1789edo: Difference between revisions

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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]].

On the patent val in the 7-limit, 1789edo supports 99 & 373 temperament called maviloid. In addition, it also tempers out [[2401/2400]].

~~Since it has a very precise 31/29, it supports tricesimoprimal miracloid~~ - ~~a version of secor with 31/29 as~~ the ~~generator and a flat, meantone-esque fifth of about 692.23 cents~~. ~~Using~~ the ~~maximal evenness method, we find a 52 & 1789 temperament. Best subgroup~~ for ~~it is 2.5.7.11.19.29.31, since both 52edo and 1789edo support it well, and~~ the ~~comma basis is 10241/10240, 5858783/5856400, 4093705/4090624, 15109493/15089800, 102942875/102834688~~.

==== 1789bd val ====

1789bd val in the 13-limit is better tuned than the patent val. It provides the optimal patent val for the [[hemiluna]] temperament.

1789edo supports the 2.9.5.11.~~13 subgroup temperament which Eliora proposes be called ''commatose''~~, and ~~which uses the Pythagorean comma as a generator. It is defined as a 460 & 1789 temperament~~, and ~~its~~ comma basis is ~~62748517~~/~~62726400~~, ~~479773125~~/~~479756288~~, ~~and 30530193408~~/~~30517578125~~.

==== Tricesimoprimal miracloid ====

Since 1789edo has a very precise 31/29, it supports tricesimoprimal miracloid - a version of secor with 31/29 as the generator and a flat, meantone-esque fifth of about 692.23 cents. Using the maximal evenness method, we find a 52 & 1789 temperament. Best subgroup for it is 2.5.7.11.19.29.31, since both 52edo and 1789edo support it well, and the comma basis is 10241/10240, 5858783/5856400, 4093705/4090624, 15109493/15089800, 102942875/102834688.

==== Commatose ====

1789edo supports the 2.9.5.11.13 subgroup temperament called ''commatose'' which uses the Pythagorean comma as a generator. It is defined as a 460 & 1789 temperament, and its comma basis is 62748517/62726400, 479773125/479756288, and 30530193408/30517578125.

==== Estates General ====

1789edo supports the 2.5.11.13.19 subgroup temperament called ''estates general'' defined as 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. It is unambiguous in the 2.5.11.13.19.23.29.31 subgroup.

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| 531441/524288

| [[Commatose]]

|-

|144\1789

|96.59

|200/189

|[[Hemiluna]] (1789bd)

|-

| 172\1789

@@ Line 35: / Line 35: @@
 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]].
 On the patent val in the 7-limit, 1789edo supports 99 & 373 temperament called maviloid. In addition, it also tempers out [[2401/2400]].
-Since it has a very precise 31/29, it supports tricesimoprimal miracloid - a version of secor with 31/29 as the generator and a flat, meantone-esque fifth of about 692.23 cents. Using the maximal evenness method, we find a 52 & 1789 temperament. Best subgroup for it is 2.5.7.11.19.29.31, since both 52edo and 1789edo support it well, and the comma basis is 10241/10240, 5858783/5856400, 4093705/4090624, 15109493/15089800, 102942875/102834688.
+==== 1789bd val ====
+bd val in the 13-limit is better tuned than the patent val. It provides the optimal patent val for the [[hemiluna]] temperament.
-edo supports the 2.9.5.11.13 subgroup temperament which Eliora proposes be called ''commatose'', and which uses the Pythagorean comma as a generator. It is defined as a 460 & 1789 temperament, and its comma basis is 62748517/62726400, 479773125/479756288, and 30530193408/30517578125.
+==== Tricesimoprimal miracloid ====
+Since 1789edo has a very precise 31/29, it supports tricesimoprimal miracloid - a version of secor with 31/29 as the generator and a flat, meantone-esque fifth of about 692.23 cents. Using the maximal evenness method, we find a 52 & 1789 temperament. Best subgroup for it is 2.5.7.11.19.29.31, since both 52edo and 1789edo support it well, and the comma basis is 10241/10240, 5858783/5856400, 4093705/4090624, 15109493/15089800, 102942875/102834688.
+==== Commatose ====
+edo supports the 2.9.5.11.13 subgroup temperament called ''commatose'' which uses the Pythagorean comma as a generator. It is defined as a 460 & 1789 temperament, and its comma basis is 62748517/62726400, 479773125/479756288, and 30530193408/30517578125.
+==== Estates General ====
 edo supports the 2.5.11.13.19 subgroup temperament called ''estates general'' defined as 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. It is unambiguous in the 2.5.11.13.19.23.29.31 subgroup.
@@ Line 213: / Line 219: @@
 | 531441/524288
 | [[Commatose]]
+|-
+|144\1789
+|96.59
+|200/189
+|[[Hemiluna]] (1789bd)
 |-
 | 172\1789