2687:
1582:
1725:
1251:
1659:
1541:
1320:
1218:
1509:
1833:
1624:
1463:
1361:
1288:
1692:
1394:
1186:
1800:
1760:
1431:
1153:
1900:
152:
2974:
140:
43:
1786:
1567:
1495:
908:
2450:
785:
747:
709:
667:
778:
740:
702:
660:
588:
instruments), it is also convenient to call the component partials "harmonics", but not strictly correct, because harmonics are numbered the same even when missing, while partials and overtones are only counted when present. This chart demonstrates how the three types of names (partial, overtone, and
578:
is any partial higher than the lowest partial in a compound tone. The relative strengths and frequency relationships of the component partials determine the timbre of an instrument. The similarity between the terms overtone and partial sometimes leads to their being loosely used interchangeably in a
870:
While it is true that electronically produced periodic tones (e.g. square waves or other non-sinusoidal waves) have "harmonics" that are whole number multiples of the fundamental frequency, practical instruments do not all have this characteristic. For example, higher "harmonics" of piano notes are
1046:
of harmonics by the slight pressure of the finger on the open string is more useful. When produced by pressing slightly on the various nodes of the open strings they are called 'natural harmonics'. ... Violinists are well aware that the longer the string in proportion to its thickness, the greater
1062:
The following table displays the stop points on a stringed instrument at which gentle touching of a string will force it into a harmonic mode when vibrated. String harmonics (flageolet tones) are described as having a "flutelike, silvery quality" that can be highly effective as a special color or
412:
In music, harmonics are used on string instruments and wind instruments as a way of producing sound on the instrument, particularly to play higher notes and, with strings, obtain notes that have a unique sound quality or "tone colour". On strings, bowed harmonics have a "glassy", pure tone. On
413:
stringed instruments, harmonics are played by touching (but not fully pressing down the string) at an exact point on the string while sounding the string (plucking, bowing, etc.); this allows the harmonic to sound, a pitch which is always higher than the fundamental frequency of the string.
1860:, produced by playing an overtone on an already stopped string. As a performance technique, it is accomplished by using two fingers on the fingerboard, the first to shorten the string to the desired fundamental, with the second touching the node corresponding to the appropriate harmonic.
454:
Most acoustic instruments emit complex tones containing many individual partials (component simple tones or sinusoidal waves), but the untrained human ear typically does not perceive those partials as separate phenomena. Rather, a musical note is perceived as one sound, the quality or
478:, and thus are composed of partials that are nearly matched to the integer multiples of fundamental frequency and therefore resemble the ideal harmonics and are called "harmonic partials" or simply "harmonics" for convenience (although it's not strictly accurate to call a
583:
context, but they are counted differently, leading to some possible confusion. In the special case of instrumental timbres whose component partials closely match a harmonic series (such as with most strings and winds) rather than being inharmonic partials (such as with most
1037:
case, advancing the bow from the usual place where the fundamental note is produced, towards the bridge, the whole scale of harmonics may be produced in succession, on an old and highly resonant instrument. The employment of this means produces the effect called
234:
power supply frequency, the frequencies of the first three higher harmonics are 100 Hz (2nd harmonic), 150 Hz (3rd harmonic), 200 Hz (4th harmonic) and any addition of waves with these frequencies is periodic at 50 Hz.
1945:
Demonstration of 16 harmonics using electronic sine tones, starting with 110 Hz fundamental, 0.5s each. Note that each harmonic is presented at the same signal level as the fundamental; the sample tones sound louder as they increase in
551:, drum heads, and most percussion instruments, naturally produce an abundance of inharmonic partials and do not imply any particular pitch, and therefore cannot be used melodically or harmonically in the same way other instruments can.
1583:
439:
A whizzing, whistling tonal character, distinguishes all the harmonics both natural and artificial from the firmly stopped intervals; therefore their application in connection with the latter must always be carefully considered.
421:
Harmonics may be called "overtones", "partials", or "upper partials", and in some music contexts, the terms "harmonic", "overtone" and "partial" are used fairly interchangeably. But more precisely, the term "harmonic" includes
1726:
1252:
1660:
1542:
1321:
1219:
1510:
1834:
1625:
1464:
1362:
1289:
1693:
1395:
1187:
399:
one of these positions, then these other characteristic modes will be suppressed. The tonal harmonics from these other characteristic modes will then also be suppressed. Consequently, the tonal harmonics from the
1801:
1761:
1432:
1939:
1918:
1154:
2454:
887:. Examples of these "other" instruments are xylophones, drums, bells, chimes, etc.; not all of their overtone frequencies make a simple whole number ratio with the fundamental frequency. (The
562:
introduces the notion of pseudo-harmonic partials, in which the frequency of each partial is aligned to match the pitch of a corresponding note in a pseudo-just tuning, thereby maximizing the
2313:
1916:
1937:
1031:
994:
957:
390:
358:
306:
274:
509:
harmonics—at least in theory. In practical use, no real acoustic instrument behaves as perfectly as the simplified physical models predict; for example, instruments made of
922:
Harmonics may be singly produced (1) by varying the point of contact with the bow, or (2) by slightly pressing the string at the nodes, or divisions of its aliquot parts (
1938:
1917:
1071:. It is unusual to encounter natural harmonics higher than the fifth partial on any stringed instrument except the double bass, on account of its much longer strings.
531:. Some acoustic instruments emit a mix of harmonic and inharmonic partials but still produce an effect on the ear of having a definite fundamental pitch, such as
2161:— Minimally technical summary of string acoustics research given at conference; discusses listeners' perceptions of pianos' inharmonic partials.
1053:
843:
the tuning of strings that are not tuned to the unison. For example, lightly fingering the node found halfway down the highest string of a
2583:
3010:
493:, and are often long and thin, such as a guitar string or a column of air open at both ends (as with the metallic modern orchestral
155:
Two different notations of natural harmonics on the cello. First as sounded (more common), then as fingered (easier to sightread).
2896:
3339:
2459:
2133:
3359:
2591:
2338:
3268:
226:, electronic power transmission, radio technology, and other fields. For example, if the fundamental frequency is 50
2623:
2232:
107:
2252:
126:
79:
839:
by string players, which have an eerie quality, as well as being high in pitch. Harmonics may be used to check at a
213:
at the fundamental frequency, the sum of harmonics is also periodic at that frequency. The set of harmonics forms a
426:
pitches in a harmonic series (including the fundamental frequency) while the term "overtone" only includes pitches
2465:
797:, it is possible to play the upper harmonics without the fundamental note being present. In a simple case (e.g.,
86:
3003:
64:
2485:
2141:
798:
3110:
247:> 1, will have nodes that are not vibrating. For example, the 3rd characteristic mode will have nodes at
1994:
871:
not true harmonics but are "overtones" and can be very sharp, i.e. a higher frequency than given by a pure
93:
3349:
3344:
3105:
999:
962:
925:
805:, but in more complex cases many other pitch variations are obtained. In some cases it also changes the
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2996:
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1930:
1909:
366:
334:
282:
250:
75:
60:
31:
17:
3172:
3033:
2911:
892:
2066:
521:
3293:
2791:
2648:
2616:
2358:
2079:
872:
459:
of that sound being a result of the relative strengths of the individual partials. Many acoustic
215:
53:
3263:
3065:
2730:
2640:
2382:
2257:
2538:
505:, also produce partials resembling harmonics. However they only produce partials matching the
3313:
3278:
3058:
3043:
2871:
2769:
2673:
2526:
2347:
1131:
888:
189:
3227:
1741:
1410:
527:
Partials whose frequencies are not integer multiples of the fundamental are referred to as
513:
8:
3308:
2891:
2801:
2029:
2004:
1999:
1857:
876:
794:
510:
231:
2577:
2566:
3334:
2977:
2823:
2813:
2774:
2609:
2401:
2330:
2276:
2200:
2083:
2024:
2019:
828:
820:
585:
168:
2686:
2112:
Petrucci Music
Library / International Music Score Library Project (IMSLP) (imslp.org)
100:
3232:
3209:
3202:
3182:
3177:
3162:
3135:
3080:
3048:
2947:
2779:
2280:
2228:
2192:
2087:
2044:
1989:
622:
475:
210:
2405:
3298:
3237:
3152:
2957:
2876:
2840:
2808:
2759:
2668:
2534:
2493:
2469:
2420:
2391:
2373:
2354:
2334:
2322:
2305:
2301:
2266:
2248:
2218:
2184:
2145:
2075:
2034:
1969:
1873:
1598:
1486:
1447:
1341:
1336:
1267:
896:
880:
864:
810:
650:
559:
555:
494:
2377:
3242:
3187:
3157:
3145:
3100:
3085:
2952:
2906:
2747:
2705:
2222:
1984:
1869:
1640:
1098:
916:
832:
194:
176:
2561:
1785:
1566:
1494:
489:
Oscillators that produce harmonic partials behave somewhat like one-dimensional
3354:
2901:
2886:
2833:
1979:
1039:
144:
2396:
2326:
2271:
1876:
is able to bring out different harmonics on the single string of his modified
30:
This article is about the components of periodic signals. For other uses, see
3328:
3197:
3075:
3070:
2866:
2828:
2796:
2751:
2713:
2663:
2658:
2572:
2424:
2196:
2107:
1885:
1643:
1604:
1558:
1525:
1304:
1202:
1068:
616:
528:
809:
of the note. This is part of the normal method of obtaining higher notes in
539:, vibraphones, marimbas, and certain pure-sounding bells or chimes. Antique
3140:
2861:
1744:
1413:
1108:
1102:
544:
540:
151:
3117:
3090:
3053:
2881:
2693:
2039:
1964:
1881:
1877:
1817:
1777:
1272:
824:
815:
468:
464:
3288:
2204:
3127:
2942:
2932:
2718:
1955:
563:
460:
222:
The term is employed in various disciplines, including music, physics,
566:
of that pseudo-harmonic timbre with notes of that pseudo-just tuning.
497:). Wind instruments whose air column is open at only one end, such as
3273:
3258:
3095:
3038:
3025:
2723:
2653:
2632:
2596:
2497:
2188:
2014:
1084:
899:
of the collection of vibrations in some single periodic phenomenon.)
884:
536:
490:
327:
have nodes at these points. These other characteristic modes will be
223:
180:
164:
42:
27:
Wave with frequency an integer multiple of the fundamental frequency
3283:
2988:
2818:
2501:
2158:
There are many ways to make matters worse, but very few to improve.
1884:
technique halfway between hitting and bowing the strings. Composer
1709:
863:
of the way down the second highest string. For the human voice see
575:
502:
486:, the first being actual and the second being theoretical).
139:
3303:
2764:
2009:
1974:
1480:
589:
harmonic) are counted (assuming that the harmonics are present):
548:
498:
184:
160:
3219:
2576:
1676:
1378:
1235:
1170:
1137:
1064:
840:
806:
802:
517:
471:
456:
1868:
Harmonics may be either used in or considered as the basis of
907:
801:) this has the effect of making the note go up in pitch by an
3166:
2937:
844:
580:
532:
227:
2601:
2567:
Harmonics, partials and overtones from fundamental frequency
2251:; Milne, A.; Tiedje, S.; Prechtl, A.; Plamondon, J. (2009).
784:
746:
708:
666:
2927:
831:
it is possible to produce very pure sounding notes, called
408:
is a multiple of 3, will be made relatively more prominent.
2247:
777:
739:
701:
659:
2253:"Spectral tools for dynamic tonality and audio morphing"
2132:
Galembo, Alexander; Cuddly, Lola L. (2 December 1997).
2418:
2371:
2299:
1047:
the number of upper harmonics it can be made to yield.
1004:
967:
930:
847:
produces the same pitch as lightly fingering the node
543:
are known for producing multiple harmonic partials or
371:
339:
287:
255:
1002:
965:
928:
569:
369:
337:
285:
253:
875:. This is especially true of instruments other than
474:
string, produce complex tones that are more or less
1924:
Violin natural harmonic stop points on the A string
67:. Unsourced material may be challenged and removed.
2114:(site sub-index & mini-bio for Scholz). Canada
2065:
1025:
988:
951:
384:
352:
300:
268:
1888:uses harmonics to generate music electronically.
3326:
2378:"Invariant fingerings across a tuning continuum"
2520:
2518:
197:. The fundamental frequency is also called the
3004:
2617:
2241:
2131:
2587:(11th ed.). Cambridge University Press.
2515:
2483:
2080:10.1287/7648739e-8e59-466e-82cb-3ded22bbebf6
524:, tend to have not-quite-integer partials.
315:is the length of the string. In fact, each
3011:
2997:
2624:
2610:
2562:The Feynman Lectures on Physics: Harmonics
902:
2395:
2270:
1054:Grove's Dictionary of Music and Musicians
127:Learn how and when to remove this message
2571:
2524:
2365:
2217:
906:
150:
138:
2539:10.1093/gmo/9781561592630.article.14882
2412:
2293:
1851:
516:wood, instead of metal, or strung with
14:
3327:
2306:"Tuning continua and keyboard layouts"
2134:"Large grand and small upright pianos"
2063:
1856:Occasionally a score will call for an
2992:
2605:
2304:; Plamondon, James (29 August 2008).
2170:
3018:
1863:
147:of a vibrating string are harmonics.
65:adding citations to reliable sources
36:
2430:(technical report). Thumtronics Inc
2211:
1026:{\displaystyle {\tfrac {\ 1\ }{4}}}
989:{\displaystyle {\tfrac {\ 1\ }{3}}}
952:{\displaystyle {\tfrac {\ 1\ }{2}}}
203:; the other harmonics are known as
24:
2171:Court, Sophie R.A. (April 1927). "
1954:Problems playing these files? See
1898:
570:Partials, overtones, and harmonics
433:
25:
3371:
2597:Hear and see harmonics on a Piano
2555:
2973:
2972:
2685:
2453: This article incorporates
2448:
2344:from the original on 2022-10-09.
2314:Journal of Mathematics and Music
1935:
1914:
1880:by slightly altering his unique
1784:
1565:
1493:
783:
776:
745:
738:
707:
700:
665:
658:
41:
2490:MyFavoritegamez.com / SciVee.tv
2477:
2466:General Services Administration
2441:
2376:; Plamondon, J. (Winter 2007).
2224:Tuning, Timbre, Spectrum, Scale
385:{\displaystyle {\tfrac {2}{3}}}
353:{\displaystyle {\tfrac {1}{3}}}
301:{\displaystyle {\tfrac {2}{3}}}
269:{\displaystyle {\tfrac {1}{3}}}
52:needs additional citations for
2164:
2125:
2100:
2064:Walker, Russell (2019-06-14).
2057:
911:Playing a harmonic on a string
416:
13:
1:
3340:Guitar performance techniques
2631:
2142:Acoustical Society of America
2050:
547:. Other oscillators, such as
444:
3360:Spectrum (physical sciences)
3173:Perception as interpretation
2525:Marrocco, W. Thomas (2001).
2486:"Free Online Games for Kids"
1995:Harmonics (electrical power)
827:also produces harmonics. On
404:characteristic modes, where
7:
2533:. Oxford University Press.
2484:George alike (2011-01-21).
1891:
10:
3376:
2108:"Category:Scholz, Richard"
914:
323:not a multiple of 3, will
29:
3251:
3218:
3126:
3024:
2968:
2920:
2849:
2746:
2704:
2680:
2639:
2397:10.1162/comj.2007.31.4.15
2327:10.1080/17459730701828677
2272:10.1162/comj.2009.33.2.71
2237:– via Google books.
1067:) when used and heard in
319:characteristic mode, for
243:characteristic mode, for
32:Harmonic (disambiguation)
2423:; Plamondon, J. (2006).
1107:
1097:
867:, which uses harmonics.
3294:Relational frame theory
3269:Higher nervous activity
2649:Architectural acoustics
2584:Encyclopædia Britannica
2359:University of Wisconsin
903:On stringed instruments
209:. As all harmonics are
3264:Experiential avoidance
2736:Fletcher–Munson curves
2731:Equal-loudness contour
2641:Acoustical engineering
2461:Federal Standard 1037C
2455:public domain material
2383:Computer Music Journal
2258:Computer Music Journal
1903:
1342:septimal minor seventh
1060:
1027:
990:
953:
912:
522:brass or steel strings
452:
410:
386:
354:
302:
270:
156:
148:
3279:Ironic process theory
3044:Cognitive flexibility
2872:Hermann von Helmholtz
2770:Fundamental frequency
2674:Sympathetic resonance
2357:pers. academic site.
1902:
1028:
991:
954:
920:
910:
889:fundamental frequency
813:, where it is called
437:
387:
355:
303:
271:
237:
190:fundamental frequency
154:
142:
1852:Artificial harmonics
1000:
963:
926:
367:
335:
283:
251:
61:improve this article
3309:Thought suppression
2892:Werner Meyer-Eppler
2802:Missing fundamental
2531:Oxford Music Online
2175:Hanna Rademacher".
2030:Spherical harmonics
2005:Harmonic oscillator
2000:Harmonic generation
1858:artificial harmonic
795:musical instruments
529:inharmonic partials
183:that is a positive
3350:String instruments
3345:Telecommunications
2775:Frequency spectrum
2025:Scale of harmonics
2020:Pythagorean tuning
1904:
1872:systems. Composer
1609:(‘the lost chord’)
1346:(‘the lost chord’)
1115:(offset by octave)
1044:(2) The production
1023:
1021:
986:
984:
949:
947:
913:
829:string instruments
821:extended technique
586:pitched percussion
535:, strings plucked
443:— Richard Scholz (
430:the fundamental.
382:
380:
350:
348:
298:
296:
266:
264:
169:telecommunications
157:
149:
3322:
3321:
3081:Critical thinking
3049:Cognitive liberty
2986:
2985:
2948:Musical acoustics
2780:harmonic spectrum
2302:Sethares, William
2173:Golo und Genovefa
2140:(Press release).
2045:Xenharmonic music
1990:Harmonic analysis
1940:
1919:
1864:Other information
1845:
1844:
1610:
1479:lesser undecimal
1347:
1123:
1116:
1095:
1020:
1015:
1009:
983:
978:
972:
946:
941:
935:
791:
790:
623:Longitudinal wave
482: a
379:
347:
331:at the positions
295:
263:
137:
136:
129:
111:
16:(Redirected from
3367:
3019:Mental processes
3013:
3006:
2999:
2990:
2989:
2976:
2975:
2877:Carleen Hutchins
2809:Combination tone
2696:
2689:
2669:String vibration
2626:
2619:
2612:
2603:
2602:
2588:
2580:
2578:"Harmonic"
2549:
2548:
2546:
2545:
2522:
2513:
2512:
2510:
2509:
2500:. Archived from
2498:10.4016/26742.01
2481:
2475:
2474:
2473:
2468:. Archived from
2452:
2451:
2445:
2439:
2438:
2436:
2435:
2429:
2416:
2410:
2409:
2399:
2369:
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2343:
2310:
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2288:
2287:
2274:
2245:
2239:
2238:
2215:
2209:
2208:
2189:10.2307/40043442
2168:
2162:
2160:
2155:
2153:
2144:. Archived from
2129:
2123:
2122:
2120:
2119:
2104:
2098:
2097:
2095:
2094:
2069:
2067:"Russell Walker"
2061:
2035:Stretched octave
1970:Electronic tuner
1942:
1941:
1931:Harmonics 110x16
1921:
1920:
1910:Violin harmonics
1901:
1874:Arnold Dreyblatt
1841:
1840:
1839:
1837:
1808:
1807:
1806:
1804:
1789:
1788:
1768:
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1766:
1764:
1733:
1732:
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1700:
1699:
1698:
1696:
1667:
1666:
1665:
1663:
1632:
1631:
1630:
1628:
1608:
1599:harmonic seventh
1590:
1589:
1588:
1586:
1570:
1569:
1549:
1548:
1547:
1545:
1517:
1516:
1515:
1513:
1498:
1497:
1487:augmented fourth
1471:
1470:
1469:
1467:
1448:just major third
1439:
1438:
1437:
1435:
1402:
1401:
1400:
1398:
1369:
1368:
1367:
1365:
1345:
1337:harmonic seventh
1328:
1327:
1326:
1324:
1296:
1295:
1294:
1292:
1268:just major third
1259:
1258:
1257:
1255:
1234:doubled perfect
1226:
1225:
1224:
1222:
1194:
1193:
1192:
1190:
1161:
1160:
1159:
1157:
1122:(octave shifted)
1121:
1114:
1091:
1078:
1077:
1058:
1045:
1036:
1035:(1) In the first
1032:
1030:
1029:
1024:
1022:
1016:
1013:
1007:
1005:
995:
993:
992:
987:
985:
979:
976:
970:
968:
958:
956:
955:
950:
948:
942:
939:
933:
931:
865:Overtone singing
862:
860:
859:
856:
853:
811:wind instruments
787:
780:
763:
757:
749:
742:
725:
719:
711:
704:
687:
681:
677:
669:
662:
651:fundamental tone
643:
637:
633:
603:
592:
591:
560:dynamic tonality
495:transverse flute
449:
448: 1888-1912
446:
395:. If the player
391:
389:
388:
383:
381:
372:
359:
357:
356:
351:
349:
340:
307:
305:
304:
299:
297:
288:
275:
273:
272:
267:
265:
256:
206:higher harmonics
187:multiple of the
132:
125:
121:
118:
112:
110:
69:
45:
37:
21:
3375:
3374:
3370:
3369:
3368:
3366:
3365:
3364:
3325:
3324:
3323:
3318:
3247:
3214:
3122:
3101:Problem solving
3086:Decision-making
3020:
3017:
2987:
2982:
2964:
2916:
2907:D. Van Holliday
2845:
2814:Mersenne's laws
2748:Audio frequency
2742:
2706:Psychoacoustics
2700:
2699:
2692:
2678:
2635:
2630:
2558:
2553:
2552:
2543:
2541:
2523:
2516:
2507:
2505:
2482:
2478:
2458:
2449:
2447:
2446:
2442:
2433:
2431:
2427:
2417:
2413:
2370:
2366:
2350:
2346:
2341:
2308:
2300:Milne, Andrew;
2298:
2294:
2285:
2283:
2246:
2242:
2235:
2216:
2212:
2179:(book review).
2169:
2165:
2151:
2149:
2130:
2126:
2117:
2115:
2106:
2105:
2101:
2092:
2090:
2062:
2058:
2053:
1985:Guitar harmonic
1961:
1960:
1952:
1950:
1949:
1948:
1947:
1943:
1936:
1933:
1927:
1926:
1925:
1922:
1915:
1912:
1905:
1899:
1894:
1870:just intonation
1866:
1854:
1835:
1832:
1831:
1802:
1799:
1798:
1783:
1762:
1759:
1758:
1727:
1724:
1723:
1694:
1691:
1690:
1675:fourth perfect
1661:
1658:
1657:
1626:
1623:
1622:
1607:
1602:
1584:
1581:
1580:
1564:
1543:
1540:
1539:
1511:
1508:
1507:
1492:
1485:undecimal semi-
1484:
1465:
1462:
1461:
1433:
1430:
1429:
1417:harmonic ninth
1416:
1396:
1393:
1392:
1363:
1360:
1359:
1344:
1340:
1322:
1319:
1318:
1290:
1287:
1286:
1271:
1253:
1250:
1249:
1220:
1217:
1216:
1188:
1185:
1184:
1155:
1152:
1151:
1135:
1120:
1112:
1099:Audio frequency
1093:
1090:
1059:
1051:
1043:
1034:
1006:
1003:
1001:
998:
997:
969:
966:
964:
961:
960:
932:
929:
927:
924:
923:
919:
917:String harmonic
905:
895:of the longest
873:harmonic series
857:
854:
851:
850:
848:
761:
758:= 1760 Hz
755:
723:
720:= 1320 Hz
717:
685:
679:
675:
641:
635:
631:
625:representation
619:representation
601:
599:
572:
554:Building on of
451:
447:
436:
434:Characteristics
419:
370:
368:
365:
364:
338:
336:
333:
332:
286:
284:
281:
280:
254:
252:
249:
248:
216:harmonic series
195:periodic signal
177:sinusoidal wave
133:
122:
116:
113:
70:
68:
58:
46:
35:
28:
23:
22:
15:
12:
11:
5:
3373:
3363:
3362:
3357:
3352:
3347:
3342:
3337:
3320:
3319:
3317:
3316:
3311:
3306:
3301:
3296:
3291:
3289:Mental fatigue
3286:
3281:
3276:
3271:
3266:
3261:
3255:
3253:
3249:
3248:
3246:
3245:
3240:
3235:
3230:
3224:
3222:
3216:
3215:
3213:
3212:
3207:
3206:
3205:
3200:
3195:
3185:
3180:
3175:
3170:
3160:
3155:
3150:
3149:
3148:
3138:
3132:
3130:
3124:
3123:
3121:
3120:
3115:
3114:
3113:
3108:
3098:
3093:
3088:
3083:
3078:
3073:
3068:
3063:
3062:
3061:
3051:
3046:
3041:
3036:
3030:
3028:
3022:
3021:
3016:
3015:
3008:
3001:
2993:
2984:
2983:
2981:
2980:
2969:
2966:
2965:
2963:
2962:
2961:
2960:
2955:
2945:
2940:
2935:
2930:
2924:
2922:
2921:Related topics
2918:
2917:
2915:
2914:
2909:
2904:
2902:Joseph Sauveur
2899:
2894:
2889:
2887:Marin Mersenne
2884:
2879:
2874:
2869:
2864:
2859:
2853:
2851:
2847:
2846:
2844:
2843:
2838:
2837:
2836:
2826:
2821:
2816:
2811:
2806:
2805:
2804:
2799:
2794:
2784:
2783:
2782:
2772:
2767:
2762:
2756:
2754:
2744:
2743:
2741:
2740:
2739:
2738:
2728:
2727:
2726:
2721:
2710:
2708:
2702:
2701:
2698:
2697:
2690:
2682:
2681:
2679:
2677:
2676:
2671:
2666:
2661:
2656:
2651:
2645:
2643:
2637:
2636:
2629:
2628:
2621:
2614:
2606:
2600:
2599:
2594:
2589:
2575:, ed. (1911).
2573:Chisholm, Hugh
2569:
2564:
2557:
2556:External links
2554:
2551:
2550:
2527:"Kennan, Kent"
2514:
2476:
2472:on 2022-01-22.
2440:
2421:Sethares, W.A.
2411:
2374:Sethares, W.A.
2364:
2292:
2249:Sethares, W.A.
2240:
2234:978-1852337971
2233:
2219:Sethares, W.A.
2210:
2163:
2124:
2099:
2055:
2054:
2052:
2049:
2048:
2047:
2042:
2037:
2032:
2027:
2022:
2017:
2012:
2007:
2002:
1997:
1992:
1987:
1982:
1980:Fourier series
1977:
1972:
1967:
1951:
1944:
1934:
1929:
1928:
1923:
1913:
1908:
1907:
1906:
1897:
1896:
1895:
1893:
1890:
1865:
1862:
1853:
1850:
1849:
1848:
1847:
1846:
1843:
1842:
1829:
1826:
1823:
1820:
1814:
1810:
1809:
1796:
1793:
1790:
1780:
1774:
1770:
1769:
1756:
1753:
1750:
1747:
1739:
1735:
1734:
1721:
1718:
1715:
1712:
1706:
1702:
1701:
1688:
1685:
1682:
1679:
1673:
1669:
1668:
1655:
1652:
1649:
1646:
1638:
1634:
1633:
1620:
1617:
1614:
1611:
1596:
1592:
1591:
1578:
1575:
1572:
1561:
1555:
1551:
1550:
1537:
1534:
1531:
1528:
1523:
1519:
1518:
1505:
1502:
1499:
1489:
1477:
1473:
1472:
1459:
1456:
1453:
1450:
1445:
1441:
1440:
1427:
1424:
1421:
1418:
1408:
1404:
1403:
1390:
1387:
1384:
1381:
1377:third perfect
1375:
1371:
1370:
1357:
1354:
1351:
1348:
1334:
1330:
1329:
1316:
1313:
1310:
1307:
1302:
1298:
1297:
1284:
1281:
1278:
1275:
1265:
1261:
1260:
1247:
1244:
1241:
1238:
1232:
1228:
1227:
1214:
1211:
1208:
1205:
1200:
1196:
1195:
1182:
1179:
1176:
1173:
1169:first perfect
1167:
1163:
1162:
1149:
1146:
1143:
1140:
1129:
1125:
1124:
1117:
1106:
1096:
1087:
1082:
1049:
1040:sul ponticello
1019:
1012:
982:
975:
945:
938:
915:Main article:
904:
901:
789:
788:
781:
774:
771:
768:
765:
759:
751:
750:
743:
736:
733:
730:
727:
721:
713:
712:
705:
698:
695:
692:
689:
683:
671:
670:
663:
656:
653:
648:
645:
639:
627:
626:
620:
614:
611:
608:
605:
596:
571:
568:
463:, such as the
442:
435:
432:
418:
415:
397:gently touches
378:
375:
346:
343:
294:
291:
262:
259:
135:
134:
49:
47:
40:
26:
9:
6:
4:
3:
2:
3372:
3361:
3358:
3356:
3353:
3351:
3348:
3346:
3343:
3341:
3338:
3336:
3333:
3332:
3330:
3315:
3312:
3310:
3307:
3305:
3302:
3300:
3297:
3295:
3292:
3290:
3287:
3285:
3282:
3280:
3277:
3275:
3272:
3270:
3267:
3265:
3262:
3260:
3257:
3256:
3254:
3250:
3244:
3241:
3239:
3236:
3234:
3231:
3229:
3228:Consolidation
3226:
3225:
3223:
3221:
3217:
3211:
3208:
3204:
3201:
3199:
3196:
3194:
3191:
3190:
3189:
3186:
3184:
3181:
3179:
3176:
3174:
3171:
3168:
3164:
3161:
3159:
3156:
3154:
3151:
3147:
3144:
3143:
3142:
3139:
3137:
3134:
3133:
3131:
3129:
3125:
3119:
3116:
3112:
3109:
3107:
3104:
3103:
3102:
3099:
3097:
3094:
3092:
3089:
3087:
3084:
3082:
3079:
3077:
3076:Consciousness
3074:
3072:
3071:Comprehension
3069:
3067:
3064:
3060:
3057:
3056:
3055:
3052:
3050:
3047:
3045:
3042:
3040:
3037:
3035:
3032:
3031:
3029:
3027:
3023:
3014:
3009:
3007:
3002:
3000:
2995:
2994:
2991:
2979:
2971:
2970:
2967:
2959:
2956:
2954:
2951:
2950:
2949:
2946:
2944:
2941:
2939:
2936:
2934:
2931:
2929:
2926:
2925:
2923:
2919:
2913:
2910:
2908:
2905:
2903:
2900:
2898:
2897:Lord Rayleigh
2895:
2893:
2890:
2888:
2885:
2883:
2880:
2878:
2875:
2873:
2870:
2868:
2867:Ernst Chladni
2865:
2863:
2860:
2858:
2855:
2854:
2852:
2848:
2842:
2839:
2835:
2832:
2831:
2830:
2829:Standing wave
2827:
2825:
2822:
2820:
2817:
2815:
2812:
2810:
2807:
2803:
2800:
2798:
2797:Inharmonicity
2795:
2793:
2790:
2789:
2788:
2785:
2781:
2778:
2777:
2776:
2773:
2771:
2768:
2766:
2763:
2761:
2758:
2757:
2755:
2753:
2749:
2745:
2737:
2734:
2733:
2732:
2729:
2725:
2722:
2720:
2717:
2716:
2715:
2712:
2711:
2709:
2707:
2703:
2695:
2691:
2688:
2684:
2683:
2675:
2672:
2670:
2667:
2665:
2664:Soundproofing
2662:
2660:
2659:Reverberation
2657:
2655:
2652:
2650:
2647:
2646:
2644:
2642:
2638:
2634:
2627:
2622:
2620:
2615:
2613:
2608:
2607:
2604:
2598:
2595:
2593:
2590:
2586:
2585:
2579:
2574:
2570:
2568:
2565:
2563:
2560:
2559:
2540:
2536:
2532:
2528:
2521:
2519:
2504:on 2021-02-14
2503:
2499:
2495:
2491:
2487:
2480:
2471:
2467:
2463:
2462:
2456:
2444:
2426:
2422:
2415:
2407:
2403:
2398:
2393:
2389:
2385:
2384:
2379:
2375:
2368:
2360:
2356:
2349:
2340:
2336:
2332:
2328:
2324:
2320:
2316:
2315:
2307:
2303:
2296:
2282:
2278:
2273:
2268:
2264:
2260:
2259:
2254:
2250:
2244:
2236:
2230:
2226:
2225:
2220:
2214:
2206:
2202:
2198:
2194:
2190:
2186:
2182:
2178:
2174:
2167:
2159:
2148:on 2012-02-09
2147:
2143:
2139:
2138:acoustics.org
2135:
2128:
2113:
2109:
2103:
2089:
2085:
2081:
2077:
2073:
2072:Authors group
2068:
2060:
2056:
2046:
2043:
2041:
2038:
2036:
2033:
2031:
2028:
2026:
2023:
2021:
2018:
2016:
2013:
2011:
2008:
2006:
2003:
2001:
1998:
1996:
1993:
1991:
1988:
1986:
1983:
1981:
1978:
1976:
1973:
1971:
1968:
1966:
1963:
1962:
1959:
1957:
1932:
1911:
1889:
1887:
1886:Lawrence Ball
1883:
1879:
1875:
1871:
1861:
1859:
1838:
1830:
1827:
1824:
1821:
1819:
1815:
1812:
1811:
1805:
1797:
1794:
1791:
1787:
1781:
1779:
1775:
1772:
1771:
1765:
1757:
1754:
1751:
1748:
1746:
1743:
1740:
1737:
1736:
1730:
1722:
1719:
1716:
1713:
1711:
1708:septidecimal
1707:
1704:
1703:
1697:
1689:
1686:
1683:
1680:
1678:
1674:
1671:
1670:
1664:
1656:
1653:
1650:
1647:
1645:
1644:major seventh
1642:
1639:
1636:
1635:
1629:
1621:
1618:
1615:
1612:
1606:
1605:minor seventh
1600:
1597:
1594:
1593:
1587:
1579:
1576:
1573:
1568:
1562:
1560:
1559:neutral sixth
1556:
1553:
1552:
1546:
1538:
1535:
1532:
1529:
1527:
1526:perfect fifth
1524:
1521:
1520:
1514:
1506:
1503:
1500:
1496:
1490:
1488:
1482:
1478:
1475:
1474:
1468:
1460:
1457:
1454:
1451:
1449:
1446:
1443:
1442:
1436:
1428:
1425:
1422:
1419:
1415:
1412:
1409:
1406:
1405:
1399:
1391:
1388:
1385:
1382:
1380:
1376:
1373:
1372:
1366:
1358:
1355:
1352:
1349:
1343:
1338:
1335:
1332:
1331:
1325:
1317:
1314:
1311:
1308:
1306:
1305:perfect fifth
1303:
1300:
1299:
1293:
1285:
1282:
1279:
1276:
1274:
1269:
1266:
1263:
1262:
1256:
1248:
1245:
1242:
1239:
1237:
1233:
1230:
1229:
1223:
1215:
1212:
1209:
1206:
1204:
1203:perfect fifth
1201:
1198:
1197:
1191:
1183:
1180:
1177:
1174:
1172:
1168:
1165:
1164:
1158:
1150:
1147:
1144:
1141:
1139:
1133:
1130:
1127:
1126:
1118:
1110:
1104:
1100:
1088:
1086:
1083:
1080:
1079:
1076:
1075:
1074:
1073:
1072:
1070:
1069:orchestration
1066:
1056:
1055:
1048:
1041:
1017:
1010:
980:
973:
943:
936:
918:
909:
900:
898:
894:
890:
886:
882:
878:
874:
868:
866:
846:
842:
838:
834:
830:
826:
822:
818:
817:
812:
808:
804:
800:
796:
786:
782:
779:
775:
773:4th harmonic
772:
770:3rd overtone
769:
766:
760:
753:
752:
748:
744:
741:
737:
735:3rd harmonic
734:
732:2nd overtone
731:
728:
722:
715:
714:
710:
706:
703:
699:
697:2nd harmonic
696:
694:1st overtone
693:
690:
684:
673:
672:
668:
664:
661:
657:
655:1st harmonic
654:
652:
649:
646:
640:
629:
628:
624:
621:
618:
617:Standing wave
615:
612:
609:
606:
597:
594:
593:
590:
587:
582:
577:
567:
565:
561:
557:
552:
550:
546:
542:
541:singing bowls
538:
534:
530:
525:
523:
519:
515:
512:
508:
504:
500:
496:
492:
487:
485:
481:
477:
473:
470:
466:
462:
458:
441:
431:
429:
425:
414:
409:
407:
403:
398:
394:
376:
373:
362:
344:
341:
330:
326:
322:
318:
314:
310:
292:
289:
278:
260:
257:
246:
242:
236:
233:
229:
225:
220:
218:
217:
212:
208:
207:
202:
201:
196:
192:
191:
186:
182:
178:
174:
170:
166:
162:
153:
146:
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:
3192:
2912:Thomas Young
2862:Jens Blauert
2850:Acousticians
2786:
2582:
2542:. Retrieved
2530:
2506:. Retrieved
2502:the original
2489:
2479:
2470:the original
2460:
2443:
2432:. Retrieved
2414:
2390:(4): 15–32.
2387:
2381:
2367:
2318:
2312:
2295:
2284:. Retrieved
2265:(2): 71–84.
2262:
2256:
2243:
2227:. Springer.
2223:
2213:
2183:(2): 34–36.
2180:
2177:Books Abroad
2176:
2172:
2166:
2157:
2150:. Retrieved
2146:the original
2137:
2127:
2116:. Retrieved
2111:
2102:
2091:. Retrieved
2071:
2059:
1953:
1867:
1855:
1776:nanodecimal
1745:major second
1414:major second
1113:fundamental
1094:open string)
1092:(relative to
1089:Note sounded
1063:tone color (
1061:
1052:
921:
869:
836:
825:multiphonics
814:
792:
767:4th partial
729:3rd partial
691:2nd partial
682:880 Hz
647:1st partial
638:440 Hz
613:Name 3
610:Name 2
607:Name 1
573:
553:
545:multiphonics
526:
511:non-linearly
506:
488:
483:
479:
453:
438:
427:
423:
420:
411:
405:
401:
396:
392:
360:
328:
324:
320:
316:
312:
308:
276:
244:
240:
238:
221:
214:
205:
204:
200:1st harmonic
199:
198:
188:
172:
158:
123:
114:
104:
97:
90:
83:
71:
59:Please help
54:verification
51:
3118:Prospection
3091:Imagination
3054:Forecasting
3034:Association
2882:Franz Melde
2857:John Backus
2841:Subharmonic
2694:Spectrogram
2419:Milne, A.;
2372:Milne, A.;
2321:(1): 1–19.
2040:Subharmonic
1965:Aristoxenus
1878:double bass
1818:major third
1778:minor third
1742:Pythagorean
1714:4·P8 + m2⇟
1613:3·P8 + m7⤈
1557:tridecimal
1411:Pythagorean
1350:2·P8 + m7↓
1273:major third
1132:fundamental
897:time period
823:of playing
816:overblowing
520:instead of
465:human voice
461:oscillators
417:Terminology
230:, a common
117:August 2020
3329:Categories
3299:Mental set
3178:Peripheral
3128:Perception
3111:strategies
2943:Ultrasound
2933:Infrasound
2719:Bark scale
2544:2020-12-21
2508:2020-12-21
2434:2020-05-02
2286:2009-09-20
2152:13 January
2118:2020-12-21
2093:2020-12-21
2051:References
1956:media help
1822:4·P8 + M3
1749:4·P8 + M2
1648:3·P8 + M7
1530:3·P8 + P5
1452:3·P8 + M3
1420:3·P8 + M2
1309:2·P8 + P5
1277:2·P8 + M3
893:reciprocal
837:flageolets
595:Frequency
564:consonance
491:resonators
87:newspapers
76:"Harmonic"
3335:Acoustics
3274:Intention
3259:Attention
3193:Harmonics
3146:RGB model
3096:Intuition
3066:Foresight
3059:affective
3039:Awareness
3026:Cognition
2824:Resonance
2724:Mel scale
2654:Monochord
2633:Acoustics
2592:Harmonics
2348:"Alt URL"
2281:216636537
2197:0006-7431
2088:241172832
2015:Pure tone
1946:frequency
1782:4·P8 + m3
1603:septimal
1563:3·P8 + n6
1491:3·P8 + a4
1085:Stop note
1081:Harmonic
1033:, etc.).
885:woodwinds
833:harmonics
537:pizzicato
503:clarinets
329:vibrating
224:acoustics
181:frequency
165:acoustics
18:Harmonics
3314:Volition
3304:Thinking
3284:Learning
3233:Encoding
2978:Category
2819:Overtone
2787:Harmonic
2425:X System
2406:27906745
2355:Sethares
2339:Archived
2221:(2004).
2205:40043442
1892:See also
1710:semitone
1654:1,088.3
1207:P8 + P5
1136:perfect
1050:—
799:recorder
793:In many
576:overtone
558:(2004),
556:Sethares
499:trumpets
484:harmonic
476:periodic
311:, where
211:periodic
173:harmonic
3238:Storage
3106:methods
2765:Formant
2335:1549755
2010:Harmony
1975:Formant
1825:12,000
1792:11,400
1752:10,800
1717:10,200
1481:tritone
891:is the
877:strings
861:
849:
581:musical
549:cymbals
514:elastic
480:partial
185:integer
179:with a
161:physics
101:scholar
3243:Recall
3220:Memory
3210:Visual
3203:Speech
3183:Social
3163:Haptic
3136:Amodal
2958:Violin
2792:Series
2404:
2333:
2279:
2231:
2203:
2195:
2086:
1882:bowing
1828:386.3
1795:297.5
1755:203.9
1720:105.0
1684:9,600
1677:octave
1651:9,000
1619:968.8
1616:8,400
1577:840.5
1574:7,800
1536:702.0
1533:7,200
1504:551.3
1501:6,600
1458:386.3
1455:6,000
1426:203.9
1423:5,400
1386:4,800
1379:octave
1356:968.8
1353:4,200
1315:702.0
1312:3,600
1283:386.3
1280:3,000
1243:2,400
1236:octave
1213:702.0
1210:1,800
1178:1,200
1171:octave
1138:unison
1065:timbre
1057:(1879)
1014:
1008:
977:
971:
940:
934:
841:unison
819:. The
807:timbre
803:octave
533:pianos
472:violin
457:timbre
167:, and
103:
96:
89:
82:
74:
3355:Sound
3252:Other
3198:Pitch
3188:Sound
3167:Touch
3153:Depth
3141:Color
2953:Piano
2938:Sound
2752:pitch
2714:Pitch
2457:from
2428:(PDF)
2402:S2CID
2351:(PDF)
2342:(PDF)
2331:S2CID
2309:(PDF)
2277:S2CID
2201:JSTOR
2084:S2CID
1816:just
1681:4·P8
1383:3·P8
1240:2·P8
1119:Audio
1111:above
1109:Cents
883:, or
881:brass
845:cello
598:Order
469:bowed
467:or a
428:above
193:of a
175:is a
145:nodes
108:JSTOR
94:books
3158:Form
2928:Echo
2834:Node
2760:Beat
2750:and
2229:ISBN
2193:ISSN
2154:2024
1836:Play
1803:Play
1763:Play
1728:Play
1695:Play
1687:0.0
1662:Play
1641:just
1627:Play
1585:Play
1544:Play
1512:Play
1466:Play
1434:Play
1397:Play
1389:0.0
1364:Play
1323:Play
1291:Play
1254:Play
1246:0.0
1221:Play
1189:Play
1181:0.0
1156:Play
1148:0.0
1145:600
764:= 4
754:4 ×
726:= 3
716:3 ×
688:= 2
674:2 ×
644:= 1
630:1 ×
501:and
363:and
279:and
171:, a
143:The
80:news
2535:doi
2494:doi
2392:doi
2323:doi
2267:doi
2185:doi
2076:doi
1813:20
1773:19
1738:18
1705:17
1672:16
1637:15
1595:14
1554:13
1522:12
1476:11
1444:10
1175:P8
1142:P1
1042:.'
835:or
574:An
518:gut
507:odd
424:all
325:not
239:An
159:In
63:by
3331::
2581:.
2529:.
2517:^
2492:.
2488:.
2464:.
2400:.
2388:31
2386:.
2380:.
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2311:.
2275:.
2263:33
2261:.
2255:.
2199:.
2191:.
2156:.
2136:.
2110:.
2082:.
2074:.
2070:.
1571:↓
1407:9
1374:8
1333:7
1301:6
1264:5
1231:4
1199:3
1166:2
1128:1
1105:)
1103:Hz
996:,
959:,
879:,
858:3
852:1
678:=
634:=
604:)
445:c.
232:AC
228:Hz
219:.
163:,
3169:)
3165:(
3012:e
3005:t
2998:v
2625:e
2618:t
2611:v
2547:.
2537::
2511:.
2496::
2437:.
2408:.
2394::
2361:.
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2319:2
2289:.
2269::
2207:.
2187::
2181:1
2121:.
2096:.
2078::
1958:.
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1339:,
1270:,
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1101:(
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1018:4
1011:1
981:3
974:1
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937:1
855:/
762:n
756:f
724:n
718:f
686:n
680:0
676:f
642:n
636:0
632:f
602:n
600:(
450:)
406:n
402:n
393:L
377:3
374:2
361:L
345:3
342:1
321:n
317:n
313:L
309:L
293:3
290:2
277:L
261:3
258:1
245:n
241:n
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105:·
98:·
91:·
84:·
57:.
34:.
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