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270edo: Difference between revisions

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Commas and more, possibly not the most reasonable, feel free to add/remove
Line 223: Line 223:
* It is even better in the 2.3.5.7.11.13.19 subgroup, having the least absolute error until [[552edo|552]], and the least relative error until [[2190edo|2190]].
* It is even better in the 2.3.5.7.11.13.19 subgroup, having the least absolute error until [[552edo|552]], and the least relative error until [[2190edo|2190]].
* It is also notable in the 17-limit, with lower absolute errors than smaller equal temperaments despite inconsistency in the corresponding odd limit.
* It is also notable in the 17-limit, with lower absolute errors than smaller equal temperaments despite inconsistency in the corresponding odd limit.
=== Commas ===
{| class="commatable wikitable center-1 center-2 right-4 center-5"
![[Harmonic limit|Prime]]
[[Harmonic limit|limit]]
![[Ratio]]<ref group="note">{{rd}}</ref>
![[Cent|Cents]]
![[Monzo]]
! colspan="2" |[[Color name]]
!Name(s)
|-
|5
|<abbr title="10485760000/10460353203">[[Vulture comma|(22 digits)]]</abbr>
|4.20
|{{Monzo|24 -21 4}}
|Sasaquadyo
|ssy<sup>4</sup>
|Vulture comma
|-
|5
|[[Vishnuzma|(20 digits)]]
|3.34
|[23 6 -14⟩
|Sasepbigu
|sg<sup>14</sup>
|Vishnuzma
|-
|7
|[[33554432/33480783|(16 digits)]]
|3.80
|{{monzo|25 -14 0 -1}}
|Sasaru
|ssr
|Garischisma
|-
|7
|[[2401/2400]]
|0.72
|{{monzo|-5 -1 -2 4}}
|Bizozogu
|z<sup>4</sup>gg
|Breedsma
|-
|7
|[[4375/4374]]
|0.40
|{{Monzo|-1 -7 4 1}}
|Zoquadyo
|zy<sup>4</sup>
|Ragisma
|-
|7
|[[Quasiorwellisma|(16 digits)]]
|3.73
|[22 -1 -10 1⟩
|Sazoquinbigu
|szg<sup>10</sup>
|Quasiorwellisma
|-
|11
|<abbr title="94489280512/94143178827">[[Pythrabian comma|(22 digits)]]</abbr>
|6.35
|{{Monzo|33 -23 0 0 1}}
|Trisalo
|s1o<sup>3</sup>
|Pythrabian comma
|-
|11
|[[5632/5625]]
|2.15
|[9 -2 -4 0 1⟩
|Saloquagu
|s1og<sup>4</sup>
|Vishdel comma
|-
|11
|[[Nexus comma|(12 digits)]]
|2.04
|[-16 -3 0 0 6⟩
|Tribilo
|1o<sup>3</sup>
|Nexus comma
|-
|11
|[[3025/3024]]
|0.57
|{{monzo|-4 -3 2 -1 2}}
|Loloruyoyo
|1ooryy
|Lehmerisma
|-
|11
|[[9801/9800]]
|0.18
|[-3 4 -2 -2 2⟩
|Bilorugu
|(1org)<sup>2</sup>
|Kalisma
|-
|13
|[[676/675]]
|2.56
|{{Monzo|2 -3 -2 0 0 2}}
|Bithogu
|3oogg
|Island comma, parizeksma
|-
|13
|[[1001/1000]]
|1.73
|{{Monzo|-3 0 -3 1 1 1}}
|Tholozotrigu
|3o1ozg<sup>3</sup>
|Fairytale comma, sinbadma
|-
|13
|[[2080/2079]]
|0.83
|{{Monzo|5 -3 1 -1 -1 1}}
|Tholuruyo
|3o1ury
|Ibnsinma, sinaisma
|-
|13
|[[4096/4095]]
|0.42
|{{Monzo|12 -2 -1 -1 0 -1}}
|Sathurugu
|s3urg
|Minisma
|-
|17
|[[12376/12375]]
|0.14
|[3 -2 -3 1 -1 1 1⟩
|Sotholuzotrigu
|7o3o1uzg<sup>3</sup>
|Flashma
|-
|19
|[[1216/1215]]
|1.42
|[6 -5 -1 0 0 0 0 1⟩
|Sanogu
|s9og
|Password, Eratosthenes' comma
|-
|23
|[[529/528]]
|3.24
|2.3.11.23 [-4 -1 -1 2⟩
|Bitwetho-alu
|23oo1u
|Preziosisma
|-
|29
|[[784/783]]
|2.20
|2.3.7.29 [4 -3 2 -1⟩
|Twenuzozo
|23uzz
|Biminorisma
|-
|31
|[[621/620]]
|2.79
|2.3.5.23.31 [-2 3 -1 1 -1⟩
|Thiwutwethogu
|31u23og
|Owowhatsthisma
|}


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
Line 236: Line 407:
| 1
| 1
| 1\270
| 1\270
| 4.44
| 4.<u>4</u>
| 385/384
| 385/384
| [[Keenanose]]
| [[Keenanose]]
Line 242: Line 413:
| 1
| 1
| 29\270
| 29\270
| 128.89
| 128.<u>8</u>
| 14/13
| 14/13
| [[Tertiathirds]]
| [[Tertiathirds]]
Line 248: Line 419:
| 1
| 1
| 61\270
| 61\270
| 271.11
| 271.<u>1</u>
| 90/77
| 90/77
| [[Quasiorwell]]
| [[Quasiorwell]]
Line 254: Line 425:
| 1
| 1
| 71\270
| 71\270
| 315.56
| 315.<u>5</u>
| 6/5
| 6/5
| [[Acrokleismic]] / counteracro
| [[Acrokleismic]] / counteracro
Line 260: Line 431:
| 1
| 1
| 79\270
| 79\270
| 351.11
| 351.<u>1</u>
| 49/40
| 49/40
| [[Newt]]
| [[Newt]]
Line 266: Line 437:
| 1
| 1
| 97\270
| 97\270
| 431.11
| 431.<u>1</u>
| 77/60
| 77/60
| [[Lockerbie]]
| [[Lockerbie]]
Line 272: Line 443:
| 1
| 1
| 107\270
| 107\270
| 475.56
| 475.<u>5</u>
| 25/19
| 25/19
| [[Vulture]]
| [[Vulture]]
Line 278: Line 449:
| 2
| 2
| 14\270
| 14\270
| 62.22
| 62.<u>2</u>
| 28/27
| 28/27
| [[Eagle]]
| [[Eagle]]
Line 284: Line 455:
| 2
| 2
| 16\270
| 16\270
| 71.11
| 71.<u>1</u>
| 25/24
| 25/24
| [[Vishnu]] / ananta / acyuta
| [[Vishnu]] / ananta / acyuta
|-
|2
|112\270
(23\270)
|497.<u>7</u>
(102.<u>2</u>)
|4/3
|[[Gary]] / [[Gariwizmic]]
|-
|-
| 2
| 2
| 28\270
| 28\270
| 124.44
| 124.<u>4</u>
| 275/256
| 275/256
| [[Semivulture]]
| [[Semivulture]]
Line 296: Line 475:
| 2
| 2
| 47\270
| 47\270
| 208.89
| 208.<u>8</u>
| 44/39
| 44/39
| [[Abigail]]
| [[Abigail]]
Line 302: Line 481:
| 2
| 2
| 52\270
| 52\270
| 231.11
| 231.<u>1</u>
| 8/7
| 8/7
| [[Orga]]
| [[Orga]]
Line 308: Line 487:
| 2
| 2
| 131\270<br>(4\270)
| 131\270<br>(4\270)
| 582.22<br>(17.78)
| 582.<u>2</u><br>(17.<u>7</u>)
| 7/5<br>(99/98)
| 7/5<br>(99/98)
| [[Quarvish]]
| [[Quarvish]]
Line 314: Line 493:
| 3
| 3
| 17\270
| 17\270
| 75.56
| 75.<u>5</u>
| 24/23
| 24/23
| [[Terture]]
| [[Terture]]
Line 320: Line 499:
| 3
| 3
| 31\270
| 31\270
| 137.78
| 137.<u>7</u>
| 13/12
| 13/12
| [[Avicenna]]
| [[Avicenna]]
Line 326: Line 505:
| 5
| 5
| 83\270<br>(25\270)
| 83\270<br>(25\270)
| 368.89<br>(111.11)
| 368.<u>8</u><br>(111.<u>1</u>)
| 1024/891<br>(16/15)
| 1024/891<br>(16/15)
| [[Quintosec]]
| [[Quintosec]]
Line 332: Line 511:
| 6
| 6
| 112\270<br>(4\270)
| 112\270<br>(4\270)
| 497.78<br>(97.78)
| 497.<u>7</u><br>(97.<u>7</u>)
| 4/3<br>(128/121)
| 4/3<br>(128/121)
| [[Sextile]]
| [[Sextile]]
Line 338: Line 517:
| 9
| 9
| 71\270<br>(11\270)
| 71\270<br>(11\270)
| 315.56<br>(48.89)
| 315.<u>5</u><br>(48.<u>8</u>)
| 6/5<br>(36/35)
| 6/5<br>(36/35)
| [[Ennealimmal]] / ennealimmia
| [[Ennealimmal]] / ennealimmia
Line 344: Line 523:
| 10
| 10
| 16\270<br>(11\270)
| 16\270<br>(11\270)
| 71.11<br>(48.89)
| 71.<u>1</u><br>(48.<u>8</u>)
| 25/24<br>(36/35)
| 25/24<br>(36/35)
| [[Decavish]]
| [[Decavish]]
Line 350: Line 529:
| 10
| 10
| 56\270<br>(2\270)
| 56\270<br>(2\270)
| 248.89<br>(8.89)
| 248.<u>8</u><br>(8.<u>8</u>)
| 15/13<br>(176/175)
| 15/13<br>(176/175)
| [[Decoid]]
| [[Decoid]]
Line 356: Line 535:
| 10
| 10
| 71\270<br>(10\270)
| 71\270<br>(10\270)
| 315.56<br>(44.44)
| 315.<u>5</u><br>(44.<u>4</u>)
| 6/5<br>(40/39)
| 6/5<br>(40/39)
| [[Deca]]
| [[Deca]]
Line 362: Line 541:
| 18
| 18
| 71\270<br>(4\270)
| 71\270<br>(4\270)
| 248.89<br>(17.78)
| 248.<u>8</u><br>(17.<u>7</u>)
| 15/13<br>(99/98)
| 15/13<br>(99/98)
| [[Hemiennealimmal]]
| [[Hemiennealimmal]]
Line 368: Line 547:
| 18
| 18
| 71\270<br>(2\270)
| 71\270<br>(2\270)
| 475.56<br>(8.89)
| 475.<u>5</u><br>(8.<u>8</u>)
| 1053/800<br>(1287/1280)
| 1053/800<br>(1287/1280)
| [[Semihemiennealimmal]]
| [[Semihemiennealimmal]]
Line 374: Line 553:
| 27
| 27
| 61\270<br>(1\270)
| 61\270<br>(1\270)
| 271.11<br>(4.44)
| 271.<u>1</u><br>(4.44)
| 1375/1176<br>(385/384)
| 1375/1176<br>(385/384)
| [[Trinealimmal]]
| [[Trinealimmal]]
Line 380: Line 559:
| 30
| 30
| 82\270<br>(1\270)
| 82\270<br>(1\270)
| 364.44<br>(4.44)
| 364.<u>4</u><br>(4.44)
| 216/175<br>(385/384)
| 216/175<br>(385/384)
| [[Zinc]]
| [[Zinc]]
Line 386: Line 565:
| 45
| 45
| 59\270<br>(1\270)
| 59\270<br>(1\270)
| 262.22<br>(4.44)
| 262.<u>2</u><br>(4.44)
| 64/55<br>(385/384)
| 64/55<br>(385/384)
| [[Rhodium]]
| [[Rhodium]]
Retrieved from "https://en.xen.wiki/w/270edo"