1789edo: Difference between revisions
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Perhaps the most notable fact about 1789edo is that it [[tempering out|tempers out]] the jacobin comma ([[6656/6655]]), and it is also consistent to distance 2 on the subgroup 2.5.11.13 of the comma, which is naming-wise appropriate for edo's number while also providing an extremely strong tuning. Although there are temperaments which are better suited for tempering this comma, 1789edo is unique in that its number is the hallmark year of the French Revolution, thus making the tempering of the jacobin comma on topic. | Perhaps the most notable fact about 1789edo is that it [[tempering out|tempers out]] the jacobin comma ([[6656/6655]]), and it is also consistent to distance 2 on the subgroup 2.5.11.13 of the comma, which is naming-wise appropriate for edo's number while also providing an extremely strong tuning. Although there are temperaments which are better suited for tempering this comma, 1789edo is unique in that its number is the hallmark year of the French Revolution, thus making the tempering of the jacobin comma on topic. | ||
2.9.5.11.13 subgroup is also represented strongly in 1789edo, where it tunes a temperament | 2.9.5.11.13 subgroup is also represented strongly in 1789edo, where it tunes a temperament which [[Eliora]] calls ''commatose'', defined as {{nowrap| 460 & 1789 }}, which uses the Pythagorean comma as a generator. In the full 13-limit, 1789bd val, {{val| 1789 '''2836''' 4154 '''5023''' }} is of additional interest as it is better tuned than the patent val, where it tunes [[hemiluna]]. | ||
On the patent val in the 7-limit, 1789edo supports {{nowrap|99 & 373}} temperament called [[maviloid]]. In addition, it also tempers out [[2401/2400]]. | On the patent val in the 7-limit, 1789edo supports {{nowrap|99 & 373}} temperament called [[maviloid]]. In addition, it also tempers out [[2401/2400]]. | ||
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=== Miscellany === | === Miscellany === | ||
For higher harmonics, 1789edo can be adapted for use with the 2.9.5.21.11.13.29.31.47.59.61 subgroup. | For higher harmonics, 1789edo can be adapted for use with the 2.9.5.21.11.13.29.31.47.59.61 subgroup. [[45/32]] and [[51/32]] are also strongly approximated. | ||
Since the 5/4 of 1789edo is on the 576th step, a highly divisible number, 1789edo can replicate a lot of [[ed5/4]] temperaments—more exactly those which are divisors of 576, and that includes all from [[2ed5/4]] to [[9ed5/4]], skipping [[7ed5/4]]. One of these, hemiluna (4ed5/4), is mentioned above. | Since the 5/4 of 1789edo is on the 576th step, a highly divisible number, 1789edo can replicate a lot of [[ed5/4]] temperaments—more exactly those which are divisors of 576, and that includes all from [[2ed5/4]] to [[9ed5/4]], skipping [[7ed5/4]]. One of these, hemiluna (4ed5/4), is mentioned above. | ||
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