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1102:–F. A chord's odd limit is the largest of the odd limits of each of the numbers in the chord's extended ratio. For example, the major triad in close position is 4:5:6. These three numbers have odd limits of 1, 5 and 3 respectively. The largest of the three is 5, thus the chord has an odd limit of 5. Its melodic inverse 10:12:15 has an odd limit of 15, which is greater, therefore the major triad is otonal. A chord's odd limit is independent of its voicing, so alternate voicings such as 5:6:8, 3:4:5:6, etc. are also otonal.
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meets the definition of otonal. A better, narrower definition requires that the harmonic (or subharmonic) series members be adjacent. Thus 4:5:6 is an otonality, but 10:12:15 is not. (Alternate voicings of 4:5:6, such as 5:6:8, 3:4:5:6, etc. would presumably also be otonalities.) Under this
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If otonality and utonality are defined broadly, every just intonation chord is both an otonality and a utonality. For example, the minor triad in root position is made up of the 10th, 12th and 15th harmonics, and
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can be considered a utonality, or 7-limit utonal tetrad, which it closely approximates if the tuning is meantone, though presumably less well in the tuning of a
Wagnerian orchestra.
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chord (8:10:12:15). Ambitonal chords often can be reasonably interpreted as either major or minor. For example, CM, in certain contexts or voicings, can be interpreted as Am.
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Though Partch presents otonality and utonality as being equal and symmetric concepts, when played on most physical instruments an otonality sounds much more
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from the root of the chord, rather than upward. The analogy, in this case, is not to the harmonic series but to the subharmonic, or undertone series.
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chords that don't use 5 as a prime factor reverse this association. For example, 6:7:9 is otonal but minor, and 14:18:21 is utonal but major.
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A Utonality is a ...chord that is the inversion of an
Otonality: it is formed by building the same interval sequence as that of an Otonality
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All otonalities are otonal, but not all otonal chords are otonalities. Likewise, all utonalities are a subset of utonal chords.
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Microtonalists have extended the concept of otonal and utonal to apply to all just intonation chords. A chord is otonal if its
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naturally produce otonalities, and indeed otonalities are inherent in the harmonics of a single fundamental tone.
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definition, only a few chord types qualify as otonalities or utonalities. The only otonality triads are the
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Utonality is the opposite, corresponding to a subharmonic series of frequencies, or an arithmetic series of
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Starting from the symmetrical chords, otonal chords flatten one note, while utonal chords sharpen one note.
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has been theorized as being derived from harmonics 8 through 14 without 12: 8:9:10:11:13:14 (C:D:E:F
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Partch said that his 1931 coinage of "otonality" and "utonality" was "hastened" by having read
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5-limit otonality and utonality: overtone and "undertone" series, partials 1-5 numbered
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Genesis of a music : an account of a creative work, its roots and its fulfillments
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Genesis of a music : an account of a creative work, its roots and its fulfillments
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Genesis of a music : an account of a creative work, its roots and its fulfillments
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published a microtonal diagram that compares series of otonal and utonal scales with
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Utonality under G = lower line of the tonality diamond bottom right to top left.
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otonality is simply a just major chord, and the 5-limit utonality is a just
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An
Otonality is that set of pitches generated by the numerical factors (...
30:"Otonal" redirects here. For a Spanish word "otoñal" meaning autumnal, see
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chord 8:10:12:15:18 is also otonal. Examples of ambitonal chords are the
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often uses the otonal as an expanded tonic chord: 4:5:6:7:11:13 (C:E:G:B
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An otonality is a collection of pitches which can be expressed in
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1940:. Gilmore, Bob, 1961-2015. Urbana: University of Illinois Press.
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Partch coined the term "Monophony" (not to be confused with
1693:(Second edition, enlarged ed.). New York. p. 75.
1635:(Second edition, enlarged ed.). New York. p. 72.
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chords associate otonal with major and utonal with minor,
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than a similar utonality, due to the presence of the
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singers produce otonalities with their vocal tracts.
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Twelve
Microtonal Etudes for Electronic Music Media
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975:. This term is used extensively by Harry Partch in
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1753:(Second edition, enlarged ed.). New York.
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1938:"Maximum clarity" and other writings on music
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2856:List of intervals in 5-limit just intonation
1990:http://www.hypercustom.nl/utonaldiagram.jpg
1970:Experimental Encounters in Music and Beyond
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939:) form a utonality, sometimes written as
127:Learn how and when to remove this message
1749:Partch, Harry, 1901-1974 (August 1974).
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1310:adding citations to reliable sources
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1910:Walker, Robert (August 31, 2020).
1585:with a set of electric microtonal
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1689:Partch, Harry, 1901-1974 (1974).
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2931:Ptolemy's intense diatonic scale
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1968:Coessens, Kathleen; ed. (2017).
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2894:Harry Partch's 43-tone scale
2591:Harry Partch's 43-tone scale
1116:chord (12:15:18:20) and the
2714:Sonata for Microtonal Piano
1895:Partch, Harry (1928–1933).
1187:Minor as upside down major.
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2861:List of meantone intervals
2721:Suite for Microtonal Piano
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2851:List of musical intervals
2846:Consonance and dissonance
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2661:Boston Microtonal Society
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1835:Harry Partch: A Biography
1808:Harry Partch: A Biography
560:bottom left to top right.
76:"Otonality and utonality"
2014:Utonality and EDL system
2005:Otonality and ADO system
244:are terms introduced by
2623:Otonality and Utonality
2132:Otonality and Utonality
2127:Quadrangularis Reversum
1936:Johnston, Ben. (2006).
1897:Exposition of Monophony
1879:Otonality and utonality
1018:arithmetical proportion
2320:Claus-Steffen Mahnkopf
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1203:otonality, called the
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2440:Tui St. George Tucker
2137:Odentity and Udentity
1810:, p.431, n.69. Yale.
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1147:New Musical Resources
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185:Play minor chord on F
173:Play major chord on C
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2921:List of compositions
2750:Generalized keyboard
2245:Easley Blackwood Jr.
2095:Delusion of the Fury
1368:Mystic chord as the
1306:improve this section
1247:, for example, F-B-D
1193:meantone temperament
1094:melodically inverted
61:improve this article
27:Music theory concept
2745:Enharmonic keyboard
2696:quarter tone pieces
2690:Beauty in the Beast
2370:Ivan Wyschnegradsky
2070:List of instruments
1092:increases on being
1016:of frequency). The
218:13-limit utonality
199:31-limit otonality
3155:Chinese musicology
2941:Scale of harmonics
2936:Pythagorean tuning
2884:Euler–Fokker genus
2667:Genesis of a Music
2295:Christiaan Huygens
2087:Genesis of a Music
1912:"Musical Geometry"
1857:Genesis of a Music
1599:Scale of harmonics
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1972:, p.104. Leuven.
1947:978-0-252-09157-5
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1713:
1701:
1688:
1687:
1680:
1655:
1643:
1630:
1629:
1622:
1617:
1595:
1579:harmonic series
1566:
1562:
1561:
1554:
1547:
1539:
1535:
1528:
1525:
1520:
1519:
1512:
1504:
1500:
1493:
1488:
1487:
1480:
1475:
1474:
1467:
1463:
1454:
1453:
1446:
1442:
1437:
1436:
1429:
1413:
1411:
1410:
1409:
1401:
1399:
1398:
1397:
1396:approximation)
1362:
1354:harmonic series
1338:
1327:
1321:
1318:
1303:
1287:
1276:
1255:
1254:
1249:
1248:
1236:
1234:
1233:
1232:
1228:
1227:
1220:
1215:
1214:
1209:
1208:
1139:
1133:
1098:
1097:
1066:
1063:
1060:
1059:
1057:
1050:
1047:
1044:
1043:
1041:
1034:
1031:
1028:
1027:
1025:
965:
962:
959:
958:
956:
949:
946:
943:
942:
940:
933:
930:
927:
926:
924:
917:
914:
911:
910:
908:
900:
897:
894:
893:
891:
882:
879:
876:
875:
873:
864:
861:
858:
857:
855:
851:harmonic series
843:
840:
837:
836:
834:
827:
824:
821:
820:
818:
811:
808:
805:
804:
802:
787:
784:
781:
780:
778:
769:
766:
763:
762:
760:
751:
748:
745:
744:
742:
740:. For example,
717:
716:
715:
714:
711:
704:
701:
698:
697:
695:
687:
686:
685:
682:
681:
680:
673:
670:
667:
666:
664:
657:
654:
651:
650:
648:
640:
639:
638:
635:
634:
633:
626:
623:
620:
619:
617:
609:
608:
607:
604:
603:
602:
595:
592:
589:
588:
586:
579:
576:
573:
572:
570:
564:
563:
562:
561:
554:
547:
544:
541:
540:
538:
531:
530:
525:
524:
523:
522:
521:
514:
511:
508:
507:
505:
498:
495:
492:
491:
489:
482:
481:
476:
475:
474:
473:
472:
465:
462:
459:
458:
456:
449:
448:
443:
442:
441:
440:
439:
432:
429:
426:
425:
423:
416:
413:
410:
409:
407:
401:
372:
369:
366:
365:
363:
354:
351:
348:
347:
345:
336:
333:
330:
329:
327:
320:
317:
312:
311:
309:
302:
299:
294:
293:
291:
284:
281:
276:
275:
273:
223:
221:
220:
219:
204:
202:
201:
200:
184:
182:
181:
180:
172:
170:
169:
168:
160:
158:
157:
156:
148:
146:
145:
144:
133:
122:
116:
113:
70:
68:
58:
46:
35:
28:
23:
22:
15:
12:
11:
5:
3316:
3314:
3306:
3305:
3303:Musical tuning
3300:
3295:
3290:
3280:
3279:
3273:
3272:
3270:
3269:
3263:
3258:
3253:
3248:
3243:
3238:
3232:
3230:
3226:
3225:
3223:
3222:
3217:
3212:
3202:
3197:
3192:
3191:
3190:
3185:
3180:
3175:
3167:
3162:
3157:
3151:
3149:
3143:
3142:
3139:
3138:
3112:
3110:
3106:
3105:
3103:
3102:
3097:
3092:
3087:
3082:
3067:
3065:
3059:
3058:
3056:
3055:
3050:
3045:
3040:
3035:
3030:
3025:
3020:
3010:
3005:
3000:
2995:
2990:
2985:
2980:
2974:
2972:
2963:
2957:
2956:
2954:
2953:
2948:
2943:
2938:
2933:
2928:
2923:
2918:
2917:
2916:
2911:
2901:
2896:
2891:
2889:Harmonic scale
2886:
2880:
2878:
2872:
2871:
2869:
2868:
2863:
2858:
2853:
2848:
2843:
2838:
2836:Interval ratio
2833:
2828:
2823:
2818:
2813:
2807:
2805:
2801:
2800:
2795:
2793:
2792:
2785:
2778:
2770:
2761:
2760:
2758:
2757:
2752:
2747:
2741:
2739:
2735:
2734:
2732:
2731:
2724:
2717:
2710:
2703:
2698:
2693:
2685:
2683:
2679:
2678:
2676:
2675:
2670:
2663:
2657:
2655:
2649:
2648:
2646:
2645:
2640:
2638:Xenharmonicity
2635:
2630:
2625:
2620:
2614:
2612:
2606:
2605:
2602:
2601:
2599:
2598:
2593:
2587:
2585:
2579:
2578:
2576:
2575:
2570:
2565:
2560:
2555:
2550:
2545:
2540:
2535:
2530:
2525:
2520:
2515:
2509:
2507:
2501:
2500:
2498:
2497:
2491:
2486:
2481:
2476:
2470:
2468:
2457:
2451:
2450:
2448:
2447:
2442:
2437:
2432:
2427:
2422:
2420:Adriaan Fokker
2417:
2412:
2407:
2401:
2399:
2395:
2394:
2382:
2380:
2378:
2377:
2375:La Monte Young
2372:
2367:
2362:
2357:
2352:
2347:
2342:
2340:John Schneider
2337:
2332:
2327:
2322:
2317:
2312:
2307:
2302:
2297:
2292:
2287:
2285:Bjørn Fongaard
2282:
2277:
2272:
2267:
2265:Mildred Couper
2262:
2257:
2252:
2247:
2242:
2237:
2231:
2229:
2225:
2224:
2219:
2217:
2216:
2209:
2202:
2194:
2185:
2184:
2174:
2171:
2170:
2168:
2167:
2161:
2159:
2155:
2154:
2152:
2151:
2146:
2141:
2140:
2139:
2129:
2124:
2118:
2116:
2112:
2111:
2104:
2102:
2100:
2099:
2091:
2082:
2080:
2076:
2075:
2073:
2072:
2067:
2061:
2058:
2057:
2052:
2050:
2049:
2042:
2035:
2027:
2021:
2020:
2011:
2000:
1999:External links
1997:
1994:
1993:
1982:
1961:
1946:
1928:
1902:
1887:
1870:
1847:
1837:, p.68. Yale.
1820:
1796:
1759:
1736:
1699:
1678:
1641:
1619:
1618:
1616:
1613:
1612:
1611:
1606:
1601:
1594:
1591:
1361:
1358:
1340:
1339:
1290:
1288:
1281:
1275:
1272:
1191:In the era of
1135:Main article:
1132:
1129:
1077:4:5:6 and the
712:
568:
567:
566:
565:
555:
405:
404:
403:
402:
400:
397:
391:numerary nexus
161:Play utonality
149:Play otonality
135:
134:
49:
47:
40:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
3315:
3304:
3301:
3299:
3298:Pitch (music)
3296:
3294:
3291:
3289:
3286:
3285:
3283:
3267:
3264:
3262:
3259:
3257:
3254:
3252:
3249:
3247:
3244:
3242:
3239:
3237:
3234:
3233:
3231:
3227:
3221:
3218:
3216:
3213:
3210:
3209:Carnatic raga
3206:
3203:
3201:
3198:
3196:
3193:
3189:
3186:
3184:
3181:
3179:
3178:Turkish makam
3176:
3174:
3171:
3170:
3168:
3166:
3163:
3161:
3158:
3156:
3153:
3152:
3150:
3144:
3135:
3131:
3127:
3123:
3119:
3115:
3111:
3107:
3101:
3098:
3096:
3093:
3091:
3088:
3086:
3083:
3080:
3076:
3075:quarter-comma
3072:
3069:
3068:
3066:
3064:
3060:
3054:
3051:
3049:
3046:
3044:
3041:
3039:
3036:
3034:
3031:
3029:
3026:
3024:
3021:
3018:
3014:
3011:
3009:
3006:
3004:
3001:
2999:
2996:
2994:
2991:
2989:
2986:
2984:
2981:
2979:
2976:
2975:
2973:
2971:
2967:
2964:
2962:
2958:
2952:
2951:Tonality flux
2949:
2947:
2944:
2942:
2939:
2937:
2934:
2932:
2929:
2927:
2924:
2922:
2919:
2915:
2912:
2910:
2907:
2906:
2905:
2902:
2900:
2897:
2895:
2892:
2890:
2887:
2885:
2882:
2881:
2879:
2877:
2873:
2867:
2864:
2862:
2859:
2857:
2854:
2852:
2849:
2847:
2844:
2842:
2839:
2837:
2834:
2832:
2829:
2827:
2824:
2822:
2819:
2817:
2814:
2812:
2809:
2808:
2806:
2802:
2798:
2791:
2786:
2784:
2779:
2777:
2772:
2771:
2768:
2756:
2753:
2751:
2748:
2746:
2743:
2742:
2740:
2736:
2730:
2729:
2725:
2723:
2722:
2718:
2716:
2715:
2711:
2709:
2708:
2704:
2702:
2699:
2697:
2694:
2692:
2691:
2687:
2686:
2684:
2680:
2674:
2671:
2669:
2668:
2664:
2662:
2659:
2658:
2656:
2650:
2644:
2641:
2639:
2636:
2634:
2631:
2629:
2626:
2624:
2621:
2619:
2616:
2615:
2613:
2607:
2597:
2594:
2592:
2589:
2588:
2586:
2584:
2580:
2574:
2571:
2569:
2566:
2564:
2561:
2559:
2556:
2554:
2551:
2549:
2546:
2544:
2541:
2539:
2536:
2534:
2531:
2529:
2526:
2524:
2521:
2519:
2516:
2514:
2511:
2510:
2508:
2506:
2502:
2495:
2492:
2490:
2487:
2485:
2482:
2480:
2477:
2475:
2472:
2471:
2469:
2467:
2461:
2458:
2452:
2446:
2443:
2441:
2438:
2436:
2433:
2431:
2428:
2426:
2423:
2421:
2418:
2416:
2413:
2411:
2408:
2406:
2403:
2402:
2400:
2396:
2391:
2386:
2376:
2373:
2371:
2368:
2366:
2365:Elaine Walker
2363:
2361:
2360:Claude Vivier
2358:
2356:
2353:
2351:
2348:
2346:
2343:
2341:
2338:
2336:
2335:Roger Redgate
2333:
2331:
2328:
2326:
2323:
2321:
2318:
2316:
2315:Stu Mackenzie
2313:
2311:
2310:György Ligeti
2308:
2306:
2303:
2301:
2298:
2296:
2293:
2291:
2288:
2286:
2283:
2281:
2278:
2276:
2273:
2271:
2268:
2266:
2263:
2261:
2258:
2256:
2253:
2251:
2248:
2246:
2243:
2241:
2238:
2236:
2233:
2232:
2230:
2226:
2222:
2215:
2210:
2208:
2203:
2201:
2196:
2195:
2192:
2182:
2172:
2166:
2163:
2162:
2160:
2156:
2150:
2149:Tonality flux
2147:
2145:
2142:
2138:
2135:
2134:
2133:
2130:
2128:
2125:
2123:
2122:43-tone scale
2120:
2119:
2117:
2113:
2108:
2097:
2096:
2092:
2089:
2088:
2084:
2083:
2081:
2077:
2071:
2068:
2066:
2065:List of works
2063:
2062:
2059:
2055:
2048:
2043:
2041:
2036:
2034:
2029:
2028:
2025:
2019:
2015:
2012:
2010:
2006:
2003:
2002:
1998:
1991:
1986:
1983:
1979:
1978:9789462701106
1975:
1971:
1965:
1962:
1957:
1953:
1949:
1943:
1939:
1932:
1929:
1917:
1913:
1906:
1903:
1898:
1891:
1888:
1884:
1880:
1874:
1871:
1867:
1866:0-306-80106-X
1863:
1859:
1858:
1851:
1848:
1844:
1843:9780300065213
1840:
1836:
1832:
1827:
1825:
1821:
1817:
1816:9780300065213
1813:
1809:
1805:
1800:
1797:
1792:
1788:
1784:
1778:
1770:
1766:
1762:
1760:0-306-71597-X
1756:
1752:
1745:
1743:
1741:
1737:
1732:
1728:
1724:
1718:
1710:
1706:
1702:
1700:0-306-71597-X
1696:
1692:
1685:
1683:
1679:
1674:
1670:
1666:
1660:
1652:
1648:
1644:
1642:0-306-71597-X
1638:
1634:
1627:
1625:
1621:
1614:
1610:
1607:
1605:
1604:Tonality flux
1602:
1600:
1597:
1596:
1592:
1590:
1588:
1584:
1583:transposition
1580:
1576:
1572:
1558:
1551:
1543:
1532:
1516:
1508:
1497:
1484:
1471:
1461:
1450:
1433:
1427:
1416:
1404:
1395:
1391:
1387:
1383:
1379:
1375:
1371:
1366:
1359:
1357:
1355:
1351:
1347:
1336:
1333:
1325:
1315:
1311:
1307:
1301:
1300:
1296:
1291:This section
1289:
1285:
1280:
1279:
1273:
1271:
1269:
1265:
1260:
1246:
1245:Tristan chord
1239:
1224:
1206:
1202:
1198:
1194:
1185:
1181:
1179:
1175:
1174:perfect fifth
1171:
1167:
1163:
1154:
1150:
1148:
1144:
1138:
1130:
1128:
1126:
1121:
1119:
1118:major seventh
1115:
1111:
1106:
1103:
1095:
1091:
1086:
1084:
1080:
1076:
1021:
1019:
1015:
1011:
1006:
1004:
1001:
997:
993:
989:
985:
980:
978:
974:
906:
888:
870:
852:
800:
797:
793:
775:
757:
739:
735:
731:
725:
723:
559:
398:
395:
393:
392:
387:
381:
375:
357:
339:
315:
297:
279:
271:
267:
263:
259:
255:
254:pitch classes
251:
247:
243:
242:
237:
236:
226:
216:
207:
197:
187:
175:
163:
151:
141:
131:
128:
120:
109:
106:
102:
99:
95:
92:
88:
85:
81:
78: –
77:
73:
72:Find sources:
66:
62:
56:
55:
50:This article
48:
44:
39:
38:
33:
19:
3293:Harry Partch
3266:Lambda scale
3173:Arabic maqam
3130:Werckmeister
2961:Temperaments
2738:Other topics
2726:
2719:
2712:
2705:
2688:
2682:Compositions
2665:
2654:publications
2609:Concepts and
2494:Lambda scale
2435:Harry Partch
2430:Yuri Landman
2425:Lou Harrison
2410:Wendy Carlos
2405:Glenn Branca
2305:Ben Johnston
2300:Charles Ives
2260:Franklin Cox
2250:Heinz Bohlen
2093:
2085:
2054:Harry Partch
2017:
2008:
1985:
1969:
1964:
1937:
1931:
1921:September 9,
1919:. Retrieved
1915:
1905:
1896:
1890:
1882:
1873:
1855:
1850:
1834:
1831:Gilmore, Bob
1807:
1804:Gilmore, Bob
1799:
1750:
1690:
1632:
1571:Yuri Landman
1460:mystic chord
1426:Ben Johnston
1423:
1394:quarter tone
1343:
1328:
1322:October 2013
1319:
1304:Please help
1292:
1261:
1190:
1178:Hugo Riemann
1159:
1146:
1143:Henry Cowell
1140:
1122:
1107:
1104:
1087:
1022:
1017:
1007:
981:
976:
734:denominators
727:
721:
719:
389:
385:
383:
373:
355:
337:
313:
295:
277:
262:subharmonics
248:to describe
246:Harry Partch
240:
239:
234:
233:
232:
123:
117:January 2013
114:
104:
97:
90:
83:
71:
59:Please help
54:verification
51:
3261:Delta scale
3256:Gamma scale
3246:Alpha scale
3148:non-Western
3146:Traditional
2841:Pitch class
2821:Millioctave
2804:Measurement
2701:just pieces
2489:Delta scale
2484:Gamma scale
2474:Alpha scale
2464:Non-octave-
2454:Tunings and
2415:Ivor Darreg
2240:Béla Bartók
1392:harmonics (
1170:minor third
1166:minor chord
1114:major sixth
1110:major ninth
1075:major triad
1010:wavelengths
988:frequencies
799:major chord
18:Utonalities
3282:Categories
3251:Beta scale
3229:Non-octave
3220:Tetrachord
3122:Kirnberger
3085:Schismatic
2652:Groups and
2611:techniques
2479:Beta scale
2330:Joe Maneri
2290:Alois Hába
2270:John Eaton
1615:References
1274:Consonance
738:numerators
399:Definition
386:identities
87:newspapers
3241:A12 scale
3195:Octoechos
3160:Shí-èr-lǜ
3109:Irregular
2926:Otonality
2866:Microtone
2633:Sonido 13
2398:Inventors
2350:Ezra Sims
2228:Composers
1956:811408988
1777:cite book
1717:cite book
1659:cite book
1414:Play 7-13
1402:Play 8-14
1346:consonant
1293:does not
1125:monohpony
1090:odd limit
258:harmonics
241:utonality
235:Otonality
32:es:otoñal
3126:Vallotti
3079:septimal
3071:Meantone
2831:Interval
2628:Semitone
2181:Category
1833:(1998).
1806:(1998).
1593:See also
1577:and the
1563:♭
1521:♯
1489:♭
1476:♭
1455:♭
1438:♭
1262:Whereas
1256:♯
1250:♯
1229:♭
1216:♭
1210:♭
1149:(1930).
1099:♭
955:, or as
722:downward
688:♭
641:♭
610:♭
526:♮
477:♯
444:♮
326:,... or
270:identity
256:are the
3288:Harmony
3215:Slendro
3165:Dastgah
3090:Miracle
3053:96-tone
3048:72-tone
3043:58-tone
3038:53-tone
3033:41-tone
3028:34-tone
3023:31-tone
3013:24-tone
3008:23-tone
3003:22-tone
2998:19-tone
2993:17-tone
2988:15-tone
2983:12-tone
2914:7-limit
2909:5-limit
2158:Related
1314:removed
1299:sources
1268:7-limit
1264:5-limit
1201:7-limit
1070:
1058:
1054:
1042:
1038:
1026:
1014:inverse
1003:Khoomei
969:
966:7:6:5:4
957:
953:
950:4:5:6:7
941:
937:
925:
921:
909:
904:
892:
886:
874:
868:
856:
847:
835:
831:
819:
815:
803:
791:
779:
773:
761:
755:
743:
708:
696:
677:
665:
661:
649:
630:
618:
599:
587:
583:
571:
551:
539:
518:
506:
502:
490:
469:
457:
436:
424:
420:
408:
378:
364:
360:
346:
342:
328:
324:
310:
306:
292:
288:
274:
101:scholar
3183:Mugham
3169:Maqam
3063:Linear
3017:pieces
2978:6-tone
2899:Hexany
2826:Savart
2707:Mother
2456:scales
2345:Sevish
2115:Topics
2098:(1966)
2090:(1949)
2018:96-EDO
2009:96-EDO
1976:
1954:
1944:
1864:
1841:
1814:
1769:624666
1767:
1757:
1709:624666
1707:
1697:
1651:624666
1649:
1639:
1388:, and
1205:tetrad
1172:and a
1160:The 5-
907:, and
776:, and
730:ratios
663:), C(=
585:), F(=
504:), D(=
422:), A(=
380:,....
252:whose
250:chords
179:, and
103:
96:
89:
82:
74:
3200:Pelog
3188:Muqam
3134:Young
3095:Magic
2970:Equal
2904:Limit
2811:Pitch
2618:Limit
2079:Works
1587:kotos
1575:12TET
1162:limit
1012:(the
1000:Tuvan
108:JSTOR
94:books
3205:Raga
2816:Cent
1974:ISBN
1952:OCLC
1942:ISBN
1923:2024
1862:ISBN
1839:ISBN
1812:ISBN
1791:link
1787:link
1783:link
1765:OCLC
1755:ISBN
1731:link
1727:link
1723:link
1705:OCLC
1695:ISBN
1673:link
1669:link
1665:link
1647:OCLC
1637:ISBN
1386:13th
1374:11th
1297:any
1295:cite
1237:Play
1213:-C-E
1108:The
1056:and
796:just
266:tone
238:and
224:Play
205:Play
80:news
2016:at
2007:at
1881:",
1538::)A
1524::(G
1390:9th
1382:5th
1378:7th
1370:1st
1360:Use
1308:by
986:of
694:A(=
679:),
647:D(=
632:),
616:E(=
601:),
569:G(=
537:F(=
520:),
488:B(=
471:),
455:B(=
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406:G(=
260:or
63:by
3284::
3132:,
3128:,
3124:,
3077:,
2573:96
2568:72
2563:58
2558:53
2553:41
2548:34
2543:31
2538:24
2533:23
2528:22
2523:19
2518:17
2513:15
1950:.
1914:.
1823:^
1779:}}
1775:{{
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1715:{{
1703:.
1681:^
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1657:{{
1645:.
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1546::B
1511::F
1503::E
1479::B
1466::A
1445::A
1441::F
1384:,
1380:,
1376:,
1372:,
1253:-G
1219:-G
1195:,
1180::
1067:10
1061:15
1051:10
1045:12
1040:,
1035:10
1029:10
994:.
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889:,
871:,
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817:,
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3207:(
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3120:(
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3081:)
3073:(
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2782:t
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1980:.
1958:.
1925:.
1899:.
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1868:.
1845:.
1818:.
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1771:.
1733:)
1711:.
1675:)
1653:.
1567:-
1536:-
1526:↑
1501:-
1464:↑
1443:↑
1420:)
1408:(
1335:)
1329:(
1324:)
1320:(
1316:.
1302:.
1064:/
1048:/
1032:/
963:/
960:7
947:/
944:1
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928:7
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915:/
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898:/
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883:5
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877:7
865:4
862:/
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841:/
838:6
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822:5
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806:4
794:(
788:2
785:/
782:3
770:4
767:/
764:5
752:1
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705:7
702:/
699:8
683:7
674:3
671:/
668:4
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624:/
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596:9
593:/
580:1
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574:1
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548:4
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450:5
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417:1
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349:1
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296:2
285:1
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278:1
268:(
191:.
130:)
124:(
119:)
115:(
105:·
98:·
91:·
84:·
57:.
34:.
20:)
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