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Topic: Harmonic series

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Harmonic series (music)

Microtonal music

Musical tuning

Equal temperament

Sound synthesis

FM synthesis

Just intonation

Harry Partch

Logarithm

Clarinet

Physical modelling synthesis

Woodwind instrument

ADSR

	Harmonic series (music) - Wikipedia, the free encyclopedia
		If the first 15 harmonics are transposed into the span of one octave, they approximate what the West has adopted as the major scale based on the fundamental tone.
		Rather than perceiving the individual harmonics of a musical tone, we perceive them together as a tone color or timbre, and we hear the overall pitch as the fundamental of the harmonic series being experienced.
		Notes that are not in the harmonic series are played by changing the effective length of the resonator, usually by opening a venting hole in the side of the instrument.
	en.wikipedia.org /wiki/Harmonic_series_(music) (2011 words)

	Harmonic series (music): Definition and Links by Encyclopedian.com - All about Harmonic series (music) (Site not responding. Last check: 2007-11-06)
		Pitched musical instruments are usually based on some sort of harmonic oscillator, for example a string or a column of air, which can oscillate at a number of frequencies.
		The second harmonic (or first overtone) is twice the frequency of the fundamental, which makes it an octave higher.
		On most wind instruments, for example the saxophone, oboe, or bassoon, there is an octave key which opens a small hole in the tube, prompting the instrument to oscillate at the second harmonic and giving the second octave of the instrument.
	www.encyclopedian.com /ha/Harmonic-series-(music).html (429 words)

	Harmonic series (mathematics) - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-06)
		In mathematics, the harmonic series is the infinite series
		Even the sum of the reciprocals of the prime numbers diverges to infinity (although that is much harder to prove; see proof that the sum of the reciprocals of the primes diverges).
		This is a consequence of the Taylor series of the natural logarithm.
	en.wikipedia.org /wiki/Harmonic_series_(mathematics) (270 words)

	Harmonic Series (Site not responding. Last check: 2007-11-06)
		Notice that the fourth harmonic is also twice the frequency of the second harmonic, and the sixth harmonic is also twice the frequency of the third harmonic.
		The fifth and tenth harmonics; the sixth and twelfth harmonics; the seventh and fourteenth harmonics; and the eighth and sixteenth harmonics
		The thinner, quieter sound of the harmonics is caused by the fact that much of the harmonic series is missing from the sound, which will of course be heard in the timbre.
	cnx.rice.edu /content/m11118/latest (2857 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		On most wind instruments, for example the saxophone, oboe, or bassoon, there is an octave key which opens a small hole in the tube, prompting the instrument to oscillate at the second harmonic partial and giving the second octave of the instrument.
		Some harmonics correspond very nearly to named pitches; others, for example the 7th harmonic, are signifigantly off from the equal tempered tones.
		In just intonation all notes are exact in regards to the harmonic series, and all intervals are based on ratios of the lower integers.
	www.informationgenius.com /encyclopedia/h/ha/harmonic_series__music_.html (588 words)

	The Harmonic Series
		Harmonics are generated (produced) by a fundamental sound wave that divides its length into smaller vibrating sections (which sound higher and softer).
		The octave is the lowest interval in the harmonic series and enjoys its unique and characteristic sound quality because of the distance between the fundamental tone and the first overtone of the harmonic series.
		Sound "quality" is determined by the harmonic profile or sound signature as a direct result of the specific pattern of intensity of individual components of the harmonic series of the sound source.
	www.cartage.org.lb /en/themes/Arts/music/elements/generalities/harmonic/harmonic.htm (1495 words)

	Harmonic Series
		The fundamental is the loudest, the first harmonic is the second loudest, and so-on.
		Ratio to Fundamental is the ratio in hertz between the harmonic and the fundamental.
		Harmonics refer to notes sounding above the fundamental as predicted by the harmonic series.
	www.organicdesign.org /peterson/tuning/harmonic_series.html (405 words)

	BAIN: The Harmonic Series (Overtone Series)
		For example, the series of frequencies 1000, 2000, 3000, 4000, 5000, 6000, etc., given in Hertz (Hz.), is a harmonic series; so is the series 500, 1000, 1500, 2000, 2500, 3000, etc. Notice that the difference between adjacent members of both series is constant, that is to say, the harmonics are equally-spaced.
		So that rather than perceiving the many individual harmonics of a musical tone, we ordinarily perceive an identifiable tone color, or timbre, whose pitch is associated with the fundamental of the harmonic series being experienced.
		During the Middle Ages (c476-1453) a Pythagorean tuning, a tuning derived from a series of six 3:2 fifths, was an accepted "standard" for tuning the seven tones of a diatonic scale.
	www.music.sc.edu /fs/bain/atmi02/hs/index-audio.html (3444 words)

	Harmonic series (music) (Site not responding. Last check: 2007-11-06)
		Put another way: since the harmonic series is an arithmetic series (1f, 2f, 3f, 4f...), and the octave, or octave series,is a geometric series (f, 2×f, 4×f, 8×f...), this causes theovertone series to divide the octave into increasingly smaller parts as it ascends.
		The third harmonic partial, at three times the frequency of the fundamental, is a perfect fifth above the second harmonic.Similarly, the fourth harmonic partial is four times the frequency of the fundamental; it is a perfect fourth above the thirdpartial (two octaves above the fundamental).
		Some harmonics correspond very nearly tonamed pitches; others, for example the 7th harmonic, are signifigantly off from the equal tempered tones.
	www.therfcc.org /harmonic-series-music--19312.html (661 words)

	Harmonic series (music) - Education - Information - Educational Resources - Encyclopedia - Music
		This is the note created from the vibration of the full string length (the first transverse vibrational mode) of a stringed instrument or from air compression waves vibrating through the whole length of a woodwind instrument (the first longitudinal vibrational mode).
		Put another way: since the harmonic series is an arithmetic series (1f, 2f, 3f, 4f...), and the octave, or octave series, is a geometric series (f, 2×f, 4×f, 8×f...), this causes the overtone series to divide the octave into increasingly smaller parts as it ascends.
		Some harmonics correspond very nearly to named pitches of the equal tempered scale; others, for example the 7th harmonic, are significantly off from the equal tempered tones.
	www.music.us /education/H/Harmonic-series-(music).htm (1316 words)

	PlanetMath: prime harmonic series
		harmonic series (also known as series of reciprocals of primes) is the infinite sum
		The series is in some ways similar to the Harmonic series
		This is version 13 of prime harmonic series, born on 2005-03-09, modified 2005-07-15.
	planetmath.org /encyclopedia/PrimeHarmonicSeries.html (206 words)

	SchenkerGUIDE: Harmonic Series
		This is the series of harmonics (or overtones, or partials) that resonate when you play a given note.
		Schenker argues that the harmonic series shows that the rising fifth is the basic motion of tonal music.
		The rising fifth in the harmonic series is the reason that our key system is best understood in terms of what is called the circle of fifths.
	www.schenkerguide.com /harmony2.html (327 words)

	Encyclopedia: Harmonic series (music) (Site not responding. Last check: 2007-11-06)
		A harmonic oscillator is either a mechanical system in which there exists a returning force F directly proportional to the displacement x, i.
		For cylindrical-bore brass instruments such as trumpet and trombone, the second harmonic is the lowest playable note.
		Throat singing, also known in the western world as overtone singing, harmonic singing, or harmonic chant; and many other regional names, is a type of singing that manipulates the harmonic resonances (or formants) created as air travels through the human vocal folds and out the lips.
	www.nationmaster.com /encyclopedia/Harmonic-series-(music) (3688 words)

	How harmonic are harmonics? (Site not responding. Last check: 2007-11-06)
		So this is no longer an exact harmonic series, and you can vary the departure from harmonicity by varying the size of the mass in the middle of the string.
		The two effects are related: when the series is harmonic, we hear a clear pitch, when it is far from harmonic, we usually do not hear a clear pitch, and the sound is more like that of a percussion instrument.
		The harmonic series is special because any combination of its vibrations produces a periodic or repeated vibration at the fundamental frequency f.
	www.phys.unsw.edu.au /~jw/harmonics.html (961 words)

	Rearranging The Alternating Harmonic Series (Intro)
		Conditionally convergent series are those series that converge as written, but do not converge when each of their terms is replaced by the corresponding absolute value.
		It is clear, however, that even with such a simple example as the alternating harmonic series one cannot hope for a closed form solution to the problem of rearranging it to sum to an arbitrary real number.
		The latter two questions are completely answered by Riemann's theorem for rearrangements of arbitrary conditionally convergent series, but our goal is to provide a more concrete setting of Riemann's results within the context of the alternating harmonic series with the hope that the reader will then have a better understanding of the general theory.
	ecademy.agnesscott.edu /~lriddle/series/rear.htm (552 words)

	A Tour Up The Harmonic Series
		By definition, the harmonic series is that sequence of frequencies which is all whole-number multiples of any particular fundamental frequency (see Figure (GIF) or EPS version).
		For example, the ratio 7/5 is the interval from the fifth harmonic to the seventh.
		The harmonic series occurs naturally in a variety of physical situations, but the most accessible example is that of a stretched string.
	www.redshift.com /~dcanright/harmser (2131 words)

	Why two notes of the harmonic series sound well together (Site not responding. Last check: 2007-11-06)
		The notes both belong to the harmonic series of their difference tone (if a note belongs to a harmonic series, so also do all the notes in its harmonic series).
		The clip goes up to the 30th harmonic, which is as far as one can go using the 15 simultaneous pitch bends available in MIDI (one for each melodic channel).
		so the 31st harmonic brings the number of simultaneous pitch bends needed to 16, and one of the earlier notes in the harmonic series would need to be switched off at that point.
	www.tunesmithy.connectfree.co.uk /harmonic_series_notes_sound_well_together.htm (451 words)

	Artifact
		All pitches are part of the harmonic series of a RphantomS 1/1, which is actually the III (A) string of the bass itself.
		Horn (for Krystyna Bobrowski) is a version of the harmonic idea I first used in Psaltery (one of several such "orchestrations" I've done over the past fifteen years): a continual modulation between three harmonic series.
		After building up the initial series on 1 in the first section, pitches from the next series (5, or the major third) begin to replace their closest neighbors in pitch from the series on 1 until the series on 5 is complete.
	www.perkis.com /artifact/release.php?id=1011 (1747 words)

	AllRefer.com - harmonic (Music: Theory, Forms, And Instruments) - Encyclopedia
		At most the first 16 tones in such a series can be heard by the human ear; the character or timbre of a fundamental tone is determined by the number of its subsidiary tones heard and their relative intensity.
		The subsidiary tones have been loosely called harmonics (as a noun), but they are properly called partials, the fundamental tone being the first partial.
		Similarly harmonics are produced separately in an air column by overblowing or in brass wind instruments by the use of valves.
	reference.allrefer.com /encyclopedia/H/harmonic.html (299 words)

	PlanetMath: harmonic series
		A harmonic series is any series of the form
		A harmonic series which is not summed to
		This is version 3 of harmonic series, born on 2002-09-09, modified 2005-02-28.
	planetmath.org /encyclopedia/HarmonicSeries.html (92 words)

	Explanation of the Harmonic Overtone Series
		When a string, tube, or reed is excited to periodic vibration, it produces a tone consisting of a fundamental tone at the lowest, primary frequency of vibration, and also a set of harmonic overtones.
		The frequencies of harmonic partials are integer multiples of the fundamental tone.
		The series then repeats without the drone, this time sustaining the notes so that up to 8 of them overlap and sound together.
	www.elvenminstrel.com /tolkien/otone.htm (505 words)

	HARMONIC SERIES IN - Online Information article about HARMONIC SERIES IN
		key; the third harmonic, which on the open tube would be B5, now becomes A; the fifth harmonic, which was G, is now F#, and so on.
		compass there must be seven positions or different lengths of tubing available, as on the trombone, each having its proper harmonic series.
		HARMONIC SERIES OF THE CONTRABASS BOMBARDON IN C
	encyclopedia.jrank.org /HAN_HEG/HARMONIC_SERIES_IN.html (2235 words)

	harmonic on Encyclopedia.com
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		Harmonic introduces high-performance video transport for small and mid-sized cable networks; MAXLink R series enables flexible and cost-effective delivery of analogue and digital television services.
		Harmonic announces digital compression products for the broadband network headend; TRANsend products offer communication service providers second generation advantages; support deployment of near- and on-demand video,...
	www.encyclopedia.com /html/h1/harmonic.asp (466 words)

	Math Lair - The Harmonic Series
		This series is called the harmonic series, a series that has been studied since ancient times.
		An interesting question to ask is whether the harmonic series converges (approaches a finite value as the number of terms in the series approaches infinity) or diverges (approaches infinity as the number of terms in the series approaches infinity).
		1323-1382), the Bishop of Lisieux, France, proved that the harmonic series diverged and was therefore unbounded.
	www.stormloader.com /ajy/harmonic.html (239 words)

	Exhibit Cross Reference - Harmonic Series Wheel (Site not responding. Last check: 2007-11-06)
		The HARMONIC SERIES WHEEL produces a palette of tones which can be used to explore the influence of harmonics on tone quality.
		The knobs control the intensity of 16 tones: a fundamental tone, followed by 15 tones in the harmonic series.
		By playing the fundamental tone and adding different harmonics, you can see and hear how the harmonic combinations affect the overall sound being produced and relate this to the characteristic tone qualities of different instruments.
	www.exploratorium.edu /xref/exhibits/harmonic_series_wheel.html (76 words)

	Harmonic Phasors and Fourier Series
		Fourier series description for periodic signals are based on alternate ways of writing a cosine signal.
		The Gibbs effect is the overshoot phenomenon exhibited by the truncated Fourier series at points of discontinuity.
		However, from the truncated series in the applet, it is clear that the Gibbs effect is present, and also that some type of convergence might be possible.
	www.jhu.edu /~signals/phasorlecture2/indexphasorlect2.htm (943 words)

	Untitled Document (Site not responding. Last check: 2007-11-06)
		The harmonic series can be compared to the idea of white light being made up of many different colours; every sound we hear is made up of many harmonics, but our ear picks up the most prominent one.
		Obviously, playing only the notes in the harmonic series (these are called ‘open’ notes) does not allow the player to produce every note in the scale, and this limitation led to many people experimenting with different ways of producing the notes they wanted.
		This way round the limitations of the harmonic series was in use from at least the mid 18th century, and is still taught to horn players today, although the hand-stopped note is now used as more of a special effect.
	www.students.arts.gla.ac.uk /0304mad/0005259/project/html/3.General%20Info/4.Workings/How%20Brass%20Works.htm (1245 words)

	BAIN: The Overtone/Harmonic Series
		Though musicians often use the two terms interchangeably, the term harmonic series specifically refers to a set of numbers related by whole number ratios.
		Though this traditional way of notating the harmonic series is obviously less precise at conveying frequency than the mathematical sequence notation used above, it does provide a convenient way for musicians to memorize the series as a kind-of chord/scale of nature.
		The 19th-Century physicist Herman von Helmholtz proposed a theory of consonance and dissonance based on the harmonic series, beating and roughness.
	www.music.sc.edu /fs/bain/atmi98/examples/os/index.html (2028 words)

	Convergence Criteria (Site not responding. Last check: 2007-11-06)
		But, on the other hand, the harmonic series is divergent while the hyper harmonic series is convergent.
		Note that this is essentially the hyperharmonic series version of an improper integrals result, namely (5.3.7).
		This series is convergent (6.2.7) but taking the absolute value of each term would make it the harmonic series, which is divergent (6.2.2).
	www.math.uconn.edu /~corluy/calculus/lecturenotes/node22.html (477 words)

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