Syntonic–limmic equivalence continuum: Difference between revisions

The 5-limit version of uncle tempers out [[4096/3645]]. It is generated by a fifth that is supposedly sharper than [[5edo|3\5]], so it leads to an [[5L 3s|oneirotonic]] scale, or otherwise a [[5L 2s|diatonic]] scale with negative small steps. The interval class of 5 is found at -6 fifths, as a major 2-step in oneirotonic, or a diminished fifth (C–Gb) in diatonic. It corresponds to {{nowrap| ''n'' {{=}} -1/2 }} or {{nowrap| ''m'' {{=}} 1/3 }}.  

Dirt tempers out the [[dirt comma]], 1342177280/1162261467. It is generated by a perfect fifth. The interval class of 5 is found at +19 fifths, as a double-augmented seventh (C–Bx). It corresponds to {{nowrap| ''n'' {{=}} 1/3 }} and {{nowrap| ''m'' {{=}} -1/2 }}.  

Laconic tempers out [[2187/2000]], which is the difference between a stack of three [[10/9|ptolemaic whole tones (10/9)]]'s and a perfect fifth (3/2). Although a higher-error temperament, it does pop up enough in the low-numbered edos to be useful, most notably in [[16edo]] and [[21edo]]. The only 7-limit extension that makes any sense to use is to add the gamelisma to the comma list. It corresponds to {{nowrap| ''n'' {{=}} -3 }}.