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1434:
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20:
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332:
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1208:(not tempered) with a frequency ratio of 7:5 one gets, for example, 700 − 500 = 200 (1st order combination tone) and 500 − 200 = 300 (2nd order). The rest of the combination tones are octaves of 100 Hz so the 7:5 interval actually contains four notes: 100 Hz (and its octaves), 300 Hz, 500 Hz and 700 Hz. The lowest combination tone (100 Hz) is a seventeenth (two octaves and a
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of 100 Hz (the difference between 300 Hz and 200 Hz); that is, an octave below the lower (actual sounding) note. This 100 Hz first-order combination tone then interacts with both notes of the interval to produce second-order combination tones of 200 (300 − 100) and
378:
occur with varying prominence and give each instrument its characteristic tone quality. The fact that a string is fixed at each end means that the longest allowed wavelength on the string (which gives the fundamental frequency) is twice the length of the string (one round trip, with a half cycle
1361:
is heard as the fundamental of the harmonic series being experienced. If a sound is heard that is made up of even just a few simultaneous sine tones, and if the intervals among those tones form part of a harmonic series, the brain tends to group this input into a sensation of the pitch of the
304:, tone color, or character. When writing or speaking of overtones and partials numerically, care must be taken to designate each correctly to avoid any confusion of one for the other, so the second overtone may not be the third partial, because it is the second sound in a series.
299:
is any partial above the lowest partial. The term overtone does not imply harmonicity or inharmonicity and has no other special meaning other than to exclude the fundamental. It is mostly the relative strength of the different overtones that give an instrument its particular
1356:
Human ears tend to group phase-coherent, harmonically-related frequency components into a single sensation. Rather than perceiving the individual partials–harmonic and inharmonic, of a musical tone, humans perceive them together as a tone color or timbre, and the overall
602:
1194:
The frequencies of the harmonic series, being integer multiples of the fundamental frequency, are naturally related to each other by whole-numbered ratios and small whole-numbered ratios are likely the basis of the consonance of musical intervals (see
355:
was originally a valveless instrument that could play only the notes of the harmonic series"), although these are complicated by having the possibility of anti-nodes (that is, the air column is closed at one end and open at the other),
603:
617:, "the interval-distance of the natural-tone-row , counting up to 20, includes everything from the octave to the quarter tone, (and) useful and useless musical tones. The natural-tone-row justifies everything, that means, nothing."
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1435:
416:
at frequencies that are integer multiples of (e.g. 2, 3, 4 times) the fundamental frequency. Physical characteristics of the vibrating medium and/or the resonator it vibrates against often alter these frequencies. (See
1447:
1204:
100 (200 − 100) Hz and all further nth-order combination tones are all the same, being formed from various subtraction of 100, 200, and 300. When one contrasts this with a dissonant interval such as a
1407:
429:.) However, those alterations are small, and except for precise, highly specialized tuning, it is reasonable to think of the frequencies of the harmonic series as integer multiples of the fundamental frequency.
254:, and in instrument design, it is convenient, although not strictly accurate, to speak of the partials in those instruments' sounds as "harmonics", even though they may have some degree of inharmonicity. The
1423:
567:
258:, one of the most important instruments of western tradition, contains a certain degree of inharmonicity among the frequencies generated by each string. Other pitched instruments, especially certain
1898:
282:
contain mostly inharmonic partials, yet may give the ear a good sense of pitch because of a few strong partials that resemble harmonics. Unpitched, or indefinite-pitched instruments, such as
1349:-numbered harmonics are less present. The saxophone's resonator is conical, which allows the even-numbered harmonics to sound more strongly and thus produces a more complex tone. The
1199:). This objective structure is augmented by psychoacoustic phenomena. For example, a perfect fifth, say 200 and 300 Hz (cycles per second), causes a listener to perceive a
323:). Synthesizers can also combine pure frequencies into more complex tones, such as to simulate other instruments. Certain flutes and ocarinas are very nearly without overtones.
600:
347:
divides it into an integer number (1, 2, 3, 4, etc.) of equal-sized sections resonating at increasingly higher frequencies. Similar arguments apply to vibrating air columns in
613:
wrote: "The order of the
Consonances is natural, and ... the way we count them, starting from unity up to the number six and beyond is founded in nature." However, to quote
468:
is the fundamental frequency), the difference between consecutive harmonics is therefore constant and equal to the fundamental. But because human ears respond to sound
89:
simultaneously. At the frequencies of each vibrating mode, waves travel in both directions along the string or air column, reinforcing and canceling each other to form
374:
In most pitched musical instruments, the fundamental (first harmonic) is accompanied by other, higher-frequency harmonics. Thus shorter-wavelength, higher-frequency
511:
The second harmonic, whose frequency is twice the fundamental, sounds an octave higher; the third harmonic, three times the frequency of the fundamental, sounds a
526:
An illustration in musical notation of the harmonic series (on C) up to the 20th harmonic. The numbers above the harmonic indicate the difference – in
1951:
601:
564:
578:
Harmonic series as musical notation with intervals between harmonics labeled. Blue notes differ most significantly from equal temperament. One can listen to
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2040:. Eindhoven, Holland: Natuurkundig Laboratorium der N. V. Philips' Gloeilampenfabrieken (communicated by Prof. G. Holst at the meeting). pp. 356–65
1914:
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above the third harmonic (two octaves above the fundamental). Double the harmonic number means double the frequency (which sounds an octave higher).
145:
A "complex tone" (the sound of a note with a timbre particular to the instrument playing the note) "can be described as a combination of many simple
1377:, are caused by a combination of metal stiffness and the interaction of the vibrating air or string with the resonating body of the instrument.
1513:
1599:
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1989:
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1455:), respectively. The just minor third appears between harmonics 5 and 6 while the just fifth appears lower, between harmonics 2 and 3.
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637:, which is slightly out of tune with many of the harmonics, especially the 7th, 11th, and 13th harmonics. In the late 1930s, composer
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1955:
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1235:
is consonant with only the first 6 harmonics of the series (the seventh harmonic, a minor seventh, is not in the Ionian mode). The
1231:
is consonant with the first 10 harmonics of the harmonic series (the 11th harmonic, a tritone, is not in the
Mixolydian mode). The
633:
has adopted as the chromatic scale based on the fundamental tone. The
Western chromatic scale has been modified into twelve equal
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make sounds (produce spectra) that are rich in inharmonic partials and may give no impression of implying any particular pitch.
2092:] (in Russian) (Издание Третье, Исправленное и Дополненное = Third Edition, Revised and Enlarged ed.). Moscow: Музыка.
1396:) is determined by its approximation to a lower and stronger, or higher and weaker, position in the harmonic series. See also:
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fundamental pitch. These variations, most clearly documented in the piano and other stringed instruments but also apparent in
1609:
1579:
1523:
2118:
652:(12TET), octave displaced and compressed into the span of one octave. Tinted fields highlight differences greater than 5
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of air inside a chamber whose mouthpiece end is considered closed. Because the clarinet's resonator is cylindrical, the
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534:(rounded to the nearest integer). Blue notes are very flat and red notes are very sharp. Listeners accustomed to more
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are designed to have partials that are close to being whole-number ratios with very low inharmonicity; therefore, in
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above the second harmonic. The fourth harmonic vibrates at four times the frequency of the fundamental and sounds a
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579:
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Harmonics on C, from 1st (fundamental) to 32nd harmonic (five octaves higher). Notation used is based on the
1797:
555:
1811:
1274:
1865:
1627:, p. 143: "let it be understood, the second overtone is not the third tone of the series, but the second"
670:" for notes played one after the other (smaller differences are noticeable with notes played simultaneously).
2727:
308:
106:
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of a steady tone from such an instrument is strongly affected by the relative strength of each harmonic.
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over the full length of the string or air column, or a higher harmonic chosen by the player. The musical
192:) of which a complex tone is composed, not necessarily with an integer multiple of the lowest harmonic.
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2230:
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ringing of the instrument's metal resonator is even more prominent in the sounds of brass instruments.
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2002:
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fitting between the nodes at the two ends). Other allowed wavelengths are reciprocal multiples (e.g.
223:
is any real partial component of a complex tone that matches (or nearly matches) an ideal harmonic.
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2406:
236:
is a measure of the deviation of a partial from the closest ideal harmonic, typically measured in
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2701:
2143:
2111:
1979:
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1263:
559:
364:
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2225:
2135:
1509:
433:
368:
472:, higher harmonics are perceived as "closer together" than lower ones. On the other hand, the
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1922:
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Quantifying Music: The science of music at the first stage of scientific revolution 1580–1650
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477:
208:
189:
121:
57:
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1601:
The
Historical Harpsichord Volume Two: The Metallurgy of 17th- and 18th- Century Music Wire
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in the harmonic series is divided into increasingly "smaller" and more numerous intervals.
185:
23:
Harmonics of a string showing the periods of the pure-tone harmonics (period = 1/frequency)
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8:
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from no flare, cone flare, or exponentially shaped flares (such as in various bells).
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2011:
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343:, as in the illustration; the string has fixed points at each end, and each harmonic
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1882:
1693:(Summer 1991). "Ben Johnston's Extended Just Intonation: A guide for interpreters".
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170:
2004:
Genesis of a Music: An
Account of a Creative Work, Its Roots, and Its Fulfillments
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97:, which travel away from the instrument. Because of the typical spacing of the
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19:
1993:. Vol. 12 (11th ed.). Cambridge University Press. pp. 956, 958.
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1216:. All the intervals succumb to similar analysis as has been demonstrated by
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1998:
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Staff notation of partials 1, 3, 5, 7, 11, 13, 17, and 19 on C. These are "
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271:
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237:
40:
1545:
On the
Sensations of Tone as a Physiological Basis for the Theory of Music
648:
Below is a comparison between the first 31 harmonics and the intervals of
625:
If the harmonics are octave displaced and compressed into the span of one
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3010:
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1974:
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1224:, although he rejected the use of harmonics from the seventh and beyond.
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1277: in this section. Unsourced material may be challenged and removed.
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Experimental
Analysis of Shrutis from Performances in Hindustani Music
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Even-numbered string harmonics from 2nd up to the 64th (five octaves)
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216:
102:
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Music, Thought, and
Feeling: Understanding the Psychology of Music
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for alterations specific to wire-stringed instruments and certain
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Frequencies, wavelengths, and musical intervals in example systems
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1931:(in German). Braunschweig: Vieweg und Sohn. pp. I–XII, 1–606
1806:(London: Schott & Co; New York: Associated Music Publishers.
1392:, in which an interval's strength, consonance, or stability (see
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1213:
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101:, these frequencies are mostly limited to integer multiples, or
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1952:"Electropedia: The World's Online Electrotechnical Vocabulary"
1869:. Translated by John South Shedlock. London: Augener & Co.
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Variations in the frequency of harmonics can also affect the
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1309:(strengths) of the various harmonics primarily determine the
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2422:
1799:
The Craft of
Musical Composition: Book 1 – Theoretical Part
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146:
141:
Partial, harmonic, fundamental, inharmonicity, and overtone
1777:(1972). "Struktur und Expression bei Alexander Skrjabin",
2034:
The residue, a new component in subjective sound analysis
1325:, and inharmonicities also play a role. For example, the
629:, some of them are approximated by the notes of what the
1239:
is consonant with the first 14 harmonics of the series.
1885:. Huygens-Fokker Foundation centre for microtonal music
412:
Theoretically, these shorter wavelengths correspond to
105:, of the lowest frequency, and such multiples form the
1508:
230:
is any partial that does not match an ideal harmonic.
199:
is any member of the harmonic series, an ideal set of
93:. Interaction with the surrounding air causes audible
2084:Тюлин, Юрий Николаевич (1966). Беспалова, Н. (ed.).
1897:
Datta, A. K.; Sengupta, R.; Dey, N.; Nag, D. (2006).
1538:
641:
ranked musical intervals according to their relative
496:, ...), and people perceive these distances as "
1903:. Kolkata, India: SRD ITC SRA. pp. I–X, 1–103.
645:based on these and similar harmonic relationships.
2010:(2nd enlarged ed.). New York: Da Capo Press.
1313:of different instruments and sounds, though onset
1928:Die Lehre von dem Tonempfindungen. Zweite ausgabe
3090:
1838:, p. 40–41. New York, New York: Schirmer Books.
1431:), since they approximate a just perfect fifth (
1242:
1212:) below the lower (actual sounding) note of the
456:, ...). In terms of frequency (measured in
1562:
2728:
2513:
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116:of a note is usually perceived as the lowest
1789:
1787:
1552:(2nd ed.). Longmans, Green. p. 23.
339:One of the simplest cases to visualise is a
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2735:
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2506:
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2119:
2105:
1669:(3rd ed.). McGraw-Hill. p. 102.
666:of a semitone), which is the human ear's "
1956:International Electrotechnical Commission
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1293:Learn how and when to remove this message
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1636:
1572:Music, Cognition, and Computerized Sound
588:
573:
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18:
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1836:Techniques of the Contemporary Composer
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1518:. Oxford University Press. p. 46.
1403:Thus, an equal-tempered perfect fifth (
620:
3091:
2052:Волконский, Андрей Михайлович (1998).
1639:The Physics and Psychophysics of Music
1364:even if the fundamental is not present
2716:
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2100:
2031:Schouten, J. F. (February 24, 1940).
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1415:) is stronger than an equal-tempered
1825:
1380:
1275:adding citations to reliable sources
1246:
584:(110 Hz) and 15 of its partials
546:, notice many other notes are "off".
315:, can play a pure frequency with no
504:. In terms of what one hears, each
124:), which may be the one created by
13:
2058:(in Russian). Композитор, Москва.
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219:because it is one times itself. A
14:
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1341:, and both produce sound through
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1222:The Craft of Musical Composition
598:
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409:times) that of the fundamental.
1751:
1388:(1997) suggests the concept of
1262:needs additional citations for
367:, or end-openings that run the
157:each with its own frequency of
1883:"List of intervals (Compiled)"
1759:The Development of Harmony in
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1:
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1243:Timbre of musical instruments
1598:and Jay Scott Odell (1987).
1362:fundamental of that series,
188:calls them when translating
117:
7:
1458:
10:
3115:
1802:, pp. 15ff. Translated by
1637:Roederer, Juan G. (1995).
1570:. In Perry R. Cook (ed.).
668:just noticeable difference
432:The harmonic series is an
351:(for example, "the French
81:or a column of air, which
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2870:Music On A Long Thin Wire
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2759:
2702:List of musical intervals
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2515:Consonance and dissonance
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2415:
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1980:"Harmonic Analysis"
1737:. Springer. p. 103.
1696:Perspectives of New Music
1665:; Payne, Dorothy (1995).
1641:. Springer. p. 106.
1394:consonance and dissonance
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650:12-tone equal temperament
2766:Hornbostel–Sachs numbers
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1443:) and just minor third (
3099:Harmonic series (music)
2144:Architectural acoustics
2090:The teaching on harmony
1990:Encyclopædia Britannica
1757:Sabbagh, Peter (2003).
1568:"Consonance and Scales"
1475:Otonality and Utonality
184:(or "simple tones", as
16:Sequence of frequencies
2847:Long-string instrument
2231:Fletcher–Munson curves
2226:Equal-loudness contour
2136:Acoustical engineering
1510:William Forde Thompson
607:
586:
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556:extended just notation
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434:arithmetic progression
336:
309:electronic instruments
207:multiples of a common
70:are often based on an
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2367:Hermann von Helmholtz
2265:Fundamental frequency
2169:Sympathetic resonance
1540:Hermann von Helmholtz
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478:geometric progression
334:
262:instruments, such as
209:fundamental frequency
122:fundamental frequency
58:fundamental frequency
35:) is the sequence of
22:
1881:Coul, Manuel Op de.
1765:, p. 12. Universal.
1703:(2): 106–137 (121).
1550:Alexander John Ellis
1271:improve this article
679:Interval as a ratio
621:Harmonics and tuning
248:acoustic instruments
2387:Werner Meyer-Eppler
2297:Missing fundamental
1866:Dictionary of Music
1604:. Pendragon Press.
1237:Rishabhapriya ragam
682:Interval in binary
68:musical instruments
2854:Melde's experiment
2270:Frequency spectrum
1943:Sensations of Tone
1818:2014-07-01 at the
1485:Scale of harmonics
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500:" in the sense of
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240:for each partial.
228:inharmonic partial
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2842:Longitudinal wave
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2443:Musical acoustics
2275:harmonic spectrum
2086:Учение о гармонии
2055:Основы темперации
1781:, Vol. 6, p. 229.
1611:978-0-918728-54-8
1581:978-0-262-53190-0
1525:978-0-19-537707-1
1390:interval strength
1381:Interval strength
1375:brass instruments
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544:well temperaments
532:equal temperament
458:cycles per second
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2372:Carleen Hutchins
2304:Combination tone
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2164:String vibration
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2068:. Archived from
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2024:
2009:
1994:
1982:
1970:
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1967:
1958:. Archived from
1939:
1937:
1936:
1918:
1913:. Archived from
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1779:Musik des Ostens
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1548:. Translated by
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1490:Undertone series
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171:Fourier analysis
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2991:Japanese fiddle
2929:
2920:
2911:Transverse wave
2859:Mersenne's laws
2837:String harmonic
2769:
2755:
2741:
2711:
2706:
2693:
2657:
2606:
2602:
2597:
2517:
2512:
2482:
2477:
2459:
2411:
2402:D. Van Holliday
2340:
2309:Mersenne's laws
2243:Audio frequency
2237:
2201:Psychoacoustics
2195:
2194:
2187:
2173:
2130:
2125:
2087:
2083:
2075:
2073:
2066:
2056:
2051:
2043:
2041:
2037:
2030:
2022:
2020:
2018:
2007:
1997:
1973:
1965:
1963:
1949:
1934:
1932:
1921:
1911:
1896:
1888:
1886:
1880:
1877:
1875:Further reading
1851:
1850:
1830:
1826:
1820:Wayback Machine
1794:Hindemith, Paul
1792:
1785:
1756:
1752:
1745:
1728:
1724:
1688:
1684:
1677:
1660:
1656:
1649:
1635:
1631:
1623:
1619:
1612:
1593:
1589:
1582:
1561:
1557:
1537:
1533:
1526:
1507:
1503:
1498:
1480:Piano acoustics
1461:
1448:
1445:
1444:
1436:
1433:
1432:
1424:
1421:
1420:
1408:
1405:
1404:
1398:Lipps–Meyer law
1383:
1299:
1288:
1282:
1279:
1268:
1256:
1245:
1229:Mixolydian mode
1197:just intonation
1109:
1108:
1103:
1102:
1017:
1016:
1011:
1010:
925:
924:
919:
918:
827:
826:
821:
820:
759:
758:
753:
752:
685:12TET interval
662:
658:
657:
623:
599:
583:
563:
427:electric pianos
405:
401:
400:
395:
391:
390:
385:
381:
380:
329:
143:
138:
107:harmonic series
33:overtone series
29:harmonic series
17:
12:
11:
5:
3112:
3102:
3101:
3084:
3083:
3081:
3080:
3075:
3070:
3065:
3060:
3055:
3050:
3045:
3040:
3035:
3030:
3029:
3028:
3023:
3018:
3013:
3008:
3003:
2993:
2988:
2983:
2978:
2973:
2968:
2963:
2958:
2957:
2956:
2949:Bladder fiddle
2946:
2941:
2935:
2933:
2922:
2921:
2919:
2918:
2913:
2908:
2903:
2898:
2893:
2888:
2883:
2878:
2873:
2866:
2861:
2856:
2851:
2850:
2849:
2839:
2822:
2817:
2812:
2807:
2802:
2797:
2792:
2791:
2790:
2780:
2774:
2771:
2770:
2760:
2757:
2756:
2740:
2739:
2732:
2725:
2717:
2708:
2707:
2705:
2704:
2698:
2695:
2694:
2692:
2691:
2686:
2681:
2676:
2671:
2665:
2663:
2659:
2658:
2656:
2655:
2650:
2645:
2640:
2635:
2633:Perfect fourth
2630:
2625:
2620:
2614:
2612:
2608:
2607:
2600:
2598:
2596:
2595:
2590:
2589:
2588:
2583:
2578:
2573:
2571:Changing tones
2568:
2558:
2553:
2548:
2543:
2538:
2533:
2528:
2522:
2519:
2518:
2511:
2510:
2503:
2496:
2488:
2479:
2478:
2476:
2475:
2464:
2461:
2460:
2458:
2457:
2456:
2455:
2450:
2440:
2435:
2430:
2425:
2419:
2417:
2416:Related topics
2413:
2412:
2410:
2409:
2404:
2399:
2397:Joseph Sauveur
2394:
2389:
2384:
2382:Marin Mersenne
2379:
2374:
2369:
2364:
2359:
2354:
2348:
2346:
2342:
2341:
2339:
2338:
2333:
2332:
2331:
2321:
2316:
2311:
2306:
2301:
2300:
2299:
2294:
2289:
2279:
2278:
2277:
2267:
2262:
2257:
2251:
2249:
2239:
2238:
2236:
2235:
2234:
2233:
2223:
2222:
2221:
2216:
2205:
2203:
2197:
2196:
2193:
2192:
2185:
2177:
2176:
2174:
2172:
2171:
2166:
2161:
2156:
2151:
2146:
2140:
2138:
2132:
2131:
2124:
2123:
2116:
2109:
2101:
2095:
2094:
2081:
2064:
2049:
2028:
2016:
1995:
1985:Chisholm, Hugh
1971:
1947:
1919:
1917:on 2012-01-18.
1909:
1894:
1876:
1873:
1872:
1871:
1849:
1848:
1824:
1783:
1775:Dahlhaus, Carl
1750:
1743:
1722:
1709:10.2307/833435
1691:Fonville, John
1682:
1675:
1663:Kostka, Stefan
1654:
1647:
1629:
1617:
1610:
1596:Martha Goodway
1587:
1580:
1564:John R. Pierce
1555:
1531:
1524:
1500:
1499:
1497:
1494:
1493:
1492:
1487:
1482:
1477:
1472:
1467:
1465:Fourier series
1460:
1457:
1382:
1379:
1301:
1300:
1259:
1257:
1250:
1244:
1241:
1218:Paul Hindemith
1190:
1189:
1186:
1183:
1182:31/16 (1.9375)
1180:
1177:
1175:
1173:
1171:
1168:
1167:
1164:
1161:
1158:
1155:
1152:
1149:
1146:
1144:
1142:
1139:
1138:
1135:
1132:
1131:29/16 (1.8125)
1129:
1126:
1124:
1122:
1120:
1117:
1116:
1113:
1099:
1096:
1093:
1090:
1087:
1084:
1081:
1079:
1076:
1075:
1072:
1069:
1066:
1063:
1062:27/16 (1.6875)
1060:
1057:
1055:
1053:
1051:
1048:
1047:
1044:
1041:
1038:
1035:
1032:
1030:
1028:
1025:
1024:
1021:
1007:
1004:
1001:
1000:25/16 (1.5625)
998:
995:
993:
991:
989:
986:
985:
982:
979:
976:
973:
970:
967:
964:
961:
958:
955:
954:
951:
948:
947:23/16 (1.4375)
945:
942:
940:
938:
936:
933:
932:
929:
915:
912:
909:
906:
903:
900:
898:
896:
893:
892:
889:
886:
883:
880:
879:21/16 (1.3125)
877:
874:
872:
870:
868:
865:
864:
861:
858:
855:
852:
849:
846:
843:
840:
838:
835:
834:
831:
817:
814:
811:
810:19/16 (1.1875)
808:
805:
803:
801:
799:
796:
795:
792:
789:
786:
783:
780:
777:
774:
772:
770:
767:
766:
763:
749:
746:
743:
742:17/16 (1.0625)
740:
737:
735:
733:
731:
728:
727:
724:
721:
720:prime (octave)
718:
715:
712:
709:
706:
703:
700:
696:
695:
689:
686:
683:
680:
677:
639:Paul Hindemith
622:
619:
611:Marin Mersenne
581:
517:perfect fourth
360:as opposed to
328:
325:
180:is any of the
169:". (See also,
147:periodic waves
142:
139:
137:
134:
91:standing waves
55:multiple of a
15:
9:
6:
4:
3:
2:
3111:
3100:
3097:
3096:
3094:
3079:
3076:
3074:
3071:
3069:
3066:
3064:
3061:
3059:
3058:Tromba marina
3056:
3054:
3051:
3049:
3046:
3044:
3041:
3039:
3036:
3034:
3031:
3027:
3024:
3022:
3019:
3017:
3014:
3012:
3009:
3007:
3004:
3002:
2999:
2998:
2997:
2994:
2992:
2989:
2987:
2984:
2982:
2979:
2977:
2974:
2972:
2969:
2967:
2964:
2962:
2959:
2955:
2952:
2951:
2950:
2947:
2945:
2942:
2940:
2937:
2936:
2934:
2932:
2927:
2923:
2917:
2914:
2912:
2909:
2907:
2904:
2902:
2901:Standing wave
2899:
2897:
2894:
2892:
2889:
2887:
2884:
2882:
2879:
2877:
2874:
2872:
2871:
2867:
2865:
2862:
2860:
2857:
2855:
2852:
2848:
2845:
2844:
2843:
2840:
2838:
2834:
2830:
2826:
2823:
2821:
2818:
2816:
2813:
2811:
2808:
2806:
2803:
2801:
2798:
2796:
2793:
2789:
2786:
2785:
2784:
2781:
2779:
2776:
2775:
2772:
2767:
2763:
2758:
2754:
2750:
2746:
2738:
2733:
2731:
2726:
2724:
2719:
2718:
2715:
2703:
2700:
2699:
2696:
2690:
2689:Major seventh
2687:
2685:
2684:Minor seventh
2682:
2680:
2677:
2675:
2672:
2670:
2667:
2666:
2664:
2660:
2654:
2651:
2649:
2646:
2644:
2641:
2639:
2638:Perfect fifth
2636:
2634:
2631:
2629:
2626:
2624:
2621:
2619:
2616:
2615:
2613:
2609:
2594:
2591:
2587:
2584:
2582:
2579:
2577:
2574:
2572:
2569:
2567:
2564:
2563:
2562:
2561:Nonchord tone
2559:
2557:
2554:
2552:
2549:
2547:
2544:
2542:
2539:
2537:
2534:
2532:
2529:
2527:
2524:
2523:
2520:
2516:
2509:
2504:
2502:
2497:
2495:
2490:
2489:
2486:
2474:
2466:
2465:
2462:
2454:
2451:
2449:
2446:
2445:
2444:
2441:
2439:
2436:
2434:
2431:
2429:
2426:
2424:
2421:
2420:
2418:
2414:
2408:
2405:
2403:
2400:
2398:
2395:
2393:
2392:Lord Rayleigh
2390:
2388:
2385:
2383:
2380:
2378:
2375:
2373:
2370:
2368:
2365:
2363:
2362:Ernst Chladni
2360:
2358:
2355:
2353:
2350:
2349:
2347:
2343:
2337:
2334:
2330:
2327:
2326:
2325:
2324:Standing wave
2322:
2320:
2317:
2315:
2312:
2310:
2307:
2305:
2302:
2298:
2295:
2293:
2292:Inharmonicity
2290:
2288:
2285:
2284:
2283:
2280:
2276:
2273:
2272:
2271:
2268:
2266:
2263:
2261:
2258:
2256:
2253:
2252:
2250:
2248:
2244:
2240:
2232:
2229:
2228:
2227:
2224:
2220:
2217:
2215:
2212:
2211:
2210:
2207:
2206:
2204:
2202:
2198:
2190:
2186:
2183:
2179:
2178:
2170:
2167:
2165:
2162:
2160:
2159:Soundproofing
2157:
2155:
2154:Reverberation
2152:
2150:
2147:
2145:
2142:
2141:
2139:
2137:
2133:
2129:
2122:
2117:
2115:
2110:
2108:
2103:
2102:
2099:
2091:
2082:
2072:on 2023-04-18
2071:
2067:
2065:5-85285-184-1
2061:
2057:
2050:
2036:
2035:
2029:
2019:
2017:0-306-80106-X
2013:
2006:
2005:
2000:
1999:Partch, Harry
1996:
1992:
1991:
1986:
1981:
1976:
1972:
1962:on 2016-06-19
1961:
1957:
1953:
1948:
1945:
1944:
1930:
1929:
1924:
1923:Helmholtz, H.
1920:
1916:
1912:
1910:81-903818-0-6
1906:
1902:
1901:
1895:
1884:
1879:
1878:
1868:
1867:
1862:
1861:Riemann, Hugo
1858:
1857:
1856:
1855:
1845:
1844:0-02-864737-8
1841:
1837:
1833:
1828:
1821:
1817:
1813:
1809:
1805:
1804:Arthur Mendel
1801:
1800:
1795:
1790:
1788:
1780:
1776:
1772:
1771:9781581125955
1768:
1764:
1762:
1754:
1746:
1744:9789401576864
1740:
1736:
1732:
1726:
1718:
1714:
1710:
1706:
1702:
1698:
1697:
1692:
1686:
1678:
1676:0-07-035874-5
1672:
1668:
1667:Tonal Harmony
1664:
1658:
1650:
1648:0-387-94366-8
1644:
1640:
1633:
1626:
1621:
1613:
1607:
1603:
1602:
1597:
1591:
1583:
1577:
1574:. MIT Press.
1573:
1569:
1565:
1559:
1551:
1547:
1546:
1541:
1535:
1527:
1521:
1517:
1516:
1511:
1505:
1501:
1491:
1488:
1486:
1483:
1481:
1478:
1476:
1473:
1471:
1470:Klang (music)
1468:
1466:
1463:
1462:
1456:
1451:
1439:
1427:
1418:
1411:
1401:
1399:
1395:
1391:
1387:
1378:
1376:
1372:
1367:
1365:
1360:
1354:
1352:
1348:
1344:
1340:
1336:
1333:have similar
1332:
1328:
1324:
1320:
1316:
1312:
1308:
1305:The relative
1297:
1294:
1286:
1283:November 2011
1276:
1272:
1266:
1265:
1260:This section
1258:
1254:
1249:
1248:
1240:
1238:
1234:
1230:
1225:
1223:
1219:
1215:
1211:
1207:
1202:
1198:
1184:
1181:
1178:
1176:
1174:
1172:
1170:
1169:
1160:major seventh
1156:
1153:
1150:
1147:
1145:
1143:
1141:
1140:
1133:
1130:
1127:
1125:
1123:
1121:
1119:
1118:
1098:minor seventh
1094:
1091:
1088:
1085:
1082:
1080:
1078:
1077:
1070:
1067:
1064:
1061:
1058:
1056:
1054:
1052:
1050:
1049:
1042:
1039:
1036:
1033:
1031:
1029:
1027:
1026:
1002:
999:
996:
994:
992:
990:
988:
987:
983:
980:
977:
974:
971:
968:
965:
962:
959:
957:
956:
949:
946:
943:
941:
939:
937:
935:
934:
910:
907:
904:
901:
899:
897:
895:
894:
887:
884:
881:
878:
875:
873:
871:
869:
867:
866:
859:
856:
853:
850:
847:
844:
841:
839:
837:
836:
832:
818:
815:
812:
809:
806:
804:
802:
800:
798:
797:
793:
790:
787:
784:
781:
778:
775:
773:
771:
769:
768:
764:
750:
747:
744:
741:
738:
736:
734:
732:
730:
729:
725:
722:
719:
716:
713:
710:
707:
704:
701:
698:
697:
694:
690:
687:
684:
681:
678:
674:
671:
669:
655:
651:
646:
644:
640:
636:
632:
628:
618:
616:
615:Carl Dahlhaus
612:
596:
591:
585:
576:
561:
557:
552:
545:
541:
537:
533:
530:– from
529:
524:
520:
518:
514:
513:perfect fifth
509:
507:
503:
499:
495:
491:
487:
483:
479:
475:
471:
467:
463:
459:
455:
451:
447:
443:
439:
435:
430:
428:
424:
420:
419:inharmonicity
415:
410:
377:
372:
370:
366:
363:
359:
354:
350:
346:
342:
333:
324:
322:
318:
314:
310:
305:
303:
298:
297:
291:
289:
285:
281:
280:singing bowls
277:
273:
272:tubular bells
269:
265:
261:
257:
253:
249:
246:
241:
239:
235:
234:
233:Inharmonicity
229:
224:
222:
218:
214:
210:
206:
202:
198:
193:
191:
187:
183:
179:
174:
172:
168:
164:
160:
156:
152:
148:
133:
131:
127:
123:
120:present (the
119:
115:
110:
108:
104:
100:
96:
92:
88:
84:
80:
76:
73:
69:
66:
62:
60:
59:
54:
50:
46:
42:
41:musical tones
38:
34:
30:
21:
3078:Washtub bass
2931:musical bows
2891:Scale length
2868:
2828:
2788:Third bridge
2674:Major second
2669:Minor second
2592:
2556:Musical note
2407:Thomas Young
2357:Jens Blauert
2345:Acousticians
2286:
2089:
2074:. Retrieved
2070:the original
2042:. Retrieved
2033:
2021:. Retrieved
2003:
1988:
1975:Lamb, Horace
1964:. Retrieved
1960:the original
1950:IEV (1994).
1941:
1933:. Retrieved
1927:
1915:the original
1899:
1887:. Retrieved
1864:
1853:
1852:
1835:
1827:
1798:
1778:
1758:
1753:
1734:
1731:Cohen, H. F.
1725:
1700:
1694:
1685:
1666:
1657:
1638:
1632:
1625:Riemann 1896
1620:
1600:
1590:
1571:
1558:
1544:
1534:
1514:
1504:
1402:
1384:
1370:
1368:
1355:
1346:
1304:
1289:
1280:
1269:Please help
1264:verification
1261:
1226:
1221:
1220:in his book
1193:
1154:15/8 (1.875)
1040:13/8 (1.625)
908:11/8 (1.375)
788:major second
748:minor second
647:
624:
609:
560:Ben Johnston
510:
493:
489:
485:
481:
476:series is a
465:
453:
449:
445:
441:
437:
431:
411:
373:
338:
313:synthesizers
306:
294:
292:
252:music theory
242:
231:
227:
225:
220:
212:
196:
194:
177:
175:
154:
144:
136:Terminology
112:The musical
111:
85:at numerous
63:
56:
32:
28:
26:
3053:Psalmodicon
2966:Diddley bow
2825:Fundamental
2815:Fingerboard
2795:Chordophone
2753:instruments
2662:Dissonances
2648:Major sixth
2643:Minor sixth
2628:Major third
2623:Minor third
2611:Consonances
2581:Preparation
2576:Pedal point
2377:Franz Melde
2352:John Backus
2336:Subharmonic
2189:Spectrogram
1832:Cope, David
1417:minor third
1335:mouthpieces
1233:Ionian mode
1210:major third
1068:major sixth
1006:minor sixth
857:major third
816:minor third
782:9/8 (1.125)
597:harmonics".
470:nonlinearly
362:cylindrical
213:fundamental
201:frequencies
95:sound waves
2986:Ichigenkin
2981:Ground bow
2926:Monochords
2916:Tuning peg
2896:Soundboard
2810:Enharmonic
2586:Resolution
2531:Avoid note
2438:Ultrasound
2428:Infrasound
2214:Bark scale
2076:2016-06-15
2044:2016-09-26
2023:2016-06-15
1966:2016-06-15
1935:2016-10-12
1889:2016-06-15
1812:0901938300
1386:David Cope
1351:inharmonic
1315:transients
1307:amplitudes
1166:−12
1115:−31
1092:7/4 (1.75)
1023:−27
931:−49
891:−29
863:−14
851:5/4 (1.25)
643:dissonance
414:vibrations
311:, such as
268:vibraphone
260:percussion
182:sine waves
151:sine waves
99:resonances
83:oscillates
77:such as a
45:pure tones
3033:Langeleik
2971:Duxianqin
2864:Monochord
2833:Overtones
2829:Harmonics
2319:Resonance
2219:Mel scale
2149:Monochord
2128:Acoustics
1773:. Cites:
1371:perceived
1343:resonance
1331:saxophone
972:3/2 (1.5)
833:−2
691:Variance
676:Harmonic
635:semitones
321:sine wave
317:overtones
203:that are
190:Helmholtz
163:amplitude
159:vibration
155:partials,
126:vibration
103:harmonics
75:resonator
49:frequency
37:harmonics
3093:Category
3048:Onavillu
3001:Genggong
2996:Jaw harp
2944:Berimbau
2886:Re-entry
2743:Musical
2566:Cambiata
2551:Interval
2526:Argument
2473:Category
2314:Overtone
2282:Harmonic
2001:(1974).
1977:(1911).
1925:(1865).
1863:(1896).
1834:(1997).
1816:Archived
1796:(1942).
1763:'s Works
1761:Scriabin
1733:(2013).
1566:(2001).
1542:(1885).
1512:(2008).
1459:See also
1327:clarinet
1319:formants
1110:♭
1104:♯
1018:♭
1012:♯
926:♭
920:♯
828:♭
822:♯
760:♭
754:♯
540:meantone
498:the same
464:, where
296:overtone
288:tam-tams
217:harmonic
197:harmonic
72:acoustic
3068:Umuduri
3043:Masenqo
3026:Mukkuri
3021:Morsing
2961:Đàn bầu
2954:Boom-ba
2939:Ahardin
2745:strings
2679:Tritone
2593:Spectra
2541:Cadence
2536:Beating
2260:Formant
1987:(ed.).
1854:Sources
1214:tritone
1206:tritone
914:tritone
661:⁄
404:⁄
394:⁄
384:⁄
358:conical
284:cymbals
276:timpani
264:marimba
245:pitched
178:partial
149:(i.e.,
118:partial
65:Pitched
53:integer
3073:Unitar
3038:Lesiba
3016:Kubing
3011:Khomuz
3006:Gogona
2976:Ektara
2800:Course
2783:Bridge
2751:, and
2653:Octave
2618:Unison
2453:Violin
2287:Series
2062:
2014:
1907:
1842:
1810:
1769:
1741:
1717:833435
1715:
1673:
1645:
1608:
1578:
1522:
1323:noises
1311:timbre
1185:1.1111
1134:1.1101
1065:1.1011
1003:1.1001
950:1.0111
885:fourth
882:1.0101
813:1.0011
745:1.0001
627:octave
506:octave
474:octave
302:timbre
278:, and
211:. The
165:, and
130:timbre
79:string
51:is an
47:whose
31:(also
3063:Tumbi
2805:Drone
2749:wires
2546:Chord
2448:Piano
2433:Sound
2247:pitch
2209:Pitch
2088:[
2038:(PDF)
2008:(PDF)
1983:. In
1940:(see
1713:JSTOR
1496:Notes
1359:pitch
1339:reeds
1157:1.111
1043:1.101
978:fifth
911:1.011
785:1.001
693:cents
688:Note
654:cents
595:prime
536:tonal
528:cents
462:hertz
460:, or
376:waves
369:gamut
365:bores
307:Some
256:piano
243:Many
238:cents
215:is a
186:Ellis
167:phase
153:) or
114:pitch
87:modes
43:, or
2876:Node
2820:Fret
2762:List
2423:Echo
2329:Node
2255:Beat
2245:and
2060:ISBN
2012:ISBN
1905:ISBN
1840:ISBN
1808:ISBN
1767:ISBN
1739:ISBN
1671:ISBN
1643:ISBN
1606:ISBN
1576:ISBN
1520:ISBN
1449:play
1437:play
1425:play
1409:play
1347:even
1337:and
1329:and
1227:The
1188:+45
1137:+30
1095:1.11
1046:+41
953:+28
854:1.01
714:1, 2
631:West
542:and
492:, 16
421:and
353:horn
345:mode
286:and
2928:and
2881:Nut
2778:Bow
1814:).
1705:doi
1273:by
1107:, B
1074:+6
1015:, A
984:+2
975:1.1
923:, G
825:, E
794:+4
765:+5
757:, D
558:by
488:, 8
484:, 4
452:, 5
448:, 4
444:, 3
440:, 2
319:(a
293:An
226:An
173:.)
3095::
2747:,
1954:.
1786:^
1711:.
1701:29
1699:.
1400:.
1366:.
1321:,
1317:,
1179:31
1151:30
1148:15
1128:29
1089:28
1086:14
1059:27
1037:26
1034:13
997:25
969:24
966:12
944:23
905:22
902:11
876:21
848:20
845:10
807:19
779:18
739:17
726:0
711:16
663:20
480:(2
399:,
389:,
274:,
270:,
266:,
195:A
176:A
161:,
109:.
61:.
39:,
27:A
2835:/
2831:/
2827:/
2768:)
2764:(
2736:e
2729:t
2722:v
2507:e
2500:t
2493:v
2120:e
2113:t
2106:v
2079:.
2047:.
2026:.
1969:.
1946:)
1938:.
1892:.
1846:.
1822:.
1747:.
1719:.
1707::
1679:.
1651:.
1614:.
1584:.
1528:.
1419:(
1296:)
1290:(
1285:)
1281:(
1267:.
1163:B
1101:A
1083:7
1071:A
1009:G
981:G
963:6
960:3
917:F
888:F
860:E
842:5
819:D
791:D
776:9
751:C
723:C
717:1
708:8
705:4
702:2
699:1
659:1
656:(
582:2
580:A
494:f
490:f
486:f
482:f
466:f
454:f
450:f
446:f
442:f
438:f
436:(
406:4
402:1
396:3
392:1
386:2
382:1
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