Talk:Normal forms: Difference between revisions

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:: Yes, I would like it back in the article. BTW I thought of another use for IRREFs. Makes it easy to compute meets and joins if you have the IRREF for both temperaments. I don't know if it always makes it easier but it certainly makes it easier some times. --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 20:59, 16 October 2021 (UTC)

== Revision to the equave-reduced generator form ==

Actually, the equave reduction need not start with the positive generator form, but may start with the canonical form, which means a step of manipulation is saved. The result of course can be different, but sometimes perferable.

My proposed revision changes the old "equave-reduced generator form" to the "positive equave-reduced generator form", which signifies that its starting point is the positive generator form. And it has the new "equave-reduced generator form" derived from the canonical form.

Sensi is a great example to show how all these will differ from each other:

# Canonical form: [{{val| 1 6 8 11 }}, {{val| 0 7 9 13 }}] with generators ~2, ~9/14

# Positive generator form: [{{val| 1 6 8 11 }}, {{val| 0 -7 -9 -13 }}] with generators ~2, ~14/9

# Equave-reduced generator form: [{{val| 1 -1 -1 -2 }}, {{val| 0 7 9 13 }}] with generators ~2, ~9/7

# Positive equave-reduced generator form: [{{val| 1 6 8 11 }}, {{val| 0 -7 -9 -13 }}] with generators ~2, ~14/9

# Minimal generator form: [{{val| 1 -1 -1 -2 }}, {{val| 0 7 9 13 }}] with generators ~2, ~9/7

My expectation is that the positive equave-reduced generator form should be left largely obsolete since musicians will work with the new equave-reduced generator form. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 08:00, 16 January 2023 (UTC)

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 :: Yes, I would like it back in the article. BTW I thought of another use for IRREFs. Makes it easy to compute meets and joins if you have the IRREF for both temperaments. I don't know if it always makes it easier but it certainly makes it easier some times. --[[User:TallKite|TallKite]] ([[User talk:TallKite|talk]]) 20:59, 16 October 2021 (UTC)
+== Revision to the equave-reduced generator form ==
+Actually, the equave reduction need not start with the positive generator form, but may start with the canonical form, which means a step of manipulation is saved. The result of course can be different, but sometimes perferable.
+My proposed revision changes the old "equave-reduced generator form" to the "positive equave-reduced generator form", which signifies that its starting point is the positive generator form. And it has the new "equave-reduced generator form" derived from the canonical form.
+Sensi is a great example to show how all these will differ from each other:
+# Canonical form: [{{val| 1 6 8 11 }}, {{val| 0 7 9 13 }}] with generators ~2, ~9/14
+# Positive generator form: [{{val| 1 6 8 11 }}, {{val| 0 -7 -9 -13 }}] with generators ~2, ~14/9
+# Equave-reduced generator form: [{{val| 1 -1 -1 -2 }}, {{val| 0 7 9 13 }}] with generators ~2, ~9/7
+# Positive equave-reduced generator form: [{{val| 1 6 8 11 }}, {{val| 0 -7 -9 -13 }}] with generators ~2, ~14/9
+# Minimal generator form: [{{val| 1 -1 -1 -2 }}, {{val| 0 7 9 13 }}] with generators ~2, ~9/7
+My expectation is that the positive equave-reduced generator form should be left largely obsolete since musicians will work with the new equave-reduced generator form. [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 08:00, 16 January 2023 (UTC)