17:
1258:
167:
24:
979:
68:; if it is tempered out in a given tuning system, the distinction between these two intervals is lost. The septimal 1/3-tone may be derived from the
1280:
322:
1290:
291:
270:
249:
228:
143:
771:
751:
877:
115:
883:
111:
666:
1285:
1261:
999:
938:
315:
69:
96:
1059:
1054:
865:
100:
1241:
994:
901:
895:
481:
192:
184:
88:
1024:
889:
1137:
574:
308:
72:
as the interval between the twenty-seventh and twenty-eighth harmonics. It may be considered a
1079:
1019:
580:
556:
544:
525:
339:
287:
266:
245:
224:
1149:
974:
919:
913:
907:
811:
711:
684:
591:
568:
550:
495:
489:
331:
156:
92:
53:
45:
87:, and equal temperaments which divide the octave into a small multiple of 5 steps, such as
1117:
841:
629:
519:
513:
501:
444:
407:
176:
80:
16:
1097:
1091:
1085:
857:
384:
49:
1274:
1221:
1070:
989:
984:
930:
791:
731:
617:
605:
470:
433:
390:
65:
1236:
1193:
1188:
1049:
695:
452:
415:
119:
57:
1198:
1029:
464:
458:
427:
421:
1231:
1125:
623:
536:
160:
64:
1/3-tone can be viewed either as a musical interval in its own right, or as a
1131:
635:
1163:
611:
359:
187:, the greater septimal tritone (10:7). This interval is tempered out by
1169:
1157:
1143:
562:
507:
180:
153:
61:
1226:
1203:
1111:
1105:
396:
378:
263:
Archytas of
Tarentum: Pythagorean, Philosopher and Mathematician King
200:
196:
188:
104:
73:
599:
84:
41:
15:
304:
284:
Greek
Musical Writings: Volume 2, Harmonic and Acoustic Theory
163:(203.91/6=33.99 cents). An interval with the ratio of 50:49 (
48:
with the ratio of 28:27, which is the difference between the
300:
179:
is the difference between the lesser septimal (7:5)
1212:
1179:
1068:
1038:
1008:
965:
956:
929:
856:
839:
681:
664:
653:
590:
535:
480:
443:
406:
371:
353:
338:
316:
242:The Cambridge History of Western Music Theory
8:
122:) and 10:9 tone (minor tone), respectively.
1257:
962:
853:
678:
661:
368:
350:
323:
309:
301:
125:It is the difference between 7/6 and 9/8 (
203:or any other odd division of the octave.
118:and 28:27 semitone produce the 9:8 tone (
107:that take advantage of the temperament.
103:, who first analyzed 10-note subsets of
231:. 1/3-tone, Archytas inferior 1/4-tone.
221:The Mathematical Theory of Tone Systems
212:
79:The septimal 1/3-tone, along with the
7:
95:. This family of scales is known as
159:approximately the size of 1/6 of a
14:
1256:
240:Thomas Christensen, ed. (2002).
175:), about 34.98 cents, which in
1:
1281:7-limit tuning and intervals
878:septimal chromatic semitone
282:Andrew Barker, ed. (2004).
85:five-tone equal temperament
1307:
884:septimal diatonic semitone
672:(Numbers in brackets refer
1291:Superparticular intervals
1254:
674:to fractional semitones.)
667:24-tone equal temperament
20:Septimal third tone on C
1262:List of pitch intervals
1000:Subminor and supermajor
939:minor diatonic semitone
849:refer to pitch ratios.)
1060:Undecimal quarter tone
261:Huffman, Carl (2005).
33:
1055:Septimal quarter tone
866:septimal quarter tone
219:Haluska, Jan (2003).
101:Easley Blackwood, Jr.
97:Blackwood temperament
19:
1242:Incomposite interval
995:Pythagorean interval
847:(Numbers in brackets
355:(Numbers in brackets
56:. It is about 62.96
1025:Pythagorean apotome
872:septimal third tone
137:Septimal sixth tone
83:is tempered out by
1138:Septimal semicomma
148:, also called the
110:When added to the
34:
1268:
1267:
1250:
1249:
1080:Pythagorean comma
1020:Pythagorean limma
952:
951:
948:
947:
914:supermajor fourth
890:supermajor second
835:
834:
649:
648:
645:
644:
357:are the number of
38:septimal 1/3-tone
1298:
1260:
1259:
1150:Septimal kleisma
963:
920:subminor seventh
902:supermajor third
854:
842:Just intonations
827:
826:
822:
819:
807:
806:
802:
799:
787:
786:
782:
779:
767:
766:
762:
759:
747:
746:
742:
739:
727:
726:
722:
719:
707:
706:
702:
679:
662:
369:
351:
325:
318:
311:
302:
295:
280:
274:
259:
253:
238:
232:
217:
174:
173:
172:
170:
157:musical interval
54:supermajor third
31:
30:
29:
27:
1306:
1305:
1301:
1300:
1299:
1297:
1296:
1295:
1271:
1270:
1269:
1264:
1246:
1208:
1175:
1118:Septimal diesis
1064:
1034:
1004:
958:
944:
925:
848:
845:
831:
824:
820:
817:
815:
804:
800:
797:
795:
784:
780:
777:
775:
764:
760:
757:
755:
744:
740:
737:
735:
724:
720:
717:
715:
704:
700:
699:
689:
688:
687:
683:
673:
670:
657:
655:
641:
586:
531:
476:
439:
402:
363:
358:
356:
346:
344:
341:
334:
329:
299:
298:
281:
277:
260:
256:
239:
235:
218:
214:
209:
177:just intonation
168:
166:
165:
164:
139:
81:septimal diesis
70:harmonic series
25:
23:
22:
21:
12:
11:
5:
1304:
1302:
1294:
1293:
1288:
1286:Commas (music)
1283:
1273:
1272:
1266:
1265:
1255:
1252:
1251:
1248:
1247:
1245:
1244:
1239:
1234:
1229:
1224:
1218:
1216:
1210:
1209:
1207:
1206:
1201:
1196:
1191:
1185:
1183:
1177:
1176:
1174:
1173:
1167:
1161:
1154:
1153:
1147:
1141:
1135:
1129:
1122:
1121:
1115:
1112:Greater diesis
1109:
1102:
1101:
1098:Septimal comma
1095:
1092:Holdrian comma
1089:
1086:Syntonic comma
1083:
1076:
1074:
1066:
1065:
1063:
1062:
1057:
1052:
1046:
1044:
1036:
1035:
1033:
1032:
1027:
1022:
1016:
1014:
1006:
1005:
1003:
1002:
997:
992:
987:
982:
977:
971:
969:
960:
954:
953:
950:
949:
946:
945:
943:
942:
935:
933:
927:
926:
924:
923:
917:
911:
908:subminor fifth
905:
899:
896:subminor third
893:
887:
881:
875:
869:
862:
860:
851:
837:
836:
833:
832:
830:
829:
809:
789:
769:
749:
729:
709:
692:
690:
682:
676:
659:
651:
650:
647:
646:
643:
642:
640:
639:
633:
627:
621:
615:
609:
603:
596:
594:
588:
587:
585:
584:
578:
572:
566:
560:
554:
548:
541:
539:
533:
532:
530:
529:
523:
517:
511:
505:
499:
493:
486:
484:
478:
477:
475:
474:
468:
462:
456:
449:
447:
441:
440:
438:
437:
431:
425:
419:
412:
410:
404:
403:
401:
400:
394:
388:
382:
375:
373:
366:
348:
336:
335:
330:
328:
327:
320:
313:
305:
297:
296:
275:
254:
233:
211:
210:
208:
205:
138:
135:
116:21:20 semitone
112:15:14 semitone
50:perfect fourth
13:
10:
9:
6:
4:
3:
2:
1303:
1292:
1289:
1287:
1284:
1282:
1279:
1278:
1276:
1263:
1253:
1243:
1240:
1238:
1235:
1233:
1230:
1228:
1225:
1223:
1220:
1219:
1217:
1215:
1211:
1205:
1202:
1200:
1197:
1195:
1192:
1190:
1187:
1186:
1184:
1182:
1178:
1171:
1168:
1165:
1162:
1159:
1156:
1155:
1151:
1148:
1145:
1142:
1139:
1136:
1133:
1130:
1127:
1124:
1123:
1119:
1116:
1113:
1110:
1107:
1106:Lesser diesis
1104:
1103:
1099:
1096:
1093:
1090:
1087:
1084:
1081:
1078:
1077:
1075:
1073:
1072:
1067:
1061:
1058:
1056:
1053:
1051:
1048:
1047:
1045:
1043:
1042:
1041:Quarter tones
1037:
1031:
1028:
1026:
1023:
1021:
1018:
1017:
1015:
1013:
1012:
1007:
1001:
998:
996:
993:
991:
990:Pseudo-octave
988:
986:
983:
981:
978:
976:
973:
972:
970:
968:
964:
961:
955:
940:
937:
936:
934:
932:
928:
921:
918:
915:
912:
909:
906:
903:
900:
897:
894:
891:
888:
885:
882:
879:
876:
873:
870:
867:
864:
863:
861:
859:
855:
852:
850:
844:
843:
838:
813:
810:
793:
790:
773:
770:
753:
750:
733:
730:
713:
710:
697:
694:
693:
691:
686:
680:
677:
675:
669:
668:
663:
660:
652:
637:
634:
631:
628:
625:
622:
619:
616:
613:
610:
607:
604:
601:
598:
597:
595:
593:
589:
582:
579:
576:
573:
570:
567:
564:
561:
558:
555:
552:
549:
546:
543:
542:
540:
538:
534:
527:
524:
521:
518:
515:
512:
509:
506:
503:
500:
497:
494:
491:
488:
487:
485:
483:
479:
472:
469:
466:
463:
460:
457:
454:
451:
450:
448:
446:
442:
435:
432:
429:
426:
423:
420:
417:
414:
413:
411:
409:
405:
398:
395:
392:
389:
386:
383:
380:
377:
376:
374:
370:
367:
365:
361:
352:
349:
343:
337:
333:
326:
321:
319:
314:
312:
307:
306:
303:
293:
292:9780521616973
289:
285:
279:
276:
272:
271:9781139444071
268:
264:
258:
255:
251:
250:9780521623711
247:
243:
237:
234:
230:
229:0-8247-4714-3
226:
222:
216:
213:
206:
204:
202:
198:
195:, but not by
194:
190:
186:
182:
178:
171:
162:
158:
155:
151:
147:
145:
136:
134:
132:
128:
123:
121:
117:
113:
108:
106:
102:
98:
94:
90:
86:
82:
77:
75:
71:
67:
63:
59:
55:
51:
47:
43:
39:
28:
18:
1213:
1180:
1166:(0.72 cents)
1160:(1.95 cents)
1140:(13.8 cents)
1134:(10.1 cents)
1128:(19.5 cents)
1120:(35.7 cents)
1114:(62.6 cents)
1108:(41.1 cents)
1100:(27.3 cents)
1094:(22.6 cents)
1088:(21.5 cents)
1082:(23.5 cents)
1069:
1050:Quarter tone
1040:
1039:
1010:
1009:
966:
931:Higher-limit
871:
846:
840:
752:major fourth
696:quarter tone
671:
665:
354:
283:
278:
262:
257:
241:
236:
220:
215:
149:
142:
140:
130:
126:
124:
109:
99:in honor of
78:
37:
35:
1199:Millioctave
1181:Measurement
1172:(0.4 cents)
1152:(7.7 cents)
1146:(8.1 cents)
1030:Major limma
772:minor fifth
60:wide. The
1275:Categories
1232:Semiditone
1126:Diaschisma
941:(17-limit)
632:(22 or 23)
630:fourteenth
626:(20 or 21)
624:thirteenth
620:(18 or 19)
614:(17 or 18)
608:(15 or 16)
602:(13 or 14)
537:Diminished
364:interval.)
345:(post-Bach
223:, p.xxiv.
207:References
183:, and its
161:whole tone
146:sixth tone
120:major tone
1194:Centitone
1132:Semicomma
1011:Semitones
975:Microtone
959:intervals
636:fifteenth
482:Augmented
360:semitones
332:Intervals
265:, p.420.
244:, p.186.
185:inversion
150:jubilisma
1164:Breedsma
612:eleventh
592:Compound
347:Western)
342:semitone
286:, p.51.
144:septimal
131:paramesē
62:septimal
52:and the
46:interval
44:) is an
1170:Ragisma
1158:Schisma
1144:Kleisma
980:5-limit
886:(15:14)
880:(21:20)
874:(28:27)
868:(36:35)
858:7-limit
823:⁄
812:seventh
803:⁄
783:⁄
763:⁄
743:⁄
723:⁄
703:⁄
685:Neutral
658:systems
618:twelfth
575:seventh
526:seventh
471:seventh
434:seventh
372:Perfect
340:Twelve-
181:tritone
154:7-limit
152:, is a
1227:Ditone
1214:Others
1204:Savart
1071:Commas
967:Groups
916:(10:7)
712:second
656:tuning
581:octave
557:fourth
545:second
508:fourth
496:second
490:unison
453:second
416:second
397:octave
385:fourth
379:unison
362:in the
290:
269:
248:
227:
201:31-TET
197:19-TET
193:22-TET
189:12-TET
114:, the
105:15-TET
93:25-TET
89:15-TET
74:diesis
1237:Secor
985:Comma
957:Other
922:(7:4)
910:(7:5)
904:(9:7)
898:(7:6)
892:(8:7)
792:sixth
732:third
654:Other
606:tenth
600:ninth
569:sixth
563:fifth
551:third
520:sixth
514:fifth
502:third
465:sixth
459:third
445:Minor
428:sixth
422:third
408:Major
391:fifth
127:tritē
66:comma
58:cents
42:music
1222:Wolf
1189:Cent
638:(24)
583:(11)
528:(12)
522:(10)
473:(10)
436:(11)
399:(12)
288:ISBN
267:ISBN
246:ISBN
225:ISBN
191:and
169:play
141:The
129:and
91:and
40:(in
26:Play
577:(9)
571:(7)
565:(6)
559:(4)
553:(2)
547:(0)
516:(8)
510:(6)
504:(5)
498:(3)
492:(1)
467:(8)
461:(3)
455:(1)
430:(9)
424:(4)
418:(2)
393:(7)
387:(5)
381:(0)
133:).
1277::
816:10
199:,
76:.
36:A
828:)
825:2
821:1
818:+
814:(
808:)
805:2
801:1
798:+
796:8
794:(
788:)
785:2
781:1
778:+
776:6
774:(
768:)
765:2
761:1
758:+
756:5
754:(
748:)
745:2
741:1
738:+
736:3
734:(
728:)
725:2
721:1
718:+
716:1
714:(
708:)
705:2
701:1
698:(
324:e
317:t
310:v
294:.
273:.
252:.
32:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
