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Topic: Harmonic number

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	Harmonic number - Wikipedia, the free encyclopedia
		In mathematics, the n-th harmonic number is n times the inverse of the harmonic mean of the first n integers.
		Harmonic numbers were studied in antiquity and are important in various branches of number theory.
		They are sometimes loosely termed harmonic series, are closely related to the Riemann zeta function and appear in various expressions for various special functions.
	en.wikipedia.org /wiki/Harmonic_number (466 words)

	Harmonic series (mathematics) - Wikipedia, the free encyclopedia
		The harmonic series diverges, albeit slowly, to infinity.
		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).
		The difference between distinct harmonic numbers is never an integer.
	en.wikipedia.org /wiki/Harmonic_series_(mathematics) (419 words)

	Low noise fan assembly - Patent 5169288
		The number of vanes is selected for a predetermined number of blades for obtaining substantially equal values of a cut-off ratio for at least two blade passing frequency harmonics for reducing spinning mode noise from the duct.
		In other words, the number of vanes V may be relative to a predetermined number of blades B for obtaining simultaneously substantially equal values of the cut-off ratios for at least two of the harmonic numbers n.
		Since the magnitude of contribution to the overall noise spectrum decreases as the harmonic number increases, the noise attributable to the second harmonic associated with the second curve 72 is substantially greater than the noise contributed by the third harmonic associated with the third curve 74.
	www.freepatentsonline.com /5169288.html (5405 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.
		You achieve this by dividing the ratio by the appropriate power of two, (equivalent to transposing down a number of octaves) so that your result is a ratio between 1/1 and 2/1.
	www.organicdesign.org /peterson/tuning/harmonic_series.html (405 words)

	Harmonic Charts
		A harmonic horoscope is derived by multiplying the longitude of every planet by a number to arrive at the planets' new zodiacal position in that harmonic number.
		In the President's Seventh Harmonic chart, his glorified macho planets, Mars and Neptune at 14 and 18 Scorpio, are in a stressful square to Saturn at 15 Leo, suggesting a fear of impotence (Saturn square Mars).
		Harmonics is for those who love astrology because they love the mystery of order, because they see beauty in the infinite wisdom that correlates cosmic activity with human experience.
	www.newage-directory.com /harmonic.htm (2740 words)

	Fundamentals of Harmonics
		Harmonics: It surfaced as a buzzword in the early 1980s, making many people reconsider the effectiveness of their building's wiring system.
		We define harmonics as voltages or currents at frequencies that are a multiple of the fundamental frequency.
		For example, a harmonic with a frequency of 180 Hz is known as the third harmonic (60x3 = 180).
	www.ecmweb.com /mag/electric_fundamentals_harmonics (792 words)

	[No title]
		Harmonic 0 specifies that an overall (rms) amplitude envelope plot is desired.
		For each point in time the normalized spectral centroid is defined as the ratio of the sum of harmonic amplitudes each weighted by their harmonic numbers divided by the simple sum of harmonic amplitudes.
		ff--Replace each harmonic frequency deviation with the deviation of a designated harmonic scaled by k/k0, where k is the current harmonic number and k0 is the designated harmonic number.
	www.cnmat.berkeley.edu /SDIF/ICMC2000/results/CD/software/SNDAN/more-documentation/monan.doc (1797 words)

	Introduction To The Harmonic Aspects Method
		Both the Harmonic Aspect Method and Harmonic Astrology use the finding of John Addey that traditional esoteric teachings on the significance of numbers provide clues to the meanings of the various series of aspects.
		A harmonic aspect is any division of the 360-degree circle which can be defined by a fraction in which both the numerator and the denominator are integers.
		Theoretically, it is possible to analyze every horoscope in terms of any of an infinite number of Harmonic Aspect Series but, beyond about the 36th or 37th aspect series, they seem to have less and less relevance to the cognitive levels of human experience.
	accessnewage.com /articles/astro/ha_intro.htm (3006 words)

	id:A001599 - OEIS Search Results
		Harmonic or Ore numbers: numbers n such that harmonic mean of divisors of n is an integer.
		Equivalently, ntau(n)/sigma(n) is an integer, where tau(n) (A000005) is the number* of divisors of n and sigma(n) is the sum of the divisors of n (A000203).
		sigma_0(n) is the number of divisors of n (A000005).
	www.research.att.com /~njas/sequences/A001599 (417 words)

	Effects of Noise on Sampler Quantization Errors
		To investigate the generation of harmonics by quantization errors the test signal is a 20 Hz sine wave intentionally centered on one of the FFT spectrum channels to eliminate any windowing sidelobes that would obscure the sine wave's harmonics.
		The number of spurious signals is far greater than is seen with a single sine wave, although the peak spurious signal intensity is about 7 dB lower that the strongest harmonic in Figure 5.
		All of the harmonics are definitely produced by A/D quantization because the strength of the harmonics relative to the fundamental decreases with increasing fundamental amplitude.
	www.cv.nrao.edu /~rfisher/SamplerErr/harmonics.html (1863 words)

	PlanetMath: harmonic number
		, then we get what is known simply as“the harmonic number”, and it has many important properties.
		See Also: series, convergent series, harmonic series, prime harmonic series
		This is version 7 of harmonic number, born on 2002-09-05, modified 2006-08-10.
	planetmath.org /encyclopedia/HarmonicNumberOfOrder.html (120 words)

	PQ Corner: Harmonic Current and Voltage Distortion
		Distortion rms is the rms value of the harmonic voltage with the fundamental left out of the summation, and it increases the farther away you measure from the source.
		Since transformer impedance is frequency dependent, increasing with harmonic number, the impedance at the 5th harmonic is five times that of the fundamental frequency.
		These 3rd harmonic currents circulate in the primary (delta) of the distribution transformer that serves the portion of the system powering the computers and are dissipated as heat.
	www.ecmweb.com /mag/electric_harmonic_current_voltage (1912 words)

	David Hykes's HARMONIC WORLD - Harmonic Chant, Healing Sounds, Overtone Singing (Site not responding. Last check: 2007-10-31)
		The harmonic emanations of that creating the universe through the radiance of the harmonic energetic forms...the first note dividing in spectral diffusion, the octave, simultaenous realiies...
		The Harmonic Choir is very well-known internationally and has given concerts in some twenty countries since their first concert in 1975.
		JOEL BLUESTEIN (The "Harmonic Meditation" trios and "The Silent Ground") is the owner of Dreamland Recording Studio in Woodstock, New York and works as a producer, guitarist and singer in NYC.
	www.harmonicworld.com /HTML/biograph.htm (1375 words)

	Mindconnection's Electrical Connection: Harmonic Power Flow Direction
		When the phase angle of the harmonic voltage and current is between 90 degrees and 270 degrees (270 is also referred to as -90 degrees) on a properly installed CT, then it is assumed that this harmonic power flow is in the opposite direction of the fundamental power flow, or from load to source.
		The user must be cautioned that in a number of measurements, the harmonic current and voltage levels are so low that the harmonic watts number is so small that it may be meaningless, as would be the direction of power flow information.
		For example, if on a 120V/30A circuit, there is a 5th harmonic voltage of 0.05 V and harmonic current of 0.2 A, 0.01W is really insignificant and the accuracy of the direction is very low.
	www.mindconnection.com /library/electrical/harmonics_pwr_flow.htm (506 words)

	NUMBER HARMONICS CD Information Relationships Spiritual-Personal Growth Addiction Healing Wedding Business
		The Number Harmonic Spiritual Growth CD Many people who have put years of effort into their spiritual growth get to a point where they feel they are not making progress.
		The Number Harmonic Relationship and Wedding CD If you are embarking on a new relationship or a wedding, this is the ideal gift to yourself or to your loved ones.
		The Number Harmonic Healing CD If you suffer from illness or disease, we have many cases of people receiving our CD that has been tailor made for their situation, and new doorways have opened up.
	www.numberharmonics.com /harmonic_cd/index.html (515 words)

	THE LIVING LIBRARY
		Given points 1-61 and 125-132, the first pi harmonic number 1 is defined to be positive and represents the fundamental HETO wave from harmonic 1 to harmonic 2.
		The tones are anchored by harmonic 1 and each successive tone/anti-tone is a 14th root of 3/2, so doubling the tones by adding the anti-tones requires changing the calculation to 14th roots of 3/2).
		The number - 11 is located in the positive half of the HETO wave and the number +13 is located in the negative half of the HETO wave, and both numbers are defined as anti-tones (FIG.
	www.sacredscience.com /LivingLibrary/messages/97/935.html (1842 words)

	Lab 3: Harmonic series, Fourier analysis
		In this exercise, you will generate a harmonic series and sum various components of the harmonic series to generate a complex periodic wave.
		Graph the wave resulting from summing the odd harmonics, even harmonics and all harmonics.
		Repeat the analysis for the wave resulting from the odd and even harmonic series and confirm your results.
	www.clas.ufl.edu /users/rahul/3011/lab3harmonicsFourier.htm (503 words)

	PlanetMath: prime harmonic series
		harmonic series (also known as series of reciprocals of primes) is the infinite sum
		See Also: prime, harmonic series, harmonic number, series, Euler's constant
		This is version 13 of prime harmonic series, born on 2005-03-09, modified 2005-07-15.
	planetmath.org /encyclopedia/PrimeHarmonicSeries.html (208 words)

	MONAN: SNDAN program to process and display analysis files
		Note that if a large number of harmonics is requested, the resulting text will scroll up the screen, so that the early values in which you may be most interested may be lost (see Using the Windows Console).
		Inharmonicity (the degree to which harmonics deviate from their centre frequency) is measured relative to the weighted average frequency (presumed to be the true fundamental pitch), so that variations such as vibrato do not affect the calculation.
		Where a harmonic is given, the original data for that will be preserved (it must not be used in a breakpoint line), and the other specified harmonics will be created from it according to the defined transfer function.
	dream.cs.bath.ac.uk /software/sndan/monan.html (8937 words)

	Automatic determination of the presence of a microwave signal and whether the signal is CW or pulsed - Patent 5465414
		Again, the result is that, at this harmonic number, the third LO upper side band 212 covers the gap left by the side bands from the first and second LO frequencies.
		The set of equations for determining the LO frequencies and harmonic numbers for this set of frequencies can be derived similarly to the way the equations for proceeding from the top of the microwave range down were derived.
		Again repeating the process, the harmonic number at which a fifth LO is needed is N=4, and the fifth LO frequency is f.sub.LO6 =303.8 MHz.
	www.freepatentsonline.com /5465414.html (4714 words)

	MUSIC SOUND TONE THERAPY HEALING with the Pythagrorean Tradition
		At Number Harmonics we help you to discover the Music inside you, and help you understand that what you are is perhaps higher and better than what you are presently experiencing..
		The Number Harmonic CD is a refined aid to higher awareness, better health, and better relationships.
		Number Harmonics are based at Moreton Bay, Australia and have been working on Harmonic Charts and Progression charts for people for many years.
	www.numberharmonics.com (1073 words)

	Arithmetic, Geometric and Harmonic Sequences by Stephen R. Wassell for the Nexus Network Journal vol.3 no.4 Autumn 2001 (Site not responding. Last check: 2007-10-31)
		The situation is directly analogous for a geometric sequence, whereby the second of any three numbers in a row must be the geometric mean of the first and third.
		Returning to the forward direction, we see that if at any point in the generation of a harmonic sequence, the last number is double the second-to-last number, we will get a zero denominator if we try to find the next number in the sequence.
		All sequence numbers from this point onwards will be negative, and since the magnitude of the denominator will get larger and larger (in the negative direction) at each step, the magnitudes of the sequence numbers will get smaller and smaller, approaching 0 (from the negative direction).
	www.nexusjournal.com /GA3-4-Wassell.html (1824 words)

	Microtonality, Tunings and Modes
		One of the most interesting properties of the harmonic series is its fractal nature: each prime number in the series introduces a new (non-doubled) tone into the series that then becomes a "new fundamental" for generating another harmonic series.
		For example, the third harmonic in Example 2 at 300 Hz is the first frequency in the series that is not a doubling (octave) of the fundamental and generates its own series: 300, 600, 900, 1200 and so on.
		Since the harmonic series is linear but octaves are powers of two there are more and more harmonics per octave as the series rises: the first octave in the series contains 1 frequency, the second 2, the third 4, the fourth 8 and so on.
	www-camil.music.uiuc.edu /faculty/taube/nm/14/scales.html (5348 words)

	CANT 2003 (Site not responding. Last check: 2007-10-31)
		A striking recent development is the discovery that additive and combinatorial number theory can be used to solve classical problems in harmonic analysis.
		This workshop is being organized by the New York Number Theory Seminar, and is supported in part by grants from the Number Theory Foundation, the NSA Mathematical Sciences Program, and the Office of the Provost of Lehman College.
		The New York Number Theory Seminar (NYNTS) was founded in January, 1982, by David and Gregory Chudnovsky, Harvey Cohn, and Mel Nathanson, and is now in its 21st year.
	www.theoryofnumbers.com /CANT/2003/cant2003.html (223 words)

	QMH Series Harmonic Mixers and Diplexers
		These harmonic mixers are useful for subsystem applications involving frequency sampling such as phase-locked oscillators and frequency linearizers.
		Harmonic mixers can be optimized for either odd or even harmonics of the local oscillator (LO).
		Series QMH harmonic mixers have a common SMA port for LO and IF signals, and hence require an external diplexer.
	www.quinstar.com /qmh_harmonic_mixers_and_diplexers.html (257 words)

	Number theory
		The test can sometimes mistakenly mark a number as prime while it is in fact composite, but a prime number will never be mistakenly declared composite.
		Although these numbers are rare (there are only 43 such numbers between 1 and 10^6), it has recently been proven that there are infinitely many of them.
		A pair of numbers m, n has this property if the sum of the proper divisors of m is n and the sum of the proper divisors of n is m.
	yacas.sourceforge.net /refchapter4.html (1987 words)

	What is my harmonic channel number? - RC Groups
		The harmonics of your transmitter are at 2xF, 3xF, etc and will not affect other flyers' receivers.
		For single conversion wide band receivers channels 23 channel numbers apart would experience a harmonic of some sort and they refered to it as 2nd order intermodulation.
		Its not that it is a true harmonic (1x, 2x, 4x etc. from your freq).....it is actually a resonation that is created by the combination of the two channels (the difference between the two)....in this case ch-45 and ch-22..
	www.rcgroups.com /forums/showthread.php?t=15063 (906 words)

	Noncommutative Harmonic Homogeneous Polynomials in Two Variables
		are constant multiples of the harmonic polynomials generated by the recursion and are, therefore harmonic.
		The number of harmonic, homogeneous polynomials increases as the degree increases.
		gives the number of linearly independent harmonic polynomials, with the exception of degree three, which seems, for other reasons, to be an anomaly.
	www.math.ucsd.edu /~dmcallas/papers/harmonic (965 words)

	Search Scitation : Abstract View (Site not responding. Last check: 2007-10-31)
		tone having a 200-Hz fundamental and 20 equal-amplitude harmonics.
		fundamental frequencies, the highest audible harmonic number tends to be
		In this region the highest audible harmonic number can be
	www.msu.edu /user/zhangx11/Publication/CancelledHarmonics.htm (150 words)

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