2105:
2336:
harmonics 3:1; 5:3, 7:3; 7:5, 9:5; 9:7, and 15:7; while the 39-step scale includes all of those and many more (11:5, 13:5; 11:7, 13:7; 11:9, 13:9; 13:11, 15:11, 21:11, 25:11, 27:11; 15:13, 21:13, 25:13, 27:13, 33:13, and 35:13), while still missing almost all of the even harmonics (including 2:1; 3:2, 5:2; 4:3, 8:3; 6:5, 8:5; 9:8, 11:8, 13:8, and 15:8). The size of this scale is about 25 equal steps to a ratio slightly larger than an octave, so each of the 39 equal steps is slightly smaller than half of one of the 12 equal steps of the standard scale.
2251:, Manfred Stahnke, Stephen Fox, Elaine Walker, Todd Harrop, Gayle Young, Johannes Kretz, Arturo Grolimund, Kevin Foster, presented 20 papers on history and properties of the Bohlen–Pierce scale, performed more than 40 compositions in the novel system and introduced several new musical instruments. Performers included German musicians Nora-Louise Müller and Ákos Hoffman on Bohlen–Pierce clarinets and Arturo Grolimund on Bohlen–Pierce pan flute as well as Canadian ensemble tranSpectra, and US American xenharmonic band ZIA, led by Elaine Walker.
36:
1082:
1161:= 29.27 cents per step) would be quite logical for this temperament. In such a tuning, a tempered perfect twelfth (1902.4 cents, about a half cent larger than a just twelfth) is divided into 65 equal steps, resulting in a seeming paradox: Taking every fifth degree of this octave-based scale yields an excellent approximation to the non-octave-based equally tempered BP scale. Furthermore, an interval of five such steps generates (octave-based)
5831:
5826:
448:
17:
699:
690:
681:
672:
663:
654:
645:
636:
627:
618:
2135:, "but without any great tension or sense of resolution". In their 1989 study of consonance judgment, both intervals of the five chords rated most consonant by trained musicians are approximately diatonic intervals, suggesting that their training influenced their selection and that similar experience with the BP scale would similarly influence their choices.
83:) serves as the fundamental harmonic ratio, replacing the diatonic scale's 2:1 (the octave) with a perfect twelfth (an octave higher than a perfect fifth). For any pitch that is part of the BP scale, all pitches one or more tritaves higher or lower are part of the system as well, and are considered equivalent.
430:
Every tone of the Pierce 3579b scale is in a major and minor triad except for tone II of the scale. There are thirteen possible keys. Modulation is possible through changing a single note. Moving note II up one semitone causes the tonic to rise to what was note III (semitone 3),
537:
developed the first Bohlen–Pierce soprano clarinets and began offering them for sale in early 2006. He produced the first BP tenor clarinet (six steps below the soprano) in 2010 and the first epsilon clarinet (four steps above the soprano) in 2011. A contra clarinet (one tritave lower than the
2335:
Paul Erlich proposed dividing each step of the Bohlen–Pierce into thirds so that the tritave is divided into 39 equal steps instead of 13 equal steps. The scale, which can be viewed as three evenly staggered Bohlen-Pierce scales, gives additional odd harmonics. The 13-step scale hits the odd
3466:
Dividing each step of the Bohlen-Pierce scale into fifths (so that the tritave is divided into 65 steps) results in a very accurate octave (41 steps) and perfect fifth (24 steps), as well as approximations for other just intervals. The scale is practically identical to
528:
register) consists of primarily the odd harmonics, and the instrument overblows at the twelfth (or tritave) rather than the octave as most other woodwind instruments do, there is a natural affinity between it and the Bohlen–Pierce scale. At the suggestion of composer
2303:, and contains a complex network of harmonic relations due to the inclusion of coinciding harmonics of stacked 833 cent intervals. For example, "step 10 turns out to be identical with the octave (1200 cents) to the base tone, at the same time featuring the
505:, and using the prefix "tri-" (three) to distinguish it from the octave. In conventional scales, if a given pitch is part of the system, then all pitches one or more octaves higher or lower also are part of the system and, furthermore, are considered
1165:(moments of symmetry) with 8, 9, or 17 notes, and the 8-note scale (comprising degrees 0, 5, 10, 15, 20, 25, 30, and 35 of the 41-equal scale) could be considered the octave-equivalent version of the Bohlen–Pierce scale.
1049:
167:
1557:
1060:
179:
24:
2283:
2267:
323:
920:
2131:
Mathews and Pierce conclude that clear and memorable melodies may be composed in the BP scale, that "counterpoint sounds all right", and that "chordal passages sound like harmony", presumably meaning
191:
353:
2116:? Dave Benson suggests it helps to use only sounds with only odd harmonics, including clarinets or synthesized tones, but argues that because "some of the intervals sound a bit like intervals in
403:
907:
894:
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855:
842:
829:
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803:
419:
368:
338:
2322:, and Gary Morrison's 88-cent scale (13.64 steps per octave or 14 per 1232-cent stretched octave). This gives the alpha scale 15.39 steps per octave and the beta scale 18.75 steps per octave.
493:
463:
387:
6168:
2203:, directed the development of a "Stredici", a string instrument tuned to the Bohlen–Pierce scale. The five-meter long instrument was used in concerts in Boston in 2012.
1070:
A just BP scale may be constructed from four overlapping 3:5:7 chords, for example, V, II, VI, and IV, though different chords may be chosen to produce a similar scale:
2291:
and of which only the just version would be used. Additionally, the pentave can be divided into eight steps which approximates chords of the form 5:9:13:17:21:25. The
379:
A study of chromatic triads formed from arbitrary combinations of the 13 tones of the chromatic scale among twelve musicians and twelve untrained listeners found
1127:
Dividing the tritave into 13 equal steps tempers out, or reduces to a unison, both of the intervals 245:243 (about 14 cents, sometimes called the minor Bohlen–Pierce
1124:. The Bohlen–Pierce scale could be described as 8.202087-tet, because a full octave (1200 cents), divided by 146.3… cents per step, gives 8.202087 steps per octave.
1131:) and 3125:3087 (about 21 cents, sometimes called the major Bohlen–Pierce diesis) in the same way that dividing the octave into 12 equal steps reduces both 81:80 (
5369:
159:. Specifically, the BP scale steps are based on ratios of integers whose factors are 3, 5, and 7. Thus the scale contains consonant harmonies based on the odd
6296:
2216:
6154:
5652:
5598:
7544:
6228:
6361:
6141:
312:(the just major chord), more similar than that of the minor chord. This similarity suggests that our ears will also perceive 3:5:7 as consonant.
1147:
no longer has anything to do with tritave equivalences or non-octave scales, beyond the fact that it is well adapted to using them. A tuning of
4989:
315:
The 3:5:7 chord may thus be considered the major triad of the BP scale. It is approximated by an interval of 6 equal-tempered BP
4977:
6879:
6371:
5755:
7539:
1073:(5:3)(7:5) V IX III | III VII I | VI I IV | IV VIII II
5490:
5328:
5303:
5122:
5420:
Moreno, Enrique
Ignacio (Dec 1995). "Embedding Equal Pitch Spaces and The Question of Expanded Chromas: An Experimental Approach".
20:
Chord from just Bohlen–Pierce scale: C-G-A, tuned to harmonics 3, 5, and 7. "BP" above the clefs indicates Bohlen–Pierce notation.
6753:
6740:
7108:
6334:
6031:
133:
after learning of Bohlen's earlier publication. Bohlen had proposed the same scale based on consideration of the influence of
5645:
7549:
6519:
5295:
1089:" for the Bohlen–Pierce scale, with the third mode of the Lambda scale marked. The VII degree is mistakenly marked twice.
6221:
5554:
1120:
per step. The octave is divided into a fractional number of steps. Twelve equally tempered steps per octave are used in
534:
2104:
546:
A diatonic Bohlen–Pierce scale may be constructed with the following just ratios (chart shows the "Lambda" (λ) scale):
411:) was considered the most consonant by the trained subjects (because it sounds like an octave-dropped major triad) and
6457:
6136:
6301:
6161:
5904:
5780:
5675:
738:
6286:
6113:
6101:
5638:
2220:
99:
5113:
Mathews, Max V.; Pierce, John R. (1989). "The Bohlen–Pierce Scale". In
Mathews, Max V.; Pierce, John R. (eds.).
7358:
6570:
5805:
2232:
2228:
2181:
520:
The BP scale's use of odd integer ratios is appropriate for timbres containing only odd harmonics. Because the
7305:
5213:
Thrall, Michael Voyne (Summer 1997). "Synthèse 96: The 26th
International Festival of Electroacoustic Music".
155:
ratios, in contrast with the intervals in diatonic scales, which employ both odd and even ratios found in the
7271:
7397:
7333:
7013:
6874:
6540:
6366:
6291:
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5620:
748:
156:
6324:
7392:
7354:
7344:
7038:
6562:
6525:
6515:
5760:
1105:
form, which divides the tritave into thirteen equal steps, has become the most popular form. Each step is
35:
7438:
7433:
7425:
7364:
7018:
7003:
6998:
6929:
6824:
6558:
5880:
5710:
2200:
7033:
6950:
6854:
6849:
6733:
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6511:
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5993:
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5085:
3468:
1162:
1148:
743:
718:
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7443:
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7101:
6936:
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6530:
6503:
6401:
6185:
6130:
5830:
5810:
5510:
5080:
2125:
2113:
1140:
1102:
517:
pitches one or more tritaves higher or lower are part of the system and are considered equivalent.
1081:
6943:
6884:
6595:
6381:
6376:
6107:
5825:
5735:
5230:
2296:
2211:
A first Bohlen–Pierce symposium took place in Boston on March 7 to 9, 2010, produced by composer
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103:
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6078:
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5725:
5715:
5680:
5486:
5324:
5299:
5118:
4985:
2310:
Alternate scales may be specified by indicating the size of equal tempered steps, for example
2151:
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1121:
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114:
87:
68:
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5478:
5222:
5093:
5049:
5006:
2300:
1086:
723:
432:
134:
95:
2259:
Other non-octave tunings investigated by Bohlen include twelve steps in the tritave, named
1173:
The following are the thirteen notes in the scale (cents rounded to nearest whole number):
346:). A minor triad is correspondingly 6 semitones on top and 4 semitones on bottom
7517:
7511:
7505:
7493:
7463:
7292:
7215:
7190:
7185:
7175:
7157:
6899:
6889:
6834:
6814:
6788:
6726:
6676:
6316:
6023:
5765:
5287:
2292:
2236:
2224:
2163:
2117:
1094:
91:
64:
2124:", the average listener will continually feel "that something isn't quite right", due to
5435:
5402:
5089:
7475:
7415:
7407:
7387:
7379:
7349:
7255:
7134:
7125:
7094:
6920:
6894:
6844:
6819:
6783:
6354:
6329:
6276:
6237:
6147:
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5815:
5705:
5263:
2248:
2169:
2121:
1132:
610:
472:
118:
71:
52:
3471:
except that each step is slightly smaller (less than a hundredth of a cent per step).
455:
3:1 serves as the fundamental harmonic ratio, replacing the diatonic scale's 2:1 (the
447:
7533:
7469:
7369:
7301:
7282:
7245:
7147:
7028:
7008:
6839:
6749:
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6058:
5800:
5775:
5730:
1136:
733:
476:
56:
5453:
5370:"David Lieberman participates in the Electric Fields and Mini-Maker Faire | Daniels"
2279:) or similar 11 steps in the tritave, and eight steps in the octave, based on 5:7:9
7311:
7297:
7230:
7220:
7117:
6613:
6453:
6256:
5978:
5875:
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5845:
5740:
5700:
5690:
5526:
5506:
2311:
2304:
2240:
2147:
2139:
2138:
Compositions using the Bohlen–Pierce scale include "Purity", the first movement of
1117:
760:
502:
110:
7287:
7277:
7263:
7210:
7167:
7152:
7142:
7069:
7064:
7054:
6993:
6809:
6804:
6773:
6768:
6701:
6696:
6686:
6281:
6261:
5929:
5924:
5914:
5855:
5587:
5344:
4952:
4947:
4939:
4934:
2315:
2244:
2235:
of Music. The symposium participants, which included Heinz Bohlen, Max
Mathews,
2212:
2159:
728:
713:
530:
436:
145:
122:
16:
479:
when reduced by an octave), but as this terminology is based on step sizes and
7059:
6859:
6691:
6660:
5919:
5770:
5252:. 26, No. 4 (Languages and Environments for Computer Music): 6–7. Winter 2002.
5053:
2319:
6681:
6635:
6073:
5790:
4982:
Music, Cognition, and
Computerized Sound: An Introduction to Psychoacoustics
2260:
152:
5565:
5037:
6068:
525:
521:
316:
160:
6718:
5576:
6984:
6655:
6605:
5609:
5234:
1566:
753:
149:
5098:
5075:
331:) on bottom and an interval of 4 equal-tempered semitones on top
6623:
6339:
6266:
5785:
1128:
456:
60:
5226:
513:
of the pitches one or more octaves higher or lower are present, but
5630:
6975:
6640:
6628:
6206:
5577:
The Bohlen–Pierce Site: Web place of an alternative harmonic scale
2276:
1080:
59:, first described in the 1970s, that offers an alternative to the
34:
15:
538:
soprano) is now (2020) played by Nora
Mueller, Luebeck, Germany.
6645:
7090:
6722:
6210:
5634:
2199:
David
Lieberman, an associate professor of architecture at the
435:. One may consider VIII (semitone 10) the analogue of the
94:
version. Compared with octave-repeating scales, the BP scale's
5442:. Retrieved 27 November 2012. Cites: Bohlen (1978). pp. 76–86.
451:
Bohlen-Pierce clarinet family: soprano, contra(bass) and tenor
187:) serves much the same role as the 4:5:6 chord (a major triad
5076:"Four new scales based on nonsuccessive-integer-ratio chords"
2243:, David Wessel, Psyche Loui, Richard Boulanger, Georg Hajdu,
483:
not used in the BP scale, it is often called by a new name,
5163:
5161:
5148:
5146:
2172:'s "A Wild and Reckless Place" (1990), Charles Carpenter (
1547:
1544:
1541:
1538:
1535:
1532:
1529:
1526:
1523:
1520:
1517:
1514:
1511:
1508:
1498:
1495:
1481:
1478:
1475:
1461:
1458:
1455:
1441:
1438:
1435:
1432:
1418:
1415:
1403:
1400:
1397:
1394:
1391:
1388:
1385:
1382:
1379:
1376:
1373:
1370:
1367:
1346:
1343:
1340:
1337:
1334:
1331:
1328:
1325:
1322:
1319:
1316:
1313:
1310:
1307:
1297:
1294:
1286:
1283:
1280:
1272:
1269:
1266:
1258:
1255:
1252:
1249:
1241:
1238:
1226:
1223:
1220:
1217:
1214:
1211:
1208:
1205:
1202:
1199:
1196:
1193:
1190:
2108:
Octave 12-tet (left) compared with tritave 13-tet (right)
125:
and others, published his discovery in 1984, renamed the
39:
Same chord in Ben
Johnston's notation for just intonation
2112:
What does music using a Bohlen–Pierce scale sound like,
2146:. Other computer composers to use the BP scale include
427:) was judged most consonant by the untrained subjects.
86:
The BP scale divides the tritave into 13 steps, either
5189:
Benson, Dave. "Musical scales and the Baker's Dozen".
509:. In the BP scale, if a given pitch is present, then
7456:
7424:
7406:
7378:
7320:
7254:
7203:
7166:
7133:
7124:
7083:
7047:
6913:
6797:
6761:
6669:
6586:
6549:
6502:
6409:
6400:
6315:
6244:
6178:
6169:
Twelve
Microtonal Etudes for Electronic Music Media
6122:
6092:
6049:
6022:
5944:
5903:
5894:
5838:
5668:
5074:Mathews, M.V.; Roberts, L.A.; Pierce, J.R. (1984).
1143:tempers out both of these intervals; the resulting
361:). 5:7:9 is the first inversion of the major triad
5568:", Bohlen-Pierce clarinets and other instruments,
1093:Bohlen originally expressed the BP scale in both
2263:by Enrique Moreno and based on the 4:7:10 chord
5588:Kees van Prooijen: 13 tones in the 3rd harmonic
1112:= 3 = 1.08818… above the next, or 1200 log
1503:
1410:
1360:
1302:
1233:
1183:
501:), in BP contexts, referring to its role as a
77:The interval 3:1 (often called by a new name,
7102:
6734:
6222:
5646:
5167:
5152:
5137:
5115:Current Directions in Computer Music Research
8:
6297:List of intervals in 5-limit just intonation
5292:The Cambridge Companion to Electronic Music
4971:
4969:
7130:
7109:
7095:
7087:
6741:
6727:
6719:
6406:
6229:
6215:
6207:
5900:
5653:
5639:
5631:
5621:Bohlen–Pierce Scale Symposium, Boston 2010
3473:
2338:
5097:
3483:Size of equally-tempered interval (cents)
2348:Size of equally-tempered interval (cents)
109:The scale was independently described by
2217:Hochschule für Musik und Theater Hamburg
2103:
1357:
1180:
548:
471:) This interval is a perfect twelfth in
446:
175:). The chord formed by the ratio 3:5:7 (
5017:(2). Stuttgart: S. Hirzel Verlag: 76–86
4965:
3489:Size of justly-intoned interval (cents)
2354:Size of justly-intoned interval (cents)
1559:play equal tempered Bohlen–Pierce scale
1062:contrast with just major diatonic scale
2231:, the Northeastern University and the
1051:play just Bohlen–Pierce "Lambda" scale
431:which therefore may be considered the
3462:65-tone equal division of the tritave
2331:39-tone equal division of the tritave
199:) does in diatonic scales (3:5:7 = 1:
7:
5392:Bohlen (1978). footnote 26, page 84.
3469:41-tone equal division of the octave
141:impression of intervals and chords.
5038:"A Theory of Equal-Tempered Scales"
4944:Other non-octave repeating scales:
67:and other musics, specifically the
14:
90:(the most popular form), or in a
6372:Ptolemy's intense diatonic scale
5829:
5824:
3477:Number of equally-tempered steps
2342:Number of equally-tempered steps
2223:. Co-organizers were the Boston
697:
688:
679:
670:
661:
652:
643:
634:
625:
616:
383:to be the most dissonant chord (
5515:(CD). Wendy Carlos. ESD. 81552.
5483:Tuning, Timbre, Spectrum, Scale
5203:Mathews; Pierce (1989). p. 172.
5179:Mathews; Pierce (1989). p. 170.
5007:"13 Tonstufen in der Duodezime"
2299:, although it was created from
2255:Other unusual tunings or scales
1568:
1406:
1365:
1229:
1188:
144:The intervals between BP scale
102:with certain types of acoustic
5597:Song in Bohlen Pierce Scale: "
5321:Music: A Mathematical Offering
129:and its chromatic variant the
1:
5424:. Stanford University: 12–22.
5296:Cambridge Companions to Music
5265:Discography of Microtonal CDs
2275:, seven steps in the octave (
63:-repeating scales typical in
6335:Harry Partch's 43-tone scale
6032:Harry Partch's 43-tone scale
5614:Bohlen-Pierce-Conference.org
5349:Bohlen-Pierce-Conference.org
1169:Intervals and scale diagrams
1149:41 equal steps to the octave
7545:Non–octave-repeating scales
6155:Sonata for Microtonal Piano
5610:The Bohlen–Pierce Symposium
5268:, Huygens-Fokker Foundation
5248:"John Pierce (1910-2002)".
5168:Mathews & Pierce (1989)
5153:Mathews & Pierce (1989)
5138:Mathews & Pierce (1989)
5036:Prooijen, Kees van (1978).
2247:, Ron Sword, Julia Werntz,
2051:Classic augmented eleventh
2018:Quasi-tempered major tenth
1891:Greater just minor seventh
1691:Quasi-tempered minor third
7566:
6880:Ptolemy's intense diatonic
6302:List of meantone intervals
6162:Suite for Microtonal Piano
5603:Xenharmonic.Wikispaces.com
5286:d'Escrivan, Julio (2007).
5117:. MIT Press. p. 167.
4984:. MIT Press. p. 183.
4980:. In Cook, Perry R (ed.).
1141:7-limit linear temperament
7540:Just tuning and intervals
6292:List of musical intervals
6287:Consonance and dissonance
6114:Huygens-Fokker Foundation
6102:Boston Microtonal Society
5822:
5054:10.1080/09298217808570248
4848:
4845:
4842:
4817:
4814:
4811:
4766:
4763:
4760:
4735:
4732:
4729:
4544:
4541:
4538:
4353:
4350:
4347:
3602:
3599:
3596:
3480:Equally-tempered interval
3392:
3389:
3386:
3330:
3327:
3324:
3259:
3256:
3253:
3208:
3205:
3202:
3157:
3154:
3151:
2966:
2963:
2960:
2935:
2932:
2929:
2744:
2741:
2738:
2693:
2690:
2687:
2642:
2639:
2636:
2560:
2557:
2554:
2487:
2484:
2481:
2345:Equally-tempered interval
2221:Boston Microtonal Society
1588:Cents in just intonation
1582:Just intonation interval
1145:Bohlen–Pierce temperament
1077:Bohlen–Pierce temperament
1037:
1034:
1031:
1028:
1025:
1022:
1019:
1014:
1011:
999:
996:
993:
990:
987:
984:
981:
978:
975:
963:
960:
957:
954:
951:
948:
945:
942:
939:
931:
916:
903:
890:
877:
864:
851:
838:
825:
812:
799:
791:
788:
785:
782:
779:
776:
773:
770:
767:
764:
752:
747:
742:
737:
732:
727:
722:
717:
712:
709:
695:
686:
677:
668:
659:
650:
641:
632:
623:
614:
602:
597:
592:
587:
582:
577:
572:
567:
562:
557:
551:
7359:descending melodic major
7306:descending melodic minor
5599:17tppp4 Walker Love Song
5509:(2000) . "Liner notes".
4976:Pierce, John R. (2001).
2233:New England Conservatory
2229:Berklee College of Music
2084:Just twelfth, "tritave"
1775:Lesser septimal tritone
7334:ascending melodic minor
7272:ascending melodic major
6064:Otonality and Utonality
5555:The Bohlen–Pierce Scale
5374:www.daniels.utoronto.ca
4978:"Consonance and scales"
3486:Justly-intoned interval
2351:Justly-intoned interval
2156:Solemn Song for Evening
1989:Septimal minimal tenth
7345:Lydian augmented (III)
7118:Modes in Western music
5761:Claus-Steffen Mahnkopf
5531:The Bohlen–Pierce Site
5458:The Bohlen–Pierce Site
5440:The Bohlen–Pierce Site
5407:The Bohlen–Pierce Site
5403:"Other Unusual Scales"
5250:Computer Music Journal
5215:Computer Music Journal
5084:75, S10(A) (S1): S10.
5005:Bohlen, Heinz (1978).
2293:Bohlen 833 cents scale
2109:
1090:
452:
443:Timbre and the tritave
308:pattern is similar to
306:intonation sensitivity
40:
32:
7426:Double harmonic scale
7398:Phrygian dominant (V)
7393:Ukrainian Dorian (IV)
6559:Temperament ordinaire
5937:(Bohlen–Pierce scale)
5881:Tui St. George Tucker
5566:Stephen Fox Clarinets
5527:"BP Scale Structures"
5319:Benson, Dave (2006).
2201:University of Toronto
2107:
2100:Music and composition
1953:Septimal minor ninth
1733:Septimal major third
1084:
450:
298:Chords and modulation
38:
19:
7550:Musical temperaments
7439:Hungarian minor (IV)
7365:Half diminished (VI)
7355:Aeolian dominant (V)
6951:17 equal temperament
6362:List of compositions
6191:Generalized keyboard
5686:Easley Blackwood Jr.
5454:"An 833 Cents Scale"
5436:Other Unusual Scales
524:'s spectrum (in the
333:(semitones 0, 6, 10;
121:. Pierce, who, with
7434:Double harmonic (I)
6186:Enharmonic keyboard
6137:quarter tone pieces
6131:Beauty in the Beast
5811:Ivan Wyschnegradsky
5512:Beauty in the Beast
5090:1984ASAJ...75...10M
5081:J. Acoust. Soc. Am.
2126:social conditioning
1116: (3) = 146.3…
163:overtones 3:5:7:9 (
131:Bohlen–Pierce scale
45:Bohlen–Pierce scale
7416:Harmonic major (I)
7388:Harmonic minor (I)
6885:Scale of harmonics
6596:Chinese musicology
6382:Scale of harmonics
6377:Pythagorean tuning
6325:Euler–Fokker genus
6108:Genesis of a Music
5736:Christiaan Huygens
5581:Huygens-Fokker.org
5191:Musik og Matematik
5140:, pp. 165–166
2297:Fibonacci sequence
2110:
1091:
453:
127:Pierce 3579b scale
41:
33:
7527:
7526:
7452:
7451:
7199:
7198:
6988:
6979:
6965:
6963:Escala nordestina
6953:
6946:
6939:
6932:
6875:Phrygian dominant
6716:
6715:
6582:
6581:
6204:
6203:
6196:Modernism (music)
6045:
6044:
5946:Equal temperament
5716:Brian Ferneyhough
5570:SFoxClarinets.com
5479:Sethares, William
5099:10.1121/1.2021272
4991:978-0-262-53190-0
4926:
4925:
3459:
3458:
2301:combination tones
2152:Richard Boulanger
2118:twelve-tone scale
2097:
2096:
1852:Just major sixth
1585:Traditional name
1552:
1551:
1351:
1350:
1139:) to a unison. A
1099:equal temperament
1044:
1043:
533:, clarinet maker
381:semitones 0, 1, 2
325:play one semitone
148:are based on odd
135:combination tones
115:Kees van Prooijen
7557:
7131:
7111:
7104:
7097:
7088:
7039:Ukrainian Dorian
6982:
6973:
6961:
6949:
6942:
6935:
6928:
6815:Diminished scale
6743:
6736:
6729:
6720:
6555:Well temperament
6541:Regular diatonic
6407:
6387:Tonality diamond
6231:
6224:
6217:
6208:
6084:Tonality diamond
5907:repeating scales
5901:
5886:Nicola Vicentino
5833:
5828:
5796:Nicola Vicentino
5721:Michael Finnissy
5662:Microtonal music
5655:
5648:
5641:
5632:
5542:
5541:
5539:
5537:
5523:
5517:
5516:
5503:
5497:
5496:
5475:
5469:
5468:
5466:
5464:
5449:
5443:
5432:
5426:
5425:
5417:
5415:
5413:
5399:
5393:
5390:
5384:
5383:
5381:
5380:
5366:
5360:
5359:
5357:
5355:
5341:
5335:
5334:
5316:
5310:
5309:
5283:
5277:
5275:
5274:
5273:
5260:
5254:
5253:
5245:
5239:
5238:
5210:
5204:
5201:
5195:
5194:
5186:
5180:
5177:
5171:
5165:
5156:
5150:
5141:
5135:
5129:
5128:
5110:
5104:
5103:
5101:
5071:
5065:
5064:
5062:
5060:
5033:
5027:
5026:
5024:
5022:
5002:
4996:
4995:
4973:
3474:
2339:
2295:is based on the
2290:
2289:
2288:
2286:
2274:
2273:
2272:
2270:
2225:Goethe Institute
2092:
2080:
2076:
2047:
2026:
1997:
1985:
1981:
1961:
1949:
1928:
1899:
1887:
1883:
1863:
1857:
1848:
1844:
1838:
1821:
1815:
1803:
1786:
1780:
1771:
1767:
1761:
1744:
1738:
1729:
1725:
1719:
1702:
1696:
1684:
1667:
1661:
1649:
1632:
1626:
1617:
1613:
1607:
1567:
1564:
1563:
1562:
1560:
1493:
1492:
1487:
1486:
1473:
1472:
1467:
1466:
1453:
1452:
1447:
1446:
1430:
1429:
1424:
1423:
1362:Interval (cents)
1358:
1292:
1291:
1278:
1277:
1264:
1263:
1247:
1246:
1185:Interval (cents)
1181:
1160:
1159:
1155:
1111:
1110:
1087:Chromatic circle
1067:
1066:
1065:
1063:
1056:
1055:
1054:
1052:
927:
926:
925:
923:
914:
913:
912:
910:
901:
900:
899:
897:
888:
887:
886:
884:
875:
874:
873:
871:
862:
861:
860:
858:
849:
848:
847:
845:
836:
835:
834:
832:
823:
822:
821:
819:
810:
809:
808:
806:
702:
701:
693:
692:
684:
683:
675:
674:
666:
665:
657:
656:
648:
647:
639:
638:
630:
629:
621:
620:
549:
500:
499:
498:
496:
470:
469:
468:
466:
426:
425:
424:
422:
414:
410:
409:
408:
406:
398:
394:
393:
392:
390:
382:
375:
374:
373:
371:
364:
360:
359:
358:
356:
349:
345:
344:
343:
341:
334:
330:
329:
328:
326:
311:
304:
293:
291:
290:
287:
284:
280:
274:
272:
271:
268:
265:
261:
255:
253:
252:
249:
246:
242:
236:
234:
233:
230:
227:
223:
217:
215:
214:
211:
208:
204:
198:
197:
196:
194:
186:
185:
184:
182:
174:
173:
172:
170:
31:
30:
29:
27:
7565:
7564:
7560:
7559:
7558:
7556:
7555:
7554:
7530:
7529:
7528:
7523:
7457:Number of tones
7448:
7420:
7402:
7374:
7316:
7250:
7195:
7162:
7120:
7115:
7079:
7043:
7004:Hungarian minor
6999:Hungarian major
6930:Double harmonic
6909:
6900:Synthetic scale
6825:Double harmonic
6793:
6757:
6747:
6717:
6712:
6709:(Bohlen–Pierce)
6677:833 cents scale
6665:
6588:
6578:
6545:
6498:
6396:
6317:Just intonation
6311:
6240:
6238:Musical tunings
6235:
6205:
6200:
6174:
6118:
6094:
6088:
6051:
6041:
6037:Double diatonic
6024:Just intonation
6018:
5940:
5906:
5896:
5890:
5834:
5820:
5766:Joel Mandelbaum
5696:Julián Carrillo
5676:Richard Barrett
5664:
5659:
5550:
5545:
5535:
5533:
5525:
5524:
5520:
5505:
5504:
5500:
5493:
5477:
5476:
5472:
5462:
5460:
5452:Bohlen, Heinz.
5451:
5450:
5446:
5433:
5429:
5419:
5411:
5409:
5401:
5400:
5396:
5391:
5387:
5378:
5376:
5368:
5367:
5363:
5353:
5351:
5343:
5342:
5338:
5331:
5323:. p. 237.
5318:
5317:
5313:
5306:
5298:. p. 229.
5285:
5284:
5280:
5271:
5269:
5262:
5261:
5257:
5247:
5246:
5242:
5227:10.2307/3681110
5212:
5211:
5207:
5202:
5198:
5188:
5187:
5183:
5178:
5174:
5166:
5159:
5151:
5144:
5136:
5132:
5125:
5112:
5111:
5107:
5073:
5072:
5068:
5058:
5056:
5035:
5034:
5030:
5020:
5018:
5004:
5003:
4999:
4992:
4975:
4974:
4967:
4963:
4931:
3464:
2333:
2328:
2284:
2282:
2281:
2280:
2268:
2266:
2265:
2264:
2257:
2237:Clarence Barlow
2209:
2174:Frog à la Pêche
2102:
2090:
2078:
2074:
2045:
2024:
1995:
1983:
1979:
1959:
1947:
1926:
1897:
1885:
1881:
1861:
1855:
1846:
1842:
1836:
1819:
1813:
1801:
1784:
1778:
1769:
1765:
1759:
1742:
1736:
1727:
1723:
1717:
1700:
1694:
1682:
1665:
1659:
1647:
1630:
1624:
1615:
1611:
1605:
1558:
1556:
1555:
1554:
1490:
1489:
1484:
1483:
1470:
1469:
1464:
1463:
1450:
1449:
1444:
1443:
1427:
1426:
1421:
1420:
1289:
1288:
1275:
1274:
1261:
1260:
1244:
1243:
1171:
1157:
1153:
1152:
1135:) and 128:125 (
1115:
1108:
1106:
1095:just intonation
1079:
1074:
1061:
1059:
1058:
1057:
1050:
1048:
1047:
1046:
921:
919:
918:
917:
908:
906:
905:
904:
895:
893:
892:
891:
882:
880:
879:
878:
869:
867:
866:
865:
856:
854:
853:
852:
843:
841:
840:
839:
830:
828:
827:
826:
817:
815:
814:
813:
804:
802:
801:
800:
696:
687:
678:
669:
660:
651:
642:
633:
624:
615:
544:
494:
492:
491:
490:
464:
462:
461:
460:
445:
420:
418:
417:
416:
412:
404:
402:
401:
400:
396:
388:
386:
385:
384:
380:
369:
367:
366:
365:
362:
354:
352:
351:
350:
347:
339:
337:
336:
335:
332:
324:
322:
321:
320:
309:
302:
300:
288:
285:
282:
281:
278:
276:
269:
266:
263:
262:
259:
257:
250:
247:
244:
243:
240:
238:
231:
228:
225:
224:
221:
219:
212:
209:
206:
205:
202:
200:
192:
190:
189:
188:
180:
178:
177:
176:
168:
166:
165:
164:
157:harmonic series
51:) is a musical
25:
23:
22:
21:
12:
11:
5:
7563:
7561:
7553:
7552:
7547:
7542:
7532:
7531:
7525:
7524:
7522:
7521:
7515:
7509:
7503:
7497:
7491:
7485:
7479:
7473:
7467:
7460:
7458:
7454:
7453:
7450:
7449:
7447:
7446:
7441:
7436:
7430:
7428:
7422:
7421:
7419:
7418:
7412:
7410:
7408:Harmonic major
7404:
7403:
7401:
7400:
7395:
7390:
7384:
7382:
7380:Harmonic minor
7376:
7375:
7373:
7372:
7367:
7362:
7352:
7347:
7342:
7340:Dorian ♭2 (II)
7337:
7330:Jazz minor (I)
7326:
7324:
7318:
7317:
7315:
7314:
7309:
7295:
7293:Mixolydian (V)
7290:
7285:
7283:Phrygian (III)
7280:
7275:
7260:
7258:
7252:
7251:
7249:
7248:
7243:
7238:
7233:
7228:
7223:
7218:
7213:
7207:
7205:
7201:
7200:
7197:
7196:
7194:
7193:
7191:Hypomixolydian
7188:
7183:
7178:
7172:
7170:
7164:
7163:
7161:
7160:
7155:
7150:
7145:
7139:
7137:
7128:
7122:
7121:
7116:
7114:
7113:
7106:
7099:
7091:
7085:
7081:
7080:
7078:
7077:
7072:
7067:
7062:
7057:
7051:
7049:
7045:
7044:
7042:
7041:
7036:
7034:Romanian major
7031:
7026:
7021:
7016:
7011:
7006:
7001:
6996:
6991:
6990:
6989:
6980:
6968:
6967:
6966:
6956:
6955:
6954:
6947:
6940:
6933:
6923:
6917:
6915:
6911:
6910:
6908:
6907:
6902:
6897:
6895:Synthetic mode
6892:
6887:
6882:
6877:
6872:
6867:
6862:
6857:
6855:Harmonic minor
6852:
6850:Harmonic major
6847:
6842:
6837:
6832:
6827:
6822:
6820:Distance model
6817:
6812:
6807:
6801:
6799:
6795:
6794:
6792:
6791:
6786:
6781:
6776:
6771:
6765:
6763:
6759:
6758:
6750:Musical scales
6748:
6746:
6745:
6738:
6731:
6723:
6714:
6713:
6711:
6710:
6704:
6699:
6694:
6689:
6684:
6679:
6673:
6671:
6667:
6666:
6664:
6663:
6658:
6653:
6643:
6638:
6633:
6632:
6631:
6626:
6621:
6616:
6608:
6603:
6598:
6592:
6590:
6584:
6583:
6580:
6579:
6553:
6551:
6547:
6546:
6544:
6543:
6538:
6533:
6528:
6523:
6508:
6506:
6500:
6499:
6497:
6496:
6491:
6486:
6481:
6476:
6471:
6466:
6461:
6451:
6446:
6441:
6436:
6431:
6426:
6421:
6415:
6413:
6404:
6398:
6397:
6395:
6394:
6389:
6384:
6379:
6374:
6369:
6364:
6359:
6358:
6357:
6352:
6342:
6337:
6332:
6330:Harmonic scale
6327:
6321:
6319:
6313:
6312:
6310:
6309:
6304:
6299:
6294:
6289:
6284:
6279:
6277:Interval ratio
6274:
6269:
6264:
6259:
6254:
6248:
6246:
6242:
6241:
6236:
6234:
6233:
6226:
6219:
6211:
6202:
6201:
6199:
6198:
6193:
6188:
6182:
6180:
6176:
6175:
6173:
6172:
6165:
6158:
6151:
6144:
6139:
6134:
6126:
6124:
6120:
6119:
6117:
6116:
6111:
6104:
6098:
6096:
6090:
6089:
6087:
6086:
6081:
6079:Xenharmonicity
6076:
6071:
6066:
6061:
6055:
6053:
6047:
6046:
6043:
6042:
6040:
6039:
6034:
6028:
6026:
6020:
6019:
6017:
6016:
6011:
6006:
6001:
5996:
5991:
5986:
5981:
5976:
5971:
5966:
5961:
5956:
5950:
5948:
5942:
5941:
5939:
5938:
5932:
5927:
5922:
5917:
5911:
5909:
5898:
5892:
5891:
5889:
5888:
5883:
5878:
5873:
5868:
5863:
5861:Adriaan Fokker
5858:
5853:
5848:
5842:
5840:
5836:
5835:
5823:
5821:
5819:
5818:
5816:La Monte Young
5813:
5808:
5803:
5798:
5793:
5788:
5783:
5781:John Schneider
5778:
5773:
5768:
5763:
5758:
5753:
5748:
5743:
5738:
5733:
5728:
5726:Bjørn Fongaard
5723:
5718:
5713:
5708:
5706:Mildred Couper
5703:
5698:
5693:
5688:
5683:
5678:
5672:
5670:
5666:
5665:
5660:
5658:
5657:
5650:
5643:
5635:
5629:
5628:
5617:
5606:
5595:
5584:
5573:
5562:
5549:
5548:External links
5546:
5544:
5543:
5518:
5498:
5491:
5485:. p. 60.
5470:
5444:
5427:
5394:
5385:
5361:
5336:
5329:
5311:
5304:
5278:
5255:
5240:
5205:
5196:
5181:
5172:
5170:, pp. 171
5157:
5155:, pp. 169
5142:
5130:
5123:
5105:
5066:
5028:
4997:
4990:
4964:
4962:
4959:
4958:
4957:
4956:
4955:
4950:
4942:
4937:
4930:
4927:
4924:
4923:
4920:
4917:
4914:
4911:
4908:
4904:
4903:
4900:
4897:
4893:
4892:
4889:
4886:
4882:
4881:
4878:
4875:
4871:
4870:
4867:
4864:
4860:
4859:
4856:
4853:
4850:
4847:
4844:
4840:
4839:
4836:
4833:
4829:
4828:
4825:
4822:
4819:
4816:
4813:
4809:
4808:
4805:
4802:
4799:
4796:
4793:
4789:
4788:
4785:
4782:
4778:
4777:
4774:
4771:
4768:
4765:
4762:
4758:
4757:
4754:
4751:
4747:
4746:
4743:
4740:
4737:
4734:
4731:
4727:
4726:
4723:
4720:
4717:
4714:
4711:
4707:
4706:
4703:
4700:
4697:
4694:
4691:
4687:
4686:
4683:
4680:
4677:
4674:
4671:
4667:
4666:
4663:
4660:
4657:
4654:
4651:
4647:
4646:
4643:
4640:
4637:
4634:
4631:
4627:
4626:
4623:
4620:
4617:
4614:
4611:
4607:
4606:
4603:
4600:
4597:
4594:
4591:
4587:
4586:
4583:
4580:
4577:
4574:
4571:
4567:
4566:
4563:
4560:
4556:
4555:
4552:
4549:
4546:
4543:
4540:
4536:
4535:
4532:
4529:
4526:
4523:
4520:
4516:
4515:
4512:
4509:
4506:
4503:
4500:
4496:
4495:
4492:
4489:
4486:
4483:
4480:
4476:
4475:
4472:
4469:
4466:
4463:
4460:
4456:
4455:
4452:
4449:
4446:
4443:
4440:
4436:
4435:
4432:
4429:
4426:
4423:
4420:
4416:
4415:
4412:
4409:
4406:
4403:
4400:
4396:
4395:
4392:
4389:
4386:
4383:
4380:
4376:
4375:
4372:
4369:
4365:
4364:
4361:
4358:
4355:
4352:
4349:
4345:
4344:
4341:
4338:
4335:
4332:
4329:
4325:
4324:
4321:
4318:
4315:
4312:
4309:
4305:
4304:
4301:
4298:
4295:
4292:
4289:
4285:
4284:
4281:
4278:
4275:
4272:
4269:
4265:
4264:
4261:
4258:
4255:
4252:
4249:
4245:
4244:
4241:
4238:
4235:
4232:
4229:
4225:
4224:
4221:
4218:
4215:
4212:
4209:
4205:
4204:
4201:
4198:
4195:
4192:
4189:
4185:
4184:
4181:
4178:
4175:
4172:
4169:
4165:
4164:
4161:
4158:
4155:
4152:
4149:
4145:
4144:
4141:
4138:
4135:
4132:
4129:
4125:
4124:
4121:
4118:
4115:
4112:
4109:
4105:
4104:
4101:
4098:
4095:
4092:
4089:
4085:
4084:
4081:
4078:
4075:
4072:
4069:
4065:
4064:
4061:
4058:
4055:
4052:
4049:
4045:
4044:
4041:
4038:
4035:
4032:
4029:
4025:
4024:
4021:
4018:
4015:
4012:
4009:
4005:
4004:
4001:
3998:
3995:
3992:
3989:
3985:
3984:
3981:
3978:
3975:
3972:
3969:
3965:
3964:
3961:
3958:
3955:
3952:
3949:
3945:
3944:
3941:
3938:
3935:
3932:
3929:
3925:
3924:
3921:
3918:
3915:
3912:
3909:
3905:
3904:
3901:
3898:
3895:
3892:
3889:
3885:
3884:
3881:
3878:
3875:
3872:
3869:
3865:
3864:
3861:
3858:
3855:
3852:
3849:
3845:
3844:
3841:
3838:
3835:
3832:
3829:
3825:
3824:
3821:
3818:
3815:
3812:
3809:
3805:
3804:
3801:
3798:
3795:
3792:
3789:
3785:
3784:
3781:
3778:
3775:
3772:
3769:
3765:
3764:
3761:
3758:
3755:
3752:
3749:
3745:
3744:
3741:
3738:
3735:
3732:
3729:
3725:
3724:
3721:
3718:
3715:
3712:
3709:
3705:
3704:
3701:
3698:
3695:
3692:
3689:
3685:
3684:
3681:
3678:
3675:
3672:
3669:
3665:
3664:
3661:
3658:
3655:
3652:
3649:
3645:
3644:
3641:
3638:
3635:
3632:
3629:
3625:
3624:
3621:
3618:
3614:
3613:
3610:
3607:
3604:
3601:
3598:
3594:
3593:
3590:
3587:
3584:
3581:
3578:
3574:
3573:
3570:
3567:
3564:
3561:
3558:
3554:
3553:
3550:
3547:
3544:
3541:
3538:
3534:
3533:
3530:
3527:
3524:
3521:
3518:
3514:
3513:
3510:
3507:
3504:
3501:
3498:
3494:
3493:
3492:Error (cents)
3490:
3487:
3484:
3481:
3478:
3463:
3460:
3457:
3456:
3453:
3450:
3447:
3444:
3441:
3437:
3436:
3433:
3430:
3426:
3425:
3422:
3419:
3415:
3414:
3411:
3408:
3404:
3403:
3400:
3397:
3394:
3391:
3388:
3384:
3383:
3380:
3377:
3374:
3371:
3368:
3364:
3363:
3360:
3357:
3353:
3352:
3349:
3346:
3342:
3341:
3338:
3335:
3332:
3329:
3326:
3322:
3321:
3318:
3315:
3312:
3309:
3306:
3302:
3301:
3298:
3295:
3292:
3289:
3286:
3282:
3281:
3278:
3275:
3271:
3270:
3267:
3264:
3261:
3258:
3255:
3251:
3250:
3247:
3244:
3241:
3238:
3235:
3231:
3230:
3227:
3224:
3220:
3219:
3216:
3213:
3210:
3207:
3204:
3200:
3199:
3196:
3193:
3190:
3187:
3184:
3180:
3179:
3176:
3173:
3169:
3168:
3165:
3162:
3159:
3156:
3153:
3149:
3148:
3145:
3142:
3139:
3136:
3133:
3129:
3128:
3125:
3122:
3119:
3116:
3113:
3109:
3108:
3105:
3102:
3099:
3096:
3093:
3089:
3088:
3085:
3082:
3079:
3076:
3073:
3069:
3068:
3065:
3062:
3059:
3056:
3053:
3049:
3048:
3045:
3042:
3039:
3036:
3033:
3029:
3028:
3025:
3022:
3019:
3016:
3013:
3009:
3008:
3005:
3002:
2999:
2996:
2993:
2989:
2988:
2985:
2982:
2978:
2977:
2974:
2971:
2968:
2965:
2962:
2958:
2957:
2954:
2951:
2947:
2946:
2943:
2940:
2937:
2934:
2931:
2927:
2926:
2923:
2920:
2917:
2914:
2911:
2907:
2906:
2903:
2900:
2897:
2894:
2891:
2887:
2886:
2883:
2880:
2877:
2874:
2871:
2867:
2866:
2863:
2860:
2857:
2854:
2851:
2847:
2846:
2843:
2840:
2837:
2834:
2831:
2827:
2826:
2823:
2820:
2817:
2814:
2811:
2807:
2806:
2803:
2800:
2797:
2794:
2791:
2787:
2786:
2783:
2780:
2777:
2774:
2771:
2767:
2766:
2763:
2760:
2756:
2755:
2752:
2749:
2746:
2743:
2740:
2736:
2735:
2732:
2729:
2726:
2723:
2720:
2716:
2715:
2712:
2709:
2705:
2704:
2701:
2698:
2695:
2692:
2689:
2685:
2684:
2681:
2678:
2675:
2672:
2669:
2665:
2664:
2661:
2658:
2654:
2653:
2650:
2647:
2644:
2641:
2638:
2634:
2633:
2630:
2627:
2624:
2621:
2618:
2614:
2613:
2610:
2607:
2604:
2601:
2598:
2594:
2593:
2590:
2587:
2583:
2582:
2579:
2576:
2572:
2571:
2568:
2565:
2562:
2559:
2556:
2552:
2551:
2548:
2545:
2542:
2539:
2536:
2532:
2531:
2528:
2525:
2521:
2520:
2517:
2514:
2510:
2509:
2506:
2503:
2499:
2498:
2495:
2492:
2489:
2486:
2483:
2479:
2478:
2475:
2472:
2469:
2466:
2463:
2459:
2458:
2455:
2452:
2449:
2446:
2443:
2439:
2438:
2435:
2432:
2429:
2426:
2423:
2419:
2418:
2415:
2412:
2409:
2406:
2403:
2399:
2398:
2395:
2392:
2389:
2386:
2383:
2379:
2378:
2375:
2372:
2369:
2366:
2363:
2359:
2358:
2357:Error (cents)
2355:
2352:
2349:
2346:
2343:
2332:
2329:
2327:
2324:
2318:and 63.8-cent
2256:
2253:
2249:Larry Polansky
2208:
2205:
2170:Ami Radunskaya
2162:, Juan Reyes'
2101:
2098:
2095:
2094:
2088:
2085:
2082:
2072:
2069:
2066:
2063:
2059:
2058:
2055:
2052:
2049:
2042:
2039:
2036:
2033:
2029:
2028:
2022:
2019:
2016:
2013:
2010:
2007:
2004:
2000:
1999:
1993:
1990:
1987:
1977:
1974:
1971:
1968:
1964:
1963:
1957:
1954:
1951:
1944:
1941:
1938:
1935:
1931:
1930:
1924:
1921:
1918:
1915:
1912:
1909:
1906:
1902:
1901:
1895:
1892:
1889:
1879:
1876:
1873:
1870:
1866:
1865:
1859:
1853:
1850:
1840:
1834:
1831:
1828:
1824:
1823:
1817:
1811:
1808:
1805:
1799:
1796:
1793:
1789:
1788:
1782:
1776:
1773:
1763:
1757:
1754:
1751:
1747:
1746:
1740:
1734:
1731:
1721:
1715:
1712:
1709:
1705:
1704:
1698:
1692:
1689:
1686:
1680:
1677:
1674:
1670:
1669:
1663:
1657:
1654:
1651:
1645:
1642:
1639:
1635:
1634:
1628:
1622:
1619:
1609:
1603:
1600:
1597:
1593:
1592:
1589:
1586:
1583:
1580:
1577:
1574:
1571:
1550:
1549:
1546:
1543:
1540:
1537:
1534:
1531:
1528:
1525:
1522:
1519:
1516:
1513:
1510:
1507:
1501:
1500:
1497:
1494:
1480:
1477:
1474:
1460:
1457:
1454:
1440:
1437:
1434:
1431:
1417:
1414:
1408:
1407:
1405:
1402:
1399:
1396:
1393:
1390:
1387:
1384:
1381:
1378:
1375:
1372:
1369:
1366:
1364:
1354:Equal-tempered
1349:
1348:
1345:
1342:
1339:
1336:
1333:
1330:
1327:
1324:
1321:
1318:
1315:
1312:
1309:
1306:
1300:
1299:
1296:
1293:
1285:
1282:
1279:
1271:
1268:
1265:
1257:
1254:
1251:
1248:
1240:
1237:
1231:
1230:
1228:
1225:
1222:
1219:
1216:
1213:
1210:
1207:
1204:
1201:
1198:
1195:
1192:
1189:
1187:
1170:
1167:
1133:syntonic comma
1113:
1078:
1075:
1072:
1042:
1041:
1039:
1036:
1033:
1030:
1027:
1024:
1021:
1018:
1013:
1010:
1008:
1004:
1003:
1001:
998:
995:
992:
989:
986:
983:
980:
977:
974:
972:
968:
967:
965:
962:
959:
956:
953:
950:
947:
944:
941:
938:
936:
933:
929:
928:
915:
902:
889:
876:
863:
850:
837:
824:
811:
798:
794:
793:
790:
787:
784:
781:
778:
775:
772:
769:
766:
763:
757:
756:
751:
746:
741:
736:
731:
726:
721:
716:
711:
708:
704:
703:
694:
685:
676:
667:
658:
649:
640:
631:
622:
613:
607:
606:
601:
596:
591:
586:
581:
576:
571:
566:
561:
556:
553:
543:
540:
475:nomenclature (
444:
441:
299:
296:
237:and 4:5:6 = 2:
119:John R. Pierce
88:equal tempered
72:diatonic scale
69:equal-tempered
13:
10:
9:
6:
4:
3:
2:
7562:
7551:
7548:
7546:
7543:
7541:
7538:
7537:
7535:
7519:
7516:
7513:
7510:
7507:
7504:
7501:
7498:
7495:
7492:
7489:
7486:
7483:
7480:
7477:
7474:
7471:
7468:
7465:
7462:
7461:
7459:
7455:
7445:
7442:
7440:
7437:
7435:
7432:
7431:
7429:
7427:
7423:
7417:
7414:
7413:
7411:
7409:
7405:
7399:
7396:
7394:
7391:
7389:
7386:
7385:
7383:
7381:
7377:
7371:
7370:Altered (VII)
7368:
7366:
7363:
7360:
7356:
7353:
7351:
7350:Acoustic (IV)
7348:
7346:
7343:
7341:
7338:
7335:
7331:
7328:
7327:
7325:
7323:
7319:
7313:
7312:Locrian (VII)
7310:
7307:
7303:
7302:natural minor
7299:
7296:
7294:
7291:
7289:
7286:
7284:
7281:
7279:
7276:
7273:
7269:
7268:natural major
7265:
7262:
7261:
7259:
7257:
7253:
7247:
7246:Reciting tone
7244:
7242:
7239:
7237:
7234:
7232:
7229:
7227:
7224:
7222:
7219:
7217:
7214:
7212:
7209:
7208:
7206:
7202:
7192:
7189:
7187:
7184:
7182:
7179:
7177:
7174:
7173:
7171:
7169:
7165:
7159:
7156:
7154:
7151:
7149:
7146:
7144:
7141:
7140:
7138:
7136:
7132:
7129:
7127:
7123:
7119:
7112:
7107:
7105:
7100:
7098:
7093:
7092:
7089:
7086:
7082:
7076:
7075:Bohlen–Pierce
7073:
7071:
7068:
7066:
7063:
7061:
7058:
7056:
7053:
7052:
7050:
7046:
7040:
7037:
7035:
7032:
7030:
7027:
7025:
7022:
7020:
7019:Jewish nusach
7017:
7015:
7012:
7010:
7007:
7005:
7002:
7000:
6997:
6995:
6992:
6987:
6986:
6981:
6978:
6977:
6972:
6971:
6969:
6964:
6960:
6959:
6957:
6952:
6948:
6945:
6941:
6938:
6937:Major Locrian
6934:
6931:
6927:
6926:
6924:
6922:
6919:
6918:
6916:
6914:Ethnic origin
6912:
6906:
6903:
6901:
6898:
6896:
6893:
6891:
6888:
6886:
6883:
6881:
6878:
6876:
6873:
6871:
6870:Major Locrian
6868:
6866:
6863:
6861:
6858:
6856:
6853:
6851:
6848:
6846:
6843:
6841:
6840:Flamenco mode
6838:
6836:
6833:
6831:
6828:
6826:
6823:
6821:
6818:
6816:
6813:
6811:
6808:
6806:
6803:
6802:
6800:
6796:
6790:
6787:
6785:
6782:
6780:
6777:
6775:
6772:
6770:
6767:
6766:
6764:
6760:
6755:
6751:
6744:
6739:
6737:
6732:
6730:
6725:
6724:
6721:
6708:
6705:
6703:
6700:
6698:
6695:
6693:
6690:
6688:
6685:
6683:
6680:
6678:
6675:
6674:
6672:
6668:
6662:
6659:
6657:
6654:
6651:
6650:Carnatic raga
6647:
6644:
6642:
6639:
6637:
6634:
6630:
6627:
6625:
6622:
6620:
6619:Turkish makam
6617:
6615:
6612:
6611:
6609:
6607:
6604:
6602:
6599:
6597:
6594:
6593:
6591:
6585:
6576:
6572:
6568:
6564:
6560:
6556:
6552:
6548:
6542:
6539:
6537:
6534:
6532:
6529:
6527:
6524:
6521:
6517:
6516:quarter-comma
6513:
6510:
6509:
6507:
6505:
6501:
6495:
6492:
6490:
6487:
6485:
6482:
6480:
6477:
6475:
6472:
6470:
6467:
6465:
6462:
6459:
6455:
6452:
6450:
6447:
6445:
6442:
6440:
6437:
6435:
6432:
6430:
6427:
6425:
6422:
6420:
6417:
6416:
6414:
6412:
6408:
6405:
6403:
6399:
6393:
6392:Tonality flux
6390:
6388:
6385:
6383:
6380:
6378:
6375:
6373:
6370:
6368:
6365:
6363:
6360:
6356:
6353:
6351:
6348:
6347:
6346:
6343:
6341:
6338:
6336:
6333:
6331:
6328:
6326:
6323:
6322:
6320:
6318:
6314:
6308:
6305:
6303:
6300:
6298:
6295:
6293:
6290:
6288:
6285:
6283:
6280:
6278:
6275:
6273:
6270:
6268:
6265:
6263:
6260:
6258:
6255:
6253:
6250:
6249:
6247:
6243:
6239:
6232:
6227:
6225:
6220:
6218:
6213:
6212:
6209:
6197:
6194:
6192:
6189:
6187:
6184:
6183:
6181:
6177:
6171:
6170:
6166:
6164:
6163:
6159:
6157:
6156:
6152:
6150:
6149:
6145:
6143:
6140:
6138:
6135:
6133:
6132:
6128:
6127:
6125:
6121:
6115:
6112:
6110:
6109:
6105:
6103:
6100:
6099:
6097:
6091:
6085:
6082:
6080:
6077:
6075:
6072:
6070:
6067:
6065:
6062:
6060:
6057:
6056:
6054:
6048:
6038:
6035:
6033:
6030:
6029:
6027:
6025:
6021:
6015:
6012:
6010:
6007:
6005:
6002:
6000:
5997:
5995:
5992:
5990:
5987:
5985:
5982:
5980:
5977:
5975:
5972:
5970:
5967:
5965:
5962:
5960:
5957:
5955:
5952:
5951:
5949:
5947:
5943:
5936:
5933:
5931:
5928:
5926:
5923:
5921:
5918:
5916:
5913:
5912:
5910:
5908:
5902:
5899:
5893:
5887:
5884:
5882:
5879:
5877:
5874:
5872:
5869:
5867:
5864:
5862:
5859:
5857:
5854:
5852:
5849:
5847:
5844:
5843:
5841:
5837:
5832:
5827:
5817:
5814:
5812:
5809:
5807:
5806:Elaine Walker
5804:
5802:
5801:Claude Vivier
5799:
5797:
5794:
5792:
5789:
5787:
5784:
5782:
5779:
5777:
5776:Roger Redgate
5774:
5772:
5769:
5767:
5764:
5762:
5759:
5757:
5756:Stu Mackenzie
5754:
5752:
5751:György Ligeti
5749:
5747:
5744:
5742:
5739:
5737:
5734:
5732:
5729:
5727:
5724:
5722:
5719:
5717:
5714:
5712:
5709:
5707:
5704:
5702:
5699:
5697:
5694:
5692:
5689:
5687:
5684:
5682:
5679:
5677:
5674:
5673:
5671:
5667:
5663:
5656:
5651:
5649:
5644:
5642:
5637:
5636:
5633:
5626:
5622:
5618:
5615:
5611:
5607:
5604:
5600:
5596:
5593:
5589:
5585:
5582:
5578:
5574:
5571:
5567:
5563:
5560:
5556:
5552:
5551:
5547:
5532:
5528:
5522:
5519:
5514:
5513:
5508:
5507:Carlos, Wendy
5502:
5499:
5494:
5492:1-85233-797-4
5488:
5484:
5480:
5474:
5471:
5459:
5455:
5448:
5445:
5441:
5437:
5431:
5428:
5423:
5408:
5404:
5398:
5395:
5389:
5386:
5375:
5371:
5365:
5362:
5350:
5346:
5340:
5337:
5332:
5330:9780521853873
5326:
5322:
5315:
5312:
5307:
5305:9780521868617
5301:
5297:
5293:
5289:
5288:Collins, Nick
5282:
5279:
5267:
5266:
5259:
5256:
5251:
5244:
5241:
5236:
5232:
5228:
5224:
5221:(2): 90–92 .
5220:
5216:
5209:
5206:
5200:
5197:
5192:
5185:
5182:
5176:
5173:
5169:
5164:
5162:
5158:
5154:
5149:
5147:
5143:
5139:
5134:
5131:
5126:
5124:9780262631396
5120:
5116:
5109:
5106:
5100:
5095:
5091:
5087:
5083:
5082:
5077:
5070:
5067:
5055:
5051:
5047:
5043:
5039:
5032:
5029:
5016:
5013:(in German).
5012:
5008:
5001:
4998:
4993:
4987:
4983:
4979:
4972:
4970:
4966:
4960:
4954:
4951:
4949:
4946:
4945:
4943:
4941:
4938:
4936:
4933:
4932:
4928:
4921:
4918:
4915:
4912:
4909:
4906:
4905:
4901:
4898:
4895:
4894:
4890:
4887:
4884:
4883:
4879:
4876:
4873:
4872:
4868:
4865:
4862:
4861:
4857:
4854:
4851:
4841:
4837:
4834:
4831:
4830:
4826:
4823:
4820:
4810:
4806:
4803:
4800:
4797:
4794:
4791:
4790:
4786:
4783:
4780:
4779:
4775:
4772:
4769:
4759:
4755:
4752:
4749:
4748:
4744:
4741:
4738:
4728:
4724:
4721:
4718:
4715:
4712:
4709:
4708:
4704:
4701:
4698:
4695:
4692:
4689:
4688:
4684:
4681:
4678:
4675:
4672:
4669:
4668:
4664:
4661:
4658:
4655:
4652:
4649:
4648:
4644:
4641:
4638:
4635:
4632:
4629:
4628:
4624:
4621:
4618:
4615:
4612:
4609:
4608:
4604:
4601:
4598:
4595:
4592:
4589:
4588:
4584:
4581:
4578:
4575:
4572:
4569:
4568:
4564:
4561:
4558:
4557:
4553:
4550:
4547:
4537:
4533:
4530:
4527:
4524:
4521:
4518:
4517:
4513:
4510:
4507:
4504:
4501:
4498:
4497:
4493:
4490:
4487:
4484:
4481:
4478:
4477:
4473:
4470:
4467:
4464:
4461:
4458:
4457:
4453:
4450:
4447:
4444:
4441:
4438:
4437:
4433:
4430:
4427:
4424:
4421:
4418:
4417:
4413:
4410:
4407:
4404:
4401:
4398:
4397:
4393:
4390:
4387:
4384:
4381:
4378:
4377:
4373:
4370:
4367:
4366:
4362:
4359:
4356:
4346:
4342:
4339:
4336:
4333:
4330:
4327:
4326:
4322:
4319:
4316:
4313:
4310:
4307:
4306:
4302:
4299:
4296:
4293:
4290:
4287:
4286:
4282:
4279:
4276:
4273:
4270:
4267:
4266:
4262:
4259:
4256:
4253:
4250:
4247:
4246:
4242:
4239:
4236:
4233:
4230:
4227:
4226:
4222:
4219:
4216:
4213:
4210:
4207:
4206:
4202:
4199:
4196:
4193:
4190:
4187:
4186:
4182:
4179:
4176:
4173:
4170:
4167:
4166:
4162:
4159:
4156:
4153:
4150:
4147:
4146:
4142:
4139:
4136:
4133:
4130:
4127:
4126:
4122:
4119:
4116:
4113:
4110:
4107:
4106:
4102:
4099:
4096:
4093:
4090:
4087:
4086:
4082:
4079:
4076:
4073:
4070:
4067:
4066:
4062:
4059:
4056:
4053:
4050:
4047:
4046:
4042:
4039:
4036:
4033:
4030:
4027:
4026:
4022:
4019:
4016:
4013:
4010:
4007:
4006:
4002:
3999:
3996:
3993:
3990:
3987:
3986:
3982:
3979:
3976:
3973:
3970:
3967:
3966:
3962:
3959:
3956:
3953:
3950:
3947:
3946:
3942:
3939:
3936:
3933:
3930:
3927:
3926:
3922:
3919:
3916:
3913:
3910:
3907:
3906:
3902:
3899:
3896:
3893:
3890:
3887:
3886:
3882:
3879:
3876:
3873:
3870:
3867:
3866:
3862:
3859:
3856:
3853:
3850:
3847:
3846:
3842:
3839:
3836:
3833:
3830:
3827:
3826:
3822:
3819:
3816:
3813:
3810:
3807:
3806:
3802:
3799:
3796:
3793:
3790:
3787:
3786:
3782:
3779:
3776:
3773:
3770:
3767:
3766:
3762:
3759:
3756:
3753:
3750:
3747:
3746:
3742:
3739:
3736:
3733:
3730:
3727:
3726:
3722:
3719:
3716:
3713:
3710:
3707:
3706:
3702:
3699:
3696:
3693:
3690:
3687:
3686:
3682:
3679:
3676:
3673:
3670:
3667:
3666:
3662:
3659:
3656:
3653:
3650:
3647:
3646:
3642:
3639:
3636:
3633:
3630:
3627:
3626:
3622:
3619:
3616:
3615:
3611:
3608:
3605:
3595:
3591:
3588:
3585:
3582:
3579:
3576:
3575:
3571:
3568:
3565:
3562:
3559:
3556:
3555:
3551:
3548:
3545:
3542:
3539:
3536:
3535:
3531:
3528:
3525:
3522:
3519:
3516:
3515:
3511:
3508:
3505:
3502:
3499:
3496:
3495:
3491:
3488:
3485:
3482:
3479:
3476:
3475:
3472:
3470:
3461:
3454:
3451:
3448:
3445:
3442:
3439:
3438:
3434:
3431:
3428:
3427:
3423:
3420:
3417:
3416:
3412:
3409:
3406:
3405:
3401:
3398:
3395:
3385:
3381:
3378:
3375:
3372:
3369:
3366:
3365:
3361:
3358:
3355:
3354:
3350:
3347:
3344:
3343:
3339:
3336:
3333:
3323:
3319:
3316:
3313:
3310:
3307:
3304:
3303:
3299:
3296:
3293:
3290:
3287:
3284:
3283:
3279:
3276:
3273:
3272:
3268:
3265:
3262:
3252:
3248:
3245:
3242:
3239:
3236:
3233:
3232:
3228:
3225:
3222:
3221:
3217:
3214:
3211:
3201:
3197:
3194:
3191:
3188:
3185:
3182:
3181:
3177:
3174:
3171:
3170:
3166:
3163:
3160:
3150:
3146:
3143:
3140:
3137:
3134:
3131:
3130:
3126:
3123:
3120:
3117:
3114:
3111:
3110:
3106:
3103:
3100:
3097:
3094:
3091:
3090:
3086:
3083:
3080:
3077:
3074:
3071:
3070:
3066:
3063:
3060:
3057:
3054:
3051:
3050:
3046:
3043:
3040:
3037:
3034:
3031:
3030:
3026:
3023:
3020:
3017:
3014:
3011:
3010:
3006:
3003:
3000:
2997:
2994:
2991:
2990:
2986:
2983:
2980:
2979:
2975:
2972:
2969:
2959:
2955:
2952:
2949:
2948:
2944:
2941:
2938:
2928:
2924:
2921:
2918:
2915:
2912:
2909:
2908:
2904:
2901:
2898:
2895:
2892:
2889:
2888:
2884:
2881:
2878:
2875:
2872:
2869:
2868:
2864:
2861:
2858:
2855:
2852:
2849:
2848:
2844:
2841:
2838:
2835:
2832:
2829:
2828:
2824:
2821:
2818:
2815:
2812:
2809:
2808:
2804:
2801:
2798:
2795:
2792:
2789:
2788:
2784:
2781:
2778:
2775:
2772:
2769:
2768:
2764:
2761:
2758:
2757:
2753:
2750:
2747:
2737:
2733:
2730:
2727:
2724:
2721:
2718:
2717:
2713:
2710:
2707:
2706:
2702:
2699:
2696:
2686:
2682:
2679:
2676:
2673:
2670:
2667:
2666:
2662:
2659:
2656:
2655:
2651:
2648:
2645:
2635:
2631:
2628:
2625:
2622:
2619:
2616:
2615:
2611:
2608:
2605:
2602:
2599:
2596:
2595:
2591:
2588:
2585:
2584:
2580:
2577:
2574:
2573:
2569:
2566:
2563:
2553:
2549:
2546:
2543:
2540:
2537:
2534:
2533:
2529:
2526:
2523:
2522:
2518:
2515:
2512:
2511:
2507:
2504:
2501:
2500:
2496:
2493:
2490:
2480:
2476:
2473:
2470:
2467:
2464:
2461:
2460:
2456:
2453:
2450:
2447:
2444:
2441:
2440:
2436:
2433:
2430:
2427:
2424:
2421:
2420:
2416:
2413:
2410:
2407:
2404:
2401:
2400:
2396:
2393:
2390:
2387:
2384:
2381:
2380:
2376:
2373:
2370:
2367:
2364:
2361:
2360:
2356:
2353:
2350:
2347:
2344:
2341:
2340:
2337:
2330:
2325:
2323:
2321:
2317:
2313:
2308:
2306:
2302:
2298:
2294:
2287:
2278:
2271:
2262:
2254:
2252:
2250:
2246:
2242:
2238:
2234:
2230:
2226:
2222:
2218:
2214:
2206:
2204:
2202:
2197:
2195:
2191:
2187:
2183:
2182:Elaine Walker
2179:
2176:(1994) &
2175:
2171:
2168:(1999-2000),
2167:
2166:
2161:
2157:
2153:
2149:
2145:
2141:
2136:
2134:
2129:
2127:
2123:
2119:
2115:
2114:aesthetically
2106:
2099:
2089:
2086:
2083:
2073:
2070:
2067:
2064:
2061:
2060:
2056:
2053:
2050:
2043:
2040:
2037:
2034:
2031:
2030:
2023:
2020:
2017:
2015:63:25 = 2.52
2014:
2011:
2008:
2005:
2002:
2001:
1994:
1991:
1988:
1978:
1975:
1972:
1969:
1966:
1965:
1958:
1955:
1952:
1945:
1942:
1939:
1936:
1933:
1932:
1925:
1922:
1919:
1917:49:25 = 1.96
1916:
1913:
1910:
1907:
1904:
1903:
1896:
1893:
1890:
1880:
1877:
1874:
1871:
1868:
1867:
1860:
1854:
1851:
1841:
1835:
1832:
1829:
1826:
1825:
1818:
1812:
1809:
1807:75:49 = 1.53
1806:
1800:
1797:
1794:
1791:
1790:
1783:
1777:
1774:
1764:
1758:
1755:
1752:
1749:
1748:
1741:
1735:
1732:
1722:
1716:
1713:
1710:
1707:
1706:
1699:
1693:
1690:
1688:25:21 = 1.19
1687:
1681:
1678:
1675:
1672:
1671:
1664:
1658:
1655:
1653:27:25 = 1.08
1652:
1646:
1643:
1640:
1637:
1636:
1629:
1623:
1620:
1610:
1604:
1601:
1598:
1595:
1594:
1590:
1587:
1584:
1581:
1578:
1575:
1572:
1569:
1565:
1561:
1506:
1502:
1413:
1409:
1363:
1359:
1356:
1355:
1305:
1301:
1236:
1232:
1186:
1182:
1179:
1178:
1174:
1168:
1166:
1164:
1150:
1146:
1142:
1138:
1137:5-limit limma
1134:
1130:
1125:
1123:
1119:
1104:
1100:
1096:
1088:
1083:
1076:
1071:
1068:
1064:
1053:
1040:
1017:
1009:
1006:
1005:
1002:
973:
970:
969:
966:
937:
934:
930:
924:
911:
898:
885:
872:
859:
846:
833:
820:
807:
796:
795:
762:
759:
758:
755:
750:
745:
740:
735:
730:
725:
720:
715:
706:
705:
700:
691:
682:
673:
664:
655:
646:
637:
628:
619:
612:
609:
608:
605:
600:
595:
590:
585:
580:
575:
570:
565:
560:
554:
550:
547:
541:
539:
536:
532:
527:
523:
518:
516:
512:
508:
504:
497:
488:
487:
482:
478:
477:perfect fifth
474:
467:
458:
449:
442:
440:
438:
434:
428:
423:
407:
391:
377:
372:
357:
342:
327:
318:
313:
310:4:5:6 s
307:
303:3:5:7 s
297:
295:
195:
183:
171:
162:
158:
154:
151:
147:
146:pitch classes
142:
140:
136:
132:
128:
124:
120:
116:
112:
107:
105:
101:
97:
93:
89:
84:
82:
81:
75:
73:
70:
66:
62:
58:
54:
50:
46:
37:
28:
18:
7444:Oriental (V)
7298:Aeolian (VI)
7181:Hypophrygian
7074:
6983:
6974:
6944:Quarter tone
6762:Main Western
6707:Lambda scale
6706:
6614:Arabic maqam
6571:Werckmeister
6402:Temperaments
6179:Other topics
6167:
6160:
6153:
6146:
6129:
6123:Compositions
6106:
6095:publications
6050:Concepts and
5935:Lambda scale
5934:
5876:Harry Partch
5871:Yuri Landman
5866:Lou Harrison
5851:Wendy Carlos
5846:Glenn Branca
5746:Ben Johnston
5741:Charles Ives
5701:Franklin Cox
5691:Heinz Bohlen
5624:
5613:
5602:
5591:
5580:
5569:
5559:ZiaSpace.com
5558:
5557:" Research,
5534:. Retrieved
5530:
5521:
5511:
5501:
5482:
5473:
5461:. Retrieved
5457:
5447:
5439:
5430:
5422:Dissertation
5421:
5410:. Retrieved
5406:
5397:
5388:
5377:. Retrieved
5373:
5364:
5352:. Retrieved
5348:
5339:
5320:
5314:
5291:
5281:
5270:, retrieved
5264:
5258:
5249:
5243:
5218:
5214:
5208:
5199:
5193:. 28/06: 16.
5190:
5184:
5175:
5133:
5114:
5108:
5079:
5069:
5057:. Retrieved
5045:
5041:
5031:
5019:. Retrieved
5014:
5010:
5000:
4981:
3465:
2334:
2312:Wendy Carlos
2309:
2307:to step 3".
2305:Golden Ratio
2258:
2241:Curtis Roads
2210:
2198:
2194:Greater Good
2193:
2189:
2185:
2177:
2173:
2164:
2155:
2148:Jon Appleton
2143:
2140:Curtis Roads
2137:
2130:
2120:, but badly
2111:
1656:Great limma
1579:Cents in EQ
1576:EQ interval
1553:
1505:Note (cents)
1504:
1411:
1361:
1353:
1352:
1304:Note (cents)
1303:
1234:
1184:
1177:Justly tuned
1176:
1175:
1172:
1144:
1126:
1092:
1069:
1045:
603:
598:
593:
588:
583:
578:
573:
568:
563:
558:
545:
519:
514:
510:
503:pseudooctave
485:
484:
454:
429:
378:
314:
301:
143:
130:
126:
111:Heinz Bohlen
108:
92:justly tuned
85:
79:
78:
76:
48:
44:
42:
7288:Lydian (IV)
7278:Dorian (II)
7236:Hypolocrian
7226:Hypoaeolian
6798:Other types
6702:Delta scale
6697:Gamma scale
6687:Alpha scale
6589:non-Western
6587:Traditional
6282:Pitch class
6262:Millioctave
6245:Measurement
6142:just pieces
5930:Delta scale
5925:Gamma scale
5915:Alpha scale
5905:Non-octave-
5895:Tunings and
5856:Ivor Darreg
5681:Béla Bartók
5625:YouTube.com
5536:27 November
5463:27 November
5412:27 November
5354:27 November
5059:27 November
5021:27 November
4953:Gamma scale
4948:Delta scale
4940:Square wave
4935:Double reed
2316:alpha scale
2245:Paul Erlich
2213:Georg Hajdu
2160:Georg Hajdu
2133:progression
2122:out of tune
1591:Difference
542:Just tuning
535:Stephen Fox
531:Georg Hajdu
437:subdominant
123:Max Mathews
7534:Categories
7500:Heptatonic
7488:Pentatonic
7482:Tetratonic
7322:Jazz minor
7264:Ionian (I)
7241:Pentatonic
7216:Hypoionian
7186:Hypolydian
7176:Hypodorian
7158:Mixolydian
7048:Non-octave
7024:Neapolitan
6905:Whole tone
6865:Jazz minor
6830:Enharmonic
6779:Pentatonic
6692:Beta scale
6670:Non-octave
6661:Tetrachord
6563:Kirnberger
6526:Schismatic
6093:Groups and
6052:techniques
5920:Beta scale
5771:Joe Maneri
5731:Alois Hába
5711:John Eaton
5379:2023-01-04
5345:"Concerts"
5272:2016-12-13
4961:References
2326:Expansions
2320:beta scale
2314:' 78-cent
2219:) and the
2144:Clang-Tint
1920:BP eighth
507:equivalent
348:(0, 4, 10;
7518:Chromatic
7512:Decatonic
7506:Octatonic
7494:Hexatonic
7464:Monotonic
7135:Authentic
7126:Gregorian
6890:Symmetric
6835:Enigmatic
6789:Chromatic
6682:A12 scale
6636:Octoechos
6601:Shí-èr-lǜ
6550:Irregular
6367:Otonality
6307:Microtone
6074:Sonido 13
5839:Inventors
5791:Ezra Sims
5669:Composers
5048:: 45–56.
5042:Interface
5011:Acoustica
4120:1017.5963
4100:1049.3629
4080:1088.2687
4060:1115.5328
4040:1137.0391
4020:1165.0244
4000:1200.0000
3980:1231.7667
3960:1253.2729
3940:1284.4672
3920:1319.4428
3900:1350.6371
3880:1382.4037
3860:1403.9100
3840:1431.1741
3820:1466.8709
3800:1494.1350
3780:1515.6413
3760:1554.5471
3740:1586.3137
3720:1607.8200
3700:1635.0841
3680:1670.7809
3660:1698.0450
3640:1719.5513
3620:1751.3179
3609:1754.5269
3589:1782.5122
3569:1817.4878
3549:1848.6821
3529:1866.2582
3509:1901.9550
2207:Symposium
2196:(2011)).
2190:Love Song
2186:Stick Men
2158:(1990)),
2068:3 = 3.00
2038:3 = 2.76
2009:3 = 2.53
1973:3 = 2.33
1940:3 = 2.14
1911:3 = 1.97
1875:3 = 1.81
1833:3 = 1.66
1810:BP fifth
1798:3 = 1.53
1756:3 = 1.40
1714:3 = 1.29
1679:3 = 1.18
1644:3 = 1.09
1602:3 = 1.00
1412:Note name
1235:Note name
526:chalumeau
481:functions
397:0, 11, 13
363:(0, 4, 7;
317:semitones
153:frequency
100:consonant
98:are more
96:intervals
7476:Tritonic
7256:Diatonic
7148:Phrygian
7014:Japanese
6970:Gamelan
6921:Algerian
6845:Harmonic
6784:Diatonic
6567:Vallotti
6520:septimal
6512:Meantone
6272:Interval
6069:Semitone
5481:(2004).
4929:See also
4784:111.7313
4773:119.4428
4753:147.4281
4742:150.6371
4722:182.4037
4702:203.9100
4682:231.1741
4662:266.8709
4642:294.1350
4622:315.6413
4602:347.4079
4582:386.3137
4562:407.8200
4551:413.5778
4531:435.0841
4511:470.7809
4491:498.0450
4471:519.5513
4451:551.3179
4431:582.5122
4411:617.4878
4391:648.6821
4371:666.2582
4360:670.1883
4340:701.9550
4320:729.2191
4300:764.9159
4280:786.4222
4260:813.6863
4240:852.5921
4220:884.3587
4200:905.8650
4180:933.1291
4160:968.8259
4140:996.0900
2694:1511.81
2643:1609.35
2488:1853.19
2188:(1991),
2087:1901.96
2071:1901.96
2054:1768.72
2041:1755.66
2021:1600.11
2012:1609.35
1992:1466.87
1976:1463.05
1956:1319.44
1943:1316.74
1923:1165.02
1914:1170.44
1894:1017.60
1878:1024.13
1491:♭
1485:♯
1471:♭
1465:♯
1451:♭
1445:♯
1428:♭
1422:♯
1290:♭
1276:♭
1262:♭
1245:♭
1103:tempered
792:1901.96
789:1768.72
786:1466.87
783:1319.44
780:1017.60
522:clarinet
473:diatonic
433:dominant
413:0, 7, 10
277:1
258:1
239:2
220:2
201:1
161:harmonic
49:BP scale
7470:Ditonic
7231:Locrian
7221:Aeolian
7029:Persian
7009:Istrian
6985:Slendro
6958:Brazil
6925:Arabic
6656:Slendro
6606:Dastgah
6531:Miracle
6494:96-tone
6489:72-tone
6484:58-tone
6479:53-tone
6474:41-tone
6469:34-tone
6464:31-tone
6454:24-tone
6449:23-tone
6444:22-tone
6439:19-tone
6434:17-tone
6429:15-tone
6424:12-tone
6355:7-limit
6350:5-limit
5592:Kees.cc
5418:Cites:
5290:(ed.).
5235:3681110
5086:Bibcode
4899:27.2641
4888:31.1943
4877:31.7667
4866:34.9756
4855:35.6968
4835:53.2729
4824:62.9609
4804:84.4672
4114:1024.13
4094:1053.39
4074:1082.65
4054:1111.91
4034:1141.17
4014:1170.43
3994:1199.69
3974:1228.96
3954:1258.22
3934:1287.48
3914:1316.74
3894:1346.00
3874:1375.26
3854:1404.52
3834:1433.78
3814:1463.04
3794:1492.30
3774:1521.56
3754:1550.82
3734:1580.09
3714:1609.35
3694:1638.61
3674:1667.87
3654:1697.13
3634:1726.39
3603:1755.65
3583:1784.91
3563:1814.17
3543:1843.43
3523:1872.69
3503:1901.96
3443:1.0000
3390:1.0286
3379:101.87
3370:1.0580
3359:138.57
3348:147.43
3337:150.64
3331:146.30
3328:1.0882
3291:243.84
3288:1.1512
3240:341.38
3237:1.2180
3118:585.22
3115:1.4022
3058:731.52
3055:1.5258
2922:1017.60
2916:1024.13
2902:1071.70
2896:1072.90
2882:1119.46
2876:1121.67
2862:1165.02
2856:1170.43
2842:1217.58
2836:1219.20
2822:1265.34
2816:1267.97
2802:1319.44
2796:1316.74
2782:1365.00
2776:1365.51
2762:1412.77
2751:1421.31
2745:1414.27
2731:1466.87
2725:1463.04
2711:1506.79
2700:1515.64
2691:2.3947
2680:1554.55
2674:1560.58
2660:1612.75
2649:1600.11
2640:2.5335
2629:1654.21
2623:1658.11
2609:1714.61
2603:1706.88
2589:1751.32
2578:1754.53
2567:1763.38
2561:1755.65
2547:1800.09
2541:1804.42
2527:1847.85
2516:1848.68
2505:1853.18
2494:1856.39
2485:2.9167
2474:1901.96
2468:1901.96
2457:-10.36
2454:2400.00
2448:2389.64
2434:2786.31
2428:2779.78
2414:3368.83
2408:3365.00
2394:4151.32
2388:4145.29
2385:10.9617
2374:4440.53
2368:4437.90
2365:12.9802
2180:), and
2081:= 3.00
2057:−13.06
2048:= 2.78
1986:= 2.33
1950:= 2.14
1888:= 1.80
1858:884.36
1849:= 1.67
1839:877.83
1816:736.93
1804:731.52
1781:582.51
1772:= 1.40
1762:585.22
1739:435.08
1730:= 1.29
1720:438.91
1697:301.85
1685:292.61
1662:133.24
1650:146.30
1621:Unison
1618:= 1.00
1156:⁄
1107:√
1038:133.24
1035:301.85
1032:147.43
1029:301.85
1026:133.24
1023:301.85
1020:147.43
1012:301.85
777:884.36
774:582.51
771:435.08
768:301.85
486:tritave
395:), but
292:
273:
256::3 = 1:
254:
235:
216:
150:integer
139:Gestalt
137:on the
104:spectra
80:tritave
65:Western
7211:Ionian
7168:Plagal
7153:Lydian
7143:Dorian
6624:Mugham
6610:Maqam
6504:Linear
6458:pieces
6419:6-tone
6340:Hexany
6267:Savart
6148:Mother
5897:scales
5786:Sevish
5489:
5327:
5302:
5233:
5121:
4988:
4919:0.0000
4910:1.0000
4891:-1.93
4880:-2.51
4869:-5.71
4858:-6.44
4846:1.0170
4827:-4.44
4815:1.0344
4795:1.0520
4776:-2.40
4767:117.04
4764:1.0699
4756:-1.12
4745:-4.33
4736:146.30
4733:1.0882
4725:-6.84
4716:175.57
4713:1.1067
4696:204.83
4693:1.1256
4676:234.09
4673:1.1448
4665:-3.52
4656:263.35
4653:1.1643
4645:-1.53
4636:292.61
4633:1.1841
4616:321.87
4613:1.2043
4596:351.13
4593:1.2249
4585:-5.92
4576:380.39
4573:1.2457
4554:-3.93
4545:409.65
4542:1.2670
4525:438.91
4522:1.2886
4514:-2.61
4505:468.17
4502:1.3105
4494:-0.61
4485:497.43
4482:1.3329
4465:526.70
4462:1.3556
4445:555.96
4442:1.3787
4425:585.22
4422:1.4022
4414:-3.01
4405:614.48
4402:1.4261
4394:-4.94
4385:643.74
4382:1.4504
4354:673.00
4351:1.4751
4334:702.26
4331:1.5003
4314:731.52
4311:1.5258
4303:-4.13
4294:760.78
4291:1.5518
4274:790.04
4271:1.5783
4254:819.30
4251:1.6052
4243:-4.03
4234:848.56
4231:1.6326
4223:-6.53
4214:877.83
4211:1.6604
4194:907.09
4191:1.6887
4174:936.35
4171:1.7175
4163:-3.22
4154:965.61
4151:1.7468
4143:-1.22
4134:994.87
4131:1.7765
4111:1.8068
4091:1.8376
4083:-5.62
4071:1.8689
4063:-3.62
4051:1.9008
4031:1.9332
4011:1.9661
4003:-0.31
3991:1.9996
3983:-2.81
3971:2.0337
3951:2.0684
3931:2.1037
3923:-2.70
3911:2.1395
3903:-4.64
3891:2.1760
3883:-7.14
3871:2.2131
3851:2.2508
3831:2.2892
3823:-3.83
3811:2.3282
3803:-1.83
3791:2.3679
3771:2.4082
3763:-3.72
3751:2.4493
3743:-6.23
3731:2.4910
3711:2.5335
3691:2.5767
3683:-2.91
3671:2.6206
3663:-0.92
3651:2.6653
3631:2.7107
3606:135/49
3600:2.7569
3580:2.8039
3572:-3.32
3560:2.8517
3552:-5.25
3540:2.9003
3526:144/49
3520:2.9497
3500:3.0000
3432:45.56
3429:77/75
3421:48.77
3418:36/35
3413:-4.50
3410:53.27
3407:33/32
3402:-5.34
3399:54.11
3396:65/63
3393:48.77
3382:-4.33
3376:35/33
3373:97.54
3356:13/12
3351:-1.12
3345:49/45
3340:-4.33
3334:12/11
3317:187.34
3311:195.07
3308:1.1193
3300:-3.90
3297:247.74
3280:-9.24
3277:301.85
3266:289.21
3260:292.61
3257:1.1841
3249:-6.03
3246:347.41
3226:386.31
3218:-5.02
3215:395.17
3209:390.14
3206:1.2528
3195:435.08
3189:438.91
3186:1.2886
3175:480.65
3167:-1.51
3164:489.19
3158:487.68
3155:1.3254
3147:-0.50
3144:536.95
3138:536.45
3135:1.3632
3124:582.51
3107:-2.63
3104:636.62
3098:633.99
3095:1.4422
3087:-1.63
3084:684.38
3078:682.75
3075:1.4835
3067:-5.41
3064:736.93
3047:-2.20
3044:782.49
3038:780.29
3035:1.5694
3027:-1.20
3024:830.25
3018:829.06
3015:1.6143
3007:-6.53
3004:884.36
2998:877.83
2995:1.6604
2987:-3.33
2984:929.92
2976:-6.54
2973:933.13
2967:926.59
2964:1.7078
2953:968.83
2942:972.03
2939:135/77
2936:975.36
2933:1.7566
2913:1.8068
2893:1.8584
2873:1.9115
2853:1.9661
2833:2.0223
2813:2.0801
2805:-2.70
2793:2.1395
2773:2.2006
2759:147/65
2754:-7.04
2742:2.2635
2734:-3.83
2722:2.3282
2708:117/49
2703:-3.83
2671:2.4631
2663:-3.40
2620:2.6059
2612:-7.73
2600:2.6803
2575:135/49
2570:-7.73
2558:2.7569
2538:2.8357
2524:189/65
2497:-3.21
2491:225/77
2465:3.0000
2445:3.9761
2437:-6.53
2425:4.9812
2417:-3.83
2405:6.9845
2397:-6.03
2377:-2.63
2227:, the
2192:, and
2006:A♯/B♭
1998:−3.82
1962:−2.70
1908:H♯/J♭
1864:−6.53
1822:−5.41
1795:F♯/G♭
1703:−9.24
1668:13.06
1641:C♯/D♭
1570:Steps
1129:diesis
1122:12-tet
1101:. The
1016:133.24
1007:Cents
1000:27:25
997:25:21
994:49:45
991:25:21
988:27:25
985:25:21
982:49:45
979:27:25
976:25:21
971:Ratio
707:Ratio
611:Degree
457:octave
61:octave
53:tuning
7204:Other
7084:Modes
7070:Delta
7065:Gamma
7055:Alpha
6994:Gypsy
6976:Pelog
6810:Blues
6805:Bebop
6774:Minor
6769:Major
6641:Pelog
6629:Muqam
6575:Young
6536:Magic
6411:Equal
6345:Limit
6252:Pitch
6059:Limit
5231:JSTOR
4922:0.00
4902:2.00
4896:64/63
4885:56/55
4874:55/54
4863:50/49
4852:49/48
4849:29.26
4838:5.25
4832:33/32
4821:28/27
4818:58.52
4807:3.32
4801:21/20
4798:87.78
4787:5.31
4781:16/15
4770:15/14
4750:49/45
4739:12/11
4705:0.92
4685:2.91
4639:32/27
4625:6.23
4605:3.72
4565:1.83
4559:81/64
4548:80/63
4534:3.83
4508:21/16
4474:7.14
4468:27/20
4454:4.64
4434:2.70
4388:16/11
4374:6.74
4368:72/49
4363:2.81
4357:81/55
4343:0.31
4323:2.30
4317:32/21
4283:3.62
4277:63/40
4263:5.62
4237:18/11
4203:1.22
4197:27/16
4183:3.22
4123:6.53
4103:4.03
4057:40/21
4043:4.13
4037:27/14
4023:5.41
4017:49/25
3977:55/27
3963:4.94
3957:33/16
3943:3.01
3937:21/10
3897:24/11
3863:0.61
3843:2.61
3797:64/27
3783:5.92
3757:27/11
3723:1.53
3717:81/32
3703:3.52
3643:6.84
3637:27/10
3623:4.33
3612:1.12
3592:2.40
3546:32/11
3532:6.44
3512:0.00
3455:0.00
3452:0.00
3446:0.00
3435:3.21
3424:0.00
3362:7.73
3320:7.73
3314:39/35
3294:15/13
3274:25/21
3269:3.40
3263:13/11
3229:3.83
3212:49/39
3198:3.83
3178:7.04
3172:33/25
3161:65/49
3141:15/11
3127:2.70
3081:49/33
3061:75/49
3021:21/13
2981:77/45
2956:6.54
2945:3.33
2925:6.53
2905:1.20
2885:2.20
2879:21/11
2865:5.41
2859:49/25
2845:1.63
2839:99/49
2825:2.63
2819:27/13
2785:0.50
2765:1.51
2748:25/11
2714:5.02
2683:6.03
2677:27/11
2657:33/13
2652:9.24
2646:63/25
2632:3.90
2606:35/13
2592:4.33
2581:1.12
2564:36/13
2550:4.33
2544:99/35
2530:5.34
2519:4.50
2513:32/11
2508:0.00
2502:35/12
2477:0.00
2277:7-tet
2178:Splat
2093:0.00
2027:9.24
1929:5.42
1900:6.53
1787:2.71
1745:3.83
1633:0.00
1627:0.00
1608:0.00
1573:Name
1548:1902
1545:1756
1542:1609
1539:1463
1536:1317
1533:1170
1530:1024
1347:1902
1344:1769
1341:1600
1338:1467
1335:1319
1332:1165
1329:1018
1163:MOSes
1118:cents
935:Name
932:Step
797:Midi
761:Cents
714:25:21
555:Name
552:Note
57:scale
7520:(12)
7514:(10)
7304:and
7270:and
7060:Beta
6860:Jazz
6754:list
6646:Raga
6257:Cent
5623:" ,
5538:2012
5487:ISBN
5465:2012
5414:2012
5356:2012
5325:ISBN
5300:ISBN
5119:ISBN
5061:2012
5023:2012
4986:ISBN
4913:0.00
4719:10/9
4599:11/9
4448:11/8
4408:10/7
4297:14/9
4177:12/7
4137:16/9
4097:11/6
4077:15/8
3917:15/7
3877:20/9
3837:16/7
3777:12/5
3697:18/7
3677:21/8
3617:11/4
3586:14/5
3566:20/7
3449:1/1
3243:11/9
3101:13/9
3041:11/7
2970:12/7
2899:13/7
2799:15/7
2779:11/5
2697:12/5
2626:13/5
2586:11/7
2391:11/1
2371:13/1
2285:Play
2269:Play
2044:25:9
1946:15:7
1527:878
1524:732
1521:585
1518:439
1515:293
1512:146
1404:146
1401:146
1398:146
1395:146
1392:146
1389:146
1386:146
1383:146
1380:146
1377:146
1374:146
1371:146
1368:146
1326:884
1323:737
1320:583
1317:435
1314:302
1311:133
1227:133
1224:169
1221:133
1218:148
1215:154
1212:147
1209:134
1206:147
1203:154
1200:148
1197:133
1194:169
1191:133
1154:1200
1097:and
749:25:9
739:15:7
710:1:1
511:none
495:play
465:play
459:). (
421:play
405:play
389:play
370:play
355:play
340:play
193:play
181:play
169:play
117:and
55:and
43:The
26:Play
7508:(8)
7502:(7)
7496:(6)
7490:(5)
7484:(4)
7478:(3)
7472:(2)
7466:(1)
5612:",
5601:",
5590:",
5579:",
5438:",
5223:doi
5094:doi
5050:doi
4916:1/1
4699:9/8
4679:8/7
4659:7/6
4619:6/5
4579:5/4
4528:9/7
4488:4/3
4428:7/5
4337:3/2
4257:8/5
4217:5/3
4157:7/4
4117:9/5
3997:2/1
3857:9/4
3817:7/3
3737:5/2
3657:8/3
3506:3/1
3223:5/4
3192:9/7
3121:7/5
3112:12
3052:15
3001:5/3
2950:7/4
2919:9/5
2728:7/3
2688:31
2637:33
2482:38
2471:3/1
2451:4/1
2431:5/1
2411:7/1
2261:A12
2165:ppP
2077:3:1
2062:13
2032:12
2003:11
1982:7:3
1967:10
1884:9:5
1845:5:3
1768:7:5
1726:9:7
1625:000
1614:1:1
1606:000
754:3:1
744:7:3
734:9:5
729:5:3
724:7:5
719:9:7
515:all
376:).
294:).
7536::
6573:,
6569:,
6565:,
6518:,
6014:96
6009:72
6004:58
5999:53
5994:41
5989:34
5984:31
5979:24
5974:23
5969:22
5964:19
5959:17
5954:15
5529:.
5456:.
5405:.
5372:.
5347:.
5294:.
5229:.
5219:21
5217:.
5160:^
5145:^
5092:.
5078:.
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5040:.
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4968:^
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4379:22
4348:23
4328:24
4308:25
4288:26
4268:27
4248:28
4228:29
4208:30
4188:31
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4148:33
4128:34
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3808:50
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3708:55
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3648:58
3628:59
3597:60
3577:61
3557:62
3537:63
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3440:0
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3367:2
3325:3
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3092:13
3072:14
3032:16
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2992:18
2961:19
2930:20
2910:21
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2870:23
2850:24
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2790:27
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2739:29
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2442:49
2422:57
2402:69
2382:85
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2128:.
2091:−0
2065:C
2035:B
2025:−0
1970:A
1937:J
1934:9
1927:−0
1905:8
1898:−0
1872:H
1869:7
1830:G
1827:6
1792:5
1785:−0
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1750:4
1743:−0
1711:E
1708:3
1676:D
1673:2
1638:1
1631:−0
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1509:0
1499:C
1496:B
1488:/B
1479:A
1476:J
1468:/J
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1433:D
1425:/D
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1298:C
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226:1
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207:2
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