3270:
3242:
2114:
770:
510:
3358:
2649:
2434:
3448:
3412:
3436:
3400:
2228:
3304:
1247:
646:
785:
2382:
2041:
605:
2416:
2020:
2371:
984:
812:
804:
2080:
695:
2068:
146:
5396:
5079:
2399:
964:
5205:
975:
3638:
1237:
344:
1275:
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
3460:
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
722:
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
675:
621:
2407:
2030:
1263:
2932:
1342:
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
2390:
1990:, 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
3636:
3156:
3035:
356:
2809:
2051:
3271:
1138:
3243:
2115:
838:
622:
2638:
2544:
3359:
2650:
2408:
2322:
2031:
1264:
2435:
154:
2197:
771:
3219:(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
673:
2391:
2229:
1239:." 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
1896:
357:
3317:(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.
3449:
3437:
3413:
2052:
3401:
3305:
3642:
1749:
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
837:
3279:) 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
674:
511:
1965:
155:
1733:
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.
2002:
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
1818:
3378:
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
316:
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
3386:
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).
836:
666:
2849:
619:
3073:
2952:
2662:(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
2405:
1261:
2726:
2028:
888:, 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.
2388:
1232:{\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)}
354:
1399:
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.
936:. (Restricting the notation to only minor seconds is impractical, as the same example would have a rapidly increasing number of accidentals, written enharmonically as
2049:
3832:. "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."
2559:
2465:
152:
2262:
620:
2406:
2029:
1262:
2137:
281:
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
2389:
1311:
harmonic framework was fully formed, and the various musical functions of the semitone were rigorously understood. Later in this period the adoption of
355:
2050:
1844:
3692:
1355:, and instrumental use of the semitone was not at all problematic for the performer. The composer was free to write semitones wherever he wished.
839:
5113:
2643:
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".
153:
5399:
4800:
3859:. Since lowering either note of a perfect unison would actually increase its size, the perfect unison cannot be diminished, only augmented.
854:, 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
2678:) to indicate a note is lowered 70.7 cents. (This is the standard practice for just intonation, but not for all other microtunings.)
1126:"As late as the 13th century the half step was experienced as a problematic interval not easily understood, as the irrational [
3957:
301:, 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
1738:
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.
203:
In a 12-note approximately equally divided scale, any interval can be defined in terms of an appropriate number of semitones (e.g. a
3623:
1280:). By the 16th century, the semitone had become a more versatile interval, sometimes even appearing as an augmented unison in very
1918:
194:), visually seen on a keyboard as the distance between two keys that are adjacent to each other. For example, C is adjacent to C
3854:
3787:
3741:
3554:
3397:
distinguishes between the chromatic and diatonic semitones; in this tuning, the chromatic semitone is one step of the scale (
2104:, these semitones are rational. Also, unlike most meantone temperaments, the chromatic semitone is larger than the diatonic.
3544:
2685:
defines 12 semitones as the 12 intervals between the 13 adjacent notes, spanning a full octave (e.g. from C
5106:
4143:
3650:
3367:), and the minor diatonic semitone is 17:16 or 105.0 cents, and septendecimal limma is 18:17 or 98.95 cents.
1784:
906:. Its use is also often the consequence of a melody proceeding in semitones, regardless of harmonic underpinning, e.g.
4302:
4115:
4098:
4063:
3942:
3905:
3884:
3829:
3808:
3678:
3657:
3585:
2451:. This is a practical just semitone, since it is the interval that occurs twice within the diatonic scale between a:
266:, where the diatonic semitone is distinguished from and larger than the chromatic semitone (augmented unison), or in
436:
124:
1383:, similar to meantone tuning, has two, but in other systems of just intonation there are many more possibilities.
1319:
equivalences increased the ease with which a semitone could be applied. Its function remained similar through the
3288:
3640:
1754:(approximately 1.05946), or 100 cents, and is 11.7 cents narrower than the 16:15 ratio (its most common form in
719:
183:
5251:
5099:
2927:{\displaystyle S_{2}={\tfrac {25}{24}}\times {\tfrac {81}{80}}={\tfrac {135}{128}}\approx 92.2\ {\hbox{cents}}}
2646:
An "augmented unison" (sharp) in just intonation is a different, smaller semitone, with frequency ratio 25:24 (
1058:
In addition to this kind of usage, harmonic augmented unisons are frequently written in modern works involving
5221:
278:
5323:
5192:
4592:
4572:
4698:
3264:
5165:
3151:{\displaystyle S_{4}={\tfrac {9}{5}}\div {\tfrac {5}{3}}={\tfrac {27}{25}}\approx 133.2\ {\hbox{cents}}}
3030:{\displaystyle S_{3}={\tfrac {4}{3}}\div {\tfrac {5}{4}}={\tfrac {16}{15}}\approx 111.7\ {\hbox{cents}}}
1323:
period, and though it was used more frequently as the language of tonality became more chromatic in the
4704:
4412:
3475:
3425:
also distinguishes between these two intervals, which become 2 and 3 steps of the scale, respectively.
3236:
2804:{\displaystyle S_{1}={\tfrac {5}{4}}\div {\tfrac {6}{5}}={\tfrac {25}{24}}\approx 70.7\ {\hbox{cents}}}
2694:
310:
4265:
4228:
714:
In unusual situations, the minor second can add a great deal of character to the music. For instance,
5348:
4487:
3991:
3223:(2048:2025 or 19.6 cents), the outer differ by the greater diesis (648:625 or 62.6 cents).
1746:
760:
733:
613:
582:
2006:
had a slightly different sonic color or character, beyond the limitations of conventional notation.
5423:
5418:
899:
548:
991:
5428:
5082:
4820:
4759:
4136:
3986:
3485:
2663:
2100:. This creates two distinct semitones, but because Pythagorean tuning is also a form of 3-limit
1078:
The semitone appeared in the music theory of Greek antiquity as part of a diatonic or chromatic
5328:
5276:
5241:
4880:
4357:
3256:
1403:
348:
298:
4174:
5122:
4875:
4686:
3917:
1765:
All diatonic intervals can be expressed as an equivalent number of semitones. For instance a
903:
894:, an augmented unison very frequently occurs when proceeding to a chromatic chord, such as a
609:
3355:
In 17 limit just intonation, the major diatonic semitone is 15:14 or 119.4 cents (
5271:
5236:
5062:
4815:
4722:
4716:
3505:
3470:
3430:
3426:
3422:
3394:
2633:{\displaystyle \ \left(\ {\tfrac {2}{1}}\div {\tfrac {15}{8}}={\tfrac {16}{15}}\ \right)~.}
2539:{\displaystyle \ \left(\ {\tfrac {4}{3}}\div {\tfrac {5}{4}}={\tfrac {16}{15}}\ \right)\ ,}
2355:
2252:
1904:
1392:
1368:
1082:, and it has always had a place in the diatonic scales of Western music since. The various
851:
715:
685:
655:
373:
263:
32:
271:
8:
5353:
5213:
4845:
4710:
4692:
3790:. Specific example of an A1 not given but general example of perfect intervals described.
3510:
1751:
1407:
1288:, in the 16th century the repeated melodic semitone became associated with weeping, see:
829:
594:
186:
when sounded harmonically. It is defined as the interval between two adjacent notes in a
3619:
3549:(First published as a Norton paperback. ed.). New York: W. W. Norton. p. 163.
2317:{\displaystyle {\frac {2187}{2048}}={\frac {3^{7}}{2^{11}}}\approx 113.7{\text{ cents}}}
5373:
5305:
5226:
5145:
4958:
4395:
4129:
4008:
2340:
2336:
2215:
2093:
1380:
895:
816:
627:
282:
267:
5091:
5014:
3617:
1969:
659:
323:
The condition of having semitones is called hemitonia; that of having no semitones is
5358:
5286:
5231:
4900:
4840:
4401:
4377:
4365:
4346:
4160:
4111:
4094:
4086:
4059:
3938:
3901:
3880:
3850:
3825:
3804:
3783:
3737:
3674:
3632:
3621:
3581:
3550:
2351:
1830:
1395:
systems, there are two different semitones. This results because of the break in the
1372:
1352:
1331:
1001:, augmented unisons are quite rare in tonal repertoire. In the example to the right,
872:
824:
728:
590:
572:
324:
313:
294:
259:
41:
3762:
A manual of harmony for use in music-schools and seminaries and for self-instruction
3429:
has an even closer match to the two semitones with 3 and 5 steps of its scale while
2697:
of 5 limit tuning have four different sizes, and can be classified as follows:
2192:{\displaystyle {\frac {256}{243}}={\frac {2^{8}}{3^{5}}}\approx 90.2{\text{ cents}}}
1246:
1048:
chord, and the augmented unison is the result of superimposing this harmony upon an
5298:
5187:
5140:
4970:
4795:
4740:
4734:
4728:
4632:
4532:
4505:
4389:
4371:
4316:
4310:
4152:
4082:
4000:
3847:
Alfred's
Essentials of Music Theory: A Complete Self-Study Course for All Musicians
3480:
3260:
2097:
2073:
Pythagorean limma as five descending just perfect fifths from C (the inverse is B+)
1987:
1822:
1425:, the chromatic and diatonic semitones are 76.0 and 117.1 cents wide respectively.
1396:
1376:
1335:
1312:
1289:
1240:
1045:
885:
820:
798:
681:
598:
544:
179:
45:
3761:
5343:
5338:
5175:
5057:
4938:
4662:
4450:
4340:
4334:
4322:
3668:
3625:
3461:
two types of semitones and closely match their just intervals (25/24 and 16/15).
2682:
2424:
2359:
2101:
1773:
1755:
1339:
1320:
1285:
1272:
1102:
1098:
963:
752:
540:
306:
187:
134:
107:
335:
containing semitones is called hemitonic; one without semitones is anhemitonic.
285:, seven semitones out of twelve are diatonic, with ratio 256:243 or 90.2 cents (
5261:
5160:
4918:
4912:
4906:
4678:
4205:
4104:
4051:
3842:
3766:
3500:
3490:
3297:
3216:
2841:
2553:
2459:
1900:
1364:
1324:
1087:
1063:
739:
724:
560:
480:
419:
231:
97:
2381:
1891:{\displaystyle {\sqrt{\frac {2}{3-{\sqrt {2}}}}}\approx 100.4{\text{ cents,}}}
784:
5412:
5383:
5266:
5042:
4891:
4810:
4805:
4751:
4612:
4552:
4438:
4426:
4291:
4254:
4211:
3982:
3872:
3628:
3252:
2658:) or 1.0416... (approximately 70.7 cents). It is the interval between a
2549:
2332:
2207:
1410:
1344:
1304:
1251:
1059:
974:
764:
586:
556:
493:
332:
328:
212:
37:
604:
539:, this interval is very frequently used, and is of particular importance in
5291:
5009:
4870:
4516:
4273:
4236:
3495:
3314:
3284:
3280:
3215:
The smaller chromatic and diatonic semitones differ from the larger by the
2444:
2415:
2238:
2040:
1402:
The chromatic semitone is usually smaller than the diatonic. In the common
1348:
1277:
1112:
1083:
552:
530:
476:
429:
248:(an interval between two notes at the same staff position, e.g. from C to C
219:
117:
3922:
On the
Sensations of Tone as a Physiological Basis for the Theory of Music
3736:(2nd ed.). Mississauga, Ontario: Frederick Harris Music. p. 17.
289:), and the other five are chromatic, with ratio 2187:2048 or 113.7 cents (
5363:
5170:
5150:
5019:
4850:
4285:
4279:
4248:
4242:
3708:
2659:
2455:
2370:
2019:
2003:
1766:
1347:) as a source of cacophony in their music (e.g. the early piano works of
1293:
1123:
move by contrary motion toward a unison, each having moved a whole tone.
1120:
1052:
1002:
987:
983:
756:
564:
452:
208:
16:
This article is about the musical interval. For the printing method, see
811:
803:
5378:
5281:
5052:
4946:
4444:
3841:
3220:
2347:
1999:
1316:
1107:
1091:
1079:
706:
343:
255:
204:
191:
4012:
2079:
694:
5333:
5155:
5126:
4952:
4456:
3546:
How equal temperament ruined harmony : (and why you should care)
1978:
For more examples, see
Pythagorean and Just systems of tuning below.
1371:
have two distinct types of semitones, but in the exceptional case of
1281:
855:
347:
The melodic minor second is an integral part of most cadences of the
2681:
Two other kinds of semitones are produced by 5 limit tuning. A
2067:
1101:, in the early polyphony of the 11th century this was not the case.
182:
commonly used in
Western tonal music, and it is considered the most
145:
5182:
4984:
4432:
4004:
2398:
1308:
520:
17:
4990:
4978:
4964:
4383:
4328:
3232:
2203:
1998:
semitone in the tuning. Well temperament was constructed so that
1826:
998:
578:
568:
309:
typically define three or four kinds of semitones. For instance,
1351:). By now, enharmonic equivalence was a commonplace property of
5204:
5047:
5024:
4932:
4926:
4217:
4199:
2328:
1735:
1297:
1133:
891:
536:
302:
4420:
4039:) ratio ... this raises a note approximately 70.6 cents.
2428:
2419:
Relationship between the 4 common 5 limit semitones
1776:
or otherwise, to the equal-tempered semitone. To cite a few:
1327:
period, the musical function of the semitone did not change.
1097:
Though it would later become an integral part of the musical
4121:
2715:
between harmonically related flats and sharps e.g. between E
2327:
It can be thought of as the difference between four perfect
1960:{\displaystyle (139/138)^{8}\approx 99.9995{\text{ cents,}}}
463:(F) in C major), and between the seventh and eighth degree (
3161:
The most frequently occurring semitones are the just ones (
2672:) to indicate a note is raised 70.7 cents, or a flat (
1111:
other alternatives: either proceeding by whole tone from a
2354:
apart, in contrast to diatonic and chromatic semitones in
3989:'s extended just intonation – a guide for interpreters".
1128:
305:
of ratio 128:125 or 41.1 cents. 12-tone scales tuned in
5121:
3898:
Encyclopedia of the
History of Arabic Science, Volume 2
3694:
Sound: An
Elementary Text-book for Schools and Colleges
3142:
3121:
3106:
3091:
3021:
3000:
2985:
2970:
2918:
2897:
2882:
2867:
2795:
2774:
2759:
2744:
2605:
2590:
2575:
2511:
2496:
2481:
1207:
1173:
1148:
759:
between B & C and E & F, and is "the sharpest
270:, where the diatonic semitone is smaller instead. See
3313:), but it lies on the boundary between the minor and
3294:
Under 11 limit tuning, there is a fairly common
3076:
2955:
2852:
2729:
2562:
2468:
2265:
2202:
It can be thought of as the difference between three
2140:
1921:
1847:
1787:
1315:
for instrumental tuning and the more frequent use of
1141:
884:). The augmented unison is also the inversion of the
262:
is used; for example, they are not the same thing in
1250:
Dramatic chromatic scale in the opening measures of
1090:
theory were all based upon this diatonic pattern of
1132:] remainder between the perfect fourth and the
815:Augmented unisons often appear as a consequence of
3811:. "There is no such thing as a diminished unison."
3755:
3753:
3670:The Complete Idiot's Guide to Music Theory, 2nd ed
3150:
3029:
2926:
2803:
2632:
2538:
2346:The Pythagorean limma and Pythagorean apotome are
2316:
2191:
1959:
1890:
1812:
1231:
3336:tone (13:12 or 138.57 cents) and tridecimal
1813:{\displaystyle 18/17\approx 99.0{\text{ cents,}}}
1358:
858:alteration of the same step. It is also called a
533:sharper than C, and then by both tones together.
5410:
4058:. University Press of the Pacific. p. 325.
2085:Pythagorean apotome as seven just perfect fifths
1330:In the 20th century, however, composers such as
1041:to make the tone's function clear as part of an
575:, wherever the tonic falls to the leading-tone.
3879:. Princeton University Press: Princeton, 1990.
3750:
3320:In 13 limit tuning, there is a tridecimal
1375:, there is only one. The unevenly distributed
581:, the interval usually occurs as some form of
5107:
4137:
3845:; Karen Farnum Surmani; Morton Manus (2009).
2350:equivalents (chromatic semitones) and only a
819:, such as those in the soprano voice of this
513:Listen to a minor second in equal temperament
5400:List of dodecaphonic and serial compositions
3226:
3179:occurs at 6 short intervals out of 12,
1363:The exact size of a semitone depends on the
112:16:15, 17:16, 27:25, 135:128, 25:24, 256:243
3977:
3975:
3965:. Great Britain: Royal Society: 531. 1880.
3868:
3866:
3389:
1722:
1715:
1710:
1703:
1696:
1689:
1684:
1614:
1609:
1604:
1599:
1594:
1589:
1584:
1579:
1574:
1569:
1564:
1559:
1554:
1544:
1541:
1533:
1530:
1522:
1519:
1511:
1508:
1505:
1497:
1494:
1486:
1483:
1469:
1460:
1453:
1446:
1437:
1243:because it lacked clarity as an interval."
200:; the interval between them is a semitone.
5395:
5114:
5100:
5078:
4144:
4130:
3958:Proceedings of the Royal Society of London
3877:Studies in the Origin of Harmonic Tonality
2365:
723:second appears in many other works of the
3967:digitized 26 Feb 2008; Harvard University
2443:) or 1.0666... (approximately 111.7
297:of ratio 531441:524288 or 23.5 cents. In
274:for more details about this terminology.
3981:
3972:
3863:
3849:. Alfred Music Publishing. p. 135.
3690:
3538:
3536:
3534:
3532:
3530:
3528:
3526:
3251:) available in between the 5 limit
2414:
2397:
2380:
2369:
1245:
982:
810:
802:
746:
737:. More recently, the music to the movie
603:
593:. It may also appear in inversions of a
455:, between the third and fourth degree, (
342:
230:(an interval encompassing two different
144:
3731:
3578:The Mathematical Theory of Tone Systems
2693:). The 12 semitones produced by a
1386:
1271:However, beginning in the 13th century
471:(C) in C major). It is also called the
290:
286:
207:or major second is 2 semitones wide, a
5411:
4502:
3890:
3725:
3570:
3542:
862:. The augmented unison is abbreviated
571:. It also occurs in many forms of the
5095:
4125:
4050:
3780:Music: In Theory and Practice, Vol. I
3523:
3409:), and the diatonic semitone is two (
2828:, e.g. between C and an accute C
2009:
755:a 16:15 minor second arises in the C
2947:, e.g. between E and F (5:4 to 4:3):
1759:
1741:
626:The minor second may be viewed as a
317:
3200:at only one interval (if diatonic D
1981:
1972:as part of a sixteenth-tone system.
792:
563:, it appears as the falling of the
13:
4091:A History of Western Music, 6th ed
4076:
3616:are all variously used in sources.
3352:tone (27:26 or 65.34 cents).
3056:(5:3 to 9:5), or C and chromatic D
2127:. It is also sometimes called the
1379:contain many different semitones.
644:
551:it appears as a resolution of the
483:. The minor second is abbreviated
222:, a distinction is made between a
14:
5440:
2427:typically corresponds to a pitch
2375:
2211:
5394:
5203:
5077:
4110:. New York: W. W. Norton, 1978.
2403:
2386:
2078:
2066:
2047:
2039:
2026:
2018:
1259:
973:
962:
834:
783:
705:Problems playing this file? See
693:
671:
617:
352:
150:
4044:
3948:
3927:
3911:
3875:, trans. Gjerdingen, Robert O.
3835:
3814:
3793:
3263:(7:4). There is also a smaller
3212:and sharp notes are not used).
1772:There are many approximations,
1677:
1549:
1478:
1430:
1427:
850:, the interval produced by the
612:'s Prelude in C major from the
338:
3935:Music: A Mathematical Offering
3772:
3701:
3691:Capstick, John Walton (1913).
3684:
3661:
3591:
2223:Pythagorean chromatic semitone
1937:
1922:
1907:and more accurate alternative,
1359:Semitones in different tunings
1189:
1176:
743:exemplifies the minor second.
734:Ballet of the Unhatched Chicks
272:Interval (music) § Number
1:
4151:
3896:Rashed, Roshdi (ed.) (1996).
3734:Elementary Rudiments of Music
3697:. Cambridge University Press.
3635:, and others use "half tone".
3516:
2109:Pythagorean diatonic semitone
634:resolving into the following
279:twelve-tone equal temperament
260:twelve-tone equal temperament
5324:All-interval twelve-tone row
3778:Benward & Saker (2003).
2402:'Larger' or major limma on C
2241:. It may also be called the
7:
4699:septimal chromatic semitone
3900:, pp. 588, 608. Routledge.
3464:
3287:used the latter as part of
3265:septimal chromatic semitone
2123:), and is often called the
2092:Like meantone temperament,
10:
5445:
4705:septimal diatonic semitone
4493:(Numbers in brackets refer
4093:. New York: Norton, 2001.
3476:List of meantone intervals
3257:7 limit minor seventh
3237:septimal diatonic semitone
2247:Pythagorean major semitone
2225:has a ratio of 2187/2048 (
2131:. It is about 90.2 cents.
2129:Pythagorean minor semitone
1073:
796:
475:because it occurs between
15:
5392:
5316:
5250:
5212:
5201:
5133:
5075:
5033:
5000:
4889:
4859:
4829:
4786:
4777:
4750:
4677:
4660:
4495:to fractional semitones.)
4488:24-tone equal temperament
4485:
4474:
4411:
4356:
4301:
4264:
4227:
4192:
4159:
3992:Perspectives of New Music
3820:Day and Pilhofer (2007).
3799:Kostka and Payne (2003).
3732:Wharram, Barbara (2010).
3481:List of musical intervals
3471:12-tone equal temperament
3423:31-tone equal temperament
3395:19-tone equal temperament
3227:Extended just intonations
2813:Larger chromatic semitone
1747:12-tone equal temperament
1736:31-tone equal temperament
1720:
1708:
1701:
1694:
1682:
1474:
1467:
1465:
1458:
1451:
1444:
1442:
1105:suggested instead in his
833:Op. 102 No. 3, mm. 47–49.
608:Harmonic minor second in
437:12-Tone equal temperament
435:
428:
418:
408:
403:
395:
387:
382:
372:
256:enharmonically equivalent
139:112, 105, 133, 92, 71, 90
133:
125:12-Tone equal temperament
123:
116:
106:
96:
86:
81:
73:
57:
52:
31:
3822:Music Theory for Dummies
3543:Duffin, Ross W. (2008).
3390:Other equal temperaments
3039:Larger diatonic semitone
2818:major chromatic semitone
2713:minor chromatic semitone
2366:Just 5-limit intonation
2111:has a ratio of 256/243 (
2046:Pythagorean apotome on C
1986:There are many forms of
900:diminished seventh chord
589:that is not part of the
491:). Its inversion is the
44:(for augmented unison);
5083:List of pitch intervals
4821:Subminor and supermajor
4760:minor diatonic semitone
4670:refer to pitch ratios.)
3486:List of pitch intervals
3048:major diatonic semitone
2945:minor diatonic semitone
2701:Just chromatic semitone
2385:16:15 diatonic semitone
1769:equals nine semitones.
870:. Its inversion is the
48:(for diminished unison)
5329:All-trichord hexachord
5277:Second Viennese School
4881:Undecimal quarter tone
3457:) steps of its scale.
3289:his 43 tone scale
3152:
3068:and G (25:18 and 3:2):
3050:, e.g. between A and B
3031:
2936:Just diatonic semitone
2928:
2805:
2634:
2540:
2449:just diatonic semitone
2420:
2412:
2395:
2378:
2318:
2193:
2025:Pythagorean limma on C
1961:
1892:
1814:
1406:, tuned as a cycle of
1404:quarter-comma meantone
1268:
1233:
1119:having two notes at a
995:
843:
808:
649:
639:
529:, which is a tone 100
361:
349:Common practice period
299:quarter-comma meantone
293:); they differ by the
159:
5123:Twelve-tone technique
4876:Septimal quarter tone
4687:septimal quarter tone
3933:Benson, Dave (2006).
3918:Hermann von Helmholtz
3769:, trans. G. Schirmer.
3656:is "chiefly N. Amer."
3645:One source says that
3576:Haluska, Jan (2003).
3153:
3032:
2929:
2806:
2695:commonly used version
2635:
2541:
2418:
2401:
2384:
2373:
2335:, and functions as a
2319:
2237:). It is about 113.7
2210:, and functions as a
2194:
1962:
1893:
1815:
1369:Meantone temperaments
1249:
1234:
986:
904:augmented sixth chord
814:
807:Augmented unison on C
806:
747:In other temperaments
648:
607:
346:
148:
5272:Josef Matthias Hauer
5237:Retrograde inversion
5063:Incomposite interval
4816:Pythagorean interval
4668:(Numbers in brackets
4176:(Numbers in brackets
4033:ratio is the sharp (
3759:Paul, Oscar (1885).
3588:. Overtone semitone.
3506:Pythagorean interval
3206:replaces chromatic D
3074:
2953:
2850:
2844:) (1:1 and 135:128):
2727:
2721:and E (6:5 and 5:4):
2560:
2466:
2356:meantone temperament
2263:
2253:Pythagorean interval
2138:
1919:
1845:
1785:
1387:Meantone temperament
1307:(1600 to 1750), the
1139:
992:Transcendental Étude
264:meantone temperament
40:(for minor second);
5354:Formula composition
4846:Pythagorean apotome
4693:septimal third tone
3713:www.musictheory.net
3511:Regular temperament
3233:7 limit tuning
2243:Pythagorean apotome
1115:to a unison, or an
1032:was preferred to a
817:secondary dominants
720:Étude Op. 25, No. 5
667:Étude Op. 25, No. 5
595:major seventh chord
391:semitone, half step
369:
291:Pythagorean apotome
211:4 semitones, and a
28:
4959:Septimal semicomma
4105:Hoppin, Richard H.
3148:
3146:
3130:
3115:
3100:
3027:
3025:
3009:
2994:
2979:
2924:
2922:
2906:
2891:
2876:
2801:
2799:
2783:
2768:
2753:
2705:chromatic semitone
2630:
2614:
2599:
2584:
2536:
2520:
2505:
2490:
2423:A minor second in
2421:
2413:
2396:
2379:
2341:Pythagorean tuning
2337:chromatic semitone
2314:
2216:Pythagorean tuning
2189:
2094:Pythagorean tuning
2010:Pythagorean tuning
1957:
1888:
1810:
1432:Chromatic semitone
1381:Pythagorean tuning
1290:passus duriusculus
1276:practice known as
1269:
1229:
1222:
1194:
1163:
1023:in the bass. Here
996:
896:secondary dominant
860:chromatic semitone
844:
830:Song Without Words
809:
650:
640:
616:, book 1, mm. 7–9.
591:functional harmony
549:deceptive cadences
367:
362:
283:Pythagorean tuning
268:Pythagorean tuning
242:chromatic semitone
234:, e.g. from C to D
178:, is the smallest
160:
69:chromatic semitone
67:diminished unison,
63:diatonic semitone,
26:
5406:
5405:
5359:Modernism (music)
5287:Arnold Schoenberg
5089:
5088:
5071:
5070:
4901:Pythagorean comma
4841:Pythagorean limma
4773:
4772:
4769:
4768:
4735:supermajor fourth
4711:supermajor second
4656:
4655:
4470:
4469:
4466:
4465:
4178:are the number of
4087:Claude V. Palisca
4083:Grout, Donald Jay
3856:978-0-7390-3635-8
3788:978-0-07-294262-0
3743:978-1-55440-283-0
3709:"musictheory.net"
3673:. : Alpha, 2005.
3667:Miller, Michael.
3633:Leonard Bernstein
3556:978-0-393-33420-3
3382:counterpart to a
3370:Though the names
3145:
3140:
3129:
3114:
3099:
3024:
3019:
3008:
2993:
2978:
2921:
2916:
2905:
2890:
2875:
2798:
2793:
2782:
2767:
2752:
2626:
2618:
2613:
2598:
2583:
2573:
2565:
2532:
2524:
2519:
2504:
2489:
2479:
2471:
2409:
2392:
2376:diatonic semitone
2352:Pythagorean comma
2312:
2301:
2274:
2212:diatonic semitone
2187:
2176:
2149:
2125:Pythagorean limma
2053:
2032:
1955:
1886:
1875:
1869:
1866:
1808:
1742:Equal temperament
1731:
1730:
1725:
1718:
1713:
1706:
1699:
1692:
1687:
1679:Diatonic semitone
1617:
1612:
1607:
1602:
1597:
1592:
1587:
1582:
1577:
1572:
1567:
1562:
1557:
1472:
1463:
1456:
1449:
1440:
1377:well temperaments
1373:equal temperament
1353:equal temperament
1332:Arnold Schoenberg
1313:well temperaments
1265:
1218:
1187:
1159:
873:diminished octave
840:
825:Felix Mendelssohn
729:Modest Mussorgsky
692:
676:
623:
599:added tone chords
573:imperfect cadence
473:diatonic semitone
445:
444:
358:
314:five-limit tuning
295:Pythagorean comma
287:Pythagorean limma
224:diatonic semitone
156:
143:
142:
65:augmented unison,
42:diminished octave
5436:
5398:
5397:
5317:Related articles
5299:Charles Wuorinen
5207:
5141:Combinatoriality
5116:
5109:
5102:
5093:
5092:
5081:
5080:
4971:Septimal kleisma
4784:
4783:
4741:subminor seventh
4723:supermajor third
4675:
4674:
4663:Just intonations
4648:
4647:
4643:
4640:
4628:
4627:
4623:
4620:
4608:
4607:
4603:
4600:
4588:
4587:
4583:
4580:
4568:
4567:
4563:
4560:
4548:
4547:
4543:
4540:
4528:
4527:
4523:
4500:
4499:
4483:
4482:
4190:
4189:
4172:
4171:
4146:
4139:
4132:
4123:
4122:
4070:
4069:
4048:
4042:
4041:
4038:
4037:
4032:
4030:
4029:
4026:
4023:
3985:(Summer 1991). "
3979:
3970:
3969:
3952:
3946:
3931:
3925:
3915:
3909:
3894:
3888:
3870:
3861:
3860:
3839:
3833:
3818:
3812:
3797:
3791:
3776:
3770:
3757:
3748:
3747:
3729:
3723:
3722:
3720:
3719:
3705:
3699:
3698:
3688:
3682:
3665:
3659:
3649:is "chiefly US",
3595:
3589:
3574:
3568:
3567:
3565:
3563:
3540:
3456:
3455:
3454:
3452:
3451:play 116.7 cents
3444:
3443:
3442:
3440:
3420:
3419:
3418:
3416:
3415:play 126.3 cents
3408:
3407:
3406:
3404:
3366:
3365:
3364:
3362:
3351:
3349:
3348:
3345:
3342:
3335:
3333:
3332:
3329:
3326:
3312:
3311:
3310:
3308:
3278:
3277:
3276:
3274:
3261:harmonic seventh
3250:
3249:
3248:
3246:
3211:
3210:
3205:
3204:
3196:
3189:
3182:
3171:
3164:
3157:
3155:
3154:
3149:
3147:
3143:
3138:
3131:
3122:
3116:
3107:
3101:
3092:
3086:
3085:
3067:
3066:
3061:
3060:
3055:
3054:
3036:
3034:
3033:
3028:
3026:
3022:
3017:
3010:
3001:
2995:
2986:
2980:
2971:
2965:
2964:
2933:
2931:
2930:
2925:
2923:
2919:
2914:
2907:
2898:
2892:
2883:
2877:
2868:
2862:
2861:
2839:
2838:
2833:
2832:
2810:
2808:
2807:
2802:
2800:
2796:
2791:
2784:
2775:
2769:
2760:
2754:
2745:
2739:
2738:
2720:
2719:
2677:
2676:
2671:
2670:
2657:
2656:
2655:
2653:
2639:
2637:
2636:
2631:
2624:
2623:
2619:
2616:
2615:
2606:
2600:
2591:
2585:
2576:
2571:
2563:
2545:
2543:
2542:
2537:
2530:
2529:
2525:
2522:
2521:
2512:
2506:
2497:
2491:
2482:
2477:
2469:
2442:
2441:
2440:
2438:
2411:
2410:
2394:
2393:
2323:
2321:
2320:
2315:
2313:
2310:
2302:
2300:
2299:
2290:
2289:
2280:
2275:
2267:
2236:
2235:
2234:
2232:
2198:
2196:
2195:
2190:
2188:
2185:
2177:
2175:
2174:
2165:
2164:
2155:
2150:
2142:
2122:
2121:
2120:
2118:
2098:circle of fifths
2082:
2070:
2055:
2054:
2043:
2034:
2033:
2022:
1988:well temperament
1982:Well temperament
1966:
1964:
1963:
1958:
1956:
1953:
1945:
1944:
1932:
1897:
1895:
1894:
1889:
1887:
1884:
1876:
1874:
1868:
1867:
1862:
1850:
1849:
1823:Vincenzo Galilei
1819:
1817:
1816:
1811:
1809:
1806:
1795:
1723:
1716:
1711:
1704:
1697:
1690:
1685:
1615:
1610:
1605:
1600:
1595:
1590:
1585:
1580:
1575:
1570:
1565:
1560:
1555:
1539:
1538:
1528:
1527:
1517:
1516:
1503:
1502:
1492:
1491:
1470:
1461:
1454:
1447:
1438:
1428:
1424:
1423:
1418:
1417:
1397:circle of fifths
1267:
1266:
1238:
1236:
1235:
1230:
1228:
1224:
1223:
1219:
1211:
1202:
1201:
1200:
1195:
1188:
1180:
1169:
1164:
1160:
1152:
1070:for piano solo.
1046:dominant seventh
1039:
1038:
1030:
1029:
1021:
1020:
1012:
1011:
978:
977:
967:
966:
956:
955:
947:
946:
934:
933:
917:
916:
886:augmented octave
848:augmented unison
842:
841:
799:Augmented unison
793:Augmented unison
787:
778:
777:
776:
774:
727:period, such as
697:
690:
682:Martha Goldstein
678:
677:
658:'s "wrong note"
647:
625:
624:
528:
527:
523:is followed by D
518:
517:
516:
514:
370:
366:
364:Musical interval
360:
359:
253:
252:
246:augmented unison
239:
238:
199:
198:
180:musical interval
166:, also called a
158:
157:
46:augmented octave
29:
25:
23:Musical interval
5444:
5443:
5439:
5438:
5437:
5435:
5434:
5433:
5424:Seconds (music)
5419:Minor intervals
5409:
5408:
5407:
5402:
5388:
5344:Duration series
5339:Chromatic scale
5312:
5253:
5246:
5208:
5199:
5176:Cross partition
5146:Complementation
5129:
5120:
5090:
5085:
5067:
5029:
4996:
4939:Septimal diesis
4885:
4855:
4825:
4779:
4765:
4746:
4669:
4666:
4652:
4645:
4641:
4638:
4636:
4625:
4621:
4618:
4616:
4605:
4601:
4598:
4596:
4585:
4581:
4578:
4576:
4565:
4561:
4558:
4556:
4545:
4541:
4538:
4536:
4525:
4521:
4520:
4510:
4509:
4508:
4504:
4494:
4491:
4478:
4476:
4462:
4407:
4352:
4297:
4260:
4223:
4184:
4179:
4177:
4167:
4165:
4162:
4155:
4150:
4079:
4077:Further reading
4074:
4073:
4066:
4049:
4045:
4035:
4034:
4027:
4024:
4021:
4020:
4018:
3980:
3973:
3954:
3953:
3949:
3932:
3928:
3916:
3912:
3895:
3891:
3871:
3864:
3857:
3843:Surmani, Andrew
3840:
3836:
3819:
3815:
3798:
3794:
3777:
3773:
3758:
3751:
3744:
3730:
3726:
3717:
3715:
3707:
3706:
3702:
3689:
3685:
3666:
3662:
3644:
3627:
3596:
3592:
3575:
3571:
3561:
3559:
3557:
3541:
3524:
3519:
3467:
3450:
3447:
3446:
3439:play 66.7 cents
3438:
3435:
3434:
3414:
3411:
3410:
3403:play 63.2 cents
3402:
3399:
3398:
3392:
3360:
3357:
3356:
3346:
3343:
3340:
3339:
3337:
3330:
3327:
3324:
3323:
3321:
3306:
3303:
3302:
3272:
3269:
3268:
3255:(15:8) and the
3244:
3241:
3240:
3229:
3208:
3207:
3202:
3201:
3199:
3194:
3192:
3187:
3185:
3180:
3178:
3174:
3169:
3167:
3162:
3141:
3120:
3105:
3090:
3081:
3077:
3075:
3072:
3071:
3064:
3063:
3058:
3057:
3052:
3051:
3020:
2999:
2984:
2969:
2960:
2956:
2954:
2951:
2950:
2917:
2896:
2881:
2866:
2857:
2853:
2851:
2848:
2847:
2836:
2835:
2830:
2829:
2794:
2773:
2758:
2743:
2734:
2730:
2728:
2725:
2724:
2717:
2716:
2692:
2688:
2683:chromatic scale
2674:
2673:
2668:
2667:
2651:
2648:
2647:
2604:
2589:
2574:
2570:
2566:
2561:
2558:
2557:
2552:(15:8) and the
2510:
2495:
2480:
2476:
2472:
2467:
2464:
2463:
2436:
2433:
2432:
2425:just intonation
2404:
2387:
2368:
2360:just intonation
2309:
2295:
2291:
2285:
2281:
2279:
2266:
2264:
2261:
2260:
2230:
2227:
2226:
2184:
2170:
2166:
2160:
2156:
2154:
2141:
2139:
2136:
2135:
2116:
2113:
2112:
2102:just intonation
2090:
2089:
2088:
2087:
2086:
2083:
2075:
2074:
2071:
2060:
2059:
2058:
2057:
2056:
2048:
2044:
2036:
2035:
2027:
2023:
2012:
1984:
1970:Julián Carrillo
1967:
1952:
1940:
1936:
1928:
1920:
1917:
1916:
1898:
1883:
1870:
1861:
1854:
1848:
1846:
1843:
1842:
1820:
1805:
1791:
1786:
1783:
1782:
1760:discussed below
1756:just intonation
1744:
1536:
1535:
1525:
1524:
1514:
1513:
1500:
1499:
1489:
1488:
1421:
1420:
1415:
1414:
1389:
1361:
1340:Igor Stravinsky
1260:
1221:
1220:
1210:
1206:
1196:
1193:
1192:
1179:
1172:
1171:
1170:
1165:
1162:
1161:
1151:
1147:
1146:
1142:
1140:
1137:
1136:
1103:Guido of Arezzo
1094:and semitones.
1076:
1036:
1035:
1027:
1026:
1018:
1017:
1009:
1008:
1005:had written an
972:
961:
953:
952:
944:
943:
931:
930:
914:
913:
835:
801:
795:
790:
789:
788:
772:
769:
768:
753:just intonation
749:
716:Frédéric Chopin
712:
711:
703:
701:
700:
699:
698:
689:
679:
672:
669:
663:
656:Frédéric Chopin
651:
645:
636:A minor seventh
618:
525:
524:
512:
509:
508:
365:
353:
341:
307:just intonation
258:if and only if
250:
249:
236:
235:
232:staff positions
196:
195:
151:
135:Just intonation
68:
66:
64:
62:
24:
21:
12:
11:
5:
5442:
5432:
5431:
5429:Units of level
5426:
5421:
5404:
5403:
5393:
5390:
5389:
5387:
5386:
5381:
5376:
5371:
5366:
5361:
5356:
5351:
5346:
5341:
5336:
5331:
5326:
5320:
5318:
5314:
5313:
5311:
5310:
5301:
5296:
5295:
5294:
5289:
5284:
5274:
5269:
5264:
5262:Milton Babbitt
5258:
5256:
5248:
5247:
5245:
5244:
5242:Multiplication
5239:
5234:
5229:
5224:
5218:
5216:
5210:
5209:
5202:
5200:
5198:
5197:
5196:
5195:
5190:
5180:
5179:
5178:
5168:
5163:
5161:Interval class
5158:
5153:
5148:
5143:
5137:
5135:
5131:
5130:
5119:
5118:
5111:
5104:
5096:
5087:
5086:
5076:
5073:
5072:
5069:
5068:
5066:
5065:
5060:
5055:
5050:
5045:
5039:
5037:
5031:
5030:
5028:
5027:
5022:
5017:
5012:
5006:
5004:
4998:
4997:
4995:
4994:
4988:
4982:
4975:
4974:
4968:
4962:
4956:
4950:
4943:
4942:
4936:
4933:Greater diesis
4930:
4923:
4922:
4919:Septimal comma
4916:
4913:Holdrian comma
4910:
4907:Syntonic comma
4904:
4897:
4895:
4887:
4886:
4884:
4883:
4878:
4873:
4867:
4865:
4857:
4856:
4854:
4853:
4848:
4843:
4837:
4835:
4827:
4826:
4824:
4823:
4818:
4813:
4808:
4803:
4798:
4792:
4790:
4781:
4775:
4774:
4771:
4770:
4767:
4766:
4764:
4763:
4756:
4754:
4748:
4747:
4745:
4744:
4738:
4732:
4729:subminor fifth
4726:
4720:
4717:subminor third
4714:
4708:
4702:
4696:
4690:
4683:
4681:
4672:
4658:
4657:
4654:
4653:
4651:
4650:
4630:
4610:
4590:
4570:
4550:
4530:
4513:
4511:
4503:
4497:
4480:
4472:
4471:
4468:
4467:
4464:
4463:
4461:
4460:
4454:
4448:
4442:
4436:
4430:
4424:
4417:
4415:
4409:
4408:
4406:
4405:
4399:
4393:
4387:
4381:
4375:
4369:
4362:
4360:
4354:
4353:
4351:
4350:
4344:
4338:
4332:
4326:
4320:
4314:
4307:
4305:
4299:
4298:
4296:
4295:
4289:
4283:
4277:
4270:
4268:
4262:
4261:
4259:
4258:
4252:
4246:
4240:
4233:
4231:
4225:
4224:
4222:
4221:
4215:
4209:
4203:
4196:
4194:
4187:
4169:
4157:
4156:
4149:
4148:
4141:
4134:
4126:
4120:
4119:
4108:Medieval Music
4102:
4078:
4075:
4072:
4071:
4064:
4043:
4005:10.2307/833435
3999:(2): 106–137.
3971:
3947:
3926:
3910:
3889:
3873:Dahlhaus, Carl
3862:
3855:
3834:
3813:
3792:
3771:
3767:Theodore Baker
3749:
3742:
3724:
3700:
3683:
3660:
3590:
3569:
3555:
3521:
3520:
3518:
3515:
3514:
3513:
3508:
3503:
3501:Neutral second
3498:
3493:
3491:Approach chord
3488:
3483:
3478:
3473:
3466:
3463:
3391:
3388:
3298:neutral second
3228:
3225:
3217:syntonic comma
3197:
3190:
3186:3 times,
3183:
3176:
3172:
3165:
3159:
3158:
3137:
3134:
3128:
3125:
3119:
3113:
3110:
3104:
3098:
3095:
3089:
3084:
3080:
3069:
3040:
3037:
3016:
3013:
3007:
3004:
2998:
2992:
2989:
2983:
2977:
2974:
2968:
2963:
2959:
2948:
2937:
2934:
2913:
2910:
2904:
2901:
2895:
2889:
2886:
2880:
2874:
2871:
2865:
2860:
2856:
2845:
2842:syntonic comma
2814:
2811:
2790:
2787:
2781:
2778:
2772:
2766:
2763:
2757:
2751:
2748:
2742:
2737:
2733:
2722:
2702:
2690:
2686:
2666:used a sharp (
2641:
2640:
2629:
2622:
2612:
2609:
2603:
2597:
2594:
2588:
2582:
2579:
2569:
2554:perfect octave
2547:
2535:
2528:
2518:
2515:
2509:
2503:
2500:
2494:
2488:
2485:
2475:
2460:perfect fourth
2447:), called the
2367:
2364:
2325:
2324:
2308:
2305:
2298:
2294:
2288:
2284:
2278:
2273:
2270:
2200:
2199:
2183:
2180:
2173:
2169:
2163:
2159:
2153:
2148:
2145:
2084:
2077:
2076:
2072:
2065:
2064:
2063:
2062:
2061:
2045:
2038:
2037:
2024:
2017:
2016:
2015:
2014:
2013:
2011:
2008:
1983:
1980:
1976:
1975:
1974:
1973:
1951:
1948:
1943:
1939:
1935:
1931:
1927:
1924:
1911:
1910:
1909:
1908:
1901:Marin Mersenne
1882:
1879:
1873:
1865:
1860:
1857:
1853:
1837:
1836:
1835:
1834:
1804:
1801:
1798:
1794:
1790:
1743:
1740:
1729:
1728:
1726:
1721:
1719:
1714:
1709:
1707:
1702:
1700:
1695:
1693:
1688:
1683:
1681:
1675:
1674:
1672:
1670:
1668:
1666:
1664:
1662:
1660:
1658:
1656:
1654:
1652:
1650:
1648:
1646:
1644:
1642:
1640:
1638:
1636:
1634:
1632:
1630:
1628:
1626:
1624:
1622:
1619:
1618:
1613:
1608:
1603:
1598:
1593:
1588:
1583:
1578:
1573:
1568:
1563:
1558:
1553:
1547:
1546:
1543:
1540:
1532:
1529:
1521:
1518:
1510:
1507:
1504:
1496:
1493:
1485:
1482:
1476:
1475:
1473:
1468:
1466:
1464:
1459:
1457:
1452:
1450:
1445:
1443:
1441:
1436:
1434:
1388:
1385:
1360:
1357:
1256:Solo e pensoso
1227:
1217:
1214:
1209:
1208:
1205:
1199:
1191:
1186:
1183:
1178:
1175:
1174:
1168:
1158:
1155:
1150:
1149:
1145:
1088:medieval music
1075:
1072:
1064:Iannis Xenakis
797:Main article:
794:
791:
782:
781:
780:
773:Play B & C
763:found in the
748:
745:
702:
684:playing on an
680:
670:
665:
664:
653:
652:
643:
642:
641:
597:, and in many
561:plagal cadence
481:diatonic scale
451:occurs in the
443:
442:
439:
433:
432:
426:
425:
422:
420:Interval class
416:
415:
412:
406:
405:
401:
400:
397:
393:
392:
389:
385:
384:
380:
379:
376:
363:
340:
337:
190:(or half of a
141:
140:
137:
131:
130:
127:
121:
120:
114:
113:
110:
104:
103:
100:
98:Interval class
94:
93:
90:
84:
83:
79:
78:
75:
71:
70:
59:
55:
54:
50:
49:
35:
22:
9:
6:
4:
3:
2:
5441:
5430:
5427:
5425:
5422:
5420:
5417:
5416:
5414:
5401:
5391:
5385:
5382:
5380:
5377:
5375:
5372:
5370:
5367:
5365:
5362:
5360:
5357:
5355:
5352:
5350:
5347:
5345:
5342:
5340:
5337:
5335:
5332:
5330:
5327:
5325:
5322:
5321:
5319:
5315:
5308:
5307:
5302:
5300:
5297:
5293:
5290:
5288:
5285:
5283:
5280:
5279:
5278:
5275:
5273:
5270:
5268:
5267:Pierre Boulez
5265:
5263:
5260:
5259:
5257:
5255:
5249:
5243:
5240:
5238:
5235:
5233:
5230:
5228:
5225:
5223:
5220:
5219:
5217:
5215:
5211:
5206:
5194:
5191:
5189:
5186:
5185:
5184:
5181:
5177:
5174:
5173:
5172:
5169:
5167:
5164:
5162:
5159:
5157:
5154:
5152:
5149:
5147:
5144:
5142:
5139:
5138:
5136:
5132:
5128:
5124:
5117:
5112:
5110:
5105:
5103:
5098:
5097:
5094:
5084:
5074:
5064:
5061:
5059:
5056:
5054:
5051:
5049:
5046:
5044:
5041:
5040:
5038:
5036:
5032:
5026:
5023:
5021:
5018:
5016:
5013:
5011:
5008:
5007:
5005:
5003:
4999:
4992:
4989:
4986:
4983:
4980:
4977:
4976:
4972:
4969:
4966:
4963:
4960:
4957:
4954:
4951:
4948:
4945:
4944:
4940:
4937:
4934:
4931:
4928:
4927:Lesser diesis
4925:
4924:
4920:
4917:
4914:
4911:
4908:
4905:
4902:
4899:
4898:
4896:
4894:
4893:
4888:
4882:
4879:
4877:
4874:
4872:
4869:
4868:
4866:
4864:
4863:
4862:Quarter tones
4858:
4852:
4849:
4847:
4844:
4842:
4839:
4838:
4836:
4834:
4833:
4828:
4822:
4819:
4817:
4814:
4812:
4811:Pseudo-octave
4809:
4807:
4804:
4802:
4799:
4797:
4794:
4793:
4791:
4789:
4785:
4782:
4776:
4761:
4758:
4757:
4755:
4753:
4749:
4742:
4739:
4736:
4733:
4730:
4727:
4724:
4721:
4718:
4715:
4712:
4709:
4706:
4703:
4700:
4697:
4694:
4691:
4688:
4685:
4684:
4682:
4680:
4676:
4673:
4671:
4665:
4664:
4659:
4634:
4631:
4614:
4611:
4594:
4591:
4574:
4571:
4554:
4551:
4534:
4531:
4518:
4515:
4514:
4512:
4507:
4501:
4498:
4496:
4490:
4489:
4484:
4481:
4473:
4458:
4455:
4452:
4449:
4446:
4443:
4440:
4437:
4434:
4431:
4428:
4425:
4422:
4419:
4418:
4416:
4414:
4410:
4403:
4400:
4397:
4394:
4391:
4388:
4385:
4382:
4379:
4376:
4373:
4370:
4367:
4364:
4363:
4361:
4359:
4355:
4348:
4345:
4342:
4339:
4336:
4333:
4330:
4327:
4324:
4321:
4318:
4315:
4312:
4309:
4308:
4306:
4304:
4300:
4293:
4290:
4287:
4284:
4281:
4278:
4275:
4272:
4271:
4269:
4267:
4263:
4256:
4253:
4250:
4247:
4244:
4241:
4238:
4235:
4234:
4232:
4230:
4226:
4219:
4216:
4213:
4210:
4207:
4204:
4201:
4198:
4197:
4195:
4191:
4188:
4186:
4182:
4173:
4170:
4164:
4158:
4154:
4147:
4142:
4140:
4135:
4133:
4128:
4127:
4124:
4117:
4116:0-393-09090-6
4113:
4109:
4106:
4103:
4100:
4099:0-393-97527-4
4096:
4092:
4088:
4084:
4081:
4080:
4067:
4065:1-4102-1920-8
4061:
4057:
4053:
4047:
4040:
4017:... the
4014:
4010:
4006:
4002:
3998:
3994:
3993:
3988:
3984:
3978:
3976:
3968:
3964:
3960:
3959:
3951:
3944:
3943:0-521-85387-7
3940:
3936:
3930:
3923:
3919:
3914:
3907:
3906:0-415-12411-5
3903:
3899:
3893:
3886:
3885:0-691-09135-8
3882:
3878:
3874:
3869:
3867:
3858:
3852:
3848:
3844:
3838:
3831:
3830:0-7645-7838-3
3827:
3823:
3817:
3810:
3809:0-07-285260-7
3806:
3802:
3801:Tonal Harmony
3796:
3789:
3785:
3781:
3775:
3768:
3764:
3763:
3756:
3754:
3745:
3739:
3735:
3728:
3714:
3710:
3704:
3696:
3695:
3687:
3680:
3679:1-59257-437-8
3676:
3672:
3671:
3664:
3658:
3655:
3651:
3648:
3643:
3641:
3639:
3637:
3634:
3630:
3629:Aaron Copland
3626:
3624:
3622:
3620:
3618:
3615:
3611:
3607:
3603:
3599:
3594:
3587:
3586:0-8247-4714-3
3583:
3579:
3573:
3558:
3552:
3548:
3547:
3539:
3537:
3535:
3533:
3531:
3529:
3527:
3522:
3512:
3509:
3507:
3504:
3502:
3499:
3497:
3494:
3492:
3489:
3487:
3484:
3482:
3479:
3477:
3474:
3472:
3469:
3468:
3462:
3458:
3453:
3441:
3432:
3428:
3424:
3417:
3405:
3396:
3387:
3385:
3381:
3377:
3373:
3368:
3363:
3353:
3318:
3316:
3309:
3300:
3299:
3292:
3290:
3286:
3282:
3275:
3266:
3262:
3258:
3254:
3253:major seventh
3247:
3238:
3235:there is the
3234:
3224:
3222:
3218:
3213:
3168:, 16:15, and
3135:
3132:
3126:
3123:
3117:
3111:
3108:
3102:
3096:
3093:
3087:
3082:
3078:
3070:
3062:(27:25), or F
3049:
3045:
3041:
3038:
3014:
3011:
3005:
3002:
2996:
2990:
2987:
2981:
2975:
2972:
2966:
2961:
2957:
2949:
2946:
2942:
2938:
2935:
2911:
2908:
2902:
2899:
2893:
2887:
2884:
2878:
2872:
2869:
2863:
2858:
2854:
2846:
2843:
2827:
2823:
2819:
2815:
2812:
2788:
2785:
2779:
2776:
2770:
2764:
2761:
2755:
2749:
2746:
2740:
2735:
2731:
2723:
2714:
2710:
2706:
2703:
2700:
2699:
2698:
2696:
2684:
2679:
2665:
2661:
2654:
2644:
2627:
2620:
2610:
2607:
2601:
2595:
2592:
2586:
2580:
2577:
2567:
2555:
2551:
2550:major seventh
2548:
2533:
2526:
2516:
2513:
2507:
2501:
2498:
2492:
2486:
2483:
2473:
2461:
2457:
2454:
2453:
2452:
2450:
2446:
2439:
2430:
2426:
2417:
2400:
2383:
2377:
2372:
2363:
2361:
2357:
2353:
2349:
2344:
2342:
2338:
2334:
2330:
2306:
2303:
2296:
2292:
2286:
2282:
2276:
2271:
2268:
2259:
2258:
2257:
2255:
2254:
2248:
2244:
2240:
2233:
2224:
2219:
2217:
2213:
2209:
2205:
2181:
2178:
2171:
2167:
2161:
2157:
2151:
2146:
2143:
2134:
2133:
2132:
2130:
2126:
2119:
2110:
2105:
2103:
2099:
2095:
2081:
2069:
2042:
2021:
2007:
2005:
2001:
1997:
1993:
1989:
1979:
1971:
1949:
1946:
1941:
1933:
1929:
1925:
1915:
1914:
1913:
1912:
1906:
1905:constructible
1902:
1899:suggested by
1880:
1877:
1871:
1863:
1858:
1855:
1851:
1841:
1840:
1839:
1838:
1832:
1828:
1824:
1821:suggested by
1802:
1799:
1796:
1792:
1788:
1781:
1780:
1779:
1778:
1777:
1775:
1770:
1768:
1763:
1761:
1757:
1753:
1748:
1739:
1737:
1727:
1680:
1676:
1673:
1671:
1669:
1667:
1665:
1663:
1661:
1659:
1657:
1655:
1653:
1651:
1649:
1647:
1645:
1643:
1641:
1639:
1637:
1635:
1633:
1631:
1629:
1627:
1625:
1623:
1621:
1620:
1552:
1548:
1481:
1477:
1435:
1433:
1429:
1426:
1412:
1409:
1405:
1400:
1398:
1394:
1384:
1382:
1378:
1374:
1370:
1367:system used.
1366:
1356:
1354:
1350:
1346:
1345:tone clusters
1341:
1337:
1333:
1328:
1326:
1322:
1318:
1314:
1310:
1306:
1301:
1299:
1295:
1291:
1287:
1283:
1279:
1274:
1257:
1253:
1252:Luca Marenzio
1248:
1244:
1242:
1225:
1215:
1212:
1203:
1197:
1184:
1181:
1166:
1156:
1153:
1143:
1135:
1131:
1130:
1124:
1122:
1118:
1114:
1110:
1109:
1104:
1100:
1095:
1093:
1089:
1085:
1081:
1071:
1069:
1065:
1061:
1060:tone clusters
1056:
1054:
1051:
1047:
1044:
1040:
1031:
1022:
1013:
1004:
1000:
993:
989:
985:
981:
979:
976:
968:
965:
957:
948:
939:
935:
926:
922:
918:
909:
905:
901:
897:
893:
889:
887:
883:
879:
875:
874:
869:
865:
861:
857:
853:
849:
832:
831:
826:
822:
818:
813:
805:
800:
786:
779:
775:
766:
762:
758:
754:
744:
742:
741:
736:
735:
730:
726:
721:
717:
710:
708:
696:
687:
683:
668:
662:
661:
657:
637:
633:
629:
615:
611:
606:
602:
600:
596:
592:
588:
587:nonchord tone
584:
580:
576:
574:
570:
566:
562:
558:
554:
550:
546:
542:
538:
534:
532:
522:
515:
506:
504:
500:
496:
495:
494:major seventh
490:
486:
482:
478:
474:
470:
466:
462:
458:
454:
450:
440:
438:
434:
431:
427:
423:
421:
417:
413:
411:
407:
402:
398:
394:
390:
386:
381:
378:major seventh
377:
375:
371:
350:
345:
336:
334:
330:
329:musical scale
326:
321:
319:
315:
312:
308:
304:
300:
296:
292:
288:
284:
280:
275:
273:
269:
265:
261:
257:
254:). These are
247:
243:
233:
229:
225:
221:
216:
215:7 semitones.
214:
213:perfect fifth
210:
206:
201:
193:
189:
188:12-tone scale
185:
181:
177:
173:
169:
165:
147:
138:
136:
132:
128:
126:
122:
119:
115:
111:
109:
108:Just interval
105:
101:
99:
95:
91:
89:
85:
80:
76:
72:
61:minor second,
60:
56:
51:
47:
43:
39:
38:major seventh
36:
34:
30:
19:
5368:
5304:
5292:Anton Webern
5214:Permutations
5134:Fundamentals
5034:
5001:
4987:(0.72 cents)
4981:(1.95 cents)
4961:(13.8 cents)
4955:(10.1 cents)
4949:(19.5 cents)
4941:(35.7 cents)
4935:(62.6 cents)
4929:(41.1 cents)
4921:(27.3 cents)
4915:(22.6 cents)
4909:(21.5 cents)
4903:(23.5 cents)
4890:
4871:Quarter tone
4861:
4860:
4831:
4830:
4787:
4752:Higher-limit
4667:
4661:
4573:major fourth
4517:quarter tone
4492:
4486:
4180:
4175:
4107:
4090:
4055:
4046:
4016:
3996:
3990:
3987:Ben Johnston
3983:Fonville, J.
3966:
3962:
3956:
3950:
3934:
3929:
3921:
3913:
3897:
3892:
3876:
3846:
3837:
3821:
3816:
3800:
3795:
3779:
3774:
3760:
3733:
3727:
3716:. Retrieved
3712:
3703:
3693:
3686:
3669:
3663:
3653:
3646:
3613:
3609:
3605:
3601:
3597:
3593:
3577:
3572:
3560:. Retrieved
3545:
3496:Major second
3459:
3393:
3383:
3379:
3375:
3371:
3369:
3354:
3319:
3315:major second
3295:
3293:
3230:
3214:
3160:
3047:
3043:
2944:
2940:
2840:raised by a
2826:major chroma
2825:
2822:larger limma
2821:
2817:
2712:
2708:
2704:
2680:
2664:Ben Johnston
2645:
2642:
2448:
2422:
2358:and 5-limit
2345:
2326:
2250:
2246:
2242:
2222:
2220:
2201:
2128:
2124:
2108:
2106:
2096:is a broken
2091:
1995:
1991:
1985:
1977:
1954: cents,
1885: cents,
1825:and used by
1807: cents,
1771:
1764:
1745:
1732:
1678:
1550:
1479:
1431:
1401:
1390:
1362:
1349:Henry Cowell
1329:
1302:
1286:Semantically
1278:musica ficta
1270:
1255:
1127:
1125:
1116:
1113:major second
1106:
1096:
1077:
1067:
1057:
1049:
1042:
1033:
1024:
1015:
1006:
999:Harmonically
997:
994:, measure 63
970:
959:
950:
941:
937:
928:
924:
920:
911:
907:
890:
881:
877:
871:
867:
863:
859:
852:augmentation
847:
845:
828:
750:
738:
732:
713:
704:
691:Opening bars
654:
635:
631:
579:Harmonically
577:
553:leading-tone
535:
507:
502:
498:
492:
488:
484:
472:
468:
464:
460:
456:
449:minor second
448:
446:
409:
396:Abbreviation
368:minor second
339:Minor second
322:
276:
245:
241:
228:minor second
227:
223:
220:music theory
217:
202:
175:
171:
168:minor second
167:
163:
161:
149:Minor second
87:
74:Abbreviation
5364:Punctualism
5349:Equivalence
5020:Millioctave
5002:Measurement
4993:(0.4 cents)
4973:(7.7 cents)
4967:(8.1 cents)
4851:Major limma
4593:minor fifth
3580:, p. xxiv.
3193:twice, and
3175:, 25:24): S
2660:major third
2456:major third
2333:just fifths
2311: cents
2208:just fifths
2186: cents
1831:Renaissance
1767:major sixth
1336:BĂ©la BartĂłk
1305:Baroque era
1294:lament bass
1258:, ca. 1580.
1121:major third
1053:pedal point
1014:against an
988:Franz Liszt
892:Melodically
757:major scale
565:subdominant
537:Melodically
453:major scale
388:Other names
325:anhemitonia
209:major third
58:Other names
5413:Categories
5379:Time point
5374:Set theory
5282:Alban Berg
5227:Retrograde
5166:Invariance
5151:Derivation
5053:Semiditone
4947:Diaschisma
4762:(17-limit)
4453:(22 or 23)
4451:fourteenth
4447:(20 or 21)
4445:thirteenth
4441:(18 or 19)
4435:(17 or 18)
4429:(15 or 16)
4423:(13 or 14)
4358:Diminished
4185:interval.)
4166:(post-Bach
3937:, p. 369.
3824:, p. 113.
3765:, p. 165.
3718:2024-01-04
3517:References
3296:undecimal
3267:of 21:20 (
3239:of 15:14 (
3221:diaschisma
2458:(5:4) and
2431:of 16:15 (
2348:enharmonic
2331:and seven
2000:enharmonic
1317:enharmonic
1284:passages.
1108:Micrologus
1086:scales of
1080:tetrachord
1062:, such as
990:'s second
761:dissonance
707:media help
628:suspension
610:J. S. Bach
583:dissonance
311:Asymmetric
205:whole tone
192:whole step
5334:Atonality
5254:composers
5232:Inversion
5222:Prime row
5188:Aggregate
5171:Partition
5156:Hexachord
5127:serialism
5015:Centitone
4953:Semicomma
4832:Semitones
4796:Microtone
4780:intervals
4457:fifteenth
4303:Augmented
4181:semitones
4153:Intervals
4052:Prout, E.
3924:, p. 454.
3803:, p. 21.
3782:, p. 54.
3654:half-tone
3652:and that
3614:half-tone
3606:half tone
3602:half step
3445:) and 7 (
3380:chromatic
3376:chromatic
3301:(12:11) (
3133:≈
3103:÷
3012:≈
2982:÷
2909:≈
2879:×
2786:≈
2756:÷
2587:÷
2493:÷
2304:≈
2206:and five
2179:≈
1996:chromatic
1947:≈
1878:≈
1859:−
1800:≈
1321:Classical
1282:chromatic
1241:clausulae
856:chromatic
559:. In the
543:. In the
410:Semitones
184:dissonant
176:half tone
172:half step
88:Semitones
5369:Semitone
5183:Tone row
4985:Breedsma
4433:eleventh
4413:Compound
4168:Western)
4163:semitone
4054:(2004).
4036:♯
3920:(1885).
3681:. p. 19.
3610:halftone
3598:Semitone
3465:See also
3433:uses 4 (
3384:diatonic
3372:diatonic
3283:, while
3209:♭
3203:♭
3065:♯
3059:♭
3053:♭
2837:♯
2831:♯
2718:♭
2675:♭
2669:♯
1992:diatonic
1968:used by
1827:luthiers
1774:rational
1537:♭
1526:♯
1515:♯
1501:♭
1490:♯
1422:♯
1416:♭
1408:tempered
1393:meantone
1325:Romantic
1273:cadences
1117:occursus
1037:♯
1028:♭
1019:♮
1010:♭
954:♭
945:♭
932:♯
915:♯
902:, or an
821:sequence
725:Romantic
541:cadences
526:♭
521:middle C
519:. Here,
489:−2
467:(B) and
459:(E) and
251:♯
240:) and a
237:♭
197:♯
164:semitone
27:semitone
18:Halftone
5252:Notable
4991:Ragisma
4979:Schisma
4965:Kleisma
4801:5-limit
4707:(15:14)
4701:(21:20)
4695:(28:27)
4689:(36:35)
4679:7-limit
4644:⁄
4633:seventh
4624:⁄
4604:⁄
4584:⁄
4564:⁄
4544:⁄
4524:⁄
4506:Neutral
4479:systems
4439:twelfth
4396:seventh
4347:seventh
4292:seventh
4255:seventh
4193:Perfect
4161:Twelve-
4056:Harmony
4031:
4019:
3562:28 June
3350:
3338:
3334:
3322:
3044:greater
2941:smaller
2709:smaller
2329:octaves
2245:or the
2204:octaves
1950:99.9995
1829:of the
1303:By the
1099:cadence
1074:History
1068:Evryali
630:of the
569:mediant
567:to the
555:to the
545:perfect
479:in the
374:Inverse
174:, or a
33:Inverse
5048:Ditone
5035:Others
5025:Savart
4892:Commas
4788:Groups
4737:(10:7)
4533:second
4477:tuning
4402:octave
4378:fourth
4366:second
4329:fourth
4317:second
4311:unison
4274:second
4237:second
4218:octave
4206:fourth
4200:unison
4183:in the
4114:
4097:
4085:, and
4062:
4013:833435
4011:
3941:
3904:
3883:
3853:
3828:
3807:
3786:
3740:
3677:
3612:, and
3584:
3553:
3285:Partch
3281:Cowell
3139:
3018:
2915:
2792:
2625:
2617:
2572:
2564:
2556:(2:1)
2531:
2523:
2478:
2470:
2462:(4:3)
2374:16:15
1616:1200.0
1611:1082.9
1606:1006.8
1413:from E
1411:fifths
1365:tuning
1338:, and
1298:pianto
1296:, and
1134:ditone
688:(1851)
638:chord.
303:diesis
77:m2; A1
5384:Trope
5058:Secor
4806:Comma
4778:Other
4743:(7:4)
4731:(7:5)
4725:(9:7)
4719:(7:6)
4713:(8:7)
4613:sixth
4553:third
4475:Other
4427:tenth
4421:ninth
4390:sixth
4384:fifth
4372:third
4341:sixth
4335:fifth
4323:third
4286:sixth
4280:third
4266:Minor
4249:sixth
4243:third
4229:Major
4212:fifth
4009:JSTOR
3431:72-ET
3427:53-ET
3144:cents
3136:133.2
3023:cents
3015:111.7
2943:, or
2920:cents
2824:, or
2820:, or
2797:cents
2711:, or
2707:, or
2546:and a
2445:cents
2429:ratio
2339:in a
2307:113.7
2239:cents
2214:in a
1903:as a
1881:100.4
1724:117.1
1717:117.1
1712:117.1
1705:117.1
1698:117.1
1691:117.1
1686:117.1
1601:889.7
1596:772.6
1591:696.6
1586:579.5
1581:503.4
1576:386.3
1571:310.3
1566:193.2
1551:Cents
1480:Pitch
1309:tonal
1092:tones
1084:modal
1003:Liszt
882:dim 8
880:, or
868:aug 1
866:, or
823:from
765:scale
686:Érard
660:Étude
585:or a
557:tonic
531:cents
477:steps
441:100.0
430:Cents
333:chord
318:below
226:, or
118:Cents
5306:more
5193:List
5125:and
5043:Wolf
5010:Cent
4459:(24)
4404:(11)
4349:(12)
4343:(10)
4294:(10)
4257:(11)
4220:(12)
4112:ISBN
4095:ISBN
4060:ISBN
3955:"".
3939:ISBN
3902:ISBN
3881:ISBN
3851:ISBN
3826:ISBN
3805:ISBN
3784:ISBN
3738:ISBN
3675:ISBN
3647:step
3582:ISBN
3564:2017
3551:ISBN
3374:and
3361:Play
3307:play
3273:play
3245:play
2912:92.2
2789:70.7
2689:to C
2652:play
2437:play
2272:2048
2269:2187
2251:See
2231:play
2221:The
2182:90.2
2117:play
2107:The
1994:and
1803:99.0
1561:76.0
1471:76.0
1462:76.0
1455:76.0
1448:76.0
1439:76.0
1419:to G
898:, a
846:The
740:Jaws
547:and
487:(or
447:The
404:Size
383:Name
327:. A
82:Size
53:Name
5309:...
5303:...
4398:(9)
4392:(7)
4386:(6)
4380:(4)
4374:(2)
4368:(0)
4337:(8)
4331:(6)
4325:(5)
4319:(3)
4313:(1)
4288:(8)
4282:(3)
4276:(1)
4251:(9)
4245:(4)
4239:(2)
4214:(7)
4208:(5)
4202:(0)
4001:doi
3421:).
3231:In
3046:or
3042:or
2939:or
2903:128
2900:135
2816:or
2256:.)
2249:. (
2147:243
2144:256
2004:key
1934:138
1926:139
1762:).
1556:0.0
1391:In
1254:'s
1216:243
1213:256
1129:sic
980:).
827:'s
767:."
751:In
731:'s
718:'s
614:WTC
505:).
503:Ma7
501:or
331:or
277:In
244:or
218:In
129:100
5415::
4637:10
4089:.
4028:24
4022:25
4015:.
4007:.
3997:29
3995:.
3974:^
3963:30
3961:.
3865:^
3752:^
3711:.
3631:,
3608:,
3604:,
3600:,
3525:^
3291:.
3259:/
3127:25
3124:27
3006:15
3003:16
2888:80
2885:81
2873:24
2870:25
2834:(C
2780:24
2777:25
2611:15
2608:16
2593:15
2517:15
2514:16
2362:.
2343:.
2297:11
2218:.
1797:17
1789:18
1758:,
1545:C
1542:B
1531:A
1520:G
1509:F
1506:E
1495:D
1484:C
1334:,
1300:.
1292:,
1066:'
1055:.
969:,
958:,
949:,
940:,
927:,
923:,
919:,
910:,
878:d8
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3118:=
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3088:=
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2997:=
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2967:=
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2864:=
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632:B
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102:1
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