126:
43:
1360:
37:
56:
201:, the major tone and minor tone are replaced by a "mean tone" which is somewhere in between the two. Two of these tones make a ditone or major third. This major third is exactly the just (5:4) major third in quarter-comma meantone. This is the source of the name: the note exactly halfway between the bounding tones of the major third is called the "
95:. The size of a ditone varies according to the sizes of the two tones of which it is compounded. The largest is the Pythagorean ditone, with a ratio of 81:64, also called a comma-redundant major third; the smallest is the interval with a ratio of 100:81, also called a comma-deficient major third.
127:
44:
217:. For example, "In modern acoustics, the equal-tempered semitone has 100 cents, the tone 200 cents, the ditone or major third 400 cents, the perfect fourth 500 cents, and so on. …”
143:, etc.) is more properly known as the Pythagorean ditone and consists of two major and two minor semitones (2M+2m). This is the interval that is extremely sharp, at 408c (the
189:
of 9:8 and 10:9, respectively. The difference between the two systems is that
Didymus places the minor tone below the major, whereas Ptolemy does the opposite.
312:, second edition, revised and expanded; Publications of the Early Music Institute (Bloomington and Indianapolis: Indiana University Press, 2007), p.281.
388:, edited by Gerard Assayag, Hans Georg Feichtinger, and José Francesco Rodrigues, 1–17 (Berlin, Heidelberg, and New York: Springer, 2002): 5.
1081:
123:(81/80, 21.51 cents). Because it is a comma wider than a "perfect" major third of 5:4, it is called a "comma-redundant" interval.
17:
1387:
338:
317:
280:
424:
182:
1392:
583:
372:
393:
873:
853:
333:(East Lansing: Michigan State College Press, 1951): 21. Paperback reprint (Mineola, NY: Dover Books, 2004)
275:(East Lansing: Michigan State College Press, 1951): v. Paperback reprint (Mineola, NY: Dover Books, 2004).
979:
985:
693:
546:
509:
768:
1382:
1397:
1363:
1101:
1040:
417:
294:
The Cyclopædia, or
Universal Dictionary of Arts, Sciences, and Literature. In Thirty-Nine Volumes
257:
The Cyclopædia, or
Universal Dictionary of Arts, Sciences, and Literature. In Thirty-Nine Volumes
186:
1161:
638:
305:
213:
Modern writers occasionally use the word "ditone" to describe the interval of a major third in
165:
of the 81:64 ditone is 3^4/2^6 (or 3/1 * 3/1 * 3/1 * 3/1 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2).
80:
455:
185:
tunings, the ditone is a just major third with a ratio of 5:4, made up of two unequal tones—a
1156:
967:
1343:
1096:
1003:
997:
268:
236:
198:
174:
8:
1126:
991:
973:
1239:
676:
410:
108:
1295:
1181:
1121:
682:
658:
646:
627:
441:
389:
334:
313:
276:
214:
119:(9/8 or 203.91 cents) and is wider than a just major third (5/4, 386.31 cents) by a
1251:
1076:
1021:
1015:
1009:
913:
813:
786:
670:
652:
597:
591:
433:
88:
1338:
1219:
943:
731:
621:
615:
603:
1199:
1193:
1187:
959:
486:
120:
72:
1376:
1323:
1172:
1091:
1086:
1032:
893:
833:
719:
707:
572:
535:
492:
368:
151:
1290:
1151:
797:
554:
517:
162:
112:
1300:
1131:
566:
560:
529:
523:
92:
31:
1333:
1227:
725:
384:
Manuel Pedro
Ferreira, "Proportions in Ancient and Medieval Music", in
231:
116:
1233:
737:
1265:
713:
461:
296:, vol. 13 (London: Longman, Hurst, Rees, Orme, & Brown, 1819) .
259:, vol. 12 (London: Longman, Hurst, Rees, Orme, & Brown, 1819) .
1271:
1259:
1245:
664:
609:
226:
178:
1305:
1213:
1207:
498:
480:
155:
137:"The major third that appears commonly in the system (C–E, D–F
350:
Mimi
Waitzman, "Meantone Temperament in Theory and Practice",
36:
701:
64:
402:
202:
55:
111:, which has an interval ratio of 81:64, which is 407.82
115:. The Pythagorean ditone is evenly divisible by two
386:
1374:
365:The New Grove Dictionary of Music and Musicians
150:It may also be thought of as four justly tuned
59:Pythagorean ditone as four just perfect fifths
418:
331:Tuning and Temperament: A Historical Survey
273:Tuning and Temperament: A Historical Survey
1359:
425:
411:
354:5, no. 4 (May 1981): 3–15. Citation on 4.
310:A Performer's Guide to Renaissance Music
54:
35:
192:
14:
1375:
783:
406:
375:(London: Macmillan Publishers, 2001).
98:
255:Abraham Rees, "Ditone, Ditonum", in
208:
24:
168:
25:
1409:
292:Abraham Rees, "Inconcinnous", in
1358:
378:
357:
344:
323:
299:
286:
262:
249:
13:
1:
432:
242:
1388:3-limit tuning and intervals
367:, second edition, edited by
147:major third is only 386c)."
7:
980:septimal chromatic semitone
220:
10:
1414:
986:septimal diatonic semitone
774:(Numbers in brackets refer
84:
29:
1393:Just tuning and intervals
1356:
1314:
1281:
1170:
1140:
1110:
1067:
1058:
1031:
958:
941:
776:to fractional semitones.)
769:24-tone equal temperament
766:
755:
692:
637:
582:
545:
508:
473:
440:
87:, "of two tones") is the
40:Pythagorean ditone on C
1364:List of pitch intervals
1102:Subminor and supermajor
1041:minor diatonic semitone
951:refer to pitch ratios.)
18:Pythagorean major third
1162:Undecimal quarter tone
363:Anonymous, "Ditonus",
329:James Murray Barbour,
187:major and a minor tone
107:is the major third in
76:
60:
52:
1157:Septimal quarter tone
968:septimal quarter tone
306:Jeffrey T. Kite-Powel
199:meantone temperaments
58:
39:
1344:Incomposite interval
1097:Pythagorean interval
949:(Numbers in brackets
457:(Numbers in brackets
269:James Murray Barbour
237:Pythagorean interval
193:Meantone temperament
1127:Pythagorean apotome
974:septimal third tone
163:prime factorization
1240:Septimal semicomma
109:Pythagorean tuning
105:Pythagorean ditone
99:Pythagorean tuning
61:
53:
1370:
1369:
1352:
1351:
1182:Pythagorean comma
1122:Pythagorean limma
1054:
1053:
1050:
1049:
1016:supermajor fourth
992:supermajor second
937:
936:
751:
750:
747:
746:
459:are the number of
339:978-0-486-43406-3
318:978-0-253-34866-1
281:978-0-486-43406-3
215:equal temperament
209:Equal temperament
27:Interval in music
16:(Redirected from
1405:
1362:
1361:
1252:Septimal kleisma
1065:
1064:
1022:subminor seventh
1004:supermajor third
956:
955:
944:Just intonations
929:
928:
924:
921:
909:
908:
904:
901:
889:
888:
884:
881:
869:
868:
864:
861:
849:
848:
844:
841:
829:
828:
824:
821:
809:
808:
804:
781:
780:
764:
763:
471:
470:
453:
452:
427:
420:
413:
404:
403:
397:
382:
376:
361:
355:
348:
342:
327:
321:
303:
297:
290:
284:
266:
260:
253:
177:'s diatonic and
142:
141:
134:
133:
132:
130:
86:
51:
50:
49:
47:
21:
1413:
1412:
1408:
1407:
1406:
1404:
1403:
1402:
1383:Major intervals
1373:
1372:
1371:
1366:
1348:
1310:
1277:
1220:Septimal diesis
1166:
1136:
1106:
1060:
1046:
1027:
950:
947:
933:
926:
922:
919:
917:
906:
902:
899:
897:
886:
882:
879:
877:
866:
862:
859:
857:
846:
842:
839:
837:
826:
822:
819:
817:
806:
802:
801:
791:
790:
789:
785:
775:
772:
759:
757:
743:
688:
633:
578:
541:
504:
465:
460:
458:
448:
446:
443:
436:
431:
401:
400:
383:
379:
362:
358:
349:
345:
328:
324:
304:
300:
291:
287:
267:
263:
254:
250:
245:
223:
211:
195:
171:
169:Just intonation
139:
138:
128:
125:
124:
101:
45:
42:
41:
34:
28:
23:
22:
15:
12:
11:
5:
1411:
1401:
1400:
1398:Thirds (music)
1395:
1390:
1385:
1368:
1367:
1357:
1354:
1353:
1350:
1349:
1347:
1346:
1341:
1336:
1331:
1326:
1320:
1318:
1312:
1311:
1309:
1308:
1303:
1298:
1293:
1287:
1285:
1279:
1278:
1276:
1275:
1269:
1263:
1256:
1255:
1249:
1243:
1237:
1231:
1224:
1223:
1217:
1214:Greater diesis
1211:
1204:
1203:
1200:Septimal comma
1197:
1194:Holdrian comma
1191:
1188:Syntonic comma
1185:
1178:
1176:
1168:
1167:
1165:
1164:
1159:
1154:
1148:
1146:
1138:
1137:
1135:
1134:
1129:
1124:
1118:
1116:
1108:
1107:
1105:
1104:
1099:
1094:
1089:
1084:
1079:
1073:
1071:
1062:
1056:
1055:
1052:
1051:
1048:
1047:
1045:
1044:
1037:
1035:
1029:
1028:
1026:
1025:
1019:
1013:
1010:subminor fifth
1007:
1001:
998:subminor third
995:
989:
983:
977:
971:
964:
962:
953:
939:
938:
935:
934:
932:
931:
911:
891:
871:
851:
831:
811:
794:
792:
784:
778:
761:
753:
752:
749:
748:
745:
744:
742:
741:
735:
729:
723:
717:
711:
705:
698:
696:
690:
689:
687:
686:
680:
674:
668:
662:
656:
650:
643:
641:
635:
634:
632:
631:
625:
619:
613:
607:
601:
595:
588:
586:
580:
579:
577:
576:
570:
564:
558:
551:
549:
543:
542:
540:
539:
533:
527:
521:
514:
512:
506:
505:
503:
502:
496:
490:
484:
477:
475:
468:
450:
438:
437:
430:
429:
422:
415:
407:
399:
398:
377:
356:
352:In Theory Only
343:
322:
298:
285:
261:
247:
246:
244:
241:
240:
239:
234:
229:
222:
219:
210:
207:
194:
191:
170:
167:
121:syntonic comma
100:
97:
26:
9:
6:
4:
3:
2:
1410:
1399:
1396:
1394:
1391:
1389:
1386:
1384:
1381:
1380:
1378:
1365:
1355:
1345:
1342:
1340:
1337:
1335:
1332:
1330:
1327:
1325:
1322:
1321:
1319:
1317:
1313:
1307:
1304:
1302:
1299:
1297:
1294:
1292:
1289:
1288:
1286:
1284:
1280:
1273:
1270:
1267:
1264:
1261:
1258:
1257:
1253:
1250:
1247:
1244:
1241:
1238:
1235:
1232:
1229:
1226:
1225:
1221:
1218:
1215:
1212:
1209:
1208:Lesser diesis
1206:
1205:
1201:
1198:
1195:
1192:
1189:
1186:
1183:
1180:
1179:
1177:
1175:
1174:
1169:
1163:
1160:
1158:
1155:
1153:
1150:
1149:
1147:
1145:
1144:
1143:Quarter tones
1139:
1133:
1130:
1128:
1125:
1123:
1120:
1119:
1117:
1115:
1114:
1109:
1103:
1100:
1098:
1095:
1093:
1092:Pseudo-octave
1090:
1088:
1085:
1083:
1080:
1078:
1075:
1074:
1072:
1070:
1066:
1063:
1057:
1042:
1039:
1038:
1036:
1034:
1030:
1023:
1020:
1017:
1014:
1011:
1008:
1005:
1002:
999:
996:
993:
990:
987:
984:
981:
978:
975:
972:
969:
966:
965:
963:
961:
957:
954:
952:
946:
945:
940:
915:
912:
895:
892:
875:
872:
855:
852:
835:
832:
815:
812:
799:
796:
795:
793:
788:
782:
779:
777:
771:
770:
765:
762:
754:
739:
736:
733:
730:
727:
724:
721:
718:
715:
712:
709:
706:
703:
700:
699:
697:
695:
691:
684:
681:
678:
675:
672:
669:
666:
663:
660:
657:
654:
651:
648:
645:
644:
642:
640:
636:
629:
626:
623:
620:
617:
614:
611:
608:
605:
602:
599:
596:
593:
590:
589:
587:
585:
581:
574:
571:
568:
565:
562:
559:
556:
553:
552:
550:
548:
544:
537:
534:
531:
528:
525:
522:
519:
516:
515:
513:
511:
507:
500:
497:
494:
491:
488:
485:
482:
479:
478:
476:
472:
469:
467:
463:
454:
451:
445:
439:
435:
428:
423:
421:
416:
414:
409:
408:
405:
395:
391:
387:
381:
374:
370:
369:Stanley Sadie
366:
360:
353:
347:
340:
336:
332:
326:
319:
315:
311:
307:
302:
295:
289:
282:
278:
274:
270:
265:
258:
252:
248:
238:
235:
233:
230:
228:
225:
224:
218:
216:
206:
204:
200:
190:
188:
184:
180:
176:
166:
164:
159:
157:
153:
148:
146:
135:
131:
122:
118:
114:
110:
106:
96:
94:
90:
82:
81:Ancient Greek
78:
74:
70:
66:
57:
48:
38:
33:
19:
1328:
1315:
1282:
1268:(0.72 cents)
1262:(1.95 cents)
1242:(13.8 cents)
1236:(10.1 cents)
1230:(19.5 cents)
1222:(35.7 cents)
1216:(62.6 cents)
1210:(41.1 cents)
1202:(27.3 cents)
1196:(22.6 cents)
1190:(21.5 cents)
1184:(23.5 cents)
1171:
1152:Quarter tone
1142:
1141:
1112:
1111:
1068:
1033:Higher-limit
948:
942:
854:major fourth
798:quarter tone
773:
767:
456:
385:
380:
373:John Tyrrell
364:
359:
351:
346:
330:
325:
309:
301:
293:
288:
272:
264:
256:
251:
212:
196:
172:
160:
149:
144:
136:
104:
102:
68:
62:
1301:Millioctave
1283:Measurement
1274:(0.4 cents)
1254:(7.7 cents)
1248:(8.1 cents)
1132:Major limma
874:minor fifth
117:major tones
93:major third
32:Major third
1377:Categories
1334:Semiditone
1228:Diaschisma
1043:(17-limit)
734:(22 or 23)
732:fourteenth
728:(20 or 21)
726:thirteenth
722:(18 or 19)
716:(17 or 18)
710:(15 or 16)
704:(13 or 14)
639:Diminished
466:interval.)
447:(post-Bach
394:3540437274
243:References
154:minus two
30:See also:
1296:Centitone
1234:Semicomma
1113:Semitones
1077:Microtone
1061:intervals
738:fifteenth
584:Augmented
462:semitones
434:Intervals
1266:Breedsma
714:eleventh
694:Compound
449:Western)
444:semitone
221:See also
183:syntonic
140:♯
89:interval
1272:Ragisma
1260:Schisma
1246:Kleisma
1082:5-limit
988:(15:14)
982:(21:20)
976:(28:27)
970:(36:35)
960:7-limit
925:⁄
914:seventh
905:⁄
885:⁄
865:⁄
845:⁄
825:⁄
805:⁄
787:Neutral
760:systems
720:twelfth
677:seventh
628:seventh
573:seventh
536:seventh
474:Perfect
442:Twelve-
227:Tritone
205:tone".
179:Ptolemy
175:Didymus
156:octaves
85:δίτονος
79:, from
77:ditonus
1329:Ditone
1316:Others
1306:Savart
1173:Commas
1069:Groups
1018:(10:7)
814:second
758:tuning
683:octave
659:fourth
647:second
610:fourth
598:second
592:unison
555:second
518:second
499:octave
487:fourth
481:unison
464:in the
392:
337:
316:
279:
152:fifths
69:ditone
1339:Secor
1087:Comma
1059:Other
1024:(7:4)
1012:(7:5)
1006:(9:7)
1000:(7:6)
994:(8:7)
894:sixth
834:third
756:Other
708:tenth
702:ninth
671:sixth
665:fifth
653:third
622:sixth
616:fifth
604:third
567:sixth
561:third
547:Minor
530:sixth
524:third
510:Major
493:fifth
113:cents
91:of a
73:Latin
65:music
1324:Wolf
1291:Cent
740:(24)
685:(11)
630:(12)
624:(10)
575:(10)
538:(11)
501:(12)
390:ISBN
371:and
335:ISBN
314:ISBN
277:ISBN
232:Tone
203:mean
161:The
145:pure
129:Play
103:The
67:, a
46:Play
679:(9)
673:(7)
667:(6)
661:(4)
655:(2)
649:(0)
618:(8)
612:(6)
606:(5)
600:(3)
594:(1)
569:(8)
563:(3)
557:(1)
532:(9)
526:(4)
520:(2)
495:(7)
489:(5)
483:(0)
308:l,
197:In
181:'s
173:In
158:.
63:In
1379::
918:10
271:,
83::
75::
930:)
927:2
923:1
920:+
916:(
910:)
907:2
903:1
900:+
898:8
896:(
890:)
887:2
883:1
880:+
878:6
876:(
870:)
867:2
863:1
860:+
858:5
856:(
850:)
847:2
843:1
840:+
838:3
836:(
830:)
827:2
823:1
820:+
818:1
816:(
810:)
807:2
803:1
800:(
426:e
419:t
412:v
396:.
341:.
320:.
283:.
71:(
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
