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Elements of Music

8 9 undErstandIng scalEs streets and stairways A scale is a collection of discrete tones that are a subset of the pitch continuum and that normally climb an octave in a certain number of steps, often seven. Most of the unique and beautifully diverse musical scales from around the world owe a large part of their heritage to the overtone series and use the fifth, the first tuned note, as the fundamental unit. Fifths are piled up, one atop another, and then transposed back down to a single octave. Thirds can also be prioritised to derive a scale e.g., meantone tuning and a myriad of other methods all sculpt the different tuning systems that have emerged each of them trying to solve the problem of locking a fluid, infinite curve or spiral into a grid or circle. The scale becomes a playground for a melodic drama unfolding the relative tensions of these overtones with the tones between them. The basic stations are 1 3 5 1, created by the overtones 21 the octave, the only note that when reached gives the distinctive impression of the fundamental tone below it, the same, yet different, then from 31, the 5, which has the next quality of sameness, though it is in fact a different pitch entirely. Then 41, another octave, then 51, which becomes the 3, generally conveying the major or minor quality of a chord, scale, or melody. Many 5note and 7note scales utilise this underlying structure, and in many variations, but the fundamental structures are 123 56 and 1234567. Seven is born from five. A 7note scale in a 12note environment means that 5 notes will always be missing. In MiddleEastern systems 7 notes are chosen in performance from 17 in India 7 are chosen from 22. Above The seven classical modes with their Greek names. Left By sliding the starting point of the scale set one note to the right, all whole steps and half steps move to the left, creating six further modes from a seven note scale. Right A way to generate the modes compared to the major scale Ionian by making a few chromatic adjustments, flat or sharp. W W H W W W H W H W W W H W H W W W H W W W W W H W W H W W H W W H W W H W W H W W H W W H W W W Half steps H A L F W H O L E Whole steps Left This modified Penrose staircase shows the paradox of the musical octave. As we traverse a scale either ascending or descending, there is a simultaneous departure and return we are coming and going at the same time. Half steps In chromatic tuning, e.g., on a keyboard, the distance from any note to its neighbor, white or black, is a half step or semitone. Western chromatic tuning has twelve equal half steps to the octave. CC DD EFF GA bAB bBC Whole steps Whole steps or tones are equivalent to two half steps. They too can traverse white or black, depending upon where they fall on the keyboard. The pair of mutually exclusive scales made solely of whole steps are CDEF G B b and D bE bFGAC b C D F F G A B G A E D C
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