1248:
1236:
1224:
1212:
1264:
549:
165:
142:
476:
543:
1171:
470:
213:
989:
777:
403:
36:
133:
221:
1782:, which tunes major thirds justly in the ratio of 5:4 and divides them into two whole tones of equal size – this is achieved by flattening the fifths of the Pythagorean system slightly (by a quarter of a syntonic comma). However, the fifth may be flattened to a greater or lesser degree than this and the tuning system retains the essential qualities of meantone temperament. Historical examples include
156:
2069:
255:) in relation to a given reference pitch. While an instrument might be in tune relative to its own range of notes, it may not be considered 'in tune' if it does not match the chosen reference pitch. Some instruments become 'out of tune' with temperature, humidity, damage, or simply time, and must be readjusted or repaired.
367:, who tune to the keyboard if part of the performance. When only strings are used, then the principal string (violinist) typically has sounded the tuning pitch, but some orchestras have used an electronic tone machine for tuning. Tuning can also be done through a prior recording; this method uses simultaneous audio.
1711:
4:3, 729:512, 3:2, 128:81, 27:16, 16:9, 243:128, 2:1. Also called "3-limit" because there are no prime factors other than 2 and 3, this
Pythagorean system was of primary importance in Western musical development in the Medieval and Renaissance periods. As with nearly all just intonation systems, it has a
1847:
Any one of a number of systems where the ratios between intervals are unequal, but approximate to ratios used in just intonation. Unlike meantone temperament, the amount of divergence from just ratios varies according to the exact notes being tuned, so that C–E is probably tuned closer to a 5:4 ratio
1161:
The creation of a tuning system is complicated because musicians want to make music with more than just a few differing tones. As the number of tones is increased, conflicts arise in how each tone combines with every other. Finding a successful combination of tunings has been the cause of debate, and
538:
To tune an instrument, often only one reference pitch is given. This reference is used to tune one string, to which the other strings are tuned in the desired intervals. On a guitar, often the lowest string is tuned to an E. From this, each successive string can be tuned by fingering the fifth fret
1710:
A Pythagorean tuning is technically a type of just intonation, in which the frequency ratios of the notes are all derived from the number ratio 3:2. Using this approach for example, the 12 notes of the
Western chromatic scale would be tuned to the following ratios: 1:1, 256:243, 9:8, 32:27, 81:64,
374:
are used to objectively measure the accuracy of tuning. As the two pitches approach a harmonic relationship, the frequency of beating decreases. When tuning a unison or octave it is desired to reduce the beating frequency until it cannot be detected. For other intervals, this is dependent on the
947:
often employ alternate tunings for dance songs and ballads. The most commonly used tuning is A-E-A-E. Likewise banjo players in this tradition use many tunings to play melody in different keys. A common alternative banjo tuning for playing in D is A-D-A-D-E. Many Folk guitar players also used
1689:). Harmonic fragment scales form a rare exception to this issue. In tunings such as 1:1 9:8 5:4 3:2 7:4 2:1, all the pitches are chosen from the harmonic series (divided by powers of 2 to reduce them to the same octave), so all the intervals are related to each other by simple numeric ratios.
1601:. The same issue occurs with most just intonation tunings. This can be dealt with to some extent using alternative pitches for the notes. Even that, however, is only a partial solution, as an example makes clear: If one plays the sequence C G D A E C in just intonation, using the intervals
539:
of an already tuned string and comparing it with the next higher string played open. This works with the exception of the G string, which must be stopped at the fourth fret to sound B against the open B string above. Alternatively, each string can be tuned to its own reference tone.
1249:
1237:
1685:, the musical context may sometimes require playing musical intervals that are not pure. Instrumentalists with the ability to vary the pitch of their instrument may micro-adjust some of the intervals naturally; there are also systems for adaptive tuning in software (
1225:
1213:
1836:
1759:
1699:
389:) while bowing produces the same pitch as doing the same a third of the way down its second-highest string. The resulting unison is more easily and quickly judged than the quality of the perfect fifth between the fundamentals of the two strings.
1868:
1838:
1366:
1312:
is nearly a quarter tone away from the octave (1200 cents). So there is no way to have both the octave and the major third in just intonation for all the intervals in the same twelve-tone system. Similar issues arise with the fifth
550:
1761:
1265:
1701:
166:
1870:
1368:
1681:". Each time around the comma pump, the pitch continues to spiral upwards. This shows that it is impossible to keep to any small fixed system of pitches if one wants to stack musical intervals this way. So, even with
143:
477:
239:
is the process of adjusting the pitch of one or many tones from musical instruments to establish typical intervals between these tones. Tuning is usually based on a fixed reference, such as
1837:
1760:
1700:
1869:
1745:
to C). The major and minor thirds are also impure, but at the time when this system was at its zenith, the third was considered a dissonance, so this was of no concern. See also:
1367:
883:
in E-flat major (K. 364), all the strings of the solo viola are raised one half-step, ostensibly to give the instrument a brighter tone so the solo violin does not overshadow it.
1902:
However, the octave can be divided into other than 12 equal divisions, some of which may be more harmonically pleasing, as far as thirds and sixths are concerned, such as
2337:
1205:
385:
may be used to facilitate tuning of strings that are not themselves tuned to the unison. For example, lightly touching the highest string of a cello at the middle (at a
1891:. Since this scale divides an octave into twelve equal-ratio steps and an octave has a frequency ratio of two, the frequency ratio between adjacent notes is then the
573:
or to compensate and play in equal temperament, such as when playing with other instruments such as the piano. For example, the cello, which is tuned down from
281:
on strings so as to control the pitch. Instruments such as the harp, piano, and harpsichord require a wrench to turn the tuning pegs, while others such as the
1879:
The standard twelve-tone equal temperament is a special case of meantone temperament (extended eleventh-comma), in which the twelve notes are separated by
879:
1162:
has led to the creation of many different tuning systems across the world. Each tuning system has its own characteristics, strengths and weaknesses.
1778:
A system of tuning that averages out pairs of ratios used for the same interval (such as 9:8 and 10:9). The best known form of this temperament is
1076:
Tuning pitched percussion follows the same patterns as tuning any other instrument, but tuning unpitched percussion does not produce a specific
1529:
to define the ratios for the seven notes in a C major scale. In this example, though many intervals are pure, the interval from D to A (
2476:
1385:
In just intonation, the frequencies of the scale notes are related to one another by simple numeric ratios, a common example of this being
1887:(.ogg format, 96.9 KB). This is the most common tuning system used in Western music, and is the standard system used as a basis for
584:
This table lists open strings on some common string instruments and their standard tunings from low to high unless otherwise noted.
2408:
1352:
Many different compromise methods are used to deal with this, each with its own characteristics, and advantages and disadvantages.
1135:, various tone combinations sound more or less "natural" in combination with various timbres. For example, using harmonic timbres:
3033:
2541:
2920:
581:
off from the equal tempered perfect fifth, making its lowest string, C−, about six cents more flat than the equal tempered C.
100:
565:, string instruments without frets, such as those of the violin family, are not. The violin, viola, and cello are tuned to
72:
2551:
304:, or similar instrument to adjust the pitch. In woodwind instruments, this is usually done by adjusting the instrument's
1705:
Prelude No. 1, C major, BWV 846, from the Well-Tempered
Clavier by Johann Sebastian Bach. Played in Pythagorean tuning.
1874:
Prelude No. 1, C major, BWV 846, from the Well-Tempered
Clavier by Johann Sebastian Bach. Played in equal temperament.
79:
2379:
1842:
Prelude No. 1, C major, BWV 846, from the Well-Tempered
Clavier by Johann Sebastian Bach. Played in well temperament.
1036:
824:
450:
119:
1018:
806:
432:
920:, the solo violin is tuned one whole step high to produce a harsh sound evoking Death as the Fiddler. In Bartók's
2514:
2216:"Effects of natural and artificial ageing on the physical and acoustic properties of wood in musical instruments"
1977:
1066:
1010:
798:
424:
313:
53:
1146:
A tone caused by a vibration three times the frequency of another (the ratio of 1:3) forms the natural sounding
335:
Tuning may be done aurally by sounding two pitches and adjusting one of them to match or relate to the other. A
86:
2264:
1014:
802:
428:
57:
907:
2699:
2123:
1054:
17:
2401:
68:
1139:
A tone caused by a vibration twice the frequency of another (the ratio of 1:2) forms the natural sounding
507:(excepting the G and B strings in standard tuning, which are tuned to a third), as are the strings of the
3026:
2637:
464:
2913:
2481:
852:
843:
Violin scordatura was employed in the 17th and 18th centuries by
Italian and German composers, namely,
2215:
569:
just perfect fifths and ensembles such as string quartets and orchestras tend to play in fifths based
3097:
2466:
732:
G, C, E, A (the G string is higher than the C and E, and two half steps below the A string, known as
339:
or electronic tuning device may be used as a reference pitch, though in ensemble rehearsals often a
3077:
2750:
1258:
999:
787:
413:
3217:
3002:
2886:
2720:
2546:
2471:
2394:
1991:
1003:
917:
874:
791:
417:
325:
308:
or neck to change the pitch. In brass instruments, this is usually done by moving a tuning slide.
160:
46:
2291:"A System for Tuning Instruments Using Recorded Music Instead of Theory-Based Frequency Presets"
1939:
Tuning systems that are not produced with exclusively just intervals are usually referred to as
1179:
3019:
2742:
2705:
2695:
2504:
2049:
1779:
561:
Note that while the guitar and other modern stringed instruments with fixed frets are tuned in
895:
3087:
3065:
2966:
2906:
2738:
1770:
1766:
1377:
1373:
968:
951:
A musical instrument that has had its pitch deliberately lowered during tuning is said to be
948:
different tunings from standard, such as D-A-D-G-A-D, which is very popular for Irish music.
864:
574:
356:
305:
240:
916:
so as to have the most accented note of the main theme sound on an open string. In Mahler's
93:
2746:
2691:
2673:
2668:
2663:
2658:
2653:
2648:
2643:
2628:
2623:
2618:
2613:
2608:
2603:
2148:
2044:
2039:
2034:
2029:
1932:
1928:
1903:
1752:
225:
8:
2976:
2960:
2955:
2940:
2710:
2683:
2581:
2097:
2054:
1941:
1892:
869:
321:
278:
887:
3164:
2986:
2775:
2561:
2556:
2318:
2243:
2128:
2103:
2018:
1692:
1175:
1088:
570:
3123:
2950:
2754:
2715:
2590:
2529:
2375:
2310:
2247:
2235:
1861:
960:
562:
301:
2780:
2354:
Harmonic
Experience: Tonal Harmony from Its Natural Origins to Its Modern Expression
1884:
1746:
3179:
3159:
2981:
2945:
2734:
2598:
2566:
2486:
2451:
2322:
2302:
2227:
2188:
2183:
2163:
2133:
2113:
2108:
2024:
1961:
1829:
1281:
1082:
903:
886:
Scordatura for the violin was also used in the 19th and 20th centuries in works by
860:
859:
prescribes a great variety of scordaturas, including crossing the middle strings),
747:
733:
566:
371:
352:
293:
542:
3082:
2856:
2496:
2231:
2178:
2173:
2118:
1715:. In the example given, it is the interval between the 729:512 and the 256:243 (F
1359:
1277:
1147:
1128:
891:
848:
289:
959:. Common examples include the electric guitar and electric bass in contemporary
606:
3128:
3113:
2534:
2509:
2456:
2153:
1801:
1656:
972:
741:
535:) exist to change the sound of the instrument or create other playing options.
504:
386:
258:
Different methods of sound production require different methods of adjustment:
1170:
577:, has three more strings (four total) and the just perfect fifth is about two
469:
3211:
3143:
3138:
3060:
3046:
2829:
2798:
2571:
2524:
2431:
2314:
2239:
2168:
1855:
1712:
1151:
1113:
1077:
964:
899:
844:
528:
248:
200:
3191:
3133:
3118:
2929:
2793:
2633:
2436:
2074:
2012:
1981:
1888:
940:
675:
636:
578:
348:
267:
252:
3196:
3092:
2881:
2876:
2866:
2461:
2441:
2306:
2193:
2008:
2004:
1996:
1158:
More complex musical effects can be created through other relationships.
654:
646:
624:
512:
508:
336:
137:
3186:
3169:
3072:
2971:
2871:
2840:
2290:
2158:
2138:
2091:
2000:
1686:
1678:
1093:
1070:
838:
755:
650:
632:
532:
274:
3011:
3042:
2861:
2815:
1880:
1121:
344:
297:
988:
776:
402:
212:
35:
1985:
1109:
602:
382:
364:
132:
2386:
1655:, then the second C in the sequence is higher than the first by a
750:, with the short 5th string tuned an octave above the 3rd string)
220:
2835:
2785:
1965:
1957:
1954:
Natural overtone scale, a scale derived from the harmonic series.
1058:
727:
628:
343:
is used (as its pitch cannot be adjusted for each performance).
2898:
2803:
2519:
2446:
2059:
1349:, or any other choice of harmonic-series based pure intervals.
1140:
1132:
944:
665:
598:
516:
500:
329:
317:
282:
1165:
967:. This is not to be confused with electronically changing the
910:", the high string of the violin is lower half a tone to the E
496:
refers to the fundamental note of the unstopped, full string.
155:
2820:
2808:
1971:
1117:
1062:
978:
620:
616:
524:
520:
489:
340:
179:
1284:
are pure. For instance, three pure major thirds stack up to
1120:. In other words, it is the choice of number and spacing of
2825:
2143:
360:
229:
963:, whereby one or more strings are often tuned lower than
203:
used to tune an instrument, and their theoretical bases.
936:
to facilitate the playing of tritones on open strings.
27:
Terms for tuning an instrument and a systems of pitches
1182:
324:, and have irregular overtones not conforming to the
2064:
1080:. For this reason and others, the traditional terms
60:. Unsourced material may be challenged and removed.
1199:
247:" refers to a pitch/tone that is either too high (
330:§ Tuning of unpitched percussion instruments
3209:
873:calls for the lowering of the A string to G. In
1885:A harmonized C major scale in equal temperament
1854:–F. Because of this, well temperaments have no
288:Modifying the length or width of the tube of a
2374:. East Lansing: Michigan State College Press.
3027:
2914:
2402:
262:Tuning to a pitch with one's voice is called
232:OT-120 Wide 8 Octave Orchestral Digital Tuner
2477:List of intervals in 5-limit just intonation
2222:. Wooden Musical Instruments Special Issue.
2372:Tuning and Temperament: A Historical Survey
1166:Systems for the twelve-note chromatic scale
1017:. Unsourced material may be challenged and
805:. Unsourced material may be challenged and
431:. Unsourced material may be challenged and
193:, the act of tuning an instrument or voice.
3034:
3020:
2921:
2907:
2409:
2395:
2265:"Why does the orchestra tune to the oboe?"
1765:Prelude No. 1, C major, BWV 846, from the
1372:Prelude No. 1, C major, BWV 846, from the
979:Tuning of unpitched percussion instruments
359:, respectively, provided by the principal
1276:It is impossible to tune the twelve-note
1037:Learn how and when to remove this message
825:Learn how and when to remove this message
473:The pitches of open strings on a violin.
451:Learn how and when to remove this message
120:Learn how and when to remove this message
1866:
1834:
1757:
1697:
1364:
1169:
541:
531:. However, non-standard tunings (called
468:
312:The sounds of some instruments, notably
219:
211:
154:
131:
3041:
2288:
2213:
760:D, G, B, D (standard Brazilian tuning)
266:and is the most basic skill learned in
14:
3210:
2335:
2259:
2257:
1948:
1931:(extended quarter-comma meantone) and
216:Man turning tuning pegs to tune guitar
3015:
2902:
2390:
1015:adding citations to reliable sources
982:
803:adding citations to reliable sources
770:
429:adding citations to reliable sources
396:
190:
182:, there are two common meanings for
58:adding citations to reliable sources
29:
2416:
2254:
1154:(ratio of 2:3) when octave-reduced.
1108:is the system used to define which
870:Fifth Suite For Unaccompanied Cello
376:
196:
136:Two differently tuned thirds: Just
24:
2363:
766:
207:
25:
3229:
1773:. Played in meantone temperament.
1099:
2928:
2552:Ptolemy's intense diatonic scale
2067:
1067:unpitched percussion instruments
1049:Many percussion instruments are
987:
939:American folk violinists of the
775:
401:
34:
1974:, the other main gamelan scale.
392:
314:unpitched percussion instrument
45:needs additional citations for
2346:
2336:Sfetcu, Nicolae (2014-05-07).
2329:
2282:
2214:Obataya, Eiichi (2017-10-01).
2207:
1935:(extended Pythagorean tuning).
1055:pitched percussion instruments
13:
1:
2289:Bozkurt, Barış (2012-09-01).
2200:
2124:Mathematics of musical scales
1883:equal distances (100 cents):
2515:Harry Partch's 43-tone scale
2232:10.1016/j.culher.2016.02.011
2220:Journal of Cultural Heritage
1380:. Played in just intonation.
277:to increase or decrease the
7:
2370:Barbour, J. Murray (1951).
2081:
465:Stringed instrument tunings
10:
3234:
2482:List of meantone intervals
1200:{\displaystyle {}_{4}^{6}}
971:, which is referred to as
853:Heinrich Ignaz Franz Biber
836:
462:
3152:
3106:
3098:Scientific pitch notation
3053:
3000:
2936:
2849:
2766:
2729:
2682:
2589:
2580:
2495:
2472:List of musical intervals
2467:Consonance and dissonance
2424:
1131:interaction of tones and
1053:by the player, including
199:, the various systems of
3078:Helmholtz pitch notation
1966:Indonesian gamelan music
1677:. This is the infamous "
1583:instead of the expected
159:And the slightly wider:
3003:List of music theorists
1174:Comparison of tunings:
924:, the violin is tuned G
746:G, D, G, B, D (another
660:(B*,) E, A, D, G, (C*)
161:Pythagorean major third
2295:Computer Music Journal
2050:Schismatic temperament
1875:
1843:
1780:quarter-comma meantone
1774:
1706:
1381:
1331:, and the minor third
1273:
1267:Play equal temperament
1201:
1116:, to use when playing
1092:are avoided in recent
558:
503:are normally tuned to
485:
285:can be tuned manually.
233:
217:
175:
152:
3088:Piano key frequencies
2739:Temperament ordinaire
2352:W. A. Mathieu (1997)
1873:
1841:
1771:Johann Sebastian Bach
1767:Well-Tempered Clavier
1764:
1704:
1378:Johann Sebastian Bach
1374:Well-Tempered Clavier
1371:
1251:Play well temperament
1202:
1173:
969:fundamental frequency
865:Johann Sebastian Bach
545:
527:strings are tuned to
472:
223:
215:
158:
135:
2542:List of compositions
2307:10.1162/COMJ_a_00128
2269:RockfordSymphony.com
2149:MIDI tuning standard
2045:53 equal temperament
2040:31 equal temperament
2035:22 equal temperament
2030:19 equal temperament
1933:53 equal temperament
1929:31 equal temperament
1904:19 equal temperament
1753:Meantone temperament
1180:
1011:improve this section
880:Sinfonia Concertante
799:improve this section
546:Cello open strings.
425:improve this section
54:improve this article
2356:. Inner Traditions.
2098:Beauty in the Beast
2055:Miracle temperament
1992:Bohlen–Pierce scale
1949:Other scale systems
1893:twelfth root of two
1727:, if one tunes the
1355:The main ones are:
1196:
906:. In Saint-Saëns' "
896:Camille Saint-Saëns
351:usually tune to an
345:Symphony orchestras
322:indeterminate pitch
2776:Chinese musicology
2562:Scale of harmonics
2557:Pythagorean tuning
2505:Euler–Fokker genus
2104:Chinese musicology
2019:Quarter tone scale
1876:
1844:
1775:
1707:
1693:Pythagorean tuning
1382:
1274:
1197:
1183:
1089:untuned percussion
571:Pythagorean tuning
559:
486:
234:
218:
176:
153:
3205:
3204:
3124:Pitch circularity
3009:
3008:
2896:
2895:
2762:
2761:
2342:. Nicolae Sfetcu.
1871:
1862:Equal temperament
1839:
1762:
1702:
1369:
1245:(quarter-comma),
1047:
1046:
1039:
961:heavy metal music
835:
834:
827:
764:
763:
670:E, A, D, G, B, E
607:Irish tenor banjo
563:equal temperament
499:The strings of a
461:
460:
453:
130:
129:
122:
104:
16:(Redirected from
3225:
3160:Electronic tuner
3036:
3029:
3022:
3013:
3012:
2923:
2916:
2909:
2900:
2899:
2735:Well temperament
2721:Regular diatonic
2587:
2586:
2567:Tonality diamond
2411:
2404:
2397:
2388:
2387:
2357:
2350:
2344:
2343:
2333:
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2326:
2286:
2280:
2279:
2277:
2276:
2261:
2252:
2251:
2211:
2189:Vibrating string
2184:Stretched tuning
2164:Physics of music
2134:Microtonal music
2114:Electronic tuner
2109:Dynamic tonality
2077:
2072:
2071:
2070:
2025:Thirteenth Sound
1962:pentatonic scale
1926:
1924:
1923:
1921:
1920:
1917:
1914:
1901:
1899:
1872:
1853:
1852:
1840:
1830:Well temperament
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1800:
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1560:
1557:
1554:
1546:
1545:
1543:
1542:
1539:
1536:
1528:
1527:
1525:
1524:
1521:
1518:
1510:
1509:
1507:
1506:
1503:
1500:
1492:
1491:
1489:
1488:
1485:
1482:
1474:
1473:
1471:
1470:
1467:
1464:
1456:
1455:
1453:
1452:
1449:
1446:
1438:
1437:
1435:
1434:
1431:
1428:
1420:
1419:
1417:
1416:
1413:
1410:
1402:
1401:
1399:
1398:
1395:
1392:
1370:
1348:
1347:
1345:
1344:
1341:
1338:
1330:
1329:
1327:
1326:
1323:
1320:
1311:
1309:
1308:
1301:
1300:
1298:
1297:
1294:
1291:
1272:
1271:
1270:
1268:
1256:
1255:
1254:
1252:
1244:
1243:
1242:
1240:
1232:
1231:
1230:
1228:
1227:Play Pythagorean
1220:
1219:
1218:
1216:
1206:
1204:
1203:
1198:
1195:
1190:
1185:
1083:tuned percussion
1042:
1035:
1031:
1028:
1022:
991:
983:
935:
934:
929:
928:
915:
914:
888:Niccolò Paganini
861:Johann Pachelbel
830:
823:
819:
816:
810:
779:
771:
748:reentrant tuning
734:reentrant tuning
721:
720:
715:
714:
709:
708:
703:
702:
697:
696:
691:
690:
685:
684:
587:
586:
557:
556:
555:
553:
484:
483:
482:
480:
456:
449:
445:
442:
436:
405:
397:
294:brass instrument
173:
172:
171:
169:
150:
149:
148:
146:
125:
118:
114:
111:
105:
103:
69:"Musical tuning"
62:
38:
30:
21:
3233:
3232:
3228:
3227:
3226:
3224:
3223:
3222:
3208:
3207:
3206:
3201:
3165:Mersenne's laws
3148:
3102:
3083:Letter notation
3049:
3040:
3010:
3005:
2996:
2963:
2932:
2927:
2897:
2892:
2889:(Bohlen–Pierce)
2857:833 cents scale
2845:
2768:
2758:
2725:
2678:
2576:
2497:Just intonation
2491:
2420:
2418:Musical tunings
2415:
2385:
2366:
2364:Further reading
2361:
2360:
2351:
2347:
2339:The Music Sound
2334:
2330:
2287:
2283:
2274:
2272:
2263:
2262:
2255:
2212:
2208:
2203:
2198:
2179:Standard tuning
2174:Psychoacoustics
2129:Mersenne's laws
2119:Ethnomusicology
2086:
2084:
2073:
2068:
2066:
1951:
1918:
1915:
1912:
1911:
1909:
1908:
1907:
1897:
1896:
1881:logarithmically
1867:
1850:
1849:
1835:
1817:
1814:
1811:
1810:
1808:
1807:
1806:
1794:
1791:
1788:
1787:
1785:
1784:
1783:
1758:
1738:
1735:
1732:
1731:
1729:
1728:
1723:
1722:
1717:
1716:
1698:
1683:adaptive tuning
1670:
1667:
1664:
1663:
1661:
1660:
1648:
1645:
1642:
1641:
1639:
1638:
1630:
1627:
1624:
1623:
1621:
1620:
1612:
1609:
1606:
1605:
1603:
1602:
1594:
1591:
1588:
1587:
1585:
1584:
1576:
1573:
1570:
1569:
1567:
1566:
1558:
1555:
1552:
1551:
1549:
1548:
1540:
1537:
1534:
1533:
1531:
1530:
1522:
1519:
1516:
1515:
1513:
1512:
1504:
1501:
1498:
1497:
1495:
1494:
1486:
1483:
1480:
1479:
1477:
1476:
1468:
1465:
1462:
1461:
1459:
1458:
1450:
1447:
1444:
1443:
1441:
1440:
1432:
1429:
1426:
1425:
1423:
1422:
1414:
1411:
1408:
1407:
1405:
1404:
1396:
1393:
1390:
1389:
1387:
1386:
1365:
1360:Just intonation
1342:
1339:
1336:
1335:
1333:
1332:
1324:
1321:
1318:
1317:
1315:
1314:
1306:
1304:
1303:
1295:
1292:
1289:
1288:
1286:
1285:
1278:chromatic scale
1266:
1263:
1262:
1250:
1247:
1246:
1238:
1235:
1234:
1226:
1223:
1222:
1214:
1211:
1210:
1191:
1186:
1184:
1181:
1178:
1177:
1168:
1148:perfect twelfth
1102:
1043:
1032:
1026:
1023:
1008:
992:
981:
932:
931:
926:
925:
912:
911:
892:Robert Schumann
849:Antonio Vivaldi
841:
831:
820:
814:
811:
796:
780:
769:
767:Altered tunings
718:
717:
712:
711:
706:
705:
700:
699:
694:
693:
688:
687:
682:
681:
551:
548:
547:
478:
475:
474:
467:
457:
446:
440:
437:
422:
406:
395:
326:harmonic series
290:wind instrument
241:A = 440 Hz
226:Sébastien Érard
210:
208:Tuning practice
191:Tuning practice
167:
164:
163:
144:
141:
140:
126:
115:
109:
106:
63:
61:
51:
39:
28:
23:
22:
15:
12:
11:
5:
3231:
3221:
3220:
3218:Musical tuning
3203:
3202:
3200:
3199:
3194:
3189:
3184:
3183:
3182:
3175:Musical tuning
3172:
3167:
3162:
3156:
3154:
3150:
3149:
3147:
3146:
3141:
3136:
3131:
3129:Relative pitch
3126:
3121:
3116:
3114:Absolute pitch
3110:
3108:
3104:
3103:
3101:
3100:
3095:
3090:
3085:
3080:
3075:
3070:
3069:
3068:
3057:
3055:
3051:
3050:
3039:
3038:
3031:
3024:
3016:
3007:
3006:
3001:
2998:
2997:
2995:
2994:
2989:
2984:
2979:
2974:
2969:
2964:
2958:
2953:
2948:
2943:
2937:
2934:
2933:
2926:
2925:
2918:
2911:
2903:
2894:
2893:
2891:
2890:
2884:
2879:
2874:
2869:
2864:
2859:
2853:
2851:
2847:
2846:
2844:
2843:
2838:
2833:
2823:
2818:
2813:
2812:
2811:
2806:
2801:
2796:
2788:
2783:
2778:
2772:
2770:
2764:
2763:
2760:
2759:
2733:
2731:
2727:
2726:
2724:
2723:
2718:
2713:
2708:
2703:
2688:
2686:
2680:
2679:
2677:
2676:
2671:
2666:
2661:
2656:
2651:
2646:
2641:
2631:
2626:
2621:
2616:
2611:
2606:
2601:
2595:
2593:
2584:
2578:
2577:
2575:
2574:
2569:
2564:
2559:
2554:
2549:
2544:
2539:
2538:
2537:
2532:
2522:
2517:
2512:
2510:Harmonic scale
2507:
2501:
2499:
2493:
2492:
2490:
2489:
2484:
2479:
2474:
2469:
2464:
2459:
2457:Interval ratio
2454:
2449:
2444:
2439:
2434:
2428:
2426:
2422:
2421:
2414:
2413:
2406:
2399:
2391:
2384:
2383:
2367:
2365:
2362:
2359:
2358:
2345:
2328:
2281:
2253:
2205:
2204:
2202:
2199:
2197:
2196:
2191:
2186:
2181:
2176:
2171:
2166:
2161:
2156:
2154:Musical theory
2151:
2146:
2141:
2136:
2131:
2126:
2121:
2116:
2111:
2106:
2101:
2094:
2088:
2083:
2080:
2079:
2078:
2063:
2062:
2057:
2052:
2047:
2042:
2037:
2032:
2027:
2022:
2016:
1994:
1989:
1984:, an American
1975:
1969:
1955:
1950:
1947:
1937:
1936:
1898:2 ≋ 1.05946309
1889:tuning a piano
1877:
1864:
1859:
1856:wolf intervals
1845:
1832:
1827:
1776:
1755:
1750:
1708:
1695:
1690:
1657:syntonic comma
1383:
1362:
1194:
1189:
1167:
1164:
1156:
1155:
1144:
1129:psychoacoustic
1101:
1100:Tuning systems
1098:
1045:
1044:
995:
993:
986:
980:
977:
973:pitch shifting
918:Symphony No. 4
857:Rosary Sonatas
837:Main article:
833:
832:
783:
781:
774:
768:
765:
762:
761:
758:
752:
751:
744:
742:5-string banjo
738:
737:
730:
724:
723:
678:
672:
671:
668:
662:
661:
658:
643:
642:
639:
613:
612:
609:
595:
594:
591:
463:Main article:
459:
458:
409:
407:
400:
394:
391:
310:
309:
286:
271:
264:matching pitch
251:) or too low (
209:
206:
205:
204:
197:Tuning systems
194:
128:
127:
110:September 2021
42:
40:
33:
26:
9:
6:
4:
3:
2:
3230:
3219:
3216:
3215:
3213:
3198:
3195:
3193:
3190:
3188:
3185:
3181:
3178:
3177:
3176:
3173:
3171:
3168:
3166:
3163:
3161:
3158:
3157:
3155:
3151:
3145:
3144:Virtual pitch
3142:
3140:
3139:Tone deafness
3137:
3135:
3132:
3130:
3127:
3125:
3122:
3120:
3117:
3115:
3112:
3111:
3109:
3105:
3099:
3096:
3094:
3091:
3089:
3086:
3084:
3081:
3079:
3076:
3074:
3071:
3067:
3064:
3063:
3062:
3061:Concert pitch
3059:
3058:
3056:
3052:
3048:
3044:
3037:
3032:
3030:
3025:
3023:
3018:
3017:
3014:
3004:
2999:
2993:
2990:
2988:
2985:
2983:
2980:
2978:
2975:
2973:
2970:
2968:
2965:
2962:
2959:
2957:
2954:
2952:
2949:
2947:
2944:
2942:
2939:
2938:
2935:
2931:
2924:
2919:
2917:
2912:
2910:
2905:
2904:
2901:
2888:
2885:
2883:
2880:
2878:
2875:
2873:
2870:
2868:
2865:
2863:
2860:
2858:
2855:
2854:
2852:
2848:
2842:
2839:
2837:
2834:
2831:
2830:Carnatic raga
2827:
2824:
2822:
2819:
2817:
2814:
2810:
2807:
2805:
2802:
2800:
2799:Turkish makam
2797:
2795:
2792:
2791:
2789:
2787:
2784:
2782:
2779:
2777:
2774:
2773:
2771:
2765:
2756:
2752:
2748:
2744:
2740:
2736:
2732:
2728:
2722:
2719:
2717:
2714:
2712:
2709:
2707:
2704:
2701:
2697:
2696:quarter-comma
2693:
2690:
2689:
2687:
2685:
2681:
2675:
2672:
2670:
2667:
2665:
2662:
2660:
2657:
2655:
2652:
2650:
2647:
2645:
2642:
2639:
2635:
2632:
2630:
2627:
2625:
2622:
2620:
2617:
2615:
2612:
2610:
2607:
2605:
2602:
2600:
2597:
2596:
2594:
2592:
2588:
2585:
2583:
2579:
2573:
2572:Tonality flux
2570:
2568:
2565:
2563:
2560:
2558:
2555:
2553:
2550:
2548:
2545:
2543:
2540:
2536:
2533:
2531:
2528:
2527:
2526:
2523:
2521:
2518:
2516:
2513:
2511:
2508:
2506:
2503:
2502:
2500:
2498:
2494:
2488:
2485:
2483:
2480:
2478:
2475:
2473:
2470:
2468:
2465:
2463:
2460:
2458:
2455:
2453:
2450:
2448:
2445:
2443:
2440:
2438:
2435:
2433:
2430:
2429:
2427:
2423:
2419:
2412:
2407:
2405:
2400:
2398:
2393:
2392:
2389:
2381:
2380:0-486-43406-0
2377:
2373:
2369:
2368:
2355:
2349:
2341:
2340:
2332:
2324:
2320:
2316:
2312:
2308:
2304:
2300:
2296:
2292:
2285:
2270:
2266:
2260:
2258:
2249:
2245:
2241:
2237:
2233:
2229:
2225:
2221:
2217:
2210:
2206:
2195:
2192:
2190:
2187:
2185:
2182:
2180:
2177:
2175:
2172:
2170:
2169:Pseudo-octave
2167:
2165:
2162:
2160:
2157:
2155:
2152:
2150:
2147:
2145:
2142:
2140:
2137:
2135:
2132:
2130:
2127:
2125:
2122:
2120:
2117:
2115:
2112:
2110:
2107:
2105:
2102:
2100:
2099:
2095:
2093:
2090:
2089:
2087:
2076:
2065:
2061:
2058:
2056:
2053:
2051:
2048:
2046:
2043:
2041:
2038:
2036:
2033:
2031:
2028:
2026:
2023:
2020:
2017:
2014:
2010:
2006:
2002:
1998:
1995:
1993:
1990:
1987:
1983:
1980:, created by
1979:
1978:43-tone scale
1976:
1973:
1970:
1967:
1963:
1959:
1956:
1953:
1952:
1946:
1944:
1943:
1934:
1930:
1905:
1894:
1890:
1886:
1882:
1878:
1865:
1863:
1860:
1857:
1846:
1833:
1831:
1828:
1803:
1781:
1777:
1772:
1768:
1756:
1754:
1751:
1748:
1714:
1713:wolf interval
1709:
1696:
1694:
1691:
1688:
1684:
1680:
1658:
1384:
1379:
1375:
1363:
1361:
1358:
1357:
1356:
1353:
1350:
1283:
1279:
1269:
1260:
1253:
1241:
1239:Play meantone
1229:
1217:
1208:
1192:
1187:
1172:
1163:
1159:
1153:
1152:perfect fifth
1149:
1145:
1142:
1138:
1137:
1136:
1134:
1130:
1125:
1124:values used.
1123:
1119:
1115:
1111:
1107:
1106:tuning system
1097:
1095:
1091:
1090:
1085:
1084:
1079:
1074:
1072:
1068:
1064:
1060:
1056:
1052:
1041:
1038:
1030:
1020:
1016:
1012:
1006:
1005:
1001:
996:This section
994:
990:
985:
984:
976:
974:
970:
966:
965:concert pitch
962:
958:
954:
949:
946:
942:
937:
923:
919:
909:
908:Danse Macabre
905:
901:
900:Gustav Mahler
897:
893:
889:
884:
882:
881:
876:
872:
871:
866:
862:
858:
854:
850:
846:
845:Biagio Marini
840:
829:
826:
818:
808:
804:
800:
794:
793:
789:
784:This section
782:
778:
773:
772:
759:
757:
754:
753:
749:
745:
743:
740:
739:
735:
731:
729:
726:
725:
679:
677:
674:
673:
669:
667:
664:
663:
659:
656:
652:
648:
645:
644:
640:
638:
634:
630:
626:
622:
618:
615:
614:
610:
608:
604:
600:
597:
596:
592:
589:
588:
585:
582:
580:
576:
572:
568:
564:
554:
544:
540:
536:
534:
530:
526:
522:
518:
514:
510:
506:
502:
497:
495:
491:
481:
471:
466:
455:
452:
444:
434:
430:
426:
420:
419:
415:
410:This section
408:
404:
399:
398:
390:
388:
384:
380:
378:
377:tuning system
373:
370:Interference
368:
366:
362:
358:
354:
350:
349:concert bands
346:
342:
338:
333:
331:
327:
323:
319:
315:
307:
303:
299:
295:
291:
287:
284:
280:
276:
272:
269:
265:
261:
260:
259:
256:
254:
250:
246:
242:
238:
231:
227:
222:
214:
202:
198:
195:
192:
189:
188:
187:
185:
181:
170:
162:
157:
147:
139:
134:
124:
121:
113:
102:
99:
95:
92:
88:
85:
81:
78:
74:
71: –
70:
66:
65:Find sources:
59:
55:
49:
48:
43:This article
41:
37:
32:
31:
19:
18:Tuning system
3192:Savart wheel
3174:
3134:Tonal memory
3119:Ear training
2991:
2930:Music theory
2887:Lambda scale
2794:Arabic maqam
2751:Werckmeister
2582:Temperaments
2417:
2371:
2353:
2348:
2338:
2331:
2301:(3): 43–56.
2298:
2294:
2284:
2273:. Retrieved
2271:. 2019-03-11
2268:
2223:
2219:
2209:
2096:
2085:
2075:Music portal
2013:Wendy Carlos
2009:gamma scales
1982:Harry Partch
1942:temperaments
1940:
1938:
1848:than, say, D
1682:
1354:
1351:
1280:so that all
1275:
1259:Werckmeister
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1105:
1103:
1087:
1081:
1075:
1069:such as the
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1027:October 2014
1024:
1009:Please help
997:
956:
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941:Appalachians
938:
921:
885:
878:
868:
856:
855:(who in the
842:
821:
815:October 2014
812:
797:Please help
785:
722:(repeating)
676:concert harp
637:tenor guitar
583:
560:
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498:
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447:
441:October 2014
438:
423:Please help
411:
393:Open strings
381:
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369:
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268:ear training
263:
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243:. The term "
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52:Please help
47:verification
44:
3197:Tuning fork
3093:Pitch class
2967:Mathematics
2956:Composition
2882:Delta scale
2877:Gamma scale
2867:Alpha scale
2769:non-Western
2767:Traditional
2462:Pitch class
2442:Millioctave
2425:Measurement
2226:: S63–S69.
2194:Xenharmonic
1927:meantone),
1687:microtuners
1302:, which at
1127:Due to the
904:Béla Bartók
655:bass guitar
647:double bass
641:C, G, D, A
625:tenor banjo
611:G, D, A, E
590:Instrument
513:double bass
509:bass guitar
494:open string
492:, the term
365:clarinetist
337:tuning fork
245:out of tune
228:harp using
138:major third
3187:Pitch pipe
3170:Microtuner
3107:Perception
3073:Enharmonic
2987:Set theory
2982:Psychology
2977:Philosophy
2972:Musicology
2961:Definition
2941:Aesthetics
2872:Beta scale
2850:Non-octave
2841:Tetrachord
2743:Kirnberger
2706:Schismatic
2275:2022-08-29
2201:References
2159:Open chord
2139:Microtuner
2092:3rd bridge
1906:(extended
1679:comma pump
1094:organology
1071:snare drum
957:tuned down
953:down-tuned
839:scordatura
756:cavaquinho
651:mando-bass
633:mandocello
533:scordatura
306:mouthpiece
224:Tuning of
80:newspapers
3043:Frequency
2862:A12 scale
2816:Octoechos
2781:Shí-èr-lǜ
2730:Irregular
2547:Otonality
2487:Microtone
2315:0148-9267
2248:138058574
2240:1296-2074
1826:meantone.
1747:Shí-èr-lǜ
1282:intervals
1215:Play just
1122:frequency
998:does not
922:Contrasts
786:does not
412:does not
383:Harmonics
355:440 or a
320:, are of
3212:Category
3153:See also
3054:Notation
2946:Analysis
2747:Vallotti
2700:septimal
2692:Meantone
2452:Interval
2082:See also
1986:composer
1964:used in
1851:♭
1724:♭
1718:♯
1057:such as
933:♭
927:♯
913:♭
867:, whose
719:♭
713:♭
707:♭
701:♭
695:♭
689:♭
683:♭
603:mandolin
567:beatless
316:such as
273:Turning
3180:Beating
2951:Aspects
2836:Slendro
2786:Dastgah
2711:Miracle
2674:96-tone
2669:72-tone
2664:58-tone
2659:53-tone
2654:41-tone
2649:34-tone
2644:31-tone
2634:24-tone
2629:23-tone
2624:22-tone
2619:19-tone
2614:17-tone
2609:15-tone
2604:12-tone
2535:7-limit
2530:5-limit
2323:1576941
1958:Slendro
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1133:timbres
1114:pitches
1059:timpani
1019:removed
1004:sources
807:removed
792:sources
728:ukulele
629:mandola
593:Tuning
505:fourths
433:removed
418:sources
318:cymbals
279:tension
201:pitches
94:scholar
2992:Tuning
2804:Mugham
2790:Maqam
2684:Linear
2638:pieces
2599:6-tone
2520:Hexany
2447:Savart
2378:
2321:
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2060:Hexany
2007:, and
1637:, and
1141:octave
1065:, and
945:Ozarks
930:-D-A-E
902:, and
875:Mozart
666:guitar
599:violin
529:fifths
523:, and
517:Violin
501:guitar
361:oboist
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283:violin
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184:tuning
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2755:Young
2716:Magic
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2432:Pitch
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2244:S2CID
2005:delta
1997:Alpha
1972:Pelog
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1900:... .
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1310:cents
1150:, or
1118:music
1112:, or
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1051:tuned
621:cello
617:viola
579:cents
525:cello
521:viola
490:music
372:beats
341:piano
249:sharp
180:music
101:JSTOR
87:books
3066:A440
3045:and
2826:Raga
2437:Cent
2376:ISBN
2311:ISSN
2236:ISSN
2144:MIDI
2001:beta
1960:, a
1805:and
1721:to D
1290:125
1176:I IV
1086:and
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1000:cite
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863:and
790:any
788:cite
575:A220
552:Play
511:and
479:Play
416:any
414:cite
387:node
347:and
302:bell
298:pipe
275:pegs
253:flat
230:Korg
168:Play
145:Play
73:news
2303:doi
2228:doi
2011:of
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