2118edo: Difference between revisions

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== Theory ==

Primes approximated with less than 1 standard deviation in 2118edo are: 2, 3, 5, 7, 11, 19, 23, 29, 31, 43. Overall, it offers excellent double-13's 31-limit harmony, as both mappings of 13 (2118 and 2118f vals) have useful interpretations.

2118edo provides a 43-limit approximation of [[secor]] with [[46/43]] (206 steps), however this reduces to 103\1059, meaning that it is a compound of two circles of such secor. In addition, it offers a 205-step generator "meantone secor" which is described by a 31 & 2118 temperament, also in the 2.3.5.7.11.23.43 subgroup, and also offers a meantone fifth. The comma basis for the "meantone secor" temperament is 5376/5375, 9317/9315, 25921/25920, 151263/151250, and 10551296/10546875.

2118edo provides a 43-limit approximation of [[secor]] with [[46/43]] (206 steps), however this reduces to 103\1059, meaning that it is a compound of two circles of such secor. In addition, it offers a 205-step generator "meantone secor" which is described by a {{nowrap|31 & 2118}} temperament, also in the 2.3.5.7.11.23.43 subgroup, and also offers a meantone fifth. The comma basis for the "meantone secor" temperament is 5376/5375, 9317/9315, 25921/25920, 151263/151250, and 10551296/10546875.

=== Prime harmonics ===

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== Regular temperament properties ==

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

|-

! rowspan="2" | [[Subgroup]]

! rowspan="2" | [[Comma list|Comma List]]

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| {{monzo| 38 -2 15 }}, {{monzo| -11 130 -84 }}

| {{mapping| 2118 3357 4918 }}

| -0.0186

| −0.0186

| 0.0156

|

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| 250047/250000, {{monzo| -1 -18 -3 13 }}, {{monzo| 38 -2 -15 }}

| {{mapping| 2118 3357 4918 5946 }}

| -0.0150

| −0.0150

| 0.0148

|

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| 9801/9800, 250047/250000, {{monzo| 25 1 -4 0 -5 }}, {{monzo| 16 -7 -9 2 3 }}

| {{mapping| 2118 3357 4918 5946 7927 }}

| -0.0096

| −0.0096

| 0.0172

|

|}

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|2118}}
+{{ED intro}}
 == Theory ==
 Primes approximated with less than 1 standard deviation in 2118edo are: 2, 3, 5, 7, 11, 19, 23, 29, 31, 43. Overall, it offers excellent double-13's 31-limit harmony, as both mappings of 13 (2118 and 2118f vals) have useful interpretations.
-edo provides a 43-limit approximation of [[secor]] with [[46/43]] (206 steps), however this reduces to 103\1059, meaning that it is a compound of two circles of such secor. In addition, it offers a 205-step generator "meantone secor" which is described by a 31 & 2118 temperament, also in the 2.3.5.7.11.23.43 subgroup, and also offers a meantone fifth. The comma basis for the "meantone secor" temperament is 5376/5375, 9317/9315, 25921/25920, 151263/151250, and 10551296/10546875.
+edo provides a 43-limit approximation of [[secor]] with [[46/43]] (206 steps), however this reduces to 103\1059, meaning that it is a compound of two circles of such secor. In addition, it offers a 205-step generator "meantone secor" which is described by a {{nowrap|31 &amp; 2118}} temperament, also in the 2.3.5.7.11.23.43 subgroup, and also offers a meantone fifth. The comma basis for the "meantone secor" temperament is 5376/5375, 9317/9315, 25921/25920, 151263/151250, and 10551296/10546875.
 === Prime harmonics ===
@@ Line 15: / Line 15: @@
 == Regular temperament properties ==
 {| class="wikitable center-4 center-5 center-6"
+|-
 ! rowspan="2" | [[Subgroup]]
 ! rowspan="2" | [[Comma list|Comma List]]
@@ Line 27: / Line 28: @@
 | {{monzo| 38 -2 15 }}, {{monzo| -11 130 -84 }}
 | {{mapping| 2118 3357 4918 }}
-| -0.0186
+| −0.0186
 | 0.0156
 |
@@ Line 34: / Line 35: @@
 | 250047/250000, {{monzo| -1 -18 -3 13 }}, {{monzo| 38 -2 -15 }}
 | {{mapping| 2118 3357 4918 5946 }}
-| -0.0150
+| −0.0150
 | 0.0148
 |
@@ Line 41: / Line 42: @@
 | 9801/9800, 250047/250000, {{monzo| 25 1 -4 0 -5 }}, {{monzo| 16 -7 -9 2 3 }}
 | {{mapping| 2118 3357 4918 5946 7927 }}
-| -0.0096
+| −0.0096
 | 0.0172
 |
 |}