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searching for Harmonic series (mathematics) 51 found (137 total)

alternate case: harmonic series (mathematics)

Harmonic seventh (1,225 words) [view diff] no match in snippet view article find links to article

ratio of 9:5 (about 1018 cents). The harmonic seventh arises from the harmonic series as the interval between the fourth harmonic (second octave of the fundamental)

Lipps–Meyer law (387 words) [view diff] no match in snippet view article find links to article

approximation to a lower, stronger, or higher, weaker, position in the harmonic series. The reason for the effect of finality of such interval ratios may

Just intonation (5,543 words) [view diff] no match in snippet view article find links to article

(and chords created by combining them) consist of tones from a single harmonic series of an implied fundamental. For example, in the diagram, if the notes

Limit (music) (1,107 words) [view diff] no match in snippet view article

tuning are 1, 3, and 5. Each odd number represents a new pitch in the harmonic series and may thus be considered an identity: C C G C E G B C D E F G ..

Harmonic (2,206 words) [view diff] no match in snippet view article find links to article

harmonics is also periodic at that frequency. The set of harmonics forms a harmonic series. The term is employed in various disciplines, including music, physics

Neutral sixth (378 words) [view diff] no match in snippet view article find links to article

neutral second from a minor seventh. Based on its positioning in the harmonic series, the undecimal neutral sixth implies a root one minor seventh above

Glenn Branca (2,000 words) [view diff] no match in snippet view article find links to article

of volume, alternative guitar tunings, repetition, droning, and the harmonic series, he was a driving force behind the genres of no wave, totalism and

List of mathematical series (4,342 words) [view diff] no match in snippet view article find links to article

This list of mathematical series contains formulae for finite and infinite sums. It can be used in conjunction with other tools for evaluating sums. Here

Størmer's theorem (1,791 words) [view diff] no match in snippet view article find links to article

specifically, they can be described as ratios between members of the harmonic series. Any musical tone can be broken into its fundamental frequency and

Minor chord (1,168 words) [view diff] no match in snippet view article find links to article

10:12:15 (play). This is the first occurrence of a minor triad in the harmonic series (if on C: E–G–B). This may be found on iii, vi, ♭vi, ♭iii, and vii

Parity (mathematics) (2,529 words) [view diff] no match in snippet view article

In mathematics, parity is the property of an integer of whether it is even or odd. An integer is even if it is divisible by 2, and odd if it is not. For

Musical tuning (2,753 words) [view diff] no match in snippet view article find links to article

indeterminate pitch, and have irregular overtones not conforming to the harmonic series. See § Tuning of unpitched percussion instruments. Tuning may be done

Dynamic tonality (3,262 words) [view diff] no match in snippet view article find links to article

generalizes the special relationship between just intonation, and the harmonic series to apply to a wider set of pseudo-just tunings and related pseudo-harmonic

Carl B. Allendoerfer Award (114 words) [view diff] no match in snippet view article find links to article

is presented annually by the Mathematical Association of America (MAA) for "expository excellence published in Mathematics Magazine." it is named after

Superparticular ratio (1,062 words) [view diff] no match in snippet view article find links to article

superparticular ratio, and similarly every pair of adjacent harmonics in the harmonic series (music) represent a superparticular ratio. Many individual superparticular

Ivan M. Niven (876 words) [view diff] no match in snippet view article find links to article

Erdős, P.; Niven, I. (1946), "Some properties of partial sums of the harmonic series", Bull. Amer. Math. Soc., 52 (4): 248–251, doi:10.1090/s0002-9904-1946-08550-x

Tonality diamond (1,204 words) [view diff] no match in snippet view article find links to article

that clarifies the relationship of Partch's tonality diamonds to the harmonic series and string lengths (as Partch also used in his Kitharas) and Landmans

Sieve of Eratosthenes (3,035 words) [view diff] no match in snippet view article find links to article

In mathematics, the sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking

Contributions of Leonhard Euler to mathematics (2,215 words) [view diff] no match in snippet view article find links to article

example, he proved the infinitude of primes using the divergence of the harmonic series, and used analytic methods to gain some understanding of the way prime

Fourier analysis (4,616 words) [view diff] no match in snippet view article find links to article

and the converse is true. An early form of harmonic series dates back to ancient Babylonian mathematics, where they were used to compute ephemerides

Hermann Kinkelin (621 words) [view diff] no match in snippet view article find links to article

Basel 16, 1903, pp. 309–328 (Internet-Archiv, dito) General theory of harmonic series with applications to number theory, Schweighauser, Basel 1862 (Google

Leibniz formula for π (1,511 words) [view diff] no match in snippet view article find links to article

In mathematics, the Leibniz formula for π, named after Gottfried Wilhelm Leibniz, states that π 4 = 1 − 1 3 + 1 5 − 1 7 + 1 9 − ⋯ = ∑ k = 0 ∞ ( − 1 )

Regular prime (3,267 words) [view diff] no match in snippet view article find links to article

W. (1994), "A p-adic Study of the Partial Sums of the Harmonic Series", Experimental Mathematics, 3 (4): 287–302, doi:10.1080/10586458.1994.10504298, Zbl 0838

Consonance and dissonance (7,957 words) [view diff] no match in snippet view article find links to article

least not by contraction) and correctly reproducing the mathematical ratios of the harmonic series[clarification needed] are truly non-dissonant. Thus the

Matemateca (980 words) [view diff] no match in snippet view article find links to article

collection of objects related to mathematics and mathematics teaching that is housed in the Institute of Mathematics and Statistics of the University

Five-limit tuning (4,606 words) [view diff] no match in snippet view article find links to article

Since the perception of consonance seems related to low numbers in the harmonic series, and 5-limit tuning relies on the three lowest primes, 5-limit tuning

Harry Partch (4,676 words) [view diff] no match in snippet view article find links to article

dividing the octave into 43 unequal tones derived from the natural harmonic series; these scales allowed for more tones of smaller intervals than in standard

Almost periodic function (2,838 words) [view diff] no match in snippet view article find links to article

In mathematics, an almost periodic function is, loosely speaking, a function of a real number that is periodic to within any desired level of accuracy

Hilbert space (17,476 words) [view diff] no match in snippet view article find links to article

In mathematics, Hilbert spaces (named after David Hilbert) allow the methods of linear algebra and calculus to be generalized from (finite-dimensional)

List of prime numbers (5,798 words) [view diff] no match in snippet view article find links to article

W. (1994). "A p-adic Study of the Partial Sums of the Harmonic Series". Experimental Mathematics. 3 (4): 287–302. doi:10.1080/10586458.1994.10504298. Zbl 0838

Borwein integral (2,724 words) [view diff] no match in snippet view article find links to article

13/928097. JSTOR 27641975. Schmuland, Byron (2003). "Random Harmonic Series". The American Mathematical Monthly. 110 (5): 407–416. doi:10.2307/3647827. JSTOR 3647827

Euclid's theorem (3,073 words) [view diff] no match in snippet view article find links to article

equivalent to say that the partial sum up to x {\displaystyle x} of the harmonic series diverges asymptotically like log ⁡ x {\displaystyle \log x} ). Then

Liouville number (5,150 words) [view diff] no match in snippet view article find links to article

2020-10-14. Zudilin, Wadim (2002-04-01). "Remarks on irrationality of q-harmonic series". Manuscripta Mathematica. 107 (4): 463–477. doi:10.1007/s002290200249

Musical acoustics (1,924 words) [view diff] no match in snippet view article find links to article

fundamental and the overtones, are called partials. Together they form the harmonic series. Overtones that are perfect integer multiples of the fundamental are

Extended vocal technique (1,167 words) [view diff] no match in snippet view article find links to article

may give rise to tones that fairly coincide with those of an inverse harmonic series. Although the octave below is the most frequently used undertone, a

Renormalization (8,436 words) [view diff] no match in snippet view article find links to article

_{n=0}^{\infty }{\frac {1}{n+a}}=-\psi (a)+\log(a)} since for the Harmonic series ∑ n = 0 ∞ 1 a n + 1 {\displaystyle \sum _{n=0}^{\infty }{\frac {1}{an+1}}}

Interval (music) (8,728 words) [view diff] no match in snippet view article

harmonic series. The root of a perfect fourth, then, is its top note because it is an octave of the fundamental in the hypothetical harmonic series.

Drone music (3,869 words) [view diff] no match in snippet view article find links to article

however, confined to Cage. Karlheinz Stockhausen's exploration of the harmonic series, notably in Stimmung (1968), has often been linked to Young's example

Dirichlet eta function (3,705 words) [view diff] no match in snippet view article find links to article

In mathematics, in the area of analytic number theory, the Dirichlet eta function is defined by the following Dirichlet series, which converges for any

Normal mode (3,261 words) [view diff] no match in snippet view article find links to article

and toroidal modes. Antiresonance Critical speed Harmonic oscillator Harmonic series (music) Infrared spectroscopy Leaky mode Mechanical resonance Modal

Regular diatonic tuning (2,609 words) [view diff] no match in snippet view article find links to article

generalization of the special relationship between Just Intonation and the Harmonic Series. Maintaining an invariant mapping between notes and partials, across

Thomas Young (scientist) (4,453 words) [view diff] no match in snippet view article

University Press. ISBN 978-0192869760.pp. 45-84 "Thomas Young". School of Mathematics and Statistics University of St Andrews, Scotland. Retrieved 30 August

Fourier transform (20,919 words) [view diff] no match in snippet view article find links to article

In physics, engineering and mathematics, the Fourier transform (FT) is an integral transform that takes as input a function and outputs another function

Guitar chord (8,032 words) [view diff] no match in snippet view article find links to article

(plectrum), it vibrates according to its harmonic series. When an open-note C-string is struck, its harmonic series begins with the terms (C,C,G,C,E,G,B♭

Multiple zeta function (5,504 words) [view diff] no match in snippet view article find links to article

arXiv:hep-th/9604128. Hoffman, Michael (1992). "Multiple Harmonic Series". Pacific Journal of Mathematics. 152 (2): 276–278. doi:10.2140/pjm.1992.152.275. MR 1141796

Index of music articles (4,230 words) [view diff] no match in snippet view article find links to article

(instrument) Harmonic Harmonic major scale Harmonic rhythm Harmonic scale Harmonic series (music) Harmonic seventh Harmonization Harmony Harp Harpsichord Harpsichord-viola

Michael Harrison (musician) (1,727 words) [view diff] no match in snippet view article

(Cantaloupe Music 21086) 2012 Rumi: Lovedrunk (remastered) 2009 The Harmonic Series – A Compilation of Works in Just Intonation (Important Records 272)

Music psychology (10,602 words) [view diff] no match in snippet view article find links to article

unnecessary. Study of topics including vibration, consonance, the harmonic series, and resonance were furthered through the scientific revolution, including

Olivier Messiaen (8,561 words) [view diff] no match in snippet view article find links to article

making harmonic use of the modes of limited transposition, he cited the harmonic series as a physical phenomenon that provides chords with a context he felt

Pythagorean hammers (6,691 words) [view diff] no match in snippet view article find links to article

and the octave appear in relation to the fundamental tone in natural harmonic series, but not the fourth or its octave equivalent. This interval of a fourth

List of guitar tunings (18,597 words) [view diff] no match in snippet view article find links to article

major-thirds tuning. C-C-G-C-E-G This open-C tuning gives the initial harmonic series when a C-string is struck. The C-C-G-C-E-G tuning uses the harmonic