2676:
1571:
1714:
1240:
1648:
1530:
1309:
1207:
1498:
1822:
1613:
1452:
1350:
1277:
1681:
1383:
1175:
1789:
1749:
1420:
1142:
1889:
141:
2963:
129:
32:
1775:
1556:
1484:
897:
2439:
774:
736:
698:
656:
767:
729:
691:
649:
577:
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
567:
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
859:
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
1035:
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
1051:
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
401:
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
402:
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.
1849:, 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.
443:
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
467:, 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
572:
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
1026:
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
223:
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.
1934:
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
540:, 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.
1572:
428:
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.
410:
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
1715:
1241:
1649:
1531:
1310:
1208:
1499:
1823:
1614:
1453:
1351:
1278:
1682:
1384:
1176:
388:
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
1790:
1750:
1421:
1928:
1907:
1143:
2443:
876:. 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
551:
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
2302:
1905:
1926:
1020:
983:
946:
379:
347:
295:
263:
498:
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
911:
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 (
1927:
1906:
1060:. 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.
520:. 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
2150:— Minimally technical summary of string acoustics research given at conference; discusses listeners' perceptions of pianos' inharmonic partials.
1042:
832:
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
2572:
2999:
482:, 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
144:
Two different notations of natural harmonics on the cello. First as sounded (more common), then as fingered (easier to sightread).
2885:
3328:
2448:
2122:
3348:
2580:
2327:
3257:
215:, electronic power transmission, radio technology, and other fields. For example, if the fundamental frequency is 50
2612:
2221:
96:
2241:
115:
68:
828:
by string players, which have an eerie quality, as well as being high in pitch. Harmonics may be used to check at a
202:
at the fundamental frequency, the sum of harmonics is also periodic at that frequency. The set of harmonics forms a
415:
pitches in a harmonic series (including the fundamental frequency) while the term "overtone" only includes pitches
2454:
786:, it is possible to play the upper harmonics without the fundamental note being present. In a simple case (e.g.,
75:
2992:
53:
2474:
2130:
787:
3099:
236:> 1, will have nodes that are not vibrating. For example, the 3rd characteristic mode will have nodes at
1983:
860:
not true harmonics but are "overtones" and can be very sharp, i.e. a higher frequency than given by a pure
82:
3338:
3333:
3094:
988:
951:
914:
794:, but in more complex cases many other pitch variations are obtained. In some cases it also changes the
2724:
2985:
2845:
1919:
1898:
355:
323:
271:
239:
64:
49:
20:
3161:
3022:
2900:
881:
2055:
510:
3282:
2780:
2637:
2605:
2347:
2068:
861:
448:
of that sound being a result of the relative strengths of the individual partials. Many acoustic
204:
42:
3252:
3054:
2719:
2629:
2371:
2246:
2527:
494:, also produce partials resembling harmonics. However they only produce partials matching the
3302:
3267:
3047:
3032:
2860:
2758:
2662:
2515:
2336:
1120:
877:
178:
3216:
1730:
1399:
516:
Partials whose frequencies are not integer multiples of the fundamental are referred to as
502:
8:
3297:
2880:
2790:
2018:
1993:
1988:
1846:
865:
783:
499:
220:
2566:
2555:
3323:
2966:
2812:
2802:
2763:
2598:
2390:
2319:
2265:
2189:
2072:
2013:
2008:
817:
809:
574:
157:
2675:
2101:
Petrucci Music
Library / International Music Score Library Project (IMSLP) (imslp.org)
89:
3221:
3198:
3191:
3171:
3166:
3151:
3124:
3069:
3037:
2936:
2768:
2269:
2217:
2181:
2076:
2033:
1978:
611:
464:
199:
2394:
3287:
3226:
3141:
2946:
2865:
2829:
2797:
2748:
2657:
2523:
2482:
2458:
2409:
2380:
2362:
2343:
2323:
2311:
2294:
2290:
2255:
2237:
2207:
2173:
2134:
2064:
2023:
1958:
1862:
1587:
1475:
1436:
1330:
1325:
1256:
885:
869:
853:
799:
639:
548:
544:
483:
2366:
3231:
3176:
3146:
3134:
3089:
3074:
2941:
2895:
2736:
2694:
2211:
1973:
1858:
1629:
1087:
905:
821:
183:
165:
2550:
1774:
1555:
1483:
478:
Oscillators that produce harmonic partials behave somewhat like one-dimensional
3343:
2890:
2875:
2822:
1968:
1028:
133:
2385:
2315:
2260:
1865:
is able to bring out different harmonics on the single string of his modified
19:
This article is about the components of periodic signals. For other uses, see
3317:
3186:
3064:
3059:
2855:
2817:
2785:
2740:
2702:
2652:
2647:
2561:
2413:
2185:
2096:
1874:
1632:
1593:
1547:
1514:
1293:
1191:
1057:
605:
517:
798:
of the note. This is part of the normal method of obtaining higher notes in
528:, vibraphones, marimbas, and certain pure-sounding bells or chimes. Antique
3129:
2850:
1733:
1402:
1097:
1091:
533:
529:
140:
3106:
3079:
3042:
2870:
2682:
2028:
1953:
1870:
1866:
1806:
1766:
1261:
813:
804:
457:
453:
3277:
2193:
3116:
2931:
2921:
2707:
1944:
552:
449:
211:
The term is employed in various disciplines, including music, physics,
555:
of that pseudo-harmonic timbre with notes of that pseudo-just tuning.
486:). Wind instruments whose air column is open at only one end, such as
3262:
3247:
3084:
3027:
3014:
2712:
2642:
2621:
2585:
2486:
2177:
2003:
1073:
888:
of the collection of vibrations in some single periodic phenomenon.)
873:
525:
479:
316:
have nodes at these points. These other characteristic modes will be
212:
169:
153:
31:
16:
Wave with frequency an integer multiple of the fundamental frequency
3272:
2977:
2807:
2490:
2147:
There are many ways to make matters worse, but very few to improve.
1873:
technique halfway between hitting and bowing the strings. Composer
1698:
852:
of the way down the second highest string. For the human voice see
564:
491:
475:, the first being actual and the second being theoretical).
128:
3292:
2753:
1998:
1963:
1469:
578:
harmonic) are counted (assuming that the harmonics are present):
537:
487:
173:
149:
3208:
2565:
1665:
1367:
1224:
1159:
1126:
1053:
829:
795:
791:
506:
460:
445:
1857:
Harmonics may be either used in or considered as the basis of
896:
790:) this has the effect of making the note go up in pitch by an
3155:
2926:
833:
569:
521:
216:
2590:
2556:
Harmonics, partials and overtones from fundamental frequency
2240:; Milne, A.; Tiedje, S.; Prechtl, A.; Plamondon, J. (2009).
773:
735:
697:
655:
2916:
820:
it is possible to produce very pure sounding notes, called
397:
is a multiple of 3, will be made relatively more prominent.
2236:
766:
728:
690:
648:
2242:"Spectral tools for dynamic tonality and audio morphing"
2121:
Galembo, Alexander; Cuddly, Lola L. (2 December 1997).
2407:
2360:
2288:
1036:
the number of upper harmonics it can be made to yield.
993:
956:
919:
836:
produces the same pitch as lightly fingering the node
532:
are known for producing multiple harmonic partials or
360:
328:
276:
244:
991:
954:
917:
558:
358:
326:
274:
242:
864:. This is especially true of instruments other than
463:
string, produce complex tones that are more or less
1913:
Violin natural harmonic stop points on the A string
56:. Unsourced material may be challenged and removed.
2103:(site sub-index & mini-bio for Scholz). Canada
2054:
1014:
977:
940:
373:
341:
289:
257:
1877:uses harmonics to generate music electronically.
3315:
2367:"Invariant fingerings across a tuning continuum"
2509:
2507:
186:. The fundamental frequency is also called the
2993:
2606:
2230:
2120:
2576:(11th ed.). Cambridge University Press.
2504:
2472:
2069:10.1287/7648739e-8e59-466e-82cb-3ded22bbebf6
513:, tend to have not-quite-integer partials.
304:is the length of the string. In fact, each
3000:
2986:
2613:
2599:
2551:The Feynman Lectures on Physics: Harmonics
891:
2384:
2259:
1043:Grove's Dictionary of Music and Musicians
116:Learn how and when to remove this message
2560:
2513:
2354:
2206:
895:
139:
127:
2528:10.1093/gmo/9781561592630.article.14882
2401:
2282:
1840:
505:wood, instead of metal, or strung with
3316:
2295:"Tuning continua and keyboard layouts"
2123:"Large grand and small upright pianos"
2052:
1845:Occasionally a score will call for an
2981:
2594:
2293:; Plamondon, James (29 August 2008).
2159:
3007:
1852:
136:of a vibrating string are harmonics.
54:adding citations to reliable sources
25:
2419:(technical report). Thumtronics Inc
2200:
1015:{\displaystyle {\tfrac {\ 1\ }{4}}}
978:{\displaystyle {\tfrac {\ 1\ }{3}}}
941:{\displaystyle {\tfrac {\ 1\ }{2}}}
192:; the other harmonics are known as
13:
2160:Court, Sophie R.A. (April 1927). "
1943:Problems playing these files? See
1887:
559:Partials, overtones, and harmonics
422:
14:
3360:
2586:Hear and see harmonics on a Piano
2544:
2962:
2961:
2674:
2442: This article incorporates
2437:
2333:from the original on 2022-10-09.
2303:Journal of Mathematics and Music
1924:
1903:
1869:by slightly altering his unique
1773:
1554:
1482:
772:
765:
734:
727:
696:
689:
654:
647:
30:
2479:MyFavoritegamez.com / SciVee.tv
2466:
2455:General Services Administration
2430:
2365:; Plamondon, J. (Winter 2007).
2213:Tuning, Timbre, Spectrum, Scale
374:{\displaystyle {\tfrac {2}{3}}}
342:{\displaystyle {\tfrac {1}{3}}}
290:{\displaystyle {\tfrac {2}{3}}}
258:{\displaystyle {\tfrac {1}{3}}}
41:needs additional citations for
2153:
2114:
2089:
2053:Walker, Russell (2019-06-14).
2046:
900:Playing a harmonic on a string
405:
1:
3329:Guitar performance techniques
2620:
2131:Acoustical Society of America
2039:
536:. Other oscillators, such as
433:
3349:Spectrum (physical sciences)
3162:Perception as interpretation
2514:Marrocco, W. Thomas (2001).
2475:"Free Online Games for Kids"
1984:Harmonics (electrical power)
816:also produces harmonics. On
393:characteristic modes, where
7:
2522:. Oxford University Press.
2473:George alike (2011-01-21).
1880:
10:
3365:
2097:"Category:Scholz, Richard"
903:
312:not a multiple of 3, will
18:
3240:
3207:
3115:
3013:
2957:
2909:
2838:
2735:
2693:
2669:
2628:
2386:10.1162/comj.2007.31.4.15
2316:10.1080/17459730701828677
2261:10.1162/comj.2009.33.2.71
2226:– via Google books.
1056:) when used and heard in
308:characteristic mode, for
232:characteristic mode, for
21:Harmonic (disambiguation)
2412:; Plamondon, J. (2006).
1096:
1086:
856:, which uses harmonics.
3283:Relational frame theory
3258:Higher nervous activity
2638:Architectural acoustics
2573:Encyclopædia Britannica
2348:University of Wisconsin
892:On stringed instruments
198:. As all harmonics are
3253:Experiential avoidance
2725:Fletcher–Munson curves
2720:Equal-loudness contour
2630:Acoustical engineering
2450:Federal Standard 1037C
2444:public domain material
2372:Computer Music Journal
2247:Computer Music Journal
1892:
1331:septimal minor seventh
1049:
1016:
979:
942:
901:
511:brass or steel strings
441:
399:
375:
343:
291:
259:
145:
137:
3268:Ironic process theory
3033:Cognitive flexibility
2861:Hermann von Helmholtz
2759:Fundamental frequency
2663:Sympathetic resonance
2346:pers. academic site.
1891:
1017:
980:
943:
909:
899:
878:fundamental frequency
802:, where it is called
426:
376:
344:
292:
260:
226:
179:fundamental frequency
143:
131:
1841:Artificial harmonics
989:
952:
915:
356:
324:
272:
240:
50:improve this article
3298:Thought suppression
2881:Werner Meyer-Eppler
2791:Missing fundamental
2520:Oxford Music Online
2164:Hanna Rademacher".
2019:Spherical harmonics
1994:Harmonic oscillator
1989:Harmonic generation
1847:artificial harmonic
784:musical instruments
518:inharmonic partials
172:that is a positive
3339:String instruments
3334:Telecommunications
2764:Frequency spectrum
2014:Scale of harmonics
2009:Pythagorean tuning
1893:
1861:systems. Composer
1598:(‘the lost chord’)
1335:(‘the lost chord’)
1104:(offset by octave)
1033:(2) The production
1012:
1010:
975:
973:
938:
936:
902:
818:string instruments
810:extended technique
575:pitched percussion
524:, strings plucked
432:— Richard Scholz (
419:the fundamental.
371:
369:
339:
337:
287:
285:
255:
253:
158:telecommunications
146:
138:
3311:
3310:
3070:Critical thinking
3038:Cognitive liberty
2975:
2974:
2937:Musical acoustics
2769:harmonic spectrum
2291:Sethares, William
2162:Golo und Genovefa
2129:(Press release).
2034:Xenharmonic music
1979:Harmonic analysis
1929:
1908:
1853:Other information
1834:
1833:
1599:
1468:lesser undecimal
1336:
1112:
1105:
1084:
1009:
1004:
998:
972:
967:
961:
935:
930:
924:
780:
779:
612:Longitudinal wave
471: a
368:
336:
320:at the positions
284:
252:
126:
125:
118:
100:
3356:
3008:Mental processes
3002:
2995:
2988:
2979:
2978:
2965:
2964:
2866:Carleen Hutchins
2798:Combination tone
2685:
2678:
2658:String vibration
2615:
2608:
2601:
2592:
2591:
2577:
2569:
2567:"Harmonic"
2538:
2537:
2535:
2534:
2511:
2502:
2501:
2499:
2498:
2489:. Archived from
2487:10.4016/26742.01
2470:
2464:
2463:
2462:
2457:. Archived from
2441:
2440:
2434:
2428:
2427:
2425:
2424:
2418:
2405:
2399:
2398:
2388:
2358:
2352:
2351:
2341:
2334:
2332:
2299:
2286:
2280:
2279:
2277:
2276:
2263:
2234:
2228:
2227:
2204:
2198:
2197:
2178:10.2307/40043442
2157:
2151:
2149:
2144:
2142:
2133:. Archived from
2118:
2112:
2111:
2109:
2108:
2093:
2087:
2086:
2084:
2083:
2058:
2056:"Russell Walker"
2050:
2024:Stretched octave
1959:Electronic tuner
1931:
1930:
1920:Harmonics 110x16
1910:
1909:
1899:Violin harmonics
1890:
1863:Arnold Dreyblatt
1830:
1829:
1828:
1826:
1797:
1796:
1795:
1793:
1778:
1777:
1757:
1756:
1755:
1753:
1722:
1721:
1720:
1718:
1689:
1688:
1687:
1685:
1656:
1655:
1654:
1652:
1621:
1620:
1619:
1617:
1597:
1588:harmonic seventh
1579:
1578:
1577:
1575:
1559:
1558:
1538:
1537:
1536:
1534:
1506:
1505:
1504:
1502:
1487:
1486:
1476:augmented fourth
1460:
1459:
1458:
1456:
1437:just major third
1428:
1427:
1426:
1424:
1391:
1390:
1389:
1387:
1358:
1357:
1356:
1354:
1334:
1326:harmonic seventh
1317:
1316:
1315:
1313:
1285:
1284:
1283:
1281:
1257:just major third
1248:
1247:
1246:
1244:
1223:doubled perfect
1215:
1214:
1213:
1211:
1183:
1182:
1181:
1179:
1150:
1149:
1148:
1146:
1111:(octave shifted)
1110:
1103:
1080:
1067:
1066:
1047:
1034:
1025:
1024:(1) In the first
1021:
1019:
1018:
1013:
1011:
1005:
1002:
996:
994:
984:
982:
981:
976:
974:
968:
965:
959:
957:
947:
945:
944:
939:
937:
931:
928:
922:
920:
854:Overtone singing
851:
849:
848:
845:
842:
800:wind instruments
776:
769:
752:
746:
738:
731:
714:
708:
700:
693:
676:
670:
666:
658:
651:
640:fundamental tone
632:
626:
622:
592:
581:
580:
549:dynamic tonality
484:transverse flute
438:
437: 1888-1912
435:
384:. If the player
380:
378:
377:
372:
370:
361:
348:
346:
345:
340:
338:
329:
296:
294:
293:
288:
286:
277:
264:
262:
261:
256:
254:
245:
195:higher harmonics
176:multiple of the
121:
114:
110:
107:
101:
99:
58:
34:
26:
3364:
3363:
3359:
3358:
3357:
3355:
3354:
3353:
3314:
3313:
3312:
3307:
3236:
3203:
3111:
3090:Problem solving
3075:Decision-making
3009:
3006:
2976:
2971:
2953:
2905:
2896:D. Van Holliday
2834:
2803:Mersenne's laws
2737:Audio frequency
2731:
2695:Psychoacoustics
2689:
2688:
2681:
2667:
2624:
2619:
2547:
2542:
2541:
2532:
2530:
2512:
2505:
2496:
2494:
2471:
2467:
2447:
2438:
2436:
2435:
2431:
2422:
2420:
2416:
2406:
2402:
2359:
2355:
2339:
2335:
2330:
2297:
2289:Milne, Andrew;
2287:
2283:
2274:
2272:
2235:
2231:
2224:
2205:
2201:
2168:(book review).
2158:
2154:
2140:
2138:
2119:
2115:
2106:
2104:
2095:
2094:
2090:
2081:
2079:
2051:
2047:
2042:
1974:Guitar harmonic
1950:
1949:
1941:
1939:
1938:
1937:
1936:
1932:
1925:
1922:
1916:
1915:
1914:
1911:
1904:
1901:
1894:
1888:
1883:
1859:just intonation
1855:
1843:
1824:
1821:
1820:
1791:
1788:
1787:
1772:
1751:
1748:
1747:
1716:
1713:
1712:
1683:
1680:
1679:
1664:fourth perfect
1650:
1647:
1646:
1615:
1612:
1611:
1596:
1591:
1573:
1570:
1569:
1553:
1532:
1529:
1528:
1500:
1497:
1496:
1481:
1474:undecimal semi-
1473:
1454:
1451:
1450:
1422:
1419:
1418:
1406:harmonic ninth
1405:
1385:
1382:
1381:
1352:
1349:
1348:
1333:
1329:
1311:
1308:
1307:
1279:
1276:
1275:
1260:
1242:
1239:
1238:
1209:
1206:
1205:
1177:
1174:
1173:
1144:
1141:
1140:
1124:
1109:
1101:
1088:Audio frequency
1082:
1079:
1048:
1040:
1032:
1023:
995:
992:
990:
987:
986:
958:
955:
953:
950:
949:
921:
918:
916:
913:
912:
908:
906:String harmonic
894:
884:of the longest
862:harmonic series
846:
843:
840:
839:
837:
750:
747:= 1760 Hz
744:
712:
709:= 1320 Hz
706:
674:
668:
664:
630:
624:
620:
614:representation
608:representation
590:
588:
561:
543:Building on of
440:
436:
425:
423:Characteristics
408:
359:
357:
354:
353:
327:
325:
322:
321:
275:
273:
270:
269:
243:
241:
238:
237:
205:harmonic series
184:periodic signal
166:sinusoidal wave
122:
111:
105:
102:
59:
57:
47:
35:
24:
17:
12:
11:
5:
3362:
3352:
3351:
3346:
3341:
3336:
3331:
3326:
3309:
3308:
3306:
3305:
3300:
3295:
3290:
3285:
3280:
3278:Mental fatigue
3275:
3270:
3265:
3260:
3255:
3250:
3244:
3242:
3238:
3237:
3235:
3234:
3229:
3224:
3219:
3213:
3211:
3205:
3204:
3202:
3201:
3196:
3195:
3194:
3189:
3184:
3174:
3169:
3164:
3159:
3149:
3144:
3139:
3138:
3137:
3127:
3121:
3119:
3113:
3112:
3110:
3109:
3104:
3103:
3102:
3097:
3087:
3082:
3077:
3072:
3067:
3062:
3057:
3052:
3051:
3050:
3040:
3035:
3030:
3025:
3019:
3017:
3011:
3010:
3005:
3004:
2997:
2990:
2982:
2973:
2972:
2970:
2969:
2958:
2955:
2954:
2952:
2951:
2950:
2949:
2944:
2934:
2929:
2924:
2919:
2913:
2911:
2910:Related topics
2907:
2906:
2904:
2903:
2898:
2893:
2891:Joseph Sauveur
2888:
2883:
2878:
2876:Marin Mersenne
2873:
2868:
2863:
2858:
2853:
2848:
2842:
2840:
2836:
2835:
2833:
2832:
2827:
2826:
2825:
2815:
2810:
2805:
2800:
2795:
2794:
2793:
2788:
2783:
2773:
2772:
2771:
2761:
2756:
2751:
2745:
2743:
2733:
2732:
2730:
2729:
2728:
2727:
2717:
2716:
2715:
2710:
2699:
2697:
2691:
2690:
2687:
2686:
2679:
2671:
2670:
2668:
2666:
2665:
2660:
2655:
2650:
2645:
2640:
2634:
2632:
2626:
2625:
2618:
2617:
2610:
2603:
2595:
2589:
2588:
2583:
2578:
2564:, ed. (1911).
2562:Chisholm, Hugh
2558:
2553:
2546:
2545:External links
2543:
2540:
2539:
2516:"Kennan, Kent"
2503:
2465:
2461:on 2022-01-22.
2429:
2410:Sethares, W.A.
2400:
2363:Sethares, W.A.
2353:
2281:
2238:Sethares, W.A.
2229:
2223:978-1852337971
2222:
2208:Sethares, W.A.
2199:
2152:
2113:
2088:
2044:
2043:
2041:
2038:
2037:
2036:
2031:
2026:
2021:
2016:
2011:
2006:
2001:
1996:
1991:
1986:
1981:
1976:
1971:
1969:Fourier series
1966:
1961:
1956:
1940:
1933:
1923:
1918:
1917:
1912:
1902:
1897:
1896:
1895:
1886:
1885:
1884:
1882:
1879:
1854:
1851:
1842:
1839:
1838:
1837:
1836:
1835:
1832:
1831:
1818:
1815:
1812:
1809:
1803:
1799:
1798:
1785:
1782:
1779:
1769:
1763:
1759:
1758:
1745:
1742:
1739:
1736:
1728:
1724:
1723:
1710:
1707:
1704:
1701:
1695:
1691:
1690:
1677:
1674:
1671:
1668:
1662:
1658:
1657:
1644:
1641:
1638:
1635:
1627:
1623:
1622:
1609:
1606:
1603:
1600:
1585:
1581:
1580:
1567:
1564:
1561:
1550:
1544:
1540:
1539:
1526:
1523:
1520:
1517:
1512:
1508:
1507:
1494:
1491:
1488:
1478:
1466:
1462:
1461:
1448:
1445:
1442:
1439:
1434:
1430:
1429:
1416:
1413:
1410:
1407:
1397:
1393:
1392:
1379:
1376:
1373:
1370:
1366:third perfect
1364:
1360:
1359:
1346:
1343:
1340:
1337:
1323:
1319:
1318:
1305:
1302:
1299:
1296:
1291:
1287:
1286:
1273:
1270:
1267:
1264:
1254:
1250:
1249:
1236:
1233:
1230:
1227:
1221:
1217:
1216:
1203:
1200:
1197:
1194:
1189:
1185:
1184:
1171:
1168:
1165:
1162:
1158:first perfect
1156:
1152:
1151:
1138:
1135:
1132:
1129:
1118:
1114:
1113:
1106:
1095:
1085:
1076:
1071:
1038:
1029:sul ponticello
1008:
1001:
971:
964:
934:
927:
904:Main article:
893:
890:
778:
777:
770:
763:
760:
757:
754:
748:
740:
739:
732:
725:
722:
719:
716:
710:
702:
701:
694:
687:
684:
681:
678:
672:
660:
659:
652:
645:
642:
637:
634:
628:
616:
615:
609:
603:
600:
597:
594:
585:
560:
557:
452:, such as the
431:
424:
421:
407:
404:
386:gently touches
367:
364:
335:
332:
283:
280:
251:
248:
124:
123:
38:
36:
29:
15:
9:
6:
4:
3:
2:
3361:
3350:
3347:
3345:
3342:
3340:
3337:
3335:
3332:
3330:
3327:
3325:
3322:
3321:
3319:
3304:
3301:
3299:
3296:
3294:
3291:
3289:
3286:
3284:
3281:
3279:
3276:
3274:
3271:
3269:
3266:
3264:
3261:
3259:
3256:
3254:
3251:
3249:
3246:
3245:
3243:
3239:
3233:
3230:
3228:
3225:
3223:
3220:
3218:
3217:Consolidation
3215:
3214:
3212:
3210:
3206:
3200:
3197:
3193:
3190:
3188:
3185:
3183:
3180:
3179:
3178:
3175:
3173:
3170:
3168:
3165:
3163:
3160:
3157:
3153:
3150:
3148:
3145:
3143:
3140:
3136:
3133:
3132:
3131:
3128:
3126:
3123:
3122:
3120:
3118:
3114:
3108:
3105:
3101:
3098:
3096:
3093:
3092:
3091:
3088:
3086:
3083:
3081:
3078:
3076:
3073:
3071:
3068:
3066:
3065:Consciousness
3063:
3061:
3060:Comprehension
3058:
3056:
3053:
3049:
3046:
3045:
3044:
3041:
3039:
3036:
3034:
3031:
3029:
3026:
3024:
3021:
3020:
3018:
3016:
3012:
3003:
2998:
2996:
2991:
2989:
2984:
2983:
2980:
2968:
2960:
2959:
2956:
2948:
2945:
2943:
2940:
2939:
2938:
2935:
2933:
2930:
2928:
2925:
2923:
2920:
2918:
2915:
2914:
2912:
2908:
2902:
2899:
2897:
2894:
2892:
2889:
2887:
2886:Lord Rayleigh
2884:
2882:
2879:
2877:
2874:
2872:
2869:
2867:
2864:
2862:
2859:
2857:
2856:Ernst Chladni
2854:
2852:
2849:
2847:
2844:
2843:
2841:
2837:
2831:
2828:
2824:
2821:
2820:
2819:
2818:Standing wave
2816:
2814:
2811:
2809:
2806:
2804:
2801:
2799:
2796:
2792:
2789:
2787:
2786:Inharmonicity
2784:
2782:
2779:
2778:
2777:
2774:
2770:
2767:
2766:
2765:
2762:
2760:
2757:
2755:
2752:
2750:
2747:
2746:
2744:
2742:
2738:
2734:
2726:
2723:
2722:
2721:
2718:
2714:
2711:
2709:
2706:
2705:
2704:
2701:
2700:
2698:
2696:
2692:
2684:
2680:
2677:
2673:
2672:
2664:
2661:
2659:
2656:
2654:
2653:Soundproofing
2651:
2649:
2648:Reverberation
2646:
2644:
2641:
2639:
2636:
2635:
2633:
2631:
2627:
2623:
2616:
2611:
2609:
2604:
2602:
2597:
2596:
2593:
2587:
2584:
2582:
2579:
2575:
2574:
2568:
2563:
2559:
2557:
2554:
2552:
2549:
2548:
2529:
2525:
2521:
2517:
2510:
2508:
2493:on 2021-02-14
2492:
2488:
2484:
2480:
2476:
2469:
2460:
2456:
2452:
2451:
2445:
2433:
2415:
2411:
2404:
2396:
2392:
2387:
2382:
2378:
2374:
2373:
2368:
2364:
2357:
2349:
2345:
2338:
2329:
2325:
2321:
2317:
2313:
2309:
2305:
2304:
2296:
2292:
2285:
2271:
2267:
2262:
2257:
2253:
2249:
2248:
2243:
2239:
2233:
2225:
2219:
2215:
2214:
2209:
2203:
2195:
2191:
2187:
2183:
2179:
2175:
2171:
2167:
2163:
2156:
2148:
2137:on 2012-02-09
2136:
2132:
2128:
2127:acoustics.org
2124:
2117:
2102:
2098:
2092:
2078:
2074:
2070:
2066:
2062:
2061:Authors group
2057:
2049:
2045:
2035:
2032:
2030:
2027:
2025:
2022:
2020:
2017:
2015:
2012:
2010:
2007:
2005:
2002:
2000:
1997:
1995:
1992:
1990:
1987:
1985:
1982:
1980:
1977:
1975:
1972:
1970:
1967:
1965:
1962:
1960:
1957:
1955:
1952:
1951:
1948:
1946:
1921:
1900:
1878:
1876:
1875:Lawrence Ball
1872:
1868:
1864:
1860:
1850:
1848:
1827:
1819:
1816:
1813:
1810:
1808:
1804:
1801:
1800:
1794:
1786:
1783:
1780:
1776:
1770:
1768:
1764:
1761:
1760:
1754:
1746:
1743:
1740:
1737:
1735:
1732:
1729:
1726:
1725:
1719:
1711:
1708:
1705:
1702:
1700:
1697:septidecimal
1696:
1693:
1692:
1686:
1678:
1675:
1672:
1669:
1667:
1663:
1660:
1659:
1653:
1645:
1642:
1639:
1636:
1634:
1633:major seventh
1631:
1628:
1625:
1624:
1618:
1610:
1607:
1604:
1601:
1595:
1594:minor seventh
1589:
1586:
1583:
1582:
1576:
1568:
1565:
1562:
1557:
1551:
1549:
1548:neutral sixth
1545:
1542:
1541:
1535:
1527:
1524:
1521:
1518:
1516:
1515:perfect fifth
1513:
1510:
1509:
1503:
1495:
1492:
1489:
1485:
1479:
1477:
1471:
1467:
1464:
1463:
1457:
1449:
1446:
1443:
1440:
1438:
1435:
1432:
1431:
1425:
1417:
1414:
1411:
1408:
1404:
1401:
1398:
1395:
1394:
1388:
1380:
1377:
1374:
1371:
1369:
1365:
1362:
1361:
1355:
1347:
1344:
1341:
1338:
1332:
1327:
1324:
1321:
1320:
1314:
1306:
1303:
1300:
1297:
1295:
1294:perfect fifth
1292:
1289:
1288:
1282:
1274:
1271:
1268:
1265:
1263:
1258:
1255:
1252:
1251:
1245:
1237:
1234:
1231:
1228:
1226:
1222:
1219:
1218:
1212:
1204:
1201:
1198:
1195:
1193:
1192:perfect fifth
1190:
1187:
1186:
1180:
1172:
1169:
1166:
1163:
1161:
1157:
1154:
1153:
1147:
1139:
1136:
1133:
1130:
1128:
1122:
1119:
1116:
1115:
1107:
1099:
1093:
1089:
1077:
1075:
1072:
1069:
1068:
1065:
1064:
1063:
1062:
1061:
1059:
1058:orchestration
1055:
1045:
1044:
1037:
1030:
1006:
999:
969:
962:
932:
925:
907:
898:
889:
887:
883:
879:
875:
871:
867:
863:
857:
855:
835:
831:
827:
823:
819:
815:
811:
807:
806:
801:
797:
793:
789:
785:
775:
771:
768:
764:
762:4th harmonic
761:
759:3rd overtone
758:
755:
749:
742:
741:
737:
733:
730:
726:
724:3rd harmonic
723:
721:2nd overtone
720:
717:
711:
704:
703:
699:
695:
692:
688:
686:2nd harmonic
685:
683:1st overtone
682:
679:
673:
662:
661:
657:
653:
650:
646:
644:1st harmonic
643:
641:
638:
635:
629:
618:
617:
613:
610:
607:
606:Standing wave
604:
601:
598:
595:
586:
583:
582:
579:
576:
571:
566:
556:
554:
550:
546:
541:
539:
535:
531:
530:singing bowls
527:
523:
519:
514:
512:
508:
504:
501:
497:
493:
489:
485:
481:
476:
474:
470:
466:
462:
459:
455:
451:
447:
430:
420:
418:
414:
403:
398:
396:
392:
387:
383:
365:
362:
351:
333:
330:
319:
315:
311:
307:
303:
299:
281:
278:
267:
249:
246:
235:
231:
225:
222:
218:
214:
209:
207:
206:
201:
197:
196:
191:
190:
185:
181:
180:
175:
171:
167:
163:
159:
155:
151:
142:
135:
130:
120:
117:
109:
98:
95:
91:
88:
84:
81:
77:
74:
70:
67: –
66:
62:
61:Find sources:
55:
51:
45:
44:
39:This article
37:
33:
28:
27:
22:
3181:
2901:Thomas Young
2851:Jens Blauert
2839:Acousticians
2775:
2571:
2531:. Retrieved
2519:
2495:. Retrieved
2491:the original
2478:
2468:
2459:the original
2449:
2432:
2421:. Retrieved
2403:
2379:(4): 15–32.
2376:
2370:
2356:
2307:
2301:
2284:
2273:. Retrieved
2254:(2): 71–84.
2251:
2245:
2232:
2216:. Springer.
2212:
2202:
2172:(2): 34–36.
2169:
2166:Books Abroad
2165:
2161:
2155:
2146:
2139:. Retrieved
2135:the original
2126:
2116:
2105:. Retrieved
2100:
2091:
2080:. Retrieved
2060:
2048:
1942:
1856:
1844:
1765:nanodecimal
1734:major second
1403:major second
1102:fundamental
1083:open string)
1081:(relative to
1078:Note sounded
1052:tone color (
1050:
1041:
910:
858:
825:
814:multiphonics
803:
781:
756:4th partial
718:3rd partial
680:2nd partial
671:880 Hz
636:1st partial
627:440 Hz
602:Name 3
599:Name 2
596:Name 1
562:
542:
534:multiphonics
515:
500:non-linearly
495:
477:
472:
468:
442:
427:
416:
412:
409:
400:
394:
390:
385:
381:
349:
317:
313:
309:
305:
301:
297:
265:
233:
229:
227:
210:
203:
194:
193:
189:1st harmonic
188:
187:
177:
161:
147:
112:
103:
93:
86:
79:
72:
60:
48:Please help
43:verification
40:
3107:Prospection
3080:Imagination
3043:Forecasting
3023:Association
2871:Franz Melde
2846:John Backus
2830:Subharmonic
2683:Spectrogram
2408:Milne, A.;
2361:Milne, A.;
2310:(1): 1–19.
2029:Subharmonic
1954:Aristoxenus
1867:double bass
1807:major third
1767:minor third
1731:Pythagorean
1703:4·P8 + m2⇟
1602:3·P8 + m7⤈
1546:tridecimal
1400:Pythagorean
1339:2·P8 + m7↓
1262:major third
1121:fundamental
886:time period
812:of playing
805:overblowing
509:instead of
454:human voice
450:oscillators
406:Terminology
219:, a common
106:August 2020
3318:Categories
3288:Mental set
3167:Peripheral
3117:Perception
3100:strategies
2932:Ultrasound
2922:Infrasound
2708:Bark scale
2533:2020-12-21
2497:2020-12-21
2423:2020-05-02
2275:2009-09-20
2141:13 January
2107:2020-12-21
2082:2020-12-21
2040:References
1945:media help
1811:4·P8 + M3
1738:4·P8 + M2
1637:3·P8 + M7
1519:3·P8 + P5
1441:3·P8 + M3
1409:3·P8 + M2
1298:2·P8 + P5
1266:2·P8 + M3
882:reciprocal
826:flageolets
584:Frequency
553:consonance
480:resonators
76:newspapers
65:"Harmonic"
3324:Acoustics
3263:Intention
3248:Attention
3182:Harmonics
3135:RGB model
3085:Intuition
3055:Foresight
3048:affective
3028:Awareness
3015:Cognition
2813:Resonance
2713:Mel scale
2643:Monochord
2622:Acoustics
2581:Harmonics
2337:"Alt URL"
2270:216636537
2186:0006-7431
2077:241172832
2004:Pure tone
1935:frequency
1771:4·P8 + m3
1592:septimal
1552:3·P8 + n6
1480:3·P8 + a4
1074:Stop note
1070:Harmonic
1022:, etc.).
874:woodwinds
822:harmonics
526:pizzicato
492:clarinets
318:vibrating
213:acoustics
170:frequency
154:acoustics
3303:Volition
3293:Thinking
3273:Learning
3222:Encoding
2967:Category
2808:Overtone
2776:Harmonic
2414:X System
2395:27906745
2344:Sethares
2328:Archived
2210:(2004).
2194:40043442
1881:See also
1699:semitone
1643:1,088.3
1196:P8 + P5
1125:perfect
1039:—
788:recorder
782:In many
565:overtone
547:(2004),
545:Sethares
488:trumpets
473:harmonic
465:periodic
300:, where
200:periodic
162:harmonic
3227:Storage
3095:methods
2754:Formant
2324:1549755
1999:Harmony
1964:Formant
1814:12,000
1781:11,400
1741:10,800
1706:10,200
1470:tritone
880:is the
866:strings
850:
838:
570:musical
538:cymbals
503:elastic
469:partial
174:integer
168:with a
150:physics
90:scholar
3232:Recall
3209:Memory
3199:Visual
3192:Speech
3172:Social
3152:Haptic
3125:Amodal
2947:Violin
2781:Series
2393:
2322:
2268:
2220:
2192:
2184:
2075:
1871:bowing
1817:386.3
1784:297.5
1744:203.9
1709:105.0
1673:9,600
1666:octave
1640:9,000
1608:968.8
1605:8,400
1566:840.5
1563:7,800
1525:702.0
1522:7,200
1493:551.3
1490:6,600
1447:386.3
1444:6,000
1415:203.9
1412:5,400
1375:4,800
1368:octave
1345:968.8
1342:4,200
1304:702.0
1301:3,600
1272:386.3
1269:3,000
1232:2,400
1225:octave
1202:702.0
1199:1,800
1167:1,200
1160:octave
1127:unison
1054:timbre
1046:(1879)
1003:
997:
966:
960:
929:
923:
830:unison
808:. The
796:timbre
792:octave
522:pianos
461:violin
446:timbre
156:, and
92:
85:
78:
71:
63:
3344:Sound
3241:Other
3187:Pitch
3177:Sound
3156:Touch
3142:Depth
3130:Color
2942:Piano
2927:Sound
2741:pitch
2703:Pitch
2446:from
2417:(PDF)
2391:S2CID
2340:(PDF)
2331:(PDF)
2320:S2CID
2298:(PDF)
2266:S2CID
2190:JSTOR
2073:S2CID
1805:just
1670:4·P8
1372:3·P8
1229:2·P8
1108:Audio
1100:above
1098:Cents
872:, or
870:brass
834:cello
587:Order
458:bowed
456:or a
417:above
182:of a
164:is a
134:nodes
97:JSTOR
83:books
3147:Form
2917:Echo
2823:Node
2749:Beat
2739:and
2218:ISBN
2182:ISSN
2143:2024
1825:Play
1792:Play
1752:Play
1717:Play
1684:Play
1676:0.0
1651:Play
1630:just
1616:Play
1574:Play
1533:Play
1501:Play
1455:Play
1423:Play
1386:Play
1378:0.0
1353:Play
1312:Play
1280:Play
1243:Play
1235:0.0
1210:Play
1178:Play
1170:0.0
1145:Play
1137:0.0
1134:600
753:= 4
743:4 ×
715:= 3
705:3 ×
677:= 2
663:2 ×
633:= 1
619:1 ×
490:and
352:and
268:and
160:, a
132:The
69:news
2524:doi
2483:doi
2381:doi
2312:doi
2256:doi
2174:doi
2065:doi
1802:20
1762:19
1727:18
1694:17
1661:16
1626:15
1584:14
1543:13
1511:12
1465:11
1433:10
1164:P8
1131:P1
1031:.'
824:or
563:An
507:gut
496:odd
413:all
314:not
228:An
148:In
52:by
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2570:.
2518:.
2506:^
2481:.
2477:.
2453:.
2389:.
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2375:.
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2264:.
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2250:.
2244:.
2188:.
2180:.
2145:.
2125:.
2099:.
2071:.
2063:.
2059:.
1560:↓
1396:9
1363:8
1322:7
1290:6
1253:5
1220:4
1188:3
1155:2
1117:1
1094:)
1092:Hz
985:,
948:,
868:,
847:3
841:1
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593:)
434:c.
221:AC
217:Hz
208:.
152:,
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2994:t
2987:v
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2607:t
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2526::
2500:.
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2426:.
2397:.
2383::
2350:.
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2308:2
2278:.
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2196:.
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2170:1
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970:3
963:1
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745:f
713:n
707:f
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665:f
631:n
625:0
621:f
591:n
589:(
439:)
395:n
391:n
382:L
366:3
363:2
350:L
334:3
331:1
310:n
306:n
302:L
298:L
282:3
279:2
266:L
250:3
247:1
234:n
230:n
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87:·
80:·
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46:.
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