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Table of rank-3 temperament lattice bases: Difference between revisions

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{{Todo|inline=1|improve synopsis|clarify|link|comments=Expand the intro to more thoroughly explain what this is. Link to here from other relevant pages.}}
Below are tabulated bases (temperamental Minkowski bases) of minimal temperamental complexity for the pitch classes of various regular temperaments.
Below are tabulated bases (temperamental Minkowski bases) of minimal temperamental complexity for the pitch classes of various regular temperaments.


=Rank three=
== Rank-3 ==
 
=== 7-limit temperaments ===
==Seven limit==
{| class="wikitable center-3 center-5 right-7"
 
{| class="wikitable"
|-
|-
! | Comma
! Comma
! | Name
! Name
! | Gen 1
! Gen 1
! | Length
! Length
! | Gen 2
! Gen 2
! | Length
! Length
! | Angle
! Angle
|-
|-
| | 686/675
| 686/675
| | [[senga]]
| [[Sengic]]
| | 15/14
| 15/14
| | 0.6977
| 0.6977
| | 3/2
| 3/2
| | 1.4208
| 1.4208
| | 103.732
| 103.732
|-
|-
| | 64/63
| 64/63
| | [[Archytas]]'
| [[Archytas]]
| | 3/2
| 3/2
| | 1.0508
| 1.0508
| | 5/4
| 5/4
| | 2.3219
| 2.3219
| | 90.000
| 90.000
|-
|-
| | 875/864
| 875/864
| | [[keema]]
| [[Keemic]]
| | 6/5
| 6/5
| | 0.8879
| 0.8879
| | 3/2
| 3/2
| | 1.3391
| 1.3391
| | 77.834
| 77.834
|-
|-
| | 81/80
| 81/80
| | [[Didymus]]'
| [[Didymus]]
| | 3/2
| 3/2
| | 0.5451
| 0.5451
| | 8/7
| 8/7
| | 2.8074
| 2.8074
| | 90.000
| 90.000
|-
|-
| | 3125/3087
| 3125/3087
| | [[gariboh]]
| [[Gariboh]]
| | 25/21
| 25/21
| | 0.5928
| 0.5928
| | 21/20
| 21/20
| | 1.2018
| 1.2018
| | 80.810
| 80.810
|-
|-
| | 2430/2401
| 2430/2401
| | [[nuwell]]
| [[Nuwell]]
| | 7/6
| 7/6
| | 0.6247
| 0.6247
| | 9/7
| 9/7
| | 1.1894
| 1.1894
| | 94.044
| 94.044
|-
|-
| | 50421/50000
| 50421/50000
| | [[trimyna]]
| [[Trimyna]]
| | 7/5
| 7/5
| | 0.3158
| 0.3158
| | 5/4
| 5/4
| | 1.7938
| 1.7938
| | 94.101
| 94.101
|-
|-
| | 245/243
| 245/243
| | [[sensamagic]]
| [[Sensamagic]]
| | 3/2
| 3/2
| | 0.9644
| 0.9644
| | 9/7
| 9/7
| | 1.0807
| 1.0807
| | 96.914
| 96.914
|-
|-
| | 126/125
| 126/125
| | [[starling]]
| [[Starling]]
| | 6/5
| 6/5
| | 1.068
| 1.068
| | 5/4
| 5/4
| | 1.206
| 1.206
| | 100.364
| 100.364
|-
|-
| | 4000/3969
| 4000/3969
| | [[octagar]]
| [[Octagar]]
| | 63/50
| 63/50
| | 0.8966
| 0.8966
| | 21/20
| 21/20
| | 1.0605
| 1.0605
| | 97.743
| 97.743
|-
|-
| | 1728/1715
| 1728/1715
| | [[orwellisma]]
| [[Orwellismic]]
| | 7/6
| 7/6
| | 0.7526
| 0.7526
| | 3/2
| 3/2
| | 1.3931
| 1.3931
| | 97.508
| 97.508
|-
|-
| | 1029/1024
| 1029/1024
| | [[gamelisma]]
| [[Gamelismic]]
| | 8/7
| 8/7
| | 0.5192
| 0.5192
| | 5/4
| 5/4
| | 2.3219
| 2.3219
| | 90.000
| 90.000
|-
|-
| | 225/224
| 225/224
| | [[marvel]]
| [[Marvel]]
| | 16/15
| 16/15
| | 1.256
| 1.256
| | 3/2
| 3/2
| | 1.369
| 1.369
| | 106.958
| 106.958
|-
|-
| | 3136/3125
| 3136/3125
| | [[hemimean]]
| [[Hemimean]]
| | 28/25
| 28/25
| | 0.5055
| 0.5055
| | 3/2
| 3/2
| | 1.5849
| 1.5849
| | 90.000
| 90.000
|-
|-
| | 5120/5103
| 5120/5103
| | [[hemifamity]]
| [[Aberschismic]]
| | 3/2
| 3/2
| | 0.5670
| 0.5670
| | 10/9
| 10/9
| | 1.8063
| 1.8063
| | 82.112
| 82.112
|-
|-
| | 6144/6125
| 6144/6125
| | [[porwell]]
| [[Porwell]]
| | 35/32
| 35/32
| | 0.9584
| 0.9584
| | 35/24
| 35/24
| | 1.1877
| 1.1877
| | 92.681
| 92.681
|-
|-
| | 65625/65536
| 65625/65536
| | [[horwell]]
| [[Horwell]]
| | 5/4
| 5/4
| | 0.6213
| 0.6213
| | 16/15
| 16/15
| | 1.3863
| 1.3863
| | 64.638
| 64.638
|-
|-
| | 703125/702464
| 703125/702464
| | [[meter]]
| [[Metric]]
| | 75/56
| 75/56
| | 0.7305
| 0.7305
| | 375/224
| 375/224
| | 0.7675
| 0.7675
| | 97.289
| 97.289
|-
|-
| | 420175/419904
| 420175/419904
| | [[wizma]]
| [[Wizmic]]
| | 245/216
| 245/216
| | 0.5541
| 0.5541
| | 324/245
| 324/245
| | 0.9731
| 0.9731
| | 79.663
| 79.663
|-
|-
| | 2401/2400
| 2401/2400
| | [[breedsma]]
| [[Breedsmic]]
| | 49/40
| 49/40
| | 0.7858
| 0.7858
| | 8/7
| 8/7
| | 1.1241
| 1.1241
| | 107.367
| 107.367
|-
|-
| | 4375/4374
| 4375/4374
| | [[ragisma]]
| [[Ragismic]]
| | 10/9
| 10/9
| | 0.7890
| 0.7890
| | 6/5
| 6/5
| | 0.9208
| 0.9208
| | 105.299
| 105.299
|}
|}


==Eleven limit==
=== 11-limit temperaments ===
 
{| class="wikitable center-3 center-5 right-7"
{| class="wikitable"
|-
|-
! | Commas
! Commas
! | Name
! Name
! | Gen 1
! Gen 1
! | Length
! Length
! | Gen 2
! Gen 2
! | Length
! Length
! | Angle
! Angle
|-
|-
| | 225/224, 385/384
| 225/224, 385/384
| | [[marvel]]
| [[Marvel]]
| | 16/15
| 16/15
| | 1.0364
| 1.0364
| | 5/4
| 5/4
| | 1.0759
| 1.0759
| | 104.028
| 104.028
|-
|-
| | 225/224, 441/440 <!-- was 441/400, presumed incorrect -->
| 225/224, 441/440 <!-- was 441/400, presumed incorrect -->
| | [[prodigy]]
| [[Prodigy]]
| | 16/15
| 16/15
| | 0.9111
| 0.9111
| | 3/2
| 3/2
| | 0.9477
| 0.9477
| | 65.933
| 65.933
|-
|-
| | 99/98, 176/175
| 99/98, 176/175
| | [[minerva]]
| [[Minerva]]
| | 16/15
| 16/15
| | 0.8997
| 0.8997
| | 5/4
| 5/4
| | 1.0457
| 1.0457
| | 98.604
| 98.604
|-
|-
| | 126/125, 176/175
| 126/125, 176/175
| | [[thrush]]
| [[Thrush]]
| | 5/4
| 5/4
| | 0.8576
| 0.8576
| | 6/5
| 6/5
| | 0.9314
| 0.9314
| | 74.624
| 74.624
|-
|-
| | 56/55, 100/99
| 56/55, 100/99
| | [[thrasher]]
| [[Thrasher]]
| | 6/5
| 6/5
| | 0.9089
| 0.9089
| | 5/4
| 5/4
| | 1.2007
| 1.2007
| | 98.845
| 98.845
|}
|}


[[Category:lattice]]
[[Category:Lattice]]
[[Category:Lists of temperaments]]
[[Category:Lists of temperaments]]
[[Category:Tables]]
[[Category:Tables]]
[[Category:todo:link]]
[[Category:todo:definition]]
Retrieved from "https://en.xen.wiki/w/Table_of_rank-3_temperament_lattice_bases"