122:
49:
1573:
43:
27:
407:
to mean that which multiplied by a perfect fourth produces 27:20 (519.55 cents); his schisma divided into a perfect fifth produces 40:27 (680.45 cents), and a major sixth times a schisma is 27:16 (905.87 cents). However, by this definition a "schisma" would be what is better known as
201:
as the twelfth root of the
Pythagorean comma, or equivalently the difference between the justly tuned fifth (3:2) and the equally tempered fifth of 700 cents (2). This value, 1.955 cents, may be well approximated by converting the ratio 886:885 to cents. This interval is also sometimes
380:
123:
50:
269:
1294:
306:
1595:
637:
796:
557:
477:
449:
1086:
1066:
212:
1192:
1198:
906:
759:
722:
981:
1600:
1576:
1314:
1253:
630:
20:
1374:
851:
394:
668:
1369:
1180:
1556:
1309:
1216:
1210:
194:
8:
1339:
1204:
1186:
421:
276:
1452:
889:
623:
1508:
1394:
1334:
895:
871:
859:
840:
654:
553:
473:
445:
292:
280:
154:
89:
597:
1464:
1289:
1234:
1228:
1222:
1126:
1026:
999:
883:
865:
810:
804:
646:
493:
81:
35:
58:. Note that the note depicted lower on the staff (B#++) is higher in pitch (than C
1551:
1432:
1156:
944:
834:
828:
816:
577:
275:. This is because the difference between a grad and a schisma is so small. So, a
136:
1412:
1406:
1400:
1172:
699:
409:
272:
172:
85:
1589:
1536:
1385:
1304:
1299:
1245:
1106:
1046:
932:
920:
785:
748:
705:
545:
139:
31:
1503:
1364:
1010:
767:
730:
519:
303:
exceed seven octaves, and therefore fail to close, by the tiny interval of
116:
1513:
1344:
779:
773:
742:
736:
150:
143:
176:
1546:
1440:
938:
465:
188:
161:
1446:
950:
400:
183:
at the beginning of the 6th century in the 3rd book of his
1478:
926:
674:
180:
1484:
1458:
877:
822:
1541:
1518:
1426:
1420:
711:
693:
42:
375:{\displaystyle \ {\frac {\ 2^{161}\ }{\ 3^{84}\ 5^{12}\ }}\ ,}
914:
69:
615:
296:
26:
309:
215:
374:
263:
115:≈ 1.00113, which corresponds to 1.9537
1587:
30:Schisma as difference in cents between 8
631:
575:
283:may be obtained by flattening the fifth by a
543:
187:. Boethius was also the first to define the
1572:
638:
624:
584:. Encyclopedia of Microtonal Music Theory
135:the difference (in cents) between 8
179:) whose musical sense was introduced by
160:the ratio of the syntonic comma and the
41:
25:
299:. Twelve of these Kirnberger fifths of
1588:
996:
439:
619:
517:
264:{\displaystyle \ 2^{1/12}\ 5^{1/7}\ }
464:
95:which is slightly larger. It equals
576:Monzo, Joe; Rousseau, Kami (2005).
175:word meaning a split or crack (see
13:
14:
1612:
569:
1571:
494:"Logarithmic interval measures"
271:is very close to 4:3, the just
550:Contemplating Music: Substance
537:
511:
486:
458:
442:Music: A mathematical offering
433:
131:). It may also be defined as:
1:
645:
427:
1596:5-limit tuning and intervals
7:
1193:septimal chromatic semitone
470:Harvard Dictionary of Music
415:
93:( 531 441 : 524 288 ),
10:
1617:
1199:septimal diatonic semitone
987:(Numbers in brackets refer
18:
1569:
1527:
1494:
1383:
1353:
1323:
1280:
1271:
1244:
1171:
1154:
989:to fractional semitones.)
982:24-tone equal temperament
979:
968:
905:
850:
795:
758:
721:
686:
653:
291:, a fact first noted by
19:Not to be confused with
1577:List of pitch intervals
1315:Subminor and supermajor
1254:minor diatonic semitone
1164:refer to pitch ratios.)
386:of 0.01536 cents.
1375:Undecimal quarter tone
395:schismatic temperament
376:
265:
185:De institutione musica
65:
39:
1370:Septimal quarter tone
1181:septimal quarter tone
440:Benson, Dave (2006).
377:
301:16 384 : 10 935
266:
113:32 805 : 32 768
45:
29:
1557:Incomposite interval
1310:Pythagorean interval
1162:(Numbers in brackets
670:(Numbers in brackets
307:
213:
195:Andreas Werckmeister
142:plus a justly tuned
1340:Pythagorean apotome
1187:septimal third tone
598:"List of intervals"
518:Monzo, Joe (2005).
422:Twelfth root of two
277:rational intonation
146:and 5 octaves;
100: 5 × 3
38:and 5 octaves.
1453:Septimal semicomma
602:Huygens-Fokker.org
498:Huygens-Fokker.org
389:Tempering out the
384:atom of Kirnberger
372:
261:
66:
40:
1583:
1582:
1565:
1564:
1395:Pythagorean comma
1335:Pythagorean limma
1267:
1266:
1263:
1262:
1229:supermajor fourth
1205:supermajor second
1150:
1149:
964:
963:
960:
959:
672:are the number of
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364:
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349:
336:
331:
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312:
293:Johann Kirnberger
281:equal temperament
260:
239:
218:
155:Pythagorean limma
90:Pythagorean comma
1608:
1575:
1574:
1465:Septimal kleisma
1278:
1277:
1235:subminor seventh
1217:supermajor third
1169:
1168:
1157:Just intonations
1142:
1141:
1137:
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578:"Septimal-comma"
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88:(81:80) and the
63:
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57:
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53:
36:just major third
16:Musical interval
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1433:Septimal diesis
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552:. p. 523.
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492:
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480:
472:. p. 188.
463:
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444:. p. 171.
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106: 2
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5:
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1601:Commas (music)
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1427:Greater diesis
1424:
1417:
1416:
1413:Septimal comma
1410:
1407:Holdrian comma
1404:
1401:Syntonic comma
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1223:subminor fifth
1220:
1214:
1211:subminor third
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752:
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663:
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571:
570:External links
568:
566:
565:
558:
546:Dahlhaus, Carl
536:
510:
485:
478:
468:, ed. (1961).
457:
450:
431:
429:
426:
425:
424:
417:
414:
410:syntonic comma
403:used the word
371:
357:
353:
344:
340:
326:
322:
287:rather than a
273:perfect fourth
255:
251:
247:
243:
234:
230:
226:
222:
166:
165:
158:
147:
140:perfect fifths
86:syntonic comma
76:(also spelled
32:perfect fifths
15:
9:
6:
4:
3:
2:
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1602:
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1451:
1448:
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1428:
1425:
1422:
1421:Lesser diesis
1419:
1418:
1414:
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1408:
1405:
1402:
1399:
1396:
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1387:
1382:
1376:
1373:
1371:
1368:
1366:
1363:
1362:
1360:
1358:
1357:
1356:Quarter tones
1352:
1346:
1343:
1341:
1338:
1336:
1333:
1332:
1330:
1328:
1327:
1322:
1316:
1313:
1311:
1308:
1306:
1305:Pseudo-octave
1303:
1301:
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629:
627:
622:
621:
618:
603:
599:
595:
583:
582:TonalSoft.com
579:
574:
573:
561:
559:0-918728-60-6
555:
551:
547:
540:
525:
524:TonalSoft.com
521:
514:
499:
495:
489:
481:
479:0-674-37501-7
475:
471:
467:
461:
453:
451:0-521-85387-7
447:
443:
436:
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423:
420:
419:
413:
411:
406:
402:
398:
396:
392:
387:
385:
369:
355:
351:
342:
338:
324:
320:
298:
295:, a pupil of
294:
290:
286:
282:
278:
274:
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220:
207:
205:
200:
196:
192:
190:
186:
182:
178:
174:
170:
163:
159:
156:
152:
149:the ratio of
148:
145:
141:
138:
134:
133:
132:
127:
118:
91:
87:
83:
79:
75:
71:
54:
46:Schisma on C
44:
37:
33:
28:
22:
1528:
1495:
1481:(0.72 cents)
1475:(1.95 cents)
1472:
1455:(13.8 cents)
1449:(10.1 cents)
1443:(19.5 cents)
1435:(35.7 cents)
1429:(62.6 cents)
1423:(41.1 cents)
1415:(27.3 cents)
1409:(22.6 cents)
1403:(21.5 cents)
1397:(23.5 cents)
1384:
1365:Quarter tone
1355:
1354:
1325:
1324:
1281:
1246:Higher-limit
1161:
1155:
1067:major fourth
1011:quarter tone
986:
980:
669:
605:. Retrieved
601:
586:. Retrieved
581:
549:
544:Katz, Ruth;
539:
527:. Retrieved
523:
513:
501:. Retrieved
497:
488:
469:
460:
441:
435:
404:
399:
390:
388:
383:
288:
284:
208:
203:
198:
197:defined the
193:
184:
168:
167:
137:justly tuned
84:between the
77:
73:
67:
34:plus 1
1514:Millioctave
1496:Measurement
1487:(0.4 cents)
1467:(7.7 cents)
1461:(8.1 cents)
1345:Major limma
1087:minor fifth
393:leads to a
382:called the
279:version of
209:Curiously,
151:major limma
144:major third
1590:Categories
1547:Semiditone
1441:Diaschisma
1256:(17-limit)
947:(22 or 23)
945:fourteenth
941:(20 or 21)
939:thirteenth
935:(18 or 19)
929:(17 or 18)
923:(15 or 16)
917:(13 or 14)
852:Diminished
679:interval.)
660:(post-Bach
428:References
189:diaschisma
162:diaschisma
1509:Centitone
1447:Semicomma
1326:Semitones
1290:Microtone
1274:intervals
951:fifteenth
797:Augmented
675:semitones
647:Intervals
412:(81:80).
401:Descartes
202:called a
80:) is the
1479:Breedsma
927:eleventh
907:Compound
662:Western)
657:semitone
548:(1987).
466:Apel, W.
416:See also
181:Boethius
82:interval
61:♮
1485:Ragisma
1473:Schisma
1459:Kleisma
1295:5-limit
1201:(15:14)
1195:(21:20)
1189:(28:27)
1183:(36:35)
1173:7-limit
1138:⁄
1127:seventh
1118:⁄
1098:⁄
1078:⁄
1058:⁄
1038:⁄
1018:⁄
1000:Neutral
973:systems
933:twelfth
890:seventh
841:seventh
786:seventh
749:seventh
687:Perfect
655:Twelve-
405:schisma
391:schisma
285:schisma
204:schisma
169:Schisma
153:to the
109:
97:
78:skhisma
74:schisma
1542:Ditone
1529:Others
1519:Savart
1386:Commas
1282:Groups
1231:(10:7)
1027:second
971:tuning
896:octave
872:fourth
860:second
823:fourth
811:second
805:unison
768:second
731:second
712:octave
700:fourth
694:unison
677:in the
607:6 June
588:6 June
556:
529:6 June
520:"Grad"
503:6 June
476:
448:
367:
361:
348:
335:
330:
317:
311:
259:
238:
217:
177:schism
72:, the
21:Schism
1552:Secor
1300:Comma
1272:Other
1237:(7:4)
1225:(7:5)
1219:(9:7)
1213:(7:6)
1207:(8:7)
1107:sixth
1047:third
969:Other
921:tenth
915:ninth
884:sixth
878:fifth
866:third
835:sixth
829:fifth
817:third
780:sixth
774:third
760:Minor
743:sixth
737:third
723:Major
706:fifth
173:Greek
171:is a
117:cents
70:music
1537:Wolf
1504:Cent
953:(24)
898:(11)
843:(12)
837:(10)
788:(10)
751:(11)
714:(12)
609:2015
590:2015
554:ISBN
531:2015
505:2015
474:ISBN
446:ISBN
408:the
297:Bach
289:grad
199:grad
125:Play
52:Play
892:(9)
886:(7)
880:(6)
874:(4)
868:(2)
862:(0)
831:(8)
825:(6)
819:(5)
813:(3)
807:(1)
782:(8)
776:(3)
770:(1)
745:(9)
739:(4)
733:(2)
708:(7)
702:(5)
696:(0)
325:161
191:.
111:or
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