524edo: Difference between revisions

(One intermediate revision by one other user not shown)

Line 1:

== Theory ==

524edo is only [[consistent]] to the [[5-odd-limit]] and [[3/1|harmonic 3]] is about halfway between its steps~~, but otherwise~~ it has a good approximation to harmonics [[7/1|7]], [[9/1|9]], [[11/1|11]], [[13/1|13]], [[15/1|15]], [[17/1|17]], and [[19/1|19]], making it suitable for a 2.9.15.7.11.13.17.19 [[subgroup]] interpretation. The 2.9.7.13.19 subgroup is particularly good, where it [[support]]s [[Eliora]]'s [[ostara]], the 93 & 524 temperament. The generator 293\524 represents the [[28/19]] interval in the 2.7.19 subgroup and it serves as ostara's generator in the no-threes 19-limit. Being around 671 cents, can also be used to as a generator for [[mavila]] or [[pelog]].

524edo is only [[consistent]] to the [[5-odd-limit]] and [[3/1|harmonic 3]] is about halfway between its steps. Otherwise it has a good approximation to harmonics [[7/1|7]], [[9/1|9]], [[11/1|11]], [[13/1|13]], [[15/1|15]], [[17/1|17]], and [[19/1|19]], making it suitable for a 2.9.15.7.11.13.17.19 [[subgroup]] interpretation. The 2.9.7.13.19 subgroup is particularly good, where it [[support]]s [[Eliora]]'s [[ostara]], the 93 & 524 temperament. The generator 293\524 represents the [[28/19]] interval in the 2.7.19 subgroup and it serves as ostara's generator in the no-threes 19-limit. Being around 671 cents, can also be used to as a generator for [[mavila]] or [[pelog]].

In the 13-limit, 524edo tempers out 1001/1000 and 6664/6655.

Line 9:

=== Odd harmonics ===

=== Subsets and supersets ===

Since 524 factors into {{factorization|524}}, 524edo has subset edos {{EDOs| 2, 4, 131, and 262 }}.

== Regular temperament properties ==

Based on treating 524edo as a no-threes system:

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

|-

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

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

Line 25:

Line 30:

| {{monzo| 1217 -524 }}

| {{mapping| 524 1217 }}

| -0.152

| −0.152

| 0.153

| 6.67

Line 32:

Line 37:

| {{monzo| 33 -13 -1 }}, {{monzo| -4 -43 37 }}

| {{mapping| 524 1217 1471 }}

| -0.087

| −0.087

| 0.155

| 6.79

Line 39:

Line 44:

| 1835008/1830125, {{monzo| 3 7 3 -8 }}, {{monzo| -13 -5 10 -1 }}

| {{mapping| 524 1217 1471 1813 }}

| -0.108

| −0.108

| 0.139

| 6.09

Line 46:

Line 51:

| 1001/1000, 742586/741125, 2097152/2093663, 14201915/14172488

| {{mapping| 524 1217 1471 1813 1939 }}

| -0.082

| −0.082

| 0.135

| 5.88

Line 53:

Line 58:

| 1001/1000, 6664/6655, 54080/54043, 147968/147875, 285719/285610

| {{mapping| 524 1217 1471 1813 1939 2142 }}

| -0.084

| −0.084

| 0.122

| 5.37

Line 59:

Line 64:

== Scales ==

* Ostara[7]: 62 62 62 107 62 62 107 - [[2L 5s]]

* Ostara[7]: 62 62 62 107 62 62 107 – [[2L 5s]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|524}}
+{{ED intro}}
 == Theory ==
-edo is only [[consistent]] to the [[5-odd-limit]] and [[3/1|harmonic 3]] is about halfway between its steps, but otherwise it has a good approximation to harmonics [[7/1|7]], [[9/1|9]], [[11/1|11]], [[13/1|13]], [[15/1|15]], [[17/1|17]], and [[19/1|19]], making it suitable for a 2.9.15.7.11.13.17.19 [[subgroup]] interpretation. The 2.9.7.13.19 subgroup is particularly good, where it [[support]]s [[Eliora]]'s [[ostara]], the 93 & 524 temperament. The generator 293\524 represents the [[28/19]] interval in the 2.7.19 subgroup and it serves as ostara's generator in the no-threes 19-limit. Being around 671 cents, can also be used to as a generator for [[mavila]] or [[pelog]].
+edo is only [[consistent]] to the [[5-odd-limit]] and [[3/1|harmonic 3]] is about halfway between its steps. Otherwise it has a good approximation to harmonics [[7/1|7]], [[9/1|9]], [[11/1|11]], [[13/1|13]], [[15/1|15]], [[17/1|17]], and [[19/1|19]], making it suitable for a 2.9.15.7.11.13.17.19 [[subgroup]] interpretation. The 2.9.7.13.19 subgroup is particularly good, where it [[support]]s [[Eliora]]'s [[ostara]], the 93 & 524 temperament. The generator 293\524 represents the [[28/19]] interval in the 2.7.19 subgroup and it serves as ostara's generator in the no-threes 19-limit. Being around 671 cents, can also be used to as a generator for [[mavila]] or [[pelog]].
 In the 13-limit, 524edo tempers out 1001/1000 and 6664/6655.
@@ Line 9: / Line 9: @@
 === Odd harmonics ===
 {{Harmonics in equal|524}}
+=== Subsets and supersets ===
+Since 524 factors into {{factorization|524}}, 524edo has subset edos {{EDOs| 2, 4, 131, and 262 }}.
 == Regular temperament properties ==
 Based on treating 524edo as a no-threes system:
 {| class="wikitable center-4 center-5 center-6"
+|-
 ! rowspan="2" | [[Subgroup]]
 ! rowspan="2" | [[Comma list|Comma List]]
@@ Line 25: / Line 30: @@
 | {{monzo| 1217 -524 }}
 | {{mapping| 524 1217 }}
-| -0.152
+| −0.152
 | 0.153
 | 6.67
@@ Line 32: / Line 37: @@
 | {{monzo| 33 -13 -1 }}, {{monzo| -4 -43 37 }}
 | {{mapping| 524 1217 1471 }}
-| -0.087
+| −0.087
 | 0.155
 | 6.79
@@ Line 39: / Line 44: @@
 | 1835008/1830125, {{monzo| 3 7 3 -8 }}, {{monzo| -13 -5 10 -1 }}
 | {{mapping| 524 1217 1471 1813 }}
-| -0.108
+| −0.108
 | 0.139
 | 6.09
@@ Line 46: / Line 51: @@
 | 1001/1000, 742586/741125, 2097152/2093663, 14201915/14172488
 | {{mapping| 524 1217 1471 1813 1939 }}
-| -0.082
+| −0.082
 | 0.135
 | 5.88
@@ Line 53: / Line 58: @@
 | 1001/1000, 6664/6655, 54080/54043, 147968/147875, 285719/285610
 | {{mapping| 524 1217 1471 1813 1939 2142 }}
-| -0.084
+| −0.084
 | 0.122
 | 5.37
@@ Line 59: / Line 64: @@
 == Scales ==
-* Ostara[7]: 62 62 62 107 62 62 107 - [[2L 5s]]
+* Ostara[7]: 62 62 62 107 62 62 107 – [[2L 5s]]