User:Squib

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Todo: short bio thingy, add more todos

list of things i do not like about the wiki

this list is here because listing all the things i do like would take too long.

  • things on here can be very hard to understand. this is not controversial.
  • It's hard to find a page you're looking for even if you know what it's about, but especially if you don't know whether such a page exists in the first place. Important pages for starters should be accessible by following links from the main page. In particular, I'd like a "bird's eye view of bird's eye view pages" page to be linked on the main page.
  • Octave equivalence is assumed everywhere. 5/2 and 5/4 are the same as much as 9/8 and 10/9 are the same; treating them the same can be useful in certain contexts, but they are not fundamentally the same thing. And in a space dedicated to exploring new tuning and music, it is very silly and annoying to constantly assume octaves essentially don't matter. (Tritave equivalence isn't a solution, it just moves the problem. I think every pitch should be considered its own thing.)

Random stuff

No-twos commas

245/243

here's a family of them

S(4n-1)/S(4n+1)

27/25, 245/243, 847/845, 2025/2023, 3971/3969, 6877/6875, 10935/10933, 16337/16335, 23275/23273, 31941/31939, 42527/42525, 55225/55223, 70227/70225, 87725/87723, 107911/107909, 130977/130975, 157115/157113, 186517/186515, 219375/219373, 255881/255879... 26578125/26578123...

No-threes commas

176/175 245/242 1001/1000 6656/6655 170/169 221/220 2200/2197 833/832

19-limit

209/208 476/475 1331/1330 1445/1444 2432/2431 6860/6859 10241/10240

here's a family of them

S(9n-5)/S(9n-4)

128/125, 10985/10976, 85184/85169, 327701/327680, 896000/895973...

list of interesting edos

19 22 31 34 41 46 53 58 72 87

159 171 205

list of detemperaments

7-limit edos

12: septimal meantone, garibaldi, septimal compton, misty, term, (12 & 270), 12 & 612

19: septimal meantone, sensi, kleismic, parakleismic, enneadecal, (19 & 270), 19 & 2859bcddd (splits 140/1 in 135 parts)

22: 22 & 118, 22 & 171



rank-twos

miracle: portent, canopus, freya, 31 & 41 & 278cd, ..., 31 & 41 & 994bbbccccddee

orwell: 22 & 31 & 311, 22 & 31 & 494

squares: jove, parimo + breedsma

23-limit 24 & 34: 24 & 34 & 41(g), 24 & 34 & 53, 24 & 34 & 94, 24 & 34 & 217

Intervals with monzos containing only ones

Non-subgroup monzos

Superparticular intervals:

It is very likely that no other such superparticular intervals exist.


Smallest for each prime limit:

2: 2/1

3: 3/2

5: 6/5

7: 15/14

11: 55/42

13: 182/165

17: 715/714

19: 3135/3094

23: 15015/14858

29: 81345/79534

31: 448630/447051

37: 2733549/2714690

41: 17490603/17395070

Subgroup monzos

A superparticular interval of this type exists if and only if the square root of 4n+1 is an integer, where n is the product of all primes in the subgroup. The result is the sum of the numerator and denominator of the superparticular interval.

(This method also works for intervals containing any number of the same prime. For example, with factors 2, 2, 2, 2, 3, and 5, n is 240 and (4n+1)^0.5 is 31, which is an integer. So these factors can form a superparticular interval whose numerator and denominator add to 31: 16/15.)

(For subgroups with rational or non-prime elements, split them into prime factors and multiply all together to get n, then determine if the final result is in the subgroup. For example, for the 11/2.13.15.19 subgroup, n is 81510 and (4n+1)^0.5 is 571, so the resulting superparticular interval is 286/285, but this is not in the subgroup because 11 and 2 are on the same side of the fraction. So no superparticular interval exists in the subgroup.)

(note about intervals like 35/33)

(this should probably get its own page lol)

All superparticular intervals with no duplicate primes, by prime limit

Found by applying this method to every possible subgroup in the prime limit, using this desmos graph.

1 (superparticular) 2 3
2-limit 2/1 - -
3-limit 3/2 3/1 -
5-limit 6/5 5/3 5/2
7-limit 7/6, 15/14 7/5 10/7
11-limit 11/10, 22/21 35/33 14/11
13-limit 14/13, 66/65, 78/77 13/11, 15/13 13/10
17-limit 34/33, 35/34, 715/714 17/15 17/14
19-limit 39/38, 210/209, 286/285 19/17, 21/19, 57/55, 665/663 22/19, 38/35, 133/130, 190/187
23-limit 23/22, 70/69, 115/114, 231/230, 323/322, 391/390 23/21, 255/253, 1311/1309 26/23, 598/595, 2093/2090
29-limit 30/29, 58/57, 494/493, 2002/2001, 2262/2261 87/85, 145/143, 437/435, 667/665 29/26, 58/55, 322/319, 377/374, 1105/1102
31-limit 31/30, 155/154, 187/186, 435/434, 714/713, 806/805, 12122/12121 31/29, 33/31, 93/91, 95/93, 715/713, 899/897, 7163/7161 34/31, 65/62, 406/403, 437/434, 10013/10010
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