be 32.
….
2^16 = 65 536 (6,5×10^4)
2^32= 4,3B (mld in czech) – 4,3×10^9
2^64=1,9×10^19
2^128=3,4×10^38
2^52= biggest value in Lua before 5.3 (2014)
2^64 – max number in Lua after 5.3 – but it is compiled Number which is “double” so it may be around 2^1024. (in nutshell – cause there may be more catches..) – it is 18 exabites 18e18..
2^256=1.1579 x 10^77
That means that in every 2x (next power) sum of digits will be 1.e
In processors (CPU – central processing unit) construction bit slicing arithmetic logic unit (ALU) goes to 8 or 16 bits (that creates on bytes)). In RGB color processing it is typical to combine 3x 256bits – that is three times 2^256=1.1579 x 10^77
2^4=16 possible values – 4bits/4digits – in 16 as single numeric value (16 + 0) 1 will be on the beginning in row of 5 digits following w/ just 0s – so digit sum is 1/, but total value (w/ counting 0) will be 17 (so it will be first number require increase from 4 to 5th bit), while last chain of 4 bit will consist of 4×1 – so sum value is 4.
2^5-32 – 5bits – in 32 1 will be on the beginning in row of 6 digits following w/ just0 – so digit sum 1/, but total value w/ counting 0 will be 32.
2^6-64
2^7-128
2^8=256
2^9=512
2^10=1024
2^11=2048
2^12=4096
2^13=8192 – 13bits – in 4096 1 will be on the beginning in row of 13 digits following w/ just0 – so digit sum 1/, but total value w/ counting 0 will be 32.
….
2^16 = 65 536 (6,5×10^4)
2^32= 4,3B (mld in czech) – 4,3×10^9
2^64=1,9×10^19
2^128=3,4×10^38
2^52= biggest value in Lua before 5.3 (2014)
2^64 – max number in Lua after 5.3 – but it is compiled Number which is “double” so it may be around 2^1024. (in nutshell – cause there may be more catches..) – it is 18 exabites 18e18..
2^256=1.1579 x 10^77
That means that in every 2x (next power) sum of digits will be 1.e
decimal | binary | |
0 | 0 | 0 ones |
1 | 1 | 1 one |
2 | 10 | 1 two and zero ones |
3 | 11 | 1 two and 1 one |
4 | 100 | 1 four, 0 twos, and 0 ones |
5 | 101 | 1 four, 0 twos, and 1 one |
6 | 110 | 1 four, 1 two, and 0 ones |
7 | 111 | 1 four, 1 two, and 1 one |
8 | 1000 | 1 eight, 0 fours, 0 twos, and 0 ones |
9 | 1001 | 1 eight, 0 fours, 0 twos, and 1 ones |
10 | 1010 | 1 eight, 0 fours, 1 two, and 0 ones |
11 | 1011 | 1 eight, 0 fours, 1 two, and 1 one |
12 | 1100 | 1 eight, 1 four, 0 twos, and 0 ones |
13 | 1101 | 1 eight, 1 four, 0 twos, and 1 one |
14 | 1110 | 1 eight, 1 four, 1 two, and 0 ones |
15 | 1111 | 1 eight, 1 four, 1 two, and 1 one |
16 | 10000 | 1 sixteen, 0 eights, 0 fours, 0 twos, and 0 ones |
– as we can see Tone is generated by sum of binary numbers.
2nd and 4th skips in the end creates similarity – kind of fractal one – second is twice large, 4th 4x large (as also was shown in code section above).
Base convertion
(Number Bases: Introduction & Binary Numbers | Purplemath)
Base2 convertion to Base10
– converting 101100101^2 (9 digits) to base10: 1×2^8 + 0×2^7 + 1×2^6 + 1×2^5 + 0×2^4 + 0×2^3 + 1×2^2 + 0×2^1 + 1×2^0 = 1×256 + 0×128 + 1×64 + 1×32 + 0×16 + 0×8 + 1×4 + 0×2 + 1×1 = 256 + 64 + 32 + 4 + 1 = 357
digits: | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 |
numbering: | 8 | 7 | 6 | 5 | 4 | 3 | 2 | 1 | 0 |
Base10 convertion to Base2
Converting 357^10 to 101100101^2.
So u just deviding by 2 and write reminder – either 0 or 1 – reminder in last 1 is first number (as u can see)..
The Architect implementation (citing AZZIN from KVR) is centered on a macro (“musi_num“) which has the following inlets:
– input: an incremental/decremental number triggered by a Metronome, for example set to 1/8
– step: (>=1), as in above code
– start: starting integer (>=0), as shown in above code above.
– base: numerical base in which the number is converted. Base 10 is as we know it (counting to 10 and repeat cycle))..
– max range: maximum midi note range on which the algorithm is bounded (def. 66)
– min range: minimum midi note range on which the algorithm is bounded (def. 46)
The main output is a number (left outlet) that can be easily converted into a midi note, while an experimental output* (right outlet) provides a number between [0-1] that is translated to midi velocity by means of a-linmap macro.
These two output can then be passed through some midi processing (execution probability, force to scale etc.). Attached there is a simple implementation with 1 Midi channel in output.
Experiment with the different parameters, esp. “step” and “base“, but also with increasing and decreasing input numbers (“UP”, “DOWN”) to get interesting sequences. To this aim, a simple graphical interface is provided, which allows the selection of the main parameters as well as scale, min/max midi velocity and channel probability. The default output is Midi OUT, so you have to attach a midi instrument outside Architect or switch the output to Track<N> (internal to Architect)
– Kindermann also urged to use besided its basic sequence also its other forms
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III. Musinum in Grid
– i think it show clearly, that even this simple sequence is marking limits of what can be done in the Grid.
– it would need some clear demonstration how to write and read values Array module and even if simple sequence could be started, it would be even harder to play with it…
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