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== Temperament pages ==
Databoxes has been canceled, but the cleanup will continue
Note:
# Order: subgroup, [[comma list]], [[mapping]], mapping generators, gencom mapping, [[gencom]], map to lattice, lattice basis, [[wedgie]], [[minimax tuning]], [[tuning ranges]], [[algebraic generator]], vals, [[badness]], [[complexity spectrum]].
# Comma list shows the simplest commas sufficient to define the temperament, stated in [[Normal lists #Normal interval list]].
# Mapping generators should show all the ratios as used in the mapping, including the period.
# Minimax tuning are based on tonality diamond, so it should explicitly state the ''odd'' limit, or a diamond function of ratios.
# Use [[Template:Val 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".
Get a family for:
* <s>Ripple (3 different 7-limit extensions)</s>
* <s>Smate (2 different 7-limit extensions)</s>
* Maybe [[parakleismic]] (2 different 7-limit extensions)
* Maybe [[superpyth]] (2 different 7-limit extensions)
Who's next?
* <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>
* [[Gamelismic clan]]
* <s>Gamelismic family</s>
* <s>Jubilismic clan</s>
* <s>Jubilismic family</s>
* <s>Didymus rank three family</s>
* <s>Kleismic family</s>
* [[Kleismic rank three family]]
* <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>
* [[Starling temperaments]]
* [[Starling family]]
* <s>Sensipent family</s>
* [[Sensamagic clan]]
* [[Sensamagic family]]
* [[Magic family]]
* [[Unicorn family]]
* [[Trisedodge family]]
== Septimal meantone ==
<span style="display: block; text-align: right;">[[:de:septimal-mitteltönig|Deutsch]]</span>


{{main| Meantone }}
{{Flat}}{{natural}}{{sharp}}
{{see also| Wikipedia: Septimal meantone temperament }}


The [[7/4]] of septimal meantone is the augmented sixth, C-A#, and other septimal intervals are [[7/6]], C-D#, the augmented second, [[7/5]], C-F#, the tritone, and [[21/16]], C-E#, the augmented third. Septimal meantone tempers out the common 7-limit commas [[126/125]] and [[225/224]] and in fact can be defined as the 7-limit temperament that tempers out any two of 81/80, 126/125 and 225/224.
&#x266D;&#x266E;&#x266F;


Subgroup: 2.3.5.7
<span class="bravura">&#xE260;</span>
<span class="bravura">&#xE261;</span>
<span class="bravura">&#xE262;</span>


[[Comma list]]: 81/80, 126/125
<span class="heji">n</span>


[[Mapping]]: [{{val|1 0 -4 -13}}, {{val|0 1 4 10}}]
== Template: Temperament data ==
{{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
}}


Mapping generators: ~2, ~3
== 5-limit rank-2 temperaments by TE simple badness ==
Breed's simple badness.


{{Multival|legend=1| 1 4 10 4 13 12 }}
=== Junk temperaments ===


[[POTE generator]]: ~3/2 = 696.495


[[Minimax tuning]]:
=== High-badness temperaments ===
* 7- and [[9-odd-limit]]
{| class="wikitable sortable center-2 center-3 center-4"
: [{{Monzo| 1 0 0 0 }}, {{Monzo| 1 0 1/4 0 }}, {{Monzo| 0 0 1 0 }}, {{Monzo| -3 0 5/2 0 }}]
: [[Eigenmonzo]]s: 2, 5
 
[[Tuning ranges]]:
* valid range: [694.737, 700.000] (11\19 to 7\12)
* nice range: [694.786, 701.955]
* strict range: [694.786, 700.000]
 
[[Algebraic generator]]: Cybozem, the real root of 15''x''<sup>3</sup> - 10''x''<sup>2</sup> - 18, 503.4257 cents. The recurrence converges quickly.
 
{{Val list|legend=1| 12, 19, 31, 81, 112b, 143b }}
 
[[Badness]]: 0.0137
 
Scales: [[meantone5]], [[meantone7]], [[meantone12]]
 
== Archytas ==
{{main| Archytas }}
 
Subgroup: 2.3.5.7
 
[[Comma list]]: 64/63
 
[[Mapping]]: [{{val| 1 0 0 6 }}, {{val| 0 1 0 -2 }}, {{val| 0 0 1 0 }}]
 
Mapping generators: ~2, ~3, ~5
 
Map to lattice: [{{val| 0 1 0 -2 }}, {{val| 0 0 1 0 }}]
 
Lattice basis:
: 3/2 length = 1.0508, 5/4 length = 2.3219
: Angle (3/2, 5/4) = 90 degrees
 
[[POTE generator]]s: ~3/2 = 709.3213, ~5/4 = 393.3747
 
[[Minimax tuning]]:
* [[7-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 2 1/3 0 -1/3 }}, {{monzo| 2 -2/3 1 -1/3 }}, {{monzo| 2 -2/3 0 2/3 }}]
: [[Eigenmonzo]]s: 2, 6/5, 7/5
* [[9-odd-limit]]
: [{{monzo| 1 0 0 0 }}, {{monzo| 3/2 1/2 0 -1/4 }}, {{monzo| 3/2 -1/2 1 -1/4 }}, {{monzo| 3 -1 0 1/2 }}]
: [[Eigenmonzo]]s: 2, 6/5, 9/7
 
{{Val list|legend=1| 5, 7, 10, 12, 15, 22, 27, 49 }}
 
Scales: [[archytas12]], [[archytas12synch]]
 
== Scale tree ==
(Bounded by branch depth = 7)
 
{| class="wikitable center-all"
! colspan="7" | Generator
! Cents
! 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
|-
|-
| || || || || || 41\71 || || 692.958 || 11 || 8 || 1.375 ||
| Uncle || 1.40 || 7.53 || 8.80 || {{mapping| 1 0 12 | 0 1 -6 }} || 4096/3645
|-
|-
| || || || || || || 67\116 || 693.103 || 18 || 13 || 1.385 ||
| Whitewood || 1.42 || 4.20 || 4.95 || {{mapping| 7 11 0 | 0 0 1 }} || 2187/2048
|-
|-
| || || || || 26\45 || || || 693.333 || 7 || 5 || 1.400 ||
| || 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"
|-
|-
| || || || || || || 63\109 || 693.578 || 17 || 12 || 1.417 ||
! Temperament !! Complexity !! Error (¢) !! Badness (moct) !! Mapping !! Comma list
|-
|-
| || || || || || 37\64 || || 693.750 || 10 || 7 || 1.429 ||
| Dicot || .521 || 7.09 || 3.08 || {{mapping| 1 1 2 | 0 2 1 }} || 25/24
|-
|-
| || || || || || || 48\83 || 693.976 || 13 || 9 || 1.444 ||
| Meantone || .711 || 1.58 || .937 || {{mapping| 1 0 -4 | 0 1 4 }} || 81/80
|-
|-
| || || 11\19 || || || || || 694.737 || 3 || 2 || 1.500 || L/s = 3/2
| Mavila || .795 || 6.06 || 4.02 || {{mapping| 1 0 7 | 0 1 -3 }} || 135/128
|-
|-
| || || || || || || 51\88 || 695.455 || 14 || 9 || 1.556 ||
| Augmented || .894 || 2.40 || 1.79 || {{mapping| 3 0 7 | 0 1 0 }} || 128/125
|-
|-
| || || || || || 40\69 || || 695.652 || 11 || 7 || 1.571 ||
| Porcupine || .960 || 2.68 || 2.14 || {{mapping| 1 2 3 | 0 -3 -5 }} || 250/243
|-
|-
| || || || || || || 69\119 || 695.798 || 19 || 12 || 1.583 ||
| Blackwood || 1.02 || 4.63 || 3.93 || {{mapping| 5 8 0 | 0 0 1 }} || 256/243
|-
|-
| || || || || 29\50 || || || 696.000 || 8 || 5 || 1.600 ||
| Diminished || 1.05 || 3.10 || 2.73 || {{mapping| 4 0 3 | 0 1 1 }} || 648/625
|-
|-
| || || || || || || 66\131 || 696.183 || 21 || |13 || 1.615 || Golden meantone
| Srutal || 1.22 || .835 || .852 || {{mapping| 2 0 11 | 0 1 -2 }} || 2048/2025
|-
|-
| || || || || || 47\81 || || 696.296 || 13 || 8 || 1.625 ||
| Magic || 1.40 || 1.11 || 1.29 || {{mapping| 1 0 2 | 0 5 1 }} || 3125/3072
|-
|-
| || || || || || || 65\112 || 696.429 || 18 || 11 || 1.636 ||  
| Hanson || 1.55 || .274 || .353 || {{mapping| 1 0 1 | 0 6 5 }} || 15625/15552
|-
|-
| || || || 18\31 || || || || 696.774 || 5 || 3 || 1.667 || Meantone is in this region
| Ripple || 1.56 || 2.82 || 3.66 || {{mapping| 1 2 3 | 0 -5 -8 }} || 6561/6250
|-
|-
| || || || || || || 61\105 || 697.143 || 17 || 10 || 1.700 ||
| Negri || 1.58 || 1.69 || 2.23 || {{mapping| 1 2 2 | 0 -4 3 }} || 16875/16384
|-
|-
| || || || || || 43\74 || || 697.297 || 12 || 7 || 1.714 ||
| Tetracot || 1.61 || .900 || 1.21 || {{mapping| 1 1 1 | 0 4 9 }} || 20000/19683
|-
|-
| || || || || || || 68\117 || 697.436 || 19 || 11 || 1.727 ||
| Superpyth || 1.70 || 2.11 || 2.99 || {{mapping| 1 0 -12 | 0 1 9 }} || 20480/19683
|-
|-
| || || || || 25\43 || || || 697.674 || 7 || 4 || 1.750 ||
| Helmholtz || 1.79 || .0570 || .0851 || {{mapping| 1 0 15 | 0 1 -8 }} || 32805/32768
|-
|-
| || || || || || || 57\98 || 697.959 || 16 || 9 || 1.778 ||
| Wesley || 1.91 || 2.75 || 4.37 || {{mapping| 1 4 3 | 0 -7 -2 }} || 78125/73728
|-
|-
| || || || || ||32\55 || || 698.182 || 9 || 5 || 1.800 ||
| Sensipent || 1.97 || .356 || .584 || {{mapping| 1 6 8 | 0 7 9 }} || 78732/78125
|-
|-
| || || || || || || 39\67 || 698.507 || 11 || 6 || 1.833 ||
| Stump || 2.02 || 1.88 || 3.16 || {{mapping| 1 0 6 | 0 3 -7 }} || 273375/262144
|-
|-
| || 7\12 || || || || || || 700.000 || 2 || 1 || 2.000 || Basic diatonic<br>(Generators smaller than this are proper)
| Passion || 2.02 || 1.57 || 2.64 || {{mapping| 1 2 2 | 0 -5 4 }} || 262144/253125
|-
|-
| || || || || || || 38\65 || 701.539 || 11 || 5 || 2.200 ||
| Doublewide || 2.06 || 2.00 || 3.43 || {{mapping| 2 1 3 | 0 4 3 }} || 390625/373248
|-
|-
| || || || || || 31\53 || || 701.887 || 9 || 4 || 2.250 ||
| Würschmidt || 2.29 || .262 || .499 || {{mapping| 1 7 3 | 0 8 1 }} || 393216/390625
|-
|-
| || || || || || || 55\94 || 702.128 || 16 || 7 || 2.286 ||
| Amity || 2.29 || .140 || .268 || {{mapping| 1 3 6 | 0 -5 -13 }} || 1600000/1594323
|-
|-
| || || || || 24\41 || || || 702.409 || 7 || 3 || 2.333 ||
| Valentine || 2.34 || .736 || 1.44 || {{mapping| 1 1 2 | 0 9 5 }} || 1990656/1953125
|-
|-
| || || || || || || 65\111 || 702.703 || 19 || 8 || 2.375 ||
| Immunity || 2.40 || 1.03 || 2.06 || {{mapping| 1 0 -8 | 0 2 13 }} || 1638400/1594323
|-
|-
| || || || || || 41\70 || || 702.857 || 12 || 5 || 2.400 ||
| Shibboleth || 2.42 || 1.24 || 2.50 || {{mapping| 1 4 5 | 0 -9 -10 }} || 1953125/1889568
|-
|-
| || || || || || || 58\99 || 703.030 || 17 || 7 || 2.428 ||
| Compton || 2.44 || .504 || 1.02 || {{mapping| 12 19 0 | 0 0 1 }} || 531441/524288
|-
|-
| || || || 17\29 || || || || 703.448 || 5 || 2 || 2.500 ||
| Orson || 2.44 || .215 || .438 || {{mapping| 1 0 3 | 0 7 -3 }} || 2109375/2097152
|-
|-
| || || || || || || 61\104 || 703.846 || 18 || 7 || 2.571 ||
| Unicorn || 2.52 || .725 || 1.52 || {{mapping| 1 2 3 | 0 -8 -13 }} || 1594323/1562500
|-
|-
| || || || || || 44\75 || || 704.000 || 13 || 5 || 2.600 ||
| Mynic || 2.60 || 1.10 || 2.37 || {{mapping| 1 9 9 | 0 -10 -9 }} || 10077696/9765625
|-
|-
| || || || || || || 71\121 || 704.132 || 21 || 8 || 2.625 || Golden neogothic
| Ampersand || 2.78 || .594 || 1.38 || {{mapping| 1 1 3 | 0 6 -7 }} || 34171875/33554432
|-
|-
| || || || || 27\46 || || || 704.348 || 8 || 3 || 2.667 ||
| Fifive || 2.91 || .643 || 1.56 || {{mapping| 2 2 3 | 0 5 7 }} || 9765625/9565938
|-
|-
| || || || || || || 64\109 || 704.587 || 19 || 7 || 2.714 ||
| Misty || 2.99 || .308 || .767 || {{mapping| 3 0 26 | 0 1 -4 }} || 67108864/66430125
|-
|-
| || || || || || 37\63 || || 704.762 || 11 || 4 || 2.750 ||
| Gravity || 2.99 || .269 || .669 || {{mapping| 1 5 12 | 0 -6 -17 }} || 129140163/128000000
|-
|-
| || || || || || || 47\80 || 705.000 || 14 || 5 || 2.800 ||
| Rodan || 3.10 || .433 || 1.12 || {{mapping| 1 1 -1 | 0 3 17 }} || {{monzo| 20 -17 3 }}
|-
|-
| || || 10\17 || || || || || 705.882 || 3 || 1 || 3.000 || L/s = 3/1
| || 3.11 || .757 || 1.96 || {{mapping| 1 0 -23 | 0 1 16 }} || {{monzo| -23 16 -1 }}
|-
|-
| || || || || || || 43\73 || 706.849 || 13 || 4 || 3.250 ||
| Mabila || 3.32 || .488 || 1.35 || {{mapping| 1 6 1 | 0 -10 3 }} || {{monzo| 28 -3 -10 }}
|-
|-
| || || || || || 33\56 || || 707.143 || 10 || 3 || 3.333 ||
| Parakleismic || 3.47 || .0798 || .231 || {{mapping| 1 5 6 | 0 -13 -14 }} || {{monzo| 8 14 -13 }}
|-
|-
| || || || || || || 56\95 || 707.368 || 17 || 5 || 3.400 ||
| Quartonic || 3.48 || .214 || .621 || {{mapping| 1 2 3 | 0 -11 -18 }} || {{monzo| 3 -18 11 }}
|-
|-
| || || || || 23\39 || || || 707.692 || 7 || 2 || 3.500 ||
| Escapade || 3.60 || .138 || .414 || {{mapping| 1 2 2 | 0 -9 7 }} || {{monzo| 32 -7 -9 }}
|-
|-
| || || || || || || 59\100 || 708.000 || 18 || 5 || 3.600 ||
| Ditonic || 3.68 || .258 || .792 || {{mapping| 1 6 3 | 0 -13 -2 }} || {{monzo| -27 -2 13 }}
|-
|-
| || || || || || 36\61 || || 708.197 || 11 || 3 || 3.667 ||
| Vishnuzmic || 3.71 || .0471 || .145 || {{mapping| 2 4 5 | 0 -7 -3 }} || {{monzo| 23 6 -14 }}
|-
|-
| || || || || || || 49\83 || 708.434 || 15 || 4 || 3.750 ||
| Vulture || 3.81 || .0576 || .183 || {{mapping| 1 0 -6 | 0 4 21 }} || {{monzo| 24 -21 4 }}
|-
|-
| || || || 13\22 || || || || 709.091 || 4 || 1 || 4.000 || Archy is in this region
| Trisedodge || 3.87 || .336 || 1.08 || {{mapping| 5 1 7 | 0 3 2 }} || {{monzo| 19 10 -15 }}
|-
|-
| || || || || || || 42\71 || 709.859 || 13 || 3 || 4.333 ||
| || 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 Prime-Optimized Tunings
|-
|-
| || || || || || 29\49 || || 710.204 || 9 || 2 || 4.500 ||
! rowspan="2" |  
! rowspan="2" | Manhattan
! colspan="2" | Euclidean
! rowspan="2" | Chebyshevian
|-
|-
| || || || || || || 45\76 || 710.526 || 14 || 3 || 4.667 ||
! Unskewed
! Skewed
|-
|-
| || || || || 16\27 || || || 711.111 || 5 || 1 || 5.000 ||
! Equilateral
| CEOP: ~3/2 = 697.654¢<br>(1/5-comma)
| CEE: ~3/2 = 696.895¢<br>(4/17-comma)
| CSEE: ~3/2 = 696.453¢<br>(11/43-comma)
| CEC: ~3/2 = 696.578¢<br>(1/4-comma)
|-
|-
| || || || || || || 35\59 || 711.864 || 11 || 2 || 5.500 ||
! Tenney
| CTOP: ~3/2 = 698.020¢
| CTE: ~3/2 = 697.214¢
| CWE: ~3/2 = 696.651¢
| CTC: ~3/2 = 696.578¢<br>(1/4-comma)
|-
|-
| || || || || || 19\32 || || 712.500 || 6 || 1 || 6.000 ||
! Benedetti, <br>Wilson
|-
| CBOP: ~3/2 = 698.160¢<br>(3/17-comma)
| || || || || || || 22\37 || 713.514 || 7 || 1 || 7.000 ||
| CBE: ~3/2 = 697.374¢<br>(36/169-comma)
|-
| CSBE: ~3/2 = 696.787¢<br>(31/129-comma)
| 3\5 || || || || || || || 720.000 || 1 || 0 || → inf ||
| CBC: ~3/2 = 696.578¢<br>(1/4-comma)
|}
|}


== Commas ==
{| class="wikitable mw-collapsible mw-collapsed"
 
|+style=white-space:nowrap | 7-limit Prime-Optimized Tunings
41edo [[tempers out]] the following [[comma]]s using its patent [[val]], {{val| 41 65 95 115 142 152 168 174 185 199 203 }}.
 
{| class="commatable wikitable center-1"
! [[Prime limit|Prime <br> limit]]
! [[Ratio]]<ref>Ratios with more than 9 digits are presented in monzos</ref>
! Name(s)
|-
|-
| 3
! rowspan="2" |  
| <abbr title="36893488147419103232/36472996377170786403">{{monzo| 65 -41 }}</abbr>
! rowspan="2" | Manhattan
| [[41-comma]]
! colspan="2" | Euclidean
! rowspan="2" | Chebyshevian
|-
|-
| 5
! Unskewed
| <abbr title="1953125/1889568">{{Monzo| -5 -10 9 }}</abbr>
! Skewed
| [[Shibboleth]]
|-
|-
| 5
! Equilateral
| <abbr title="34171875/33554432">{{Monzo| -25 7 6 }}</abbr>
| CEOP: ~3/2 = 697.344¢
| [[Ampersand]]
| CEE: ~3/2 = 696.884¢
| CSEE: ~3/2 = 696.725¢
| CEC: ~3/2 = 696.883¢
|-
|-
| 5
! Tenney
| [[3125/3072]]
| CTOP: ~3/2 = 696.646¢
| Magic comma
| CTE: ~3/2 = 696.952¢
| CWE: ~3/2 = 696.656¢
| CTC: ~3/2 = 696.883¢
|-
|-
| 5
! Benedetti, <br>Wilson
| <abbr title="20000/19683">{{Monzo| 5 -9 4 }}</abbr>
| CBOP: ~3/2 = 697.842¢
| [[Tetracot comma]]
| CBE: ~3/2 = 697.015¢
|-
| CSBE: ~3/2 = 696.631¢
| 5
| CBC: ~3/2 = 696.883¢
| <abbr title="131072000/129140163">{{Monzo| 20 -17 3 }}</abbr>
|}
| [[Roda]]
 
|-
== Temperament pages ==
| 5
Note:
| <abbr title="32805/32768">{{Monzo| -15 8 1 }}</abbr>
# Order: [[subgroup]], [[comma list]], ([[sval]]) [[mapping]], (sval) mapping generators, gencom mapping, [[gencom]], lattice basis, [[wedgie]], [[optimal tuning]]s ([[CTE]], [[CWE]]/[[POTE]]), [[minimax tuning]], [[tuning ranges]], [[algebraic generator]], [[optimal ET sequence]], [[badness]], [[complexity spectrum]], and others.
| [[Schisma]]
# Comma list should show the simplest commas sufficient to define the temperament, stated in [[Normal lists #Normal interval list]].
|-
# Mapping generators should show all the ratios as used in the mapping, including the period.
| 7
# Since minimax tunings are based on tonality diamond, it should explicitly state the ''odd'' limit, or a diamond function of ratios.
| <abbr title="15625/15309">{{Monzo| 0 -7 6 -1 }}</abbr>
# For subgroup temperaments, "mapping" becomes "sval mapping", add "gencom mapping" and "gencom". If TE is TE is TE (''sic''), simply show "CTE/CWE", otherwise show "subgroup/inharmonic CTE/CWE" instead.
| [[Great BP diesis]]
 
|-
Get a family for:
| 7
* <s>Ripple (3 different 7-limit extensions)</s> done
| <abbr title="854296875/843308032">{{Monzo| -10 7 8 -7 }}</abbr>
* <s>Smate (2 different 7-limit extensions)</s> done
| [[Blackjackisma]]
* <s>Passion (4 different 7-limit extensions, 3 strong and 1 weak)</s> done
|-
* <s>Undim</s> done
| 7
* <s>Quintaleap</s> done
| [[875/864]]
* <s>Quindromeda</s> done
| Keema
* Parakleismic (many reasonable but unnamed 7-limit extensions)
|-
* Schismatic rank three family (perhaps)
| 7
 
| [[3125/3087]]
Who's next?
| Gariboh
* <s>Meantone family</s>
|-
* <s>Didymus rank three family</s>
| 7
* <s>Archytas clan</s>
| <abbr title="179200/177147">{{Monzo| 10 -11 2 1 }}</abbr>
* <s>Archytas family</s>
| [[Tolerma]]
* <s>Father family</s>
|-
* <s>Trienstonic clan</s>
| 7
* <s>Septisemi temperaments</s>
| <abbr title="33075/32768">{{Monzo| -15 3 2 2 }}</abbr>
* <s>Slendro clan</s>
| [[Mirwomo comma]]
* <s>Semiphore family</s>
|-
* <s>Jubilismic clan</s>
| 7
* <s>Jubilismic family</s>
| [[245/243]]
* <s>Mint temperaments</s>
| Sensamagic
* <s>Mint family</s>
|-
* <s>Ripple family</s>
| 7
* <s>Smate family</s>
| [[4000/3969]]
* <s>Augmented family</s>
| Octagar
* <s>Dimipent family</s>
|-
* <s>Dicot family</s>
| 7
* <s>Bug family</s>
| <abbr title="823543/819200">{{Monzo| -15 0 -2 7 }}</abbr>
* <s>Pelogic family</s>
| [[Quince]]
* <s>Marvel temperaments</s>
|-
* <s>Marvel family</s>
| 7
* <s>Gamelismic clan</s>
| [[1029/1024]]
* <s>Gamelismic family</s>
| Gamelisma
* <s>Starling temperaments</s>
|-
* <s>Starling family</s>
| 7
* <s>Sensamagic clan</s>
| [[225/224]]
* <s>Sensamagic family</s>
| Marvel comma
* <s>Magic family</s>
|-
* <s>Sensipent family</s>
| 7
* <s>Keemic temperaments</s>
| <abbr title="16875/16807">{{Monzo| 0 3 4 -5 }}</abbr>
* <s>Keemic family</s>
| [[Mirkwai]]
* <s>Sengic family</s>
|-
* <s>Schismatic family</s>
| 7
* <s>Kleismic family</s>
| <abbr title="10976/10935">{{Monzo| 5 -7 -1 3 }}</abbr>
* <s>Kleismic rank three family</s>
| [[Hemimage]]
* <s>Würschmidt family</s>
* <s>Unicorn family</s>
* <s>Shibboleth family</s>
* <s>Immunity family</s>
* <s>Fifive family</s>
* <s>Trisedodge family</s>
* <s>Quintosec family</s>
* <s>Pental family</s>
* <s>Sycamore family</s>
* <s>Semicomma family</s>
* <s>Orwellismic temperaments</s>
* <s>Orwellismic family</s>
* <s>Hemimean clan</s>
* <s>Hemimean family</s>
* <s>Hemifamity temperaments</s>
* <s>Hemifamity family</s>
* <s>Porwell temperaments</s>
* <s>Porwell family</s>
* <s>Hemimage temperaments</s>
* <s>Hemimage family</s>
* <s>Porcupine family</s>
* <s>Porcupine rank three family</s>
* <s>Tetracot family</s>
* <s>Diaschismic family</s>
* <s>Diaschismic rank three family</s>
* <s>Compton family</s>
* <s>Amity family</s>
* <s>Misty family</s>
* <s>Undim family</s>
* <s>Lehmerismic temperaments</s>
* <s>Kalismic temperaments</s>
* <s>Ragismic microtemperaments</s>
* <s>Ragismic family</s>
* <s>Landscape microtemperaments</s>
* <s>Landscape family</s>
* <s>Dimcomp family</s>
* <s>Mirkwai clan</s>
* <s>Mirkwai family</s>
* <s>Quince clan</s>
* <s>Breedsmic temperaments</s>
* <s>Breed family</s>
* <s>Escapade family</s>
* <s>Gravity family</s>
* <s>Cataharry temperaments</s>
* <s>Cataharry family</s>
* <s>Varunismic temperaments</s>
* <s>Rastmic rank three clan</s>
* <s>Biyatismic clan</s>
* <s>Ptolemismic clan</s>
* <s>Valinorsmic clan</s>
* <s>Pentacircle clan</s>
* <s>Keenanismic temperaments</s>
* <s>Werckismic temperaments</s>
* <s>Swetismic temperaments</s>
* <s>Wizmic microtemperaments</s>
* <s>Metric microtemperaments</s>
* <s>Horwell temperaments</s>
* <s>Horwell family</s>
* <s>Luna family</s>
* <s>Vulture family</s>
* <s>Tricot family</s>
* <s>Minortonic family</s>
* <s>Gammic family</s>
* <s>Vishnuzmic family</s>
* <s>Garischismic clan</s>
* <s>Canousmic temperaments</s>
* <s>Canou family</s>
* <s>Semicanousmic clan</s>
* <s>Semiporwellismic clan</s>
* <s>Olympic clan</s>
* <s>Alphaxenic rank three clan</s>
* <s>Mirwomo temperaments</s>
* <s>Gariboh clan</s>
* <s>Gariboh family</s>
* <s>Octagar temperaments</s>
* <s>Octagar family</s>
* <s>Wesley family</s>
* <s>Apotome family</s>
* [[Mabila family]]
* [[Maquila family]]
* [[Maja family]]
* [[Ditonmic family]]
* <s>Greenwoodmic temperaments</s>
* <s>Avicennmic temperaments</s>
 
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve Stretch (¢)
! colspan="2" | Tuning Error
|-
|-
| 7
! [[TE error|Absolute]] (¢)
| [[5120/5103]]
! [[TE simple badness|Relative]] (%)
| Hemifamity
|-
|-
| 7
| 2.3
| <abbr title="33554432/33480783">{{Monzo| 25 -14 0 -1 }}</abbr>
| {{monzo| -49 31 }}
| [[Garischisma]]
| {{mapping| 31 49 }}
| +1.63
| 1.64
| 4.22
|-
|-
| 7
| 2.3.5
| [[2401/2400]]
| 81/80, 393216/390625
| Breedsma
| {{mapping| 31 49 72 }}
| +0.98
| 1.63
| 4.20
|-
|-
| 11
| 2.3.5.7
| <abbr title="163840/161051">{{Monzo| 15 0 1 0 -5 }}</abbr>
| 81/80, 126/125, 1029/1024
| [[Thuja comma]]
| {{mapping| 31 49 72 87 }}
| +0.83
| 1.43
| 3.70
|-
|-
| 11
| 2.3.5.7.11
| [[245/242]]
| 81/80, 99/98, 121/120, 126/125
| Cassacot
| {{mapping| 31 49 72 87 107 }}
|-
| +1.21
| 11
| 1.49
| [[100/99]]
| 3.84
| Ptolemisma
|-
| 11
| [[1344/1331]]
| Hemimin
|-
| 11
| [[896/891]]
| Pentacircle
|-
| 11
| <abbr title="65536/65219">{{Monzo| 16 0 0 -2 -3 }}</abbr>
| [[Orgonisma]]
|-
| 11
| [[243/242]]
| Rastma
|-
| 11
| [[385/384]]
| Keenanisma
|-
| 11
| [[441/440]]
| Werckisma
|-
| 11
| [[1375/1372]]
| Moctdel
|-
| 11
| [[540/539]]
| Swetisma
|-
| 11
| [[3025/3024]]
| Lehmerisma
|-
| 11
| <abbr title="151263/151250">{{Monzo| -1 2 -4 5 -2 }}</abbr>
| [[Odiheim]]
|-
| 13
| [[343/338]]
|
|-
| 13
| [[105/104]]
| Animist comma
|-
| 13
| <abbr title="28672/28431">{{Monzo| 12 -7 0 1 0 -1 }}</abbr>
| [[Secorian]]
|-
| 13
| [[275/273]]
| Gassorma
|-
| 13
| [[144/143]]
| Grossma
|-
| 13
| [[196/195]]
| Mynucuma
|-
| 13
| [[640/637]]
| Huntma
|-
| 13
| [[1188/1183]]
| Kestrel comma
|-
| 13
| [[325/324]]
| Marveltwin
|-
| 13
| [[352/351]]
| Minthma
|-
| 13
| [[364/363]]
| Gentle comma
|-
| 13
| [[847/845]]
| Cuthbert
|-
| 13
| [[729/728]]
| Squbema
|-
| 13
| [[4096/4095]]
| Schismina
|-
| 13
| <abbr title="10648/10647">{{Monzo| 3 -2 0 -1 3 -2 }}</abbr>
| [[Harmonisma]]
|-
| 17
| [[2187/2176]]
| Septendecimal schisma
|-
| 17
| [[256/255]]
| Septendecimal kleisma
|-
| 17
| [[715/714]]
| Septendecimal bridge comma
|-
| 19
| [[210/209]]
| Spleen comma
|-
| 19
| [[361/360]]
| Go comma
|-
| 19
| [[513/512]]
| Undevicesimal comma
|-
| 19
| [[1216/1215]]
| Eratosthenes' comma
|-
| 23
| [[736/729]]
| Vicesimotertial comma
|-
| 29
| [[145/144]]
| 29th-partial chroma
|}
|}
<references/>
 
== Scale tree ==
; 6-tone
: <s>1L 5s</s>, [[2L 4s]], <s>3L 3s</s>, [[4L 2s]], <s>5L 1s</s>
 
; 7-tone
: <s>1L 6s</s>, <s>2L 5s</s>, <s>3L 4s</s>, <s>4L 3s</s>, <s>5L 2s</s>, <s>6L 1s</s>
 
; 8-tone
: [[1L 7s]], <s>2L 6s</s>, [[3L 5s]], <s>4L 4s</s>, <s>5L 3s</s>, <s>6L 2s</s>, [[7L 1s]]
 
; 9-tone
: [[1L 8s]], [[2L 7s]], <s>3L 6s</s>, <s>4L 5s</s>, <s>5L 4s</s>, <s>6L 3s</s>, [[7L 2s]], [[8L 1s]]
 
; 10-tone
: [[1L 9s]], <s>2L 8s</s>, <s>3L 7s</s>, <s>4L 6s</s>, <s>5L 5s</s>, <s>6L 4s</s>, <s>7L 3s</s>, [[8L 2s]], [[9L 1s]]
 
; 11-tone
: [[1L 10s]], [[2L 9s]], [[3L 8s]], <s>4L 7s</s>, <s>5L 6s</s>, <s>6L 5s</s>, <s>7L 4s</s>, [[8L 3s]], [[9L 2s]], [[10L 1s]]
 
; 12-tone
: [[1L 11s]], [[2L 10s]], [[3L 9s]], [[4L 8s]], <s>5L 7s</s>, <s>6L 6s</s>, <s>7L 5s</s>, [[8L 4s]], [[9L 3s]], [[10L 2s]], [[11L 1s]]
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