Zhenlige
Joined 23 April 2022
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::: I usually think 11-limit intervals as “neutral intervals ± fractions of rastma (243/242)”, just like how NFJS represents them. (I am not satisfied with the RoT's of FJS and NFJS, though.) For example, 11/8 is sA4 − 1/2 rastma, 33/32 is sA1 − 1/2 rastma, and so on. For intervals involving both 11 and 5 or both 11 and 7, that makes less sense, because thinking 11/10 as “n2<sub>5</sub> − 1/2 rastma” does not clearly show its properties since “n2<sub>5</sub>” is already a strange interval. For specific intervals there may be other viewpoints, e.g. 11/10 as “something between 10/9 and 12/11” or “near 1/3 of the interval 4/3”. Actually I rarely think such intervals independently, but rather as part of a larger structure. 13-limit intervals are very novel to me — actually I am even more familiar with 17 and 19 due to my early research on near-12edo intervals. --[[User:Zhenlige|Zhenlige]] ([[User talk:Zhenlige|talk]]) 02:35, 11 June 2025 (UTC) | ::: I usually think 11-limit intervals as “neutral intervals ± fractions of rastma (243/242)”, just like how NFJS represents them. (I am not satisfied with the RoT's of FJS and NFJS, though.) For example, 11/8 is sA4 − 1/2 rastma, 33/32 is sA1 − 1/2 rastma, and so on. For intervals involving both 11 and 5 or both 11 and 7, that makes less sense, because thinking 11/10 as “n2<sub>5</sub> − 1/2 rastma” does not clearly show its properties since “n2<sub>5</sub>” is already a strange interval. For specific intervals there may be other viewpoints, e.g. 11/10 as “something between 10/9 and 12/11” or “near 1/3 of the interval 4/3”. Actually I rarely think such intervals independently, but rather as part of a larger structure. 13-limit intervals are very novel to me — actually I am even more familiar with 17 and 19 due to my early research on near-12edo intervals. --[[User:Zhenlige|Zhenlige]] ([[User talk:Zhenlige|talk]]) 02:35, 11 June 2025 (UTC) | ||
:::: Funny you should mention not being satisfied with the terms of the FJS and NFJS. The nomenclature that goes with [[Alpharabian tuning]] is actually more precise. For instance, 33/32 is an ultraprime while 11/8 is a paramajor fourth. In contrast, 729/704 is an infra-augmented prime, while 243/176 is an infra-augmented fourth- you might want to look up these more complicated 2.3.11 intervals if you're not already familiar with them. I should mention that in addition to 11/10, a type of submajor second, being roughly one third of 4/3, it actually differs from an ultra-augmented prime (think an apotome plus 33/ | :::: Funny you should mention not being satisfied with the terms of the FJS and NFJS. The nomenclature that goes with [[Alpharabian tuning]] is actually more precise. For instance, 33/32 is an ultraprime while 11/8 is a paramajor fourth. In contrast, 729/704 is an infra-augmented prime, while 243/176 is an infra-augmented fourth- you might want to look up these more complicated 2.3.11 intervals if you're not already familiar with them. I should mention that in addition to 11/10, a type of submajor second, being roughly one third of 4/3, it actually differs from an ultra-augmented prime (think an apotome plus 33/32) by a schisma. This naturally means that in schismatic temperaments, these two intervals are enharmonic. Any thoughts on all this? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 09:46, 11 June 2025 (UTC) | ||