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== Temperaments == | == Temperaments == | ||
By tempering it out, the '''jacobin temperament''' is defined. Interestingly, [[1789edo]] is an edo that [[support]]s the jacobin temperament - and is consistent to distance 2 on the subgroup 2.5.11.13 | By tempering it out, the '''jacobin temperament''' is defined. Interestingly, [[1789edo]] is an edo that [[support]]s the jacobin temperament - and is consistent to distance 2 on the subgroup 2.5.11.13, the subgroup of the comma. Although 1789edo has a unique position due to its number of steps being a hallmark year of the {{W|French Revolution}}, it is more rational to use the other edos for this temperament. Miscellaneous temperaments tempering out this comma are collected in [[The Jacobins]]. | ||
The 17-limit factorization shows us a natural path of extension by adding 12376/12375. Equally, it can be conceptualized as a rank-2 temperament in 2.13/10.11 subgroup, in which case it is called ''jacobin-naiadic'', after [[13/10]] being called a naiadic by interval class. | The 17-limit factorization shows us a natural path of extension by adding 12376/12375. Equally, it can be conceptualized as a rank-2 temperament in 2.13/10.11 subgroup, in which case it is called ''jacobin-naiadic'', after [[13/10]] being called a naiadic by interval class. | ||