1107:
1189:
1166:
1158:
294:
193:
5264:
496:
5259:
283:
77:
504:
325:
1334:
274:
208:
200:
5051:
480:
1009:
1001:
993:
946:
911:
894:
886:
842:
468:
309:
517:
1138:
1180:
1126:
construct in Arabic music. The quarter tone gives musicians a "conceptual map" they can use to discuss and compare intervals by number of quarter tones, and this may be one of the reasons it accompanies a renewed interest in theory, with instruction in music theory a mainstream requirement since that
1329:
and others presented the semitone as being divided into two approximate quarter tone intervals of about the same size, while other ancient Greek theorists described the microtones resulting from dividing the semitone of the enharmonic genus as unequal in size (i.e., one smaller than a quarter tone
527:
Any tunable musical instrument can be used to perform quarter tones, if two players and two identical instruments, with one tuned a quarter tone higher, are used. As this requires neither a special instrument nor special techniques, much quarter toned music is written for pairs of pianos, violins,
531:
The following deals with the ability of single instruments to produce quarter tones. In
Western instruments, this means "in addition to the usual 12-tone system". Because many musical instruments manufactured today (2018) are designed for the 12-tone scale, not all are usable for playing quarter
966:
1270:, titled 'Unexplored possibilities of contemporary improvisation and the influence of microtonality in the creation process'. With two pianos tuned a quarter tone apart Gebruers recorded 'The Room: Time & Space' (2018) in a trio formation with drummer
1016:
919:
856:
1176:
as good possibility for a "secondary" chord in the quarter-tone scale, akin to the minor chord of traditional tonality. He considered that it may be built upon any degree of the quarter tone scale Here is the secondary "minor" and its "first inversion":
1206:
includes quarter tone descents. Several quarter-tone albums have been recorded by Jute Gyte, a one-man avantgarde black metal band from
Missouri, USA. Another quartertone metal album was issued by the Swedish band Massive Audio Nerve. Australian
342:
can refer to a number of different intervals, all very close in size. For example, some 17th- and 18th-century theorists used the term to describe the distance between a sharp and enharmonically distinct flat in mean-tone temperaments (e.g.,
1342:
1099:
was developed in the Middle East in the eighteenth century and many of the first detailed writings in the nineteenth century Syria describe the scale as being of 24 equal tones. The invention of the scale is attributed to
225:
3337:
are approximated rather poorly; the (13:10) and (15:13) ratios, involving the 13th harmonic, are matched very closely. Overall, 24-TET can be viewed as matching the 11th and 13th harmonics more closely than the 7th.
2927:
1682:
2981:
2695:
3144:
1484:
3036:
1727:
2147:
1778:
1630:
445:), 33:32 (53.27 cents), approximately half the semitone of 16:15 or 25:24. The ratio of 36:35 is only 1.23 cents narrower than a 24-TET quarter tone. This just ratio is also the difference between a
1343:
217:
2534:
2202:
1936:
3093:
2367:
2127:
1532:
598:, such as clarinets, saxophones, flutes, and oboes (though with many of these, it is still possible using non-standard techniques such as special fingerings or by the player manipulating their
3246:
3195:
2752:
226:
2644:
2424:
2232:
2043:
793:
Quarter-tone pianos have been built, which consist essentially of two pianos with two keyboards stacked one above the other in a single case, one tuned a quarter tone higher than the other.
2928:
2309:
1683:
2982:
2732:
2675:
2624:
2404:
2347:
2093:
1579:
1515:
1467:
2255:
484:) to indicate a note is raised 49 cents, or a ratio of 36:35. Johnston uses an upward and downward arrow to indicate a note is raised or lowered by a ratio of 33:32, or 53 cents. The
2591:
2477:
1990:
1886:
1836:
1816:
2694:
1665:
1610:
3145:
2961:
2907:
2289:
2020:
1485:
1437:
1420:
238:
3037:
2511:
2073:
1916:
1755:
1728:
1710:
1559:
5601:
3226:
3175:
3124:
3073:
3016:
2850:
2789:
2148:
1779:
1631:
262:
40:
2571:
2457:
1970:
1866:
528:
harps, etc. The retuning of the instrument, and then returning it to its former pitch, is easy for violins, harder for harps, and slow and relatively expensive for pianos.
250:
2873:
2809:
2535:
2203:
1937:
3094:
2366:
2128:
1533:
3921:
3247:
3196:
2753:
3408:
2645:
2425:
2233:
2182:
2044:
1104:
who wrote a book devoted to the topic but made clear that his teacher, Sheikh
Muhammad al-Attar (1764–1828), was one among many already familiar with the concept.
4003:
Preliminary
Exercises and Etudes in Contemporary Techniques for Clarinet: Introductory material for the study of multiphonics, quarter tones, and timbre variation
2310:
216:
2733:
2676:
2625:
2405:
2348:
2094:
1580:
1516:
1468:
2256:
5729:
4772:
3299:
3279:
2592:
2478:
1991:
1887:
1837:
1817:
1666:
1611:
5587:
5085:
2962:
2908:
2290:
2021:
1438:
1421:
861:
239:
2512:
2074:
1917:
1756:
1711:
1560:
5661:
3670:
3227:
3176:
3125:
3074:
3017:
2851:
2790:
971:
924:
263:
41:
5794:
5574:
2572:
2458:
1971:
1867:
249:
2874:
2810:
212:) as good possibility for a "fundamental" chord in the quarter-tone scale, akin not to the tonic but to the major chord of traditional tonality.
405:
also has equally tempered quarter-tones, and indeed contains three quarter-tone scales, since 72 is divisible by 24. The smallest interval in
1278:. In his solo project 'Playing with standards' (album release January 2023), Gebruers plays with famous songs including jazz standards. With
670:
3474:, pp. 3–12, New York: W. W. Norton, 1971, citation on pp. 8–9. "These two chords outlined above might be termed major and minor."
860:
2181:
3806:
970:
923:
5804:
5188:
4115:
1341:
1212:
1200:
224:
3947:
3905:
3721:
3438:
3389:
2926:
1681:
3300:
3280:
2980:
5767:
5464:
2696:
787:
3143:
1483:
5078:
3035:
1726:
3668:
Maalouf, Shireen (October–December 2003). "Mikhiiʾil
Mishiiqa: Virtual founder of the twenty-four equal quartertone scale".
2146:
1777:
1629:
5952:
3783:
3705:
2533:
2201:
1935:
236:
3092:
2368:
2126:
1531:
1266:
started playing and improvising with two pianos tuned a quarter-tone apart. In 2019 he started a research project at the
1110:
1019:
5654:
4564:
4544:
3245:
3194:
2751:
260:
38:
3321:
to 24-TET allows the better approximation of a number of intervals. Intervals matched particularly closely include the
2643:
2423:
2231:
2042:
1165:
1157:
293:
248:
5890:
5569:
4670:
3417:
3352:
2308:
1267:
176:
2731:
2674:
2623:
2403:
2346:
2092:
1578:
1514:
1466:
1355:
Here are the sizes of some common intervals in a 24-note equally tempered scale, with the interval names proposed by
2254:
5734:
5594:
5337:
5213:
5108:
4676:
3357:
2590:
2476:
1989:
1885:
1835:
1815:
1664:
1609:
1188:
5719:
5546:
5534:
5071:
4459:
3556:
3526:
3505:
3458:
2960:
2906:
2288:
2019:
1436:
1419:
802:
237:
88:
2510:
2072:
1915:
1754:
1709:
1558:
6003:
5238:
3225:
3174:
3123:
3072:
3015:
2849:
2788:
1326:
1217:
261:
39:
6139:
5367:
2570:
2456:
1969:
1865:
1337:
Greek Dorian enharmonic genus: two disjunct tetrachords each of a quarter tone, quarter tone, and major third.
759:
Valved brass instruments with extra, quarter-tone valves, and natural brass instruments that play through the
251:
2872:
2808:
282:
6161:
5973:
5799:
5724:
5647:
5496:
5178:
5054:
4792:
4731:
4108:
3496:
783:
760:
622:
457:
5757:
3606:
Marcus, Scott (Spring–Summer 1993). "The interface between theory and practice: Intonation in Arab music".
393:
Quarter tones and intervals close to them also occur in a number of other equally tempered tuning systems.
6166:
5995:
5958:
5948:
5193:
4852:
3935:
2183:
5991:
5313:
5143:
4847:
4658:
3608:
3488:
1452:
1131:
775:
749:
582:
520:
434:
207:
199:
192:
160:
156:
3298:
3278:
5999:
5944:
5926:
5921:
5916:
5911:
5906:
5901:
5896:
5881:
5876:
5871:
5866:
5861:
5856:
5623:
5446:
5441:
5436:
5431:
5426:
5421:
5416:
5406:
5401:
5396:
5391:
5386:
5118:
5034:
4787:
4694:
4688:
4274:
3484:
3362:
3334:
3330:
2603:
2383:
1247:(2005), that featured experiments in hip hop with quarter tone pianos, as well as electric organ and
595:
485:
450:
406:
402:
398:
394:
144:
1283:
5963:
5936:
5834:
5618:
5563:
5263:
5243:
4817:
4682:
4664:
3347:
2711:
1360:
1275:
1130:
Previously, pitches of a mode were chosen from a scale consisting of seventeen tones, developed by
164:
6028:
5814:
5809:
5540:
5258:
5168:
4930:
4367:
4101:
4028:
A Treatise on the
Harmonic System Arising from the Vibrations of the Aliquot Divisions of Strings
3979:
Bousted, Donald (Fall 2002). "Microtonality, the recorder and the quarter-tone recorder manual".
3915:
3687:
3625:
3573:
1500:
1113:
1022:
721:
560:
548:
479:
410:
6033:
5128:
3858:
1333:
629:
technique of adjusting pitch with the right hand in the bell makes this instrument an exception)
625:
tones that fall closer to quarter-tones than half-tones, make quarter-tone scales possible; the
108:
3738:
3554:
Spector, Johanna (May 1970). "Classical ʿUd Music in Egypt with
Special Reference to Maqamat".
6007:
5968:
5843:
5782:
5628:
5511:
5378:
5158:
5148:
5113:
4872:
4812:
4373:
4349:
4337:
4318:
4132:
3943:
3901:
3717:
3453:
3434:
3385:
3318:
3048:
678:
626:
414:
371:
120:
92:
3713:
3524:(Summer, 1991). "Ben Johnston's Extended Just Intonation: A Guide for Interpreters", p. 114,
5987:
5851:
5819:
5739:
5704:
5516:
5469:
5318:
5228:
5183:
5153:
5094:
4942:
4767:
4712:
4706:
4700:
4604:
4504:
4477:
4384:
4361:
4343:
4288:
4282:
4124:
3679:
3617:
3565:
2164:
1798:
1794:
1208:
810:
589:
300:
132:
124:
58:
31:
1054:
described a number of intervals in his work in music, including a number of quarter tones.
6109:
5749:
5456:
5198:
4910:
4634:
4422:
4312:
4306:
4294:
4237:
4200:
3643:
3500:
3467:
3052:
1646:
1591:
1101:
1008:
1000:
992:
945:
910:
893:
885:
841:
686:
660:
430:
152:
148:
100:
54:
495:
87:
Quarter tones have their roots in the music of the Middle East and more specifically in
5787:
5762:
5709:
5670:
5580:
5293:
5248:
5138:
4890:
4884:
4878:
4650:
4177:
3471:
3403:
3322:
2939:
2885:
2271:
2002:
1299:
1263:
829:
753:
715:
383:
172:
168:
140:
112:
76:
3761:
503:
467:
324:
308:
273:
17:
6155:
6082:
6051:
5824:
5777:
5684:
5491:
5233:
5208:
5163:
5014:
4863:
4782:
4777:
4723:
4584:
4524:
4410:
4398:
4263:
4226:
4183:
3521:
3413:
3381:
3326:
2490:
2055:
1898:
1740:
1695:
1544:
1356:
1295:
1196:
743:
739:
735:
731:
682:
607:
576:
461:
128:
116:
104:
3462:
3, no. 2 (Spring–Summer): pp. 22–31; citations on pp. 27–28; reprinted in
655:, using either special keyboard controllers or continuous-pitch controllers such as
390:. The 8-TET scale is composed of three-quarter tones. Four steps make a whole tone.
6046:
5689:
5308:
5303:
5298:
5283:
5278:
5173:
5133:
5123:
5029:
4986:
4981:
4245:
4208:
4084:
3492:
2825:
2764:
2214:
1226:
1222:
1151:
1123:
1034:
933:
870:
820:
806:
568:
516:
375:
360:
136:
70:
66:
417:
and one-fifth of a whole tone, so it may function as a quarter tone, a fifth-tone
3503:; William Schottstaedt. p.193. "Six American Composers on Nonstandard Tunnings",
3297:
3277:
3244:
3224:
3193:
3173:
3142:
3122:
3091:
3071:
3034:
3014:
2979:
2959:
2925:
2905:
2871:
2848:
2807:
2787:
2750:
2730:
2693:
2673:
2642:
2622:
2589:
2569:
2532:
2509:
2475:
2455:
2422:
2402:
2365:
2345:
2307:
2287:
2253:
2230:
2200:
2180:
2145:
2125:
2091:
2071:
2041:
2018:
1988:
1968:
1934:
1914:
1884:
1864:
1834:
1814:
1776:
1753:
1725:
1708:
1680:
1663:
1628:
1608:
1577:
1557:
1530:
1513:
1482:
1465:
1435:
1418:
1340:
969:
922:
859:
397:
contains an interval of 54.55 cents, slightly wider than a quarter-tone, whereas
223:
215:
6134:
6129:
6119:
5714:
5694:
5362:
5357:
5347:
5288:
4991:
4822:
4257:
4251:
4220:
4214:
2550:
2436:
2326:
2109:
1952:
1848:
1322:
1310:
1279:
1271:
656:
652:
446:
387:
3539:
6124:
6093:
5352:
5203:
5024:
4918:
4416:
4329:
3882:
3867:
3839:
3835:
2829:
2768:
1650:
1595:
1318:
1302:
1256:
1251:
textures, along with distorted trombone, in a post-Bitches Brew type of mixed
1240:
1236:
708:
599:
472:) as an accidental to indicate a note is lowered 49 cents, or an upside down "
825:
contain intervals of three-quarter tone size; a short list of these follows.
6114:
6068:
5506:
5223:
4924:
4428:
4012:
1248:
1051:
634:
552:
539:
play quarter tones (except by using special techniques—see below) include:
3384:(2004). The Dastgah Concept in Persian Music. Cambridge University Press.
1229:
heavily emphasize quarter-tones and used a custom-built guitar in 24
5501:
4956:
4404:
4152:
3990:
Bousted, Donald (Fall 2005). "Next step quarter-tone resources: Melody".
1314:
727:
666:
585:, if standard techniques are used, and if the instruments are not tunable
543:
Most standard or unmodified non-electronic keyboard instruments, such as
62:
4063:
Rewoldt, Todd (2000). "Altissimo quarter-tones for the alto saxophone".
99:, was made by 19th-century music theorists Heinrich Richter in 1823 and
6088:
6038:
4962:
4950:
4936:
4355:
4300:
3691:
3433:, p. 16. Translator: Laurie Schwartz. Portland, Oregon: Amadeus Press.
816:
614:
572:
564:
103:
about 1840. Composers who have written music using this scale include:
80:
3629:
3577:
726:
Wind instruments whose main means of tone-control is a slide, such as
6056:
5772:
5699:
5218:
5019:
4996:
4904:
4898:
4189:
4171:
3258:
1405:
1306:
370:
or approximately 1.0293, and divides the octave into 24 equal steps (
3683:
83:
with 3 normal valves and a quartering on the extension valve (right)
5063:
3621:
3569:
6073:
6061:
5639:
4392:
4039:
Music with
Quarter-Tones: Experiences at the bichromatic harmonium
4017:
Quarter Tones: A text with musical examples, exercises, and etudes
1332:
1187:
1136:
980:
778:, when tuning permits (e.g., timpani), or using special techniques
770:
765:
701:
694:
621:) (though, as with woodwinds, embouchure manipulation, as well as
544:
515:
489:
272:
258:
246:
234:
191:
75:
36:
6078:
1252:
1137:
618:
557:
5643:
5067:
4097:
782:
Other instruments can be used to play quarter tones when using
378:. A semitone is thus made of two steps, and three steps make a
3900:. Hanover, NH: Frog Peak Music. Chapter 5, page 49.
690:
4048:
Rees, Carla (2007). "Eva Kingma and the quarter-tone flute".
4093:
1141:
19-Limit just intonation intervals approximated in 24
30:"24 equal temperament" redirects here. For other uses, see
707:
Specially fretted string instruments (such as the
Turkish
532:
tones. Sometimes special playing techniques must be used.
196:
Composer
Charles Ives chose the four-note chord above (C–D
1112:
Audio playback is not supported in your browser. You can
1021:
Audio playback is not supported in your browser. You can
575:(though on these it is possible to play quarter tones by
756:, and a quarter tone mechanism for flutes by Eva Kingma.
508:
for a quarter tone (36:35 or 48.77 cents) up and down.
3972:. London, UK / New York, NY: Oxford University Press.
3807:"King Gizzard & the Lizard Wizard talk new album
61:
about half as wide (orally, or logarithmically) as a
6102:
6019:
5982:
5935:
5842:
5833:
5748:
5677:
5611:
5602:
Twelve Microtonal Etudes for Electronic Music Media
5555:
5525:
5482:
5455:
5377:
5336:
5327:
5271:
5101:
5005:
4972:
4861:
4831:
4801:
4758:
4749:
4722:
4649:
4632:
4474:
4457:
4446:
4383:
4328:
4273:
4236:
4199:
4164:
4146:
4131:
700:String instruments with movable frets (such as the
663:
capable of outputting quarter-tone control signals.
401:has an interval of 45.28 cents, slightly smaller.
374:). In this scale the quarter tone is the smallest
3648:al-Risāla al-shihābiyya fi 'l-ṣināʿa al-mūsīqiyya
579:, with special tunings, or with customized necks)
53:is a pitch halfway between the usual notes of a
3409:The New Grove Dictionary of Music and Musicians
91:. However, the first evidenced proposal of the
3329:, and (11:8) ratio, or the 11th harmonic. The
5655:
5079:
4109:
3652:Essay on the Art of Music for the Emir Shihāb
3509:, vol. 29, no. 1. (Winter 1991), pp. 176–211.
761:11th and 13th partials of the harmonic series
637:(although note bending is a common technique)
8:
5730:List of intervals in 5-limit just intonation
3983:. Vol. 22, no. 3. pp. 99–102.
3920:: CS1 maint: multiple names: authors list (
3449:
3447:
1038:
984:
937:
874:
833:
3994:. Vol. 25, no. 3. pp. 88–91.
752:was built by Fritz Schüller (1883–1977) of
433:the quarter tone can be represented by the
5839:
5662:
5648:
5640:
5333:
5086:
5072:
5064:
5050:
4755:
4646:
4471:
4454:
4161:
4143:
4116:
4102:
4094:
3663:
3661:
3517:
3515:
3456:(1965). "Ives' Quarter-Tone Impressions",
1286:he forms a 'Playing with standards' trio.
1122:The quarter tone scale may be primarily a
355:). In the quarter-tone scale, also called
3883:"Seppe Gebruers - Playing with Standards"
3601:
3599:
3549:
3547:
523:by Fritz Schüller viewed from four sides.
464:septimal quarter tone, uses a small "7" (
3671:Journal of the American Oriental Society
1367:
748:Specially keyed woodwind instruments. A
409:(the "diesis" of 38.71 cents) is half a
299:, 19 quarter tones. It approximates the
69:. Quarter tones divide the octave by 50
4037:Möllendorff, Willi; Monzo, Joe (2001).
3942:. Oxford, UK: Oxford University Press.
3374:
3913:
1050:The Islamic philosopher and scientist
641:Conventional musical instruments that
535:Conventional musical instruments that
73:each, and have 24 different pitches.
7:
3399:
3397:
1213:King Gizzard & the Lizard Wizard
1057:Assyrian/Syriac Church Music Scale:
3712:. Oxford University Press. p.
1039:
985:
938:
875:
834:
3737:Tremblay, Dæv (3 September 2014).
3464:Perspectives on American Composers
1351:Interval size in equal temperament
25:
4005:. Oswego, NY: Ethos Publications.
3805:Huguenor, Mike (21 August 2017).
3772:(music album). (commercial site).
1243:, made a crossover fusion album,
1239:, in conjunction with his father
1235:tuning. Jazz violinist / violist
437:, 36:35 (48.77 cents), or by the
359:(24-TET), the quarter tone is 50
5805:Ptolemy's intense diatonic scale
5262:
5257:
5049:
3592:Syria's Music Throughout History
3295:
3275:
3242:
3222:
3191:
3171:
3140:
3120:
3089:
3069:
3032:
3012:
2977:
2957:
2923:
2903:
2869:
2846:
2805:
2785:
2748:
2728:
2691:
2671:
2640:
2620:
2587:
2567:
2530:
2507:
2473:
2453:
2420:
2400:
2363:
2343:
2305:
2285:
2251:
2228:
2198:
2178:
2143:
2123:
2089:
2069:
2039:
2016:
1986:
1966:
1932:
1912:
1882:
1862:
1832:
1812:
1774:
1751:
1723:
1706:
1678:
1661:
1626:
1606:
1575:
1555:
1528:
1511:
1480:
1463:
1433:
1416:
1338:
1201:These Boots Are Made for Walkin'
1164:
1156:
1007:
999:
991:
967:
944:
920:
909:
892:
884:
857:
840:
671:continuously pitched instruments
502:
494:
478:
466:
323:
307:
292:
281:
221:
213:
206:
198:
4019:. Plainview, NY: Harold Branch.
3896:Chalmers, John H., Jr. (1993).
3857:Maneri, Mat (1 December 2005).
3815:Guitar World (guitarworld.com)
3530:, vol. 29, no. 2, pp. 106–137.
776:Pitched percussion instruments
606:quarter tones, if not a whole
583:Pitched percussion instruments
425:Just intonation tuning systems
1:
3784:"Massive Audio Nerve's album
2656:tridecimal five-quarter tone
1317:, which was divided into two
188:Equal-tempered tuning systems
5768:Harry Partch's 43-tone scale
5465:Harry Partch's 43-tone scale
3429:Touma, Habib Hassan (1996).
3412:, second edition, edited by
3305:
3288:
3285:
3268:
3262:
3252:
3235:
3232:
3215:
3209:
3201:
3184:
3181:
3164:
3158:
3150:
3133:
3130:
3113:
3107:
3099:
3082:
3079:
3062:
3056:
3042:
3025:
3022:
3005:
2999:
2987:
2970:
2967:
2950:
2944:
2933:
2916:
2913:
2896:
2890:
2879:
2862:
2856:
2839:
2833:
2815:
2798:
2795:
2778:
2772:
2758:
2741:
2738:
2721:
2715:
2701:
2684:
2681:
2664:
2658:
2650:
2633:
2630:
2613:
2607:
2597:
2580:
2577:
2560:
2554:
2540:
2523:
2517:
2500:
2494:
2483:
2466:
2463:
2446:
2440:
2430:
2413:
2410:
2393:
2387:
2373:
2356:
2353:
2336:
2330:
2315:
2298:
2295:
2278:
2275:
2261:
2244:
2238:
2221:
2218:
2208:
2191:
2188:
2171:
2168:
2153:
2136:
2133:
2116:
2113:
2099:
2082:
2079:
2062:
2059:
2049:
2032:
2026:
2009:
2006:
1996:
1979:
1976:
1959:
1956:
1942:
1925:
1922:
1905:
1902:
1892:
1875:
1872:
1855:
1852:
1842:
1825:
1822:
1805:
1802:
1784:
1767:
1761:
1747:
1744:
1733:
1719:
1716:
1702:
1699:
1688:
1674:
1671:
1657:
1654:
1636:
1622:
1616:
1602:
1599:
1585:
1571:
1565:
1551:
1548:
1538:
1524:
1521:
1507:
1504:
1490:
1476:
1473:
1459:
1456:
1443:
1429:
1426:
1412:
1409:
1109:
1018:
689:, fretless electric basses,
5588:Sonata for Microtonal Piano
4671:septimal chromatic semitone
4001:Caravan, Ronald R. (1979).
3898:Divisions of the Tetrachord
3353:List of quarter tone pieces
1268:Royal Conservatory of Ghent
1134:in the thirteenth century.
714:Fretted string instruments
645:play quarter tones include
177:List of quarter tone pieces
6183:
5735:List of meantone intervals
5595:Suite for Microtonal Piano
4677:septimal diatonic semitone
4465:(Numbers in brackets refer
3968:Bartolozzi, Bruno (1967).
3420:(London: Macmillan, 2001).
3358:List of meantone intervals
1359:(neutral third, etc.) and
800:
659:, or when controlled by a
613:Valved brass instruments (
363:, or a frequency ratio of
29:
5725:List of musical intervals
5720:Consonance and dissonance
5547:Huygens-Fokker Foundation
5535:Boston Microtonal Society
5255:
5047:
4467:to fractional semitones.)
4460:24-tone equal temperament
4030:. London, UK: T. Preston.
3527:Perspectives of New Music
3506:Perspectives of New Music
3459:Perspectives of New Music
1290:Ancient Greek tetrachords
803:Persian traditional music
357:24-tone equal temperament
89:Persian traditional music
65:, which itself is half a
4026:MacDonald, John (1822).
3809:Flying Microtonal Banana
3747:canthisbecalledmusic.com
1218:Flying Microtonal Banana
1184:In popular Western music
797:Music of the Middle East
649:Electronic instruments:
592:that use keys or valves
319:. Maneri-Sims notation:
277:The "subminor seventh":
5497:Otonality and Utonality
5055:List of pitch intervals
4793:Subminor and supermajor
4732:minor diatonic semitone
4642:refer to pitch ratios.)
4050:Pan: The Flute Magazine
3970:New Sounds for Woodwind
3710:The Foundations of Rock
3590:Asaad, Gabriel (1990).
1114:download the audio file
1023:download the audio file
784:audio signal processing
657:fingerboard controllers
95:quarter tone scale, or
5194:Claus-Steffen Mahnkopf
4853:Undecimal quarter tone
3431:The Music of the Arabs
1363:(major fourth, etc.):
1347:
1192:
1147:
697:family of instruments.
524:
439:undecimal quarter tone
335:
268:
256:
244:
230:
84:
46:
18:Undecimal quarter tone
5992:Temperament ordinaire
5370:(Bohlen–Pierce scale)
5314:Tui St. George Tucker
4848:Septimal quarter tone
4659:septimal quarter tone
4085:quarter-tone / 24-edo
3992:The Recorder Magazine
3981:The Recorder Magazine
3770:jutegyte.bandcamp.com
1453:semidiminished octave
1336:
1191:
1140:
1132:Safi al-Din al-Urmawi
750:quarter tone clarinet
693:, and members of the
521:Quarter tone clarinet
519:
512:Playing quarter tones
492:uses the accidentals
460:, to accommodate the
443:thirty-third harmonic
435:septimal quarter tone
276:
266:
254:
242:
195:
161:Tui St. George Tucker
157:Karlheinz Stockhausen
79:
44:
5795:List of compositions
5624:Generalized keyboard
5119:Easley Blackwood Jr.
5035:Incomposite interval
4788:Pythagorean interval
4640:(Numbers in brackets
4148:(Numbers in brackets
3335:septimal major third
3331:septimal minor third
2888:, greater undecimal
2604:septimal minor third
2384:septimal major third
1195:The bass descent of
596:Woodwind instruments
488:system designed for
486:Maneri-Sims notation
451:septimal minor third
407:31 equal temperament
145:Krzysztof Penderecki
97:24 equal temperament
5619:Enharmonic keyboard
5570:quarter tone pieces
5564:Beauty in the Beast
5244:Ivan Wyschnegradsky
4818:Pythagorean apotome
4665:septimal third tone
4065:Saxophone Symposium
3940:Ancient Greek Music
3348:Musical temperament
2942:, lesser undecimal
2712:septimal whole tone
1361:Ivan Wyschnegradsky
1154:chose the chord C–D
602:, to play at least
243:Neutral second on C
165:Ivan Wyschnegradsky
6029:Chinese musicology
5815:Scale of harmonics
5810:Pythagorean tuning
5758:Euler–Fokker genus
5541:Genesis of a Music
5169:Christiaan Huygens
4931:Septimal semicomma
3654:] (in Arabic).
3644:Mishaqa, Mikhiiʾil
3454:Boatwright, Howard
3406:, "Quarter-Tone",
1501:supermajor seventh
1348:
1309:or an approximate
1193:
1148:
1097:quarter-tone scale
1087:Quarter-tone scale
1064:Trayono (Hussayni)
722:Pedal steel guitar
679:string instruments
561:string instruments
525:
411:chromatic semitone
380:three-quarter tone
336:
269:
257:
245:
231:
85:
47:
6149:
6148:
6015:
6014:
5637:
5636:
5629:Modernism (music)
5478:
5477:
5379:Equal temperament
5149:Brian Ferneyhough
5061:
5060:
5043:
5042:
4873:Pythagorean comma
4813:Pythagorean limma
4745:
4744:
4741:
4740:
4707:supermajor fourth
4683:supermajor second
4628:
4627:
4442:
4441:
4438:
4437:
4150:are the number of
4041:. U.S.: J. Monzo.
3483:Douglas Keislar;
3313:
3312:
3301:
3281:
3248:
3228:
3197:
3177:
3146:
3126:
3095:
3075:
3049:diatonic semitone
3038:
3018:
2983:
2963:
2929:
2909:
2875:
2852:
2811:
2791:
2754:
2734:
2697:
2677:
2646:
2626:
2593:
2573:
2536:
2513:
2479:
2459:
2426:
2406:
2369:
2349:
2311:
2291:
2257:
2234:
2204:
2184:
2149:
2129:
2095:
2075:
2045:
2022:
1992:
1972:
1938:
1918:
1888:
1868:
1838:
1818:
1780:
1757:
1729:
1712:
1684:
1667:
1632:
1612:
1581:
1561:
1534:
1517:
1486:
1469:
1439:
1422:
1344:
1330:and one larger).
1118:
1076:Shtithoyo (ʿAjam)
1027:
972:
925:
862:
415:diatonic semitone
413:, one-third of a
372:equal temperament
267:Major second on C
264:
252:
240:
227:
218:
121:Alberto Ginastera
45:Quarter tone on C
42:
16:(Redirected from
6174:
5988:Well temperament
5974:Regular diatonic
5840:
5820:Tonality diamond
5664:
5657:
5650:
5641:
5517:Tonality diamond
5340:repeating scales
5334:
5319:Nicola Vicentino
5266:
5261:
5229:Nicola Vicentino
5154:Michael Finnissy
5095:Microtonal music
5088:
5081:
5074:
5065:
5053:
5052:
4943:Septimal kleisma
4756:
4713:subminor seventh
4695:supermajor third
4647:
4635:Just intonations
4620:
4619:
4615:
4612:
4600:
4599:
4595:
4592:
4580:
4579:
4575:
4572:
4560:
4559:
4555:
4552:
4540:
4539:
4535:
4532:
4520:
4519:
4515:
4512:
4500:
4499:
4495:
4472:
4455:
4162:
4144:
4118:
4111:
4104:
4095:
4072:
4057:
4042:
4031:
4020:
4006:
3995:
3984:
3973:
3954:
3953:
3932:
3926:
3925:
3919:
3911:
3893:
3887:
3886:
3879:
3873:
3872:
3854:
3848:
3847:
3832:
3826:
3825:
3823:
3822:
3802:
3796:
3795:
3792:blabbermouth.net
3780:
3774:
3773:
3757:
3751:
3750:
3734:
3728:
3727:
3702:
3696:
3695:
3665:
3656:
3655:
3640:
3634:
3633:
3603:
3594:
3588:
3582:
3581:
3551:
3542:
3537:
3531:
3519:
3510:
3485:Easley Blackwood
3481:
3475:
3451:
3442:
3427:
3421:
3401:
3392:
3379:
3308:
3303:
3302:
3291:
3283:
3282:
3271:
3265:
3250:
3249:
3238:
3230:
3229:
3218:
3212:
3199:
3198:
3187:
3179:
3178:
3167:
3161:
3148:
3147:
3136:
3128:
3127:
3116:
3110:
3097:
3096:
3085:
3077:
3076:
3065:
3059:
3040:
3039:
3028:
3020:
3019:
3008:
3002:
2991:
2985:
2984:
2973:
2965:
2964:
2953:
2947:
2931:
2930:
2919:
2911:
2910:
2899:
2893:
2877:
2876:
2865:
2860:
2854:
2853:
2842:
2836:
2819:
2813:
2812:
2801:
2793:
2792:
2781:
2775:
2756:
2755:
2744:
2736:
2735:
2724:
2718:
2705:
2699:
2698:
2687:
2679:
2678:
2667:
2661:
2648:
2647:
2636:
2628:
2627:
2616:
2610:
2595:
2594:
2583:
2575:
2574:
2563:
2557:
2544:
2538:
2537:
2526:
2521:
2515:
2514:
2503:
2497:
2481:
2480:
2469:
2461:
2460:
2449:
2443:
2428:
2427:
2416:
2408:
2407:
2396:
2390:
2377:
2371:
2370:
2359:
2351:
2350:
2339:
2333:
2319:
2313:
2312:
2301:
2293:
2292:
2281:
2265:
2259:
2258:
2247:
2242:
2236:
2235:
2224:
2206:
2205:
2194:
2186:
2185:
2174:
2165:septimal tritone
2157:
2151:
2150:
2139:
2131:
2130:
2119:
2103:
2097:
2096:
2085:
2077:
2076:
2065:
2047:
2046:
2035:
2030:
2024:
2023:
2012:
1994:
1993:
1982:
1974:
1973:
1962:
1946:
1940:
1939:
1928:
1920:
1919:
1908:
1890:
1889:
1878:
1870:
1869:
1858:
1840:
1839:
1828:
1820:
1819:
1808:
1799:subminor seventh
1795:supermajor sixth
1788:
1782:
1781:
1770:
1765:
1759:
1758:
1731:
1730:
1714:
1713:
1686:
1685:
1669:
1668:
1640:
1634:
1633:
1620:
1614:
1613:
1583:
1582:
1569:
1563:
1562:
1536:
1535:
1519:
1518:
1494:
1488:
1487:
1471:
1470:
1446:
1441:
1440:
1424:
1423:
1368:
1346:
1345:
1296:enharmonic genus
1234:
1233:
1209:psychedelic rock
1205:
1175:
1174:
1169:
1168:
1161:
1160:
1146:
1145:
1067:Tlithoyo (Segah)
1061:Qadmoyo (Bayati)
1042:
1041:
1012:
1011:
1004:
1003:
996:
995:
988:
987:
974:
973:
961:
960:
955:
954:
949:
948:
941:
940:
927:
926:
915:D C (descending)
914:
913:
906:
905:
897:
896:
889:
888:
878:
877:
864:
863:
851:
850:
845:
844:
837:
836:
811:Arab tone system
786:effects such as
718:to quarter tones
687:fretless guitars
590:wind instruments
507:
506:
499:
498:
483:
482:
475:
471:
470:
369:
368:
354:
353:
348:
347:
334:
333:
332:
328:
327:
318:
317:
316:
312:
311:
301:harmonic seventh
298:
297:
296:
287:
286:
285:
265:
255:8-tet scale on C
253:
241:
229:
228:
220:
219:
211:
210:
203:
202:
93:equally-tempered
43:
32:Arab tone system
27:Musical interval
21:
6182:
6181:
6177:
6176:
6175:
6173:
6172:
6171:
6152:
6151:
6150:
6145:
6142:(Bohlen–Pierce)
6110:833 cents scale
6098:
6021:
6011:
5978:
5931:
5829:
5750:Just intonation
5744:
5673:
5671:Musical tunings
5668:
5638:
5633:
5607:
5551:
5527:
5521:
5484:
5474:
5470:Double diatonic
5457:Just intonation
5451:
5373:
5339:
5329:
5323:
5267:
5253:
5199:Joel Mandelbaum
5129:Julián Carrillo
5109:Richard Barrett
5097:
5092:
5062:
5057:
5039:
5001:
4968:
4911:Septimal diesis
4857:
4827:
4797:
4751:
4737:
4718:
4641:
4638:
4624:
4617:
4613:
4610:
4608:
4597:
4593:
4590:
4588:
4577:
4573:
4570:
4568:
4557:
4553:
4550:
4548:
4537:
4533:
4530:
4528:
4517:
4513:
4510:
4508:
4497:
4493:
4492:
4482:
4481:
4480:
4476:
4466:
4463:
4450:
4448:
4434:
4379:
4324:
4269:
4232:
4195:
4156:
4151:
4149:
4139:
4137:
4134:
4127:
4122:
4080:
4075:
4062:
4047:
4036:
4025:
4011:
4000:
3989:
3978:
3967:
3963:
3961:Further reading
3958:
3957:
3950:
3936:West, Martin L.
3934:
3933:
3929:
3912:
3908:
3895:
3894:
3890:
3881:
3880:
3876:
3871:(album review).
3863:by Will Layman"
3856:
3855:
3851:
3834:
3833:
3829:
3820:
3818:
3804:
3803:
3799:
3786:Cancer Vulgaris
3782:
3781:
3777:
3764:Discontinuities
3759:
3758:
3754:
3749:(album review).
3736:
3735:
3731:
3724:
3706:Everett, Walter
3704:
3703:
3699:
3684:10.2307/3589971
3667:
3666:
3659:
3642:
3641:
3637:
3605:
3604:
3597:
3589:
3585:
3557:Ethnomusicology
3553:
3552:
3545:
3538:
3534:
3520:
3513:
3501:Joel Mandelbaum
3482:
3478:
3468:Benjamin Boretz
3452:
3445:
3428:
3424:
3402:
3395:
3380:
3376:
3371:
3344:
3306:
3296:
3289:
3276:
3269:
3263:
3243:
3236:
3223:
3216:
3210:
3207:33:32 semitone
3192:
3185:
3172:
3165:
3159:
3156:28:27 semitone
3141:
3134:
3121:
3114:
3108:
3105:21:20 semitone
3090:
3083:
3070:
3063:
3057:
3033:
3026:
3013:
3006:
3000:
2997:15:14 semitone
2989:
2978:
2971:
2958:
2951:
2945:
2924:
2917:
2904:
2897:
2891:
2870:
2863:
2858:
2847:
2840:
2834:
2817:
2806:
2799:
2786:
2779:
2773:
2749:
2742:
2729:
2722:
2716:
2703:
2692:
2685:
2672:
2665:
2659:
2641:
2634:
2621:
2614:
2608:
2588:
2581:
2568:
2561:
2555:
2542:
2531:
2524:
2519:
2508:
2501:
2495:
2474:
2467:
2454:
2447:
2441:
2421:
2414:
2401:
2394:
2388:
2375:
2364:
2357:
2344:
2337:
2331:
2317:
2306:
2299:
2286:
2279:
2263:
2252:
2245:
2240:
2229:
2222:
2199:
2192:
2179:
2172:
2155:
2144:
2137:
2124:
2117:
2101:
2090:
2083:
2070:
2063:
2040:
2033:
2028:
2017:
2010:
1987:
1980:
1967:
1960:
1944:
1933:
1926:
1913:
1906:
1883:
1876:
1863:
1856:
1833:
1826:
1813:
1806:
1786:
1775:
1768:
1763:
1752:
1724:
1707:
1679:
1662:
1647:neutral seventh
1638:
1627:
1618:
1607:
1592:neutral seventh
1576:
1567:
1556:
1529:
1512:
1492:
1481:
1464:
1444:
1434:
1417:
1399:
1391:
1380:
1375:
1353:
1339:
1305:consisted of a
1292:
1231:
1230:
1203:
1199:'s version of "
1186:
1181:
1172:
1171:
1163:
1155:
1143:
1142:
1120:
1119:
1117:
1095:in Arabic, the
1089:
1029:
1028:
1026:
1006:
998:
990:
975:
968:
958:
957:
952:
951:
943:
928:
921:
908:
903:
902:
891:
883:
865:
858:
848:
847:
839:
813:
799:
716:specially tuned
514:
501:
493:
477:
473:
465:
431:just intonation
427:
366:
364:
351:
350:
345:
344:
330:
329:
322:
320:
314:
313:
306:
304:
291:
289:
280:
278:
271:
270:
259:
247:
235:
222:
214:
205:
197:
190:
185:
153:Ammar El Sherei
149:Giacinto Scelsi
109:Julián Carrillo
101:Mikhail Mishaqa
55:chromatic scale
37:
35:
28:
23:
22:
15:
12:
11:
5:
6180:
6178:
6170:
6169:
6164:
6162:Musical scales
6154:
6153:
6147:
6146:
6144:
6143:
6137:
6132:
6127:
6122:
6117:
6112:
6106:
6104:
6100:
6099:
6097:
6096:
6091:
6086:
6076:
6071:
6066:
6065:
6064:
6059:
6054:
6049:
6041:
6036:
6031:
6025:
6023:
6017:
6016:
6013:
6012:
5986:
5984:
5980:
5979:
5977:
5976:
5971:
5966:
5961:
5956:
5941:
5939:
5933:
5932:
5930:
5929:
5924:
5919:
5914:
5909:
5904:
5899:
5894:
5884:
5879:
5874:
5869:
5864:
5859:
5854:
5848:
5846:
5837:
5831:
5830:
5828:
5827:
5822:
5817:
5812:
5807:
5802:
5797:
5792:
5791:
5790:
5785:
5775:
5770:
5765:
5763:Harmonic scale
5760:
5754:
5752:
5746:
5745:
5743:
5742:
5737:
5732:
5727:
5722:
5717:
5712:
5710:Interval ratio
5707:
5702:
5697:
5692:
5687:
5681:
5679:
5675:
5674:
5669:
5667:
5666:
5659:
5652:
5644:
5635:
5634:
5632:
5631:
5626:
5621:
5615:
5613:
5609:
5608:
5606:
5605:
5598:
5591:
5584:
5577:
5572:
5567:
5559:
5557:
5553:
5552:
5550:
5549:
5544:
5537:
5531:
5529:
5523:
5522:
5520:
5519:
5514:
5512:Xenharmonicity
5509:
5504:
5499:
5494:
5488:
5486:
5480:
5479:
5476:
5475:
5473:
5472:
5467:
5461:
5459:
5453:
5452:
5450:
5449:
5444:
5439:
5434:
5429:
5424:
5419:
5414:
5409:
5404:
5399:
5394:
5389:
5383:
5381:
5375:
5374:
5372:
5371:
5365:
5360:
5355:
5350:
5344:
5342:
5331:
5325:
5324:
5322:
5321:
5316:
5311:
5306:
5301:
5296:
5294:Adriaan Fokker
5291:
5286:
5281:
5275:
5273:
5269:
5268:
5256:
5254:
5252:
5251:
5249:La Monte Young
5246:
5241:
5236:
5231:
5226:
5221:
5216:
5214:John Schneider
5211:
5206:
5201:
5196:
5191:
5186:
5181:
5176:
5171:
5166:
5161:
5159:Bjørn Fongaard
5156:
5151:
5146:
5141:
5139:Mildred Couper
5136:
5131:
5126:
5121:
5116:
5111:
5105:
5103:
5099:
5098:
5093:
5091:
5090:
5083:
5076:
5068:
5059:
5058:
5048:
5045:
5044:
5041:
5040:
5038:
5037:
5032:
5027:
5022:
5017:
5011:
5009:
5003:
5002:
5000:
4999:
4994:
4989:
4984:
4978:
4976:
4970:
4969:
4967:
4966:
4960:
4954:
4947:
4946:
4940:
4934:
4928:
4922:
4915:
4914:
4908:
4905:Greater diesis
4902:
4895:
4894:
4891:Septimal comma
4888:
4885:Holdrian comma
4882:
4879:Syntonic comma
4876:
4869:
4867:
4859:
4858:
4856:
4855:
4850:
4845:
4839:
4837:
4829:
4828:
4826:
4825:
4820:
4815:
4809:
4807:
4799:
4798:
4796:
4795:
4790:
4785:
4780:
4775:
4770:
4764:
4762:
4753:
4747:
4746:
4743:
4742:
4739:
4738:
4736:
4735:
4728:
4726:
4720:
4719:
4717:
4716:
4710:
4704:
4701:subminor fifth
4698:
4692:
4689:subminor third
4686:
4680:
4674:
4668:
4662:
4655:
4653:
4644:
4630:
4629:
4626:
4625:
4623:
4622:
4602:
4582:
4562:
4542:
4522:
4502:
4485:
4483:
4475:
4469:
4452:
4444:
4443:
4440:
4439:
4436:
4435:
4433:
4432:
4426:
4420:
4414:
4408:
4402:
4396:
4389:
4387:
4381:
4380:
4378:
4377:
4371:
4365:
4359:
4353:
4347:
4341:
4334:
4332:
4326:
4325:
4323:
4322:
4316:
4310:
4304:
4298:
4292:
4286:
4279:
4277:
4271:
4270:
4268:
4267:
4261:
4255:
4249:
4242:
4240:
4234:
4233:
4231:
4230:
4224:
4218:
4212:
4205:
4203:
4197:
4196:
4194:
4193:
4187:
4181:
4175:
4168:
4166:
4159:
4141:
4129:
4128:
4123:
4121:
4120:
4113:
4106:
4098:
4092:
4091:
4079:
4078:External links
4076:
4074:
4073:
4059:
4058:
4044:
4043:
4033:
4032:
4022:
4021:
4008:
4007:
3997:
3996:
3986:
3985:
3975:
3974:
3964:
3962:
3959:
3956:
3955:
3948:
3927:
3906:
3888:
3874:
3849:
3846:(music album).
3827:
3797:
3775:
3752:
3729:
3722:
3697:
3678:(4): 835–840.
3657:
3635:
3622:10.2307/834466
3595:
3583:
3570:10.2307/849799
3564:(2): 243–257.
3543:
3532:
3522:Fonville, John
3511:
3476:
3472:Edward T. Cone
3443:
3422:
3404:Julian Rushton
3393:
3373:
3372:
3370:
3367:
3366:
3365:
3363:Holdrian Comma
3360:
3355:
3350:
3343:
3340:
3323:neutral second
3315:
3314:
3311:
3310:
3304:
3293:
3287:
3284:
3273:
3267:
3261:
3255:
3254:
3251:
3240:
3234:
3231:
3220:
3214:
3208:
3204:
3203:
3200:
3189:
3183:
3180:
3169:
3163:
3157:
3153:
3152:
3149:
3138:
3132:
3129:
3118:
3112:
3106:
3102:
3101:
3098:
3087:
3081:
3078:
3067:
3061:
3055:
3045:
3044:
3041:
3030:
3024:
3021:
3010:
3004:
2998:
2994:
2993:
2986:
2975:
2969:
2966:
2955:
2949:
2943:
2940:neutral second
2936:
2935:
2932:
2921:
2915:
2912:
2901:
2895:
2889:
2886:neutral second
2882:
2881:
2878:
2867:
2861:
2855:
2844:
2838:
2832:
2822:
2821:
2814:
2803:
2797:
2794:
2783:
2777:
2771:
2761:
2760:
2757:
2746:
2740:
2737:
2726:
2720:
2714:
2708:
2707:
2700:
2689:
2683:
2680:
2669:
2663:
2657:
2653:
2652:
2649:
2638:
2632:
2629:
2618:
2612:
2606:
2600:
2599:
2596:
2585:
2579:
2576:
2565:
2559:
2553:
2547:
2546:
2539:
2528:
2522:
2516:
2505:
2499:
2493:
2486:
2485:
2482:
2471:
2465:
2462:
2451:
2445:
2439:
2433:
2432:
2429:
2418:
2412:
2409:
2398:
2392:
2386:
2380:
2379:
2372:
2361:
2355:
2352:
2341:
2335:
2329:
2322:
2321:
2314:
2303:
2297:
2294:
2283:
2277:
2274:
2272:perfect fourth
2268:
2267:
2260:
2249:
2243:
2237:
2226:
2220:
2217:
2211:
2210:
2207:
2196:
2190:
2187:
2176:
2170:
2167:
2160:
2159:
2152:
2141:
2135:
2132:
2121:
2115:
2112:
2106:
2105:
2098:
2087:
2081:
2078:
2067:
2061:
2058:
2052:
2051:
2048:
2037:
2031:
2025:
2014:
2008:
2005:
2003:subminor sixth
1999:
1998:
1995:
1984:
1978:
1975:
1964:
1958:
1955:
1949:
1948:
1941:
1930:
1924:
1921:
1910:
1904:
1901:
1895:
1894:
1891:
1880:
1874:
1871:
1860:
1854:
1851:
1845:
1844:
1841:
1830:
1824:
1821:
1810:
1804:
1801:
1791:
1790:
1783:
1772:
1766:
1760:
1749:
1746:
1743:
1736:
1735:
1732:
1721:
1718:
1715:
1704:
1701:
1698:
1691:
1690:
1687:
1676:
1673:
1670:
1659:
1656:
1653:
1643:
1642:
1635:
1624:
1621:
1615:
1604:
1601:
1598:
1588:
1587:
1584:
1573:
1570:
1564:
1553:
1550:
1547:
1541:
1540:
1537:
1526:
1523:
1520:
1509:
1506:
1503:
1497:
1496:
1489:
1478:
1475:
1472:
1461:
1458:
1455:
1449:
1448:
1442:
1431:
1428:
1425:
1414:
1411:
1408:
1402:
1401:
1396:
1393:
1388:
1385:
1382:
1377:
1372:
1371:Interval name
1352:
1349:
1291:
1288:
1284:Nils Vermeulen
1264:Seppe Gebruers
1185:
1182:
1179:
1111:
1108:
1106:
1088:
1085:
1084:
1083:
1080:
1077:
1074:
1071:
1070:Rbiʿoyo (Rast)
1068:
1065:
1062:
1048:
1047:
1044:
1032:
1031:
1030:
1020:
1017:
1015:
978:
977:
976:
965:
931:
930:
929:
918:
916:
899:
868:
867:
866:
855:
798:
795:
788:pitch shifting
780:
779:
773:
768:
763:
757:
754:Markneukirchen
746:
724:
719:
712:
705:
698:
681:, such as the
675:
674:
673:
664:
639:
638:
632:
631:
630:
611:
586:
580:
555:
513:
510:
426:
423:
421:a sixth-tone.
384:neutral second
233:
232:
189:
186:
184:
181:
173:Seppe Gebruers
169:Iannis Xenakis
141:Tristan Murail
113:Mildred Couper
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
6179:
6168:
6167:Quarter tones
6165:
6163:
6160:
6159:
6157:
6141:
6138:
6136:
6133:
6131:
6128:
6126:
6123:
6121:
6118:
6116:
6113:
6111:
6108:
6107:
6105:
6101:
6095:
6092:
6090:
6087:
6084:
6083:Carnatic raga
6080:
6077:
6075:
6072:
6070:
6067:
6063:
6060:
6058:
6055:
6053:
6052:Turkish makam
6050:
6048:
6045:
6044:
6042:
6040:
6037:
6035:
6032:
6030:
6027:
6026:
6024:
6018:
6009:
6005:
6001:
5997:
5993:
5989:
5985:
5981:
5975:
5972:
5970:
5967:
5965:
5962:
5960:
5957:
5954:
5950:
5949:quarter-comma
5946:
5943:
5942:
5940:
5938:
5934:
5928:
5925:
5923:
5920:
5918:
5915:
5913:
5910:
5908:
5905:
5903:
5900:
5898:
5895:
5892:
5888:
5885:
5883:
5880:
5878:
5875:
5873:
5870:
5868:
5865:
5863:
5860:
5858:
5855:
5853:
5850:
5849:
5847:
5845:
5841:
5838:
5836:
5832:
5826:
5825:Tonality flux
5823:
5821:
5818:
5816:
5813:
5811:
5808:
5806:
5803:
5801:
5798:
5796:
5793:
5789:
5786:
5784:
5781:
5780:
5779:
5776:
5774:
5771:
5769:
5766:
5764:
5761:
5759:
5756:
5755:
5753:
5751:
5747:
5741:
5738:
5736:
5733:
5731:
5728:
5726:
5723:
5721:
5718:
5716:
5713:
5711:
5708:
5706:
5703:
5701:
5698:
5696:
5693:
5691:
5688:
5686:
5683:
5682:
5680:
5676:
5672:
5665:
5660:
5658:
5653:
5651:
5646:
5645:
5642:
5630:
5627:
5625:
5622:
5620:
5617:
5616:
5614:
5610:
5604:
5603:
5599:
5597:
5596:
5592:
5590:
5589:
5585:
5583:
5582:
5578:
5576:
5573:
5571:
5568:
5566:
5565:
5561:
5560:
5558:
5554:
5548:
5545:
5543:
5542:
5538:
5536:
5533:
5532:
5530:
5524:
5518:
5515:
5513:
5510:
5508:
5505:
5503:
5500:
5498:
5495:
5493:
5490:
5489:
5487:
5481:
5471:
5468:
5466:
5463:
5462:
5460:
5458:
5454:
5448:
5445:
5443:
5440:
5438:
5435:
5433:
5430:
5428:
5425:
5423:
5420:
5418:
5415:
5413:
5410:
5408:
5405:
5403:
5400:
5398:
5395:
5393:
5390:
5388:
5385:
5384:
5382:
5380:
5376:
5369:
5366:
5364:
5361:
5359:
5356:
5354:
5351:
5349:
5346:
5345:
5343:
5341:
5335:
5332:
5326:
5320:
5317:
5315:
5312:
5310:
5307:
5305:
5302:
5300:
5297:
5295:
5292:
5290:
5287:
5285:
5282:
5280:
5277:
5276:
5274:
5270:
5265:
5260:
5250:
5247:
5245:
5242:
5240:
5239:Elaine Walker
5237:
5235:
5234:Claude Vivier
5232:
5230:
5227:
5225:
5222:
5220:
5217:
5215:
5212:
5210:
5209:Roger Redgate
5207:
5205:
5202:
5200:
5197:
5195:
5192:
5190:
5189:Stu Mackenzie
5187:
5185:
5184:György Ligeti
5182:
5180:
5177:
5175:
5172:
5170:
5167:
5165:
5162:
5160:
5157:
5155:
5152:
5150:
5147:
5145:
5142:
5140:
5137:
5135:
5132:
5130:
5127:
5125:
5122:
5120:
5117:
5115:
5112:
5110:
5107:
5106:
5104:
5100:
5096:
5089:
5084:
5082:
5077:
5075:
5070:
5069:
5066:
5056:
5046:
5036:
5033:
5031:
5028:
5026:
5023:
5021:
5018:
5016:
5013:
5012:
5010:
5008:
5004:
4998:
4995:
4993:
4990:
4988:
4985:
4983:
4980:
4979:
4977:
4975:
4971:
4964:
4961:
4958:
4955:
4952:
4949:
4948:
4944:
4941:
4938:
4935:
4932:
4929:
4926:
4923:
4920:
4917:
4916:
4912:
4909:
4906:
4903:
4900:
4899:Lesser diesis
4897:
4896:
4892:
4889:
4886:
4883:
4880:
4877:
4874:
4871:
4870:
4868:
4866:
4865:
4860:
4854:
4851:
4849:
4846:
4844:
4841:
4840:
4838:
4836:
4835:
4834:Quarter tones
4830:
4824:
4821:
4819:
4816:
4814:
4811:
4810:
4808:
4806:
4805:
4800:
4794:
4791:
4789:
4786:
4784:
4783:Pseudo-octave
4781:
4779:
4776:
4774:
4771:
4769:
4766:
4765:
4763:
4761:
4757:
4754:
4748:
4733:
4730:
4729:
4727:
4725:
4721:
4714:
4711:
4708:
4705:
4702:
4699:
4696:
4693:
4690:
4687:
4684:
4681:
4678:
4675:
4672:
4669:
4666:
4663:
4660:
4657:
4656:
4654:
4652:
4648:
4645:
4643:
4637:
4636:
4631:
4606:
4603:
4586:
4583:
4566:
4563:
4546:
4543:
4526:
4523:
4506:
4503:
4490:
4487:
4486:
4484:
4479:
4473:
4470:
4468:
4462:
4461:
4456:
4453:
4445:
4430:
4427:
4424:
4421:
4418:
4415:
4412:
4409:
4406:
4403:
4400:
4397:
4394:
4391:
4390:
4388:
4386:
4382:
4375:
4372:
4369:
4366:
4363:
4360:
4357:
4354:
4351:
4348:
4345:
4342:
4339:
4336:
4335:
4333:
4331:
4327:
4320:
4317:
4314:
4311:
4308:
4305:
4302:
4299:
4296:
4293:
4290:
4287:
4284:
4281:
4280:
4278:
4276:
4272:
4265:
4262:
4259:
4256:
4253:
4250:
4247:
4244:
4243:
4241:
4239:
4235:
4228:
4225:
4222:
4219:
4216:
4213:
4210:
4207:
4206:
4204:
4202:
4198:
4191:
4188:
4185:
4182:
4179:
4176:
4173:
4170:
4169:
4167:
4163:
4160:
4158:
4154:
4145:
4142:
4136:
4130:
4126:
4119:
4114:
4112:
4107:
4105:
4100:
4099:
4096:
4090:
4089:TonalSoft.com
4086:
4082:
4081:
4077:
4070:
4066:
4061:
4060:
4055:
4051:
4046:
4045:
4040:
4035:
4034:
4029:
4024:
4023:
4018:
4014:
4010:
4009:
4004:
3999:
3998:
3993:
3988:
3987:
3982:
3977:
3976:
3971:
3966:
3965:
3960:
3951:
3949:0-19-814975-1
3945:
3941:
3937:
3931:
3928:
3923:
3917:
3909:
3907:0-945996-04-7
3903:
3899:
3892:
3889:
3884:
3878:
3875:
3870:
3869:
3864:
3862:
3853:
3850:
3845:
3841:
3837:
3831:
3828:
3816:
3812:
3810:
3801:
3798:
3793:
3789:
3787:
3779:
3776:
3771:
3767:
3766:
3763:
3756:
3753:
3748:
3744:
3742:
3739:"Jute Gyte –
3733:
3730:
3725:
3723:9780195310238
3719:
3715:
3711:
3707:
3701:
3698:
3693:
3689:
3685:
3681:
3677:
3673:
3672:
3664:
3662:
3658:
3653:
3649:
3645:
3639:
3636:
3631:
3627:
3623:
3619:
3615:
3611:
3610:
3602:
3600:
3596:
3593:
3587:
3584:
3579:
3575:
3571:
3567:
3563:
3559:
3558:
3550:
3548:
3544:
3541:
3540:Kingma System
3536:
3533:
3529:
3528:
3523:
3518:
3516:
3512:
3508:
3507:
3502:
3498:
3494:
3490:
3486:
3480:
3477:
3473:
3469:
3465:
3461:
3460:
3455:
3450:
3448:
3444:
3440:
3439:0-931340-88-8
3436:
3432:
3426:
3423:
3419:
3415:
3414:Stanley Sadie
3411:
3410:
3405:
3400:
3398:
3394:
3391:
3390:0-521-54206-5
3387:
3383:
3382:Hormoz Farhat
3378:
3375:
3368:
3364:
3361:
3359:
3356:
3354:
3351:
3349:
3346:
3345:
3341:
3339:
3336:
3332:
3328:
3327:neutral third
3324:
3320:
3294:
3274:
3260:
3257:
3256:
3241:
3221:
3206:
3205:
3190:
3170:
3155:
3154:
3139:
3119:
3104:
3103:
3088:
3068:
3054:
3050:
3047:
3046:
3031:
3011:
2996:
2995:
2976:
2956:
2941:
2938:
2937:
2922:
2902:
2887:
2884:
2883:
2868:
2845:
2831:
2827:
2824:
2823:
2804:
2784:
2770:
2766:
2763:
2762:
2747:
2727:
2713:
2710:
2709:
2690:
2670:
2655:
2654:
2639:
2619:
2605:
2602:
2601:
2586:
2566:
2552:
2549:
2548:
2529:
2506:
2492:
2491:neutral third
2488:
2487:
2472:
2452:
2438:
2435:
2434:
2419:
2399:
2385:
2382:
2381:
2362:
2342:
2328:
2324:
2323:
2304:
2284:
2273:
2270:
2269:
2250:
2227:
2216:
2213:
2212:
2197:
2177:
2166:
2162:
2161:
2142:
2122:
2111:
2108:
2107:
2088:
2068:
2057:
2056:perfect fifth
2054:
2053:
2038:
2015:
2004:
2001:
2000:
1985:
1965:
1954:
1951:
1950:
1931:
1911:
1900:
1899:neutral sixth
1897:
1896:
1881:
1861:
1850:
1847:
1846:
1831:
1811:
1800:
1796:
1793:
1792:
1773:
1750:
1742:
1741:minor seventh
1738:
1737:
1722:
1705:
1697:
1696:minor seventh
1693:
1692:
1677:
1660:
1652:
1648:
1645:
1644:
1625:
1605:
1597:
1593:
1590:
1589:
1574:
1554:
1546:
1545:major seventh
1543:
1542:
1527:
1510:
1502:
1499:
1498:
1479:
1462:
1454:
1451:
1450:
1432:
1415:
1407:
1404:
1403:
1397:
1394:
1389:
1386:
1383:
1378:
1373:
1370:
1369:
1366:
1365:
1364:
1362:
1358:
1350:
1335:
1331:
1328:
1324:
1320:
1316:
1312:
1308:
1304:
1301:
1297:
1289:
1287:
1285:
1281:
1277:
1276:Hugo Anthunes
1273:
1269:
1265:
1260:
1258:
1254:
1250:
1246:
1242:
1238:
1228:
1224:
1220:
1219:
1214:
1210:
1202:
1198:
1197:Nancy Sinatra
1190:
1183:
1178:
1167:
1159:
1153:
1139:
1135:
1133:
1128:
1125:
1115:
1105:
1103:
1098:
1094:
1086:
1081:
1078:
1075:
1072:
1069:
1066:
1063:
1060:
1059:
1058:
1055:
1053:
1045:
1036:
1033:
1024:
1014:
1013:
1010:
1002:
994:
982:
979:
964:
963:
947:
935:
932:
917:
912:
900:
898:C (ascending)
895:
887:
881:
880:
872:
869:
854:
853:
843:
831:
828:
827:
826:
824:
823:
818:
815:Many Persian
812:
808:
804:
796:
794:
791:
789:
785:
777:
774:
772:
769:
767:
764:
762:
758:
755:
751:
747:
745:
744:slide whistle
741:
740:slide trumpet
737:
736:P. D. Q. Bach
733:
729:
725:
723:
720:
717:
713:
710:
706:
703:
699:
696:
692:
688:
684:
683:violin family
680:
676:
672:
668:
665:
662:
658:
654:
651:
650:
648:
647:
646:
644:
636:
633:
628:
624:
620:
616:
612:
609:
605:
601:
597:
594:
593:
591:
587:
584:
581:
578:
577:pitch-bending
574:
570:
566:
562:
559:
556:
554:
550:
546:
542:
541:
540:
538:
533:
529:
522:
518:
511:
509:
505:
497:
491:
487:
481:
469:
463:
459:
454:
452:
448:
444:
440:
436:
432:
424:
422:
420:
416:
412:
408:
404:
400:
396:
391:
389:
385:
381:
377:
373:
362:
358:
341:
326:
310:
302:
295:
284:
275:
209:
201:
194:
187:
182:
180:
178:
174:
170:
166:
162:
158:
154:
150:
146:
142:
138:
134:
133:Ljubica Marić
130:
126:
125:Gérard Grisey
122:
118:
117:George Enescu
114:
110:
106:
105:Pierre Boulez
102:
98:
94:
90:
82:
78:
74:
72:
68:
64:
60:
56:
52:
33:
19:
6140:Lambda scale
6047:Arabic maqam
6004:Werckmeister
5886:
5835:Temperaments
5612:Other topics
5600:
5593:
5586:
5579:
5562:
5556:Compositions
5539:
5528:publications
5483:Concepts and
5411:
5368:Lambda scale
5309:Harry Partch
5304:Yuri Landman
5299:Lou Harrison
5284:Wendy Carlos
5279:Glenn Branca
5179:Ben Johnston
5174:Charles Ives
5134:Franklin Cox
5124:Heinz Bohlen
5006:
4973:
4959:(0.72 cents)
4953:(1.95 cents)
4933:(13.8 cents)
4927:(10.1 cents)
4921:(19.5 cents)
4913:(35.7 cents)
4907:(62.6 cents)
4901:(41.1 cents)
4893:(27.3 cents)
4887:(22.6 cents)
4881:(21.5 cents)
4875:(23.5 cents)
4862:
4843:Quarter tone
4842:
4833:
4832:
4803:
4802:
4759:
4724:Higher-limit
4639:
4633:
4545:major fourth
4489:quarter tone
4488:
4464:
4458:
4147:
4088:
4068:
4064:
4053:
4049:
4038:
4027:
4016:
4002:
3991:
3980:
3969:
3939:
3930:
3897:
3891:
3877:
3866:
3860:
3852:
3843:
3830:
3819:. Retrieved
3814:
3808:
3800:
3791:
3785:
3778:
3769:
3765:
3762:
3760:Gyte, Jute.
3755:
3746:
3741:Ressentiment
3740:
3732:
3709:
3700:
3675:
3669:
3651:
3647:
3638:
3616:(2): 39–58.
3613:
3607:
3591:
3586:
3561:
3555:
3535:
3525:
3504:
3497:Ben Johnston
3493:Lou Harrison
3479:
3466:, edited by
3463:
3457:
3430:
3425:
3418:John Tyrrell
3407:
3377:
3317:Moving from
3316:
2826:major second
2765:major second
2215:major fourth
1354:
1293:
1274:and bassist
1261:
1244:
1216:
1194:
1152:Charles Ives
1149:
1129:
1121:
1096:
1092:
1090:
1056:
1049:
821:
814:
807:Arabic music
792:
781:
734:invented by
653:Synthesizers
642:
640:
603:
569:bass guitars
536:
534:
530:
526:
458:Ben Johnston
455:
442:
438:
428:
418:
392:
386:, half of a
379:
356:
340:quarter tone
339:
337:
137:Charles Ives
96:
86:
51:quarter tone
50:
48:
6135:Delta scale
6130:Gamma scale
6120:Alpha scale
6022:non-Western
6020:Traditional
5715:Pitch class
5695:Millioctave
5678:Measurement
5575:just pieces
5363:Delta scale
5358:Gamma scale
5348:Alpha scale
5338:Non-octave-
5328:Tunings and
5289:Ivor Darreg
5114:Béla Bartók
4992:Millioctave
4974:Measurement
4965:(0.4 cents)
4945:(7.7 cents)
4939:(8.1 cents)
4823:Major limma
4565:minor fifth
4056:(4): 23–29.
3817:(interview)
3646:(c. 1840).
3609:Asian Music
2551:minor third
2437:major third
2327:major third
2325:tridecimal
2110:minor fifth
1953:minor sixth
1849:major sixth
1739:small just
1694:large just
1387:Just ratio
1323:Aristoxenos
1311:major third
1280:Paul Lytton
1272:Paul Lovens
1124:theoretical
819:and Arabic
447:minor third
388:minor third
6156:Categories
6125:Beta scale
6103:Non-octave
6094:Tetrachord
5996:Kirnberger
5959:Schismatic
5526:Groups and
5485:techniques
5353:Beta scale
5204:Joe Maneri
5164:Alois Hába
5144:John Eaton
5025:Semiditone
4919:Diaschisma
4734:(17-limit)
4425:(22 or 23)
4423:fourteenth
4419:(20 or 21)
4417:thirteenth
4413:(18 or 19)
4407:(17 or 18)
4401:(15 or 16)
4395:(13 or 14)
4330:Diminished
4157:interval.)
4138:(post-Bach
4013:Ellis, Don
3868:PopMatters
3840:Maneri, J.
3836:Maneri, M.
3821:2021-01-27
3489:John Eaton
3369:References
2830:minor tone
2769:major tone
2489:undecimal
1651:minor tone
1596:major tone
1357:Alois Hába
1319:microtones
1303:tetrachord
1241:Joe Maneri
1237:Mat Maneri
1215:'s albums
801:See also:
669:and other
600:embouchure
553:accordions
449:(6:5) and
441:(i.e. the
129:Alois Hába
67:whole tone
6115:A12 scale
6069:Octoechos
6034:Shí-èr-lǜ
5983:Irregular
5800:Otonality
5740:Microtone
5507:Sonido 13
5272:Inventors
5224:Ezra Sims
5102:Composers
4987:Centitone
4925:Semicomma
4804:Semitones
4768:Microtone
4752:intervals
4429:fifteenth
4275:Augmented
4153:semitones
4125:Intervals
3916:cite book
1249:mellotron
1150:Composer
1091:Known as
1052:Al-Farabi
728:trombones
677:Fretless
667:Theremins
661:sequencer
635:Harmonica
456:Composer
338:The term
6000:Vallotti
5953:septimal
5945:Meantone
5705:Interval
5502:Semitone
4957:Breedsma
4405:eleventh
4385:Compound
4140:Western)
4135:semitone
4071:: 56–69.
4015:(1975).
3938:(1992).
3861:Pentagon
3844:Pentagon
3842:(2005).
3788:in July"
3708:(2009).
3342:See also
1720:1017.60
1675:1035.00
1623:1049.36
1572:1088.27
1525:1137.04
1477:1151.23
1430:1200.00
1400:(cents)
1392:(cents)
1381:(cents)
1376:(steps)
1315:semitone
1313:, and a
1245:Pentagon
1173:♭
1127:period.
1079:Shbiʿoyo
1073:Hmishoyo
959:♭
953:♭
904:♭
849:♭
742:and the
732:tromboon
623:harmonic
588:Western
573:ukuleles
563:such as
352:♭
346:♯
331:♭
315:♭
63:semitone
59:interval
6089:Slendro
6039:Dastgah
5964:Miracle
5927:96-tone
5922:72-tone
5917:58-tone
5912:53-tone
5907:41-tone
5902:34-tone
5897:31-tone
5887:24-tone
5882:23-tone
5877:22-tone
5872:19-tone
5867:17-tone
5862:15-tone
5857:12-tone
5788:7-limit
5783:5-limit
4963:Ragisma
4951:Schisma
4937:Kleisma
4773:5-limit
4679:(15:14)
4673:(21:20)
4667:(28:27)
4661:(36:35)
4651:7-limit
4616:⁄
4605:seventh
4596:⁄
4576:⁄
4556:⁄
4536:⁄
4516:⁄
4496:⁄
4478:Neutral
4451:systems
4411:twelfth
4368:seventh
4319:seventh
4264:seventh
4227:seventh
4165:Perfect
4133:Twelve-
3692:3589971
3202:−12.96
3151:+15.53
3100:−11.73
3086:111.73
3043:−19.44
3029:119.44
2974:150.64
2934:−15.00
2920:165.00
2880:+17.60
2866:182.40
2802:203.91
2759:+18.83
2745:231.17
2688:247.74
2651:−16.87
2637:266.87
2598:−15.64
2584:315.64
2527:347.41
2484:+13.69
2470:386.31
2431:+14.92
2417:435.08
2360:454.21
2302:498.04
2248:551.32
2209:+17.49
2195:582.51
2163:lesser
2140:648.68
2086:701.96
2050:−14.92
2036:764.92
1997:−13.69
1983:813.69
1929:852.59
1893:+15.64
1879:884.36
1843:−18.83
1829:968.83
1771:996.09
1734:−17.60
1689:+15.00
1586:+11.73
1539:+12.96
1327:Didymos
1298:of the
1262:Later,
1102:Mishaqa
1082:Tminoyo
1046:Hoseyni
997:F G A B
907:A G F E
890:F G A B
846:F G A B
822:maqamat
817:dastgah
709:bağlama
615:trumpet
565:guitars
558:Fretted
453:(7:6).
365:√
81:Trumpet
6057:Mugham
6043:Maqam
5937:Linear
5891:pieces
5852:6-tone
5773:Hexany
5700:Savart
5581:Mother
5330:scales
5219:Sevish
5020:Ditone
5007:Others
4997:Savart
4864:Commas
4760:Groups
4709:(10:7)
4505:second
4449:tuning
4374:octave
4350:fourth
4338:second
4301:fourth
4289:second
4283:unison
4246:second
4209:second
4190:octave
4178:fourth
4172:unison
4155:in the
3946:
3904:
3720:
3690:
3630:834466
3628:
3578:849799
3576:
3437:
3388:
3319:12-TET
3259:unison
3253:−3.27
3239:53.27
3233:33:32
3188:62.96
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