Douglas Blumeyer's RTT How-To: Difference between revisions
Cmloegcmluin (talk | contribs) m →null-space: more accurate terminology |
Cmloegcmluin (talk | contribs) m →the other side of duality: more accurate terminology |
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And there’s our {{val|{{monzo|4 -4 1}}}}. Feel free to | And there’s our {{val|{{monzo|4 -4 1}}}}. Feel free to try reversing the operation by working out the mapping from this if you like. And/or you could try working out that {{val|{{monzo|4 -4 1}}}} is the null-space of any other combination of ETs we found that could specify meantone, such as 7&12, or 12&19. | ||
It’s worth noting that, just as 2 commas were exactly enough to define a rank-1 temperament, though there were an infinitude of equivalent pairs of commas we could choose to fill that role, there’s a similar thing happening here, where 2 maps are exactly enough to define a rank-2 temperament, but an infinitude of equivalent pairs of them. We can even see that we can convert between these maps using Gaussian addition and subtraction, just like we could manipulate commas to get from one to the other. For example, the map for 12-ET {{val|12 19 28}} is exactly what you get from summing the terms of 5-ET {{val|5 8 12}} and 7-ET {{val|7 11 16}}: {{val|5+7 8+11 12+16}} = {{val|12 19 28}}. Cool! | It’s worth noting that, just as 2 commas were exactly enough to define a rank-1 temperament, though there were an infinitude of equivalent pairs of commas we could choose to fill that role, there’s a similar thing happening here, where 2 maps are exactly enough to define a rank-2 temperament, but an infinitude of equivalent pairs of them. We can even see that we can convert between these maps using Gaussian addition and subtraction, just like we could manipulate commas to get from one to the other. For example, the map for 12-ET {{val|12 19 28}} is exactly what you get from summing the terms of 5-ET {{val|5 8 12}} and 7-ET {{val|7 11 16}}: {{val|5+7 8+11 12+16}} = {{val|12 19 28}}. Cool! | ||
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supposed to be a mapping for meantone? What does that even mean? | supposed to be a mapping for meantone? What does that even mean? | ||
=== rank-2 mappings === | === rank-2 mappings === | ||