1789edo: Difference between revisions
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1789edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[3/1|3]] is about halfway between its steps. Otherwise, it is excellent in approximating harmonics [[5/1|5]], [[9/1|9]], [[11/1|11]], [[13/1|13]] and [[21/1|21]], making it suitable for a 2.9.5.21.11.13 [[subgroup]] interpretation. | 1789edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[3/1|3]] is about halfway between its steps. Otherwise, it is excellent in approximating harmonics [[5/1|5]], [[9/1|9]], [[11/1|11]], [[13/1|13]] and [[21/1|21]], making it suitable for a 2.9.5.21.11.13 [[subgroup]] interpretation. | ||
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. | |||
1789bd val, {{Val|1789 '''2836''' 4154 '''5023'''}} is better tuned than the patent val, | 2.9.5.11.13 subgroup is also represented strongly in 1789edo, where it tunes a temperament called ''commatose'', defined as a {{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]]. | |||
=== Odd harmonics === | === Odd harmonics === | ||
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1789edo supports the 2.5.11.13.19 subgroup temperament called ''estates general'' defined as {{nowrap|1789 & 3125}}. This is referencing the fact that Estates General were called by Louis XVI on 5th May 1789, written as 05/05, and 3125 is 5 to the 5th power and also provides an optimal patent val for tempering out the jacobin comma, contuing the lore. | 1789edo supports the 2.5.11.13.19 subgroup temperament called ''estates general'' defined as {{nowrap|1789 & 3125}}. This is referencing the fact that Estates General were called by Louis XVI on 5th May 1789, written as 05/05, and 3125 is 5 to the 5th power and also provides an optimal patent val for tempering out the jacobin comma, contuing the lore. | ||
=== | === Miscellany === | ||
1789edo can be | For higher harmonics, 1789edo can be adapted for use with the 2.9.5.21.11.13.29.31.47.59.61 subgroup. | ||
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. | |||
=== Subsets and supersets === | === Subsets and supersets === | ||
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| | | 567\1789 | ||
| | | 380.32 | ||
| | | 34328125/27557888 | ||
| [[ | | [[Genojacobin]] | ||
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