Douglas Blumeyer's RTT How-To: Difference between revisions
Cmloegcmluin (talk | contribs) →canonical form: use Defactored Hermite form |
Cmloegcmluin (talk | contribs) →mapping-row-bases and comma-bases: link comma-basis |
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We call such a matrix a '''comma-basis'''. The plural of “basis” is “bases”, but pronounced like BAY-sees (/ˈbeɪ siz/). | We call such a matrix a '''[[comma-basis]]'''. The plural of “basis” is “bases”, but pronounced like BAY-sees (/ˈbeɪ siz/). | ||
Now how in the world could that matrix represent the same temperament as {{map|19 30 44}}? Well, they’re two different ways of describing it. {{map|19 30 44}}, as we know, tells us how many generator steps it takes to reach each prime approximation. This matrix, it turns out, is an equivalent way of stating the same information. This matrix is a minimal representation of the null-space of that mapping, or in other words, of all the commas it tempers out. (Don't worry about the word "mapping" just yet; for now, just imagine I'm writing "map". We'll explain the difference very soon.). | Now how in the world could that matrix represent the same temperament as {{map|19 30 44}}? Well, they’re two different ways of describing it. {{map|19 30 44}}, as we know, tells us how many generator steps it takes to reach each prime approximation. This matrix, it turns out, is an equivalent way of stating the same information. This matrix is a minimal representation of the null-space of that mapping, or in other words, of all the commas it tempers out. (Don't worry about the word "mapping" just yet; for now, just imagine I'm writing "map". We'll explain the difference very soon.). |