3281:
3253:
2125:
781:
521:
3369:
2660:
2445:
3459:
3423:
3447:
3411:
2239:
3315:
1258:
657:
796:
2393:
2052:
616:
2427:
2031:
2382:
995:
823:
815:
2091:
706:
2079:
157:
5407:
5090:
2410:
975:
5216:
986:
3649:
1248:
355:
1286:
begin to require motion in one voice by half step and the other a whole step in contrary motion. These cadences would become a fundamental part of the musical language, even to the point where the usual accidental accompanying the minor second in a cadence was often omitted from the written score (a
3471:
In general, because the smaller semitone can be viewed as the difference between a minor third and a major third, and the larger as the difference between a major third and a perfect fourth, tuning systems that closely match those just intervals (6/5, 5/4, and 4/3) will also distinguish between the
733:
opens with a melody accompanied by a line that plays fleeting minor seconds. These are used to humorous and whimsical effect, which contrasts with its more lyrical middle section. This eccentric dissonance has earned the piece its nickname: the "wrong note" Ă©tude. This kind of usage of the minor
686:
632:
2418:
2041:
1274:
2943:
1353:
sought alternatives or extensions of tonal harmony, and found other uses for the semitone. Often the semitone was exploited harmonically as a caustic dissonance, having no resolution. Some composers would even use large collections of harmonic semitones
2401:
2001:, but the characteristic they all share is that their semitones are of an uneven size. Every semitone in a well temperament has its own interval (usually close to the equal-tempered version of 100 cents), and there is no clear distinction between a
3647:
3167:
3046:
367:
2820:
2062:
3282:
1149:
3254:
2126:
849:
633:
2649:
2555:
3370:
2661:
2419:
2333:
2042:
1275:
2446:
165:
2208:
782:
3230:(81:80 or 21.5 cents). The smaller and larger chromatic semitones differ from the respective diatonic semitones by the same 128:125 diesis as the above meantone semitones. Finally, while the inner semitones differ by the
684:
2402:
2240:
1250:." In a melodic half step, no "tendency was perceived of the lower tone toward the upper, or of the upper toward the lower. The second tone was not taken to be the 'goal' of the first. Instead, the half step was avoided in
1907:
368:
3328:(150.6 cents). In just intonation there are infinitely many possibilities for intervals that fall within the range of the semitone (e.g. the Pythagorean semitones mentioned above), but most of them are impractical.
3460:
3448:
3424:
2063:
3412:
3316:
3653:
1760:
is a form of meantone tuning in which the diatonic and chromatic semitones are exactly the same, because its circle of fifths has no break. Each semitone is equal to one twelfth of an octave. This is a ratio of
848:
3290:) between a septimal minor seventh and a fifth (21:8) and an octave and a major third (5:2). Both are more rarely used than their 5 limit neighbours, although the former was often implemented by theorist
685:
522:
1976:
166:
1744:
Extended meantone temperaments with more than 12 notes still retain the same two semitone sizes, but there is more flexibility for the musician about whether to use an augmented unison or minor second.
2013:
equivalence could be assumed between all of these semitones, and whether they were written as a minor second or augmented unison did not effect a different sound. Instead, in these systems, each
1829:
3389:
are often used for these intervals, their musical function is not the same as the meantone semitones. For instance, 15:14 would usually be written as an augmented unison, functioning as the
327:
yields chromatic semitones with ratios 25:24 (70.7 cents) and 135:128 (92.2 cents), and diatonic semitones with ratios 16:15 (111.7 cents) and 27:25 (133.2 cents). For further details, see
3397:
16:15. These distinctions are highly dependent on the musical context, and just intonation is not particularly well suited to chromatic use (diatonic semitone function is more prevalent).
847:
677:
2860:
630:
3084:
2963:
2673:(5:4) and a minor third (6:5). In fact, it is the spacing between the minor and major thirds, sixths, and sevenths (but not necessarily the major and minor second). Composer
2416:
1272:
2737:
2039:
899:, because the interval of the diminished unison does not exist. This is because a unison is always made larger when one note of the interval is changed with an accidental.
2399:
1243:{\displaystyle \left({\begin{matrix}{\frac {4}{3}}\end{matrix}}/{{\begin{matrix}({\frac {9}{8}})\end{matrix}}^{2}}={\begin{matrix}{\frac {256}{243}}\end{matrix}}\right)}
365:
1410:
that occurs in the tuning system: diatonic semitones derive from a chain of five fifths that does not cross the break, and chromatic semitones come from one that does.
947:. (Restricting the notation to only minor seconds is impractical, as the same example would have a rapidly increasing number of accidentals, written enharmonically as
2060:
3843:. "There is no such thing as a diminished unison, because no matter how you change the unisons with accidentals, you are adding half steps to the total interval."
2570:
2476:
163:
2273:
631:
2417:
2040:
1273:
2148:
292:
all semitones are equal in size (100 cents). In other tuning systems, "semitone" refers to a family of intervals that may vary both in size and name. In
2400:
1322:
harmonic framework was fully formed, and the various musical functions of the semitone were rigorously understood. Later in this period the adoption of
366:
2061:
1855:
3703:
1366:, and instrumental use of the semitone was not at all problematic for the performer. The composer was free to write semitones wherever he wished.
850:
5124:
2654:
The 16:15 just minor second arises in the C major scale between B & C and E & F, and is, "the sharpest dissonance found in the scale".
164:
5410:
4811:
3870:. Since lowering either note of a perfect unison would actually increase its size, the perfect unison cannot be diminished, only augmented.
865:, or widening by one half step, of the perfect unison, does not occur between diatonic scale steps, but instead between a scale step and a
2689:) to indicate a note is lowered 70.7 cents. (This is the standard practice for just intonation, but not for all other microtunings.)
1137:"As late as the 13th century the half step was experienced as a problematic interval not easily understood, as the irrational [
3968:
312:, seven of them are diatonic, and 117.1 cents wide, while the other five are chromatic, and 76.0 cents wide; they differ by the lesser
1749:
is the most flexible of these, which makes an unbroken circle of 31 fifths, allowing the choice of semitone to be made for any pitch.
214:
In a 12-note approximately equally divided scale, any interval can be defined in terms of an appropriate number of semitones (e.g. a
3634:
1291:). By the 16th century, the semitone had become a more versatile interval, sometimes even appearing as an augmented unison in very
1929:
205:), visually seen on a keyboard as the distance between two keys that are adjacent to each other. For example, C is adjacent to C
3865:
3798:
3752:
3565:
3408:
distinguishes between the chromatic and diatonic semitones; in this tuning, the chromatic semitone is one step of the scale (
2115:, these semitones are rational. Also, unlike most meantone temperaments, the chromatic semitone is larger than the diatonic.
3555:
2696:
defines 12 semitones as the 12 intervals between the 13 adjacent notes, spanning a full octave (e.g. from C
5117:
4154:
3661:
3378:), and the minor diatonic semitone is 17:16 or 105.0 cents, and septendecimal limma is 18:17 or 98.95 cents.
1795:
917:. Its use is also often the consequence of a melody proceeding in semitones, regardless of harmonic underpinning, e.g.
4313:
4126:
4109:
4074:
3953:
3916:
3895:
3840:
3819:
3689:
3668:
3596:
2462:. This is a practical just semitone, since it is the interval that occurs twice within the diatonic scale between a:
277:, where the diatonic semitone is distinguished from and larger than the chromatic semitone (augmented unison), or in
447:
135:
1394:, similar to meantone tuning, has two, but in other systems of just intonation there are many more possibilities.
1330:
equivalences increased the ease with which a semitone could be applied. Its function remained similar through the
3299:
3651:
1765:(approximately 1.05946), or 100 cents, and is 11.7 cents narrower than the 16:15 ratio (its most common form in
730:
194:
5262:
5110:
2938:{\displaystyle S_{2}={\tfrac {25}{24}}\times {\tfrac {81}{80}}={\tfrac {135}{128}}\approx 92.2\ {\hbox{cents}}}
2657:
An "augmented unison" (sharp) in just intonation is a different, smaller semitone, with frequency ratio 25:24 (
1069:
In addition to this kind of usage, harmonic augmented unisons are frequently written in modern works involving
5232:
289:
5334:
5203:
4603:
4583:
4709:
3275:
5176:
3162:{\displaystyle S_{4}={\tfrac {9}{5}}\div {\tfrac {5}{3}}={\tfrac {27}{25}}\approx 133.2\ {\hbox{cents}}}
3041:{\displaystyle S_{3}={\tfrac {4}{3}}\div {\tfrac {5}{4}}={\tfrac {16}{15}}\approx 111.7\ {\hbox{cents}}}
1334:
period, and though it was used more frequently as the language of tonality became more chromatic in the
4715:
4423:
3486:
3436:
also distinguishes between these two intervals, which become 2 and 3 steps of the scale, respectively.
3247:
2815:{\displaystyle S_{1}={\tfrac {5}{4}}\div {\tfrac {6}{5}}={\tfrac {25}{24}}\approx 70.7\ {\hbox{cents}}}
2705:
321:
4276:
4239:
725:
In unusual situations, the minor second can add a great deal of character to the music. For instance,
5359:
4498:
4002:
3234:(2048:2025 or 19.6 cents), the outer differ by the greater diesis (648:625 or 62.6 cents).
1757:
771:
744:
624:
593:
17:
2017:
had a slightly different sonic color or character, beyond the limitations of conventional notation.
5434:
5429:
910:
559:
1002:
5439:
5093:
4831:
4770:
4147:
3997:
3496:
2674:
2111:. This creates two distinct semitones, but because Pythagorean tuning is also a form of 3-limit
1089:
The semitone appeared in the music theory of Greek antiquity as part of a diatonic or chromatic
5339:
5287:
5252:
4891:
4368:
3267:
1414:
359:
309:
4185:
5133:
4886:
4697:
3928:
1776:
All diatonic intervals can be expressed as an equivalent number of semitones. For instance a
914:
905:, an augmented unison very frequently occurs when proceeding to a chromatic chord, such as a
620:
3366:
In 17 limit just intonation, the major diatonic semitone is 15:14 or 119.4 cents (
5282:
5247:
5073:
4826:
4733:
4727:
3516:
3481:
3441:
3437:
3433:
3405:
2644:{\displaystyle \ \left(\ {\tfrac {2}{1}}\div {\tfrac {15}{8}}={\tfrac {16}{15}}\ \right)~.}
2550:{\displaystyle \ \left(\ {\tfrac {4}{3}}\div {\tfrac {5}{4}}={\tfrac {16}{15}}\ \right)\ ,}
2366:
2263:
1915:
1403:
1379:
1093:, and it has always had a place in the diatonic scales of Western music since. The various
862:
726:
696:
666:
384:
274:
43:
282:
8:
5364:
5224:
4856:
4721:
4703:
3801:. Specific example of an A1 not given but general example of perfect intervals described.
3521:
1762:
1418:
1299:, in the 16th century the repeated melodic semitone became associated with weeping, see:
840:
605:
197:
when sounded harmonically. It is defined as the interval between two adjacent notes in a
3630:
3560:(First published as a Norton paperback. ed.). New York: W. W. Norton. p. 163.
2328:{\displaystyle {\frac {2187}{2048}}={\frac {3^{7}}{2^{11}}}\approx 113.7{\text{ cents}}}
5384:
5316:
5237:
5156:
4969:
4406:
4140:
4019:
2351:
2347:
2226:
2104:
1391:
906:
827:
638:
293:
278:
5102:
5025:
3628:
1980:
670:
334:
The condition of having semitones is called hemitonia; that of having no semitones is
5369:
5297:
5242:
4911:
4851:
4412:
4388:
4376:
4357:
4171:
4122:
4105:
4097:
4070:
3949:
3912:
3891:
3861:
3836:
3815:
3794:
3748:
3685:
3643:
3632:
3592:
3561:
2362:
1841:
1406:
systems, there are two different semitones. This results because of the break in the
1383:
1363:
1342:
1012:, augmented unisons are quite rare in tonal repertoire. In the example to the right,
883:
835:
739:
601:
583:
335:
324:
305:
270:
52:
3773:
A manual of harmony for use in music-schools and seminaries and for self-instruction
3440:
has an even closer match to the two semitones with 3 and 5 steps of its scale while
2708:
of 5 limit tuning have four different sizes, and can be classified as follows:
2203:{\displaystyle {\frac {256}{243}}={\frac {2^{8}}{3^{5}}}\approx 90.2{\text{ cents}}}
1257:
1059:
chord, and the augmented unison is the result of superimposing this harmony upon an
5309:
5198:
5151:
4981:
4806:
4751:
4745:
4739:
4643:
4543:
4516:
4400:
4382:
4327:
4321:
4163:
4093:
4011:
3858:
Alfred's
Essentials of Music Theory: A Complete Self-Study Course for All Musicians
3491:
3271:
2108:
2084:
Pythagorean limma as five descending just perfect fifths from C (the inverse is B+)
1998:
1833:
1436:, the chromatic and diatonic semitones are 76.0 and 117.1 cents wide respectively.
1407:
1387:
1346:
1323:
1300:
1251:
1056:
896:
831:
809:
692:
609:
555:
190:
56:
3772:
5354:
5349:
5186:
5068:
4949:
4673:
4461:
4351:
4345:
4333:
3679:
3636:
3472:
two types of semitones and closely match their just intervals (25/24 and 16/15).
2693:
2435:
2370:
2112:
1784:
1766:
1350:
1331:
1296:
1283:
1113:
1109:
974:
763:
551:
317:
198:
145:
118:
346:
containing semitones is called hemitonic; one without semitones is anhemitonic.
296:, seven semitones out of twelve are diatonic, with ratio 256:243 or 90.2 cents (
5272:
5171:
4929:
4923:
4917:
4689:
4216:
4115:
4062:
3853:
3777:
3511:
3501:
3308:
3227:
2852:
2564:
2470:
1911:
1375:
1335:
1098:
1074:
750:
735:
571:
491:
430:
242:
108:
2392:
1902:{\displaystyle {\sqrt{\frac {2}{3-{\sqrt {2}}}}}\approx 100.4{\text{ cents,}}}
795:
5423:
5394:
5277:
5053:
4902:
4821:
4816:
4762:
4623:
4563:
4449:
4437:
4302:
4265:
4222:
3993:
3883:
3639:
3263:
2669:) or 1.0416... (approximately 70.7 cents). It is the interval between a
2560:
2343:
2218:
1421:
1355:
1315:
1262:
1070:
985:
775:
597:
567:
504:
343:
339:
223:
48:
615:
550:, this interval is very frequently used, and is of particular importance in
5302:
5020:
4881:
4527:
4284:
4247:
3506:
3325:
3295:
3291:
3226:
The smaller chromatic and diatonic semitones differ from the larger by the
2455:
2426:
2249:
2051:
1413:
The chromatic semitone is usually smaller than the diatonic. In the common
1359:
1288:
1123:
1094:
563:
541:
487:
440:
259:(an interval between two notes at the same staff position, e.g. from C to C
230:
128:
3933:
On the
Sensations of Tone as a Physiological Basis for the Theory of Music
3747:(2nd ed.). Mississauga, Ontario: Frederick Harris Music. p. 17.
300:), and the other five are chromatic, with ratio 2187:2048 or 113.7 cents (
5374:
5181:
5161:
5030:
4861:
4296:
4290:
4259:
4253:
3719:
2670:
2466:
2381:
2030:
2014:
1777:
1358:) as a source of cacophony in their music (e.g. the early piano works of
1304:
1134:
move by contrary motion toward a unison, each having moved a whole tone.
1131:
1063:
1013:
998:
994:
767:
575:
463:
219:
27:
This article is about the musical interval. For the printing method, see
822:
814:
5389:
5292:
5063:
4957:
4455:
3852:
3231:
2358:
2010:
1327:
1118:
1102:
1090:
717:
354:
266:
215:
202:
4023:
2090:
705:
5344:
5166:
5137:
4963:
4467:
3557:
How equal temperament ruined harmony : (and why you should care)
1989:
For more examples, see
Pythagorean and Just systems of tuning below.
1382:
have two distinct types of semitones, but in the exceptional case of
1292:
866:
358:
The melodic minor second is an integral part of most cadences of the
2692:
Two other kinds of semitones are produced by 5 limit tuning. A
2078:
1112:, in the early polyphony of the 11th century this was not the case.
193:
commonly used in
Western tonal music, and it is considered the most
156:
5193:
4995:
4443:
4015:
2409:
1319:
531:
28:
5001:
4989:
4975:
4394:
4339:
3243:
2214:
2009:
semitone in the tuning. Well temperament was constructed so that
1837:
1009:
589:
579:
320:
typically define three or four kinds of semitones. For instance,
1362:). By now, enharmonic equivalence was a commonplace property of
5215:
5058:
5035:
4943:
4937:
4228:
4210:
2339:
1746:
1308:
1144:
902:
547:
313:
4431:
4050:) ratio ... this raises a note approximately 70.6 cents.
2439:
2430:
Relationship between the 4 common 5 limit semitones
1787:
or otherwise, to the equal-tempered semitone. To cite a few:
1338:
period, the musical function of the semitone did not change.
1108:
Though it would later become an integral part of the musical
4132:
2726:
between harmonically related flats and sharps e.g. between E
2338:
It can be thought of as the difference between four perfect
1971:{\displaystyle (139/138)^{8}\approx 99.9995{\text{ cents,}}}
474:(F) in C major), and between the seventh and eighth degree (
3172:
The most frequently occurring semitones are the just ones (
2683:) to indicate a note is raised 70.7 cents, or a flat (
1122:
other alternatives: either proceeding by whole tone from a
2365:
apart, in contrast to diatonic and chromatic semitones in
4000:'s extended just intonation – a guide for interpreters".
1139:
316:
of ratio 128:125 or 41.1 cents. 12-tone scales tuned in
5132:
3909:
Encyclopedia of the
History of Arabic Science, Volume 2
3705:
Sound: An
Elementary Text-book for Schools and Colleges
3153:
3132:
3117:
3102:
3032:
3011:
2996:
2981:
2929:
2908:
2893:
2878:
2806:
2785:
2770:
2755:
2616:
2601:
2586:
2522:
2507:
2492:
1218:
1184:
1159:
770:
between B & C and E & F, and is "the sharpest
281:, where the diatonic semitone is smaller instead. See
3324:), but it lies on the boundary between the minor and
3305:
Under 11 limit tuning, there is a fairly common
3087:
2966:
2863:
2740:
2573:
2479:
2276:
2213:
It can be thought of as the difference between three
2151:
1932:
1858:
1798:
1326:
for instrumental tuning and the more frequent use of
1152:
895:). The augmented unison is also the inversion of the
273:
is used; for example, they are not the same thing in
1261:
Dramatic chromatic scale in the opening measures of
1101:
theory were all based upon this diatonic pattern of
1143:] remainder between the perfect fourth and the
826:Augmented unisons often appear as a consequence of
3822:. "There is no such thing as a diminished unison."
3766:
3764:
3681:The Complete Idiot's Guide to Music Theory, 2nd ed
3161:
3040:
2937:
2814:
2643:
2549:
2357:The Pythagorean limma and Pythagorean apotome are
2327:
2202:
1970:
1901:
1823:
1242:
3347:tone (13:12 or 138.57 cents) and tridecimal
1824:{\displaystyle 18/17\approx 99.0{\text{ cents,}}}
1369:
869:alteration of the same step. It is also called a
544:sharper than C, and then by both tones together.
5421:
4069:. University Press of the Pacific. p. 325.
2096:Pythagorean apotome as seven just perfect fifths
1341:In the 20th century, however, composers such as
1052:to make the tone's function clear as part of an
586:, wherever the tonic falls to the leading-tone.
3890:. Princeton University Press: Princeton, 1990.
3761:
3331:In 13 limit tuning, there is a tridecimal
1386:, there is only one. The unevenly distributed
592:, the interval usually occurs as some form of
5118:
4148:
3856:; Karen Farnum Surmani; Morton Manus (2009).
2361:equivalents (chromatic semitones) and only a
830:, such as those in the soprano voice of this
524:Listen to a minor second in equal temperament
5411:List of dodecaphonic and serial compositions
3237:
3190:occurs at 6 short intervals out of 12,
1374:The exact size of a semitone depends on the
123:16:15, 17:16, 27:25, 135:128, 25:24, 256:243
3988:
3986:
3976:. Great Britain: Royal Society: 531. 1880.
3879:
3877:
3400:
1733:
1726:
1721:
1714:
1707:
1700:
1695:
1625:
1620:
1615:
1610:
1605:
1600:
1595:
1590:
1585:
1580:
1575:
1570:
1565:
1555:
1552:
1544:
1541:
1533:
1530:
1522:
1519:
1516:
1508:
1505:
1497:
1494:
1480:
1471:
1464:
1457:
1448:
1254:because it lacked clarity as an interval."
211:; the interval between them is a semitone.
5406:
5125:
5111:
5089:
4155:
4141:
3969:Proceedings of the Royal Society of London
3888:Studies in the Origin of Harmonic Tonality
2376:
734:second appears in many other works of the
3978:digitized 26 Feb 2008; Harvard University
2454:) or 1.0666... (approximately 111.7
308:of ratio 531441:524288 or 23.5 cents. In
285:for more details about this terminology.
3992:
3983:
3874:
3860:. Alfred Music Publishing. p. 135.
3701:
3549:
3547:
3545:
3543:
3541:
3539:
3537:
3262:) available in between the 5 limit
2425:
2408:
2391:
2380:
1256:
993:
821:
813:
757:
748:. More recently, the music to the movie
614:
604:. It may also appear in inversions of a
466:, between the third and fourth degree, (
353:
241:(an interval encompassing two different
155:
3742:
3589:The Mathematical Theory of Tone Systems
2704:). The 12 semitones produced by a
1397:
1282:However, beginning in the 13th century
482:(C) in C major). It is also called the
301:
297:
218:or major second is 2 semitones wide, a
14:
5422:
4513:
3901:
3736:
3581:
3553:
873:. The augmented unison is abbreviated
582:. It also occurs in many forms of the
5106:
4136:
4061:
3791:Music: In Theory and Practice, Vol. I
3534:
3420:), and the diatonic semitone is two (
2839:, e.g. between C and an accute C
2020:
766:a 16:15 minor second arises in the C
2958:, e.g. between E and F (5:4 to 4:3):
1770:
1752:
637:The minor second may be viewed as a
328:
3211:at only one interval (if diatonic D
1992:
1983:as part of a sixteenth-tone system.
803:
574:, it appears as the falling of the
24:
4102:A History of Western Music, 6th ed
4087:
3627:are all variously used in sources.
3363:tone (27:26 or 65.34 cents).
3067:(5:3 to 9:5), or C and chromatic D
2138:. It is also sometimes called the
1390:contain many different semitones.
655:
562:it appears as a resolution of the
494:. The minor second is abbreviated
233:, a distinction is made between a
25:
5451:
2438:typically corresponds to a pitch
2386:
2222:
5405:
5214:
5088:
4121:. New York: W. W. Norton, 1978.
2414:
2397:
2089:
2077:
2058:
2050:
2037:
2029:
1270:
984:
973:
845:
794:
716:Problems playing this file? See
704:
682:
628:
363:
161:
4055:
3959:
3938:
3922:
3886:, trans. Gjerdingen, Robert O.
3846:
3825:
3804:
3274:(7:4). There is also a smaller
3223:and sharp notes are not used).
1783:There are many approximations,
1688:
1560:
1489:
1441:
1438:
861:, the interval produced by the
623:'s Prelude in C major from the
349:
3946:Music: A Mathematical Offering
3783:
3712:
3702:Capstick, John Walton (1913).
3695:
3672:
3602:
2234:Pythagorean chromatic semitone
1948:
1933:
1918:and more accurate alternative,
1370:Semitones in different tunings
1200:
1187:
754:exemplifies the minor second.
745:Ballet of the Unhatched Chicks
283:Interval (music) § Number
13:
1:
4162:
3907:Rashed, Roshdi (ed.) (1996).
3745:Elementary Rudiments of Music
3708:. Cambridge University Press.
3646:, and others use "half tone".
3527:
2120:Pythagorean diatonic semitone
645:resolving into the following
290:twelve-tone equal temperament
271:twelve-tone equal temperament
5335:All-interval twelve-tone row
3789:Benward & Saker (2003).
2413:'Larger' or major limma on C
2252:. It may also be called the
7:
4710:septimal chromatic semitone
3911:, pp. 588, 608. Routledge.
3475:
3298:used the latter as part of
3276:septimal chromatic semitone
2134:), and is often called the
2103:Like meantone temperament,
10:
5456:
4716:septimal diatonic semitone
4504:(Numbers in brackets refer
4104:. New York: Norton, 2001.
3487:List of meantone intervals
3268:7 limit minor seventh
3248:septimal diatonic semitone
2258:Pythagorean major semitone
2236:has a ratio of 2187/2048 (
2142:. It is about 90.2 cents.
2140:Pythagorean minor semitone
1084:
807:
486:because it occurs between
26:
5403:
5327:
5261:
5223:
5212:
5144:
5086:
5044:
5011:
4900:
4870:
4840:
4797:
4788:
4761:
4688:
4671:
4506:to fractional semitones.)
4499:24-tone equal temperament
4496:
4485:
4422:
4367:
4312:
4275:
4238:
4203:
4170:
4003:Perspectives of New Music
3831:Day and Pilhofer (2007).
3810:Kostka and Payne (2003).
3743:Wharram, Barbara (2010).
3492:List of musical intervals
3482:12-tone equal temperament
3434:31-tone equal temperament
3406:19-tone equal temperament
3238:Extended just intonations
2824:Larger chromatic semitone
1758:12-tone equal temperament
1747:31-tone equal temperament
1731:
1719:
1712:
1705:
1693:
1485:
1478:
1476:
1469:
1462:
1455:
1453:
1116:suggested instead in his
844:Op. 102 No. 3, mm. 47–49.
619:Harmonic minor second in
448:12-Tone equal temperament
446:
439:
429:
419:
414:
406:
398:
393:
383:
267:enharmonically equivalent
150:112, 105, 133, 92, 71, 90
144:
136:12-Tone equal temperament
134:
127:
117:
107:
97:
92:
84:
68:
63:
42:
3833:Music Theory for Dummies
3554:Duffin, Ross W. (2008).
3401:Other equal temperaments
3050:Larger diatonic semitone
2829:major chromatic semitone
2724:minor chromatic semitone
2377:Just 5-limit intonation
2122:has a ratio of 256/243 (
2057:Pythagorean apotome on C
1997:There are many forms of
911:diminished seventh chord
600:that is not part of the
502:). Its inversion is the
55:(for augmented unison);
5094:List of pitch intervals
4832:Subminor and supermajor
4771:minor diatonic semitone
4681:refer to pitch ratios.)
3497:List of pitch intervals
3059:major diatonic semitone
2956:minor diatonic semitone
2712:Just chromatic semitone
2396:16:15 diatonic semitone
1780:equals nine semitones.
881:. Its inversion is the
59:(for diminished unison)
5340:All-trichord hexachord
5288:Second Viennese School
4892:Undecimal quarter tone
3468:) steps of its scale.
3300:his 43 tone scale
3163:
3079:and G (25:18 and 3:2):
3061:, e.g. between A and B
3042:
2947:Just diatonic semitone
2939:
2816:
2645:
2551:
2460:just diatonic semitone
2431:
2423:
2406:
2389:
2329:
2204:
2036:Pythagorean limma on C
1972:
1903:
1825:
1417:, tuned as a cycle of
1415:quarter-comma meantone
1279:
1244:
1130:having two notes at a
1006:
854:
819:
660:
650:
540:, which is a tone 100
372:
360:Common practice period
310:quarter-comma meantone
304:); they differ by the
170:
5134:Twelve-tone technique
4887:Septimal quarter tone
4698:septimal quarter tone
3944:Benson, Dave (2006).
3929:Hermann von Helmholtz
3780:, trans. G. Schirmer.
3667:is "chiefly N. Amer."
3656:One source says that
3587:Haluska, Jan (2003).
3164:
3043:
2940:
2817:
2706:commonly used version
2646:
2552:
2429:
2412:
2395:
2384:
2346:, and functions as a
2330:
2248:). It is about 113.7
2221:, and functions as a
2205:
1973:
1904:
1826:
1380:Meantone temperaments
1260:
1245:
997:
915:augmented sixth chord
825:
818:Augmented unison on C
817:
758:In other temperaments
659:
618:
357:
159:
5283:Josef Matthias Hauer
5248:Retrograde inversion
5074:Incomposite interval
4827:Pythagorean interval
4679:(Numbers in brackets
4187:(Numbers in brackets
4044:ratio is the sharp (
3770:Paul, Oscar (1885).
3599:. Overtone semitone.
3517:Pythagorean interval
3217:replaces chromatic D
3085:
2964:
2861:
2855:) (1:1 and 135:128):
2738:
2732:and E (6:5 and 5:4):
2571:
2477:
2367:meantone temperament
2274:
2264:Pythagorean interval
2149:
1930:
1856:
1796:
1398:Meantone temperament
1318:(1600 to 1750), the
1150:
1003:Transcendental Étude
275:meantone temperament
51:(for minor second);
5365:Formula composition
4857:Pythagorean apotome
4704:septimal third tone
3724:www.musictheory.net
3522:Regular temperament
3244:7 limit tuning
2254:Pythagorean apotome
1126:to a unison, or an
1043:was preferred to a
828:secondary dominants
731:Étude Op. 25, No. 5
678:Étude Op. 25, No. 5
606:major seventh chord
402:semitone, half step
380:
302:Pythagorean apotome
222:4 semitones, and a
39:
4970:Septimal semicomma
4116:Hoppin, Richard H.
3159:
3157:
3141:
3126:
3111:
3038:
3036:
3020:
3005:
2990:
2935:
2933:
2917:
2902:
2887:
2812:
2810:
2794:
2779:
2764:
2716:chromatic semitone
2641:
2625:
2610:
2595:
2547:
2531:
2516:
2501:
2434:A minor second in
2432:
2424:
2407:
2390:
2352:Pythagorean tuning
2348:chromatic semitone
2325:
2227:Pythagorean tuning
2200:
2105:Pythagorean tuning
2021:Pythagorean tuning
1968:
1899:
1821:
1443:Chromatic semitone
1392:Pythagorean tuning
1301:passus duriusculus
1287:practice known as
1280:
1240:
1233:
1205:
1174:
1034:in the bass. Here
1007:
907:secondary dominant
871:chromatic semitone
855:
841:Song Without Words
820:
661:
651:
627:, book 1, mm. 7–9.
602:functional harmony
560:deceptive cadences
378:
373:
294:Pythagorean tuning
279:Pythagorean tuning
253:chromatic semitone
245:, e.g. from C to D
189:, is the smallest
171:
80:chromatic semitone
78:diminished unison,
74:diatonic semitone,
37:
5417:
5416:
5370:Modernism (music)
5298:Arnold Schoenberg
5100:
5099:
5082:
5081:
4912:Pythagorean comma
4852:Pythagorean limma
4784:
4783:
4780:
4779:
4746:supermajor fourth
4722:supermajor second
4667:
4666:
4481:
4480:
4477:
4476:
4189:are the number of
4098:Claude V. Palisca
4094:Grout, Donald Jay
3867:978-0-7390-3635-8
3799:978-0-07-294262-0
3754:978-1-55440-283-0
3720:"musictheory.net"
3684:. : Alpha, 2005.
3678:Miller, Michael.
3644:Leonard Bernstein
3567:978-0-393-33420-3
3393:counterpart to a
3381:Though the names
3156:
3151:
3140:
3125:
3110:
3035:
3030:
3019:
3004:
2989:
2932:
2927:
2916:
2901:
2886:
2809:
2804:
2793:
2778:
2763:
2637:
2629:
2624:
2609:
2594:
2584:
2576:
2543:
2535:
2530:
2515:
2500:
2490:
2482:
2420:
2403:
2387:diatonic semitone
2363:Pythagorean comma
2323:
2312:
2285:
2223:diatonic semitone
2198:
2187:
2160:
2136:Pythagorean limma
2064:
2043:
1966:
1897:
1886:
1880:
1877:
1819:
1753:Equal temperament
1742:
1741:
1736:
1729:
1724:
1717:
1710:
1703:
1698:
1690:Diatonic semitone
1628:
1623:
1618:
1613:
1608:
1603:
1598:
1593:
1588:
1583:
1578:
1573:
1568:
1483:
1474:
1467:
1460:
1451:
1388:well temperaments
1384:equal temperament
1364:equal temperament
1343:Arnold Schoenberg
1324:well temperaments
1276:
1229:
1198:
1170:
884:diminished octave
851:
836:Felix Mendelssohn
740:Modest Mussorgsky
703:
687:
634:
610:added tone chords
584:imperfect cadence
484:diatonic semitone
456:
455:
369:
325:five-limit tuning
306:Pythagorean comma
298:Pythagorean limma
235:diatonic semitone
167:
154:
153:
76:augmented unison,
53:diminished octave
16:(Redirected from
5447:
5409:
5408:
5328:Related articles
5310:Charles Wuorinen
5218:
5152:Combinatoriality
5127:
5120:
5113:
5104:
5103:
5092:
5091:
4982:Septimal kleisma
4795:
4794:
4752:subminor seventh
4734:supermajor third
4686:
4685:
4674:Just intonations
4659:
4658:
4654:
4651:
4639:
4638:
4634:
4631:
4619:
4618:
4614:
4611:
4599:
4598:
4594:
4591:
4579:
4578:
4574:
4571:
4559:
4558:
4554:
4551:
4539:
4538:
4534:
4511:
4510:
4494:
4493:
4201:
4200:
4183:
4182:
4157:
4150:
4143:
4134:
4133:
4081:
4080:
4059:
4053:
4052:
4049:
4048:
4043:
4041:
4040:
4037:
4034:
3996:(Summer 1991). "
3990:
3981:
3980:
3963:
3957:
3942:
3936:
3926:
3920:
3905:
3899:
3881:
3872:
3871:
3850:
3844:
3829:
3823:
3808:
3802:
3787:
3781:
3768:
3759:
3758:
3740:
3734:
3733:
3731:
3730:
3716:
3710:
3709:
3699:
3693:
3676:
3670:
3660:is "chiefly US",
3606:
3600:
3585:
3579:
3578:
3576:
3574:
3551:
3467:
3466:
3465:
3463:
3462:play 116.7 cents
3455:
3454:
3453:
3451:
3431:
3430:
3429:
3427:
3426:play 126.3 cents
3419:
3418:
3417:
3415:
3377:
3376:
3375:
3373:
3362:
3360:
3359:
3356:
3353:
3346:
3344:
3343:
3340:
3337:
3323:
3322:
3321:
3319:
3289:
3288:
3287:
3285:
3272:harmonic seventh
3261:
3260:
3259:
3257:
3222:
3221:
3216:
3215:
3207:
3200:
3193:
3182:
3175:
3168:
3166:
3165:
3160:
3158:
3154:
3149:
3142:
3133:
3127:
3118:
3112:
3103:
3097:
3096:
3078:
3077:
3072:
3071:
3066:
3065:
3047:
3045:
3044:
3039:
3037:
3033:
3028:
3021:
3012:
3006:
2997:
2991:
2982:
2976:
2975:
2944:
2942:
2941:
2936:
2934:
2930:
2925:
2918:
2909:
2903:
2894:
2888:
2879:
2873:
2872:
2850:
2849:
2844:
2843:
2821:
2819:
2818:
2813:
2811:
2807:
2802:
2795:
2786:
2780:
2771:
2765:
2756:
2750:
2749:
2731:
2730:
2688:
2687:
2682:
2681:
2668:
2667:
2666:
2664:
2650:
2648:
2647:
2642:
2635:
2634:
2630:
2627:
2626:
2617:
2611:
2602:
2596:
2587:
2582:
2574:
2556:
2554:
2553:
2548:
2541:
2540:
2536:
2533:
2532:
2523:
2517:
2508:
2502:
2493:
2488:
2480:
2453:
2452:
2451:
2449:
2422:
2421:
2405:
2404:
2334:
2332:
2331:
2326:
2324:
2321:
2313:
2311:
2310:
2301:
2300:
2291:
2286:
2278:
2247:
2246:
2245:
2243:
2209:
2207:
2206:
2201:
2199:
2196:
2188:
2186:
2185:
2176:
2175:
2166:
2161:
2153:
2133:
2132:
2131:
2129:
2109:circle of fifths
2093:
2081:
2066:
2065:
2054:
2045:
2044:
2033:
1999:well temperament
1993:Well temperament
1977:
1975:
1974:
1969:
1967:
1964:
1956:
1955:
1943:
1908:
1906:
1905:
1900:
1898:
1895:
1887:
1885:
1879:
1878:
1873:
1861:
1860:
1834:Vincenzo Galilei
1830:
1828:
1827:
1822:
1820:
1817:
1806:
1734:
1727:
1722:
1715:
1708:
1701:
1696:
1626:
1621:
1616:
1611:
1606:
1601:
1596:
1591:
1586:
1581:
1576:
1571:
1566:
1550:
1549:
1539:
1538:
1528:
1527:
1514:
1513:
1503:
1502:
1481:
1472:
1465:
1458:
1449:
1439:
1435:
1434:
1429:
1428:
1408:circle of fifths
1278:
1277:
1249:
1247:
1246:
1241:
1239:
1235:
1234:
1230:
1222:
1213:
1212:
1211:
1206:
1199:
1191:
1180:
1175:
1171:
1163:
1081:for piano solo.
1057:dominant seventh
1050:
1049:
1041:
1040:
1032:
1031:
1023:
1022:
989:
988:
978:
977:
967:
966:
958:
957:
945:
944:
928:
927:
897:augmented octave
859:augmented unison
853:
852:
810:Augmented unison
804:Augmented unison
798:
789:
788:
787:
785:
738:period, such as
708:
701:
693:Martha Goldstein
689:
688:
669:'s "wrong note"
658:
636:
635:
539:
538:
534:is followed by D
529:
528:
527:
525:
381:
377:
375:Musical interval
371:
370:
264:
263:
257:augmented unison
250:
249:
210:
209:
191:musical interval
177:, also called a
169:
168:
57:augmented octave
40:
36:
34:Musical interval
21:
5455:
5454:
5450:
5449:
5448:
5446:
5445:
5444:
5435:Seconds (music)
5430:Minor intervals
5420:
5419:
5418:
5413:
5399:
5355:Duration series
5350:Chromatic scale
5323:
5264:
5257:
5219:
5210:
5187:Cross partition
5157:Complementation
5140:
5131:
5101:
5096:
5078:
5040:
5007:
4950:Septimal diesis
4896:
4866:
4836:
4790:
4776:
4757:
4680:
4677:
4663:
4656:
4652:
4649:
4647:
4636:
4632:
4629:
4627:
4616:
4612:
4609:
4607:
4596:
4592:
4589:
4587:
4576:
4572:
4569:
4567:
4556:
4552:
4549:
4547:
4536:
4532:
4531:
4521:
4520:
4519:
4515:
4505:
4502:
4489:
4487:
4473:
4418:
4363:
4308:
4271:
4234:
4195:
4190:
4188:
4178:
4176:
4173:
4166:
4161:
4090:
4088:Further reading
4085:
4084:
4077:
4060:
4056:
4046:
4045:
4038:
4035:
4032:
4031:
4029:
3991:
3984:
3965:
3964:
3960:
3943:
3939:
3927:
3923:
3906:
3902:
3882:
3875:
3868:
3854:Surmani, Andrew
3851:
3847:
3830:
3826:
3809:
3805:
3788:
3784:
3769:
3762:
3755:
3741:
3737:
3728:
3726:
3718:
3717:
3713:
3700:
3696:
3677:
3673:
3655:
3638:
3607:
3603:
3586:
3582:
3572:
3570:
3568:
3552:
3535:
3530:
3478:
3461:
3458:
3457:
3450:play 66.7 cents
3449:
3446:
3445:
3425:
3422:
3421:
3414:play 63.2 cents
3413:
3410:
3409:
3403:
3371:
3368:
3367:
3357:
3354:
3351:
3350:
3348:
3341:
3338:
3335:
3334:
3332:
3317:
3314:
3313:
3283:
3280:
3279:
3266:(15:8) and the
3255:
3252:
3251:
3240:
3219:
3218:
3213:
3212:
3210:
3205:
3203:
3198:
3196:
3191:
3189:
3185:
3180:
3178:
3173:
3152:
3131:
3116:
3101:
3092:
3088:
3086:
3083:
3082:
3075:
3074:
3069:
3068:
3063:
3062:
3031:
3010:
2995:
2980:
2971:
2967:
2965:
2962:
2961:
2928:
2907:
2892:
2877:
2868:
2864:
2862:
2859:
2858:
2847:
2846:
2841:
2840:
2805:
2784:
2769:
2754:
2745:
2741:
2739:
2736:
2735:
2728:
2727:
2703:
2699:
2694:chromatic scale
2685:
2684:
2679:
2678:
2662:
2659:
2658:
2615:
2600:
2585:
2581:
2577:
2572:
2569:
2568:
2563:(15:8) and the
2521:
2506:
2491:
2487:
2483:
2478:
2475:
2474:
2447:
2444:
2443:
2436:just intonation
2415:
2398:
2379:
2371:just intonation
2320:
2306:
2302:
2296:
2292:
2290:
2277:
2275:
2272:
2271:
2241:
2238:
2237:
2195:
2181:
2177:
2171:
2167:
2165:
2152:
2150:
2147:
2146:
2127:
2124:
2123:
2113:just intonation
2101:
2100:
2099:
2098:
2097:
2094:
2086:
2085:
2082:
2071:
2070:
2069:
2068:
2067:
2059:
2055:
2047:
2046:
2038:
2034:
2023:
1995:
1981:Julián Carrillo
1978:
1963:
1951:
1947:
1939:
1931:
1928:
1927:
1909:
1894:
1881:
1872:
1865:
1859:
1857:
1854:
1853:
1831:
1816:
1802:
1797:
1794:
1793:
1771:discussed below
1767:just intonation
1755:
1547:
1546:
1536:
1535:
1525:
1524:
1511:
1510:
1500:
1499:
1432:
1431:
1426:
1425:
1400:
1372:
1351:Igor Stravinsky
1271:
1232:
1231:
1221:
1217:
1207:
1204:
1203:
1190:
1183:
1182:
1181:
1176:
1173:
1172:
1162:
1158:
1157:
1153:
1151:
1148:
1147:
1114:Guido of Arezzo
1105:and semitones.
1087:
1047:
1046:
1038:
1037:
1029:
1028:
1020:
1019:
1016:had written an
983:
972:
964:
963:
955:
954:
942:
941:
925:
924:
846:
812:
806:
801:
800:
799:
783:
780:
779:
764:just intonation
760:
727:Frédéric Chopin
723:
722:
714:
712:
711:
710:
709:
700:
690:
683:
680:
674:
667:Frédéric Chopin
662:
656:
647:A minor seventh
629:
536:
535:
523:
520:
519:
376:
364:
352:
318:just intonation
269:if and only if
261:
260:
247:
246:
243:staff positions
207:
206:
162:
146:Just intonation
79:
77:
75:
73:
35:
32:
23:
22:
15:
12:
11:
5:
5453:
5443:
5442:
5440:Units of level
5437:
5432:
5415:
5414:
5404:
5401:
5400:
5398:
5397:
5392:
5387:
5382:
5377:
5372:
5367:
5362:
5357:
5352:
5347:
5342:
5337:
5331:
5329:
5325:
5324:
5322:
5321:
5312:
5307:
5306:
5305:
5300:
5295:
5285:
5280:
5275:
5273:Milton Babbitt
5269:
5267:
5259:
5258:
5256:
5255:
5253:Multiplication
5250:
5245:
5240:
5235:
5229:
5227:
5221:
5220:
5213:
5211:
5209:
5208:
5207:
5206:
5201:
5191:
5190:
5189:
5179:
5174:
5172:Interval class
5169:
5164:
5159:
5154:
5148:
5146:
5142:
5141:
5130:
5129:
5122:
5115:
5107:
5098:
5097:
5087:
5084:
5083:
5080:
5079:
5077:
5076:
5071:
5066:
5061:
5056:
5050:
5048:
5042:
5041:
5039:
5038:
5033:
5028:
5023:
5017:
5015:
5009:
5008:
5006:
5005:
4999:
4993:
4986:
4985:
4979:
4973:
4967:
4961:
4954:
4953:
4947:
4944:Greater diesis
4941:
4934:
4933:
4930:Septimal comma
4927:
4924:Holdrian comma
4921:
4918:Syntonic comma
4915:
4908:
4906:
4898:
4897:
4895:
4894:
4889:
4884:
4878:
4876:
4868:
4867:
4865:
4864:
4859:
4854:
4848:
4846:
4838:
4837:
4835:
4834:
4829:
4824:
4819:
4814:
4809:
4803:
4801:
4792:
4786:
4785:
4782:
4781:
4778:
4777:
4775:
4774:
4767:
4765:
4759:
4758:
4756:
4755:
4749:
4743:
4740:subminor fifth
4737:
4731:
4728:subminor third
4725:
4719:
4713:
4707:
4701:
4694:
4692:
4683:
4669:
4668:
4665:
4664:
4662:
4661:
4641:
4621:
4601:
4581:
4561:
4541:
4524:
4522:
4514:
4508:
4491:
4483:
4482:
4479:
4478:
4475:
4474:
4472:
4471:
4465:
4459:
4453:
4447:
4441:
4435:
4428:
4426:
4420:
4419:
4417:
4416:
4410:
4404:
4398:
4392:
4386:
4380:
4373:
4371:
4365:
4364:
4362:
4361:
4355:
4349:
4343:
4337:
4331:
4325:
4318:
4316:
4310:
4309:
4307:
4306:
4300:
4294:
4288:
4281:
4279:
4273:
4272:
4270:
4269:
4263:
4257:
4251:
4244:
4242:
4236:
4235:
4233:
4232:
4226:
4220:
4214:
4207:
4205:
4198:
4180:
4168:
4167:
4160:
4159:
4152:
4145:
4137:
4131:
4130:
4119:Medieval Music
4113:
4089:
4086:
4083:
4082:
4075:
4054:
4016:10.2307/833435
4010:(2): 106–137.
3982:
3958:
3937:
3921:
3900:
3884:Dahlhaus, Carl
3873:
3866:
3845:
3824:
3803:
3782:
3778:Theodore Baker
3760:
3753:
3735:
3711:
3694:
3671:
3601:
3580:
3566:
3532:
3531:
3529:
3526:
3525:
3524:
3519:
3514:
3512:Neutral second
3509:
3504:
3502:Approach chord
3499:
3494:
3489:
3484:
3477:
3474:
3402:
3399:
3309:neutral second
3239:
3236:
3228:syntonic comma
3208:
3201:
3197:3 times,
3194:
3187:
3183:
3176:
3170:
3169:
3148:
3145:
3139:
3136:
3130:
3124:
3121:
3115:
3109:
3106:
3100:
3095:
3091:
3080:
3051:
3048:
3027:
3024:
3018:
3015:
3009:
3003:
3000:
2994:
2988:
2985:
2979:
2974:
2970:
2959:
2948:
2945:
2924:
2921:
2915:
2912:
2906:
2900:
2897:
2891:
2885:
2882:
2876:
2871:
2867:
2856:
2853:syntonic comma
2825:
2822:
2801:
2798:
2792:
2789:
2783:
2777:
2774:
2768:
2762:
2759:
2753:
2748:
2744:
2733:
2713:
2701:
2697:
2677:used a sharp (
2652:
2651:
2640:
2633:
2623:
2620:
2614:
2608:
2605:
2599:
2593:
2590:
2580:
2565:perfect octave
2558:
2546:
2539:
2529:
2526:
2520:
2514:
2511:
2505:
2499:
2496:
2486:
2471:perfect fourth
2458:), called the
2378:
2375:
2336:
2335:
2319:
2316:
2309:
2305:
2299:
2295:
2289:
2284:
2281:
2211:
2210:
2194:
2191:
2184:
2180:
2174:
2170:
2164:
2159:
2156:
2095:
2088:
2087:
2083:
2076:
2075:
2074:
2073:
2072:
2056:
2049:
2048:
2035:
2028:
2027:
2026:
2025:
2024:
2022:
2019:
1994:
1991:
1987:
1986:
1985:
1984:
1962:
1959:
1954:
1950:
1946:
1942:
1938:
1935:
1922:
1921:
1920:
1919:
1912:Marin Mersenne
1893:
1890:
1884:
1876:
1871:
1868:
1864:
1848:
1847:
1846:
1845:
1815:
1812:
1809:
1805:
1801:
1754:
1751:
1740:
1739:
1737:
1732:
1730:
1725:
1720:
1718:
1713:
1711:
1706:
1704:
1699:
1694:
1692:
1686:
1685:
1683:
1681:
1679:
1677:
1675:
1673:
1671:
1669:
1667:
1665:
1663:
1661:
1659:
1657:
1655:
1653:
1651:
1649:
1647:
1645:
1643:
1641:
1639:
1637:
1635:
1633:
1630:
1629:
1624:
1619:
1614:
1609:
1604:
1599:
1594:
1589:
1584:
1579:
1574:
1569:
1564:
1558:
1557:
1554:
1551:
1543:
1540:
1532:
1529:
1521:
1518:
1515:
1507:
1504:
1496:
1493:
1487:
1486:
1484:
1479:
1477:
1475:
1470:
1468:
1463:
1461:
1456:
1454:
1452:
1447:
1445:
1399:
1396:
1371:
1368:
1267:Solo e pensoso
1238:
1228:
1225:
1220:
1219:
1216:
1210:
1202:
1197:
1194:
1189:
1186:
1185:
1179:
1169:
1166:
1161:
1160:
1156:
1099:medieval music
1086:
1083:
1075:Iannis Xenakis
808:Main article:
805:
802:
793:
792:
791:
784:Play B & C
774:found in the
759:
756:
713:
695:playing on an
691:
681:
676:
675:
664:
663:
654:
653:
652:
608:, and in many
572:plagal cadence
492:diatonic scale
462:occurs in the
454:
453:
450:
444:
443:
437:
436:
433:
431:Interval class
427:
426:
423:
417:
416:
412:
411:
408:
404:
403:
400:
396:
395:
391:
390:
387:
374:
351:
348:
201:(or half of a
152:
151:
148:
142:
141:
138:
132:
131:
125:
124:
121:
115:
114:
111:
109:Interval class
105:
104:
101:
95:
94:
90:
89:
86:
82:
81:
70:
66:
65:
61:
60:
46:
33:
9:
6:
4:
3:
2:
5452:
5441:
5438:
5436:
5433:
5431:
5428:
5427:
5425:
5412:
5402:
5396:
5393:
5391:
5388:
5386:
5383:
5381:
5378:
5376:
5373:
5371:
5368:
5366:
5363:
5361:
5358:
5356:
5353:
5351:
5348:
5346:
5343:
5341:
5338:
5336:
5333:
5332:
5330:
5326:
5319:
5318:
5313:
5311:
5308:
5304:
5301:
5299:
5296:
5294:
5291:
5290:
5289:
5286:
5284:
5281:
5279:
5278:Pierre Boulez
5276:
5274:
5271:
5270:
5268:
5266:
5260:
5254:
5251:
5249:
5246:
5244:
5241:
5239:
5236:
5234:
5231:
5230:
5228:
5226:
5222:
5217:
5205:
5202:
5200:
5197:
5196:
5195:
5192:
5188:
5185:
5184:
5183:
5180:
5178:
5175:
5173:
5170:
5168:
5165:
5163:
5160:
5158:
5155:
5153:
5150:
5149:
5147:
5143:
5139:
5135:
5128:
5123:
5121:
5116:
5114:
5109:
5108:
5105:
5095:
5085:
5075:
5072:
5070:
5067:
5065:
5062:
5060:
5057:
5055:
5052:
5051:
5049:
5047:
5043:
5037:
5034:
5032:
5029:
5027:
5024:
5022:
5019:
5018:
5016:
5014:
5010:
5003:
5000:
4997:
4994:
4991:
4988:
4987:
4983:
4980:
4977:
4974:
4971:
4968:
4965:
4962:
4959:
4956:
4955:
4951:
4948:
4945:
4942:
4939:
4938:Lesser diesis
4936:
4935:
4931:
4928:
4925:
4922:
4919:
4916:
4913:
4910:
4909:
4907:
4905:
4904:
4899:
4893:
4890:
4888:
4885:
4883:
4880:
4879:
4877:
4875:
4874:
4873:Quarter tones
4869:
4863:
4860:
4858:
4855:
4853:
4850:
4849:
4847:
4845:
4844:
4839:
4833:
4830:
4828:
4825:
4823:
4822:Pseudo-octave
4820:
4818:
4815:
4813:
4810:
4808:
4805:
4804:
4802:
4800:
4796:
4793:
4787:
4772:
4769:
4768:
4766:
4764:
4760:
4753:
4750:
4747:
4744:
4741:
4738:
4735:
4732:
4729:
4726:
4723:
4720:
4717:
4714:
4711:
4708:
4705:
4702:
4699:
4696:
4695:
4693:
4691:
4687:
4684:
4682:
4676:
4675:
4670:
4645:
4642:
4625:
4622:
4605:
4602:
4585:
4582:
4565:
4562:
4545:
4542:
4529:
4526:
4525:
4523:
4518:
4512:
4509:
4507:
4501:
4500:
4495:
4492:
4484:
4469:
4466:
4463:
4460:
4457:
4454:
4451:
4448:
4445:
4442:
4439:
4436:
4433:
4430:
4429:
4427:
4425:
4421:
4414:
4411:
4408:
4405:
4402:
4399:
4396:
4393:
4390:
4387:
4384:
4381:
4378:
4375:
4374:
4372:
4370:
4366:
4359:
4356:
4353:
4350:
4347:
4344:
4341:
4338:
4335:
4332:
4329:
4326:
4323:
4320:
4319:
4317:
4315:
4311:
4304:
4301:
4298:
4295:
4292:
4289:
4286:
4283:
4282:
4280:
4278:
4274:
4267:
4264:
4261:
4258:
4255:
4252:
4249:
4246:
4245:
4243:
4241:
4237:
4230:
4227:
4224:
4221:
4218:
4215:
4212:
4209:
4208:
4206:
4202:
4199:
4197:
4193:
4184:
4181:
4175:
4169:
4165:
4158:
4153:
4151:
4146:
4144:
4139:
4138:
4135:
4128:
4127:0-393-09090-6
4124:
4120:
4117:
4114:
4111:
4110:0-393-97527-4
4107:
4103:
4099:
4095:
4092:
4091:
4078:
4076:1-4102-1920-8
4072:
4068:
4064:
4058:
4051:
4028:... the
4025:
4021:
4017:
4013:
4009:
4005:
4004:
3999:
3995:
3989:
3987:
3979:
3975:
3971:
3970:
3962:
3955:
3954:0-521-85387-7
3951:
3947:
3941:
3934:
3930:
3925:
3918:
3917:0-415-12411-5
3914:
3910:
3904:
3897:
3896:0-691-09135-8
3893:
3889:
3885:
3880:
3878:
3869:
3863:
3859:
3855:
3849:
3842:
3841:0-7645-7838-3
3838:
3834:
3828:
3821:
3820:0-07-285260-7
3817:
3813:
3812:Tonal Harmony
3807:
3800:
3796:
3792:
3786:
3779:
3775:
3774:
3767:
3765:
3756:
3750:
3746:
3739:
3725:
3721:
3715:
3707:
3706:
3698:
3691:
3690:1-59257-437-8
3687:
3683:
3682:
3675:
3669:
3666:
3662:
3659:
3654:
3652:
3650:
3648:
3645:
3641:
3640:Aaron Copland
3637:
3635:
3633:
3631:
3629:
3626:
3622:
3618:
3614:
3610:
3605:
3598:
3597:0-8247-4714-3
3594:
3590:
3584:
3569:
3563:
3559:
3558:
3550:
3548:
3546:
3544:
3542:
3540:
3538:
3533:
3523:
3520:
3518:
3515:
3513:
3510:
3508:
3505:
3503:
3500:
3498:
3495:
3493:
3490:
3488:
3485:
3483:
3480:
3479:
3473:
3469:
3464:
3452:
3443:
3439:
3435:
3428:
3416:
3407:
3398:
3396:
3392:
3388:
3384:
3379:
3374:
3364:
3329:
3327:
3320:
3311:
3310:
3303:
3301:
3297:
3293:
3286:
3277:
3273:
3269:
3265:
3264:major seventh
3258:
3249:
3246:there is the
3245:
3235:
3233:
3229:
3224:
3179:, 16:15, and
3146:
3143:
3137:
3134:
3128:
3122:
3119:
3113:
3107:
3104:
3098:
3093:
3089:
3081:
3073:(27:25), or F
3060:
3056:
3052:
3049:
3025:
3022:
3016:
3013:
3007:
3001:
2998:
2992:
2986:
2983:
2977:
2972:
2968:
2960:
2957:
2953:
2949:
2946:
2922:
2919:
2913:
2910:
2904:
2898:
2895:
2889:
2883:
2880:
2874:
2869:
2865:
2857:
2854:
2838:
2834:
2830:
2826:
2823:
2799:
2796:
2790:
2787:
2781:
2775:
2772:
2766:
2760:
2757:
2751:
2746:
2742:
2734:
2725:
2721:
2717:
2714:
2711:
2710:
2709:
2707:
2695:
2690:
2676:
2672:
2665:
2655:
2638:
2631:
2621:
2618:
2612:
2606:
2603:
2597:
2591:
2588:
2578:
2566:
2562:
2561:major seventh
2559:
2544:
2537:
2527:
2524:
2518:
2512:
2509:
2503:
2497:
2494:
2484:
2472:
2468:
2465:
2464:
2463:
2461:
2457:
2450:
2441:
2437:
2428:
2411:
2394:
2388:
2383:
2374:
2372:
2368:
2364:
2360:
2355:
2353:
2349:
2345:
2341:
2317:
2314:
2307:
2303:
2297:
2293:
2287:
2282:
2279:
2270:
2269:
2268:
2266:
2265:
2259:
2255:
2251:
2244:
2235:
2230:
2228:
2224:
2220:
2216:
2192:
2189:
2182:
2178:
2172:
2168:
2162:
2157:
2154:
2145:
2144:
2143:
2141:
2137:
2130:
2121:
2116:
2114:
2110:
2106:
2092:
2080:
2053:
2032:
2018:
2016:
2012:
2008:
2004:
2000:
1990:
1982:
1960:
1957:
1952:
1944:
1940:
1936:
1926:
1925:
1924:
1923:
1917:
1916:constructible
1913:
1910:suggested by
1891:
1888:
1882:
1874:
1869:
1866:
1862:
1852:
1851:
1850:
1849:
1843:
1839:
1835:
1832:suggested by
1813:
1810:
1807:
1803:
1799:
1792:
1791:
1790:
1789:
1788:
1786:
1781:
1779:
1774:
1772:
1768:
1764:
1759:
1750:
1748:
1738:
1691:
1687:
1684:
1682:
1680:
1678:
1676:
1674:
1672:
1670:
1668:
1666:
1664:
1662:
1660:
1658:
1656:
1654:
1652:
1650:
1648:
1646:
1644:
1642:
1640:
1638:
1636:
1634:
1632:
1631:
1563:
1559:
1492:
1488:
1446:
1444:
1440:
1437:
1423:
1420:
1416:
1411:
1409:
1405:
1395:
1393:
1389:
1385:
1381:
1378:system used.
1377:
1367:
1365:
1361:
1357:
1356:tone clusters
1352:
1348:
1344:
1339:
1337:
1333:
1329:
1325:
1321:
1317:
1312:
1310:
1306:
1302:
1298:
1294:
1290:
1285:
1268:
1264:
1263:Luca Marenzio
1259:
1255:
1253:
1236:
1226:
1223:
1214:
1208:
1195:
1192:
1177:
1167:
1164:
1154:
1146:
1142:
1141:
1135:
1133:
1129:
1125:
1121:
1120:
1115:
1111:
1106:
1104:
1100:
1096:
1092:
1082:
1080:
1076:
1072:
1071:tone clusters
1067:
1065:
1062:
1058:
1055:
1051:
1042:
1033:
1024:
1015:
1011:
1004:
1000:
996:
992:
990:
987:
979:
976:
968:
959:
950:
946:
937:
933:
929:
920:
916:
912:
908:
904:
900:
898:
894:
890:
886:
885:
880:
876:
872:
868:
864:
860:
843:
842:
837:
833:
829:
824:
816:
811:
797:
790:
786:
777:
773:
769:
765:
755:
753:
752:
747:
746:
741:
737:
732:
728:
721:
719:
707:
698:
694:
679:
673:
672:
668:
648:
644:
640:
626:
622:
617:
613:
611:
607:
603:
599:
598:nonchord tone
595:
591:
587:
585:
581:
577:
573:
569:
565:
561:
557:
553:
549:
545:
543:
533:
526:
517:
515:
511:
507:
506:
505:major seventh
501:
497:
493:
489:
485:
481:
477:
473:
469:
465:
461:
451:
449:
445:
442:
438:
434:
432:
428:
424:
422:
418:
413:
409:
405:
401:
397:
392:
389:major seventh
388:
386:
382:
361:
356:
347:
345:
341:
340:musical scale
337:
332:
330:
326:
323:
319:
315:
311:
307:
303:
299:
295:
291:
286:
284:
280:
276:
272:
268:
265:). These are
258:
254:
244:
240:
236:
232:
227:
226:7 semitones.
225:
224:perfect fifth
221:
217:
212:
204:
200:
199:12-tone scale
196:
192:
188:
184:
180:
176:
158:
149:
147:
143:
139:
137:
133:
130:
126:
122:
120:
119:Just interval
116:
112:
110:
106:
102:
100:
96:
91:
87:
83:
72:minor second,
71:
67:
62:
58:
54:
50:
49:major seventh
47:
45:
41:
30:
19:
5379:
5315:
5303:Anton Webern
5225:Permutations
5145:Fundamentals
5045:
5012:
4998:(0.72 cents)
4992:(1.95 cents)
4972:(13.8 cents)
4966:(10.1 cents)
4960:(19.5 cents)
4952:(35.7 cents)
4946:(62.6 cents)
4940:(41.1 cents)
4932:(27.3 cents)
4926:(22.6 cents)
4920:(21.5 cents)
4914:(23.5 cents)
4901:
4882:Quarter tone
4872:
4871:
4842:
4841:
4798:
4763:Higher-limit
4678:
4672:
4584:major fourth
4528:quarter tone
4503:
4497:
4191:
4186:
4118:
4101:
4066:
4057:
4027:
4007:
4001:
3998:Ben Johnston
3994:Fonville, J.
3977:
3973:
3967:
3961:
3945:
3940:
3932:
3924:
3908:
3903:
3887:
3857:
3848:
3832:
3827:
3811:
3806:
3790:
3785:
3771:
3744:
3738:
3727:. Retrieved
3723:
3714:
3704:
3697:
3680:
3674:
3664:
3657:
3624:
3620:
3616:
3612:
3608:
3604:
3588:
3583:
3571:. Retrieved
3556:
3507:Major second
3470:
3404:
3394:
3390:
3386:
3382:
3380:
3365:
3330:
3326:major second
3306:
3304:
3241:
3225:
3171:
3058:
3054:
2955:
2951:
2851:raised by a
2837:major chroma
2836:
2833:larger limma
2832:
2828:
2723:
2719:
2715:
2691:
2675:Ben Johnston
2656:
2653:
2459:
2433:
2369:and 5-limit
2356:
2337:
2261:
2257:
2253:
2233:
2231:
2212:
2139:
2135:
2119:
2117:
2107:is a broken
2102:
2006:
2002:
1996:
1988:
1965: cents,
1896: cents,
1836:and used by
1818: cents,
1782:
1775:
1756:
1743:
1689:
1561:
1490:
1442:
1412:
1401:
1373:
1360:Henry Cowell
1340:
1313:
1297:Semantically
1289:musica ficta
1281:
1266:
1138:
1136:
1127:
1124:major second
1117:
1107:
1088:
1078:
1068:
1060:
1053:
1044:
1035:
1026:
1017:
1010:Harmonically
1008:
1005:, measure 63
981:
970:
961:
952:
948:
939:
935:
931:
922:
918:
901:
892:
888:
882:
878:
874:
870:
863:augmentation
858:
856:
839:
761:
749:
743:
724:
715:
702:Opening bars
665:
646:
642:
590:Harmonically
588:
564:leading-tone
546:
518:
513:
509:
503:
499:
495:
483:
479:
475:
471:
467:
460:minor second
459:
457:
420:
407:Abbreviation
379:minor second
350:Minor second
333:
287:
256:
252:
239:minor second
238:
234:
231:music theory
228:
213:
186:
182:
179:minor second
178:
174:
172:
160:Minor second
98:
85:Abbreviation
5375:Punctualism
5360:Equivalence
5031:Millioctave
5013:Measurement
5004:(0.4 cents)
4984:(7.7 cents)
4978:(8.1 cents)
4862:Major limma
4604:minor fifth
3591:, p. xxiv.
3204:twice, and
3186:, 25:24): S
2671:major third
2467:major third
2344:just fifths
2322: cents
2219:just fifths
2197: cents
1842:Renaissance
1778:major sixth
1347:BĂ©la BartĂłk
1316:Baroque era
1305:lament bass
1269:, ca. 1580.
1132:major third
1064:pedal point
1025:against an
999:Franz Liszt
903:Melodically
768:major scale
576:subdominant
548:Melodically
464:major scale
399:Other names
336:anhemitonia
220:major third
69:Other names
5424:Categories
5390:Time point
5385:Set theory
5293:Alban Berg
5238:Retrograde
5177:Invariance
5162:Derivation
5064:Semiditone
4958:Diaschisma
4773:(17-limit)
4464:(22 or 23)
4462:fourteenth
4458:(20 or 21)
4456:thirteenth
4452:(18 or 19)
4446:(17 or 18)
4440:(15 or 16)
4434:(13 or 14)
4369:Diminished
4196:interval.)
4177:(post-Bach
3948:, p. 369.
3835:, p. 113.
3776:, p. 165.
3729:2024-01-04
3528:References
3307:undecimal
3278:of 21:20 (
3250:of 15:14 (
3232:diaschisma
2469:(5:4) and
2442:of 16:15 (
2359:enharmonic
2342:and seven
2011:enharmonic
1328:enharmonic
1295:passages.
1119:Micrologus
1097:scales of
1091:tetrachord
1073:, such as
1001:'s second
772:dissonance
718:media help
639:suspension
621:J. S. Bach
594:dissonance
322:Asymmetric
216:whole tone
203:whole step
5345:Atonality
5265:composers
5243:Inversion
5233:Prime row
5199:Aggregate
5182:Partition
5167:Hexachord
5138:serialism
5026:Centitone
4964:Semicomma
4843:Semitones
4807:Microtone
4791:intervals
4468:fifteenth
4314:Augmented
4192:semitones
4164:Intervals
4063:Prout, E.
3935:, p. 454.
3814:, p. 21.
3793:, p. 54.
3665:half-tone
3663:and that
3625:half-tone
3617:half tone
3613:half step
3456:) and 7 (
3391:chromatic
3387:chromatic
3312:(12:11) (
3144:≈
3114:÷
3023:≈
2993:÷
2920:≈
2890:×
2797:≈
2767:÷
2598:÷
2504:÷
2315:≈
2217:and five
2190:≈
2007:chromatic
1958:≈
1889:≈
1870:−
1811:≈
1332:Classical
1293:chromatic
1252:clausulae
867:chromatic
570:. In the
554:. In the
421:Semitones
195:dissonant
187:half tone
183:half step
99:Semitones
18:Half step
5380:Semitone
5194:Tone row
4996:Breedsma
4444:eleventh
4424:Compound
4179:Western)
4174:semitone
4065:(2004).
4047:♯
3931:(1885).
3692:. p. 19.
3621:halftone
3609:Semitone
3476:See also
3444:uses 4 (
3395:diatonic
3383:diatonic
3294:, while
3220:♭
3214:♭
3076:♯
3070:♭
3064:♭
2848:♯
2842:♯
2729:♭
2686:♭
2680:♯
2003:diatonic
1979:used by
1838:luthiers
1785:rational
1548:♭
1537:♯
1526:♯
1512:♭
1501:♯
1433:♯
1427:♭
1419:tempered
1404:meantone
1336:Romantic
1284:cadences
1128:occursus
1048:♯
1039:♭
1030:♮
1021:♭
965:♭
956:♭
943:♯
926:♯
913:, or an
832:sequence
736:Romantic
552:cadences
537:♭
532:middle C
530:. Here,
500:−2
478:(B) and
470:(E) and
262:♯
251:) and a
248:♭
208:♯
175:semitone
38:semitone
29:Halftone
5263:Notable
5002:Ragisma
4990:Schisma
4976:Kleisma
4812:5-limit
4718:(15:14)
4712:(21:20)
4706:(28:27)
4700:(36:35)
4690:7-limit
4655:⁄
4644:seventh
4635:⁄
4615:⁄
4595:⁄
4575:⁄
4555:⁄
4535:⁄
4517:Neutral
4490:systems
4450:twelfth
4407:seventh
4358:seventh
4303:seventh
4266:seventh
4204:Perfect
4172:Twelve-
4067:Harmony
4042:
4030:
3573:28 June
3361:
3349:
3345:
3333:
3055:greater
2952:smaller
2720:smaller
2340:octaves
2256:or the
2215:octaves
1961:99.9995
1840:of the
1314:By the
1110:cadence
1085:History
1079:Evryali
641:of the
580:mediant
578:to the
566:to the
556:perfect
490:in the
385:Inverse
185:, or a
44:Inverse
5059:Ditone
5046:Others
5036:Savart
4903:Commas
4799:Groups
4748:(10:7)
4544:second
4488:tuning
4413:octave
4389:fourth
4377:second
4340:fourth
4328:second
4322:unison
4285:second
4248:second
4229:octave
4217:fourth
4211:unison
4194:in the
4125:
4108:
4096:, and
4073:
4024:833435
4022:
3952:
3915:
3894:
3864:
3839:
3818:
3797:
3751:
3688:
3623:, and
3595:
3564:
3296:Partch
3292:Cowell
3150:
3029:
2926:
2803:
2636:
2628:
2583:
2575:
2567:(2:1)
2542:
2534:
2489:
2481:
2473:(4:3)
2385:16:15
1627:1200.0
1622:1082.9
1617:1006.8
1424:from E
1422:fifths
1376:tuning
1349:, and
1309:pianto
1307:, and
1145:ditone
699:(1851)
649:chord.
314:diesis
88:m2; A1
5395:Trope
5069:Secor
4817:Comma
4789:Other
4754:(7:4)
4742:(7:5)
4736:(9:7)
4730:(7:6)
4724:(8:7)
4624:sixth
4564:third
4486:Other
4438:tenth
4432:ninth
4401:sixth
4395:fifth
4383:third
4352:sixth
4346:fifth
4334:third
4297:sixth
4291:third
4277:Minor
4260:sixth
4254:third
4240:Major
4223:fifth
4020:JSTOR
3442:72-ET
3438:53-ET
3155:cents
3147:133.2
3034:cents
3026:111.7
2954:, or
2931:cents
2835:, or
2831:, or
2808:cents
2722:, or
2718:, or
2557:and a
2456:cents
2440:ratio
2350:in a
2318:113.7
2250:cents
2225:in a
1914:as a
1892:100.4
1735:117.1
1728:117.1
1723:117.1
1716:117.1
1709:117.1
1702:117.1
1697:117.1
1612:889.7
1607:772.6
1602:696.6
1597:579.5
1592:503.4
1587:386.3
1582:310.3
1577:193.2
1562:Cents
1491:Pitch
1320:tonal
1103:tones
1095:modal
1014:Liszt
893:dim 8
891:, or
879:aug 1
877:, or
834:from
776:scale
697:Érard
671:Étude
596:or a
568:tonic
542:cents
488:steps
452:100.0
441:Cents
344:chord
329:below
237:, or
129:Cents
5317:more
5204:List
5136:and
5054:Wolf
5021:Cent
4470:(24)
4415:(11)
4360:(12)
4354:(10)
4305:(10)
4268:(11)
4231:(12)
4123:ISBN
4106:ISBN
4071:ISBN
3966:"".
3950:ISBN
3913:ISBN
3892:ISBN
3862:ISBN
3837:ISBN
3816:ISBN
3795:ISBN
3749:ISBN
3686:ISBN
3658:step
3593:ISBN
3575:2017
3562:ISBN
3385:and
3372:Play
3318:play
3284:play
3256:play
2923:92.2
2800:70.7
2700:to C
2663:play
2448:play
2283:2048
2280:2187
2262:See
2242:play
2232:The
2193:90.2
2128:play
2118:The
2005:and
1814:99.0
1572:76.0
1482:76.0
1473:76.0
1466:76.0
1459:76.0
1450:76.0
1430:to G
909:, a
857:The
751:Jaws
558:and
498:(or
458:The
415:Size
394:Name
338:. A
93:Size
64:Name
5320:...
5314:...
4409:(9)
4403:(7)
4397:(6)
4391:(4)
4385:(2)
4379:(0)
4348:(8)
4342:(6)
4336:(5)
4330:(3)
4324:(1)
4299:(8)
4293:(3)
4287:(1)
4262:(9)
4256:(4)
4250:(2)
4225:(7)
4219:(5)
4213:(0)
4012:doi
3432:).
3242:In
3057:or
3053:or
2950:or
2914:128
2911:135
2827:or
2267:.)
2260:. (
2158:243
2155:256
2015:key
1945:138
1937:139
1773:).
1567:0.0
1402:In
1265:'s
1227:243
1224:256
1140:sic
991:).
838:'s
778:."
762:In
742:'s
729:'s
625:WTC
516:).
514:Ma7
512:or
342:or
288:In
255:or
229:In
140:100
5426::
4648:10
4100:.
4039:24
4033:25
4026:.
4018:.
4008:29
4006:.
3985:^
3974:30
3972:.
3876:^
3763:^
3722:.
3642:,
3619:,
3615:,
3611:,
3536:^
3302:.
3270:/
3138:25
3135:27
3017:15
3014:16
2899:80
2896:81
2884:24
2881:25
2845:(C
2791:24
2788:25
2622:15
2619:16
2604:15
2528:15
2525:16
2373:.
2354:.
2308:11
2229:.
1808:17
1800:18
1769:,
1556:C
1553:B
1542:A
1531:G
1520:F
1517:E
1506:D
1495:C
1345:,
1311:.
1303:,
1077:'
1066:.
980:,
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3129:=
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3008:=
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2978:=
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2905:=
2875:=
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