Pitch circle

“ Suppose the circle whose centre is O and one of the points of intersection A to remain fixed, while the second circle turns round that point in such a manner that the second point of intersection B becomes ultimately consecutive to A; then, since the line OO′ always bisects AB, we see that when B ultimately becomes consecutive to A, the line OO′ passes through A. In consequence of the motion, the common chord will become in the limit a tangent to each circle, as in the second diagram.—Comberousse, Géométrie Plane, page 57. ”

“ Have your circus on top of a large table, or on the floor, or out of doors on the bare ground. Almost any place will do where there is a good-sized level surface.
Make the circus ring about forty inches in diameter, outline it with chalk and cover the marked line with either sawdust or dry corn meal built into a narrow ridge similar to that of earth around the large rings; then your circle will look just like the ring of a real circus. ”

“ At completion of the second circle the line separates, each leader leading his line to right or left as they reach the front—across front to sides—up sides to rear, where they go out as they came in. As each boy reaches the side where he turns to go toward the exit, he reaches his wand out to the audience, gives one emphatic shake of the bell, then as he turns away lets his hand fall to his side. ”

“ Music then commenced, which consisted of pounding upon stones with clubs and horn, and the drawing of a small string like a fiddle-bow across distended bark. They ran, and jumped, and danced in the wildest and most furious manner about us, but keeping a regular circle. [134] Each, on coming to a certain point in the circle, marked by a removed piece of turf in the ground, would bend himself or herself nearly to the ground, uttering at the same time a most frightful yell, and making a violent gesticulation and stamping. ”

“ A ring of 44 feet outer and 30 feet inner dimensions, has been formed by constructing a sunken circle about 12 inches below the level of the original floor, which is rendered capable of removal to just such an extent as will disclose the ring, the boarding being replaced to form the ordinary promenade, at such times as the circus performances are not going on. ”

“ It is a very important proposition, theoretically and practically, for it enables us to find the center of a circle if we know any part of its arc. A civil engineer, for example, who wishes to find the center of the circle of which some curve (like that on a running track, on a railroad, or in a park) is an arc, takes two chords, say of one hundred feet each, and erects perpendicular bisectors. It is well to ask a class why, in practice, it is better to take these chords some distance apart. ”

“ The band or head keeps marching in an ever-narrowing circle, while its train of dancing followers becomes coiled round it in circle after circle. Then the band, taking a sharp turn about, begins to retrace the circle, still followed as before, and a number of young men, with long leafy branches in their hands as standards, direct this counter-movement. ”

“ The startling analogy between Australian and old Scottish markings saute aux yeux.
On the cover of Sir James Simpson's book, stamped in gold, is a central set of six concentric circles, surrounding a cup. From the inmost circle a groove goes to the circumference of the outer circle (the circles often occur without this radial groove) , and there the line gives a wriggle, suggesting that the circle was evolved out of a spiral. ”

“ Let us now see how these forces operate in the case of the riders in a circus. The equestrian leans inward so much that, if he were to stand still in that position, he would inevitably fall off the horse; but the centrifugal force, which has a tendency to impel him outward from the circle, or in a straight line of motion, sustains him, and he careers onward safely 117and gracefully. The tendency of the centrifugal force to impel him outward is counteracted by the inward leaning, while it forms an invisible support to the overhanging body. ”

“ A few times I have seen men dance in the center of the circle somewhat as the women do, but with more movement, with a balancing and tilting of the body and especially of the arms, and with rapid trembling and quivering of the hands. The most spectacular dance is that of the man who dances in the circle brandishing a head-ax. ”

“ CIRCLE (from the Lat. circulus, the diminutive of circus, a ring; the cognate Gr. word is κιρκος, generally used in the form κρίκος) , a plane curve definable as the locus of a point which moves so that its distance from a fixed point is constant.
The form of a circle is familiar to all; and we proceed to define certain lines, points, &c., which constantly occur in studying its geometry. The fixed point in the preceding definition is termed the “centre” (C in fig. 1) ; the constant distance, e.g. CG, the “radius.” The curve itself is sometimes termed the “circumference.” ”

“ When pitching, three poles lashed to one another with a long line, somewhat below the thinner points, are raised perpendicularly, and the thicker ends are spread out in a tripod to the perimeter of the circle which is to form the lodge floor ”

“ Four times during the revolution of the great circle each large clock emits for a couple of minutes a species of chime, the nature of which my ignorance of music renders me unable to describe:—viz., when the line dividing the green and black semicircles is horizontal at noon and midnight, and an hour before, at average sunrise and sunset, it becomes perpendicular. ”

“ A circle may be a great circle of either the celestial sphere, the earth, or even of a baseball. The poles of a great circle are the points on the surface of its sphere, penetrated by the diameter perpendicular to the plane of the great circle. As for example, the poles of the earth are connected by the diameter that is perpendicular to the plane of the equator. An angle at any pole is measured on the great circle which subtends it. For instance, angles at the poles of the earth are measured on the equator; angles at the zenith on the horizon. ”

“ Pitch, for example, behaves as an absolutely solid body when subjected to blows and percussion, but, given time, it begins to flow under the influence of gravity; a piece of cork cannot be forced through a sheet of pitch, but after a lengthy period its slight buoyancy is sufficient to allow it to rise slowly through the pitch from the bottom of a vessel. ”

“ An observer in the plane of the motion can easily hear a change in the pitch as the pitch-pipe moves to and from him.
Musical Quality or Timbre.—Though a musical note has definite pitch or frequency, notes of the same pitch emitted by different instruments have quite different quality or timbre. The three characteristics of a longitudinal periodic disturbance are its amplitude, the length after which it repeats itself, and its form, which may be represented by the shape of the displacement curve. ”

“ I’m talking of a big pitch, when we go through all our ‘slang,’ as we say. But then we have our little pitches, which don’t last more than a quarter of an hour—our flying pitches, as we call them, and for them 5s. is an out-and-outer, and we are well contented if we get half-a-crown. ”

“ The circle was undoubtedly known to the early civilizations, its simplicity specially recommending it as an object for study. Euclid defines it (Book I. def. 15) as a “plane figure enclosed by one line, all the straight lines drawn to which from one point within the figure are equal to one another.” In the succeeding three definitions the centre, diameter and the semicircle are defined, while the third postulate of the same book demands the possibility of describing a circle for every “centre” and “distance.” ”

“ When players are familiar with the winding and unwinding process, the game may be played in circle formation instead of line formation; that is, it will start with all of the players facing inward as they clasp hands to form a circle, and the locking or winding will bring them facing in single file around the circle. ”

“ Instead of two bands meeting each other in lines in opposite directions, and parting, to meet again at the other side of the room, they were formed into a circle, one-half moving in one direction, and one-half moving in the opposite, by which means the circle was never broken. ”

“ We may take any point along the major axis, as shown, for instance, in Fig. 149. Let B be this point, taken at random. Then describe the half circle (C) . We may, also, arbitrarily, take any point, as, for instance, D on the minor axis E, and by drawing the diagonal lines (F) we find marks on the circle (C) , which are the meeting lines for the large curve (H) , with the small curve (C) . In this case we have formed an ovate or an oval form. Experience will soon make perfect in following out these directions.
Focal Points.—The focal point of a circle is its center, and is called the focus. ”

“ I am well aware that a few musicians have this gift of absolute pitch, and perhaps a greater number still, from long practice with one fixed sound—like the singing master with his C tuning fork—are able to guess the pitch of that one sound with moderate success, but for a musician to have the pitch of all the range of sounds so thoroughly established, as to feel a sense of disappointment if an isolated note was sounded either slightly above, or below concert pitch, is almost an impossibility, if such an one does exist he must be considered an exception to the above. ”

“ Figure 274 illustrates the manner of finding essential points in drawing or marking out cut-off cams. With X as a centre, and a radius of 2 feet, draw the circle E 1, showing the path of the crank-pin in making a revolution. This circle has a diameter of 4 feet, equal to the stroke of the engine. Draw the horizontal line B, passing through the centre of circle E 1. Within the limits of circle E 1, subdivide line B into eight equal parts, as at 1, 2, 3, 4, etc. Draw the vertical lines, 1, 2, 3, 4, etc., until they each intersect the circle E 1. ”

“ In the centre there is a circle of pillars, on the top of each of which is a pot of flowers with gas jets, and between them an arch of gas jets. In the midst of this is another circle, forming a pavilion for musicians, also brilliantly illuminated, and containing a large cotillion band of the most finished performers. Around this you find thousands of gentlemen and ladies strolling, singly, in pairs, or in groups. ”

“ The head by Van Dyck carries with it the repose which belongs to the completeness of the circle.
Like Saturn and his ring, this sphere within the circle is typical of harmony in unity, and for this reason, though detached as we know it to be, it has a greater completeness than though joined to a body. It is on this general principle that all circular compositions are based—absorption of the attention within the circuit. ”

“ The players stand in a circle with one of their number in the center, who represents the farmer in the dell. At the singing of the second verse, where the farmer takes a wife, the center player beckons to another, who goes in and stands by her. The circle keeps moving while each verse is sung, and each time the player last called in beckons to another; that is, the wife beckons one into the circle as the child, the child beckons one for the nurse, etc., until six are standing in the circle. ”

“ CIRCLE FORM.—When players are proficient in catching in opposite lines or ranks, they should form a circle, facing around in single file, each player being provided with a wand which is tossed backward over the head and caught by the player behind. ”

“ The beginning of a whole Turn, or turn quite round, is more difficult to find out, because the Circle, which is the Mark of it, has neither beginning nor End: But it is nevertheless to be known by a Point plac’d on the side of the Step; from which Point the beginning being known, you make Use of the same Rules as above. When a Turn is to be made but half a quarter round, it must be mark’d a quarter of a Circle on the side of the Step, without joining it to the Step. ”

“ After making the circuit once or twice, one of the men bounds into the circle and follows her from side to side with outstretched arms, as though offering her an embrace. She deftly eludes the advance, casting backward glances from the corners of her eyes to tempt him on. ”

“ The action within the ring of a circus presents a more stimulating show, and yet it is not quite satisfying as an artistic composition of motion, because we cannot help feeling that it is not natural, that it is unfit for a horse to turn forever within a forty-foot ring. In the æsthetic dance, on the other hand, a circling movement can always be of satisfying beauty, full of graceful vitality and yet delightfully reposeful, too, because it never flies away from its axis fixed within our area of vision. ”

“ Chamber Music Pitch. Formerly absolute pitch did not exist. During the sixteenth and seventeenth centuries the pitch was high. This we find according to the old organs, which are some of them a tone higher than our present French diapason. Chamber pitch in olden times differed from church pitch. The adoption of a uniform pitch is very much to be desired at the present time.
Divertimento, a kind of chamber music suite, or combination of pieces of a pleasing and diverting kind.
Gudok, a violin-like Russian instrument with drones. ”