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Superpartient ratio

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

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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
ISBN

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