281:
244:
128:
122:
1339:
282:
245:
129:
213:
form the interval of an augmented second. This distinguishing feature of harmonic minor scales occurs as a consequence of the seventh scale degree having been chromatically raised in order to allow
207:). In harmonic minor scales, the augmented second occurs between the sixth and seventh scale degrees. For example, in the scale of A harmonic minor, the notes F and G
1060:
372:
316:
403:
562:
337:
100:
181:. For instance, the interval from C to D is a major second, two semitones wide, and the interval from C to D
1361:
852:
832:
958:
964:
672:
525:
488:
747:
254:
234:
158:
1366:
1342:
1080:
1019:
396:
221:
observed in major keys, where the V chord is "dominant" (that is, contains a major triad plus a
1140:
617:
258:
434:
1135:
946:
1322:
1075:
982:
976:
269:
262:
170:
25:
8:
1105:
970:
952:
1218:
655:
389:
319:. Specific example of an A2 not given but general example of major intervals described.
178:
30:
1274:
1160:
1100:
661:
637:
625:
606:
420:
333:
312:
373:
A manual of harmony for use in music-schools and seminaries and for self-instruction
1230:
1055:
1000:
994:
988:
892:
792:
765:
649:
631:
570:
412:
154:
1317:
1198:
922:
710:
600:
594:
582:
218:
146:
142:
110:
83:
1178:
1172:
1166:
938:
465:
196:
73:
1355:
1302:
1151:
1070:
1065:
1011:
872:
812:
698:
686:
551:
514:
471:
222:
214:
1269:
1130:
776:
533:
496:
204:
174:
93:
1279:
1110:
545:
539:
508:
502:
238:
200:
162:
121:
1312:
1206:
704:
257:, but this does not hold true in most tunings. In any tuning close to
1212:
716:
353:, p.89-90. Thurgate & Sons. Digitized Aug 16, 2007. Archaically:
166:
1244:
692:
440:
63:
1250:
1238:
1224:
643:
588:
1307:
1284:
1192:
1186:
477:
459:
680:
268:
The 75:64 just augmented second arises in the justly tuned C
195:
Augmented seconds occur in many scales, most importantly the
381:
199:
and its various modes. They also occur in the various
187:is an augmented second, spanning three semitones.
1353:
203:(which consist almost entirely of augmented and
397:
376:, p.165. Theodore Baker, trans. G. Schirmer.
217:in a minor key to follow the same rules of
1338:
404:
390:
303:
301:
261:it will be close to the 7:6 ratio of the
88:75:64, 125:108, 15:13, 19:16, 19683:16384
120:
330:The Mathematical Theory of Tone Systems
1354:
762:
322:
298:
385:
309:Music: In Theory and Practice, Vol. I
13:
14:
1378:
1337:
351:Music: Its Theory & Practice
161:, is sonically equivalent to a
364:
343:
1:
411:
292:
307:Benward & Saker (2003).
7:
959:septimal chromatic semitone
340:. Classic augmented second.
10:
1383:
965:septimal diatonic semitone
753:(Numbers in brackets refer
1335:
1293:
1260:
1149:
1119:
1089:
1046:
1037:
1010:
937:
920:
755:to fractional semitones.)
748:24-tone equal temperament
745:
734:
671:
616:
561:
524:
487:
452:
419:
255:12-tone equal temperament
235:enharmonically equivalent
228:
159:12-tone equal temperament
115:275, 253, 247.7, 298, 318
109:
101:12-Tone equal temperament
99:
92:
82:
72:
62:
57:
49:
41:
36:
24:
190:
1343:List of pitch intervals
1081:Subminor and supermajor
1020:minor diatonic semitone
930:refer to pitch ratios.)
349:Hoffmann, F.A. (1881).
233:An augmented second is
1141:Undecimal quarter tone
259:quarter-comma meantone
138:
125:Augmented second on C
1136:Septimal quarter tone
947:septimal quarter tone
328:Haluska, Jan (2003).
124:
1323:Incomposite interval
1076:Pythagorean interval
928:(Numbers in brackets
436:(Numbers in brackets
370:Paul, Oscar (1885).
359:extreme sharp second
270:harmonic minor scale
263:septimal minor third
169:, and is created by
1362:Augmented intervals
1106:Pythagorean apotome
953:septimal third tone
21:
1219:Septimal semicomma
179:chromatic semitone
139:
31:diminished seventh
19:
1349:
1348:
1331:
1330:
1161:Pythagorean comma
1101:Pythagorean limma
1033:
1032:
1029:
1028:
995:supermajor fourth
971:supermajor second
916:
915:
730:
729:
726:
725:
438:are the number of
317:978-0-07-294262-0
165:, spanning three
119:
118:
1374:
1341:
1340:
1231:Septimal kleisma
1044:
1043:
1001:subminor seventh
983:supermajor third
935:
934:
923:Just intonations
908:
907:
903:
900:
888:
887:
883:
880:
868:
867:
863:
860:
848:
847:
843:
840:
828:
827:
823:
820:
808:
807:
803:
800:
788:
787:
783:
760:
759:
743:
742:
450:
449:
432:
431:
406:
399:
392:
383:
382:
377:
368:
362:
347:
341:
326:
320:
305:
289:
288:
287:
285:
277:
276:
252:
251:
250:
248:
212:
211:
186:
185:
151:augmented second
136:
135:
134:
132:
22:
20:Augmented second
18:
16:Musical interval
1382:
1381:
1377:
1376:
1375:
1373:
1372:
1371:
1367:Seconds (music)
1352:
1351:
1350:
1345:
1327:
1289:
1256:
1199:Septimal diesis
1145:
1115:
1085:
1039:
1025:
1006:
929:
926:
912:
905:
901:
898:
896:
885:
881:
878:
876:
865:
861:
858:
856:
845:
841:
838:
836:
825:
821:
818:
816:
805:
801:
798:
796:
785:
781:
780:
770:
769:
768:
764:
754:
751:
738:
736:
722:
667:
612:
557:
520:
483:
444:
439:
437:
427:
425:
422:
415:
410:
380:
369:
365:
348:
344:
327:
323:
306:
299:
295:
283:
280:
279:
274:
273:
246:
243:
242:
231:
209:
208:
193:
183:
182:
147:Western culture
143:classical music
130:
127:
126:
111:Just intonation
17:
12:
11:
5:
1380:
1370:
1369:
1364:
1347:
1346:
1336:
1333:
1332:
1329:
1328:
1326:
1325:
1320:
1315:
1310:
1305:
1299:
1297:
1291:
1290:
1288:
1287:
1282:
1277:
1272:
1266:
1264:
1258:
1257:
1255:
1254:
1248:
1242:
1235:
1234:
1228:
1222:
1216:
1210:
1203:
1202:
1196:
1193:Greater diesis
1190:
1183:
1182:
1179:Septimal comma
1176:
1173:Holdrian comma
1170:
1167:Syntonic comma
1164:
1157:
1155:
1147:
1146:
1144:
1143:
1138:
1133:
1127:
1125:
1117:
1116:
1114:
1113:
1108:
1103:
1097:
1095:
1087:
1086:
1084:
1083:
1078:
1073:
1068:
1063:
1058:
1052:
1050:
1041:
1035:
1034:
1031:
1030:
1027:
1026:
1024:
1023:
1016:
1014:
1008:
1007:
1005:
1004:
998:
992:
989:subminor fifth
986:
980:
977:subminor third
974:
968:
962:
956:
950:
943:
941:
932:
918:
917:
914:
913:
911:
910:
890:
870:
850:
830:
810:
790:
773:
771:
763:
757:
740:
732:
731:
728:
727:
724:
723:
721:
720:
714:
708:
702:
696:
690:
684:
677:
675:
669:
668:
666:
665:
659:
653:
647:
641:
635:
629:
622:
620:
614:
613:
611:
610:
604:
598:
592:
586:
580:
574:
567:
565:
559:
558:
556:
555:
549:
543:
537:
530:
528:
522:
521:
519:
518:
512:
506:
500:
493:
491:
485:
484:
482:
481:
475:
469:
463:
456:
454:
447:
429:
417:
416:
409:
408:
401:
394:
386:
379:
378:
363:
342:
321:
296:
294:
291:
230:
227:
197:harmonic minor
192:
189:
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:
9:
6:
4:
3:
2:
1379:
1368:
1365:
1363:
1360:
1359:
1357:
1344:
1334:
1324:
1321:
1319:
1316:
1314:
1311:
1309:
1306:
1304:
1301:
1300:
1298:
1296:
1292:
1286:
1283:
1281:
1278:
1276:
1273:
1271:
1268:
1267:
1265:
1263:
1259:
1252:
1249:
1246:
1243:
1240:
1237:
1236:
1232:
1229:
1226:
1223:
1220:
1217:
1214:
1211:
1208:
1205:
1204:
1200:
1197:
1194:
1191:
1188:
1187:Lesser diesis
1185:
1184:
1180:
1177:
1174:
1171:
1168:
1165:
1162:
1159:
1158:
1156:
1154:
1153:
1148:
1142:
1139:
1137:
1134:
1132:
1129:
1128:
1126:
1124:
1123:
1122:Quarter tones
1118:
1112:
1109:
1107:
1104:
1102:
1099:
1098:
1096:
1094:
1093:
1088:
1082:
1079:
1077:
1074:
1072:
1071:Pseudo-octave
1069:
1067:
1064:
1062:
1059:
1057:
1054:
1053:
1051:
1049:
1045:
1042:
1036:
1021:
1018:
1017:
1015:
1013:
1009:
1002:
999:
996:
993:
990:
987:
984:
981:
978:
975:
972:
969:
966:
963:
960:
957:
954:
951:
948:
945:
944:
942:
940:
936:
933:
931:
925:
924:
919:
894:
891:
874:
871:
854:
851:
834:
831:
814:
811:
794:
791:
778:
775:
774:
772:
767:
761:
758:
756:
750:
749:
744:
741:
733:
718:
715:
712:
709:
706:
703:
700:
697:
694:
691:
688:
685:
682:
679:
678:
676:
674:
670:
663:
660:
657:
654:
651:
648:
645:
642:
639:
636:
633:
630:
627:
624:
623:
621:
619:
615:
608:
605:
602:
599:
596:
593:
590:
587:
584:
581:
578:
575:
572:
569:
568:
566:
564:
560:
553:
550:
547:
544:
541:
538:
535:
532:
531:
529:
527:
523:
516:
513:
510:
507:
504:
501:
498:
495:
494:
492:
490:
486:
479:
476:
473:
470:
467:
464:
461:
458:
457:
455:
451:
448:
446:
442:
433:
430:
424:
418:
414:
407:
402:
400:
395:
393:
388:
387:
384:
375:
374:
367:
360:
356:
352:
346:
339:
338:0-8247-4714-3
335:
331:
325:
318:
314:
310:
304:
302:
297:
290:
286:
271:
266:
264:
260:
256:
249:
240:
236:
226:
224:
223:minor seventh
220:
216:
206:
205:minor seconds
202:
198:
188:
180:
176:
172:
168:
164:
160:
156:
152:
148:
144:
133:
123:
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:
1294:
1261:
1247:(0.72 cents)
1241:(1.95 cents)
1221:(13.8 cents)
1215:(10.1 cents)
1209:(19.5 cents)
1201:(35.7 cents)
1195:(62.6 cents)
1189:(41.1 cents)
1181:(27.3 cents)
1175:(22.6 cents)
1169:(21.5 cents)
1163:(23.5 cents)
1150:
1131:Quarter tone
1121:
1120:
1091:
1090:
1047:
1012:Higher-limit
927:
921:
833:major fourth
777:quarter tone
752:
746:
576:
435:
371:
366:
358:
354:
350:
345:
329:
324:
308:
267:
232:
201:Gypsy scales
194:
175:major second
150:
140:
50:Abbreviation
1280:Millioctave
1262:Measurement
1253:(0.4 cents)
1233:(7.7 cents)
1227:(8.1 cents)
1111:Major limma
853:minor fifth
239:minor third
163:minor third
42:Other names
1356:Categories
1313:Semiditone
1207:Diaschisma
1022:(17-limit)
713:(22 or 23)
711:fourteenth
707:(20 or 21)
705:thirteenth
701:(18 or 19)
695:(17 or 18)
689:(15 or 16)
683:(13 or 14)
618:Diminished
445:interval.)
426:(post-Bach
332:, p.xxvi.
293:References
1275:Centitone
1213:Semicomma
1092:Semitones
1056:Microtone
1040:intervals
717:fifteenth
563:Augmented
441:semitones
413:Intervals
355:redundant
272:between A
167:semitones
157:that, in
64:Semitones
1245:Breedsma
693:eleventh
673:Compound
428:Western)
423:semitone
311:, p.54.
275:♭
210:♯
184:♯
171:widening
155:interval
1251:Ragisma
1239:Schisma
1225:Kleisma
1061:5-limit
967:(15:14)
961:(21:20)
955:(28:27)
949:(36:35)
939:7-limit
904:⁄
893:seventh
884:⁄
864:⁄
844:⁄
824:⁄
804:⁄
784:⁄
766:Neutral
739:systems
699:twelfth
656:seventh
607:seventh
552:seventh
515:seventh
453:Perfect
421:Twelve-
278:and B.
219:cadence
26:Inverse
1308:Ditone
1295:Others
1285:Savart
1152:Commas
1048:Groups
997:(10:7)
793:second
737:tuning
662:octave
638:fourth
626:second
589:fourth
577:second
571:unison
534:second
497:second
478:octave
466:fourth
460:unison
443:in the
336:
315:
229:Tuning
215:chords
153:is an
1318:Secor
1066:Comma
1038:Other
1003:(7:4)
991:(7:5)
985:(9:7)
979:(7:6)
973:(8:7)
873:sixth
813:third
735:Other
687:tenth
681:ninth
650:sixth
644:fifth
632:third
601:sixth
595:fifth
583:third
546:sixth
540:third
526:Minor
509:sixth
503:third
489:Major
472:fifth
253:) in
237:to a
191:Usage
177:by a
149:, an
145:from
94:Cents
1303:Wolf
1270:Cent
719:(24)
664:(11)
609:(12)
603:(10)
554:(10)
517:(11)
480:(12)
334:ISBN
313:ISBN
284:Play
247:Play
131:Play
58:Size
37:Name
658:(9)
652:(7)
646:(6)
640:(4)
634:(2)
628:(0)
597:(8)
591:(6)
585:(5)
579:(3)
573:(1)
548:(8)
542:(3)
536:(1)
511:(9)
505:(4)
499:(2)
474:(7)
468:(5)
462:(0)
357:or
225:).
141:In
105:300
1358::
897:10
300:^
265:.
173:a
53:A2
909:)
906:2
902:1
899:+
895:(
889:)
886:2
882:1
879:+
877:8
875:(
869:)
866:2
862:1
859:+
857:6
855:(
849:)
846:2
842:1
839:+
837:5
835:(
829:)
826:2
822:1
819:+
817:3
815:(
809:)
806:2
802:1
799:+
797:1
795:(
789:)
786:2
782:1
779:(
405:e
398:t
391:v
361:.
241:(
137:.
78:3
68:3
45:-
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
