Xenharmonic Wiki

41edo: Difference between revisions

← Older editNewer edit →
VisualWikitext
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,264 edits
→Scales and modes: Restructure because some things were written twice unnecessarily
Line 696: Line 696:
{| class="wikitable center-4 center-5 center-6"
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve Stretch (¢)
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning Error
! colspan="2" | Tuning error
|-
|-
! [[TE error|Absolute]] (¢)
! [[TE error|Absolute]] (¢)
Line 706: Line 706:
| 2.3
| 2.3
| {{monzo| 65 -41 }}
| {{monzo| 65 -41 }}
| [{{val| 41 65 }}]
| {{mapping| 41 65 }}
| −0.153
| −0.153
| 0.15
| 0.15
Line 713: Line 713:
| 2.3.5
| 2.3.5
| 3125/3072, 20000/19683
| 3125/3072, 20000/19683
| [{{val| 41 65 95 }}]
| {{mapping| 41 65 95 }}
| +0.734
| +0.734
| 1.26
| 1.26
Line 720: Line 720:
| 2.3.5.7
| 2.3.5.7
| 225/224, 245/243, 1029/1024
| 225/224, 245/243, 1029/1024
| [{{val| 41 65 95 115 }}]
| {{mapping| 41 65 95 115 }}
| +0.815
| +0.815
| 1.10
| 1.10
Line 727: Line 727:
| 2.3.5.7.11
| 2.3.5.7.11
| 100/99, 225/224, 243/242, 245/242
| 100/99, 225/224, 243/242, 245/242
| [{{val| 41 65 95 115 142 }}]
| {{mapping| 41 65 95 115 142 }}
| +0.375
| +0.375
| 1.32
| 1.32
Line 734: Line 734:
| 2.3.5.7.11.13
| 2.3.5.7.11.13
| 100/99, 105/104, 144/143, 196/195, 243/242
| 100/99, 105/104, 144/143, 196/195, 243/242
| [{{val| 41 65 95 115 142 152 }}]
| {{mapping| 41 65 95 115 142 152 }}
| −0.060
| −0.060
| 1.55
| 1.55
Line 741: Line 741:
| 2.3.5.7.11.13.19
| 2.3.5.7.11.13.19
| 100/99, 105/104, 133/132, 144/143, 171/169, 196/195
| 100/99, 105/104, 133/132, 144/143, 171/169, 196/195
| [{{val| 41 65 95 115 142 152 174 }}]
| {{mapping| 41 65 95 115 142 152 174 }}
| +0.111
| +0.111
| 1.49
| 1.49
| 5.10
| 5.10
|}
|}
 
* 41et is lower in relative error than any previous equal temperaments in the 3-, 13- and 19-limit. The next equal temperaments doing better in these subgroups are 53, 53, and 46, respectively. It is even more prominent in the 2.3.5.7.11.19 and 2.3.5.7.11.13.19 subgroup. The next equal temperaments doing better in these subgroups are 72 and 53, respectively.  
41et is lower in relative error than any previous equal temperaments in the 3-, 13- and 19-limit. The next ETs doing better in these subgroups are 53, 53, and 46, respectively. It is even more prominent in the 2.3.5.7.11.19 and 2.3.5.7.11.13.19 subgroup. The next ETs doing better in these subgroups are 72 and 53, respectively.  


=== Commas ===
=== Commas ===
Line 753: Line 752:


{| class="commatable wikitable center-1 center-2 right-3 center-6"
{| class="commatable wikitable center-1 center-2 right-3 center-6"
! [[Prime limit|Prime<br>Limit]]
! [[Harmonic limit|Prime<br>limit]]
! [[Ratio]]<ref>Ratios with more than 8 digits are presented by placeholders with informative hints</ref>
! [[Ratio]]<ref>Ratios with more than 8 digits are presented by placeholders with informative hints</ref>
! [[Cents]]
! [[Cents]]
! [[Monzo]]
! [[Monzo]]
! colspan="2" | [[Color name|Color Name]]
! colspan="2" | [[Color name]]
! Name(s)
! Name(s)
|-
|-
Line 958: Line 957:
| Luluzozoyo
| Luluzozoyo
| 1uuzzy
| 1uuzzy
| Cassacot
| Frostma
|-
|-
| 11
| 11
Line 974: Line 973:
| Trilu-azo
| Trilu-azo
| 1u<sup>3</sup>z
| 1u<sup>3</sup>z
| Hemimin
| Hemimin comma
|-
|-
| 11
| 11
Line 982: Line 981:
| Saluzo
| Saluzo
| s1uz
| s1uz
| [[Pentacircle]]
| [[Pentacircle comma]]
|-
|-
| 11
| 11
Line 1,022: Line 1,021:
| Lotriruyo
| Lotriruyo
| 1or<sup>3</sup>y
| 1or<sup>3</sup>y
| Moctdel
| Moctdel comma
|-
|-
| 11
| 11
Line 1,046: Line 1,045:
| Luluquinzo-aquadgu
| Luluquinzo-aquadgu
| 1uuz<sup>5</sup>g<sup>4</sup>
| 1uuz<sup>5</sup>g<sup>4</sup>
| [[Odiheim]]
| [[Odiheim comma]]
|-
|-
| 13
| 13
Line 1,062: Line 1,061:
| Thuzoyo
| Thuzoyo
| 3uzy
| 3uzy
| Animist
| Animist comma
|-
|-
| 13
| 13
Line 1,134: Line 1,133:
| Thulo
| Thulo
| 3u1o
| 3u1o
| Minthma
| Major minthma
|-
|-
| 13
| 13
Line 1,142: Line 1,141:
| Tholuluzo
| Tholuluzo
| 3o1uuz
| 3o1uuz
| Gentle comma
| Minor minthma
|-
|-
| 13
| 13
Line 1,150: Line 1,149:
| Thuthulolozogu
| Thuthulolozogu
| 3uu1oozg
| 3uu1oozg
| Cuthbert
| Cuthbert comma
|-
|-
| 13
| 13
Line 1,206: Line 1,205:
| Sugu
| Sugu
| 17ug
| 17ug
| Septendecimal kleisma
| Charisma
|-
|-
| 17
| 17
Line 1,276: Line 1,275:
! Temperament(s)
! Temperament(s)
! [[Pergen]]
! [[Pergen]]
! MOS Scales
! Mos scales
|-
|-
| 1
| 1
Line 1,282: Line 1,281:
| [[Slendi]]
| [[Slendi]]
| (P8, P4/17)
| (P8, P4/17)
| Pathological 38-tone MOS
| Pathological 38-tone mos
|-
|-
| 2
| 2
Line 1,288: Line 1,287:
| [[Hemimiracle]]<br>[[Dodecacot]]
| [[Hemimiracle]]<br>[[Dodecacot]]
| (P8, P5/12)
| (P8, P5/12)
| 21-tone MOS
| 21-tone mos
|-
|-
| 3
| 3
Line 1,294: Line 1,293:
| [[Octacot]]
| [[Octacot]]
| (P8, P5/8)
| (P8, P5/8)
| 14-tone MOS: 3 3 3 3 3 3 3 3 3 3 3 3 3 2
| 14-tone mos: 3 3 3 3 3 3 3 3 3 3 3 3 3 2
|-
|-
| 4
| 4
Line 1,300: Line 1,299:
| [[Miracle]]
| [[Miracle]]
| (P8, P5/6)
| (P8, P5/6)
| 11-tone MOS: 4 4 4 4 4 4 4 4 4 4 1
| 11-tone mos: 4 4 4 4 4 4 4 4 4 4 1
|-
|-
| 5
| 5
Line 1,306: Line 1,305:
| [[BPS]] / [[bohpier]]
| [[BPS]] / [[bohpier]]
| (P8, P12/13)
| (P8, P12/13)
| 20-tone MOS
| 20-tone mos
|-
|-
| 6
| 6
Line 1,312: Line 1,311:
| [[Tetracot]] / [[bunya]] / [[monkey]]<br>[[Sesquiquartififths]] / [[sesquart]]
| [[Tetracot]] / [[bunya]] / [[monkey]]<br>[[Sesquiquartififths]] / [[sesquart]]
| (P8, P5/4)
| (P8, P5/4)
| 13-tone MOS: 1 5 1 5 1 5 1 5 5 1 5 1 5
| 13-tone mos: 1 5 1 5 1 5 1 5 5 1 5 1 5
|-
|-
| 7
| 7
Line 1,318: Line 1,317:
| [[Baldy]]<br>[[Quadrimage]]
| [[Baldy]]<br>[[Quadrimage]]
| (P8, c<sup>3</sup>P4/20)
| (P8, c<sup>3</sup>P4/20)
| 11-tone MOS: 6 1 6 6 1 6 1 6 1 6 1
| 11-tone mos: 6 1 6 6 1 6 1 6 1 6 1
|-
|-
| 8
| 8
Line 1,324: Line 1,323:
| [[Slendric]] / [[rodan]] / [[guiron]]
| [[Slendric]] / [[rodan]] / [[guiron]]
| (P8, P5/3)
| (P8, P5/3)
| 11-tone MOS: 7 1 7 1 7 1 7 1 1 7 1
| 11-tone mos: 7 1 7 1 7 1 7 1 1 7 1
|-
|-
| 9
| 9
Line 1,330: Line 1,329:
| [[Septimin]]
| [[Septimin]]
| (P8, ccP4/11)
| (P8, ccP4/11)
| 9-tone MOS: 5 4 5 5 4 5 4 5 4
| 9-tone mos: 5 4 5 5 4 5 4 5 4
|-
|-
| 10
| 10
Line 1,336: Line 1,335:
| [[Quasitemp]]
| [[Quasitemp]]
| (P8, c<sup>3</sup>P4/14)
| (P8, c<sup>3</sup>P4/14)
| 29-tone MOS
| 29-tone mos
|-
|-
| 11
| 11
Line 1,342: Line 1,341:
| [[Superkleismic]]
| [[Superkleismic]]
| (P8, ccP4/9)
| (P8, ccP4/9)
| 11-tone MOS: 5 3 5 3 3 5 3 3 5 3 3
| 11-tone mos: 5 3 5 3 3 5 3 3 5 3 3
|-
|-
| 12
| 12
Line 1,348: Line 1,347:
| [[Hemif]] / [[hemififths]] / [[salsa]]<br>[[Karadeniz]]
| [[Hemif]] / [[hemififths]] / [[salsa]]<br>[[Karadeniz]]
| (P8, P5/2)
| (P8, P5/2)
| 10-tone MOS: 5 2 5 5 2 5 5 5 2 5
| 10-tone mos: 5 2 5 5 2 5 5 5 2 5
|-
|-
| 13
| 13
Line 1,354: Line 1,353:
| [[Magic]] / [[witchcraft]]<br>[[Quanharuk]]
| [[Magic]] / [[witchcraft]]<br>[[Quanharuk]]
| (P8, P12/5)
| (P8, P12/5)
| 10-tone MOS: 2 9 2 2 9 2 2 9 2 2
| 10-tone mos: 2 9 2 2 9 2 2 9 2 2
|-
|-
| 14
| 14
Line 1,360: Line 1,359:
| [[Hocum]]<br>[[Hocus]]
| [[Hocum]]<br>[[Hocus]]
| (P8, c<sup>3</sup>P4/10)
| (P8, c<sup>3</sup>P4/10)
| 32-tone MOS
| 32-tone mos
|-
|-
| 15
| 15
Line 1,366: Line 1,365:
| [[Superthird]]
| [[Superthird]]
| (P8, c<sup>6</sup>P5/18)
| (P8, c<sup>6</sup>P5/18)
| 11-tone MOS: 4 3 4 4 4 3 4 4 3 4 4
| 11-tone mos: 4 3 4 4 4 3 4 4 3 4 4
|-
|-
| 16
| 16
Line 1,372: Line 1,371:
| [[Barbad]]
| [[Barbad]]
| (P8, c<sup>7</sup>P4/19)
| (P8, c<sup>7</sup>P4/19)
| 8-tone MOS: 7 2 7 7 2 7 7 2
| 8-tone mos: 7 2 7 7 2 7 7 2
|-
|-
| 17
| 17
Line 1,378: Line 1,377:
| [[Helmholtz]] / [[garibaldi]] / [[cassandra]] / [[andromeda]]<br>[[Kwai]]
| [[Helmholtz]] / [[garibaldi]] / [[cassandra]] / [[andromeda]]<br>[[Kwai]]
| (P8, P5)
| (P8, P5)
| 12-tone MOS: 4 3 4 3 3 4 3 4 3 4 3 4 3 3
| 12-tone mos: 4 3 4 3 3 4 3 4 3 4 3 4 3 3
|-
|-
| 18
| 18
Line 1,384: Line 1,383:
| [[Trismegistus]]
| [[Trismegistus]]
| (P8, c<sup>6</sup>P5/15)
| (P8, c<sup>6</sup>P5/15)
| 9-tone MOS: 5 5 3 5 5 5 5 3 5
| 9-tone mos: 5 5 3 5 5 5 5 3 5
|-
|-
| 19
| 19
Line 1,390: Line 1,389:
| [[Alphorn]]
| [[Alphorn]]
| (P8, c<sup>7</sup>P4/16)
| (P8, c<sup>7</sup>P4/16)
| 9-tone MOS: 3 3 3 10 3 3 3 3 10
| 9-tone mos: 3 3 3 10 3 3 3 3 10
|-
|-
| 20
| 20
Line 1,396: Line 1,395:
| [[Pluto]]<br>[[Merman]]
| [[Pluto]]<br>[[Merman]]
| (P8, c<sup>3</sup>P4/7)
| (P8, c<sup>3</sup>P4/7)
| Pathological 35-tone MOS
| Pathological 35-tone mos
|}
|}


Retrieved from "https://en.xen.wiki/w/41edo"