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...particular kind of [[continuous function]] between [[topological space]]s. Perfect maps are weaker than [[homeomorphism]]s, but strong enough to preserve some ...r each <math>y</math> in <math>Y</math>. Then <math>p</math> is known as a perfect map. ...

...essbooks.pub/openmusictheory/chapter/intervals-in-integer-notation/ |title=Intervals in Integer Notation |website=viva.pressbooks.pub |access-date=2024-02-08}}< == Pitch Intervals == ...

...es if they are separated by [[minor third]] (/), [[major third]] (\), or [[perfect fifth]] (–).]] ...you further in the same direction. Lattices in just intonation (limited to intervals comprising primes, their powers, and their products) are theoretically infi ...

...r-tuning, one major-third interval is interjected amid four perfect-fourth intervals.]] interjects exactly one [[major third]] amid four [[perfect fourth]]s for the intervals between its successive [[open string (music)|open string]]s. In contrast, t ...

...of golden ratio intervals in Hz.png|thumb|400px|Stack of golden ratio (φ) intervals, measured in Hz ((11.09 + 6.854) ÷ 11.09 = 11.09 ÷ 6.854 = 1.618).]] ...olden ratios on the unison (center), on the perfect fourth (left), and the perfect fifth (right)]] ...

...o|Perfect fourth on C.mid|Play}}, Beta scale: 512 cents {{audio|Beta scale perfect fourth on C.mid|Play}})]] ...sup|{{frac|11}}}} ≈ 63.8 cents]. It may be approximated by splitting the [[perfect fourth]] (4:3) into two equal parts [(4:3){{sup|{{1/2}}}}],<ref name="Milan ...

..., requiring an [[octave]] (2:1). It may be approximated by splitting the [[perfect fifth]] (3:2) into 20 equal parts (3:2{{sup|{{frac|20}}}}≈35.1 cents),{{Cit "It produces nearly perfect triads."<ref name="Milano">Milano, Dominic (November 1986). [http://www.wen ...

Below are some intervals in 96-EDO and how well they approximate just intonation. | {{Audio|Perfect octave on C.mid|play}} ...

...ic divisions of the octave |via=WendyCarlos.com |quote=9&nbsp;steps to the perfect (no kidding) fifth." ''The alpha scale'' "splits the minor third exactly in ....mid|Play}}{{big|)}} to approximate the interval {{nobr|{{math| {{sfrac| [[perfect fifth|3:2]] | [[major third|5:4]] }} {{=}} 6:5 }} }} {{big|(}}E{{music|b}}, ...

{{Short description|Intersection graph of unit intervals on the real number line}} ...n graph]]s of sets of [[unit interval]]s, or of properly nested intervals (intervals none of which contains any other one). Based on these two types of interval ...

==Confidence intervals== {{cleanup merge|21=section|Robust confidence intervals}} ...

...unings]], '''regular&nbsp;tunings''' have equal [[interval (music)|musical intervals]] between the paired [[note (music)|note]]s of their successive [[open stri ...ct-fourth]]s (E–A, A–D, D–G), then the [[major third]] G–B, and the fourth perfect-fourth B–E. ...

...tunings are constructed entirely from stacking of three basic purely-tuned intervals (octaves, thirds and fifths). Since the perception of consonance seems rela ...) power of any prime equals any power of any other prime, so the available intervals can be imagined to extend indefinitely in a 3-dimensional [[Lattice (music) ...

...itolerance order. An order is a bitolerance order if and only if there are intervals I_''x'' and real numbers ''t''₁(''x'') and ''t''<sub>' Like all incomparability graphs, trapezoid graphs are [[perfect graph|perfect]]. ...

# Each partner privately partitions the cake to ''n'' intervals that he considers to be of equal value; these are called ''candidate pieces ...candidates intersected by it. Step #2 is then repeated with the remaining intervals of the remaining ''n''&nbsp;−&nbsp;1 partners. ...

...orean tuning]] as points of the [[chromatic circle]]. Edges indicate the [[perfect fifth]]s used to construct the tuning; the two longer gap lengths between c ...rational multiple of <math>2\pi</math>, and similarly other common musical intervals other than the octave do not correspond to rational angles.{{r|barcal}} ...

...s of arithmetic operations on random variables of unknown dependency using intervals. ''Reliable Computing'' '''4''': 147–165.</ref><ref name=Fersonetal04>Ferso ...rline{F} \in \mathbb{D}</math>, <math>m</math> and <math>v</math> are real intervals, and <math>\mathbf{F} \subset \mathbb{D}</math>. This quintuple denotes the ...

...ometimes 20&nbsp;metres. Half chords, i.e. 15&nbsp;metre or 10&nbsp;metre intervals, are marked on the datum rail using chalk. The string, which is one full c ...sine in an overlapping pattern along the curve. The versine values for the perfect circular curve would have the same number.<ref>{{cite book|last=Ellis|first ...

...ch class's nearest neighbors and itself form perfect fifth and major third intervals. ...ct how close the center of effect are to the fundamental, major third, and perfect fifth of the chord. By changing the relative values of these weights, the s ...

...'stable sets'', ''clumps'', ''committees'', ''externally related sets'', ''intervals'', ''nonsimplifiable subnetworks'', and ''partitive sets'' {{harv|Brandstäd ...e [[perfect graph theorem#Characterizations and the perfect graph theorems|perfect graph theorem]] (Golumbic, 1980). ...