2520edo: Difference between revisions

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== Theory ==

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=== Subsets and supersets ===

In addition to being a highly composite number, 2520 is the least common multiple of numbers from 1 to 10, meaning 2520edo is the smallest superset of first 10 edos. Its subset edos are {{EDOs| 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 56, 60, 63, 70, 72, 84, 90, 105, 120, 126, 140, 168, 180, 210, 252, 280, 315, 360, 420, 504, 630, 840, 1260 }}. It is a superabundant edo in addition to being highly composite, with abundancy index of 19/7 = 2.714.

In addition to being a highly composite number, 2520 is the least common multiple of numbers from 1 to 10, meaning 2520edo is the smallest superset of first 10 edos. Its subset edos are {{EDOs| 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 56, 60, 63, 70, 72, 84, 90, 105, 120, 126, 140, 168, 180, 210, 252, 280, 315, 360, 420, 504, 630, 840, 1260 }}. It is a superabundant edo in addition to being highly composite, with abundancy index of {{nowrap|19/7 {{=}} 2.714}}.

Furthermore, one step of 2520edo is 8 pians ([[20160edo|20160/8]]).

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=== Rank-2 temperaments ===

{| class="wikitable center-all left-5"

! Periods per 8ve

|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator

|-

! Periods per 8ve

! Generator*

! Cents*

! Associated ~~Ratio~~

! Associated ratio*

! Temperaments

|-

| 9

| 663\2520 (103\2520)

| 663\2520 (103\2520)

| 315.714 (49.048)

| 315.714 (49.048)

| 6/5 (36/35)

| 6/5 (36/35)

| [[Ennealimmal]] (2520d)

|-

| 18

| 523\2520 (103\2520)

| 523\2520 (103\2520)

| 249.047 (49.048)

| 249.047 (49.048)

| 231/200 (99/98)

| 231/200 (99/98)

| [[Hemiennealimmal]] (2520de)

|-

| 56

| 1046\2520 (11\2520)

| 1046\2520 (11\2520)

| 498.095 (5.238)

| 498.095 (5.238)

| 4/3 (126/125)

| 4/3 (126/125)

| [[Barium]]

|}

<nowiki>*~~</nowiki>~~ [[Normal lists|~~octave~~-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if ~~it is~~ distinct

<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct

[[Category:Jacobin]]

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|2520}}
+{{ED intro}}
 == Theory ==
@@ Line 13: / Line 13: @@
 === Subsets and supersets ===
-In addition to being a highly composite number, 2520 is the least common multiple of numbers from 1 to 10, meaning 2520edo is the smallest superset of first 10 edos. Its subset edos are {{EDOs| 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 56, 60, 63, 70, 72, 84, 90, 105, 120, 126, 140, 168, 180, 210, 252, 280, 315, 360, 420, 504, 630, 840, 1260 }}. It is a superabundant edo in addition to being highly composite, with abundancy index of 19/7 = 2.714.
+In addition to being a highly composite number, 2520 is the least common multiple of numbers from 1 to 10, meaning 2520edo is the smallest superset of first 10 edos. Its subset edos are {{EDOs| 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 15, 18, 20, 21, 24, 28, 30, 35, 36, 40, 42, 45, 56, 60, 63, 70, 72, 84, 90, 105, 120, 126, 140, 168, 180, 210, 252, 280, 315, 360, 420, 504, 630, 840, 1260 }}. It is a superabundant edo in addition to being highly composite, with abundancy index of {{nowrap|19/7 {{=}} 2.714}}.
 Furthermore, one step of 2520edo is 8 pians ([[20160edo|20160/8]]).
@@ Line 20: / Line 20: @@
 === Rank-2 temperaments ===
 {| class="wikitable center-all left-5"
-! Periods<br>per 8ve
+|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
+|-
+! Periods<br />per 8ve
 ! Generator*
 ! Cents*
-! Associated<br>Ratio
+! Associated<br />ratio*
 ! Temperaments
 |-
 | 9
-| 663\2520<br>(103\2520)
+| 663\2520<br />(103\2520)
-| 315.714<br>(49.048)
+| 315.714<br />(49.048)
-| 6/5<br>(36/35)
+| 6/5<br />(36/35)
 | [[Ennealimmal]] (2520d)
 |-
 | 18
-| 523\2520<br>(103\2520)
+| 523\2520<br />(103\2520)
-| 249.047<br>(49.048)
+| 249.047<br />(49.048)
-| 231/200<br>(99/98)
+| 231/200<br />(99/98)
 | [[Hemiennealimmal]] (2520de)
 |-
 | 56
-| 1046\2520<br>(11\2520)
+| 1046\2520<br />(11\2520)
-| 498.095<br>(5.238)
+| 498.095<br />(5.238)
-| 4/3<br>(126/125)
+| 4/3<br />(126/125)
 | [[Barium]]
 |}
-<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct
+<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
 [[Category:Jacobin]]