147:). For Aristoxenus himself, these shades were dynamic: that is, they were not fixed in an ordered scale, and the shades were flexible along a continuum within certain limits. Instead, they described characteristic functional progressions of intervals, which he called "roads" (ὁδοί), possessing different ascending and descending patterns while nevertheless remaining recognisable. For his successors, however, the genera became fixed intervallic successions, and their shades became precisely defined subcategories. Furthermore, in sharp contrast to the Pythagoreans, Aristoxenos deliberately avoids numerical ratios. Instead, he defines a whole tone as the difference between a perfect fifth and a perfect fourth, and then divides that tone into
1185:
649:
122:. The upper tone, lichanos, can vary over the range of a whole tone, whereas the lower note, parhypate, is restricted to the span of a quarter tone. However, their variation in position must always be proportional. This interval between the fixed hypate and movable parhypate cannot ever be larger than the interval between the two movable tones. When the composite of the two smaller intervals is less than the remaining (
1227:
1207:
1162:
1146:
1065:
1041:
1246:
1235:
1215:
1170:
1154:
1107:
1093:
1085:
1073:
1049:
1265:
trichord in which a perfect fourth was divided by a single "infix"—an additional note dividing the fourth into a semitone plus a major third (e.g., E, F, A, where F is the infix dividing the fourth E–A). Such a division of a fourth necessarily produces a scale of the type called pentatonic, because
641:
common today, on the other hand, also has twelve pitches to the octave, but the semitones are all of the same size. In contrast, the ancient Greek chromatic scale had seven pitches (i.e. heptatonic) to the octave (assuming alternating conjunct and disjunct tetrachords), and had incomposite minor
302:
as "through". See also Barsky: "There are two possible ways of translating the Greek term 'diatonic': (1) 'running through tones', i.e. through the whole tones; or (2) a 'tensed' tetrachord filled up with the widest intervals". The second interpretation would be justified by consideration of the
1032:
Modern notation for enharmonic notes requires two special symbols for raised and lowered quarter tones or half-semitones or quarter steps. Some symbols used for a quarter-tone flat are a downward-pointing arrow ↓, or a flat combined with an upward-pointing arrow ↑. Similarly, for a quarter-tone
303:
pitches in the diatonic tetrachord, which are more equally distributed ("stretched out") than in the chromatic and enharmonic tetrachords, and are also the result of tighter stretching of the two variable strings. It is perhaps also sounder on linguistic morphological grounds. Compare
396:
The fact that τόνος itself has at least four distinct meanings in Greek theory of music contributes to the uncertainty of the exact meaning and derivation of διατονικός, even among ancient writers: τόνος may refer to a pitch, an interval, a "key" or register of the voice, or a mode.
1033:
sharp, an upward-pointing arrow may be used, or else a sharp with a downward-pointing arrow. Three-quarter flat and sharp symbols are formed similarly. A further modern notation involves reversed flat signs for quarter-flat, so that an enharmonic tetrachord may be represented:
1316:
hypate parhypate lichanos mese 4:3 31:24 5:4 1:1 |32:31 |31:30 | 5:4 | -498 -443 -386 0
1290:
hypate parhypate lichanos mese 4:3 9:7 5:4 1:1 | 28:27 |36:35| 5:4 | -498 -435 -386 0
905:
hypate parhypate lichanos mese 4:3 5:4 6:5 1:1 | 16:15 | 25:24 | 6:5 | -498 -386 -316 0
879:
hypate parhypate lichanos mese 4:3 9:7 32:27 1:1 | 28:27 | 243:224 | 32:27 | -498 -435 -294 0
866:
hypate parhypate lichanos mese 4:3 81:64 32:27 1:1 | 256:243 | 2187:2048 | 32:27 | -498 -408 -294 0
546:
hypate parhypate lichanos mese 4:3 11:9 10:9 1:1 | 12:11 | 11:10 | 10:9 | -498 -347 -182 0
524:
hypate parhypate lichanos mese 4:3 80:63 8:7 1:1 | 21:20 | 10:9 | 8:7 | -498 -413 -231 0
514:
hypate parhypate lichanos mese 4:3 5:4 10:9 1:1 | 16:15 | 9:8 | 10:9 | -498 -386 -182 0
500:
hypate parhypate lichanos mese 4:3 5:4 9:8 1:1 | 16:15 | 10:9 | 9:8 | -498 -386 -204 0
487:
hypate parhypate lichanos mese 4:3 9:7 9:8 1:1 | 28:27 | 8:7 | 9:8 | -498 -435 -204 0
465:
hypate parhypate lichanos mese 4:3 81:64 9:8 1:1 | 256:243 | 9:8 | 9:8 | -498 -408 -204 0
797:
The number and nature of the shades of the chromatic genus vary amongst the Greek theorists. The major division is between the
Aristoxenians and the Pythagoreans. Aristoxenus and Cleonides agree there are three, called soft, hemiolic, and tonic.
316:
appeals to the generation of the diatonic scale from "two tones": "Because the musical scale is based entirely on octaves and fifths, that is, two notes, it is called the 'diatonic scale' ". But this ignores the fact that it is the element
1308:
of the string lengths (if one wishes to think in terms of frequencies, rather than string lengths or interval distance down from the tonic, as the example below does, splitting the interval between the frequencies 4:3 and 5:4 by their
1194:
1123:
also had seven notes to the octave (assuming alternating conjunct and disjunct tetrachords), not 24 as one might imagine by analogy to the modern chromatic scale. A scale generated from two disjunct enharmonic tetrachords is:
1130:
660:
1272:
1089:) is used for modern notation of the third tone in the tetrachord to follow modern convention of keeping scale notes as a letter sequence, and to remind the reader that the third tone in an enharmonic tetrachord (say F
823:
442:
405:
The diatonic tetrachord can be "tuned" using several shades or tunings. Aristoxenus (and
Cleonides, following his example; see also Ptolemy's tunings) describes two shades of the diatonic, which he calls συντονόν
1195:
1131:
661:
1273:
824:
1266:
compounding two such segments into an octave produces a scale with just five steps. This became an enharmonic tetrachord by the division of the semitone into two quarter tones (E, E↑, F, A).
441:
393:; see also the Prout citation, at the same location). This is not in accord with any accepted Greek meaning, and in Greek theory it would fail to exclude the other tetrachords.
959:) as the "highest and most difficult for the senses". Historically it has been the most mysterious and controversial of the three genera. Its characteristic interval is a
426:
can be translated as "tense" ("taut") and "relaxed" ("lax, loose"), corresponding to the tension in the strings. These are often translated as "intense" and "soft", as in
1853:
Solomon, Jon. 1980. "Cleonides: Εἰσαγωγὴ ἁρμονική ; Critical
Edition, Translation, and Commentary". PhD diss. Chapel Hill: University of North Carolina, Chapel Hill.
232:
Most plausibly, it refers to the intervals being "stretched out" in that tuning, in contrast to the other two tunings, whose lower two intervals were referred to as
1889:
1780:
1697:
436:, or alternatively as "sharp" (higher in pitch) and "soft" ("flat", lower in pitch). The structures of some of the most common tunings are the following:
1192:
1270:
1128:
821:
1732:
440:
1193:
1920:
1129:
508:
659:
1271:
507:
Ptolemy, following
Aristoxenus, also described "tense" and "relaxed" ("intense" and "soft") tunings. His "tense diatonic", as used in
822:
1867:
1770:
1753:
443:
139:, "colour"), and enharmonic (also called ἁρμονία ). The first two of these were subject to further variation, called shades—χρόαι (
1485:
1765:. Publications of the Center for the History of Music Theory and Literature 2. Lincoln and London: University of Nebraska Press.
31:
497:
described the following tuning, similar to
Ptolemy's later tense diatonic, but reversing the order of the 10:9 and 9:8, namely:
1925:
574:. Byzantine music theory distinguishes between two tunings of the diatonic genus, the so-called "hard diatonic" on which the
1902:
995:
540:
207:
275:
1789:
1744:
1706:
389:
of the scale: "The word diatonic means 'through the tones' (i.e., through the tones of the key)" (Gehrkens, 1914, see
91:
1826:Διάτονον δὲ τὸ τοῖς τόνοις, ἤτοι τοῖς μείζοσι διαστήμασι, πλεονάζον, ἐπειδὴ σφοδρότερον ἡ φωνὴ κατ' αὐτὸ διατείνεται.
539:. It is based on an equal division of string lengths (thus presumably simple to build and "rustic"), which implies a
472:
However, the most common tuning in practice from about the 4th century BC to the 2nd century AD appears to have been
1930:
1335:
The principal theorist of rhythmic genera was
Aristides Quintilianus, who considered there to be three: equal (
1097:, shown above) was not tuned quite the same as the second note in a diatonic or chromatic scale (the expected E
1797:
Mathiesen, Thomas J. 2001b. "Greece, §I: Ancient, 6: Music Theory (iii): Aristoxenian
Tradition, (c) Genera".
1327:
into two nearly equal intervals, the difference in size between 31:30 and 32:31 being less than 2 cents.
876:
used the simpler and more consonant 9:7, which he used in all three of his genera. His chromatic division is:
415:
1935:
1686:
371:
1257:
The precise ancient
Pythagorean tuning of the enharmonic genus is not known. Aristoxenus believed that the
817:' formulation of the greater perfect system, from which the diatonic and enharmonic genera can be deduced.
622:(πυκνόν), consisting of the two movable members of the tetrachord, is divided into two adjacent semitones.
171:) as the oldest and most natural of the genera. It is the division of the tetrachord from which the modern
942:
390:
198:
164:
99:
95:
58:. The tetrachordal system was inherited by the Latin medieval theory of scales and by the modal theory of
1940:
1718:
1284:
899:
481:
1297:
984:
891:
814:
494:
123:
898:
intervals, with the smallest possible numerators and denominators. The successive intervals are all
1714:
590:
are based. The hard tuning of the diatonic genus in
Byzantine music may also be referred to as the
477:
980:
979:, though they could be calculated in a variety of ways). Because it is not easily represented by
860:
451:
432:
51:
39:
1184:
645:
The (Dorian) scale generated from the chromatic genus is composed of two chromatic tetrachords:
614:) as a more recent development than the diatonic. It is characterized by an upper interval of a
648:
1863:
1806:
1766:
1749:
1728:
638:
355:
348:
135:
The positioning of these two notes defined three genera: the diatonic, chromatic (also called
114:
apart and do not vary from one genus to another. Between these are two movable notes, called
1262:
1120:
630:
176:
1234:
1214:
1169:
1153:
1106:
1092:
1084:
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1305:
1226:
1206:
1161:
1145:
1064:
1040:
918:
810:
714:
626:
559:
531:
Ptolemy described his "equable" or "even diatonic" as sounding foreign or rustic, and its
381:
Yet another derivation assumes the sense "through the tones" for διάτονος, but interprets
279:
59:
859:
does later. Someone has referred to this speculative reconstructions as the traditional
325:, which has "through" among its meanings (see Liddell and Scott). There is a Greek term
952:
653:
607:
532:
337:, which is applied to an interval equivalent to two tones. It yields the English words
172:
111:
1464:
1355:), though he also admitted that some authorities added a fourth genus, sesquitertian.
1914:
1884:
1785:
1702:
1348:
1310:
1021:
895:
391:
Diatonic and chromatic § Diatonic includes the harmonic and melodic minor scales
175:
evolved. The distinguishing characteristic of the diatonic genus is that its largest
1832:
1318:
1292:
976:
907:
881:
868:
548:
536:
526:
516:
502:
489:
467:
427:
370:, meaning "to stretch to the end", because "...the voice is most stretched by it" (
180:
152:
67:
1684:
Barbera, C. André. 1977. "Arithmetic and
Geometric Divisions of the Tetrachord".
658:
155:, to correspond to the diatonic, chromatic, and enharmonic genera, respectively.
1810:
988:
964:
615:
594:; an unfortunate name that persisted, since it can be confused with the ancient
83:
74:(in his fragmentary treatise on rhythm) calls some patterns of rhythm "genera".
71:
1008:, but spelled differently. In other tuning systems, enharmonic notes, such as C
183:. The other two intervals vary according to the tunings of the various shades.
1848:, second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan.
1801:, second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan.
1000:
625:
The scale generated by the chromatic genus is not like the modern twelve-tone
459:
55:
17:
831:
For the chromatic genus, however, all that is given is a 32:27 proportion of
1763:
Apollo's Lyre: Greek Music and Music Theory in Antiquity and the Middle Ages
1245:
563:
305:
193:
87:
272:
462:) in succession, making the other interval a Pythagorean limma (256:243):
1655:
1651:
1280:
873:
856:
843:, but there is no information at all about the position of the chromatic
473:
148:
1641:
1352:
1340:
887:
799:
476:'s diatonic, or Ptolemy's "tonic diatonic", which has an 8:7 tone (see
972:
960:
930:
634:
339:
241:
128:
27:
Classification of musical scale or key in ancient Greek music theory
1268:
1190:
1126:
819:
647:
438:
63:
1313:
31:24 will result in the same sequence of intervals as below):
1900:
Dunsby, Jonathan (2002). "Diatonic". In Latham, Alison (ed.).
971:
to be divided by two intervals smaller than a semitone called
484:
28:27 instead of the complex 256:243 for the lowest interval:
287:
802:, representing a Pythagorean view, held that there are five.
312:
A completely separate explanation of the origins of the term
102:—the paradigmatic tetrachord was bounded by the fixed tones
50:"type, kind") is a term used to describe certain classes of
365:
332:
297:
265:
253:
239:
224:
212:
1524:(London; Faber and Faber, 1978), pp. 335–40: "Tonos".
1434:
1432:
1430:
1532:
1530:
62:; it may have been one source of the later theory of the
1609:
1607:
1605:
1393:
1391:
270:, to mean "interval of a tone"; see Liddell and Scott's
1636:
1634:
1480:
Phillips, Stephen, "Pythagorean aspects of music", in
1188:, with the corresponding conjunct tetrachords forming
1024:(an interval smaller than a semitone, like a diesis).
1906:. Oxford, UK / New York, NY: Oxford University Press.
1283:
used 9:7 in all three of his genera; here it is the
521:
Ptolemy's "relaxed diatonic" ("soft diatonic") was:
359:
326:
291:
259:
247:
233:
218:
637:, and consists of semitones of various sizes; the
1020:, may be close but not identical, differing by a
1300:uses the same major third (5:4) but divides the
851:into two semitones, though it may have been the
582:are based, and the "soft diatonic" on which the
566:are based on the diatonic genus, apart from the
1890:The New Grove Dictionary of Music and Musicians
1846:The New Grove Dictionary of Music and Musicians
1799:The New Grove Dictionary of Music and Musicians
1781:The New Grove Dictionary of Music and Musicians
1698:The New Grove Dictionary of Music and Musicians
1243:or, transposed to E like the previous example:
1695:Barbera, André. 2001. "Archytas of Tarentum".
921:the chromatic genus is the genus on which the
376:"... σφοδρότερον ἡ φωνὴ κατ’ αὐτὸ διατείνεται"
1522:The Music of Ancient Greece: An Encyclopaedia
642:thirds as well as semitones and whole tones.
8:
987:, there was much fascination with it in the
941:Aristoxenus describes the enharmonic genus (
1837:Music Notation: A Manual of Modern Practice
1748:. Lebanon, New Hampshire: Frog Peak Music.
1119:Like the diatonic scale, the ancient Greek
606:Aristoxenus describes the chromatic genus (
351:), but it is quite distinct from διάτονος.
283:and Barsky (second interpretation), below.
126:) interval, the three-note group is called
1667:
1508:
1496:
1409:
1397:
633:chromatic scale has twelve pitches to the
290:claims) "through the tones", interpreting
258:, 'dense, compressed'. This takes
163:Aristoxenus describes the diatonic genus (
1438:
1421:
1382:
1893:(first ed.). London, UK: Macmillan.
1883:Drabkin, William (1980). "Diatonic". In
1613:
1572:
1560:
1548:
1536:
1370:
1363:
1323:This method splits the 16:15 half-step
588:fourth mode (both authentic and plagal)
568:second mode (both authentic and plagal)
1287:of 4:3 and 5:4, as (4+5):(3+4) = 9:7:
584:first mode (both authentic and plagal)
1778:Mathiesen, Thomas J. 2001a. "Genus".
1182:or, in music notation starting on E:
847:and therefore of the division of the
7:
1625:
1596:
1584:
967:in modern terminology), leaving the
713:whereas in modern music theory, a "
458:, has two identical 9:8 tones (see
1844:Richter, Lukas. 2001. "Didymus ".
957:enarmonium, enarmonicum, harmonia
535:are reminiscent of scales used in
321:that means "two", not the element
54:of the two movable notes within a
25:
1727:] (in Greek) (4th ed.).
1720:Λεξικό της Νέας Ελληνικής Γλώσσας
286:Alternatively, it could mean (as
1244:
1233:
1225:
1213:
1205:
1183:
1168:
1160:
1152:
1144:
1105:
1091:
1083:
1071:
1063:
1047:
1039:
656:
509:Ptolemy's intense diatonic scale
32:musical system of ancient Greece
1858:West, Martin Litchfield. 1992.
994:In the modern tuning system of
813:gives an incomplete account of
595:
454:of the diatonic, also known as
358:consider the term derived from
652:Chromatic genus of the Dorian
571:
410:, from συντονός) and μαλακόν (
1:
1903:The Oxford Companion to Music
996:twelve-tone equal temperament
933:is also based on this genus.
612:χρωματικὸν γένος or χρωματική
1784:, second edition, edited by
1701:, second edition, edited by
1690:21, no. 2 (Autumn): 294–323.
929:are based. The "extra" mode
629:. The modern (18th-century)
366:
333:
309:as "across/width distance".
298:
266:
254:
240:
225:
213:
1862:. Oxford: Clarendon Press.
1745:Divisions of the Tetrachord
1261:evolved from an originally
82:According to the system of
1957:
1921:Ancient Greek music theory
1839:. Boston: Allyn and Bacon.
1824:] (in Ancient Greek).
1761:Mathiesen, Thomas J. 1999
1725:Dictionary of Modern Greek
1654:— no original writings by
946:
839:. This leaves 9:8 for the
456:Ptolemy's ditonic diatonic
375:
360:
327:
292:
260:
248:
234:
219:
202:
168:
1484:, Vol. 3, available also
1158: G ‖ A B
1004:refers to tones that are
611:
562:most of the modes of the
229:, of disputed etymology.
132:(meaning "compressed").
1817:
1719:
1081:The double-flat symbol (
894:'s chromatic has only 5-
863:of the chromatic genus:
1687:Journal of Music Theory
1454:, Routledge, 1996, p. 2
354:The Byzantine theorist
197:is ultimately from the
179:is about the size of a
1926:Byzantine music theory
1742:Chalmers, John. 1990.
1469:Merriam-Webster Online
1277:
1199:
1135:
956:
900:superparticular ratios
828:
665:
570:which is based on the
543:of pitch frequencies:
447:
100:Aristides Quintilianus
1276:
1198:
1134:
827:
651:
446:
1807:Pachymeres, Georgius
1792:. London: Macmillan.
1715:Babiniotis, Georgios
1709:. London: Macmillan.
985:meantone temperament
815:Thrasyllus of Mendes
1860:Ancient Greek Music
1670:, (i) Pythagoreans.
1599:, pp. 254–273.
1520:Solon Michaelides,
478:septimal whole tone
151:, third-tones, and
143:)—or species—εἶδη (
1450:Barsky, Vladimir,
1343:), sesquialteran (
1278:
1200:
1136:
981:Pythagorean tuning
927:second plagal mode
861:Pythagorean tuning
829:
666:
452:Pythagorean tuning
448:
433:Genesis of a Music
278:2011-03-05 at the
86:and his followers—
1734:978-960-89751-5-6
1668:Mathiesen (2001b)
1274:
1196:
1132:
890:'s calculations,
825:
662:
639:equal temperament
444:
401:Shades or tunings
356:George Pachymeres
349:Pythagorean comma
211:
191:The English word
98:, Bryennius, and
16:(Redirected from
1948:
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1482:Music and Psyche
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1121:enharmonic scale
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596:enharmonic genus
592:enharmonic genus
450:The traditional
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169:διατονικὸν γένος
38:(Greek: γένος ,
21:
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1931:Music of Greece
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1910:
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1877:Further reading
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1614:Chalmers (1990)
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1497:Babiniotis 2012
1495:
1491:
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1437:
1428:
1420:
1416:
1410:Mathiesen 2001b
1408:
1404:
1398:Mathiesen 2001a
1396:
1389:
1385:, 311–312, 326.
1381:
1377:
1369:
1365:
1361:
1333:
1331:Rhythmic genera
1321:
1306:arithmetic mean
1295:
1269:
1255:
1239: G
1232:
1224:
1212:
1204:
1191:
1167:
1159:
1151:
1143:
1127:
1117:
1104:
1099:
1098:
1090:
1082:
1077: D .
1070:
1062:
1053: G ,
1046:
1038:
1030:
1016:
1015:
1010:
1009:
975:(approximately
947:
939:
919:Byzantine music
915:
913:Byzantine music
910:
884:
871:
855:of 256:243, as
820:
811:Theon of Smyrna
808:
795:
780:
779:
777:
771:
770:
754:
753:
751:
741:
740:
738:
732:
731:
715:chromatic scale
701:
700:
680:
679:
657:
627:chromatic scale
604:
578:and two of the
572:chromatic genus
560:Byzantine music
556:
554:Byzantine music
551:
541:harmonic series
533:neutral seconds
529:
519:
505:
492:
482:superparticular
470:
439:
430:'s influential
403:
387:individual note
280:Wayback Machine
189:
161:
80:
70:. In addition,
60:Byzantine music
28:
23:
22:
15:
12:
11:
5:
1954:
1952:
1944:
1943:
1938:
1936:Musical scales
1933:
1928:
1923:
1913:
1912:
1909:
1908:
1896:
1895:
1885:Sadie, Stanley
1878:
1875:
1873:
1872:
1855:
1850:
1841:
1829:
1803:
1794:
1775:
1758:
1739:
1733:
1711:
1692:
1680:
1678:
1675:
1673:
1672:
1660:
1630:
1628:, p. 163.
1618:
1601:
1589:
1587:, p. 143.
1577:
1565:
1553:
1541:
1526:
1513:
1509:Pachymeres n.d
1501:
1489:
1473:
1456:
1443:
1439:Mathiesen 1999
1426:
1422:Mathiesen 1999
1414:
1402:
1387:
1383:Mathiesen 1999
1375:
1362:
1360:
1357:
1347:), and duple (
1332:
1329:
1315:
1289:
1254:
1251:
1241:
1240:
1180:
1179:
1116:
1113:
1079:
1078:
1055:
1054:
1029:
1026:
938:
935:
914:
911:
904:
878:
865:
807:
804:
794:
791:
790:
789:
711:
710:
654:octave species
603:
600:
555:
552:
545:
523:
513:
499:
486:
464:
402:
399:
372:Medieval Greek
217:, itself from
188:
185:
173:diatonic scale
160:
157:
112:perfect fourth
110:, which are a
79:
76:
42:γένη , Latin:
26:
24:
18:Diatonic genus
14:
13:
10:
9:
6:
4:
3:
2:
1953:
1942:
1939:
1937:
1934:
1932:
1929:
1927:
1924:
1922:
1919:
1918:
1916:
1905:
1904:
1898:
1897:
1892:
1891:
1886:
1881:
1880:
1876:
1869:
1868:0-19-814975-1
1865:
1861:
1856:
1851:
1847:
1842:
1838:
1834:
1833:Read, Gardner
1830:
1827:
1823:
1812:
1808:
1804:
1800:
1795:
1791:
1787:
1786:Stanley Sadie
1783:
1782:
1776:
1772:
1771:9780803230798
1768:
1764:
1759:
1755:
1754:0-945996-04-7
1751:
1747:
1746:
1740:
1736:
1730:
1726:
1722:
1716:
1712:
1708:
1704:
1703:Stanley Sadie
1700:
1699:
1693:
1689:
1688:
1682:
1681:
1676:
1669:
1664:
1661:
1657:
1653:
1647:
1643:
1637:
1635:
1631:
1627:
1622:
1619:
1615:
1610:
1608:
1606:
1602:
1598:
1593:
1590:
1586:
1581:
1578:
1574:
1569:
1566:
1562:
1557:
1554:
1550:
1545:
1542:
1538:
1533:
1531:
1527:
1523:
1517:
1514:
1510:
1505:
1502:
1498:
1493:
1490:
1487:
1483:
1477:
1474:
1470:
1466:
1460:
1457:
1453:
1447:
1444:
1440:
1435:
1433:
1431:
1427:
1423:
1418:
1415:
1411:
1406:
1403:
1399:
1394:
1392:
1388:
1384:
1379:
1376:
1372:
1367:
1364:
1358:
1356:
1354:
1350:
1346:
1342:
1338:
1330:
1328:
1326:
1320:
1314:
1312:
1311:harmonic mean
1307:
1303:
1299:
1294:
1288:
1286:
1282:
1267:
1264:
1260:
1252:
1250:
1247:
1236:
1228:
1222:
1216:
1208:
1202:
1201:
1189:
1186:
1177:
1171:
1163:
1155:
1147:
1141:
1138:
1137:
1125:
1122:
1114:
1112:
1108:
1094:
1086:
1074:
1066:
1060:
1059:
1058:
1050:
1042:
1036:
1035:
1034:
1027:
1025:
1023:
1007:
1003:
1002:
997:
992:
990:
986:
982:
978:
977:quarter tones
974:
970:
966:
962:
958:
954:
944:
943:Ancient Greek
936:
934:
932:
928:
924:
920:
912:
909:
903:
901:
897:
893:
889:
886:According to
883:
877:
875:
870:
864:
862:
858:
854:
850:
846:
842:
838:
834:
818:
816:
812:
805:
803:
801:
792:
788:
775:
766:
762:
749:
736:
727:
723:
720:
719:
718:
716:
709:
705:
696:
692:
688:
684:
675:
671:
668:
667:
655:
650:
646:
643:
640:
636:
632:
631:well-tempered
628:
623:
621:
617:
609:
601:
599:
597:
593:
589:
585:
581:
577:
573:
569:
565:
561:
553:
550:
544:
542:
538:
534:
528:
522:
518:
512:
510:
504:
498:
496:
491:
485:
483:
479:
475:
469:
463:
461:
457:
453:
437:
435:
434:
429:
425:
421:
417:
413:
409:
400:
398:
394:
392:
388:
384:
379:
373:
368:
357:
352:
350:
346:
342:
341:
335:
324:
320:
315:
310:
308:
307:
300:
289:
284:
282:
281:
277:
274:
273:Greek Lexicon
268:
256:
244:
243:
230:
227:
215:
209:
200:
199:Ancient Greek
196:
195:
186:
184:
182:
178:
174:
166:
165:Ancient Greek
158:
156:
154:
153:quarter tones
150:
146:
142:
138:
133:
131:
130:
125:
121:
117:
113:
109:
105:
101:
97:
93:
89:
85:
77:
75:
73:
69:
65:
61:
57:
53:
49:
45:
41:
37:
33:
19:
1941:Melody types
1901:
1888:
1859:
1845:
1836:
1825:
1821:
1798:
1790:John Tyrrell
1779:
1762:
1743:
1724:
1707:John Tyrrell
1696:
1685:
1663:
1645:
1621:
1616:, p. 9.
1592:
1580:
1573:Richter 2001
1568:
1561:Barbera 2001
1556:
1549:Barbera 1977
1544:
1537:Solomon 1980
1521:
1516:
1504:
1492:
1481:
1476:
1468:
1459:
1452:Chromaticism
1451:
1446:
1417:
1405:
1378:
1371:Solomon 1980
1366:
1334:
1324:
1322:
1301:
1296:
1279:
1258:
1256:
1242:
1220:
1181:
1175:
1139:
1118:
1103:instead of F
1080:
1056:
1031:
1005:
999:
993:
968:
940:
926:
922:
916:
885:
872:
852:
848:
844:
840:
836:
832:
830:
809:
796:
786:
768:
764:
760:
747:
729:
725:
721:
712:
707:
698:
694:
690:
686:
677:
673:
669:
644:
624:
619:
605:
591:
587:
583:
579:
575:
567:
557:
537:Arabic music
530:
520:
506:
493:
471:
455:
449:
431:
428:Harry Partch
423:
419:
411:
407:
404:
395:
386:
382:
380:
353:
344:
338:
322:
318:
313:
311:
304:
285:
271:
231:
192:
190:
181:major second
162:
144:
140:
136:
134:
127:
119:
115:
107:
103:
90:, Bacchius,
81:
68:Arabic music
47:
43:
35:
29:
1818:Τετράβιβλος
1811:"Chapter E"
1626:West (1992)
1597:West (1992)
1585:Read (1964)
1551:, 306, 309.
989:Renaissance
965:major third
937:Enharmonic
923:second mode
616:minor third
580:grave modes
385:as meaning
124:incomposite
84:Aristoxenus
78:Tetrachords
72:Aristoxenus
52:intonations
1915:Categories
1822:Quadrivium
1463:See also "
1424:, 310–311.
1359:References
1263:pentatonic
1203:A B
1061:A B
1037:D E
1001:enharmonic
948:ἐναρμόνιον
576:third mode
480:) and the
460:major tone
214:diatonikós
203:διατονικός
92:Gaudentius
56:tetrachord
1646:Harmonics
1341:anapestic
1304:with the
1006:identical
845:parhypate
602:Chromatic
564:octoechos
208:romanized
187:Etymology
149:semitones
116:parhypate
88:Cleonides
1835:. 1964.
1809:(n.d.).
1717:(2012).
1656:Archytas
1652:Archytas
1648:. ii.14.
1465:diatonic
1353:trochaic
1337:dactylic
1281:Archytas
1231: F
1211: C
1166: C
1150: F
1142: E
1100:♭
1069: C
1045: F
1028:Notation
1017:♭
1011:♯
874:Archytas
857:Boethius
837:lichanos
781:♭
772:♭
755:♭
742:♭
733:♭
702:♭
681:♭
586:and the
474:Archytas
420:Syntonón
408:syntonón
367:diateíno
361:διατείνω
314:diatonic
306:diameter
276:Archived
226:diátonos
220:διάτονος
194:diatonic
177:interval
159:Diatonic
120:lichanos
1887:(ed.).
1677:Sources
1658:survive
1650:quotes
1642:Ptolemy
1345:paeonic
1298:Didymus
1285:mediant
1253:Tunings
1174:
892:Didymus
888:Ptolemy
806:Tunings
800:Ptolemy
495:Didymus
424:malakón
416:μαλακός
414:, from
412:malakón
345:ditonic
334:dítonos
328:δίτονος
246:, from
210::
96:Alypius
30:In the
1866:
1769:
1752:
1731:
1539:, 259.
1486:online
1441:, 310.
1349:iambic
1325:pyknon
1302:pyknon
1259:pyknon
1178:
973:dieses
969:pyknon
961:ditone
931:nenano
849:pyknon
841:pyknon
793:Shades
717:" is:
635:octave
620:pyknon
618:. The
511:, is:
340:ditone
255:pyknós
249:πυκνός
242:pyknón
235:πυκνόν
141:chroai
137:chroma
129:pyknon
104:hypate
48:genera
46:, pl.
1820:[
1814:(PDF)
1723:[
1467:" in
1373:, vi.
1319:cents
1293:cents
1223:| E
1115:Scale
1022:comma
1014:and D
953:Latin
908:cents
896:limit
882:cents
869:cents
853:limma
608:Greek
549:cents
527:cents
517:cents
503:cents
490:cents
468:cents
347:(see
267:tónos
261:τόνος
44:genus
36:genus
1864:ISBN
1788:and
1767:ISBN
1750:ISBN
1729:ISBN
1705:and
1351:and
1219:|
963:(or
925:and
833:mese
422:and
383:tone
343:and
323:dia-
145:eidē
118:and
108:mese
106:and
64:jins
1816:.
1339:or
1111:).
1057:or
983:or
917:In
835:to
778:D−E
739:G−A
689:||
558:In
418:).
378:).
319:di-
299:diá
293:διά
288:OED
66:of
40:pl.
1917::
1644:.
1633:^
1604:^
1529:^
1429:^
1390:^
1249:.
998:,
991:.
955::
951:;
945::
902::
610::
598:.
374::
364:,
331:,
296:,
264:,
252:,
238:,
223:,
205:,
201::
167::
94:,
34:,
1870:.
1773:.
1756:.
1737:.
1575:.
1563:.
1511:.
1499:.
1471:.
1412:.
1400:.
1221:D
1176:D
1140:D
787:E
784:−
776:−
769:D
767:−
765:C
763:−
761:B
758:−
752:B
750:−
748:A
745:−
737:−
730:G
728:−
726:F
724:−
722:E
708:E
706:−
699:D
697:−
695:C
693:−
691:B
687:A
685:−
678:G
676:−
674:F
672:−
670:E
406:(
20:)
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