Xen concepts for beginners: Difference between revisions

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An important way that MOS scales vary is [[hardness]], the ratio of the size of the L step to the size of the s step. Hardness can range from 1 to infinity. The larger the hardness, the harder the MOS tuning; the smaller (closer to 1) the hardness, the softer the tuning. The two extremes are where the MOS pattern no longer holds; 1 is where L and s steps are equal, and infinity is where s is so small that it disappears.

12edo has basic (L/s = 2/1) diatonic, 17edo has hard (L/s = 3/1) diatonic, and 19edo has soft (L/s = 3/2) diatonic. To adjust the hardness of a MOS provided by an edo, we can add two edos, obtaining an edo where the hardness is the mediant of the two original edos'. Any given MOS pattern is available in more than one edo, and the basic tuning of a MOS pattern gives the smallest edo that provides that MOS pattern.

Any given MOS pattern is available in more than one edo, and the basic tuning of a MOS pattern gives the smallest edo that provides that MOS pattern. To adjust the hardness of a MOS provided by an edo, we can add two edos, obtaining an edo where the hardness is the mediant of the two original edos'. For a diatonic example, 12edo has basic (L/s = 2/1) diatonic, 17edo has hard (L/s = 3/1) diatonic, and 19edo has soft (L/s = 3/2) diatonic.

The generator size and the period thus determine the MOS scales that can be obtained. Hardness varies with generator size within a MOS's range.

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 An important way that MOS scales vary is [[hardness]], the ratio of the size of the L step to the size of the s step. Hardness can range from 1 to infinity. The larger the hardness, the harder the MOS tuning; the smaller (closer to 1) the hardness, the softer the tuning. The two extremes are where the MOS pattern no longer holds; 1 is where L and s steps are equal, and infinity is where s is so small that it disappears.
-edo has basic (L/s = 2/1) diatonic, 17edo has hard (L/s = 3/1) diatonic, and 19edo has soft (L/s = 3/2) diatonic. To adjust the hardness of a MOS provided by an edo, we can add two edos, obtaining an edo where the hardness is the mediant of the two original edos'. Any given MOS pattern is available in more than one edo, and the basic tuning of a MOS pattern gives the smallest edo that provides that MOS pattern.
+Any given MOS pattern is available in more than one edo, and the basic tuning of a MOS pattern gives the smallest edo that provides that MOS pattern. To adjust the hardness of a MOS provided by an edo, we can add two edos, obtaining an edo where the hardness is the mediant of the two original edos'. For a diatonic example, 12edo has basic (L/s = 2/1) diatonic, 17edo has hard (L/s = 3/1) diatonic, and 19edo has soft (L/s = 3/2) diatonic.
 The generator size and the period thus determine the MOS scales that can be obtained. Hardness varies with generator size within a MOS's range.