Reduced mapping: Difference between revisions

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We start with the mapping above, which must be an upper triangular matrix. First we combine the nth element in each row so that we can see the data for each prime rather than for each generator: ⟨2,0,0 0,2,0 1,1,2 3,1,3 7,-2,3 -1,4,2 5,2,0]

Then we ~~optionally~~ mark the number of times the first generator is stacked modulo the number of periods per most reasonable equave with apostrophes or numbers in parentheses, then throw the rest of the data for the first generator away. We can also delete the first 2,0,0 because it always becomes 0, replacing it with "2 |" to indicate that there are two periods per 2/1. If this number were 1, we would leave out the number. (If we were using an equave other than 2/1, like 3/1, for example, we would have used "2<3/1> |".) Thus we have ⟨2 | 2,0 '1,2 '1,3 '-2,3 '4,2 '2,0]

Then we mark the number of times the first generator is stacked modulo the number of periods per most reasonable equave with apostrophes or numbers in parentheses, then throw the rest of the data for the first generator away. We can also delete the first 2,0,0 because it always becomes 0, replacing it with "2 |" to indicate that there are two periods per 2/1. If this number were 1, we would leave out the number. (If we were using an equave other than 2/1, like 3/1, for example, we would have used "2<3/1> |".) Thus we have ⟨2 | 2,0 '1,2 '1,3 '-2,3 '4,2 '2,0]

Then we reduce the generator sizes to become less than the period, then take the period-complement of every generator except the first if it is larger than half the period. At this point we now note that the sizes of the second and third generators in cents have became 249c and 18c. This gives us ⟨2 | -2,0 '-1,2 -1,3 2,3 '-4,2 '-2,0]

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 We start with the mapping above, which must be an upper triangular matrix. First we combine the nth element in each row so that we can see the data for each prime rather than for each generator: ⟨2,0,0 0,2,0 1,1,2 3,1,3 7,-2,3 -1,4,2 5,2,0]
-Then we optionally mark the number of times the first generator is stacked modulo the number of periods per most reasonable equave with apostrophes or numbers in parentheses, then throw the rest of the data for the first generator away. We can also delete the first 2,0,0 because it always becomes 0, replacing it with "2 |" to indicate that there are two periods per 2/1. If this number were 1, we would leave out the number. (If we were using an equave other than 2/1, like 3/1, for example, we would have used "2<3/1> |".) Thus we have ⟨2 | 2,0 '1,2 '1,3 '-2,3 '4,2 '2,0]
+Then we mark the number of times the first generator is stacked modulo the number of periods per most reasonable equave with apostrophes or numbers in parentheses, then throw the rest of the data for the first generator away. We can also delete the first 2,0,0 because it always becomes 0, replacing it with "2 |" to indicate that there are two periods per 2/1. If this number were 1, we would leave out the number. (If we were using an equave other than 2/1, like 3/1, for example, we would have used "2<3/1> |".) Thus we have ⟨2 | 2,0 '1,2 '1,3 '-2,3 '4,2 '2,0]
 Then we reduce the generator sizes to become less than the period, then take the period-complement of every generator except the first if it is larger than half the period. At this point we now note that the sizes of the second and third generators in cents have became 249c and 18c. This gives us ⟨2 | -2,0 '-1,2 -1,3 2,3 '-4,2 '-2,0]