Tags: Mobile edit Mobile web edit Advanced mobile edit |
|
| (17 intermediate revisions by the same user not shown) |
| Line 1: |
Line 1: |
| {{todo|inline=1|short bio thingy|add more todos}}
| | hi im squib :) |
| {{Special:PrefixIndex/User:Squib/}}
| |
|
| |
|
| ==pages to work on==
| | i think miracle temperament is the one that's worth investing a large portion of my time in, although i might dabble in other things sometimes |
| ===miracle/mirage/extensions/prism===
| |
| [[rastmic rank-3 clan #mirage]]
| |
|
| |
|
| [https://en.xen.wiki/index.php?title=Mirage&redirect=no mirage] dedicated page
| | i am currently working on figuring out how to use software to turn my ideas into actual music. |
|
| |
|
| [[miracle extensions]]
| |
|
| |
|
| [[gamelismic clan #miracle]]
| |
|
| |
|
| [[User:Squib/Miracle extensions and mirage]]
| | my user subpages are listed here for my own reference |
| | | {{Special:PrefixIndex/User:Squib/}} |
| ===5.7.11.13===
| |
| [[5.7.11.13 subgroup]]
| |
| | |
| [[10ed5]]
| |
| | |
| [[847/845]]
| |
| | |
| [[57ed5]]
| |
| | |
| [[125/121]]
| |
| | |
| [[175/169]]
| |
| | |
| ====possible 5.7.11.13 comma pages to create====
| |
| [[15625/15488]]
| |
| | |
| [[78125/77077]]
| |
| | |
| [[2941225/2924207]]
| |
| | |
| [[27217619/26796875]]
| |
| | |
| [[49098049/48828125]]
| |
| | |
| [[524596891/519921875]]
| |
| | |
| [[97302987925/96889010407]]
| |
| | |
| ===other randomness===
| |
| [[325/323]] (no-2 no-3, tempered out by 19-limit mirage) (210/209 * 715/714) (273/272 * 400/399) (286/285 * 375/374) (325/324 * 324/323)
| |
| | |
| [[104976/104975]] (s324)
| |
| | |
| [[364/361]]
| |
| | |
| [[1403830272/1403737447]] (equidistance 715/714, 833/832, 936/935)
| |
| | |
| [[21736/21735]]
| |
| | |
| ==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]]...
| |
| | |
| ===structurally important edos===
| |
| {| class="wikitable" | |
| |-
| |
| ! edo
| |
| ! subgroup
| |
| ! notes
| |
| |-
| |
| | 10
| |
| | 13-limit
| |
| | higher primes?
| |
| |-
| |
| | 12
| |
| | 2.3.5.13/11.19
| |
| |-
| |
| | 17
| |
| | 2.3.7.11
| |
| | ?
| |
| |-
| |
| | 19
| |
| | 2.3.5.7.13
| |
| |-
| |
| | 22
| |
| | 2.3.5.7.11.17
| |
| |-
| |
| | 24
| |
| | 2.3.5.11.13
| |
| |-
| |
| | 31
| |
| | 2.3.5.7.11.17/13.19/13
| |
| |-
| |
| | 34
| |
| | 2.3.5.11.13.17.23
| |
| |-
| |
| | 41
| |
| |-
| |
| | 46
| |
| |-
| |
| | 53
| |
| |-
| |
| | 58
| |
| |-
| |
| | 72
| |
| |-
| |
| | 87
| |
| |-
| |
| | 99
| |
| | 2.3.5.7.13/11
| |
| | higher primes?
| |
| |-
| |
| |-
| |
| | 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
| |
| | |
| ===strong temperaments by rank===
| |
| temperaments that are strong extensions of all of their restrictions
| |
| ====rank-1====
| |
| every prime is mapped to 1 step (or -1 step)
| |
| ====rank-2====
| |
| max 3 primes, 1 comma. equates one prime with the product of the other two (or tempers the product of all three). examples: 14/13, 23/21, 165/1
| |
| ====rank-3====
| |
| max 4 primes 1 comma, although i'm not confident about that. examples: 31/30, 145/143
| |
| ====rank-4====
| |
| 5 primes 1 comma: 406/403, 494/493, 667/665
| |
| | |
| 6 primes 2 commas: uh oh i think it might just be 1 comma max for all the ranks
| |
| | |
| ==Intervals with monzos containing only ones==
| |
| ===Non-subgroup monzos===
| |
| Superparticular intervals:
| |
| *[[2/1]]
| |
| *[[3/2]]
| |
| *[[6/5]]
| |
| *[[15/14]]
| |
| *[[715/714]]
| |
| No other such superparticular intervals exist (at least in the first 100,000 prime limits).
| |
| | |
| | |
| 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 [https://www.desmos.com/calculator/0qnrxfzey0 this desmos graph].
| |
| {| class="wikitable"
| |
| |+
| |
| |
| |
| !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]]
| |
| |}
| |