S(n) Rep Sequence no. 8

Casey Mongoven

April 30, 2005

description of sequence: number of unique representations of n using sums of distinct elements of the Fibonacci sequence beginning 1,2,3,5,8,…

number of members in sequence used: 4181

orientation: descending

temperament: φ⁸ + 1

highest pitch: 530 Hertz

lowest pitch: 169.9464131227 Hertz

length: 200.688 seconds

note value: .048 seconds

waveform: sine 0° → saw 0°

simulated spatial location: 23° → -23°

dynamic values: mp → fff

starting attack: .005 seconds

attack roll-off: .000035 seconds

starting release: .008 seconds

release roll-off: .000056 seconds

values used:

# pitch in Hertz waveform s.s.l. dynamic attack release

1 530.0000000000 sine 0° 23° mp .005000 .008000

2 518.9534345875 .004965 .007944

3 508.1371080569 m ¦ c .004930 .007888

4 497.5462216367 o ¦ r .004895 .007832

5 487.1760765743 r ¦ e .004860 .007776

6 477.0220720511 p ¦ s .004825 .007720

7 467.0797031414 h ¦ c .004790 .007664

8 457.3445588139 ¦ e .004755 .007608

9 447.8123199743 ¦ ¦ n .004720 .007552

10 438.4787575495 ¦ ¦ d .004685 .007496

11 429.3397306112 ¦ ¦ o .004650 .007440

12 420.3911845388 ¦ ¦ .004615 .007384

13 411.6291492202 ¦ ¦ ¦ .004580 .007328

14 403.0497372908 ¦ ¦ ¦ .004545 .007272

15 394.6491424088 ¦ ¦ ¦ .004510 .007216

16 386.4236375661 ¦ ¦ ¦ .004475 .007160

17 378.3695734353 ¦ ¦ ¦ .004440 .007104

18 370.4833767503 ¦ ¦ ¦ .004405 .007048

19 362.7615487210 ¦ ¦ ¦ .004370 .006992

20 355.2006634812 ¦ ¦ ¦ .004335 .006936

21 347.7973665685 ¦ ¦ ¦ .004300 .006880

22 340.5483734363 ¦ ¦ ¦ .004265 .006824

23 333.4504679961 ¦ ¦ ¦ .004230 .006768

24 326.5005011913 ¦ ¦ ¦ .004195 .006712

25 319.6953895995 ¦ ¦ ¦ .004160 .006656

26 313.0321140650 ¦ ¦ ¦ .004125 .006600

27 306.5077183589 ¦ ¦ ¦ .004090 .006544

28 300.1193078678 ¦ ¦ ¦ .004055 .006488

29 293.8640483094 ¦ ¦ ¦ .004020 .006432

30 287.7391644754 ¦ ¦ ¦ .003985 .006376

31 281.7419389997 ¦ ¦ ¦ .003950 .006320

32 275.8697111532 ¦ ¦ ¦ .003915 .006264

33 270.1198756635 ¦ ¦ ¦ .003880 .006208

34 264.4898815583 ¦ ¦ ¦ .003845 .006152

35 258.9772310345 ¦ ¦ ¦ .003810 .006096

36 253.5794783497 ¦ ¦ ¦ .003775 .006040

37 248.2942287367 ¦ ¦ ¦ .003740 .005984

38 243.1191373418 ¦ ¦ ¦ .003705 .005928

39 238.0519081839 ¦ ¦ ¦ .003670 .005872

40 233.0902931362 ¦ ¦ ¦ .003635 .005816

41 228.2320909283 ¦ ¦ ¦ .003600 .005760

42 223.4751461704 ¦ ¦ ¦ .003565 .005704

43 218.8173483964 ¦ ¦ ¦ .003530 .005648

44 214.2566311276 ¦ ¦ ¦ .003495 .005592

45 209.7909709562 ¦ ¦ ¦ .003460 .005536

46 205.4183866475 ¦ ¦ ¦ .003425 .005480

47 201.1369382607 ¦ ¦ ¦ .003390 .005424

48 196.9447262883 ¦ ¦ ¦ .003355 .005368

49 192.8398908136 ¦ ¦ ¦ .003320 .005312

50 188.8206106852 ¦ ¦ ¦ .003285 .005256

51 184.8851027094 ¦ ¦ ¦ .003250 .005200

52 181.0316208587 ¦ ¦ ¦ .003215 .005144

53 177.2584554973 ¦ ¦ ¦ .003180 .005088

54 173.5639326226 .003145 .005032

55 169.9464131227 saw 0° -23° fff .003110 .004976

sequence values:

1 1 2 1 2 2 1 3 2 2 3 1 3 3 2 4 2 3 3 1 4 3 3 5 2 4 4 2 5 3 3 4 1 4 4 3 6 3 5 5 2 6 4 4 6 2 5 5 3 6 3 4 4 1 5 4 4 7 3 6 6 3 8 5 5 7 2 6 6 4 8 4 6 6 2 7 5 5 8 3 6 6 3 7 4 4 5 1 5 5 4 8 4 7 7 3 9 6 6 9 3 8 8 5 10 5 7 7 2 8 6 6 10 4 8 8 4 10 6 6 8 2 7 7 5 10 5 8 8 3 9 6 6 9 3 7 7 4 8 4 5 5 1 6 5 5 9 4 8 8 4 11 7 7 10 3 9 9 6 12 6 9 9 3 11 8 8 13 5 10 10 5 12 7 7 9 2 8 8 6 12 6 10 10 4 12 8 8 12 4 10 10 6 12 6 8 8 2 9 7 7 12 5 10 10 5 13 8 8 11 3 9 9 6 12 6 9 9 3 10 7 7 11 4 8 8 4 9 5 5 6 1 6 6 5 10 5 9 9 4 12 8 8 12 4 11 11 7 14 7 10 10 3 12 9 9 15 6 12 12 6 15 9 9 12 3 11 11 8 16 8 13 13 5 15 10 10 15 5 12 12 7 14 7 9 9 2 10 8 8 14 6 12 12 6 16 10 10 14 4 12 12 8 16 8 12 12 4 14 10 10 16 6 12 12 6 14 8 8 10 2 9 9 7 14 7 12 12 5 15 10 10 15 5 13 13 8 16 8 11 11 3 12 9 9 15 6 12 12 6 15 9 9 12 3 10 10 7 14 7 11 11 4 12 8 8 12 4 9 9 5 10 5 6 6 1 7 6 6 11 5 10 10 5 14 9 9 13 4 12 12 8 16 8 12 12 4 15 11 11 18 7 14 14 7 17 10 10 13 3 12 12 9 18 9 15 15 6 18 12 12 18 6 15 15 9 18 9 12 12 3 14 11 11 19 8 16 16 8 21 13 13 18 5 15 15 10 20 10 15 15 5 17 12 12 19 7 14 14 7 16 9 9 11 2 10 10 8 16 8 14 14 6 18 12 12 18 6 16 16 10 20 10 14 14 4 16 12 12 20 8 16 16 8 20 12 12 16 4 14 14 10 20 10 16 16 6 18 12 12 18 6 14 14 8 16 8 10 10 2 11 9 9 16 7 14 14 7 19 12 12 17 5 15 15 10 20 10 15 15 5 18 13 13 21 8 16 16 8 19 11 11 14 3 12 12 9 18 9 15 15 6 18 12 12 18 6 15 15 9 18 9 12 12 3 13 10 10 17 7 14 14 7 18 11 11 15 4 12 12 8 16 8 12 12 4 13 9 9 14 5 10 10 5 11 6 6 7 1 7 7 6 12 6 11 11 5 15 10 10 15 5 14 14 9 18 9 13 13 4 16 12 12 20 8 16 16 8 20 12 12 16 4 15 15 11 22 11 18 18 7 21 14 14 21 7 17 17 10 20 10 13 13 3 15 12 12 21 9 18 18 9 24 15 15 21 6 18 18 12 24 12 18 18 6 21 15 15 24 9 18 18 9 21 12 12 15 3 14 14 11 22 11 19 19 8 24 16 16 24 8 21 21 13 26 13 18 18 5 20 15 15 25 10 20 20 10 25 15 15 20 5 17 17 12 24 12 19 19 7 21 14 14 21 7 16 16 9 18 9 11 11 2 12 10 10 18 8 16 16 8 22 14 14 20 6 18 18 12 24 12 18 18 6 22 16 16 26 10 20 20 10 24 14 14 18 4 16 16 12 24 12 20 20 8 24 16 16 24 8 20 20 12 24 12 16 16 4 18 14 14 24 10 20 20 10 26 16 16 22 6 18 18 12 24 12 18 18 6 20 14 14 22 8 16 16 8 18 10 10 12 2 11 11 9 18 9 16 16 7 21 14 14 21 7 19 19 12 24 12 17 17 5 20 15 15 25 10 20 20 10 25 15 15 20 5 18 18 13 26 13 21 21 8 24 16 16 24 8 19 19 11 22 11 14 14 3 15 12 12 21 9 18 18 9 24 15 15 21 6 18 18 12 24 12 18 18 6 21 15 15 24 9 18 18 9 21 12 12 15 3 13 13 10 20 10 17 17 7 21 14 14 21 7 18 18 11 22 11 15 15 4 16 12 12 20 8 16 16 8 20 12 12 16 4 13 13 9 18 9 14 14 5 15 10 10 15 5 11 11 6 12 6 7 7 1 8 7 7 13 6 12 12 6 17 11 11 16 5 15 15 10 20 10 15 15 5 19 14 14 23 9 18 18 9 22 13 13 17 4 16 16 12 24 12 20 20 8 24 16 16 24 8 20 20 12 24 12 16 16 4 19 15 15 26 11 22 22 11 29 18 18 25 7 21 21 14 28 14 21 21 7 24 17 17 27 10 20 20 10 23 13 13 16 3 15 15 12 24 12 21 21 9 27 18 18 27 9 24 24 15 30 15 21 21 6 24 18 18 30 12 24 24 12 30 18 18 24 6 21 21 15 30 15 24 24 9 27 18 18 27 9 21 21 12 24 12 15 15 3 17 14 14 25 11 22 22 11 30 19 19 27 8 24 24 16 32 16 24 24 8 29 21 21 34 13 26 26 13 31 18 18 23 5 20 20 15 30 15 25 25 10 30 20 20 30 10 25 25 15 30 15 20 20 5 22 17 17 29 12 24 24 12 31 19 19 26 7 21 21 14 28 14 21 21 7 23 16 16 25 9 18 18 9 20 11 11 13 2 12 12 10 20 10 18 18 8 24 16 16 24 8 22 22 14 28 14 20 20 6 24 18 18 30 12 24 24 12 30 18 18 24 6 22 22 16 32 16 26 26 10 30 20 20 30 10 24 24 14 28 14 18 18 4 20 16 16 28 12 24 24 12 32 20 20 28 8 24 24 16 32 16 24 24 8 28 20 20 32 12 24 24 12 28 16 16 20 4 18 18 14 28 14 24 24 10 30 20 20 30 10 26 26 16 32 16 22 22 6 24 18 18 30 12 24 24 12 30 18 18 24 6 20 20 14 28 14 22 22 8 24 16 16 24 8 18 18 10 20 10 12 12 2 13 11 11 20 9 18 18 9 25 16 16 23 7 21 21 14 28 14 21 21 7 26 19 19 31 12 24 24 12 29 17 17 22 5 20 20 15 30 15 25 25 10 30 20 20 30 10 25 25 15 30 15 20 20 5 23 18 18 31 13 26 26 13 34 21 21 29 8 24 24 16 32 16 24 24 8 27 19 19 30 11 22 22 11 25 14 14 17 3 15 15 12 24 12 21 21 9 27 18 18 27 9 24 24 15 30 15 21 21 6 24 18 18 30 12 24 24 12 30 18 18 24 6 21 21 15 30 15 24 24 9 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