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

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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 three=


==Seven limit==
==Seven limit==
Line 7: Line 7:
{| class="wikitable"
{| class="wikitable"
|-
|-
| | Comma
! | Comma
| | Name
! | Name
| | Gen 1
! | Gen 1
| | Length
! | Length
| | Gen 2
! | Gen 2
| | Length
! | Length
| | Angle
! | Angle
|-
|-
| | 686/675
| | 686/675
| | Keema
| | [[senga]]
| | 15/14
| | 15/14
| | 0.6977
| | 0.6977
Line 24: Line 24:
|-
|-
| | 64/63
| | 64/63
| | Archytas
| | [[Archytas]]'
| | 3/2
| | 3/2
| | 1.0508
| | 1.0508
Line 32: Line 32:
|-
|-
| | 875/864
| | 875/864
| | Keema
| | [[keema]]
| | 6/5
| | 6/5
| | 0.8879
| | 0.8879
Line 40: Line 40:
|-
|-
| | 81/80
| | 81/80
| | Didymus
| | [[Didymus]]'
| | 3/2
| | 3/2
| | 0.5451
| | 0.5451
Line 48: Line 48:
|-
|-
| | 3125/3087
| | 3125/3087
| | Gariboh
| | [[gariboh]]
| | 25/21
| | 25/21
| | 0.5928
| | 0.5928
Line 56: Line 56:
|-
|-
| | 2430/2401
| | 2430/2401
| | Nuwell
| | [[nuwell]]
| | 7/6
| | 7/6
| | 0.6247
| | 0.6247
Line 64: Line 64:
|-
|-
| | 50421/50000
| | 50421/50000
| | Trimyna
| | [[trimyna]]
| | 7/5
| | 7/5
| | 0.3158
| | 0.3158
Line 72: Line 72:
|-
|-
| | 245/243
| | 245/243
| | Sensamagic
| | [[sensamagic]]
| | 3/2
| | 3/2
| | 0.9644
| | 0.9644
Line 80: Line 80:
|-
|-
| | 126/125
| | 126/125
| | Starling
| | [[starling]]
| | 6/5
| | 6/5
| | 1.068
| | 1.068
Line 88: Line 88:
|-
|-
| | 4000/3969
| | 4000/3969
| | Octagar
| | [[octagar]]
| | 63/50
| | 63/50
| | 0.8966
| | 0.8966
Line 96: Line 96:
|-
|-
| | 1728/1715
| | 1728/1715
| | Orwellisma
| | [[orwellisma]]
| | 7/6
| | 7/6
| | 0.7526
| | 0.7526
Line 104: Line 104:
|-
|-
| | 1029/1024
| | 1029/1024
| | Gamelisma
| | [[gamelisma]]
| | 8/7
| | 8/7
| | 0.5192
| | 0.5192
Line 112: Line 112:
|-
|-
| | 225/224
| | 225/224
| | Marvel
| | [[marvel]]
| | 16/15
| | 16/15
| | 1.256
| | 1.256
Line 120: Line 120:
|-
|-
| | 3136/3125
| | 3136/3125
| | Hemimean
| | [[hemimean]]
| | 28/25
| | 28/25
| | 0.5055
| | 0.5055
Line 128: Line 128:
|-
|-
| | 5120/5103
| | 5120/5103
| | Hemifamity
| | [[hemifamity]]
| | 3/2
| | 3/2
| | 0.5670
| | 0.5670
Line 136: Line 136:
|-
|-
| | 6144/6125
| | 6144/6125
| | Porwell
| | [[porwell]]
| | 35/32
| | 35/32
| | 0.9584
| | 0.9584
Line 144: Line 144:
|-
|-
| | 65625/65536
| | 65625/65536
| | Horwell
| | [[horwell]]
| | 5/4
| | 5/4
| | 0.6213
| | 0.6213
Line 152: Line 152:
|-
|-
| | 703125/702464
| | 703125/702464
| | Meter
| | [[meter]]
| | 75/56
| | 75/56
| | 0.7305
| | 0.7305
Line 159: Line 159:
| | 97.289
| | 97.289
|-
|-
| | 420175 / 419904
| | 420175/419904
| | Wizma
| | [[wizma]]
| | 245/216
| | 245/216
| | 0.5541
| | 0.5541
Line 168: Line 168:
|-
|-
| | 2401/2400
| | 2401/2400
| | Breedsma
| | [[breedsma]]
| | 49/40
| | 49/40
| | 0.7858
| | 0.7858
Line 176: Line 176:
|-
|-
| | 4375/4374
| | 4375/4374
| | Ragisma
| | [[ragisma]]
| | 10/9
| | 10/9
| | 0.7890
| | 0.7890
Line 188: Line 188:
{| class="wikitable"
{| 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
Line 204: Line 204:
| | 104.028
| | 104.028
|-
|-
| | 225/224&441/400
| | 225/224, 441/440 <!-- was 441/400, presumed incorrect -->
| | Prodigy
| | [[prodigy]]
| | 16/15
| | 16/15
| | 0.9111
| | 0.9111
Line 212: Line 212:
| | 65.933
| | 65.933
|-
|-
| | 99/98&amp;176/175
| | 99/98, 176/175
| | Minerva
| | [[minerva]]
| | 16/15
| | 16/15
| | 0.8997
| | 0.8997
Line 220: Line 220:
| | 98.604
| | 98.604
|-
|-
| | 126/125&amp;176/175
| | 126/125, 176/175
| | Thrush
| | [[thrush]]
| | 5/4
| | 5/4
| | 0.8576
| | 0.8576
Line 228: Line 228:
| | 74.624
| | 74.624
|-
|-
| | 56/55&amp;100/99
| | 56/55, 100/99
| | Thrasher
| | [[thrasher]]
| | 6/5
| | 6/5
| | 0.9089
| | 0.9089
Line 236: Line 236:
| | 98.845
| | 98.845
|}
|}
[[Category:lattice]]
[[Category:lattice]]
[[Category:overview]]
[[Category:overview]]
[[Category:table]]
[[Category:table]]
[[Category:temperaments]]
[[Category:temperament]]
[[Category:todo:link]]
[[Category:todo:link]]
[[Category:todo:definition]]
Retrieved from "https://en.xen.wiki/w/Table_of_rank-3_temperament_lattice_bases"