Talk:Mapped interval: Difference between revisions
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== Difference from tempered interval? == | == Difference from tempered interval? == | ||
Why is it not simply called a tempered interval? [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 09:18, 15 December 2022 (UTC) | Why is it not simply called a tempered interval? [[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 09:18, 15 December 2022 (UTC) | ||
: Ah, good question, and I should add this to the article itself. "Tempered" is more ambiguous. A "tempered interval" could refer to either to the merely mapped generator of meantone {{rket|0 1}} or a mapped ''and'' tuned interval such as the {{ket|0 0 1/4}} generator of quarter-comma meantone (which could be less ambiguously referred to as a "projected interval"). But "tempered interval" could even refer to the size/span (such as in cents) from mapping {{ket|-1 1 0}} by the (tempered-prime) tuning map {{map|1200 1896.578 2786.314}} to 696.578 ¢, in the same way we sometimes use "interval" to refer to the "(just) interval (span/size)" of 3/2 as 701.955 ¢. Only "''mapp''ed interval" pretty much unambiguously refers to an interval that has been transformed by the ''mapp''ing matrix. --[[User:Cmloegcmluin|Cmloegcmluin]] ([[User talk:Cmloegcmluin|talk]]) 16:03, 15 December 2022 (UTC) | |||
Latest revision as of 16:03, 15 December 2022
Difference from tempered interval?
Why is it not simply called a tempered interval? FloraC (talk) 09:18, 15 December 2022 (UTC)
- Ah, good question, and I should add this to the article itself. "Tempered" is more ambiguous. A "tempered interval" could refer to either to the merely mapped generator of meantone [0 1} or a mapped and tuned interval such as the [0 0 1/4⟩ generator of quarter-comma meantone (which could be less ambiguously referred to as a "projected interval"). But "tempered interval" could even refer to the size/span (such as in cents) from mapping [-1 1 0⟩ by the (tempered-prime) tuning map ⟨1200 1896.578 2786.314] to 696.578 ¢, in the same way we sometimes use "interval" to refer to the "(just) interval (span/size)" of 3/2 as 701.955 ¢. Only "mapped interval" pretty much unambiguously refers to an interval that has been transformed by the mapping matrix. --Cmloegcmluin (talk) 16:03, 15 December 2022 (UTC)