Ed12: Difference between revisions

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'''Ed12''' means '''Division of the Twelfth Harmonic ([[12/1]]) into n equal parts'''.
'''Ed12''' means '''Division of the Twelfth Harmonic ([[12/1]]) into n equal parts'''.


= Division of the twelfth harmonic into n equal parts =
== Overview ==
The twelfth harmonic is particularly wide as far as equivalences go. There are (at absolute most) ~3.1 dodecataves within the human hearing range; imagine if that were the case with octaves. If one does indeed deal with dodecatave equivalence, this fact shapes one's musical approach dramatically. Also, the ed12-[[edo]] correspondences fall particularly close to the harmonic series of the NTSC or PAL-M color subcarrier:
The twelfth harmonic is particularly wide as far as equivalences go. There are (at absolute most) ~3.1 dodecataves within the human hearing range; imagine if that were the case with octaves. If one does indeed deal with dodecatave equivalence, this fact shapes one's musical approach dramatically. Also, the ed12-[[edo]] correspondences fall particularly close to the harmonic series of the NTSC or PAL-M color subcarrier:


Line 291: Line 291:
|200.234216
|200.234216
|}
|}
== Table of Ed12s ==
=== 0…499 ===
{| class="wikitable center-all"
|+ style=white-space:nowrap | 0…99
| [[0ed12|0]]
| [[1ed12|1]]
| [[2ed12|2]]
| [[3ed12|3]]
| [[4ed12|4]]
| [[5ed12|5]]
| [[6ed12|6]]
| [[7ed12|7]]
| [[8ed12|8]]
| [[9ed12|9]]
|-
| [[10ed12|10]]
| [[11ed12|11]]
| [[12ed12|12]]
| [[13ed12|13]]
| [[14ed12|14]]
| [[15ed12|15]]
| [[16ed12|16]]
| [[17ed12|17]]
| [[18ed12|18]]
| [[19ed12|19]]
|-
| [[20ed12|20]]
| [[21ed12|21]]
| [[22ed12|22]]
| [[23ed12|23]]
| [[24ed12|24]]
| [[25ed12|25]]
| [[26ed12|26]]
| [[27ed12|27]]
| [[28ed12|28]]
| [[29ed12|29]]
|-
| [[30ed12|30]]
| [[31ed12|31]]
| [[32ed12|32]]
| [[33ed12|33]]
| [[34ed12|34]]
| [[35ed12|35]]
| [[36ed12|36]]
| [[37ed12|37]]
| [[38ed12|38]]
| [[39ed12|39]]
|-
| [[40ed12|40]]
| [[41ed12|41]]
| [[42ed12|42]]
| [[43ed12|43]]
| [[44ed12|44]]
| [[45ed12|45]]
| [[46ed12|46]]
| [[47ed12|47]]
| [[48ed12|48]]
| [[49ed12|49]]
|-
| [[50ed12|50]]
| [[51ed12|51]]
| [[52ed12|52]]
| [[53ed12|53]]
| [[54ed12|54]]
| [[55ed12|55]]
| [[56ed12|56]]
| [[57ed12|57]]
| [[58ed12|58]]
| [[59ed12|59]]
|-
| [[60ed12|60]]
| [[61ed12|61]]
| [[62ed12|62]]
| [[63ed12|63]]
| [[64ed12|64]]
| [[65ed12|65]]
| [[66ed12|66]]
| [[67ed12|67]]
| [[68ed12|68]]
| [[69ed12|69]]
|-
| [[70ed12|70]]
| [[71ed12|71]]
| [[72ed12|72]]
| [[73ed12|73]]
| [[74ed12|74]]
| [[75ed12|75]]
| [[76ed12|76]]
| [[77ed12|77]]
| [[78ed12|78]]
| [[79ed12|79]]
|-
| [[80ed12|80]]
| [[81ed12|81]]
| [[82ed12|82]]
| [[83ed12|83]]
| [[84ed12|84]]
| [[85ed12|85]]
| [[86ed12|86]]
| [[87ed12|87]]
| [[88ed12|88]]
| [[89ed12|89]]
|-
| [[90ed12|90]]
| [[91ed12|91]]
| [[92ed12|92]]
| [[93ed12|93]]
| [[94ed12|94]]
| [[95ed12|95]]
| [[96ed12|96]]
| [[97ed12|97]]
| [[98ed12|98]]
| [[99ed12|99]]
|}
{| class="wikitable center-all mw-collapsible mw-collapsed"
|+ style=white-space:nowrap | 100…199
| [[100ed12|100]]
| [[101ed12|101]]
| [[102ed12|102]]
| [[103ed12|103]]
| [[104ed12|104]]
| [[105ed12|105]]
| [[106ed12|106]]
| [[107ed12|107]]
| [[108ed12|108]]
| [[109ed12|109]]
|-
| [[110ed12|110]]
| [[111ed12|111]]
| [[112ed12|112]]
| [[113ed12|113]]
| [[114ed12|114]]
| [[115ed12|115]]
| [[116ed12|116]]
| [[117ed12|117]]
| [[118ed12|118]]
| [[119ed12|119]]
|-
| [[120ed12|120]]
| [[121ed12|121]]
| [[122ed12|122]]
| [[123ed12|123]]
| [[124ed12|124]]
| [[125ed12|125]]
| [[126ed12|126]]
| [[127ed12|127]]
| [[128ed12|128]]
| [[129ed12|129]]
|-
| [[130ed12|130]]
| [[131ed12|131]]
| [[132ed12|132]]
| [[133ed12|133]]
| [[134ed12|134]]
| [[135ed12|135]]
| [[136ed12|136]]
| [[137ed12|137]]
| [[138ed12|138]]
| [[139ed12|139]]
|-
| [[140ed12|140]]
| [[141ed12|141]]
| [[142ed12|142]]
| [[143ed12|143]]
| [[144ed12|144]]
| [[145ed12|145]]
| [[146ed12|146]]
| [[147ed12|147]]
| [[148ed12|148]]
| [[149ed12|149]]
|-
| [[150ed12|150]]
| [[151ed12|151]]
| [[152ed12|152]]
| [[153ed12|153]]
| [[154ed12|154]]
| [[155ed12|155]]
| [[156ed12|156]]
| [[157ed12|157]]
| [[158ed12|158]]
| [[159ed12|159]]
|-
| [[160ed12|160]]
| [[161ed12|161]]
| [[162ed12|162]]
| [[163ed12|163]]
| [[164ed12|164]]
| [[165ed12|165]]
| [[166ed12|166]]
| [[167ed12|167]]
| [[168ed12|168]]
| [[169ed12|169]]
|-
| [[170ed12|170]]
| [[171ed12|171]]
| [[172ed12|172]]
| [[173ed12|173]]
| [[174ed12|174]]
| [[175ed12|175]]
| [[176ed12|176]]
| [[177ed12|177]]
| [[178ed12|178]]
| [[179ed12|179]]
|-
| [[180ed12|180]]
| [[181ed12|181]]
| [[182ed12|182]]
| [[183ed12|183]]
| [[184ed12|184]]
| [[185ed12|185]]
| [[186ed12|186]]
| [[187ed12|187]]
| [[188ed12|188]]
| [[189ed12|189]]
|-
| [[190ed12|190]]
| [[191ed12|191]]
| [[192ed12|192]]
| [[193ed12|193]]
| [[194ed12|194]]
| [[195ed12|195]]
| [[196ed12|196]]
| [[197ed12|197]]
| [[198ed12|198]]
| [[199ed12|199]]
|}
{| class="wikitable center-all mw-collapsible mw-collapsed"
|+ style=white-space:nowrap | 200…299
| [[200ed12|200]]
| [[201ed12|201]]
| [[202ed12|202]]
| [[203ed12|203]]
| [[204ed12|204]]
| [[205ed12|205]]
| [[206ed12|206]]
| [[207ed12|207]]
| [[208ed12|208]]
| [[209ed12|209]]
|-
| [[210ed12|210]]
| [[211ed12|211]]
| [[212ed12|212]]
| [[213ed12|213]]
| [[214ed12|214]]
| [[215ed12|215]]
| [[216ed12|216]]
| [[217ed12|217]]
| [[218ed12|218]]
| [[219ed12|219]]
|-
| [[220ed12|220]]
| [[221ed12|221]]
| [[222ed12|222]]
| [[223ed12|223]]
| [[224ed12|224]]
| [[225ed12|225]]
| [[226ed12|226]]
| [[227ed12|227]]
| [[228ed12|228]]
| [[229ed12|229]]
|-
| [[230ed12|230]]
| [[231ed12|231]]
| [[232ed12|232]]
| [[233ed12|233]]
| [[234ed12|234]]
| [[235ed12|235]]
| [[236ed12|236]]
| [[237ed12|237]]
| [[238ed12|238]]
| [[239ed12|239]]
|-
| [[240ed12|240]]
| [[241ed12|241]]
| [[242ed12|242]]
| [[243ed12|243]]
| [[244ed12|244]]
| [[245ed12|245]]
| [[246ed12|246]]
| [[247ed12|247]]
| [[248ed12|248]]
| [[249ed12|249]]
|-
| [[250ed12|250]]
| [[251ed12|251]]
| [[252ed12|252]]
| [[253ed12|253]]
| [[254ed12|254]]
| [[255ed12|255]]
| [[256ed12|256]]
| [[257ed12|257]]
| [[258ed12|258]]
| [[259ed12|259]]
|-
| [[260ed12|260]]
| [[261ed12|261]]
| [[262ed12|262]]
| [[263ed12|263]]
| [[264ed12|264]]
| [[265ed12|265]]
| [[266ed12|266]]
| [[267ed12|267]]
| [[268ed12|268]]
| [[269ed12|269]]
|-
| [[270ed12|270]]
| [[271ed12|271]]
| [[272ed12|272]]
| [[273ed12|273]]
| [[274ed12|274]]
| [[275ed12|275]]
| [[276ed12|276]]
| [[277ed12|277]]
| [[278ed12|278]]
| [[279ed12|279]]
|-
| [[280ed12|280]]
| [[281ed12|281]]
| [[282ed12|282]]
| [[283ed12|283]]
| [[284ed12|284]]
| [[285ed12|285]]
| [[286ed12|286]]
| [[287ed12|287]]
| [[288ed12|288]]
| [[289ed12|289]]
|-
| [[290ed12|290]]
| [[291ed12|291]]
| [[292ed12|292]]
| [[293ed12|293]]
| [[294ed12|294]]
| [[295ed12|295]]
| [[296ed12|296]]
| [[297ed12|297]]
| [[298ed12|298]]
| [[299ed12|299]]
|}
{| class="wikitable center-all mw-collapsible mw-collapsed"
|+ style=white-space:nowrap | 300…399
| [[300ed12|300]]
| [[301ed12|301]]
| [[302ed12|302]]
| [[303ed12|303]]
| [[304ed12|304]]
| [[305ed12|305]]
| [[306ed12|306]]
| [[307ed12|307]]
| [[308ed12|308]]
| [[309ed12|309]]
|-
| [[310ed12|310]]
| [[311ed12|311]]
| [[312ed12|312]]
| [[313ed12|313]]
| [[314ed12|314]]
| [[315ed12|315]]
| [[316ed12|316]]
| [[317ed12|317]]
| [[318ed12|318]]
| [[319ed12|319]]
|-
| [[320ed12|320]]
| [[321ed12|321]]
| [[322ed12|322]]
| [[323ed12|323]]
| [[324ed12|324]]
| [[325ed12|325]]
| [[326ed12|326]]
| [[327ed12|327]]
| [[328ed12|328]]
| [[329ed12|329]]
|-
| [[330ed12|330]]
| [[331ed12|331]]
| [[332ed12|332]]
| [[333ed12|333]]
| [[334ed12|334]]
| [[335ed12|335]]
| [[336ed12|336]]
| [[337ed12|337]]
| [[338ed12|338]]
| [[339ed12|339]]
|-
| [[340ed12|340]]
| [[341ed12|341]]
| [[342ed12|342]]
| [[343ed12|343]]
| [[344ed12|344]]
| [[345ed12|345]]
| [[346ed12|346]]
| [[347ed12|347]]
| [[348ed12|348]]
| [[349ed12|349]]
|-
| [[350ed12|350]]
| [[351ed12|351]]
| [[352ed12|352]]
| [[353ed12|353]]
| [[354ed12|354]]
| [[355ed12|355]]
| [[356ed12|356]]
| [[357ed12|357]]
| [[358ed12|358]]
| [[359ed12|359]]
|-
| [[360ed12|360]]
| [[361ed12|361]]
| [[362ed12|362]]
| [[363ed12|363]]
| [[364ed12|364]]
| [[365ed12|365]]
| [[366ed12|366]]
| [[367ed12|367]]
| [[368ed12|368]]
| [[369ed12|369]]
|-
| [[370ed12|370]]
| [[371ed12|371]]
| [[372ed12|372]]
| [[373ed12|373]]
| [[374ed12|374]]
| [[375ed12|375]]
| [[376ed12|376]]
| [[377ed12|377]]
| [[378ed12|378]]
| [[379ed12|379]]
|-
| [[380ed12|380]]
| [[381ed12|381]]
| [[382ed12|382]]
| [[383ed12|383]]
| [[384ed12|384]]
| [[385ed12|385]]
| [[386ed12|386]]
| [[387ed12|387]]
| [[388ed12|388]]
| [[389ed12|389]]
|-
| [[390ed12|390]]
| [[391ed12|391]]
| [[392ed12|392]]
| [[393ed12|393]]
| [[394ed12|394]]
| [[395ed12|395]]
| [[396ed12|396]]
| [[397ed12|397]]
| [[398ed12|398]]
| [[399ed12|399]]
|}
{| class="wikitable center-all mw-collapsible mw-collapsed"
|+ style=white-space:nowrap | 400…499
| [[400ed12|400]]
| [[401ed12|401]]
| [[402ed12|402]]
| [[403ed12|403]]
| [[404ed12|404]]
| [[405ed12|405]]
| [[406ed12|406]]
| [[407ed12|407]]
| [[408ed12|408]]
| [[409ed12|409]]
|-
| [[410ed12|410]]
| [[411ed12|411]]
| [[412ed12|412]]
| [[413ed12|413]]
| [[414ed12|414]]
| [[415ed12|415]]
| [[416ed12|416]]
| [[417ed12|417]]
| [[418ed12|418]]
| [[419ed12|419]]
|-
| [[420ed12|420]]
| [[421ed12|421]]
| [[422ed12|422]]
| [[423ed12|423]]
| [[424ed12|424]]
| [[425ed12|425]]
| [[426ed12|426]]
| [[427ed12|427]]
| [[428ed12|428]]
| [[429ed12|429]]
|-
| [[430ed12|430]]
| [[431ed12|431]]
| [[432ed12|432]]
| [[433ed12|433]]
| [[434ed12|434]]
| [[435ed12|435]]
| [[436ed12|436]]
| [[437ed12|437]]
| [[438ed12|438]]
| [[439ed12|439]]
|-
| [[440ed12|440]]
| [[441ed12|441]]
| [[442ed12|442]]
| [[443ed12|443]]
| [[444ed12|444]]
| [[445ed12|445]]
| [[446ed12|446]]
| [[447ed12|447]]
| [[448ed12|448]]
| [[449ed12|449]]
|-
| [[450ed12|450]]
| [[451ed12|451]]
| [[452ed12|452]]
| [[453ed12|453]]
| [[454ed12|454]]
| [[455ed12|455]]
| [[456ed12|456]]
| [[457ed12|457]]
| [[458ed12|458]]
| [[459ed12|459]]
|-
| [[460ed12|460]]
| [[461ed12|461]]
| [[462ed12|462]]
| [[463ed12|463]]
| [[464ed12|464]]
| [[465ed12|465]]
| [[466ed12|466]]
| [[467ed12|467]]
| [[468ed12|468]]
| [[469ed12|469]]
|-
| [[470ed12|470]]
| [[471ed12|471]]
| [[472ed12|472]]
| [[473ed12|473]]
| [[474ed12|474]]
| [[475ed12|475]]
| [[476ed12|476]]
| [[477ed12|477]]
| [[478ed12|478]]
| [[479ed12|479]]
|-
| [[480ed12|480]]
| [[481ed12|481]]
| [[482ed12|482]]
| [[483ed12|483]]
| [[484ed12|484]]
| [[485ed12|485]]
| [[486ed12|486]]
| [[487ed12|487]]
| [[488ed12|488]]
| [[489ed12|489]]
|-
| [[490ed12|490]]
| [[491ed12|491]]
| [[492ed12|492]]
| [[493ed12|493]]
| [[494ed12|494]]
| [[495ed12|495]]
| [[496ed12|496]]
| [[497ed12|497]]
| [[498ed12|498]]
| [[499ed12|499]]
|}


[[Category:Edonoi]]
[[Category:Edonoi]]
[[Category:Ed12]]
[[Category:Ed12]]

Revision as of 22:24, 18 September 2024

Ed12 means Division of the Twelfth Harmonic (12/1) into n equal parts.

Overview

The twelfth harmonic is particularly wide as far as equivalences go. There are (at absolute most) ~3.1 dodecataves within the human hearing range; imagine if that were the case with octaves. If one does indeed deal with dodecatave equivalence, this fact shapes one's musical approach dramatically. Also, the ed12-edo correspondences fall particularly close to the harmonic series of the NTSC or PAL-M color subcarrier:

edo ed12 NTSC*n PAL-M*n
1 3.5849625 3.579545 MHz 3.575611 MHz
2 7.169925 7.158909 7.151222
3 10.7548875 10.7383635 10.726833
4 14.33985 14.317818 14.302444
5 17.9248125 17.8972725 17.878055
6 21.509775 21.476727 21.453666
7 25.0947375 25.0561815 25.029277
8 28.6797 28.635636 28.604888
9 32.2646625 32.2150905 32.180299
10 35.849625 35.79545 35.75611
11 39.4345875 39.374 39.331521
12 43.01955 42.953454 42.907332
13 46.6045125 46.5329085 46.482743
14 50.189475 50.112363 50.058554
15 53.7744375 53.6918175 53.634265
16 57.3594 57.271272 57.209776
17 60.9443625 60.8507265 60.785487
18 64.529325 64.430181 64.360598
19 68.1142875 68.0096355 67.936709
20 71.69925 71.58909 71.51222
21 75.2842125 75.1685445 75.087931
22 78.869175 78.747999 78.663442
23 82.4541375 82.3274535 82.239153
24 86.0391 85.906908 85.814664
25 89.6240625 89.4863625 89.390375
26 93.209025 93.065817 92.965886
27 96.7939875 96.6452715 96.541597
28 100.37895 100.224726 100.117108
29 103.9639125 103.8041805 103.692819
30 107.548875 107.38365 107.28633
31 111.1338375 110.9630895 110.894041
32 114.7188 114.542544 114.437552
33 118.3037625 118.1219985 118.045263
34 121.888725 121.701453 121.588774
35 125.4736875 125.2809075 125.096485
36 129.05865 128.860362 128.739296
37 132.6436125 132.4398165 132.247707
38 136.228575 136.019271 135.860518
39 139.8135375 139.5987255 135.398929
40 143.3985 143.17818 143.02444
41 146.41815 146.7576345 146.600151
42 150.568425 150.337089 150.175862
43 154.0533875 153.9165435 153.751373
44 157.73835 157.495998 157.326884
45 161.3233125 161.0754525 160.902595
46 164.908275 164.654907 164.478306
47 168.4932375 168.2343615 168.053817
48 172.0782 171.813816 171.629328
49 175.6631625 175.3932705 175.205039
50 179.248125 178.972725 178.78075
51 182.8330875 182.5521795 182.356261
52 186.41805 186.131634 185.931772
53 190.003125 189.7110885 189.507483
54 193.597975 193.290543 193.083194
55 197.1729375 196.869975 196.658705
56 200.7579 200.449452 200.234216

Table of Ed12s

0…499

0…99
0 1 2 3 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26 27 28 29
30 31 32 33 34 35 36 37 38 39
40 41 42 43 44 45 46 47 48 49
50 51 52 53 54 55 56 57 58 59
60 61 62 63 64 65 66 67 68 69
70 71 72 73 74 75 76 77 78 79
80 81 82 83 84 85 86 87 88 89
90 91 92 93 94 95 96 97 98 99
100…199
100 101 102 103 104 105 106 107 108 109
110 111 112 113 114 115 116 117 118 119
120 121 122 123 124 125 126 127 128 129
130 131 132 133 134 135 136 137 138 139
140 141 142 143 144 145 146 147 148 149
150 151 152 153 154 155 156 157 158 159
160 161 162 163 164 165 166 167 168 169
170 171 172 173 174 175 176 177 178 179
180 181 182 183 184 185 186 187 188 189
190 191 192 193 194 195 196 197 198 199
200…299
200 201 202 203 204 205 206 207 208 209
210 211 212 213 214 215 216 217 218 219
220 221 222 223 224 225 226 227 228 229
230 231 232 233 234 235 236 237 238 239
240 241 242 243 244 245 246 247 248 249
250 251 252 253 254 255 256 257 258 259
260 261 262 263 264 265 266 267 268 269
270 271 272 273 274 275 276 277 278 279
280 281 282 283 284 285 286 287 288 289
290 291 292 293 294 295 296 297 298 299
300…399
300 301 302 303 304 305 306 307 308 309
310 311 312 313 314 315 316 317 318 319
320 321 322 323 324 325 326 327 328 329
330 331 332 333 334 335 336 337 338 339
340 341 342 343 344 345 346 347 348 349
350 351 352 353 354 355 356 357 358 359
360 361 362 363 364 365 366 367 368 369
370 371 372 373 374 375 376 377 378 379
380 381 382 383 384 385 386 387 388 389
390 391 392 393 394 395 396 397 398 399
400…499
400 401 402 403 404 405 406 407 408 409
410 411 412 413 414 415 416 417 418 419
420 421 422 423 424 425 426 427 428 429
430 431 432 433 434 435 436 437 438 439
440 441 442 443 444 445 446 447 448 449
450 451 452 453 454 455 456 457 458 459
460 461 462 463 464 465 466 467 468 469
470 471 472 473 474 475 476 477 478 479
480 481 482 483 484 485 486 487 488 489
490 491 492 493 494 495 496 497 498 499
Retrieved from "https://en.xen.wiki/index.php?title=Ed12&oldid=155300"