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These scales are the fundamental building blocks of the European Music al tradition. The modern major and minor scales are diatonic, as are all of the so-called 'church' Modes . The seven Notes of a diatonic scale—repeated in each Octave —correspond to the white keys on a Piano . The modern musical keyboard, with its black notes grouped in twos and threes—is essentially diatonic; this arrangement not only helps musicians to find their bearings on the keyboard, but simplifies the system of key signatures compared with what would be necessary for a continuous alternation of black and white notes. Technical composition of diatonic scales Technically speaking, diatonic scales are obtained from a Chain of six successive Fifths in some version of Meantone Temperament , and resulting in two Tetrachord s separated by Interval s of a Whole Tone . If our version of meantone is the twelve tone Equal Temperament the pattern of intervals in Semitone s will be 2-2-1-2-2-2-1; these numbers stand for whole tones (2 semitones) and half tones (1 semitone). The Major Scale starts on the first note and proceeds by steps to the first octave. In Solfege , the syllables for each scale degree are "Do-Re-Mi-Fa-So-La-Ti-Do". The Natural Minor Scale can be thought of in two ways, the first is as the ''relative minor'' of the major scale, beginning on the sixth degree of the scale and proceeding step by step through the same tetrachords to the first octave of the sixth degree. In solfege "La-Ti-Do-Re-Mi-Fa-So-La." Alternately, the natural minor can be seen as a composite of two different tetrachords of the pattern 2-1-2-2-1-2-2. In solfege "Do-Re-Mé-Fa-So-Lé-Té-Do." Western Harmony from the Renaissance up until the Late 19th Century is based on the diatonic scale and the unique Hierarchical relationships, or Diatonic Functionality , created by this system of organizing seven notes. Most longer pieces of common practice music Change Key , but this leads to a hierarchical relationship of diatonic scales in one key with those in another. These unique relationships are as follows: Only certain divisions of the octave, 12 and 20 included, allow uniqueness, coherence, and transpositional simplicity, and that only the diatonic and pentatonic subsets of the 12-tone chromatic set follow these constraints (Balzano, 1980, 1982). The diatonic collection contains each interval class a unique number of times (Browne 1981 cited in Stein 2005, p.49, 49n12). , Myhill's Property , Well Formedness , the Deep Scale Property , Cardinality Equals Variety , and Structure Implies Multiplicity . There is significant evidence that the evolution of the diatonic scale is natural, because it is based on the most basic harmonics of any scale's first note, and that it has actually occurred many times over the course of human history, in which the three most common intervals across time and cultures, a tone, its 5th and 4th, produce audible overtones sufficient to influence the formation of the pentatonic, and major/minor diatonic scales. This is called the "Trio" theory in Fink, "On the Origin of Music" (2005) . There is even circumstantial evidence that a flute used by was written in it, 3,400 years ago.[http://www.greenwych.ca/evidence.htm] See also Further reading
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