Gravity family: Difference between revisions

Abergravity, first discovered by [[User:Godtone]] (but left unnamed) and rediscovered and named by [[User:2^67-1]] later, is the extension of 2.3.5.11 gravity to prime 7 by extending the streak [[121/120|S11]] = [[100/99|S10]] = [[81/80|S9]] = [[64/63|''S8'']], so that the generalized comma 121/120~100/99~81/80 discussed in [[#2.3.5.11 subgroup (larry)]] is equated with a shrunk [[~]][[64/63]], hence a flat-tending [[~]][[8/7]] is characteristic. It is the [[58edo|58]] & [[65edo|65d]] temperament, also supported by their [[val]] sum of 58 + 65d = [[123edo|123df]]. (A sharp edo tuning of prime 7 (and hence a flat tuning of 8/7) is possible if we use the extreme tuning [[51edo|51ce]] in which we also temper out [[1029/1024|S7/S8]].) An obvious extension to the 13-limit is by noticing the 'squeeze' of equated commas (S8, S9, S10, S11) as suggesting [[144/143|S12]] to be tempered out which fits the 58 & 65d join, and this is intuitively confirmed by also implying tempering out [[847/845|S11/S13]] so that the spacing is made natural, but also because it implies tempering out [[352/351]] and [[351/350]] in the 13-limit as a natural extension for [[176/175|S8/S10]] = 176/175, their product. Arguably the best edo tuning for making sense of this spacing is [[58edo]], a great tuning for [[15-odd-limit]], as there we use the distinction between 14/13 and 13/12~12/11 to have 15/14~14/13 make sense, though if you want [[marvel]] (16/15~15/14) you will want to use [[65edo]] instead.

[[Subgroup]]: 2.3.5.7