Table of zeta-stretched edos: Difference between revisions
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| Line 12: | Line 12: | ||
=== Table === | === Table === | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! | !Tuning | ||
! | !Associated edo | ||
!No. of steps per 1200 cents | !No. of steps per 1200 cents | ||
!Step size (cents) | !Step size (cents) | ||
| Line 20: | Line 20: | ||
!Gram point index | !Gram point index | ||
|- | |- | ||
|[[1zpi]] | |||
|1edo | |1edo | ||
|1.127 | |1.127 | ||
|1064.774 | |1064.774 | ||
| Line 28: | Line 28: | ||
| -1 | | -1 | ||
|- | |- | ||
|[[2zpi]] | |||
|2edo | |2edo | ||
|1.972 | |1.972 | ||
|608.519 | |608.519 | ||
| Line 36: | Line 36: | ||
|0 | |0 | ||
|- | |- | ||
|[[4zpi]] | |||
|3edo | |3edo | ||
|3.06 | |3.06 | ||
|392.157 | |392.157 | ||
| Line 44: | Line 44: | ||
|2 | |2 | ||
|- | |- | ||
|[[6zpi]] | |||
|4edo | |4edo | ||
|3.904 | |3.904 | ||
|307.377 | |307.377 | ||
| Line 52: | Line 52: | ||
|4 | |4 | ||
|- | |- | ||
|[[9zpi]] | |||
|5edo | |5edo | ||
|5.034 | |5.034 | ||
|238.379 | |238.379 | ||
| Line 60: | Line 60: | ||
|7 | |7 | ||
|- | |- | ||
|[[12zpi]] | |||
|6edo | |6edo | ||
|6.035 | |6.035 | ||
|198.840 | |198.840 | ||
| Line 68: | Line 68: | ||
|10 | |10 | ||
|- | |- | ||
|[[15zpi]] | |||
|7edo | |7edo | ||
|6.957 | |6.957 | ||
|172.488 | |172.488 | ||
| Line 76: | Line 76: | ||
|13 | |13 | ||
|- | |- | ||
|[[19zpi]] | |||
|8edo | |8edo | ||
|8.137 | |8.137 | ||
|147.474 | |147.474 | ||
| Line 84: | Line 84: | ||
|17 | |17 | ||
|- | |- | ||
|[[22zpi]] | |||
|9edo | |9edo | ||
|8.95 | |8.95 | ||
|134.078 | |134.078 | ||
| Line 92: | Line 92: | ||
|20 | |20 | ||
|- | |- | ||
|[[26zpi]] | |||
|10edo | |10edo | ||
|10.008 | |10.008 | ||
|119.904 | |119.904 | ||
| Line 100: | Line 100: | ||
|24 | |24 | ||
|- | |- | ||
|[[30zpi]] | |||
|11edo | |11edo | ||
|11.037 | |11.037 | ||
|108.725 | |108.725 | ||
| Line 108: | Line 108: | ||
|28 | |28 | ||
|- | |- | ||
|[[34zpi]] | |||
|12edo | |12edo | ||
|12.023 | |12.023 | ||
|99.809 | |99.809 | ||
| Line 116: | Line 116: | ||
|32 | |32 | ||
|- | |- | ||
|[[38zpi]] | |||
|13edo | |13edo | ||
|12.969 | |12.969 | ||
|92.528 | |92.528 | ||
| Line 124: | Line 124: | ||
|36 | |36 | ||
|- | |- | ||
|[[42zpi]] | |||
|14edo | |14edo | ||
|13.9 | |13.9 | ||
|86.331 | |86.331 | ||
| Line 132: | Line 132: | ||
|40 | |40 | ||
|- | |- | ||
|[[47zpi]] | |||
|15edo | |15edo | ||
|15.053 | |15.053 | ||
|79.718 | |79.718 | ||
| Line 140: | Line 140: | ||
|45 | |45 | ||
|- | |- | ||
|[[51zpi]] | |||
|16edo | |16edo | ||
|15.945 | |15.945 | ||
|75.259 | |75.259 | ||
| Line 148: | Line 148: | ||
|49 | |49 | ||
|- | |- | ||
|[[56zpi]] | |||
|17edo | |17edo | ||
|17.045 | |17.045 | ||
|70.402 | |70.402 | ||
| Line 156: | Line 156: | ||
|54 | |54 | ||
|- | |- | ||
|[[61zpi]] | |||
|18edo | |18edo | ||
|18.119 | |18.119 | ||
|66.229 | |66.229 | ||
| Line 164: | Line 164: | ||
|59 | |59 | ||
|- | |- | ||
|[[65zpi]] | |||
|19edo | |19edo | ||
|18.948 | |18.948 | ||
|63.331 | |63.331 | ||
| Line 172: | Line 172: | ||
|63 | |63 | ||
|- | |- | ||
|[[70zpi]] | |||
|20edo | |20edo | ||
|19.982 | |19.982 | ||
|60.054 | |60.054 | ||
| Line 180: | Line 180: | ||
|68 | |68 | ||
|- | |- | ||
|[[75zpi]] | |||
|21edo | |21edo | ||
|21.028 | |21.028 | ||
|57.067 | |57.067 | ||
| Line 188: | Line 188: | ||
|73 | |73 | ||
|- | |- | ||
|[[80zpi]] | |||
|22edo | |22edo | ||
|22.025 | |22.025 | ||
|54.484 | |54.484 | ||
| Line 196: | Line 196: | ||
|78 | |78 | ||
|- | |- | ||
|[[84zpi]] | |||
|23edo (1st peak) | |23edo (1st peak) | ||
|22.807 | |22.807 | ||
|52.615 | |52.615 | ||
| Line 204: | Line 204: | ||
|82 | |82 | ||
|- | |- | ||
|[[85zpi]] | |||
|23edo (2nd peak) | |23edo (2nd peak) | ||
|23.026 | |23.026 | ||
|52.115 | |52.115 | ||
| Line 212: | Line 212: | ||
|83 | |83 | ||
|- | |- | ||
|[[90zpi]] | |||
|24edo | |24edo | ||
|24.006 | |24.006 | ||
|49.988 | |49.988 | ||
| Line 220: | Line 220: | ||
|88 | |88 | ||
|- | |- | ||
|[[95zpi]] | |||
|25edo | |25edo | ||
|24.965 | |24.965 | ||
|48.067 | |48.067 | ||
| Line 228: | Line 228: | ||
|93 | |93 | ||
|- | |- | ||
|[[100zpi]] | |||
|26edo | |26edo | ||
|25.936 | |25.936 | ||
|46.268 | |46.268 | ||
| Line 236: | Line 236: | ||
|98 | |98 | ||
|- | |- | ||
|[[106zpi]] | |||
|27edo | |27edo | ||
|27.087 | |27.087 | ||
|44.302 | |44.302 | ||
| Line 244: | Line 244: | ||
|104 | |104 | ||
|- | |- | ||
|[[111zpi]] | |||
|28edo | |28edo | ||
|28.032 | |28.032 | ||
|42.808 | |42.808 | ||
| Line 252: | Line 252: | ||
|109 | |109 | ||
|- | |- | ||
|[[116zpi]] | |||
|29edo | |29edo | ||
|28.94 | |28.94 | ||
|41.465 | |41.465 | ||
| Line 260: | Line 260: | ||
|114 | |114 | ||
|- | |- | ||
|[[122zpi]] | |||
|30edo | |30edo | ||
|30.062 | |30.062 | ||
|39.918 | |39.918 | ||
| Line 268: | Line 268: | ||
|120 | |120 | ||
|- | |- | ||
|[[127zpi]] | |||
|31edo | |31edo | ||
|30.978 | |30.978 | ||
|38.737 | |38.737 | ||
| Line 276: | Line 276: | ||
|125 | |125 | ||
|- | |- | ||
|[[133zpi]] | |||
|32edo | |32edo | ||
|32.07 | |32.07 | ||
|37.418 | |37.418 | ||
| Line 284: | Line 284: | ||
|131 | |131 | ||
|- | |- | ||
|[[138zpi]] | |||
|33edo | |33edo | ||
|32.972 | |32.972 | ||
|36.395 | |36.395 | ||
| Line 292: | Line 292: | ||
|136 | |136 | ||
|- | |- | ||
|[[144zpi]] | |||
|34edo | |34edo | ||
|34.045 | |34.045 | ||
|35.247 | |35.247 | ||
| Line 300: | Line 300: | ||
|142 | |142 | ||
|- | |- | ||
|[[149zpi]] | |||
|35edo | |35edo | ||
|34.926 | |34.926 | ||
|34.358 | |34.358 | ||
| Line 308: | Line 308: | ||
|147 | |147 | ||
|- | |- | ||
|[[155zpi]] | |||
|36edo | |36edo | ||
|35.982 | |35.982 | ||
|33.350 | |33.350 | ||
| Line 316: | Line 316: | ||
|153 | |153 | ||
|- | |- | ||
|[[161zpi]] | |||
|37edo | |37edo | ||
|37.027 | |37.027 | ||
|32.409 | |32.409 | ||
| Line 324: | Line 324: | ||
|159 | |159 | ||
|- | |- | ||
|[[166zpi]] | |||
|38edo (1st peak) | |38edo (1st peak) | ||
|37.89 | |37.89 | ||
|31.671 | |31.671 | ||
| Line 332: | Line 332: | ||
|164 | |164 | ||
|- | |- | ||
|[[167zpi]] | |||
|38edo (2nd peak) | |38edo (2nd peak) | ||
|38.103 | |38.103 | ||
|31.494 | |31.494 | ||
| Line 340: | Line 340: | ||
|165 | |165 | ||
|- | |- | ||
|[[172zpi]] | |||
|39edo (1st peak) | |39edo (1st peak) | ||
|38.916 | |38.916 | ||
|30.836 | |30.836 | ||
| Line 348: | Line 348: | ||
|170 | |170 | ||
|- | |- | ||
|[[173zpi]] | |||
|39edo (2nd peak) | |39edo (2nd peak) | ||
|39.124 | |39.124 | ||
|30.672 | |30.672 | ||
| Line 356: | Line 356: | ||
|171 | |171 | ||
|- | |- | ||
|[[178zpi]] | |||
|40edo | |40edo | ||
|39.968 | |39.968 | ||
|30.024 | |30.024 | ||
| Line 364: | Line 364: | ||
|176 | |176 | ||
|- | |- | ||
|[[184zpi]] | |||
|41edo | |41edo | ||
|40.988 | |40.988 | ||
|29.277 | |29.277 | ||
| Line 372: | Line 372: | ||
|182 | |182 | ||
|- | |- | ||
|[[190zpi]] | |||
|42edo | |42edo | ||
|41.999 | |41.999 | ||
|28.572 | |28.572 | ||
| Line 380: | Line 380: | ||
|188 | |188 | ||
|- | |- | ||
|[[196zpi]] | |||
|43edo | |43edo | ||
|43.027 | |43.027 | ||
|27.889 | |27.889 | ||
| Line 388: | Line 388: | ||
|194 | |194 | ||
|- | |- | ||
|[[202zpi]] | |||
|44edo | |44edo | ||
|44.015 | |44.015 | ||
|27.263 | |27.263 | ||
| Line 396: | Line 396: | ||
|200 | |200 | ||
|- | |- | ||
|[[207zpi]] | |||
|45edo (1st peak) | |45edo (1st peak) | ||
|44.84 | |44.84 | ||
|26.762 | |26.762 | ||
| Line 404: | Line 404: | ||
|205 | |205 | ||
|- | |- | ||
|[[208zpi]] | |||
|45edo (2nd peak) | |45edo (2nd peak) | ||
|45.035 | |45.035 | ||
|26.646 | |26.646 | ||
| Line 412: | Line 412: | ||
|206 | |206 | ||
|- | |- | ||
|[[214zpi]] | |||
|46edo | |46edo | ||
|46.009 | |46.009 | ||
|26.082 | |26.082 | ||
| Line 420: | Line 420: | ||
|212 | |212 | ||
|- | |- | ||
|[[220zpi]] | |||
|47edo | |47edo | ||
|47.006 | |47.006 | ||
|25.529 | |25.529 | ||
| Line 428: | Line 428: | ||
|218 | |218 | ||
|- | |- | ||
|[[226zpi]] | |||
|48edo | |48edo | ||
|47.988 | |47.988 | ||
|25.006 | |25.006 | ||
| Line 436: | Line 436: | ||
|224 | |224 | ||
|- | |- | ||
|[[232zpi]] | |||
|49edo (1st peak) | |49edo (1st peak) | ||
|48.945 | |48.945 | ||
|24.517 | |24.517 | ||
| Line 444: | Line 444: | ||
|230 | |230 | ||
|- | |- | ||
|[[233zpi]] | |||
|49edo (2nd peak) | |49edo (2nd peak) | ||
|49.141 | |49.141 | ||
|24.420 | |24.420 | ||
| Line 452: | Line 452: | ||
|231 | |231 | ||
|- | |- | ||
|[[238zpi]] | |||
|50edo | |50edo | ||
|49.939 | |49.939 | ||
|24.029 | |24.029 | ||
| Line 460: | Line 460: | ||
|236 | |236 | ||
|- | |- | ||
|[[245zpi]] | |||
|51edo | |51edo | ||
|51.079 | |51.079 | ||
|23.493 | |23.493 | ||
| Line 468: | Line 468: | ||
|243 | |243 | ||
|- | |- | ||
|[[251zpi]] | |||
|52edo | |52edo | ||
|52.043 | |52.043 | ||
|23.058 | |23.058 | ||
| Line 476: | Line 476: | ||
|249 | |249 | ||
|- | |- | ||
|[[257zpi]] | |||
|53edo | |53edo | ||
|52.997 | |52.997 | ||
|22.643 | |22.643 | ||
| Line 484: | Line 484: | ||
|255 | |255 | ||
|- | |- | ||
|[[263zpi]] | |||
|54edo (1st peak) | |54edo (1st peak) | ||
|53.949 | |53.949 | ||
|22.243 | |22.243 | ||
| Line 492: | Line 492: | ||
|261 | |261 | ||
|- | |- | ||
|[[264zpi]] | |||
|54edo (2nd peak) | |54edo (2nd peak) | ||
|54.116 | |54.116 | ||
|22.175 | |22.175 | ||
| Line 500: | Line 500: | ||
|262 | |262 | ||
|- | |- | ||
|[[269zpi]] | |||
|55edo | |55edo | ||
|54.894 | |54.894 | ||
|21.860 | |21.860 | ||
| Line 508: | Line 508: | ||
|267 | |267 | ||
|- | |- | ||
|[[276zpi]] | |||
|56edo | |56edo | ||
|56.008 | |56.008 | ||
|21.426 | |21.426 | ||
| Line 516: | Line 516: | ||
|274 | |274 | ||
|- | |- | ||
|[[282zpi]] | |||
|57edo | |57edo | ||
|56.968 | |56.968 | ||
|21.064 | |21.064 | ||
| Line 524: | Line 524: | ||
|280 | |280 | ||
|- | |- | ||
|[[289zpi]] | |||
|58edo | |58edo | ||
|58.067 | |58.067 | ||
|20.666 | |20.666 | ||
| Line 532: | Line 532: | ||
|287 | |287 | ||
|- | |- | ||
|[[295zpi]] | |||
|59edo | |59edo | ||
|58.992 | |58.992 | ||
|20.342 | |20.342 | ||
| Line 540: | Line 540: | ||
|293 | |293 | ||
|- | |- | ||
|[[301zpi]] | |||
|60edo | |60edo | ||
|59.92 | |59.92 | ||
|20.027 | |20.027 | ||
| Line 548: | Line 548: | ||
|299 | |299 | ||
|- | |- | ||
|[[308zpi]] | |||
|61edo | |61edo | ||
|61.003 | |61.003 | ||
|19.671 | |19.671 | ||
| Line 556: | Line 556: | ||
|306 | |306 | ||
|- | |- | ||
|[[314zpi]] | |||
|62edo | |62edo | ||
|61.938 | |61.938 | ||
|19.374 | |19.374 | ||
| Line 564: | Line 564: | ||
|312 | |312 | ||
|- | |- | ||
|[[321zpi]] | |||
|63edo | |63edo | ||
|63.019 | |63.019 | ||
|19.042 | |19.042 | ||
| Line 572: | Line 572: | ||
|319 | |319 | ||
|- | |- | ||
|[[328zpi]] | |||
|64edo | |64edo | ||
|64.099 | |64.099 | ||
|18.721 | |18.721 | ||
| Line 580: | Line 580: | ||
|326 | |326 | ||
|- | |- | ||
|[[334zpi]] | |||
|65edo | |65edo | ||
|65.016 | |65.016 | ||
|18.457 | |18.457 | ||
| Line 588: | Line 588: | ||
|332 | |332 | ||
|- | |- | ||
|[[340zpi]] | |||
|66edo | |66edo | ||
|65.916 | |65.916 | ||
|18.205 | |18.205 | ||
| Line 596: | Line 596: | ||
|338 | |338 | ||
|- | |- | ||
|[[347zpi]] | |||
|67edo | |67edo | ||
|66.998 | |66.998 | ||
|17.911 | |17.911 | ||
| Line 604: | Line 604: | ||
|345 | |345 | ||
|- | |- | ||
|[[354zpi]] | |||
|68edo | |68edo | ||
|68.049 | |68.049 | ||
|17.634 | |17.634 | ||
| Line 612: | Line 612: | ||
|352 | |352 | ||
|- | |- | ||
|[[360zpi]] | |||
|69edo | |69edo | ||
|68.96 | |68.96 | ||
|17.401 | |17.401 | ||
| Line 620: | Line 620: | ||
|358 | |358 | ||
|- | |- | ||
|[[367zpi]] | |||
|70edo | |70edo | ||
|70.004 | |70.004 | ||
|17.142 | |17.142 | ||
| Line 628: | Line 628: | ||
|365 | |365 | ||
|- | |- | ||
|[[374zpi]] | |||
|71edo | |71edo | ||
|71.059 | |71.059 | ||
|16.887 | |16.887 | ||
| Line 636: | Line 636: | ||
|372 | |372 | ||
|- | |- | ||
|[[380zpi]] | |||
|72edo | |72edo | ||
|71.951 | |71.951 | ||
|16.678 | |16.678 | ||
| Line 644: | Line 644: | ||
|378 | |378 | ||
|- | |- | ||
|[[387zpi]] | |||
|73edo | |73edo | ||
|72.984 | |72.984 | ||
|16.442 | |16.442 | ||
| Line 652: | Line 652: | ||
|385 | |385 | ||
|- | |- | ||
|[[394zpi]] | |||
|74edo | |74edo | ||
|74.052 | |74.052 | ||
|16.205 | |16.205 | ||
| Line 660: | Line 660: | ||
|392 | |392 | ||
|- | |- | ||
|[[401zpi]] | |||
|75edo | |75edo | ||
|75.091 | |75.091 | ||
|15.981 | |15.981 | ||
| Line 668: | Line 668: | ||
|399 | |399 | ||
|- | |- | ||
|[[407zpi]] | |||
|76edo | |76edo | ||
|75.968 | |75.968 | ||
|15.796 | |15.796 | ||
| Line 676: | Line 676: | ||
|405 | |405 | ||
|- | |- | ||
|[[414zpi]] | |||
|77edo | |77edo | ||
|76.992 | |76.992 | ||
|15.586 | |15.586 | ||
| Line 684: | Line 684: | ||
|412 | |412 | ||
|- | |- | ||
|[[420zpi]] | |||
|78edo | |78edo | ||
|78.021 | |78.021 | ||
|15.380 | |15.380 | ||
| Line 692: | Line 692: | ||
|418 | |418 | ||
|- | |- | ||
|[[427zpi]] | |||
|79edo | |79edo | ||
|78.892 | |78.892 | ||
|15.211 | |15.211 | ||
| Line 700: | Line 700: | ||
|425 | |425 | ||
|- | |- | ||
|[[435zpi]] | |||
|80edo | |80edo | ||
|80.073 | |80.073 | ||
|14.986 | |14.986 | ||
| Line 708: | Line 708: | ||
|433 | |433 | ||
|- | |- | ||
|[[441zpi]] | |||
|81edo | |81edo | ||
|80.947 | |80.947 | ||
|14.825 | |14.825 | ||
| Line 716: | Line 716: | ||
|439 | |439 | ||
|- | |- | ||
|[[448zpi]] | |||
|82edo | |82edo | ||
|81.954 | |81.954 | ||
|14.642 | |14.642 | ||
| Line 724: | Line 724: | ||
|446 | |446 | ||
|- | |- | ||
|[[455zpi]] | |||
|83edo | |83edo | ||
|82.967 | |82.967 | ||
|14.464 | |14.464 | ||
| Line 732: | Line 732: | ||
|453 | |453 | ||
|- | |- | ||
|[[462zpi]] | |||
|84edo | |84edo | ||
|83.997 | |83.997 | ||
|14.286 | |14.286 | ||
| Line 740: | Line 740: | ||
|460 | |460 | ||
|- | |- | ||
|[[469zpi]] | |||
|85edo | |85edo | ||
|84.991 | |84.991 | ||
|14.119 | |14.119 | ||
| Line 748: | Line 748: | ||
|467 | |467 | ||
|- | |- | ||
|[[476zpi]] | |||
|86edo | |86edo | ||
|86.019 | |86.019 | ||
|13.950 | |13.950 | ||
| Line 756: | Line 756: | ||
|474 | |474 | ||
|- | |- | ||
|[[483zpi]] | |||
|87edo | |87edo | ||
|87.014 | |87.014 | ||
|13.791 | |13.791 | ||
| Line 764: | Line 764: | ||
|481 | |481 | ||
|- | |- | ||
|[[490zpi]] | |||
|88edo | |88edo | ||
|88.027 | |88.027 | ||
|13.632 | |13.632 | ||
| Line 772: | Line 772: | ||
|488 | |488 | ||
|- | |- | ||
|[[497zpi]] | |||
|89edo | |89edo | ||
|89.023 | |89.023 | ||
|13.480 | |13.480 | ||
| Line 780: | Line 780: | ||
|495 | |495 | ||
|- | |- | ||
|[[504zpi]] | |||
|90edo | |90edo | ||
|90.006 | |90.006 | ||
|13.332 | |13.332 | ||
| Line 788: | Line 788: | ||
|502 | |502 | ||
|- | |- | ||
|[[510zpi]] | |||
|91edo (1st peak) | |91edo (1st peak) | ||
|90.852 | |90.852 | ||
|13.208 | |13.208 | ||
| Line 796: | Line 796: | ||
|508 | |508 | ||
|- | |- | ||
|[[511zpi]] | |||
|91edo (2nd peak) | |91edo (2nd peak) | ||
|91.033 | |91.033 | ||
|13.182 | |13.182 | ||
| Line 804: | Line 804: | ||
|509 | |509 | ||
|- | |- | ||
|[[518zpi]] | |||
|92edo | |92edo | ||
|91.993 | |91.993 | ||
|13.044 | |13.044 | ||
| Line 812: | Line 812: | ||
|516 | |516 | ||
|- | |- | ||
|[[525zpi]] | |||
|93edo | |93edo | ||
|93.002 | |93.002 | ||
|12.903 | |12.903 | ||
| Line 820: | Line 820: | ||
|523 | |523 | ||
|- | |- | ||
|[[532zpi]] | |||
|94edo | |94edo | ||
|93.984 | |93.984 | ||
|12.768 | |12.768 | ||
| Line 828: | Line 828: | ||
|530 | |530 | ||
|- | |- | ||
|[[539zpi]] | |||
|95edo (1st peak) | |95edo (1st peak) | ||
|94.962 | |94.962 | ||
|12.637 | |12.637 | ||
| Line 836: | Line 836: | ||
|537 | |537 | ||
|- | |- | ||
|[[540zpi]] | |||
|95edo (2nd peak) | |95edo (2nd peak) | ||
|95.117 | |95.117 | ||
|12.616 | |12.616 | ||
| Line 844: | Line 844: | ||
|538 | |538 | ||
|- | |- | ||
|[[546zpi]] | |||
|96edo | |96edo | ||
|95.954 | |95.954 | ||
|12.506 | |12.506 | ||
| Line 852: | Line 852: | ||
|544 | |544 | ||
|- | |- | ||
|[[553zpi]] | |||
|97edo | |97edo | ||
|96.925 | |96.925 | ||
|12.381 | |12.381 | ||
| Line 860: | Line 860: | ||
|551 | |551 | ||
|- | |- | ||
|[[560zpi]] | |||
|98edo | |98edo | ||
|97.923 | |97.923 | ||
|12.255 | |12.255 | ||
| Line 868: | Line 868: | ||
|558 | |558 | ||
|- | |- | ||
|[[568zpi]] | |||
|99edo | |99edo | ||
|99.047 | |99.047 | ||
|12.115 | |12.115 | ||
| Line 876: | Line 876: | ||
|566 | |566 | ||
|- | |- | ||
|[[575zpi]] | |||
|100edo | |100edo | ||
|100.024 | |100.024 | ||
|11.997 | |11.997 | ||
| Line 884: | Line 884: | ||
|573 | |573 | ||
|- | |- | ||
|[[1936zpi]] | |||
|270edo | |270edo | ||
|270.018 | |270.018 | ||
|4.444 | |4.444 | ||
| Line 892: | Line 892: | ||
|1934 | |1934 | ||
|- | |- | ||
|[[2293zpi]] | |||
|311edo | |311edo | ||
|311.004 | |311.004 | ||
|3.858 | |3.858 | ||
| Line 900: | Line 900: | ||
|2291 | |2291 | ||
|- | |- | ||
|[[2568zpi]] | |||
|342edo | |342edo | ||
|341.975 | |341.975 | ||
|3.509 | |3.509 | ||
| Line 908: | Line 908: | ||
|2566 | |2566 | ||
|- | |- | ||
|[[3971zpi]] | |||
|494edo | |494edo | ||
|494.014 | |494.014 | ||
|2.429 | |2.429 | ||
| Line 916: | Line 916: | ||
|3969 | |3969 | ||
|- | |- | ||
|[[5818zpi]] | |||
|684edo | |684edo | ||
|683.939 | |683.939 | ||
|1.755 | |1.755 | ||
Revision as of 05:55, 30 March 2024
This table lists tuning instructions for equal divisions of the octave which have been stretched or compressed using optimal octave stretch based on zeta peaks, as described here: the Riemann zeta function and tuning.
All of the tunings listed on this page are zeta peak index tunings, e.g. 1zpi, 2zpi, 3zpi... However, not all zeta peak index tunings are listed here - only those with intervals close to the octave. For a more complete table see: zeta peak index.
Calculation instructions
How to calculate the third column using the free version of Wolfram Cloud:
- Copy-paste Plot[Abs[RiemannSiegelZ[9.06472028x]], {x, 11.9,12.1}] into a cell.
- Change "11.9" and "12.1" to whatever values you want, e.g. to view the curve around 15edo you might use the values "14.9" and "15.1".
- Ensure that cell is still selected
- In the menu select Evaluation > Evaluate Cells
Table
| Tuning | Associated edo | No. of steps per 1200 cents | Step size (cents) | Octave size (cents) | Zeta peak height | Gram point index |
|---|---|---|---|---|---|---|
| 1zpi | 1edo | 1.127 | 1064.774 | 1064.774 | 1.6 | -1 |
| 2zpi | 2edo | 1.972 | 608.519 | 1217.039 | 2.3 | 0 |
| 4zpi | 3edo | 3.06 | 392.157 | 1176.471 | 2.8 | 2 |
| 6zpi | 4edo | 3.904 | 307.377 | 1229.508 | 3.0 | 4 |
| 9zpi | 5edo | 5.034 | 238.379 | 1191.895 | 3.7 | 7 |
| 12zpi | 6edo | 6.035 | 198.840 | 1193.041 | 2.9 | 10 |
| 15zpi | 7edo | 6.957 | 172.488 | 1207.417 | 4.2 | 13 |
| 19zpi | 8edo | 8.137 | 147.474 | 1179.796 | 3.6 | 17 |
| 22zpi | 9edo | 8.95 | 134.078 | 1206.704 | 4.0 | 20 |
| 26zpi | 10edo | 10.008 | 119.904 | 1199.041 | 4.5 | 24 |
| 30zpi | 11edo | 11.037 | 108.725 | 1195.977 | 2.7 | 28 |
| 34zpi | 12edo | 12.023 | 99.809 | 1197.704 | 5.2 | 32 |
| 38zpi | 13edo | 12.969 | 92.528 | 1202.868 | 3.1 | 36 |
| 42zpi | 14edo | 13.9 | 86.331 | 1208.633 | 4.6 | 40 |
| 47zpi | 15edo | 15.053 | 79.718 | 1195.775 | 5.1 | 45 |
| 51zpi | 16edo | 15.945 | 75.259 | 1204.139 | 4.2 | 49 |
| 56zpi | 17edo | 17.045 | 70.402 | 1196.832 | 5.1 | 54 |
| 61zpi | 18edo | 18.119 | 66.229 | 1192.119 | 3.5 | 59 |
| 65zpi | 19edo | 18.948 | 63.331 | 1203.293 | 6.0 | 63 |
| 70zpi | 20edo | 19.982 | 60.054 | 1201.081 | 3.4 | 68 |
| 75zpi | 21edo | 21.028 | 57.067 | 1198.402 | 4.1 | 73 |
| 80zpi | 22edo | 22.025 | 54.484 | 1198.638 | 6.1 | 78 |
| 84zpi | 23edo (1st peak) | 22.807 | 52.615 | 1210.148 | 3.7 | 82 |
| 85zpi | 23edo (2nd peak) | 23.026 | 52.115 | 1198.645 | 2.2 | 83 |
| 90zpi | 24edo | 24.006 | 49.988 | 1199.700 | 5.7 | 88 |
| 95zpi | 25edo | 24.965 | 48.067 | 1201.682 | 3.9 | 93 |
| 100zpi | 26edo | 25.936 | 46.268 | 1202.961 | 5.6 | 98 |
| 106zpi | 27edo | 27.087 | 44.302 | 1196.146 | 6.1 | 104 |
| 111zpi | 28edo | 28.032 | 42.808 | 1198.630 | 3.7 | 109 |
| 116zpi | 29edo | 28.94 | 41.465 | 1202.488 | 5.6 | 114 |
| 122zpi | 30edo | 30.062 | 39.918 | 1197.525 | 3.3 | 120 |
| 127zpi | 31edo | 30.978 | 38.737 | 1200.852 | 7.0 | 125 |
| 133zpi | 32edo | 32.07 | 37.418 | 1197.381 | 4.5 | 131 |
| 138zpi | 33edo | 32.972 | 36.395 | 1201.019 | 3.3 | 136 |
| 144zpi | 34edo | 34.045 | 35.247 | 1198.414 | 6.7 | 142 |
| 149zpi | 35edo | 34.926 | 34.358 | 1202.543 | 4.2 | 147 |
| 155zpi | 36edo | 35.982 | 33.350 | 1200.600 | 6.0 | 153 |
| 161zpi | 37edo | 37.027 | 32.409 | 1199.125 | 5.3 | 159 |
| 166zpi | 38edo (1st peak) | 37.89 | 31.671 | 1203.484 | 5.8 | 164 |
| 167zpi | 38edo (2nd peak) | 38.103 | 31.494 | 1196.756 | 2.5 | 165 |
| 172zpi | 39edo (1st peak) | 38.916 | 30.836 | 1202.590 | 2.6 | 170 |
| 173zpi | 39edo (2nd peak) | 39.124 | 30.672 | 1196.197 | 5.6 | 171 |
| 178zpi | 40edo | 39.968 | 30.024 | 1200.961 | 4.0 | 176 |
| 184zpi | 41edo | 40.988 | 29.277 | 1200.351 | 7.6 | 182 |
| 190zpi | 42edo | 41.999 | 28.572 | 1200.029 | 2.7 | 188 |
| 196zpi | 43edo | 43.027 | 27.889 | 1199.247 | 6.2 | 194 |
| 202zpi | 44edo | 44.015 | 27.263 | 1199.591 | 4.6 | 200 |
| 207zpi | 45edo (1st peak) | 44.84 | 26.762 | 1204.282 | 5.3 | 205 |
| 208zpi | 45edo (2nd peak) | 45.035 | 26.646 | 1199.067 | 2.1 | 206 |
| 214zpi | 46edo | 46.009 | 26.082 | 1199.765 | 7.5 | 212 |
| 220zpi | 47edo | 47.006 | 25.529 | 1199.847 | 4.3 | 218 |
| 226zpi | 48edo | 47.988 | 25.006 | 1200.300 | 5.8 | 224 |
| 232zpi | 49edo (1st peak) | 48.945 | 24.517 | 1201.348 | 2.2 | 230 |
| 233zpi | 49edo (2nd peak) | 49.141 | 24.420 | 1196.557 | 5.7 | 231 |
| 238zpi | 50edo | 49.939 | 24.029 | 1201.466 | 6.7 | 236 |
| 245zpi | 51edo | 51.079 | 23.493 | 1198.144 | 4.8 | 243 |
| 251zpi | 52edo | 52.043 | 23.058 | 1199.009 | 4.1 | 249 |
| 257zpi | 53edo | 52.997 | 22.643 | 1200.068 | 8.2 | 255 |
| 263zpi | 54edo (1st peak) | 53.949 | 22.243 | 1201.134 | 2.0 | 261 |
| 264zpi | 54edo (2nd peak) | 54.116 | 22.175 | 1197.428 | 3.5 | 262 |
| 269zpi | 55edo | 54.894 | 21.860 | 1202.317 | 5.3 | 267 |
| 276zpi | 56edo | 56.008 | 21.426 | 1199.829 | 6.1 | 274 |
| 282zpi | 57edo | 56.968 | 21.064 | 1200.674 | 4.9 | 280 |
| 289zpi | 58edo | 58.067 | 20.666 | 1198.615 | 7.8 | 287 |
| 295zpi | 59edo | 58.992 | 20.342 | 1200.163 | 4.0 | 293 |
| 301zpi | 60edo | 59.92 | 20.027 | 1201.602 | 7.1 | 299 |
| 308zpi | 61edo | 61.003 | 19.671 | 1199.941 | 3.7 | 306 |
| 314zpi | 62edo | 61.938 | 19.374 | 1201.201 | 6.3 | 312 |
| 321zpi | 63edo | 63.019 | 19.042 | 1199.638 | 6.8 | 319 |
| 328zpi | 64edo | 64.099 | 18.721 | 1198.147 | 3.6 | 326 |
| 334zpi | 65edo | 65.016 | 18.457 | 1199.705 | 7.8 | 332 |
| 340zpi | 66edo | 65.916 | 18.205 | 1201.529 | 4.5 | 338 |
| 347zpi | 67edo | 66.998 | 17.911 | 1200.036 | 5.3 | 345 |
| 354zpi | 68edo | 68.049 | 17.634 | 1199.136 | 7.7 | 352 |
| 360zpi | 69edo | 68.96 | 17.401 | 1200.696 | 4.1 | 358 |
| 367zpi | 70edo | 70.004 | 17.142 | 1199.931 | 5.7 | 365 |
| 374zpi | 71edo | 71.059 | 16.887 | 1199.004 | 3.8 | 372 |
| 380zpi | 72edo | 71.951 | 16.678 | 1200.817 | 9.2 | 378 |
| 387zpi | 73edo | 72.984 | 16.442 | 1200.263 | 3.4 | 385 |
| 394zpi | 74edo | 74.052 | 16.205 | 1199.157 | 5.1 | 392 |
| 401zpi | 75edo | 75.091 | 15.981 | 1198.546 | 6.0 | 399 |
| 407zpi | 76edo | 75.968 | 15.796 | 1200.505 | 2.6 | 405 |
| 414zpi | 77edo | 76.992 | 15.586 | 1200.125 | 8.2 | 412 |
| 420zpi | 78edo | 78.021 | 15.380 | 1199.677 | 5.4 | 418 |
| 427zpi | 79edo | 78.892 | 15.211 | 1201.643 | 5.8 | 425 |
| 435zpi | 80edo | 80.073 | 14.986 | 1198.906 | 7.9 | 433 |
| 441zpi | 81edo | 80.947 | 14.825 | 1200.786 | 5.2 | 439 |
| 448zpi | 82edo | 81.954 | 14.642 | 1200.674 | 6.7 | 446 |
| 455zpi | 83edo | 82.967 | 14.464 | 1200.477 | 3.9 | 453 |
| 462zpi | 84edo | 83.997 | 14.286 | 1200.043 | 8.0 | 460 |
| 469zpi | 85edo | 84.991 | 14.119 | 1200.127 | 3.0 | 467 |
| 476zpi | 86edo | 86.019 | 13.950 | 1199.735 | 2.4 | 474 |
| 483zpi | 87edo | 87.014 | 13.791 | 1199.807 | 8.9 | 481 |
| 490zpi | 88edo | 88.027 | 13.632 | 1199.632 | 2.6 | 488 |
| 497zpi | 89edo | 89.023 | 13.480 | 1199.690 | 7.6 | 495 |
| 504zpi | 90edo | 90.006 | 13.332 | 1199.920 | 4.8 | 502 |
| 510zpi | 91edo (1st peak) | 90.852 | 13.208 | 1201.955 | 6.7 | 508 |
| 511zpi | 91edo (2nd peak) | 91.033 | 13.182 | 1199.565 | 3.4 | 509 |
| 518zpi | 92edo | 91.993 | 13.044 | 1200.091 | 4.5 | 516 |
| 525zpi | 93edo | 93.002 | 12.903 | 1199.974 | 5.6 | 523 |
| 532zpi | 94edo | 93.984 | 12.768 | 1200.204 | 8.8 | 530 |
| 539zpi | 95edo (1st peak) | 94.962 | 12.637 | 1200.480 | 0.9 | 537 |
| 540zpi | 95edo (2nd peak) | 95.117 | 12.616 | 1198.524 | 5.3 | 538 |
| 546zpi | 96edo | 95.954 | 12.506 | 1200.575 | 7.3 | 544 |
| 553zpi | 97edo | 96.925 | 12.381 | 1200.929 | 4.2 | 551 |
| 560zpi | 98edo | 97.923 | 12.255 | 1200.944 | 4.3 | 558 |
| 568zpi | 99edo | 99.047 | 12.115 | 1199.431 | 9.4 | 566 |
| 575zpi | 100edo | 100.024 | 11.997 | 1199.712 | 4.3 | 573 |
| 1936zpi | 270edo | 270.018 | 4.444 | 1199.920 | 13.4 | 1934 |
| 2293zpi | 311edo | 311.004 | 3.858 | 1199.985 | 13.1 | 2291 |
| 2568zpi | 342edo | 341.975 | 3.509 | 1200.088 | 13.5 | 2566 |
| 3971zpi | 494edo | 494.014 | 2.429 | 1199.966 | 14.7 | 3969 |
| 5818zpi | 684edo | 683.939 | 1.755 | 1200.107 | 14.3 | 5816 |