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| {{todo|inline=1|short bio thingy|add more todos}}
| | hi im squib :) |
| {{Special:PrefixIndex/User:Squib/}}
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| ==list of things i do not like about the wiki==
| | 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 |
| this list is here because listing all the things i ''do'' like would take too long.
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| * things on here can be very hard to understand. this is not controversial.
| | i am currently working on figuring out how to use software to turn my ideas into actual music. |
| * 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.
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| * 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.)
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| ==Random stuff==
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| ===No-twos commas===
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| [[245/243]]
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| ====here's a family of them====
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| S(4n-1)/S(4n+1)
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| [[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]]...
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| ===No-threes commas===
| | my user subpages are listed here for my own reference |
| [[176/175]]
| | {{Special:PrefixIndex/User:Squib/}} |
| [[245/242]]
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| [[1001/1000]]
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| [[6656/6655]]
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| [[170/169]]
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| [[221/220]]
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| [[2200/2197]]
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| [[833/832]]
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| ====19-limit====
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| [[209/208]]
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| [[476/475]]
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| [[1331/1330]]
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| [[1445/1444]]
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| [[2432/2431]]
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| [[6860/6859]]
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| [[10241/10240]]
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| ====here's a family of them====
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| S(9n-5)/S(9n-4)
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| [[128/125]], [[10985/10976]], [[85184/85169]], [[327701/327680]], [[896000/895973]]...
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| ===list of interesting edos===
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| 19
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| 22
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| 31
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| 34
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| 41
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| 46
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| 53
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| 58
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| 72
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| 87
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| 159
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| 171
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| 205
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| ===list of detemperaments===
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| ====7-limit edos====
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| 12: septimal meantone, garibaldi, septimal compton, misty, term, (12 & 270), 12 & 612
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| 19: septimal meantone, sensi, kleismic, parakleismic, enneadecal, (19 & 270), 19 & 2859bcddd (splits 140/1 in 135 parts)
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| 22: 22 & 118, 22 & 171
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| ====rank-twos====
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| miracle: portent, canopus, freya, 31 & 41 & 278cd, ..., 31 & 41 & 994bbbccccddee
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| orwell: 22 & 31 & 311, 22 & 31 & 494
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| squares: jove, parimo + breedsma
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| 23-limit 24 & 34: 24 & 34 & 41(g), 24 & 34 & 53, 24 & 34 & 94, 24 & 34 & 217
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| ==Intervals with monzos containing only ones==
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| ===Non-subgroup monzos===
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| Superparticular intervals:
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| *[[2/1]]
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| *[[3/2]]
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| *[[6/5]]
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| *[[15/14]]
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| *[[715/714]]
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| It is very likely that no other such superparticular intervals exist. I have checked up to the 97-limit.
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| Smallest for each prime limit:
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| 2: 2/1
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| 3: 3/2
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| 5: 6/5
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| 7: 15/14
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| 11: 55/42
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| 13: 182/165
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| 17: 715/714
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| 19: 3135/3094
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| 23: 15015/14858
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| 29: 81345/79534
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| 31: 448630/447051
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| 37: 2733549/2714690
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| 41: 17490603/17395070
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| ===Subgroup monzos===
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| 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.
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| (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]].)
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| (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.)
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| (note about intervals like 35/33)
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| (this should probably get its own page lol)
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| ====All superparticular intervals with no duplicate primes, by prime limit====
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| Found by applying this method to every possible subgroup in the prime limit, using [https://www.desmos.com/calculator/0qnrxfzey0 this desmos graph].
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| {| class="wikitable"
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| |+
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| !1 (superparticular)
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| !2
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| !3
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| |-
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| !2-limit
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| |[[2/1]]
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| | -
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| | -
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| |-
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| !3-limit
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| |[[3/2]]
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| |[[3/1]]
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| | -
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| |-
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| !5-limit
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| |[[6/5]]
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| |[[5/3]]
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| |[[5/2]]
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| |-
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| !7-limit
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| |[[7/6]], [[15/14]]
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| |[[7/5]]
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| |[[10/7]]
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| |-
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| !11-limit
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| |[[11/10]], [[22/21]]
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| |[[35/33]]
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| |[[14/11]]
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| |-
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| !13-limit
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| |[[14/13]], [[66/65]], [[78/77]]
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| |[[13/11]], [[15/13]]
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| |[[13/10]]
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| |-
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| !17-limit
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| |[[34/33]], [[35/34]], [[715/714]]
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| |[[17/15]]
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| |[[17/14]]
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| |-
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| !19-limit
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| |[[39/38]], [[210/209]], [[286/285]]
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| |[[19/17]], [[21/19]], [[57/55]], [[665/663]]
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| |[[22/19]], [[38/35]], [[133/130]], [[190/187]]
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| |-
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| !23-limit
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| |[[23/22]], [[70/69]], [[115/114]], [[231/230]], [[323/322]], [[391/390]]
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| |[[23/21]], [[255/253]], [[1311/1309]]
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| |[[26/23]], [[598/595]], [[2093/2090]]
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| |-
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| !29-limit
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| |[[30/29]], [[58/57]], [[494/493]], [[2002/2001]], [[2262/2261]]
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| |[[87/85]], [[145/143]], [[437/435]], [[667/665]]
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| |[[29/26]], [[58/55]], [[322/319]], [[377/374]], [[1105/1102]]
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| |-
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| !31-limit
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| |[[31/30]], [[155/154]], [[187/186]], [[435/434]], [[714/713]], [[806/805]], [[12122/12121]]
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| |[[31/29]], [[33/31]], [[93/91]], [[95/93]], [[715/713]], [[899/897]], [[7163/7161]]
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| |[[34/31]], [[65/62]], [[406/403]], [[437/434]], [[10013/10010]]
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| |}
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