1789edo: Difference between revisions

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=== ~~Jacobin~~ temperament ===

=== Onzonic temperament ===

~~A "proper"~~ jacobin ~~scale in 1789edo~~, ~~the~~ maximum evenness scale that uses 822 as a generator, contains only 37 notes. The step sizes are 48 and 49, making them indistinguishable to human ear at this scale.

Since 1789edo tempers out the jacobin comma and it is defined by stacking three 11/8s to reach 13/10, one can use that as a generator. The maximum evenness scale that uses 822 as a generator, contains only 37 notes. The step sizes are 48 and 49, making them indistinguishable to human ear at this scale. Using the maximal evenness method of finding rank two temperaments, we get a 37 & 1789 temperament with the comma basis 6656/6655 and {{monzo| -119 -46 15 47 }} in the 2.5.11.13 subgroup. The first is the jacobin comma discussed earlier.

~~Using the maximal evenness method of finding rank two temperaments, we get a 37 & 1789 temperament with~~ the ~~comma set 6656/6655 and {{monzo| -119 -46 15 47 }}. The first is the well known jacobin comma, and it means that a stack of three 11/8 is equated with 13/10.~~

Name "onzonic" comes from the French word for eleven, ''onze''.

~~The monotonicity can be fixed by using divisors of 822 as a generaator,~~ for ~~example 137\1789 "6th root of 11/8" temperament having 222 notes. In addition, this can be re-interpreted by using 13/10 as a generator instead which produces a more vibrant 1205 out of 1789~~, ~~and partitioning the resulting 13/5s in three around the octave. Addition of 29 and 31 harmonic intervals may also be suitable to spice up an otherwise monotonous scale~~.

=== French decimal temperament ===

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|}

== Rank-2 temperaments ==

=== Rank-2 temperaments ===

{| class="wikitable center-all left-4"

! Generator<br>(Reduced)

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| 23.48

| 531441/524288

| [[Commatose]]

|[[Commatose]]

|-

|144\1789

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| 521.18

| 875/648

| [[Maviloid]]

|[[Maviloid]]

|-

| 778\1789

| 521.86

| 80275/59392

| [[Estates general]]

|[[Estates general]]

|-

|822\1789

|551.37

|11/8

|[[Onzonic]]

|}

@@ Line 11: / Line 11: @@
 {{Harmonics in equal|1789|columns = 10}}
-=== Jacobin temperament ===
+=== Onzonic temperament ===
-A "proper" jacobin scale in 1789edo, the maximum evenness scale that uses 822 as a generator, contains only 37 notes. The step sizes are 48 and 49, making them indistinguishable to human ear at this scale.
+Since 1789edo tempers out the jacobin comma and it is defined by stacking three 11/8s to reach 13/10, one can use that as a generator. The maximum evenness scale that uses 822 as a generator, contains only 37 notes. The step sizes are 48 and 49, making them indistinguishable to human ear at this scale. Using the maximal evenness method of finding rank two temperaments, we get a 37 & 1789 temperament with the comma basis 6656/6655 and {{monzo| -119 -46 15 47 }} in the 2.5.11.13 subgroup. The first is the jacobin comma discussed earlier.
-Using the maximal evenness method of finding rank two temperaments, we get a 37 & 1789 temperament with the comma set 6656/6655 and {{monzo| -119 -46 15 47 }}. The first is the well known jacobin comma, and it means that a stack of three 11/8 is equated with 13/10.
+Name "onzonic" comes from the French word for eleven, ''onze''.
-The monotonicity can be fixed by using divisors of 822 as a generaator, for example 137\1789 "6th root of 11/8" temperament having 222 notes. In addition, this can be re-interpreted by using 13/10 as a generator instead which produces a more vibrant 1205 out of 1789, and partitioning the resulting 13/5s in three around the octave. Addition of 29 and 31 harmonic intervals may also be suitable to spice up an otherwise monotonous scale.
 === French decimal temperament ===
@@ Line 198: / Line 196: @@
 |}
-== Rank-2 temperaments ==
+=== Rank-2 temperaments ===
 {| class="wikitable center-all left-4"
 ! Generator<br>(Reduced)
@@ Line 208: / Line 206: @@
 | 23.48
 | 531441/524288
-| [[Commatose]]
+|[[Commatose]]
 |-
 |144\1789
@@ Line 228: / Line 226: @@
 | 521.18
 | 875/648
-| [[Maviloid]]
+|[[Maviloid]]
 |-
 | 778\1789
 | 521.86
 | 80275/59392
-| [[Estates general]]
+|[[Estates general]]
+|-
+|822\1789
+|551.37
+|11/8
+|[[Onzonic]]
 |}