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In analyses, this is represented by two crossing lines with double arrowheads indicating the exchanged pitches. A common exchange of this sort involves a progression of a third using a passing tone, the exchange notated by the interval succession 10-8-6 (if this is with the bass, the third chord is a first inversion of the first).
In music, voice crossing is the intersection of melodic lines in a composition, leaving a lower voice on a higher pitch than a higher voice (and vice versa). Because this can cause registral confusion and reduce the independence of the voices, [ 1 ] it is sometimes avoided in composition and pedagogical exercises.
Download as PDF; Printable version; In other projects Wikidata item; Appearance. move to sidebar hide. Crossing the Lines may refer to: Crossing the Lines (project ...
One of three non-alternating knots with crossing number 8. In knot theory, a knot or link diagram is alternating if the crossings alternate under, over, under, over, as one travels along each component of the link. A link is alternating if it has an alternating diagram. Many of the knots with crossing number less than 10 are
Eli Terry was using interchangeable parts using a milling machine as early as 1800. Ward Francillon, a horologist, concluded in a study that Terry had already accomplished interchangeable parts as early as 1800. The study examined several of Terry's clocks produced between 1800–1807. The parts were labelled and interchanged as needed.
Looking at the illustration in the above section, it is apparent that the needle can cross a line if the center of the needle is within l / 2 units of either side of the strip. Adding l / 2 + l / 2 from both sides and dividing by the whole width t, we obtain P 1 = l / t . The red and blue needles are both centered ...
A variation of this concept, the rectilinear crossing number, requires all edges to be straight line segments, and may differ from the crossing number. In particular, the rectilinear crossing number of a complete graph is essentially the same as the minimum number of convex quadrilaterals determined by a set of n points in general position.
In Euclidean geometry, the intersecting chords theorem, or just the chord theorem, is a statement that describes a relation of the four line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal.