Catenary
Scottish Country Dance Instruction
Catenary (3x40S) 40 bar strathspey for three couples in a three couple longwise set, Murrough Landon, 20201- 4 1st and 2nd couples advance for one, retire for one and mirror link with 1st couple casting off to 2nd place and 2nd couple dancing up to 1st place.
5- 8 1st couple advance for one, touch right hands and retire for one. Then giving right hands they turn once round to end facing out on own sides.
9-16 Relay Chain:
1-2: 1st couple chase a quarter clockwise while 2nd and 3rd couples, giving right hands, turn their partner three quarters, all ending on the centre line.
3-4: 1st man and 2nd woman, also 3rd man and 1st woman, taking promenade hold, chase a quarter clockwise while 2nd man and 3rd woman, giving left hands, turn three quarters, all ending in a line across.
5-6: 1st couple drop promenade hold and chase another quarter clockwise to the ends of the centre line while 2nd and 3rd couples, giving right hands, turn their partner three quarters on the sides ending at full arms length.
7-8: All chase a quarter clockwise ending opposite partner in the order 3,1,2.
17-20 1st couple, giving right hands, turn one and a quarter times to end on the centre line, 1st man above 1st woman.
21-24 3rd couple with 1st man and 1st woman with 2nd couple dance left hands across.
25-32 Bourrel Chain:
1-4: 3rd woman and 2nd man chase just over half way anticlockwise to end on the centre line while 3rd man and 1st woman also 1st man and 2nd woman, giving right hands, turn just over one and a half times ending on the centre line.
5-8: 2nd man and 1st woman, 3rd man and 2nd woman also 1st man and 3rd woman, giving left hands, turn half way. Then 1st couple chase round a quarter anticlockwise while 2nd and 3rd couples, giving right hands, turn three quarters to end facing out on the sides. The phrasing here is closer to 1+3 bars than 2+2.
The order is now 2,1,3 with 1st couple on opposite sides facing in.
33-36 All dance half a reel of three on the sides, 1st couple start by giving right shoulder to their 2nd corners. The corners finish the reel with extra loops.
37-40 1st couple dance half a figure of eight right shoulder around their 4th corner (1st man down, 1st woman up) to end in 2nd place own sides. The final order is 3,1,2.
(Dance crib compiled by the deviser, Murrough Landon, CC BY-SA September 2020)
Keith Rose's Crib Diagram
Dance Instruction Videos
Catenary - Scottish Country Dancing Instruction VideoDance Information
The dance includes two different chain-like figures involving three couples, neither of which is exactly the formation, originally from Linnea's Strathspey by Tim Wilson, that the RSCDS (in my opinion) misnames the "three couple chain progression".In mathematics, a catenary is the curve a chain forms when hanging from its end points.
Recommended music: Suggested tune Mrs Jessie Blair's Strathspey by Jimmy Shand, senior; suitable recording The Geordie Diamond (Robert Whitehead And The Danelaw SCD Band: The Geordie Diamond).
(Dance information by the deviser, Murrough Landon, CC BY-SA September 2020)
A catenary is the curve formed by a flexible, uniform chain or cable hanging freely under its own weight and supported at its ends.
The shape of a catenary is mathematically described by the hyperbolic cosine function, given by the equation: y = a cosh(x⁄a)
a: is a constant that depends on the physical properties of the chain, such as its length and the distance between the supports.
x: represents the horizontal distance from a chosen origin point along the curve. It is often measured from the lowest point (the vertex) of the catenary, where x=0.
y: represents the vertical height of the curve above the origin. It corresponds to the distance from the lowest point of the curve (the vertex) to the point on the curve at a given horizontal distance x.
Essentially, as x increases (or decreases) from the vertex, y gives the height of the catenary curve at that point. The parameter a, sometimes called the "scaling factor", influences the curvature or steepness of the catenary.
Catenaries appear in various natural and engineered structures. For instance, they are often used in the design of arches and bridges because the curve efficiently distributes the weight of the structure, minimizing bending forces. A famous example is the Gateway Arch in St. Louis, which approximates the shape of an inverted catenary.
Unlike a parabola, which resembles it visually, a catenary has a different mathematical foundation. While a parabola results from the trajectory of an object in uniform gravity, a catenary is the result of forces acting on a flexible material under tension and gravity. The distinction is subtle but significant in engineering and architecture.
In physics and mathematics, the catenary curve is studied for its unique properties, including its appearance in solutions to certain differential equations and its role in minimal surface problems when rotated around its axis.
Catenary Formed By Chain
Published in Catenary, reproduced here with the kind permission of the deviser, Murrough Landon, CC BY-SA.
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Text from this original Catenary article on Wikipedia.
Image copyright Kamel15, CC BY-SA 3.0, via Wikimedia Commons.
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