Diaschismic–gothmic equivalence continuum: Difference between revisions

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3. A characteristic damage of [[34edo]] which is not trivial; gothic is trivial in that it is just a subgroup restriction, and immunity, though not trivial and comparable in complexity to tetracot, is not characteristic, because it asks for a flat tuning of 5, so that it is arguably more or equally as characteristic of [[63edo]]'s or [[97edo]]'s representation of the 5-limit, but the fact that it has so many 3's in it when 34edo does not do so well in consistency of 3's to long distance should be a hint that we can do better. Compare with tetracot, which admits comparatively more and lower damage patent tunings and is clearly a type of imperfect simplification corresponding to a structural awkwardness in [[5-limit]] [[JI]] – the [[20000/19683|minimal diesis]] – so it has characteristic damage on 10/9 (flatwards) and 9/8 (sharpwards) by exaggerating the difference; this is to say, if you look at 34et's tuning of the 5-limit, its damage is strongly characteristic of tetracot. Exaggerating this difference in this way ''is'' also characteristic of immunity, but its general tunings are at odds with those of tetracot's so that they only merge in 34edo, which is arguably a more unusual tuning for immunity than it is for tetracot, where it is clearly characteristic.

4. As aforementioned, a convenient point to invert the scale to define the '''~~kleismic-tetracot~~ continuum''' nicely, discussed below.

4. As aforementioned, a convenient point to invert the scale to define the '''kleismic–tetracot continuum''' nicely, discussed below.

== Kleismic–tetracot continuum ==

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 . A characteristic damage of [[34edo]] which is not trivial; gothic is trivial in that it is just a subgroup restriction, and immunity, though not trivial and comparable in complexity to tetracot, is not characteristic, because it asks for a flat tuning of 5, so that it is arguably more or equally as characteristic of [[63edo]]'s or [[97edo]]'s representation of the 5-limit, but the fact that it has so many 3's in it when 34edo does not do so well in consistency of 3's to long distance should be a hint that we can do better. Compare with tetracot, which admits comparatively more and lower damage patent tunings and is clearly a type of imperfect simplification corresponding to a structural awkwardness in [[5-limit]] [[JI]] – the [[20000/19683|minimal diesis]] – so it has characteristic damage on 10/9 (flatwards) and 9/8 (sharpwards) by exaggerating the difference; this is to say, if you look at 34et's tuning of the 5-limit, its damage is strongly characteristic of tetracot. Exaggerating this difference in this way ''is'' also characteristic of immunity, but its general tunings are at odds with those of tetracot's so that they only merge in 34edo, which is arguably a more unusual tuning for immunity than it is for tetracot, where it is clearly characteristic.
-. As aforementioned, a convenient point to invert the scale to define the '''kleismic-tetracot continuum''' nicely, discussed below.
+. As aforementioned, a convenient point to invert the scale to define the '''kleismic–tetracot continuum''' nicely, discussed below.
 == Kleismic–tetracot continuum ==