Xen concepts for beginners: Difference between revisions

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An important way that MOS scales vary is [[hardness]], defined as the size (in cents) of the L divided by the size (in cents) 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.

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.

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. 12 + 19 = 31, and 31edo diatonic has hardness (2+3)/(1+2) = 5/3.

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]], defined as the size (in cents) of the L divided by the size (in cents) 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.
-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.
+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. 12 + 19 = 31, and 31edo diatonic has hardness (2+3)/(1+2) = 5/3.
 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.