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Ratio of two consecutive integers
In mathematics, a superparticular ratio, also called a superparticular number or epimoric ratio, is the ratio of two consecutive integer numbers. More
Superparticular_ratio
Relationship between two numbers of the same kind
(mathematics) Scale (map) Scale (ratio) Sex ratio Superparticular ratio Slope New International Encyclopedia (1916). "Ratios". www.mathsisfun.com. Retrieved
Ratio
Musical tuning based on pure intervals
mathematics Musical interval Pythagorean interval Regular number Superparticular ratio Whole-tone scale Brown, Colin. Music in Common Things, Part I: Music
Just_intonation
4th-century BC Greek philosopher, mathematician, astronomer and statesman
immortal images, in which God being versed is always God. Superparticular ratios are integer ratios of the form n + 1/ n , where n is some natural number;
Archytas
Topics referred to by the same term
warming signed in the Paris Agreement 1.5, an album by Big Data Superparticular ratio: 3/2 or 11⁄2 Perfect fifth (3/2), musical interval "1.5", a 2018
1.5
Gives a finite bound on pairs of consecutive smooth numbers
consecutive pairs of {2,3,5}-smooth numbers (in music theory, giving the superparticular ratios for just tuning) let P = {2,3,5}. There are seven P-smooth squarefree
Størmer's_theorem
Musical interval
tone or major second. This has the ratio 9/8, also known as epogdoon and it is the only other superparticular ratio of Pythagorean tuning, as shown by
Pythagorean_interval
Signed odd unit fractions sum to π/4
{29}{28}}\cdots \end{aligned}}} In this product, each term is a superparticular ratio, each numerator is an odd prime number, and each denominator is
Leibniz_formula_for_π
Numbers that evenly divide powers of 60
, x + 1 ) {\displaystyle (x,x+1)} and each such pair defines a superparticular ratio x + 1 x {\displaystyle {\tfrac {x+1}{x}}} that is meaningful as
Regular_number
Set of musical pitches
properties of the tonality diamond and the ratios contained: All ratios between neighboring ratios are superparticular ratios, those with a difference of 1 between
Tonality_diamond
superpartient ratio, also called superpartient number or epimeric ratio, is a rational number that is greater than one and is not superparticular. The term
Superpartient_ratio
Number, product of consecutive integers
integers) form a superparticular ratio: n ( n + 1 ) n 2 = n + 1 n {\displaystyle {\frac {n(n+1)}{n^{2}}}={\frac {n+1}{n}}} Due to this ratio, the nth pronic
Pronic_number
Topics referred to by the same term
a half') may refer to: Sesquialterum in mathematics, the ratio 3:2, a superparticular ratio Sesquialtera or the equivalent Greek term hemiola, three in
Sesquialtera
One over a whole number
unit fraction when used as the numerator with a given denominator Superparticular ratio, one plus a unit fraction, important in musical harmony Cavey, Laurie
Unit_fraction
Norwegian geophysicist and mathematician
Størmer describes an algorithm for finding all such pairs. The superparticular ratios generated by these consecutive pairs are of particular importance
Carl_Størmer
Musical interval
1945]. It can be expressed as a ratio by compounding suitable superparticular ratios. Whether it is assigned the ratio 64/45 or 45/32, depending on the
Tritone
sorted by frequency ratio, by cents, or alphabetically. Superparticular ratios are intervals that can be expressed as the ratio of two consecutive integers
List_of_pitch_intervals
Musical interval
81:80 is the closest superparticular ratio possible with regular numbers as numerator and denominator. A superparticular ratio is one whose numerator
Syntonic_comma
Graph with almost the max amount of edges
Erdős–Stone theorem that the upper density can only be 1 or one of the superparticular ratios 0, 1/2, 2/3, 3/4, 4/5, … n/n + 1 Lee & Streinu (2008)
Dense_graph
and tuning, the ragisma is an interval with the ratio of 4375:4374, ≈0.396 cents (a superparticular ratio). It is usually defined as the difference between
Ragisma
Infinite products of functions indexed by primes
Dirichlet character modulo 4, and converted to an Euler product of superparticular ratios (fractions where numerator and denominator differ by 1): π 4 = (
Euler_product
Ancient musical and scientific laboratory instrument
tuning (Ptolemy's Diatonic Ditonic) is easily derived starting from superparticular ratios, (n+1)/n, constructed from the first four counting numbers, the
Monochord
Logical formulation of graph properties
, as long as c {\displaystyle c} is not a superparticular ratio. If c {\displaystyle c} is superparticular, the probability of having a given property
Logic_of_graphs
Difference in pitch between two notes
are justly tuned, and their frequency ratio, shown in the table, is a superparticular number (or epimoric ratio). The same is true for the octave. Typically
Interval_(music)
Classification in ancient Greek music theory
possible numerators and denominators. The successive intervals are all superparticular ratios: hypate parhypate lichanos mese 4:3 5:4 6:5 1:1 | 16:15 | 25:24
Genus_(music)
Method of tuning a musical instrument
are justly tuned, and their frequency ratio, shown in the table, is a superparticular number (or epimoric ratio). The same is true for the octave. The
Pythagorean_tuning
Musical interval
In music, the minor diatonic semitone is a ratio of 17:16, making it the seventeenth harmonic or partial. This is in contrast to the 5-limit major diatonic
Minor_diatonic_semitone
media help. A septimal quarter tone (in music) is an interval with the ratio of 36:35, which is the difference between the septimal minor third and the
Septimal_quarter_tone
integer number lower than the distance from the fret to the bridge (see: superparticular number). On the guqin, the left end of the dotted scale is a mirror
Scale_of_harmonics
Musical interval
second play is the musical interval exactly or approximately equal to an 8/7 ratio of frequencies. It is about 231 cents wide in just intonation. 24 equal
Septimal_whole_tone
In music, the ratio 225/224 is called the septimal kleisma or marvel comma (play). It is a minute comma type interval of approximately 7.7 cents. Factoring
Septimal_kleisma
In music, septimal diesis (or slendro diesis) is an interval with the ratio of 49:48 [citation needed] play, which is the difference between the septimal
Septimal_diesis
A septimal 1/3-tone (in music) is an interval with the ratio of 28:27, which is the difference between the perfect fourth and the supermajor third. It
Septimal_third_tone
Musical interval
(8+1⁄2) seventh (10+1⁄2) Just intonations (Numbers in brackets refer to pitch ratios.) 7-limit septimal quarter tone (36:35) septimal third tone (28:27) septimal
Septimal_diatonic_semitone
Musical interval
the musical interval exactly or approximately equal to a 7/6 frequency ratio. In terms of cents, it is 267 cents, a quartertone of size 36/35 flatter
Septimal_minor_third
1st-century AD Greek philosopher, mathematician and music theorist
mathematicians have studied and provided proofs of Nicomachus's theorem. Superparticular number Superpartient number Schueller 1988, pp. 138. Dillon 1996, pp
Nicomachus
In music, the septimal semicomma, a seven-limit semicomma, is the ratio 126/125 and is equal to approximately 13.79 cents (play).[citation needed] It
Septimal_semicomma
Interval between one musical pitch and another with double its frequency
octave above is at 880 Hz, and the note one octave below is at 220 Hz. The ratio of frequencies of two notes an octave apart is therefore 2:1. Further octaves
Octave
Interval 21:20, about 84.47 cents
(8+1⁄2) seventh (10+1⁄2) Just intonations (Numbers in brackets refer to pitch ratios.) 7-limit septimal quarter tone (36:35) septimal third tone (28:27) septimal
Septimal_chromatic_semitone
In music, a breedsma is an interval between pitches with the ratio of 2401:2400, which is the difference between the septimal diesis (49:48, also known
Breedsma
Canadian composer (born 1965)
Microtuning" (PDF). Retrieved 1 December 2021. "Thomas Nicholson". superparticular.com. Retrieved 24 July 2024. "HEJI 2020" (PDF). Retrieved 1 February
Marc_Sabat
the difference between a major and septimal whole tone (with 9/8 and 8/7 ratios, respectively). Alternatively, it can be viewed as the difference between
Septimal_comma
Series of four notes separated by three intervals
from conjunct or disjunct tetrachords. This is a partial table of the superparticular divisions by Chalmers after Hofmann. [who?] Tetrachords based upon
Tetrachord
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