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| my user subpages are listed here for my own reference | | my user subpages are listed here for my own reference |
| {{Special:PrefixIndex/User:Squib/}} | | {{Special:PrefixIndex/User:Squib/}} |
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| ==things i want to do on this wiki==
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| * create pages about my ideas
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| ** [[User:Squib/Equivalence is a construct]]
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| ** [[User:Squib/Efficiency (comma metric)]]
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| ** [[User:Squib/2d MOS]]
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| ** [[User:Squib/monzos with only ones]] (with a better title) (not exploring this anymore, mostly just want to document it)
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| * miracle extensions
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| ** add extension info to pages about miracle
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| *** [[rastmic rank-3 clan #mirage]] (including [[rastmic rank-3 clan #prism|#prism]])
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| *** [[miracle extensions]] (including the 31-limit manna extension)
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| *** [[gamelismic clan #miracle]]
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| ** [[User:Squib/Miracle extensions and mirage]]
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| ** dedicated page for [https://en.xen.wiki/index.php?title=Mirage&redirect=no mirage]
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| * 5.7.11.13 (no-2 no-3 13-limit)
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| ** [[5.7.11.13 subgroup]]
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| ** [[847/845]]
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| ** [[10ed5]]
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| ** [[125/121]]
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| ** [[175/169]]
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| * misc
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| ** [[22edo #Theory]]
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| ** tritave-equivalent [[superpyth]]
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|
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| ==some things i do not like about the wiki==
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| this list is here because listing 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.
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| * 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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| * Period equivalence is assumed ''everywhere''. 5/2 and 5/4 are the same as much as 9/8 and 10/9 are; treating them identically can be useful in certain contexts, but they are not fundamentally the same thing. In a space dedicated to exploring new tuning and music, it is frankly ridiculous to make period equivalence one of the fundamental assumptions you build your theory and terminology on. To be clear, I don't have an issue with the concepts of periods or equivalence, nor am I denying their usefulness. I have an issue with the Xenharmonic Wiki (of all places) assuming that these things ''must'' exist in ''every'' musical context.
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| ** [[Cuthbert chords]] is a page about the chords enabled by tempering out [[847/845]], a comma in the [[5.7.11.13 subgroup]]. Why are we talking about the 2.5.7.11.13 subgroup? ''What is prime 2 doing here??''
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|
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| ==Random stuff that i don't have the heart to delete yet==
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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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|
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| ===No-threes commas===
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| [[176/175]]
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| [[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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|
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| ===random commas to make pages for maybe===
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| [[13013/13005]]
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| [[104976/104975]] (s324)
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| [[364/361]]
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| [[1403830272/1403737447]] (equidistance 715/714, 833/832, 936/935)
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| [[21736/21735]]
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| [[117/115]]
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| ====5.7.11.13 subgroup===
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| [[343/325]]
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| [[637/625]]
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| [[15625/15488]]
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| [[17303/16807]]
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| [[78125/77077]]
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| [[831875/823543]]
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| [[2941225/2924207]]
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| [[27217619/26796875]]
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| [[49098049/48828125]]
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| [[236513641/236328125]]
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| =====higher-limit no-2 no-3=====
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| [[121/119]]
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| [[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)
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| [[1830125/1830101]] (!!)
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|
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| ===structurally important edos===
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| {| class="wikitable"
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| |-
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| ! edo
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| ! subgroup
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| ! notes
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| |-
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| | 10
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| | 13-limit
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| | higher primes?
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| |-
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| | 12
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| | 2.3.5.13/11.19
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| |-
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| | 17
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| | 2.3.7.11
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| | ?
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| |-
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| | 19
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| | 2.3.5.7.13
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| |-
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| | 22
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| | 2.3.5.7.11.17
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| |-
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| | 24
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| | 2.3.5.11.13
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| |-
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| | 31
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| | 2.3.5.7.11.17/13.19/13
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| |-
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| | 34
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| | 2.3.5.11.13.17.23
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| |-
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| | 41
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| |-
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| | 46
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| |-
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| | 53
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| |-
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| | 58
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| |-
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| | 72
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| |-
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| | 87
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| |-
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| | 99
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| | 2.3.5.7.13/11
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| | higher primes?
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| |-
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| |-
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| | 159
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| |-
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| | 171
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| |-
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| | 205
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| |}
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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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|
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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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| No other such superparticular intervals exist (at least in the first 100,000 prime limits).
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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 (odd-particular)
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| !3 (throdd-particular)
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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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| ===strong temperaments by rank===
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| temperaments that are strong extensions of all of their restrictions
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| ====rank-1====
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| every prime is mapped to 1 step (or -1 step)
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| ====rank-2====
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| 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
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| ====rank-3====
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| max 4 primes 1 comma, although i'm not confident about that. examples: 31/30, 145/143
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| ====rank-4====
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| 5 primes 1 comma: 406/403, 494/493, 667/665
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| 6 primes 2 commas: uh oh i think it might just be 1 comma max for all the ranks
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