360edo: Difference between revisions

Line 16:

Its 23-limit patent val is <360 571 836 1011 1245 1332 1471 1529 1628|. This val tempers out the kalisma, the triaphonisma, the septendecimal bridge comma, the misty comma, hemimage, dimicomp, 2*(14/15)^10, 289/288, 352/351, 589824/588245 and 2560000000/2542277421.

Its 5-limit patent val [[support]]s misty temperament.

Its 5-limit patent val [[support]]s [[misty]] temperament.

In the 7-limit, 360edo supports the 63&99 temperament with wedgie <<9 -36 9 -78 -11 122|| which tempers out misty but has a period of 1/9 rather than 1/3 octave. Two other seven limit temperaments it supports and also provides the optimal patent val for are 41&360 = <<11 76 51 95 50 -95|| and 12&360 = <<12 -48 -108 -104 -205 -116||; neither is very good though 41&360 has a TE badness lower than any alternative 7-limit temperament for which 360 gives the optimal patent val. In the 7-limit, 360edo tempers out the [[15/14 equal-step tuning|linus comma]], meaning 15/14 corresponds to 1/10th of the octave, 36 steps.

In the 7-limit, 360edo supports the [[trimisty]] (name proposed by Eliora) 63&99 temperament with wedgie <<9 -36 9 -78 -11 122|| which tempers out misty but has a period of 1/9 rather than 1/3 octave,. Two other seven limit temperaments it supports and also provides the optimal patent val for are 41&360 = <<11 76 51 95 50 -95|| and 12&360 = <<12 -48 -108 -104 -205 -116||; neither is very good though 41&360 has a TE badness lower than any alternative 7-limit temperament for which 360 gives the optimal patent val. In the 7-limit, 360edo tempers out the [[15/14 equal-step tuning|linus comma]], meaning 15/14 corresponds to 1/10th of the octave, 36 steps.

Much better is [[Hemimage_temperaments#Degrees|degrees temperament]], the 80&140 temperament with period 20, for which 360 supplies the optimal patent val in the 11-limit and which it supports and provides an excellent tuning for in the 13-limit. In the

Line 27:

Eliora proposes notating 360edo with calendar dates, Jan 1 being the tonic, Jan 2 being the next step, etc, and each month having even 30 days. The notation is convenient because 1 month in this scenario is equal to 1 semitone, and corresponds to [[12edo]].

== Rank two temperaments by generator ==

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

!Periods

per octave

!Generator

(reduced)

!Cents

(reduced)

!Associated

ratio

!Temperaments

|-

|3

|211\360

(91\360)

|703.33

(303.33)

|3/2

|[[Misty]]

|-

|9

|211\360

(11\360)

|703.33

(36.67)

|3/2

|[[Trimisty]]

|-

|20

|211\360

(13\360)

|703.33

(43.33)

|3/2

(45/44)

|[[Degrees]]

|}

== Table of intervals ==

{| class="wikitable"

@@ Line 16: / Line 16: @@
 Its 23-limit patent val is &lt;360 571 836 1011 1245 1332 1471 1529 1628|. This val tempers out the kalisma, the triaphonisma, the septendecimal bridge comma, the misty comma, hemimage, dimicomp, 2*(14/15)^10, 289/288, 352/351, 589824/588245 and 2560000000/2542277421.
-Its 5-limit patent val [[support]]s misty temperament.
+Its 5-limit patent val [[support]]s [[misty]] temperament.
-In the 7-limit, 360edo supports the 63&amp;99 temperament with wedgie &lt;&lt;9 -36 9 -78 -11 122|| which tempers out misty but has a period of 1/9 rather than 1/3 octave. Two other seven limit temperaments it supports and also provides the optimal patent val for are 41&amp;360 = &lt;&lt;11 76 51 95 50 -95|| and 12&amp;360 = &lt;&lt;12 -48 -108 -104 -205 -116||; neither is very good though 41&amp;360 has a TE badness lower than any alternative 7-limit temperament for which 360 gives the optimal patent val. In the 7-limit, 360edo tempers out the [[15/14 equal-step tuning|linus comma]], meaning 15/14 corresponds to 1/10th of the octave, 36 steps.
+In the 7-limit, 360edo supports the [[trimisty]] (name proposed by Eliora) 63&amp;99 temperament with wedgie &lt;&lt;9 -36 9 -78 -11 122|| which tempers out misty but has a period of 1/9 rather than 1/3 octave,. Two other seven limit temperaments it supports and also provides the optimal patent val for are 41&amp;360 = &lt;&lt;11 76 51 95 50 -95|| and 12&amp;360 = &lt;&lt;12 -48 -108 -104 -205 -116||; neither is very good though 41&amp;360 has a TE badness lower than any alternative 7-limit temperament for which 360 gives the optimal patent val. In the 7-limit, 360edo tempers out the [[15/14 equal-step tuning|linus comma]], meaning 15/14 corresponds to 1/10th of the octave, 36 steps.
 Much better is [[Hemimage_temperaments#Degrees|degrees temperament]], the 80&amp;140 temperament with period 20, for which 360 supplies the optimal patent val in the 11-limit and which it supports and provides an excellent tuning for in the 13-limit. In the
@@ Line 27: / Line 27: @@
 Eliora proposes notating 360edo with calendar dates, Jan 1 being the tonic, Jan 2 being the next step, etc, and each month having even 30 days. The notation is convenient because 1 month in this scenario is equal to 1 semitone, and corresponds to [[12edo]].
+== Rank two temperaments by generator ==
+{| class="wikitable center-all left-5"
+!Periods
+per octave
+!Generator
+(reduced)
+!Cents
+(reduced)
+!Associated
+ratio
+!Temperaments
+|-
+|3
+|211\360
+(91\360)
+|703.33
+(303.33)
+|3/2
+|[[Misty]]
+|-
+|9
+|211\360
+(11\360)
+|703.33
+(36.67)
+|3/2
+|[[Trimisty]]
+|-
+|20
+|211\360
+(13\360)
+|703.33
+(43.33)
+|3/2
+(45/44)
+|[[Degrees]]
+|}
 == Table of intervals ==
 {| class="wikitable"