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{{User:FloraC/Infobox Interval
== Accidentals ==
| Ratio = 2 954 312 706 550 833 698 643 /<br>2 951 479 051 793 528 258 560
; Wiki templates : {{Flat}} {{natural}} {{sharp}}
| Monzo = -69 45 -1
; Unicode characters : &#x266D; &#x266E; &#x266F;
| Cents = 1.661325
; Bravura font : <span class="bravura">&#xE260;</span> <span class="bravura">&#xE261;</span> <span class="bravura">&#xE262;</span>
| Name = counterschisma
; Heji font : <span class="heji">e</span> <span class="heji">n</span> <span class="heji">v</span>
| Color name =  
 
| FJS name =  
== Template: Temperament data ==
| Sound =  
{{User:FloraC/Temperament data
| Subgroup = 2.3.5.7
| Comma list = 81/80, 126/125
| Mapping = {{mapping| 1 0 -4 -13 | 0 1 4 10 }}
| Mapping generators = ~2, ~3
| CTE = ~3/2 = 696.9521
| Wedgie = 1 4 10 4 13 12
| Optimal ET sequence = 12, 19, 31, 81, 112b, 143b
| Badness = 0.0137
}}
}}


== Temperament pages ==
== Catalog of 5-limit rank-2 temperaments ==
Note:
Sintel's TE logflat badness.
# Order: subgroup, [[comma list]], ([[sval]]) [[mapping]], (sval) mapping generators, gencom mapping, [[gencom]], map to lattice, lattice basis, [[wedgie]], [[POTE generator]], [[minimax tuning]], [[tuning ranges]], [[algebraic generator]], vals, [[badness]], [[complexity spectrum]], and others.
 
# Comma list should show the simplest commas sufficient to define the temperament, stated in [[Normal lists #Normal interval list]].  
Error > 25{{c}}, badness < 3
# Mapping generators should show all the ratios as used in the mapping, including the period.  
{| class="wikitable sortable center-2 center-3 center-4"
# Since minimax tuning are based on tonality diamond, it should explicitly state the ''odd'' limit, or a diamond function of ratios.
|-
# Replace "EDOs" with [[Template:Val list]].  
! Temperament !! Complexity !! Error (¢) !! Badness !! Mapping !! Comma list
# For subgroup temperaments, "mapping" becomes "sval mapping", add "gencom mapping" and "gencom". If TE is TE is TE (''sic''), simply show "POTE", otherwise show "POL2" or "POT2" instead of "POTE".  
|-
|  || 2.63 || 40.1 || .392 || {{mapping| 1 0 -1 | 0 1 2 }} || 10/9
|-
| Antitonic || 2.83 || 41.6 || .508 || {{mapping| 2 3 0 | 0 0 1 }} || 9/8
|-
| University || 5.59 || 25.3 || 2.39 || {{mapping| 1 1 2 | 0 3 2 }} || 144/125
|}
 
Complexity < 30, error < 25{{c}}, badness < 3
 
{| class="wikitable sortable center-2 center-3 center-4"
|-
! Temperament !! Complexity !! Error (¢) !! Badness !! Mapping !! Comma list
|-
| Father || 3.17 || 20.4 || .349 || {{mapping| 1 0 4 | 0 1 -1 }} || 16/15
|-
| Dicot || 3.73 || 11.0 || .306 || {{mapping| 1 1 2 | 0 2 1 }} || 25/24
|-
| Bug || 4.30 || 17.9 || .769 || {{mapping| 1 0 0 | 0 2 3 }} || 27/25
|-
| Meantone || 5.08 || 2.44 || .173 || {{mapping| 1 0 -4 | 0 1 4 }} || 81/80
|-
| Mavila || 5.68 || 9.36 || .928 || {{mapping| 1 0 7 | 0 1 -3 }} || 135/128
|-
| Augmented || 6.40 || 3.71 || .523 || {{mapping| 3 0 7 | 0 1 0 }} || 128/125
|-
| Porcupine || 6.86 || 4.14 || .722 || {{mapping| 1 2 3 | 0 3 5 }} || 250/243
|-
| Blackwood || 7.29 || 7.14 || 1.50 || {{mapping| 5 8 0 | 0 0 1 }} || 256/243
|-
| Diminished || 7.54 || 4.79 || 1.11 || {{mapping| 4 0 3 | 0 1 1 }} || 648/625
|-
| Supersharp || 7.58 || 12.3 || 2.88 || {{mapping| 2 0 -5 | 0 1 3 }} || 800/729
|-
| Diaschismic || 8.76 || 1.29 || .467 || {{mapping| 2 0 11 | 0 1 -2 }} || 2048/2025
|-
| Magic || 9.98 || 1.71 || .919 || {{mapping| 1 0 2 | 0 5 1 }} || 3125/3072
|-
| Hanson || 11.1 || .422 || .310 || {{mapping| 1 0 1 | 0 6 5 }} || 15625/15552
|-
| Negri || 11.3 || 2.61 || 2.04 || {{mapping| 1 2 2 | 0 4 -3 }} || 16875/16384
|-
| Tetracot || 11.5 || 1.39 || 1.14 || {{mapping| 1 1 1 | 0 4 9 }} || 20000/19683
|-
| Helmholtz || 12.8 || .0881 || .0999 || {{mapping| 1 0 15 | 0 1 -8 }} || 32805/32768
|-
| Sensipent || 14.1 || .550 || .826 || {{mapping| 1 6 8 | 0 7 9 }} || 78732/78125
|-
| Würschmidt || 16.3 || .404 || .952 || {{mapping| 1 7 3 | 0 8 1 }} || 393216/390625
|-
| Amity || 16.4 || .217 || .515 || {{mapping| 1 3 6 | 0 5 13 }} || 1600000/1594323
|-
| Valentine || 16.7 || 1.14 || 2.88 || {{mapping| 1 1 2 | 0 9 5 }} || 1990656/1953125
|-
| Compton || 17.4 || .778 || 2.22 || {{mapping| 12 19 0 | 0 0 1 }} || 531441/524288
|-
| Orson || 17.5 || .332 || .957 || {{mapping| 1 0 3 | 0 7 -3 }} || 2109375/2097152
|-
| Misty || 21.3 || .476 || 2.50 || {{mapping| 3 0 26 | 0 1 -4 }} || 67108864/66430125
|-
| Gravity || 21.4 || .415 || 2.19 || {{mapping| 1 5 12 | 0 6 17 }} || 129140163/128000000
|-
| Parakleismic || 24.8 || .123 || 1.02 || {{mapping| 1 5 6 | 0 13 14 }} || {{monzo| 8 14 -13 }}
|-
| Quartonic || 24.9 || .331 || 2.75 || {{mapping| 1 2 3 | 0 11 18 }} || {{monzo| 3 -18 11 }}
|-
| Escapade || 25.8 || .213 || 1.97 || {{mapping| 1 2 2 | 0 9 -7 }} || {{monzo| 32 -7 -9 }}
|-
| Vishnuzmic || 26.5 || .0727 || .731 || {{mapping| 2 4 5 | 0 7 3 }} || {{monzo| 23 6 -14 }}
|-
| Vulture || 27.3 || .0890 || .972 || {{mapping| 1 0 -6 | 0 4 21 }} || {{monzo| 24 -21 4 }}
|-
| Unidecmic || 29.3 || .143 || 1.93 || {{mapping| 2 5 8 | 0 6 11 }} || {{monzo| -7 22 -12 }}
|}
 
3 < badness < 6


Get a family for:
{| class="wikitable sortable center-2 center-3 center-4"
* <s>Ripple (3 different 7-limit extensions)</s> done
|-
* <s>Smate (2 different 7-limit extensions)</s> done
! Temperament !! Complexity !! Error (¢) !! Badness !! Mapping !! Comma list
* <s>Passion (4 different 7-limit extensions, 3 strong and 1 weak)</s> done
|-
* <s>Parakleismic (2 different 7-limit extensions)</s> canceled, not strong extensions
| Avila || 7.79 || 16.7 || 4.27 || {{mapping| 1 0 -7 | 0 1 6 }} || 729/640
* <s>Superpyth (2 different 7-limit extensions)</s> canceled, not strong extensions
|-
* Undim
| Enipucrop || 8.16 || 11.5 || 3.38 || {{mapping| 1 2 2 | 0 3 -2 }} || 1125/1024
* Quintaleap
|-
* Quindromeda
| Laconic || 8.87 || 10.1 || 3.80 || {{mapping| 1 1 1 | 0 3 7 }} || 2187/2000
|-
| Lafayette || 9.31 || 10.8 || 4.70 || {{mapping| 1 1 2 | 0 5 3 }} || 3456/3125
|-
| Symbolic || 9.38 || 9.40 || 4.19 || {{mapping| 1 3 2 | 0 4 -1 }} || 2048/1875
|-
| Sixix || 9.81 || 7.06 || 3.59 || {{mapping| 1 3 4 | 0 5 6 }} || 3125/2916
|-
| Whitewood || 10.1 || 6.49 || 3.63 || {{mapping| 7 11 0 | 0 0 1 }} || 2187/2048
|-
| Ripple || 11.2 || 4.35 || 3.26 || {{mapping| 1 2 3 | 0 5 8 }} || 6561/6250
|-
| Progress || 11.9 || 6.38 || 5.77 || {{mapping| 1 0 5 | 0 3 -5 }} || 32768/30375
|-
| Superpyth || 12.2 || 3.26 || 3.17 || {{mapping| 1 0 -12 | 0 1 9 }} || 20480/19683
|-
| Wesley || 13.6 || 4.25 || 5.81 || {{mapping| 1 4 3 | 0 7 2 }} || 78125/73728
|-
| Stump || 14.4 || 2.91 || 4.71 || {{mapping| 1 0 6 | 0 3 -7 }} || 273375/262144
|-
| Passion || 14.5 || 2.42 || 3.95 || {{mapping| 1 2 2 | 0 5 -4 }} || 262144/253125
|-
| Doublewide || 14.7 || 3.09 || 5.32 || {{mapping| 2 1 3 | 0 4 3 }} || 390625/373248
|-
| Immunity || 17.2 || 1.59 || 4.33 || {{mapping| 1 0 -8 | 0 2 13 }} || 1638400/1594323
|-
| Shibboleth || 17.3 || 1.91 || 5.34 || {{mapping| 1 4 5 | 0 9 10 }} || 1953125/1889568
|-
| Unicorn || 18.0 || 1.12 || 3.53 || {{mapping| 1 2 3 | 0 8 13 }} || 1594323/1562500
|-
| Mynic || 18.6 || 1.69 || 5.86 || {{mapping| 1 9 9 | 0 10 9 }} || 10077696/9765625
|-
| Ampersand || 19.9 || .917 || 3.89 || {{mapping| 1 1 3 | 0 6 -7 }} || 34171875/33554432
|-
| Sycamore || 20.5 || 1.06 || 4.93 || {{mapping| 2 2 3 | 0 5 7 }} || 48828125/47775744
|-
| Fifive || 20.8 || .992 || 4.83 || {{mapping| 2 2 3 | 0 5 7 }} || 9765625/9565938
|-
| Rodan || 22.2 || .669 || 3.95 || {{mapping| 1 1 -1 | 0 3 17 }} || {{monzo| 20 -17 3 }}
|-
| Mabila || 23.8 || .753 || 5.45 || {{mapping| 1 6 1 | 0 10 -3 }} || {{monzo| 28 -3 -10 }}
|-
| Ditonic || 26.3 || .399 || 3.92 || {{mapping| 1 6 3 | 0 13 2 }} || {{monzo| -27 -2 13 }}
|-
| Trisedodge || 27.7 || .518 || 5.92 || {{mapping| 5 1 7 | 0 3 2 }} || {{monzo| 19 10 -15 }}
|-
| Demibuzzard || 28.6 || .243 || 3.06 || {{mapping| 1 4 -1 | 0 8 -11 }} || {{monzo| -36 11 8 }}
|}


Who's next?
30 < complexity < 60, badness < 3
* <s>Meantone family</s>
* <s>Archytas clan</s>
* <s>Father family</s>
* <s>Trienstonic clan</s>
* <s>Septisemi temperaments</s>
* <s>Archytas family</s>
* <s>Slendro clan</s>
* <s>Semiphore family</s>
* <s>Marvel temperaments</s>
* <s>Marvel family</s>
* <s>Mint temperaments</s>
* <s>Mint family</s>
* <s>Gamelismic clan</s>
* <s>Gamelismic family</s>
* <s>Jubilismic clan</s>
* <s>Jubilismic family</s>
* <s>Didymus rank three family</s>
* <s>Kleismic family</s>
* <s>Kleismic rank three family</s>
* <s>Shibboleth family</s>
* <s>Keemic temperaments</s>
* <s>Keemic family</s>
* <s>Schismatic family</s>
* <s>Hemimean clan</s>
* <s>Hemimean family</s>
* <s>Luna family</s>
* <s>Canousmic temperaments</s>
* <s>Canou family</s>
* <s>Starling temperaments</s>
* <s>Starling family</s>
* <s>Sensipent family</s>
* <s>Sensamagic clan</s>
* <s>Sensamagic family</s>
* <s>Magic family</s>
* <s>Unicorn family</s>
* <s>Trisedodge family</s>
* <s>Sycamore family</s>
* <s>Rastmic temperaments</s>
* <s>Semicomma family</s>
* <s>Orwellismic temperaments</s>
* <s>Orwellismic family</s>
* <s>Hemimage temperaments</s>
* <s>Hemimage family</s>
* <s>Porwell temperaments</s>
* <s>Porwell family</s>
* <s>Hemifamity temperaments</s>
* <s>Hemifamity family</s>
* <s>Porcupine family</s>
* <s>Porcupine rank three family</s>
* <s>Tetracot family</s>
* <s>Misty family</s>
* <s>Diaschismic family</s>
* <s>Diaschismic rank three family</s>
* <s>Amity family</s>
* <s>Lehmerismic temperaments</s>
* <s>Kalismic temperaments</s>
* <s>Ragismic family</s>
* [[Ragismic microtemperaments]]
* <s>Landscape family</s>
* <s>Landscape microtemperaments</s>
* <s>Dimcomp family</s>
* <s>Mirkwai family</s>
* <s>Mirkwai clan</s>
* <s>Breed family</s>
* <s>Breedsmic temperaments</s>
* <s>Escapade family</s>
* <s>Gravity family</s>
* <s>Cataharry family</s>
* <s>Cataharry temperaments</s>
* <s>Varunismic temperaments</s>
* <s>Werckismic temperaments</s>
* <s>Valinorsmic temperaments</s>
* <s>Swetismic temperaments</s>
* <s>Wizmic microtemperaments</s>
* <s>Metric microtemperaments</s>
* <s>Vulture family</s>
* <s>Tricot family</s>
* [[Minortonic family]]
* <s>Gammic family</s>
* [[Mirwomo temperaments]]
* [[Augmented family]]
* [[Dimipent family]]
* [[Dicot family]]
* <s>Bug family</s>
* [[Pelogic family]]
* <s>Horwell family</s>
* [[Horwell temperaments]]
* [[Gariboh clan]]
* <s>Gariboh family</s>
* [[Octagar temperaments]]
* <s>Octagar family</s>


== Regular temperament properties ==
{| class="wikitable sortable center-2 center-3 center-4"
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" | Subgroup
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning error
|-
|-
! [[TE error|Absolute]] (¢)
! Temperament !! Complexity !! Error (¢) !! Badness !! Mapping !! Comma list
! [[TE simple badness|Relative]] (%)
|-
|-
| 2.3
| Luna || 33.5 || .0239 || .483 || {{mapping| 1 4 2 | 0 15 -2 }} || {{monzo| 38 -2 -15 }}
| {{monzo| -49 31 }}
| [{{val| 31 49 }}]
| +1.63
| 1.64
| 4.22
|-
|-
| 2.3.5
| Enneadecal || 35.8 || .0454 || 1.12 || {{mapping| 19 0 14 | 0 1 1 }} || {{monzo| -14 -19 19 }}
| 81/80, 393216/390625
| [{{val| 31 49 72 }}]
| +0.98
| 1.63
| 4.20
|-
|-
| 2.3.5.7
| Gammic || 37.2 || .0740 || 2.06 || {{mapping| 1 1 2 | 0 20 11 }} || {{monzo| -29 -11 20 }}
| 81/80, 126/125, 1029/1024
| [{{val| 31 49 72 87 }}]
| +0.83
| 1.43
| 3.70
|-
|-
| 2.3.5.7.11
| Ennealimmal || 38.7 || .0128 || .403 || {{mapping| 9 1 1 | 0 2 3 }} || {{monzo| 1 -27 18 }}
| 81/80, 99/98, 121/120, 126/125
|-
| [{{val| 31 49 72 87 107 }}]
| Alphatricot || 39.3 || .0330 || 1.08 || {{mapping| 1 0 -13 | 0 3 29 }} || {{monzo| 39 -29 3 }}
| +1.21
|-
| 1.49
| Kwazy || 43.2 || .00762 || .331 || {{mapping| 2 1 6 | 0 8 -5 }} || {{monzo| -53 10 16 }}
| 3.84
|-
| Minortone || 45.3 || .0139 || .698 || {{mapping| 1 16 32 | 0 17 35 }} || {{monzo| -16 35 -17 }}
|-
| Monzismic || 51.7 || .00326 || .244 || {{mapping| 1 0 -27 | 0 2 37 }} || {{monzo| 54 -37 2 }}
|-
| Vavoom || 54.2 || .0269 || 2.31 || {{mapping| 1 0 4 | 0 17 -18 }} || {{monzo| -68 18 17 }}
|}
|}


== Scale tree ==
== 5-limit rank-2 temperaments by TE simple badness ==
(Bounded by branch depth = 7)
Breed's TE simple badness.


{| class="wikitable center-all"
=== Junk temperaments ===
! colspan="7" | Generator
=== High-badness temperaments ===
! Cents
{| class="wikitable sortable center-2 center-3 center-4 mw-collapsible mw-collapsed"
! L
! s
! L/s
! Comments
|-
|-
| 4\7 || || || || || || || 685.714 || 1 || 1 || 1.000 ||
! Temperament !! Complexity !! Error (¢) !! Badness (moct) !! Mapping !! Comma list
|-
|-
| || || || || || || 27\47 || 689.362 || 7 || 6 || 1.167 ||
| Yo || .367 || 26.0 || 7.95 || {{mapping| 1 0 -1 | 0 1 -2 }} || 10/9
|-
|-
| || || || || || 23\40 || || 690.000 || 6 || 5 || 1.200 ||
| Antitonic || .395 || 27.0 || 8.89 || {{mapping| 2 3 0 | 0 0 1 }} || 9/8
|-
|-
| || || || || || || 42\73 || 690.411 || 11 || 9 || 1.222 ||
| Father || .443 || 13.2 || 4.87 || {{mapping| 1 0 4 | 0 1 -1 }} || 16/15
|-
|-
| || || || || 19\33 || || || 690.909 || 5 || 4 || 1.250 ||
| Bug || .602 || 11.6 || 5.81 || {{mapping| 1 0 0 | 0 2 3 }} || 27/25
|-
|-
| || || || || || || 53\92 || 691.304 || 14 || 11 || 1.273 ||
| Supersharp || 1.06 || 7.94 || 7.01 || {{mapping| 2 0 -5 | 0 1 3 }} || 800/729
|-
|-
| || || || || || 34\59 || || 691.525 || 9 || 7 || 1.286 ||
| Laconic || 1.24 || 6.52 || 6.74 || {{mapping| 1 1 1 | 0 3 7 }} || 2187/2000
|-
|-
| || || || || || || 49\85 || 691.765 || 13 || 10 || 1.300 ||
| Lafayette || 1.30 || 7.00 || 7.60 || {{mapping| 1 1 2 | 0 5 3 }} || 3456/3125
|-
|-
| || || || 15\26 || || || || 692.308 || 4 || 3 || 1.333 ||
| Symbolic || 1.31 || 6.09 || 6.66 || {{mapping| 1 3 4 | 0 5 6 }} || 2048/1875
|-
|-
| || || || || || || 56\97 || 692.784 || 15 || 11 || 1.364 ||
| Sixix || 1.37 || 4.57 || 5.22 || {{mapping| 1 3 2 | 0 4 -1 }} || 3125/2916
|-
| Uncle || 1.40 || 7.53 || 8.80 || {{mapping| 1 0 12 | 0 1 -6 }} || 4096/3645
|-
| Whitewood || 1.42 || 4.20 || 4.95 || {{mapping| 7 11 0 | 0 0 1 }} || 2187/2048
|-
| Progress || 1.66 || 4.13 || 5.72 || {{mapping| 1 0 5 | 0 3 -5 }} || 32768/30375
|}
 
=== Main sequence ===
{| class="wikitable sortable center-2 center-3 center-4 mw-collapsible mw-collapsed"
|-
|-
| || || || || || 41\71 || || 692.958 || 11 || 8 || 1.375 ||
! Temperament !! Complexity !! Error (¢) !! Badness (moct) !! Mapping !! Comma list
|-
|-
| || || || || || || 67\116 || 693.103 || 18 || 13 || 1.385 ||
| Dicot || .521 || 7.09 || 3.08 || {{mapping| 1 1 2 | 0 2 1 }} || 25/24
|-
|-
| || || || || 26\45 || || || 693.333 || 7 || 5 || 1.400 ||
| Meantone || .711 || 1.58 || .937 || {{mapping| 1 0 -4 | 0 1 4 }} || 81/80
|-
|-
| || || || || || || 63\109 || 693.578 || 17 || 12 || 1.417 ||
| Mavila || .795 || 6.06 || 4.02 || {{mapping| 1 0 7 | 0 1 -3 }} || 135/128
|-
|-
| || || || || || 37\64 || || 693.750 || 10 || 7 || 1.429 ||
| Augmented || .894 || 2.40 || 1.79 || {{mapping| 3 0 7 | 0 1 0 }} || 128/125
|-
|-
| || || || || || || 48\83 || 693.976 || 13 || 9 || 1.444 ||
| Porcupine || .960 || 2.68 || 2.14 || {{mapping| 1 2 3 | 0 3 5 }} || 250/243
|-
|-
| || || 11\19 || || || || || 694.737 || 3 || 2 || 1.500 || L/s = 3/2
| Blackwood || 1.02 || 4.63 || 3.93 || {{mapping| 5 8 0 | 0 0 1 }} || 256/243
|-
|-
| || || || || || || 51\88 || 695.455 || 14 || 9 || 1.556 ||
| Diminished || 1.05 || 3.10 || 2.73 || {{mapping| 4 0 3 | 0 1 1 }} || 648/625
|-
|-
| || || || || || 40\69 || || 695.652 || 11 || 7 || 1.571 ||
| Diaschismic || 1.22 || .835 || .852 || {{mapping| 2 0 11 | 0 1 -2 }} || 2048/2025
|-
|-
| || || || || || || 69\119 || 695.798 || 19 || 12 || 1.583 ||
| Magic || 1.40 || 1.11 || 1.29 || {{mapping| 1 0 2 | 0 5 1 }} || 3125/3072
|-
|-
| || || || || 29\50 || || || 696.000 || 8 || 5 || 1.600 ||
| Hanson || 1.55 || .274 || .353 || {{mapping| 1 0 1 | 0 6 5 }} || 15625/15552
|-
|-
| || || || || || || 66\131 || 696.183 || 21 || |13 || 1.615 || Golden meantone
| Ripple || 1.56 || 2.82 || 3.66 || {{mapping| 1 2 3 | 0 5 8 }} || 6561/6250
|-
|-
| || || || || || 47\81 || || 696.296 || 13 || 8 || 1.625 ||
| Negri || 1.58 || 1.69 || 2.23 || {{mapping| 1 2 2 | 0 4 -3 }} || 16875/16384
|-
|-
| || || || || || || 65\112 || 696.429 || 18 || 11 || 1.636 ||  
| Tetracot || 1.61 || .900 || 1.21 || {{mapping| 1 1 1 | 0 4 9 }} || 20000/19683
|-
|-
| || || || 18\31 || || || || 696.774 || 5 || 3 || 1.667 || Meantone is in this region
| Superpyth || 1.70 || 2.11 || 2.99 || {{mapping| 1 0 -12 | 0 1 9 }} || 20480/19683
|-
|-
| || || || || || || 61\105 || 697.143 || 17 || 10 || 1.700 ||
| Helmholtz || 1.79 || .0570 || .0851 || {{mapping| 1 0 15 | 0 1 -8 }} || 32805/32768
|-
|-
| || || || || || 43\74 || || 697.297 || 12 || 7 || 1.714 ||
| Wesley || 1.91 || 2.75 || 4.37 || {{mapping| 1 4 3 | 0 7 2 }} || 78125/73728
|-
|-
| || || || || || || 68\117 || 697.436 || 19 || 11 || 1.727 ||
| Sensipent || 1.97 || .356 || .584 || {{mapping| 1 6 8 | 0 7 9 }} || 78732/78125
|-
|-
| || || || || 25\43 || || || 697.674 || 7 || 4 || 1.750 ||
| Stump || 2.02 || 1.88 || 3.16 || {{mapping| 1 0 6 | 0 3 -7 }} || 273375/262144
|-
|-
| || || || || || || 57\98 || 697.959 || 16 || 9 || 1.778 ||
| Passion || 2.02 || 1.57 || 2.64 || {{mapping| 1 2 2 | 0 5 -4 }} || 262144/253125
|-
|-
| || || || || ||32\55 || || 698.182 || 9 || 5 || 1.800 ||
| Doublewide || 2.06 || 2.00 || 3.43 || {{mapping| 2 1 3 | 0 4 3 }} || 390625/373248
|-
|-
| || || || || || || 39\67 || 698.507 || 11 || 6 || 1.833 ||
| Würschmidt || 2.29 || .262 || .499 || {{mapping| 1 7 3 | 0 8 1 }} || 393216/390625
|-
|-
| || 7\12 || || || || || || 700.000 || 2 || 1 || 2.000 || Basic diatonic<br>(Generators smaller than this are proper)
| Amity || 2.29 || .140 || .268 || {{mapping| 1 3 6 | 0 5 13 }} || 1600000/1594323
|-
|-
| || || || || || || 38\65 || 701.539 || 11 || 5 || 2.200 ||
| Valentine || 2.34 || .736 || 1.44 || {{mapping| 1 1 2 | 0 9 5 }} || 1990656/1953125
|-
|-
| || || || || || 31\53 || || 701.887 || 9 || 4 || 2.250 ||
| Immunity || 2.40 || 1.03 || 2.06 || {{mapping| 1 0 -8 | 0 2 13 }} || 1638400/1594323
|-
|-
| || || || || || || 55\94 || 702.128 || 16 || 7 || 2.286 ||
| Shibboleth || 2.42 || 1.24 || 2.50 || {{mapping| 1 4 5 | 0 9 10 }} || 1953125/1889568
|-
|-
| || || || || 24\41 || || || 702.409 || 7 || 3 || 2.333 ||
| Compton || 2.44 || .504 || 1.02 || {{mapping| 12 19 0 | 0 0 1 }} || 531441/524288
|-
|-
| || || || || || || 65\111 || 702.703 || 19 || 8 || 2.375 ||
| Orson || 2.44 || .215 || .438 || {{mapping| 1 0 3 | 0 7 -3 }} || 2109375/2097152
|-
|-
| || || || || || 41\70 || || 702.857 || 12 || 5 || 2.400 ||
| Unicorn || 2.52 || .725 || 1.52 || {{mapping| 1 2 3 | 0 8 13 }} || 1594323/1562500
|-
|-
| || || || || || || 58\99 || 703.030 || 17 || 7 || 2.428 ||
| Mynic || 2.60 || 1.10 || 2.37 || {{mapping| 1 9 9 | 0 10 9 }} || 10077696/9765625
|-
|-
| || || || 17\29 || || || || 703.448 || 5 || 2 || 2.500 ||
| Ampersand || 2.78 || .594 || 1.38 || {{mapping| 1 1 3 | 0 6 -7 }} || 34171875/33554432
|-
|-
| || || || || || || 61\104 || 703.846 || 18 || 7 || 2.571 ||
| Fifive || 2.91 || .643 || 1.56 || {{mapping| 2 2 3 | 0 5 7 }} || 9765625/9565938
|-
|-
| || || || || || 44\75 || || 704.000 || 13 || 5 || 2.600 ||
| Misty || 2.99 || .308 || .767 || {{mapping| 3 0 26 | 0 1 -4 }} || 67108864/66430125
|-
|-
| || || || || || || 71\121 || 704.132 || 21 || 8 || 2.625 || Golden neogothic
| Gravity || 2.99 || .269 || .669 || {{mapping| 1 5 12 | 0 6 17 }} || 129140163/128000000
|-
|-
| || || || || 27\46 || || || 704.348 || 8 || 3 || 2.667 ||
| Rodan || 3.10 || .433 || 1.12 || {{mapping| 1 1 -1 | 0 3 17 }} || {{monzo| 20 -17 3 }}
|-
|-
| || || || || || || 64\109 || 704.587 || 19 || 7 || 2.714 ||
| || 3.11 || .757 || 1.96 || {{mapping| 1 0 -23 | 0 1 16 }} || {{monzo| -23 16 -1 }}
|-
|-
| || || || || || 37\63 || || 704.762 || 11 || 4 || 2.750 ||
| Mabila || 3.32 || .488 || 1.35 || {{mapping| 1 6 1 | 0 10 -3 }} || {{monzo| 28 -3 -10 }}
|-
|-
| || || || || || || 47\80 || 705.000 || 14 || 5 || 2.800 ||
| Parakleismic || 3.47 || .0798 || .231 || {{mapping| 1 5 6 | 0 13 14 }} || {{monzo| 8 14 -13 }}
|-
|-
| || || 10\17 || || || || || 705.882 || 3 || 1 || 3.000 || L/s = 3/1
| Quartonic || 3.48 || .214 || .621 || {{mapping| 1 2 3 | 0 11 18 }} || {{monzo| 3 -18 11 }}
|-
|-
| || || || || || || 43\73 || 706.849 || 13 || 4 || 3.250 ||
| Escapade || 3.60 || .138 || .414 || {{mapping| 1 2 2 | 0 9 -7 }} || {{monzo| 32 -7 -9 }}
|-
|-
| || || || || || 33\56 || || 707.143 || 10 || 3 || 3.333 ||
| Ditonic || 3.68 || .258 || .792 || {{mapping| 1 6 3 | 0 13 2 }} || {{monzo| -27 -2 13 }}
|-
|-
| || || || || || || 56\95 || 707.368 || 17 || 5 || 3.400 ||
| Vishnuzmic || 3.71 || .0471 || .145 || {{mapping| 2 4 5 | 0 7 3 }} || {{monzo| 23 6 -14 }}
|-
|-
| || || || || 23\39 || || || 707.692 || 7 || 2 || 3.500 ||
| Vulture || 3.81 || .0576 || .183 || {{mapping| 1 0 -6 | 0 4 21 }} || {{monzo| 24 -21 4 }}
|-
|-
| || || || || || || 59\100 || 708.000 || 18 || 5 || 3.600 ||
| Trisedodge || 3.87 || .336 || 1.08 || {{mapping| 5 1 7 | 0 3 2 }} || {{monzo| 19 10 -15 }}
|-
|-
| || || || || || 36\61 || || 708.197 || 11 || 3 || 3.667 ||
| || 4.00 || .157 || .524 || {{mapping| 1 4 -1 | 0 8 -11 }} || {{monzo| -36 11 8 }}
|}
 
== Tunings ==
{| class="wikitable mw-collapsible mw-collapsed"
|+style=white-space:nowrap | 5-limit norm-based tunings
|-
|-
| || || || || || || 49\83 || 708.434 || 15 || 4 || 3.750 ||
! rowspan="2" |  
! rowspan="2" | Manhattan
! colspan="2" | Euclidean
! rowspan="2" | Chebyshevian
|-
|-
| || || || 13\22 || || || || 709.091 || 4 || 1 || 4.000 || Archy is in this region
! Constrained
! Constrained & skewed
|-
|-
| || || || || || || 42\71 || 709.859 || 13 || 3 || 4.333 ||
! Equilateral
| CEOP: ~3/2 = 697.654{{c}}<br>(1/5-comma)
| CEE: ~3/2 = 696.895{{c}}<br>(4/17-comma)
| CSEE: ~3/2 = 696.453{{c}}<br>(11/43-comma)
| CEC: ~3/2 = 696.578{{c}}<br>(1/4-comma)
|-
|-
| || || || || || 29\49 || || 710.204 || 9 || 2 || 4.500 ||
! Tenney
| CTOP: ~3/2 = 698.020{{c}}
| CTE: ~3/2 = 697.214{{c}}
| CWE: ~3/2 = 696.651{{c}}
| CTC: ~3/2 = 696.578{{c}}<br>(1/4-comma)
|-
|-
| || || || || || || 45\76 || 710.526 || 14 || 3 || 4.667 ||
! Benedetti, <br>Wilson
| CBOP: ~3/2 = 698.160{{c}}<br>(3/17-comma)
| CBE: ~3/2 = 697.374{{c}}<br>(36/169-comma)
| CSBE: ~3/2 = 696.787{{c}}<br>(31/129-comma)
| CBC: ~3/2 = 696.578{{c}}<br>(1/4-comma)
|}
 
{| class="wikitable mw-collapsible mw-collapsed"
|+style=white-space:nowrap | 7-limit norm-based tunings
|-
|-
| || || || || 16\27 || || || 711.111 || 5 || 1 || 5.000 ||
! rowspan="2" |  
! rowspan="2" | Manhattan
! colspan="2" | Euclidean
! rowspan="2" | Chebyshevian
|-
|-
| || || || || || || 35\59 || 711.864 || 11 || 2 || 5.500 ||
! Constrained
! Constrained & skewed
|-
|-
| || || || || || 19\32 || || 712.500 || 6 || 1 || 6.000 ||
! Equilateral
| CEOP: ~3/2 = 697.344{{c}}
| CEE: ~3/2 = 696.884{{c}}
| CSEE: ~3/2 = 696.725{{c}}
| CEC: ~3/2 = 696.883{{c}}
|-
|-
| || || || || || || 22\37 || 713.514 || 7 || 1 || 7.000 ||
! Tenney
| CTOP: ~3/2 = 696.646{{c}}
| CTE: ~3/2 = 696.952{{c}}
| CWE: ~3/2 = 696.656{{c}}
| CTC: ~3/2 = 696.883{{c}}
|-
|-
| 3\5 || || || || || || || 720.000 || 1 || 0 || → inf ||
! Benedetti, <br>Wilson
| CBOP: ~3/2 = 697.842{{c}}
| CBE: ~3/2 = 697.015{{c}}
| CSBE: ~3/2 = 696.631{{c}}
| CBC: ~3/2 = 696.883{{c}}
|}
|}
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