1600edo: Difference between revisions

Line 3:

== Theory ==

1600edo is a very strong 37-limit system, being distinctly consistent in the 37-limit with a smaller [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]] than anything else with this property until [[4501edo|4501]]. It is also the first division past [[311edo|311]] with a lower 43-limit relative error. One step of it is the [[relative cent]] for [[16edo|16]]. It's high divisibility, high consistency limit, and compatibility with the decimal system make it a candidate for interval size measure. One step of 1600edo is already used as a measure called śata in the context of 16edo [[Armodue theory]].

1600edo is a very strong 37-limit system, being distinctly consistent in the 37-limit with a smaller [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]] than anything else with this property until [[4501edo|4501]]. It is also the first division past [[311edo|311]] with a lower 43-limit relative error.

In the 5-limit, it supports [[kwazy]]. In the 7-limit, it tempers out ~~the ragisma, 4375~~/~~4374. In~~ the 11-limit, it ~~supports~~ the ~~rank-3 temperament~~ [[~~thor~~]].

In the 5-limit, it supports [[kwazy]]. In the 11-limit, it supports the rank-3 temperament [[thor]]. In higher limits, it tempers out [[12376/12375]] in the 17-limit and due to being consistent higher than 33-odd-limit it enables the essentially tempered [[flashmic chords]].

===Odd harmonics===

===Subsets and supersets===

1600's divisors are {{EDOs|1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160, 200, 320, 400, 800}}.

One step of it is the [[relative cent]] for [[16edo|16]]. It's high divisibility, high consistency limit, and compatibility with the decimal system make it a candidate for interval size measure. One step of 1600edo is already used as a measure called ''śata'' in the context of 16edo [[Armodue theory]].

== Regular temperament properties ==

{| class="wikitable center-4 center-5 center-6"

Line 70:

Line 72:

| 1125/1024

| [[Kwazy]]

|-

| 32

| 23\1600

| 17.25

| ?

|[[Dike]]

|-

| 32

Line 82:

Line 90:

| 245/143<br>(?)

| [[Germanium]]

|-

~~| 32~~

~~| 23\1600~~

~~| 17.25~~

~~| ?~~

~~| [[Dike]]~~

|-

| 80

@@ Line 3: / Line 3: @@
 == Theory ==
-edo is a very strong 37-limit system, being distinctly consistent in the 37-limit with a smaller [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]] than anything else with this property until [[4501edo|4501]]. It is also the first division past [[311edo|311]] with a lower 43-limit relative error. One step of it is the [[relative cent]] for [[16edo|16]]. It's high divisibility, high consistency limit, and compatibility with the decimal system make it a candidate for interval size measure. One step of 1600edo is already used as a measure called śata in the context of 16edo [[Armodue theory]].
+edo is a very strong 37-limit system, being distinctly consistent in the 37-limit with a smaller [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]] than anything else with this property until [[4501edo|4501]]. It is also the first division past [[311edo|311]] with a lower 43-limit relative error.
-In the 5-limit, it supports [[kwazy]]. In the 7-limit, it tempers out the ragisma, 4375/4374. In the 11-limit, it supports the rank-3 temperament [[thor]].
+In the 5-limit, it supports [[kwazy]]. In the 11-limit, it supports the rank-3 temperament [[thor]]. In higher limits, it tempers out [[12376/12375]] in the 17-limit and due to being consistent higher than 33-odd-limit it enables the essentially tempered [[flashmic chords]].
 ===Odd harmonics===
 {{Harmonics in equal|1600}}
 ===Subsets and supersets===
 's divisors are {{EDOs|1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 160, 200, 320, 400, 800}}.
+One step of it is the [[relative cent]] for [[16edo|16]]. It's high divisibility, high consistency limit, and compatibility with the decimal system make it a candidate for interval size measure. One step of 1600edo is already used as a measure called ''śata'' in the context of 16edo [[Armodue theory]].
 == Regular temperament properties ==
 {| class="wikitable center-4 center-5 center-6"
@@ Line 70: / Line 72: @@
 | 1125/1024
 | [[Kwazy]]
+|-
+| 32
+| 23\1600
+| 17.25
+| ?
+|[[Dike]]
 |-
 | 32
@@ Line 82: / Line 90: @@
 | 245/143<br>(?)
 | [[Germanium]]
-|-
-| 32
-| 23\1600
-| 17.25
-| ?
-| [[Dike]]
 |-
 | 80