132:
1547:
156:
139:
351:-comma meantone will give four septimal thirds among the twelve major thirds of the tuning; this entails that three septimal major triads appear along with one chord containing a septimal major third with an ordinary minor third above it, making up a
226:
280:
183:
242:
147:
148:
326:
between its third and fifth ( 3:2 / 9:7 = 7:6 ). Similarly, the septimal major third is the interval between the third and the fifth of the septimal minor triad.
1268:
488:
361:
has a very close match to this interval. In this temperament, four fifths minus two octaves equals a septimal major third, not an ordinary major third.
568:
1569:
611:
555:
470:
386:
210:
is the musical interval exactly or approximately equal to a just 9:7 ratio of frequencies, or alternately 14:11. It is equal to 435
322:
chord. The septimal major triad can also be represented by the ratio 14:18:21. The septimal major triad contains an interval of a
517:
1060:
1040:
146:
1166:
257:
This interval has a characteristic brassy sound which is much less sweet than a pure major third, but is classed as a
1172:
955:
408:
1574:
205:
1579:
1550:
1288:
1227:
604:
403:
1348:
572:
1343:
1154:
456:
219:
196:
1530:
1283:
1184:
770:
483:
358:
330:
323:
251:
25:
1313:
1178:
1160:
333:
era the interval made its appearance as the alternative major third in remote keys, under the name
1426:
863:
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526:
461:
425:
155:
138:
1368:
1308:
869:
845:
833:
814:
628:
551:
466:
382:
334:
100:
1438:
1263:
1208:
1202:
1196:
1100:
1000:
973:
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857:
839:
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620:
497:
417:
338:
131:
1406:
1130:
918:
808:
802:
790:
733:
696:
254:
map the septimal major third and the septimal narrow fourth (21:16) to the same interval.
120:
83:
1386:
1380:
1374:
1146:
673:
73:
30:
1563:
1510:
1359:
1278:
1273:
1219:
1080:
1020:
906:
894:
759:
722:
679:
399:
266:
258:
161:
1525:
1482:
1477:
1338:
984:
741:
704:
262:
235:
211:
110:
93:
515:
Ellis, Alexander J. (1877). "On the measurement and settlement of musical pitch".
145:
1487:
1318:
753:
747:
716:
710:
215:
1520:
1414:
912:
825:
352:
1420:
924:
165:
501:
238:
the septimal major third is approximated by 9 quarter tones, or 450 cents (
1452:
900:
648:
63:
530:
1458:
1446:
1432:
851:
796:
429:
1515:
1492:
1400:
1394:
685:
667:
289:
421:
888:
173:
130:
593:
589:
152:
This, "extremely large third", is also found between C and E
292:
rather than otonal chord, being an inverted 6:7:9, i.e. a
406:'s extended Just Intonation: A guide for interpreters".
337:. Tunings of the meantone fifth in the neighborhood of
288:. However, in terms of the overtone series, this is a
1501:
1468:
1357:
1327:
1297:
1254:
1245:
1218:
1145:
1128:
970:
953:
942:
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824:
769:
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660:
642:
627:
119:
109:
99:
92:
82:
72:
62:
57:
49:
41:
36:
24:
486:(1880). "Notes of observations on musical beats".
548:Cooking with Csound: Woodwind and Brass Recipes
605:
8:
19:
452:
450:
448:
45:Supermajor third, Septimal supermajor third
1546:
1251:
1142:
967:
950:
657:
639:
612:
598:
590:
489:Proceedings of the Royal Society of London
542:
540:
379:The Mathematical Theory of Tone Systems
370:
18:
7:
546:Andrew Horner, Lydia Ayres (2002).
14:
1545:
154:
143:
137:
518:Journal of the Society of Arts
261:consonance. Together with the
1:
1570:7-limit tuning and intervals
1167:septimal chromatic semitone
457:Hermann L. F. von Helmholtz
135:9/7 major third from C to E
1596:
1173:septimal diatonic semitone
961:(Numbers in brackets refer
1543:
963:to fractional semitones.)
956:24-tone equal temperament
409:Perspectives of New Music
275:septimal supermajor triad
201:septimal supermajor third
111:24-Tone equal temperament
101:12-Tone equal temperament
442:Fonville (1991), p. 128.
269:of 3:2, it makes up the
1551:List of pitch intervals
1289:Subminor and supermajor
1228:minor diatonic semitone
1138:refer to pitch ratios.)
558:. "Super-Major Second".
389:. Septimal major third.
1349:Undecimal quarter tone
569:""Just Chord Tunings""
502:10.1098/rspl.1879.0155
214:, sharper than a just
169:
1344:Septimal quarter tone
1155:septimal quarter tone
377:Haluska, Jan (2003).
220:septimal quarter tone
197:Hermann von Helmholtz
134:
1531:Incomposite interval
1284:Pythagorean interval
1136:(Numbers in brackets
644:(Numbers in brackets
496:(200–205): 520–533.
359:22 equal temperament
324:septimal minor third
271:septimal major triad
252:19 equal temperament
178:septimal major third
31:septimal minor sixth
20:Septimal major third
1314:Pythagorean apotome
1161:septimal third tone
484:Ellis, Alexander J.
160:and may resemble a
21:
1427:Septimal semicomma
462:Sensations of Tone
191:, also called the
170:
1557:
1556:
1539:
1538:
1369:Pythagorean comma
1309:Pythagorean limma
1241:
1240:
1237:
1236:
1203:supermajor fourth
1179:supermajor second
1124:
1123:
938:
937:
934:
933:
646:are the number of
525:(1279): 664–687.
335:diminished fourth
149:
129:
128:
1587:
1549:
1548:
1439:Septimal kleisma
1252:
1209:subminor seventh
1191:supermajor third
1143:
1131:Just intonations
1116:
1115:
1111:
1108:
1096:
1095:
1091:
1088:
1076:
1075:
1071:
1068:
1056:
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1048:
1036:
1035:
1031:
1028:
1016:
1015:
1011:
1008:
996:
995:
991:
968:
951:
658:
640:
614:
607:
600:
591:
584:
583:
581:
580:
571:. Archived from
565:
559:
544:
535:
534:
512:
506:
505:
480:
474:
454:
443:
440:
434:
433:
402:(Summer 1991). "
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321:
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306:
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300:
296:
287:
286:
285:
283:
249:
248:
247:
245:
233:
232:
231:
229:
203:, and sometimes
193:supermajor third
190:
189:
188:
186:
159:
158:
151:
150:
142:
141:
22:
16:Musical interval
1595:
1594:
1590:
1589:
1588:
1586:
1585:
1584:
1575:Major intervals
1560:
1559:
1558:
1553:
1535:
1497:
1464:
1407:Septimal diesis
1353:
1323:
1293:
1247:
1233:
1214:
1137:
1134:
1120:
1113:
1109:
1106:
1104:
1093:
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820:
765:
728:
691:
652:
647:
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635:
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630:
623:
618:
588:
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578:
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567:
566:
562:
545:
538:
514:
513:
509:
482:
481:
477:
455:
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437:
398:
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376:
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367:
347:
343:
342:
318:
314:
313:
308:
304:
303:
298:
294:
293:
281:
279:
278:
277:
250:). Both 24 and
243:
241:
240:
239:
227:
225:
224:
223:
199:among others),
184:
182:
181:
180:
153:
144:
136:
121:Just intonation
17:
12:
11:
5:
1593:
1591:
1583:
1582:
1580:Thirds (music)
1577:
1572:
1562:
1561:
1555:
1554:
1544:
1541:
1540:
1537:
1536:
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1518:
1513:
1507:
1505:
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1465:
1463:
1462:
1456:
1450:
1443:
1442:
1436:
1430:
1424:
1418:
1411:
1410:
1404:
1401:Greater diesis
1398:
1391:
1390:
1387:Septimal comma
1384:
1381:Holdrian comma
1378:
1375:Syntonic comma
1372:
1365:
1363:
1355:
1354:
1352:
1351:
1346:
1341:
1335:
1333:
1325:
1324:
1322:
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1316:
1311:
1305:
1303:
1295:
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1276:
1271:
1266:
1260:
1258:
1249:
1243:
1242:
1239:
1238:
1235:
1234:
1232:
1231:
1224:
1222:
1216:
1215:
1213:
1212:
1206:
1200:
1197:subminor fifth
1194:
1188:
1185:subminor third
1182:
1176:
1170:
1164:
1158:
1151:
1149:
1140:
1126:
1125:
1122:
1121:
1119:
1118:
1098:
1078:
1058:
1038:
1018:
998:
981:
979:
971:
965:
948:
940:
939:
936:
935:
932:
931:
929:
928:
922:
916:
910:
904:
898:
892:
885:
883:
877:
876:
874:
873:
867:
861:
855:
849:
843:
837:
830:
828:
822:
821:
819:
818:
812:
806:
800:
794:
788:
782:
775:
773:
767:
766:
764:
763:
757:
751:
745:
738:
736:
730:
729:
727:
726:
720:
714:
708:
701:
699:
693:
692:
690:
689:
683:
677:
671:
664:
662:
655:
637:
625:
624:
619:
617:
616:
609:
602:
594:
586:
585:
560:
536:
507:
475:
444:
435:
422:10.2307/833435
416:(2): 106–137.
391:
369:
368:
366:
363:
127:
126:
123:
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:
1592:
1581:
1578:
1576:
1573:
1571:
1568:
1567:
1565:
1552:
1542:
1532:
1529:
1527:
1524:
1522:
1519:
1517:
1514:
1512:
1509:
1508:
1506:
1504:
1500:
1494:
1491:
1489:
1486:
1484:
1481:
1479:
1476:
1475:
1473:
1471:
1467:
1460:
1457:
1454:
1451:
1448:
1445:
1444:
1440:
1437:
1434:
1431:
1428:
1425:
1422:
1419:
1416:
1413:
1412:
1408:
1405:
1402:
1399:
1396:
1395:Lesser diesis
1393:
1392:
1388:
1385:
1382:
1379:
1376:
1373:
1370:
1367:
1366:
1364:
1362:
1361:
1356:
1350:
1347:
1345:
1342:
1340:
1337:
1336:
1334:
1332:
1331:
1330:Quarter tones
1326:
1320:
1317:
1315:
1312:
1310:
1307:
1306:
1304:
1302:
1301:
1296:
1290:
1287:
1285:
1282:
1280:
1279:Pseudo-octave
1277:
1275:
1272:
1270:
1267:
1265:
1262:
1261:
1259:
1257:
1253:
1250:
1244:
1229:
1226:
1225:
1223:
1221:
1217:
1210:
1207:
1204:
1201:
1198:
1195:
1192:
1189:
1186:
1183:
1180:
1177:
1174:
1171:
1168:
1165:
1162:
1159:
1156:
1153:
1152:
1150:
1148:
1144:
1141:
1139:
1133:
1132:
1127:
1102:
1099:
1082:
1079:
1062:
1059:
1042:
1039:
1022:
1019:
1002:
999:
986:
983:
982:
980:
975:
969:
966:
964:
958:
957:
952:
949:
941:
926:
923:
920:
917:
914:
911:
908:
905:
902:
899:
896:
893:
890:
887:
886:
884:
882:
878:
871:
868:
865:
862:
859:
856:
853:
850:
847:
844:
841:
838:
835:
832:
831:
829:
827:
823:
816:
813:
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804:
801:
798:
795:
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789:
786:
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777:
776:
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772:
768:
761:
758:
755:
752:
749:
746:
743:
740:
739:
737:
735:
731:
724:
721:
718:
715:
712:
709:
706:
703:
702:
700:
698:
694:
687:
684:
681:
678:
675:
672:
669:
666:
665:
663:
659:
656:
654:
650:
641:
638:
632:
626:
622:
615:
610:
608:
603:
601:
596:
595:
592:
575:on 2013-11-12
574:
570:
564:
561:
557:
556:0-89579-507-8
553:
549:
543:
541:
537:
532:
528:
524:
520:
519:
511:
508:
503:
499:
495:
491:
490:
485:
479:
476:
472:
471:1-60206-639-6
468:
464:
463:
458:
453:
451:
449:
445:
439:
436:
431:
427:
423:
419:
415:
411:
410:
405:
401:
395:
392:
388:
387:0-8247-4714-3
384:
380:
374:
371:
364:
362:
360:
356:
354:
340:
336:
332:
329:In the early
327:
325:
291:
284:
276:
272:
268:
267:perfect fifth
264:
260:
255:
253:
246:
237:
230:
221:
218:(5:4) by the
217:
213:
209:
207:
206:Bohlen–Pierce
202:
198:
194:
187:
179:
175:
167:
163:
162:neutral third
157:
140:
133:
124:
122:
118:
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:
1502:
1469:
1455:(0.72 cents)
1449:(1.95 cents)
1429:(13.8 cents)
1423:(10.1 cents)
1417:(19.5 cents)
1409:(35.7 cents)
1403:(62.6 cents)
1397:(41.1 cents)
1389:(27.3 cents)
1383:(22.6 cents)
1377:(21.5 cents)
1371:(23.5 cents)
1358:
1339:Quarter tone
1329:
1328:
1299:
1298:
1255:
1220:Higher-limit
1190:
1135:
1129:
1041:major fourth
985:quarter tone
960:
954:
643:
577:. Retrieved
573:the original
563:
547:
522:
516:
510:
493:
487:
478:
460:
438:
413:
407:
404:Ben Johnston
400:Fonville, J.
394:
381:, p. xxiii.
378:
373:
357:
328:
274:
270:
265:1:1 and the
256:
204:
200:
192:
177:
171:
50:Abbreviation
1488:Millioctave
1470:Measurement
1461:(0.4 cents)
1441:(7.7 cents)
1435:(8.1 cents)
1319:Major limma
1061:minor fifth
216:major third
42:Other names
1564:Categories
1521:Semiditone
1415:Diaschisma
1230:(17-limit)
921:(22 or 23)
919:fourteenth
915:(20 or 21)
913:thirteenth
909:(18 or 19)
903:(17 or 18)
897:(15 or 16)
891:(13 or 14)
826:Diminished
653:interval.)
634:(post-Bach
579:2013-11-12
550:, p. 131.
465:, p. 187.
365:References
353:wolf fifth
1483:Centitone
1421:Semicomma
1300:Semitones
1264:Microtone
1248:intervals
925:fifteenth
771:Augmented
649:semitones
621:Intervals
222:(36:35) (
166:blue note
64:Semitones
1453:Breedsma
901:eleventh
881:Compound
636:Western)
631:semitone
531:41335396
459:(2007).
331:meantone
1459:Ragisma
1447:Schisma
1433:Kleisma
1269:5-limit
1175:(15:14)
1169:(21:20)
1163:(28:27)
1157:(36:35)
1147:7-limit
1112:⁄
1101:seventh
1092:⁄
1072:⁄
1052:⁄
1032:⁄
1012:⁄
992:⁄
974:Neutral
947:systems
907:twelfth
864:seventh
815:seventh
760:seventh
723:seventh
661:Perfect
629:Twelve-
346:⁄
339:Zarlino
317:⁄
307:⁄
297:⁄
259:9-limit
53:S3, SM3
26:Inverse
1516:Ditone
1503:Others
1493:Savart
1360:Commas
1256:Groups
1205:(10:7)
1001:second
945:tuning
870:octave
846:fourth
834:second
797:fourth
785:second
779:unison
742:second
705:second
686:octave
674:fourth
668:unison
651:in the
554:
529:
469:
430:833435
428:
385:
290:utonal
236:24-TET
234:). In
176:, the
1526:Secor
1274:Comma
1246:Other
1211:(7:4)
1199:(7:5)
1193:(9:7)
1187:(7:6)
1181:(8:7)
1081:sixth
1021:third
943:Other
895:tenth
889:ninth
858:sixth
852:fifth
840:third
809:sixth
803:fifth
791:third
754:sixth
748:third
734:Minor
717:sixth
711:third
697:Major
680:fifth
527:JSTOR
426:JSTOR
273:, or
212:cents
208:third
174:music
94:Cents
1511:Wolf
1478:Cent
927:(24)
872:(11)
817:(12)
811:(10)
762:(10)
725:(11)
688:(12)
552:ISBN
467:ISBN
383:ISBN
282:play
263:root
244:play
228:play
195:(by
185:play
58:Size
37:Name
866:(9)
860:(7)
854:(6)
848:(4)
842:(2)
836:(0)
805:(8)
799:(6)
793:(5)
787:(3)
781:(1)
756:(8)
750:(3)
744:(1)
719:(9)
713:(4)
707:(2)
682:(7)
676:(5)
670:(0)
498:doi
418:doi
341:'s
172:In
164:or
125:435
115:450
105:400
88:9:7
78:~4½
68:~4½
1566::
1105:10
539:^
523:25
521:.
494:30
492:.
447:^
424:.
414:29
412:.
355:.
1117:)
1114:2
1110:1
1107:+
1103:(
1097:)
1094:2
1090:1
1087:+
1085:8
1083:(
1077:)
1074:2
1070:1
1067:+
1065:6
1063:(
1057:)
1054:2
1050:1
1047:+
1045:5
1043:(
1037:)
1034:2
1030:1
1027:+
1025:3
1023:(
1017:)
1014:2
1010:1
1007:+
1005:1
1003:(
997:)
994:2
990:1
987:(
613:e
606:t
599:v
582:.
533:.
504:.
500::
473:.
432:.
420::
348:7
344:2
319:6
315:9
312::
309:7
305:9
302::
299:9
295:9
168:.
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