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Superpartient ratio

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508: 449: 390: 33: 509: 450: 391: 226: 282: 497: 438: 379: 332: 97: 69: 567: 76: 50: 17: 116: 83: 65: 54: 544: 192: 588: 250: 166: 467: 408: 349: 302: 583: 90: 43: 285: 154: 146: 8: 149:. The term has fallen out of use in modern pure mathematics, but continues to be used in 558: 563: 442: 142: 577: 528: 150: 501: 383: 161: 32: 240: 535:"containing a whole and a fraction," literally "superpartient". 183: 284:
are also greater than one and fully reduced, but are called
255: 470: 411: 352: 305: 253: 195: 57:. Unsourced material may be challenged and removed. 491: 432: 373: 326: 276: 220: 575: 160:Superpartient ratios were written about by 214: 117:Learn how and when to remove this message 14: 576: 145:that is greater than one and is not 55:adding citations to reliable sources 26: 221:{\displaystyle {\frac {n+a}{n}}\,,} 24: 550: 25: 600: 277:{\displaystyle {\tfrac {n+1}{n}}} 492:{\displaystyle {\frac {5+3}{5}}} 433:{\displaystyle {\frac {4+3}{4}}} 374:{\displaystyle {\frac {3+2}{3}}} 327:{\displaystyle {\frac {n+a}{n}}} 31: 155:historical study of mathematics 42:needs additional citations for 13: 1: 545:Mathematics of musical scales 522: 7: 538: 527:"Superpartient" comes from 288:and are not superpartient. 173: 10: 605: 167:Introduction to Arithmetic 336:Related musical interval 556:Partch, Harry (1979). 493: 434: 375: 328: 286:superparticular ratios 278: 222: 494: 435: 376: 329: 279: 247:. Ratios of the form 223: 66:"Superpartient ratio" 468: 409: 350: 303: 251: 239:> 1) and is also 193: 180:superpartient number 135:superpartient number 51:improve this article 18:Superpartient number 293: 235:is greater than 1 ( 131:superpartient ratio 559:Genesis of a Music 489: 430: 371: 324: 291: 274: 272: 218: 178:Mathematically, a 129:In mathematics, a 589:Intervals (music) 568:978-0-306-80106-8 520: 519: 487: 428: 369: 322: 271: 212: 127: 126: 119: 101: 16:(Redirected from 596: 584:Rational numbers 516: 515: 514: 512: 498: 496: 495: 490: 488: 483: 472: 457: 456: 455: 453: 443:Harmonic seventh 439: 437: 436: 431: 429: 424: 413: 398: 397: 396: 394: 380: 378: 377: 372: 370: 365: 354: 333: 331: 330: 325: 323: 318: 307: 294: 290: 283: 281: 280: 275: 273: 267: 256: 227: 225: 224: 219: 213: 208: 197: 164:in his treatise 122: 115: 111: 108: 102: 100: 59: 35: 27: 21: 604: 603: 599: 598: 597: 595: 594: 593: 574: 573: 553: 551:Further reading 541: 525: 510: 507: 506: 473: 471: 469: 466: 465: 451: 448: 447: 414: 412: 410: 407: 406: 392: 389: 388: 355: 353: 351: 348: 347: 308: 306: 304: 301: 300: 257: 254: 252: 249: 248: 198: 196: 194: 191: 190: 176: 147:superparticular 143:rational number 133:, also called 123: 112: 106: 103: 60: 58: 48: 36: 23: 22: 15: 12: 11: 5: 602: 592: 591: 586: 572: 571: 552: 549: 548: 547: 540: 537: 524: 521: 518: 517: 504: 499: 486: 482: 479: 476: 463: 459: 458: 445: 440: 427: 423: 420: 417: 404: 400: 399: 386: 381: 368: 364: 361: 358: 345: 341: 340: 337: 334: 321: 317: 314: 311: 298: 270: 266: 263: 260: 229: 228: 217: 211: 207: 204: 201: 175: 172: 139:epimeric ratio 125: 124: 39: 37: 30: 9: 6: 4: 3: 2: 601: 590: 587: 585: 582: 581: 579: 569: 565: 561: 560: 555: 554: 546: 543: 542: 536: 534: 530: 513: 505: 503: 500: 484: 480: 477: 474: 464: 461: 460: 454: 446: 444: 441: 425: 421: 418: 415: 405: 402: 401: 395: 387: 385: 382: 366: 362: 359: 356: 346: 343: 342: 338: 335: 319: 315: 312: 309: 299: 296: 295: 289: 287: 268: 264: 261: 258: 246: 242: 238: 234: 215: 209: 205: 202: 199: 189: 188: 187: 185: 181: 171: 169: 168: 163: 158: 156: 152: 148: 144: 140: 136: 132: 121: 118: 110: 99: 96: 92: 89: 85: 82: 78: 75: 71: 68: –  67: 63: 62:Find sources: 56: 52: 46: 45: 40:This article 38: 34: 29: 28: 19: 557: 532: 526: 244: 236: 232: 230: 186:of the form 179: 177: 165: 159: 151:music theory 138: 134: 130: 128: 113: 104: 94: 87: 80: 73: 61: 49:Please help 44:verification 41: 502:Minor sixth 384:Major sixth 153:and in the 578:Categories 162:Nicomachus 107:April 2015 77:newspapers 531:ἐπιμερής 523:Etymology 292:Examples 562:, p.68. 539:See also 533:epimeres 174:Overview 241:coprime 141:, is a 91:scholar 566:  339:Audio 297:Ratio 231:where 93:  86:  79:  72:  64:  529:Greek 184:ratio 182:is a 98:JSTOR 84:books 564:ISBN 511:Play 452:Play 393:Play 70:news 462:8:5 403:7:4 344:5:3 243:to 170:. 137:or 53:by 580:: 157:. 570:. 485:5 481:3 478:+ 475:5 426:4 422:3 419:+ 416:4 367:3 363:2 360:+ 357:3 320:n 316:a 313:+ 310:n 269:n 265:1 262:+ 259:n 245:n 237:a 233:a 216:, 210:n 206:a 203:+ 200:n 120:) 114:( 109:) 105:( 95:· 88:· 81:· 74:· 47:. 20:)

Index

Superpartient number

verification
improve this article
adding citations to reliable sources
"Superpartient ratio"
news
newspapers
books
scholar
JSTOR
Learn how and when to remove this message
rational number
superparticular
music theory
historical study of mathematics
Nicomachus
Introduction to Arithmetic
ratio
coprime
superparticular ratios
Major sixth
Play
Harmonic seventh
Play
Minor sixth
Play
Greek
Mathematics of musical scales
Genesis of a Music

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