4320edo: Difference between revisions

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Other notable divisors 4320edo has are [[12edo]], the dominant tuning system in the world today, [[15edo]], known for use by [[Easley Blackwood Jr]]., [[72edo]], which has found usage in Byzantine chanting and various other applications, [[96edo]] notable for its use by Julian Carrillo, [[270edo]], notable for its excellent closed representation of the 13-limit relative to its size, [[360edo]], notable for being a number of degrees in a circle and carrying the interval size measure Dröbisch angle.

==== Proposal for an interval size measure ====

Eliora proposes that 1 step of 4320edo be called a '''click'''. This is because 4320 kilometers per hour equals 1200 meters per second, and "clicks" or "clicks" is a slang name for kilometers per hour. Therefore if one were to think of cents as meters per second, this would make steps of 4320edo correspond kilometers per hour.

For example, a perfect fifth is 701.955 cents. Since 701.955 m/s = 2527.038 km/h, this means that perfect fifth in 4320edo is 2527 steps. And checking the harmonics table, it is.

=== Regular temperament theory ===

4320edo tempers out the [[Kirnberger's atom]], and aside from tuning the atomic temperament, it supports period-60 temperament [[minutes]]. It also supports the period-80 temperament [[mercury]].

In the 7-limit, 4320edo tempers out the [[landscape comma]], and in the 11-limit, the [[kalisma]]. It is a tuning for the [[hemiennealimmal]] temperament and the rank-3 temperament [[odin]].

===Prime harmonics===

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4320edo has a possible usage in [[Georgian]] folk music. 4320edo maps the 3/2 interval to 2527 steps, which factors as 7 x 19^2, and thus 4/3 to 1793 steps, factoring as 11 x 163. Since Georgian traditional music is based on dividing 3/2 and 4/3 into an arbitrary number of steps, it is able to support a variety of [[Kartvelian scales]] on the patent val, for example a combination of [[7edf]] and [[11ed4/3]].

== Regular temperament properties ==

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

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

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

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

! rowspan="2" |Optimal

8ve stretch (¢)

! colspan="2" |Tuning error

|-

![[TE error|Absolute]] (¢)

![[TE simple badness|Relative]] (%)

|-

|2.3

| -6847 4320

|[{{val| 4320 6847}}]

|0.003

|1.20

|-

|2.3.5

|60 31 -47, 161 -84 -12

|[{{val| 4320 6847 10031}}]

|<nowiki>-0.009</nowiki>

|0.017

|6.12

|-

|2.3.5.7

|250047/250000, [-55 30 2 1⟩, [33 19 -3 -20⟩

|[{{val| 4320 6847 10031 12128}}]

|<nowiki>-0.012</nowiki>

|0.016

|5.74

|-

|2.3.5.7.11

|9801/9800, 250047/250000, [24 -10 -5 0 1⟩, [17 19 4 -9 -9⟩

|

|-

|2.3.5.7.11.13

|9801/9800, 67392/67375, 151263/151250, 479773125/479756288, 371293/371250

|

|}

== Miscellany ==

4320edo is the 69th highly abundant EDO. Nice.

[[Category:Equal divisions of the octave|####]]

[[Category:Atomic]]

@@ Line 10: / Line 10: @@
 Other notable divisors 4320edo has are [[12edo]], the dominant tuning system in the world today, [[15edo]], known for use by [[Easley Blackwood Jr]]., [[72edo]], which has found usage in Byzantine chanting and various other applications, [[96edo]] notable for its use by Julian Carrillo, [[270edo]], notable for its excellent closed representation of the 13-limit relative to its size, [[360edo]], notable for being a number of degrees in a circle and carrying the interval size measure Dröbisch angle.
+==== Proposal for an interval size measure ====
+Eliora proposes that 1 step of 4320edo be called a '''click'''. This is because 4320 kilometers per hour equals 1200 meters per second, and "clicks" or "clicks" is a slang name for kilometers per hour. Therefore if one were to think of cents as meters per second, this would make steps of 4320edo correspond kilometers per hour.
+For example, a perfect fifth is 701.955 cents. Since 701.955 m/s = 2527.038 km/h, this means that perfect fifth in 4320edo is 2527 steps. And checking the harmonics table, it is.
 === Regular temperament theory ===
 edo tempers out the [[Kirnberger's atom]], and aside from tuning the atomic temperament, it supports period-60 temperament [[minutes]]. It also supports the period-80 temperament [[mercury]].
+In the 7-limit, 4320edo tempers out the [[landscape comma]], and in the 11-limit, the [[kalisma]]. It is a tuning for the [[hemiennealimmal]] temperament and the rank-3 temperament [[odin]].
 ===Prime harmonics===
@@ Line 22: / Line 29: @@
 edo has a possible usage in [[Georgian]] folk music. 4320edo maps the 3/2 interval to 2527 steps, which factors as 7 x 19^2, and thus 4/3 to 1793 steps, factoring as 11 x 163. Since Georgian traditional music is based on dividing 3/2 and 4/3 into an arbitrary number of steps, it is able to support a variety of [[Kartvelian scales]] on the patent val, for example a combination of [[7edf]] and [[11ed4/3]].
+== Regular temperament properties ==
+{| class="wikitable center-4 center-5 center-6"
+! rowspan="2" |[[Subgroup]]
+! rowspan="2" |[[Comma list|Comma List]]
+! rowspan="2" |[[Mapping]]
+! rowspan="2" |Optimal
+ve stretch (¢)
+! colspan="2" |Tuning error
+|-
+![[TE error|Absolute]] (¢)
+![[TE simple badness|Relative]] (%)
+|-
+|2.3
+| -6847 4320
+|[{{val| 4320 6847}}]
+|0.003
+|0.003
+|1.20
+|-
+|2.3.5
+|60  31 -47, 161 -84 -12
+|[{{val| 4320 6847 10031}}]
+|<nowiki>-0.009</nowiki>
+|0.017
+|6.12
+|-
+|2.3.5.7
+|250047/250000, [-55 30 2 1⟩, [33 19 -3 -20⟩
+|[{{val| 4320 6847 10031 12128}}]
+|<nowiki>-0.012</nowiki>
+|0.016
+|5.74
+|-
+|2.3.5.7.11
+|9801/9800, 250047/250000, [24 -10 -5 0 1⟩, [17 19 4 -9 -9⟩
+|
+|
+|
+|
+|-
+|2.3.5.7.11.13
+|9801/9800, 67392/67375, 151263/151250, 479773125/479756288, 371293/371250
+|
+|
+|
+|
+|}
 == Miscellany ==
 edo is the 69th highly abundant EDO. Nice.
 [[Category:Equal divisions of the octave|####]]
 [[Category:Atomic]]