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Elements of Music

36 37 MorE IntErvals the big get bigger and the small get smaller Just as chords are invertible, so too are their constituent intervals. 3rds invert to become 6ths, and 7ths become 2nds. Inverted major intervals become minor, inverted diminished intervals become augmented, and vice versa. Inverted intervals have the same basic function as their noninverted counterparts, but possess a greater sense of uncertainty. Composers play with them by further raising and lowering them. For example, extending a major 6th yields the interval of an augmented 6th, identical in sound to a minor 7th, but functioning quite differently. Remember that spelling counts, and that a minor 7th tends to resolve inwards, while an augmented 6th tends to resolve outwardsbig gets bigger and small gets smaller. Similarly, contracting a minor 7th yields a diminished 7th, the same as a major 6th, but again functioning wholly differently. As a major 6th is likely to fall by a whole step to the 5th, or rise to the major 7th, a diminished 7th almost always falls by a half step. Spelling and syntax indicate behavior and directionality. Shown below are the only three possible octatonic or diminished scales, since they are symmetrical. They fall into the repeating pattern of halfwhole or wholehalf. Also shown are the only two wholetone scales, built entirely of whole steps. They can evoke a mysterious sense of ambiguity and the unknown. Left Enharmonicism Chromaticism. Combining the circle of fifths with the spiral of fifths produces all of the possible 35 spellings for the 12 notes. Remember there are 7 members of the scale, ABCDEFG, and 5 chroma colours for each. The outermost and innermost spellings are rarely used Bx, Ex, F , C. Whenever a chromatic alteration must be made to a scale, an accidental is correspondingly used a lowered flat is double flat, a raised flat is natural, a lowered sharp is natural, a raised natural is sharp, and a raised sharp is double sharp. This diagram is of equivalence between spellings and assumes equal temperament. It should not be confused with a common diagram demonstrating tuning problems created by the Pythagorean Comma not covered in this book see Harmonograph, by Anthony Ashton. Left The imperfect consonances 3rds and 6ths and dissonances 2nds and 7ths occasionally come in two extreme forms beyond major and minor. Chromatically extending a major interval further turns it into an augmented interval. Likewise further contracting a minor interval makes it diminished, just as a perfect interval becomes diminished when contracted. Complex and chromatically rich music sometimes will use these enhanced or stretched intervals to push and pull with even more energy against the overall tonal structure. I N V E R S I O N S I N V E R S I O N S
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