Xenharmonic Wiki

Octave (interval region): Difference between revisions

← Older editNewer edit →
VisualWikitext
Lériendil (talk | contribs)
8,046 edits
Undo revision 189892 by Xenllium (talk)
Tag: Undo
Lériendil (talk | contribs)
8,046 edits
Undo revision 189882 by Xenllium (talk)
Tag: Undo
Line 17: Line 17:


Several notable ones are:
Several notable ones are:
{| class="wikitable"
{{todo|inline=1|complete list}}
|-
! Interval
! Size <br>(cents)
! Prime limit
|-
| [[2/1]]
| 1200
| 2
|-
| [[1048576/531441]]
| 1176.54
| rowspan="2" | 3
|-
| [[531441/262144]]
| 1223.46
|-
| [[160/81]]
| 1178.49
| rowspan="2" | 5
|-
| [[81/40]]
| 1221.51
|-
| [[35/18]]
| 1151.23
| rowspan="10" | 7
|-
| [[96/49]]
| 1164.30
|-
| [[49/25]]
| 1165.02
|-
| [[63/32]]
| 1172.74
|-
| [[125/63]]
| 1186.21
|-
| [[252/125]]
| 1213.79
|-
| [[128/63]]
| 1227.26
|-
| [[100/49]]
| 1234.98
|-
| [[49/24]]
| 1235.70
|-
| [[72/35]]
| 1248.77
|}


== In tempered scales ==
== In tempered scales ==
Line 79: Line 25:
|-
|-
! EDO
! EDO
! colspan="2"| Suboctaves
! Suboctaves
|-
| [[21edo|21]]
| 20＼21
| 1142.9{{c}}
|-
| [[22edo|22]]
| 21＼22
| 1145.5{{c}}
|-
|-
| [[23edo|23]]
| 22
| 22＼23
| 1145{{c}}
| 1147.8{{c}}
|-
|-
| [[24edo|24]]
| 24
| 23＼24
| 1150{{c}}
| 1150{{c}}
|-
|-
| [[25edo|25]]
| 25
| 24＼25
| 1152{{c}}
| 1152{{c}}
|-
|-
| [[26edo|26]]
| 26
| 25＼26
| 1154{{c}}
| 1153.8{{c}}
|-
| [[27edo|27]]
| 26＼27
| 1155.6{{c}}
|-
| [[28edo|28]]
| 27＼28
| 1157.1{{c}}
|-
| [[29edo|29]]
| 28＼29
| 1158.6{{c}}
|-
|-
| [[30edo|30]]
| 27
| 29＼30
| 1156{{c}}
| 1160{{c}}
|-
|-
| [[31edo|31]]
| 29
| 30＼31
| 1159{{c}}
| 1161.3{{c}}
|-
|-
| [[32edo|32]]
| 31
| 31＼32
| 1161{{c}}
| 1162.5{{c}}
|-
|-
| [[33edo|33]]
| 34
| 32＼33
| 1165{{c}}
| 1163.6{{c}}
|-
|-
| [[34edo|34]]
| 41
| 33＼34
| 1142{{c}}, 1171{{c}}
| 1164.7{{c}}
|-
|-
| [[35edo|35]]
| 53
| 34＼35
| 1155{{c}}, 1177{{c}}
| 1165.7{{c}}
|-
| [[36edo|36]]
| 35＼36
| 1166.7{{c}}
|-
| [[37edo|37]]
| 36＼37
| 1167.6{{c}}
|-
| [[38edo|38]]
| 37＼38
| 1168.4{{c}}
|-
| [[39edo|39]]
| 38＼39
| 1169.2{{c}}
|-
| [[40edo|40]]
| 39＼40
| 1170{{c}}
|-
| [[41edo|41]]
| 39＼41 <br>40＼41
| 1141.5{{c}} <br>1170.7{{c}}
|-
| [[42edo|42]]
| 40＼42 <br>41＼42
| 1142.9{{c}} <br>1171.4{{c}}
|-
| [[43edo|43]]
| 41＼43 <br>42＼43
| 1144.2{{c}} <br>1172.1{{c}}
|-
| [[44edo|44]]
| 42＼44 <br>43＼44
| 1145.5{{c}} <br>1172.7{{c}}
|-
| [[45edo|45]]
| 43＼45 <br>44＼45
| 1146.7{{c}} <br>1173.3{{c}}
|-
| [[46edo|46]]
| 44＼46 <br>45＼46
| 1147.8{{c}} <br>1173.9{{c}}
|-
| [[47edo|47]]
| 45＼47 <br>46＼47
| 1148.9{{c}} <br>1174.5{{c}}
|-
| [[48edo|48]]
| 46＼48 <br>47＼48
| 1150{{c}} <br>1175{{c}}
|-
| [[49edo|49]]
| 47＼49 <br>48＼49
| 1151.0{{c}} <br>1175.5{{c}}
|-
| [[50edo|50]]
| 48＼50 <br>49＼50
| 1152{{c}} <br>1176{{c}}
|-
| [[51edo|51]]
| 49＼51 <br>50＼51
| 1152.9{{c}} <br>1176.5{{c}}
|-
| [[52edo|52]]
| 50＼52 <br>51＼52
| 1153.8{{c}} <br>1176.9{{c}}
|-
| [[53edo|53]]
| 51＼53 <br>52＼53
| 1154.7{{c}} <br>1177.4{{c}}
|-
| [[54edo|54]]
| 52＼54 <br>53＼54
| 1155.6{{c}} <br>1177.8{{c}}
|-
| [[55edo|55]]
| 53＼55 <br>54＼55
| 1156.4{{c}} <br>1178.2{{c}}
|-
| [[56edo|56]]
| 54＼56 <br>55＼56
| 1157.1{{c}} <br>1178.6{{c}}
|-
| [[57edo|57]]
| 55＼57 <br>56＼57
| 1157.9{{c}} <br>1178.9{{c}}
|-
| [[58edo|58]]
| 56＼58 <br>57＼58
| 1158.6{{c}} <br>1179.3{{c}}
|-
| [[59edo|59]]
| 57＼59 <br>58＼59
| 1159.3{{c}} <br>1179.7{{c}}
|-
| [[60edo|60]]
| 58＼60 <br>59＼60
| 1160{{c}} <br>1180{{c}}
|}
|}


2/1 is also represented perfectly in most temperaments, or the most common tunings thereof, and is mainly involved in octave-reducing intervals (such as saying that, in meantone, four 3/2s (octave-reduced) stack to 5/4).
2/1 is also represented perfectly in most temperaments, or the most common tunings thereof, and is mainly involved in octave-reducing intervals (such as saying that, in meantone, four 3/2s (octave-reduced) stack to 5/4).
{{todo|inline=1|complete table}}


{{Navbox intervals}}
{{Navbox intervals}}
Retrieved from "https://en.xen.wiki/w/Octave_(interval_region)"