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Table of 270edo intervals: Difference between revisions

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Prime 17 can be considered good enough
 
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This '''table of 270edo intervals''' assumes the [[31-limit]] [[patent val]] of [[270edo]] {{val| 270 428 647 758 934 999 1104 1147 1221 1312 1338 }}. [[Prime harmonic]]s are in '''bold'''; inconsistently mapped intervals are in ''italic''. As is analysed in the main article, besides being a strong 13-limit system, 270edo can be used in the full 23-limit with a handful of inconsistencies into the 27-odd-limit, or as a no-17 no-23 31-limit system, fully consistent to the 31-odd-limit. For this reason, intervals of 17 and 23 are given in parentheses.  
This '''table of 270edo intervals''' assumes the [[31-limit]] [[patent val]] of [[270edo]] {{val| 270 428 647 758 934 999 1104 1147 1221 1312 1338 }}. [[Prime harmonic]]s are in '''bold'''; inconsistently mapped intervals are in ''italic''. As is analysed in the main article, besides being a strong 13-limit system, 270edo can be used in the full 23-limit with a handful of inconsistencies into the 27-odd-limit, or as a no-17/13 no-23 31-limit system, fully consistent to the 35-odd-limit. For this reason, intervals of 23 are given in parentheses.  


{| class="wikitable center-all right-1 right-2"
{| class="wikitable center-all right-1 right-2"
Line 240: Line 240:
| [[128/121]]
| [[128/121]]
| [[55/52]]
| [[55/52]]
| ([[18/17]])
| [[18/17]]
| "
| "
|-
|-
Line 260: Line 260:
| "
| "
| [[117/110]]
| [[117/110]]
| ('''[[17/16]]''')
| '''[[17/16]]'''
| [[33/31]]
| "
|-
|-
| 25
| 25
Line 300: Line 300:
| [[189/176]]
| [[189/176]]
| [[130/121]]
| [[130/121]]
| ([[102/95]])
| [[102/95]]
| [[29/27]]
| [[29/27]]
|-
|-
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| "
| "
| [[169/154]]
| [[169/154]]
| ([[56/51]])
| [[56/51]]
| ([[34/31]])
| [[34/31]]
|-
|-
| 37
| 37
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| "
| "
| "
| "
| ([[19/17]])
| [[19/17]]
| [[29/26]]
| "
|-
|-
| 44
| 44
Line 510: Line 510:
| "
| "
| [[143/126]]
| [[143/126]]
| ([[17/15]])
| [[17/15]]
| "
| "
|-
|-
Line 550: Line 550:
| [[55/48]]
| [[55/48]]
| "
| "
| ([[39/34]])
| [[39/34]]
| "
| "
|-
|-
Line 641: Line 641:
| "
| "
| "
| "
| ([[34/29]])
| [[34/29]]
|-
|-
| 63
| 63
Line 650: Line 650:
| "
| "
| "
| "
| ([[20/17]])
| [[20/17]]
| "
| "
|-
|-
Line 710: Line 710:
| [[105/88]]
| [[105/88]]
| "
| "
| ([[68/57]])
| [[68/57]]
| [[31/26]]
| [[31/26]]
|-
|-
Line 780: Line 780:
| [[147/121]]
| [[147/121]]
| "
| "
| ([[17/14]])
| [[17/14]]
| "
| "
|-
|-
Line 840: Line 840:
| "
| "
| "
| "
| ([[21/17]])
| [[21/17]]
| "
| "
|-
|-
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| [[441/352]]
| [[441/352]]
| [[351/280]]
| [[351/280]]
| ([[64/51]])
| [[64/51]]
| "
| "
|-
|-
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| "
| "
| "
| "
| ([[34/27]])
| [[34/27]]
| [[39/31]]
| "
|-
|-
| 91
| 91
Line 1,020: Line 1,020:
| [[128/99]]
| [[128/99]]
| [[84/65]]
| [[84/65]]
| ([[22/17]])
| [[22/17]]
| [[31/24]]
| "
|-
|-
| 101
| 101
Line 1,070: Line 1,070:
| [[55/42]]
| [[55/42]]
| "
| "
| (''[[17/13]]'')
| ''[[17/13]]''
| [[38/29]]
| [[38/29]]
|-
|-
Line 1,110: Line 1,110:
| [[160/121]]
| [[160/121]]
| [[143/108]]
| [[143/108]]
| ([[45/34]])
| [[45/34]]
| "
| "
|-
|-
Line 1,130: Line 1,130:
| [[512/385]]
| [[512/385]]
| [[117/88]]
| [[117/88]]
| ([[85/64]])
| [[85/64]]
| "
| "
|-
|-
Line 1,150: Line 1,150:
| [[147/110]]
| [[147/110]]
| "
| "
| ([[91/68]])
| [[91/68]]
| "
| "
|-
|-
Line 1,170: Line 1,170:
| [[121/90]]
| [[121/90]]
| "
| "
| ([[51/38]])
| [[51/38]]
| [[39/29]]
| [[39/29]]
|-
|-
Line 1,220: Line 1,220:
| "
| "
| "
| "
| ([[34/25]])
| [[34/25]]
| "
| "
|-
|-
Line 1,360: Line 1,360:
| "
| "
| [[55/39]]
| [[55/39]]
| ([[24/17]])
| [[24/17]]
| [[31/22]]
| "
|-
|-
| 135
| 135
Line 1,380: Line 1,380:
| [[343/242]]
| [[343/242]]
| [[78/55]]
| [[78/55]]
| ([[17/12]])
| [[17/12]]
| [[44/31]]
| "
|-
|-
| 137
| 137
Line 1,520: Line 1,520:
| "
| "
| "
| "
| ([[25/17]])
| [[25/17]]
| "
| "
|-
|-
Line 1,570: Line 1,570:
| "
| "
| "
| "
| ([[76/51]])
| [[76/51]]
| [[58/39]]
| [[58/39]]
|-
|-
Line 1,580: Line 1,580:
| "
| "
| "
| "
| ([[85/57]])
| [[85/57]]
| "
| "
|-
|-
Line 1,590: Line 1,590:
| [[220/147]]
| [[220/147]]
| [[175/117]]
| [[175/117]]
| ([[136/91]])
| [[136/91]]
| "
| "
|-
|-
Line 1,610: Line 1,610:
| [[385/256]]
| [[385/256]]
| [[176/117]]
| [[176/117]]
| ([[128/85]])
| [[128/85]]
| "
| "
|-
|-
Line 1,630: Line 1,630:
| [[121/80]]
| [[121/80]]
| "
| "
| ([[68/45]])
| [[68/45]]
| "
| "
|-
|-
Line 1,670: Line 1,670:
| [[55/36]]
| [[55/36]]
| "
| "
| (''[[26/17]]'')
| ''[[26/17]]''
| [[29/19]]
| [[29/19]]
|-
|-
Line 1,720: Line 1,720:
| [[99/64]]
| [[99/64]]
| [[65/42]]
| [[65/42]]
| ([[17/11]])
| [[17/11]]
| [[48/31]]
| "
|-
|-
| 171
| 171
Line 1,820: Line 1,820:
| "
| "
| "
| "
| ([[27/17]])
| [[27/17]]
| [[62/39]]
| "
|-
|-
| 181
| 181
Line 1,840: Line 1,840:
| "
| "
| [[351/220]]
| [[351/220]]
| ([[51/32]])
| [[51/32]]
| "
| "
|-
|-
Line 1,900: Line 1,900:
| "
| "
| "
| "
| ([[34/21]])
| [[34/21]]
| "
| "
|-
|-
Line 1,960: Line 1,960:
| [[242/147]]
| [[242/147]]
| "
| "
| ([[28/17]])
| [[28/17]]
| "
| "
|-
|-
Line 2,030: Line 2,030:
| [[176/105]]
| [[176/105]]
| "
| "
| ([[57/34]])
| [[57/34]]
| [[52/31]]
| [[52/31]]
|-
|-
Line 2,090: Line 2,090:
| "
| "
| [[143/84]]
| [[143/84]]
| ([[17/10]])
| [[17/10]]
| "
| "
|-
|-
Line 2,101: Line 2,101:
| "
| "
| "
| "
| ([[29/17]])
| [[29/17]]
|-
|-
| 209
| 209
Line 2,190: Line 2,190:
| [[96/55]]
| [[96/55]]
| "
| "
| ([[68/39]])
| [[68/39]]
| "
| "
|-
|-
Line 2,230: Line 2,230:
| "
| "
| [[143/81]]
| [[143/81]]
| ([[30/17]])
| [[30/17]]
| "
| "
|-
|-
Line 2,290: Line 2,290:
| "
| "
| "
| "
| ([[34/19]])
| [[34/19]]
| [[52/29]]
| "
|-
|-
| 228
| 228
Line 2,360: Line 2,360:
| "
| "
| "
| "
| ([[51/28]])
| [[51/28]]
| ([[31/17]])
| [[31/17]]
|-
|-
| 235
| 235
Line 2,440: Line 2,440:
| [[225/121]]
| [[225/121]]
| [[121/65]]
| [[121/65]]
| ([[95/51]])
| [[95/51]]
| [[54/29]]
| [[54/29]]
|-
|-
Line 2,480: Line 2,480:
| [[847/450]]
| [[847/450]]
| [[220/117]]
| [[220/117]]
| ('''[[32/17]]''')
| '''[[32/17]]'''
| [[62/33]]
| [[62/33]]
|-
|-
Line 2,500: Line 2,500:
| [[121/64]]
| [[121/64]]
| [[104/55]]
| [[104/55]]
| ([[17/9]])
| [[17/9]]
| "
| "
|-
|-
Line 2,590: Line 2,590:
| [[242/125]]
| [[242/125]]
| [[176/91]]
| [[176/91]]
| (''[[85/44]]'')
| ''[[85/44]]''
| [[29/15]]
| [[29/15]]
|-
|-
Line 2,600: Line 2,600:
| [[64/33]]
| [[64/33]]
| "
| "
| ([[33/17]])
| [[33/17]]
| '''[[31/16]]'''
| '''[[31/16]]'''
|-
|-
Line 2,650: Line 2,650:
| [[55/28]]
| [[55/28]]
| "
| "
| (''[[51/26]]'')
| ''[[51/26]]''
| "
| "
|-
|-
Line 2,710: Line 2,710:
| [[539/270]]
| [[539/270]]
| [[351/176]]
| [[351/176]]
| (''[[255/128]]'')
| ''[[255/128]]''
| "
| "
|-
|-
Retrieved from "https://en.xen.wiki/w/Table_of_270edo_intervals"