Generator ranges of MOS: Difference between revisions

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Below are ranges of generators for various L-s patterns of MOS, with the number of steps in the scale from 2 to 29. The ranges are given in fractions of the interval of equivalence, which is normally an octave. The tables give the range of possible generators in the second column, normalized so that the lower end of the range is where L/s = 1 (Nedo). The third column gives the midpoint of the range. Finally, the fourth column gives the boundaries of propriety, maximum expressiveness and diatonicity.

Below are ranges of generators for various L-s patterns of [[MOS scale]]s, with the number of steps in the scale from 2 to 29. The ranges are given in fractions of the interval of equivalence, which is normally an octave. The tables give the range of possible generators in the second column, normalized so that the lower end of the range is where L/s = 1 (Nedo). The third column gives the midpoint of the range. Finally, the fourth column gives the boundaries of propriety, maximum expressiveness and diatonicity.

If the number of the [[Interval_class|generic interval]] to which the generator g belongs is C, and there are N scale steps to the interval of equivalence, then the average the size of an interval in class C is C/N. We have normalized so that C/N is the lower bound of the range of generators; since therefore g > C/N, g is larger than average and hence is the larger of the two sizes of intervals in its class, which means we have normalized to the [[Modal_UDP_Notation|chroma-positive]] generator. We have normalized to the formula fir the step size where the leading term is positive.

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	Below are ranges of generators for various L-s patterns of MOS, with the number of steps in the scale from 2 to 29. The ranges are given in fractions of the interval of equivalence, which is normally an octave. The tables give the range of possible generators in the second column, normalized so that the lower end of the range is where L/s = 1 (Nedo). The third column gives the midpoint of the range. Finally, the fourth column gives the boundaries of propriety, maximum expressiveness and diatonicity.		Below are ranges of generators for various L-s patterns of [[MOS scale]]s, with the number of steps in the scale from 2 to 29. The ranges are given in fractions of the interval of equivalence, which is normally an octave. The tables give the range of possible generators in the second column, normalized so that the lower end of the range is where L/s = 1 (Nedo). The third column gives the midpoint of the range. Finally, the fourth column gives the boundaries of propriety, maximum expressiveness and diatonicity.

	If the number of the [[Interval_class\|generic interval]] to which the generator g belongs is C, and there are N scale steps to the interval of equivalence, then the average the size of an interval in class C is C/N. We have normalized so that C/N is the lower bound of the range of generators; since therefore g > C/N, g is larger than average and hence is the larger of the two sizes of intervals in its class, which means we have normalized to the [[Modal_UDP_Notation\|chroma-positive]] generator. We have normalized to the formula fir the step size where the leading term is positive.		If the number of the [[Interval_class\|generic interval]] to which the generator g belongs is C, and there are N scale steps to the interval of equivalence, then the average the size of an interval in class C is C/N. We have normalized so that C/N is the lower bound of the range of generators; since therefore g > C/N, g is larger than average and hence is the larger of the two sizes of intervals in its class, which means we have normalized to the [[Modal_UDP_Notation\|chroma-positive]] generator. We have normalized to the formula fir the step size where the leading term is positive.