User:2^67-1/Sandbox: Difference between revisions

Godtone (talk | contribs)
m →Testing: make squared ratios link to corresponding temperaments and note some simple JIPs
2^67-1 (talk | contribs)
Added note regarding JIPs
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* log<sub>2</sub>(256/243) / log<sub>2</sub>(25/24 * 50/49) = 0.8540148427 ; this is the JIP of p=2, q=-1 (equiv. to p=-2, q=1)
* log<sub>2</sub>(256/243) / log<sub>2</sub>(25/24 * 50/49) = 0.8540148427 ; this is the JIP of p=2, q=-1 (equiv. to p=-2, q=1)


Importantly, each JIP corresponds to a ''rational'', so that, for example, (''p'', ''q'') = (1, -2) is equivalent to (''p'', ''q'') = (2, -4) and to (''p'', ''q'') = (-1, 2) '''but not to (1, 2)'''.
Importantly, each JIP corresponds to a ''rational'', so that, for example, (''p'', ''q'') = (1, -2) is equivalent to (''p'', ''q'') = (2, -4) and to (''p'', ''q'') = (-1, 2) '''but not to (1, 2)'''. Note that all these JIPs lie on the JIL (just intonation line).


Also note that continua separated by 2401/2400 are meaningfully different, but due to the efficiency of 2401/2400, one may want to examine the continuum of all 7-limit temperaments supported by [[10edo]] for which [[2401/2400]] is tempered.
Also note that continua separated by 2401/2400 are meaningfully different, but due to the efficiency of 2401/2400, one may want to examine the continuum of all 7-limit temperaments supported by [[10edo]] for which [[2401/2400]] is tempered.