122:
1484:
396:
294:
157:
129:
275:, the chromatic semitone and diminished third are in fact represented by the same interval of 141.18 cents, which allows the minor third to be evenly divided in half. In
1205:
306:, such as 31-equal temperament, it will come close to that value; for instance in 31-equal temperament the diminished third is a cent sharp of 8/7.
450:
548:
516:
471:
279:, the diminished third is ~ 109 cents while the chromatic semitone is ~ 163 cents and the diatonic semitone is ~ 55 cents.
1506:
283:
997:
977:
1103:
1109:
419:
892:
201:
194:
181:. For instance, the interval from A to C is a minor third, three semitones wide, and both the intervals from A
1511:
1487:
1225:
1164:
541:
271:
In superpythagorean tunings, the diminished third is narrower than the major second. In the special case of
1285:
303:
1280:
1091:
322:
287:
232:
it has a more typical value of 232.3 cents. In a twelve-note keyboard tuned in a meantone tuning from E
1467:
1220:
1127:
1121:
707:
276:
272:
229:
221:
217:
25:
220:
tunings with fifths flatter than 700 cents, the diminished third is wider than the major second. In
1250:
1115:
1097:
1363:
800:
534:
310:
178:
1305:
1245:
806:
782:
770:
751:
565:
467:
446:
100:
1375:
1200:
1145:
1139:
1133:
1037:
937:
910:
817:
794:
721:
715:
557:
225:
166:
1343:
1067:
855:
745:
739:
727:
670:
633:
318:
314:
146:
142:
110:
83:
30:
1323:
1317:
1311:
1083:
610:
73:
121:
1500:
1447:
1296:
1215:
1210:
1156:
1017:
957:
843:
831:
696:
659:
616:
517:
A manual of harmony for use in music-schools and seminaries and for self-instruction
1462:
1419:
1414:
1275:
921:
678:
641:
213:
209:
93:
325:
thereby contain the diminished third as well. For example, a German sixth chord E
1424:
1255:
690:
684:
653:
647:
193:
are diminished thirds, two semitones wide. Being diminished, it is considered a
174:
1457:
1351:
849:
762:
205:
170:
1357:
861:
1389:
837:
585:
63:
1395:
1383:
1369:
788:
733:
1452:
1429:
1337:
1331:
622:
604:
286:
the diminished third is considered to approximate the interval of a
825:
120:
302:), with ratio 8/7, and in any meantone tuning in the vicinity of
496:, p.89-90. Thurgate & Sonsasaetd. Digitized August 16, 2007.
530:
526:
1438:
1405:
1294:
1264:
1234:
1191:
1182:
1155:
1082:
1065:
907:
890:
879:
816:
761:
706:
669:
632:
597:
579:
564:
109:
99:
92:
82:
72:
62:
57:
49:
41:
36:
24:
361:' which complements the augmented sixth between E
380:arises in the extended C major scale between F
224:it is in fact enharmonically equivalent to an
542:
8:
520:, p.165. Theodore Baker, trans. G. Schirmer.
19:
1483:
1188:
1079:
904:
887:
594:
576:
549:
535:
527:
244:, the dimininished third appears between C
228:, both having a value of 252.6 cents. In
437:
435:
464:The Mathematical Theory of Tone Systems
431:
349:' exhibits a diminished third between C
18:
443:Music: In Theory and Practice, Vol. I
7:
14:
505:Benward & Saker (2003), p.92.
1482:
494:Music: Its Theory & Practice
483:Haluska, ibid. Diminished third.
313:to the diminished third is the
1:
317:, and the numerous chords of
284:septimal meantone temperament
212:, both having a value of 200
88:144:125, 256:225, 65536:59049
441:Benward & Saker (2003).
1104:septimal chromatic semitone
474:. Classic diminished third.
1528:
1110:septimal diatonic semitone
898:(Numbers in brackets refer
420:List of meantone intervals
1480:
900:to fractional semitones.)
893:24-tone equal temperament
202:12-tone equal temperament
101:12-Tone equal temperament
1488:List of pitch intervals
1226:Subminor and supermajor
1165:minor diatonic semitone
1075:refer to pitch ratios.)
492:Hoffmann, F.A. (1881).
1286:Undecimal quarter tone
323:augmented sixth chords
311:complementary interval
304:quarter-comma meantone
204:a diminished third is
138:
1281:Septimal quarter tone
1092:septimal quarter tone
462:Haluska, Jan (2003).
378:just diminished third
288:septimal major second
256:, and again between G
187:to C, and from A to C
124:
1507:Diminished intervals
1468:Incomposite interval
1221:Pythagorean interval
1073:(Numbers in brackets
581:(Numbers in brackets
514:Paul, Oscar (1885).
277:22 equal temperament
273:17 equal temperament
230:31 equal temperament
222:19 equal temperament
1251:Pythagorean apotome
1098:septimal third tone
404:and between B and D
321:music described as
21:
1364:Septimal semicomma
179:chromatic semitone
139:
1494:
1493:
1476:
1475:
1306:Pythagorean comma
1246:Pythagorean limma
1178:
1177:
1174:
1173:
1140:supermajor fourth
1116:supermajor second
1061:
1060:
875:
874:
871:
870:
583:are the number of
451:978-0-07-294262-0
125:Diminished third
119:
118:
1519:
1486:
1485:
1376:Septimal kleisma
1189:
1146:subminor seventh
1128:supermajor third
1080:
1068:Just intonations
1053:
1052:
1048:
1045:
1033:
1032:
1028:
1025:
1013:
1012:
1008:
1005:
993:
992:
988:
985:
973:
972:
968:
965:
953:
952:
948:
945:
933:
932:
928:
905:
888:
595:
577:
551:
544:
537:
528:
521:
512:
506:
503:
497:
490:
484:
481:
475:
460:
454:
439:
409:
408:
403:
402:
401:
399:
391:
390:
385:
384:
372:
371:
366:
365:
360:
359:
354:
353:
348:
347:
342:
341:
336:
335:
330:
329:
301:
300:
299:
297:
267:
266:
261:
260:
255:
254:
249:
248:
243:
242:
237:
236:
226:augmented second
192:
191:
186:
185:
167:musical interval
164:
163:
162:
160:
151:diminished third
136:
135:
134:
132:
22:
20:diminished third
16:Musical interval
1527:
1526:
1522:
1521:
1520:
1518:
1517:
1516:
1497:
1496:
1495:
1490:
1472:
1434:
1401:
1344:Septimal diesis
1290:
1260:
1230:
1184:
1170:
1151:
1074:
1071:
1057:
1050:
1046:
1043:
1041:
1030:
1026:
1023:
1021:
1010:
1006:
1003:
1001:
990:
986:
983:
981:
970:
966:
963:
961:
950:
946:
943:
941:
930:
926:
925:
915:
914:
913:
909:
899:
896:
883:
881:
867:
812:
757:
702:
665:
628:
589:
584:
582:
572:
570:
567:
560:
555:
525:
524:
513:
509:
504:
500:
491:
487:
482:
478:
461:
457:
440:
433:
428:
416:
406:
405:
397:
395:
394:
393:
388:
387:
382:
381:
369:
368:
363:
362:
357:
356:
351:
350:
345:
344:
339:
338:
333:
332:
327:
326:
319:common practice
315:augmented sixth
295:
293:
292:
291:
264:
263:
258:
257:
252:
251:
246:
245:
240:
239:
234:
233:
189:
188:
183:
182:
158:
156:
155:
154:
147:Western culture
143:classical music
130:
128:
127:
126:
111:Just intonation
31:augmented sixth
17:
12:
11:
5:
1525:
1523:
1515:
1514:
1512:Thirds (music)
1509:
1499:
1498:
1492:
1491:
1481:
1478:
1477:
1474:
1473:
1471:
1470:
1465:
1460:
1455:
1450:
1444:
1442:
1436:
1435:
1433:
1432:
1427:
1422:
1417:
1411:
1409:
1403:
1402:
1400:
1399:
1393:
1387:
1380:
1379:
1373:
1367:
1361:
1355:
1348:
1347:
1341:
1338:Greater diesis
1335:
1328:
1327:
1324:Septimal comma
1321:
1318:Holdrian comma
1315:
1312:Syntonic comma
1309:
1302:
1300:
1292:
1291:
1289:
1288:
1283:
1278:
1272:
1270:
1262:
1261:
1259:
1258:
1253:
1248:
1242:
1240:
1232:
1231:
1229:
1228:
1223:
1218:
1213:
1208:
1203:
1197:
1195:
1186:
1180:
1179:
1176:
1175:
1172:
1171:
1169:
1168:
1161:
1159:
1153:
1152:
1150:
1149:
1143:
1137:
1134:subminor fifth
1131:
1125:
1122:subminor third
1119:
1113:
1107:
1101:
1095:
1088:
1086:
1077:
1063:
1062:
1059:
1058:
1056:
1055:
1035:
1015:
995:
975:
955:
935:
918:
916:
908:
902:
885:
877:
876:
873:
872:
869:
868:
866:
865:
859:
853:
847:
841:
835:
829:
822:
820:
814:
813:
811:
810:
804:
798:
792:
786:
780:
774:
767:
765:
759:
758:
756:
755:
749:
743:
737:
731:
725:
719:
712:
710:
704:
703:
701:
700:
694:
688:
682:
675:
673:
667:
666:
664:
663:
657:
651:
645:
638:
636:
630:
629:
627:
626:
620:
614:
608:
601:
599:
592:
574:
562:
561:
556:
554:
553:
546:
539:
531:
523:
522:
507:
498:
485:
476:
455:
430:
429:
427:
424:
423:
422:
415:
412:
216:. However, in
117:
116:
113:
107:
106:
103:
97:
96:
90:
89:
86:
80:
79:
76:
74:Interval class
70:
69:
66:
60:
59:
55:
54:
51:
47:
46:
43:
39:
38:
34:
33:
28:
15:
13:
10:
9:
6:
4:
3:
2:
1524:
1513:
1510:
1508:
1505:
1504:
1502:
1489:
1479:
1469:
1466:
1464:
1461:
1459:
1456:
1454:
1451:
1449:
1446:
1445:
1443:
1441:
1437:
1431:
1428:
1426:
1423:
1421:
1418:
1416:
1413:
1412:
1410:
1408:
1404:
1397:
1394:
1391:
1388:
1385:
1382:
1381:
1377:
1374:
1371:
1368:
1365:
1362:
1359:
1356:
1353:
1350:
1349:
1345:
1342:
1339:
1336:
1333:
1332:Lesser diesis
1330:
1329:
1325:
1322:
1319:
1316:
1313:
1310:
1307:
1304:
1303:
1301:
1299:
1298:
1293:
1287:
1284:
1282:
1279:
1277:
1274:
1273:
1271:
1269:
1268:
1267:Quarter tones
1263:
1257:
1254:
1252:
1249:
1247:
1244:
1243:
1241:
1239:
1238:
1233:
1227:
1224:
1222:
1219:
1217:
1216:Pseudo-octave
1214:
1212:
1209:
1207:
1204:
1202:
1199:
1198:
1196:
1194:
1190:
1187:
1181:
1166:
1163:
1162:
1160:
1158:
1154:
1147:
1144:
1141:
1138:
1135:
1132:
1129:
1126:
1123:
1120:
1117:
1114:
1111:
1108:
1105:
1102:
1099:
1096:
1093:
1090:
1089:
1087:
1085:
1081:
1078:
1076:
1070:
1069:
1064:
1039:
1036:
1019:
1016:
999:
996:
979:
976:
959:
956:
939:
936:
923:
920:
919:
917:
912:
906:
903:
901:
895:
894:
889:
886:
878:
863:
860:
857:
854:
851:
848:
845:
842:
839:
836:
833:
830:
827:
824:
823:
821:
819:
815:
808:
805:
802:
799:
796:
793:
790:
787:
784:
781:
778:
775:
772:
769:
768:
766:
764:
760:
753:
750:
747:
744:
741:
738:
735:
732:
729:
726:
723:
720:
717:
714:
713:
711:
709:
705:
698:
695:
692:
689:
686:
683:
680:
677:
676:
674:
672:
668:
661:
658:
655:
652:
649:
646:
643:
640:
639:
637:
635:
631:
624:
621:
618:
615:
612:
609:
606:
603:
602:
600:
596:
593:
591:
587:
578:
575:
569:
563:
559:
552:
547:
545:
540:
538:
533:
532:
529:
519:
518:
511:
508:
502:
499:
495:
489:
486:
480:
477:
473:
472:0-8247-4714-3
469:
465:
459:
456:
452:
448:
444:
438:
436:
432:
425:
421:
418:
417:
413:
411:
400:
379:
374:
324:
320:
316:
312:
307:
305:
298:
289:
285:
280:
278:
274:
269:
231:
227:
223:
219:
215:
211:
207:
203:
198:
196:
180:
176:
172:
168:
161:
152:
148:
144:
133:
123:
115:245, 223, 180
114:
112:
108:
104:
102:
98:
95:
91:
87:
85:
84:Just interval
81:
77:
75:
71:
67:
65:
61:
56:
52:
48:
44:
40:
35:
32:
29:
27:
23:
1439:
1406:
1392:(0.72 cents)
1386:(1.95 cents)
1366:(13.8 cents)
1360:(10.1 cents)
1354:(19.5 cents)
1346:(35.7 cents)
1340:(62.6 cents)
1334:(41.1 cents)
1326:(27.3 cents)
1320:(22.6 cents)
1314:(21.5 cents)
1308:(23.5 cents)
1295:
1276:Quarter tone
1266:
1265:
1236:
1235:
1192:
1157:Higher-limit
1072:
1066:
978:major fourth
922:quarter tone
897:
891:
776:
580:
515:
510:
501:
493:
488:
479:
463:
458:
442:
377:
375:
308:
281:
270:
210:major second
199:
169:produced by
150:
140:
50:Abbreviation
1425:Millioctave
1407:Measurement
1398:(0.4 cents)
1378:(7.7 cents)
1372:(8.1 cents)
1256:Major limma
998:minor fifth
175:minor third
42:Other names
1501:Categories
1458:Semiditone
1352:Diaschisma
1167:(17-limit)
858:(22 or 23)
856:fourteenth
852:(20 or 21)
850:thirteenth
846:(18 or 19)
840:(17 or 18)
834:(15 or 16)
828:(13 or 14)
763:Diminished
590:interval.)
571:(post-Bach
466:, p.xxvi.
426:References
206:enharmonic
197:interval.
1420:Centitone
1358:Semicomma
1237:Semitones
1201:Microtone
1185:intervals
862:fifteenth
708:Augmented
586:semitones
558:Intervals
208:with the
195:dissonant
171:narrowing
165:) is the
64:Semitones
1390:Breedsma
838:eleventh
818:Compound
573:Western)
568:semitone
445:, p.54.
414:See also
407:♭
389:♭
383:♯
370:♯
364:♭
358:♭
352:♯
346:♭
340:♯
334:♭
328:♭
265:♭
259:♯
253:♭
247:♯
241:♯
235:♭
218:meantone
190:♭
184:♯
1396:Ragisma
1384:Schisma
1370:Kleisma
1206:5-limit
1112:(15:14)
1106:(21:20)
1100:(28:27)
1094:(36:35)
1084:7-limit
1049:⁄
1038:seventh
1029:⁄
1009:⁄
989:⁄
969:⁄
949:⁄
929:⁄
911:Neutral
884:systems
844:twelfth
801:seventh
752:seventh
697:seventh
660:seventh
598:Perfect
566:Twelve-
26:Inverse
1453:Ditone
1440:Others
1430:Savart
1297:Commas
1193:Groups
1142:(10:7)
938:second
882:tuning
807:octave
783:fourth
771:second
734:fourth
722:second
716:unison
679:second
642:second
623:octave
611:fourth
605:unison
588:in the
470:
449:
1463:Secor
1211:Comma
1183:Other
1148:(7:4)
1136:(7:5)
1130:(9:7)
1124:(7:6)
1118:(8:7)
1018:sixth
958:third
880:Other
832:tenth
826:ninth
795:sixth
789:fifth
777:third
746:sixth
740:fifth
728:third
691:sixth
685:third
671:Minor
654:sixth
648:third
634:Major
617:fifth
386:and A
367:and C
355:and E
262:and B
250:and E
214:cents
177:by a
145:from
94:Cents
1448:Wolf
1415:Cent
864:(24)
809:(11)
754:(12)
748:(10)
699:(10)
662:(11)
625:(12)
468:ISBN
447:ISBN
398:Play
376:The
331:-G-B
309:The
296:play
238:to G
159:Play
149:, a
131:Play
58:Size
37:Name
803:(9)
797:(7)
791:(6)
785:(4)
779:(2)
773:(0)
742:(8)
736:(6)
730:(5)
724:(3)
718:(1)
693:(8)
687:(3)
681:(1)
656:(9)
650:(4)
644:(2)
619:(7)
613:(5)
607:(0)
282:In
200:In
141:In
105:200
1503::
1042:10
434:^
410:.
392:,
373:.
343:-E
337:-C
268:.
173:a
53:d3
1054:)
1051:2
1047:1
1044:+
1040:(
1034:)
1031:2
1027:1
1024:+
1022:8
1020:(
1014:)
1011:2
1007:1
1004:+
1002:6
1000:(
994:)
991:2
987:1
984:+
982:5
980:(
974:)
971:2
967:1
964:+
962:3
960:(
954:)
951:2
947:1
944:+
942:1
940:(
934:)
931:2
927:1
924:(
550:e
543:t
536:v
453:.
290:(
153:(
137:.
78:2
68:2
45:-
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
