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| {{Infobox ET}} | | {{Infobox ET}} |
| {{EDO intro|360}} | | {{ED intro}} |
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| == Theory == | | == Theory == |
| 360edo is consistent in the 7-limit. Its 5-limit patent val [[support]]s [[misty]] temperament, and in the 7-limit 360edo supports the [[trimisty]] (name proposed by Eliora) 63 & 99 temperament with the comma basis 10976/10935, 2097152/2083725, which is similar to the misty temperament but has a period of 1/9 rather than 1/3 octave. In addition, 360edo provides the optimal patent val for the 41 & 360 temperament with comma basis 10976/10935, 16384000000/16209796869, on which it has lower badness than any other 7-limit temperament for which 360edo gives the optimal patent val. It also supports 12 & 360 with the comma basis 390625/388962, 67108864/66430125. 360edo tempers out the [[15/14 equal-step tuning|linus comma]], meaning 15/14 corresponds to 1/10th of the octave, 36 steps. | | 360edo is [[consistent]] to the [[7-odd-limit]], but [[harmonic]] [[3/1|3]] is about halfway between its steps. It can also be used with 2.5.9.13 subgroup. |
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| | In the 5-limit, the [[patent val]] [[support]]s the [[misty]] temperament, and in the 7-limit 360edo supports the [[trimisty]] (name proposed by Eliora) 63 & 99 temperament with the comma basis {[[10976/10935]], 2097152/2083725}, which is similar to the misty temperament but has a period of 1/9- rather than 1/3-octave. |
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| | 360edo provides the optimal patent val in the 11-limit, and otherwise a good tuning in the 13-limit for [[degrees]], the {{nowrap|140 & 220}} temperament with period 1\20. Aside from that, it provides the optimal patent val for the {{nowrap|41 & 360}} temperament with comma basis {10976/10935, 16384000000/16209796869}, on which it has lower badness than any other 7-limit temperament for which 360edo gives the optimal patent val. It also supports {{nowrap|12 & 360}} with the comma basis {[[390625/388962]], 67108864/66430125}. |
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| | Aside from the patent val, there is a number of mappings to be considered. The 360d val, {{val|360 571 836 '''1010'''}}, tempers out 3136/3125, 5120/5103, and extends the misty temperament in to the 7-limit. It is also a tuning for the 12th-octave [[magnesium]] temperament. |
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| 360edo provides the optimal patent val in the 11-limit, and otherwise a good tuning in the 13-limit for the [[Hemimage_temperaments#Degrees|degrees temperament]], the 80&140 temperament with period 20.
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| === As an interval size measure ===
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| 360 is the 13th [[highly composite EDO]], with many proper divisors: 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180.
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| One step of 360edo is known as '''the Dröbisch angle''', being first proposed by Moritz Dröbisch in the 19th century at first merely by the name "angle".
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| === Odd harmonics === | | === Odd harmonics === |
| {{harmonics in equal|360}} | | {{Harmonics in equal|360}} |
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| | === Subsets and supersets === |
| | 360 is the 13th [[highly composite edo]], with many proper divisors: {{EDOs| 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180 }}. One step of 360edo is known as '''the Dröbisch angle''', an [[interval size measure]] first proposed by Moritz Dröbisch in the 19th century at first merely by the name "angle". |
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| == Table of intervals == | | == Table of intervals == |
| 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]]. | | [[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]]. |
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| Any other notation system involving the number 360 can also be used. | | Any other notation system involving the number 360 can also be used. |
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| {{Interval table|additional=Calendar notation
| | See: [[Table of 360edo intervals]] |
| January 1
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| January 2
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| January 3
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| January 4
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| January 5
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| January 6
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| January 7
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| January 8
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| January 9
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| January 10
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| January 11
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| January 12
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| January 13
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| January 14
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| January 15
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| January 16
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| January 17
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| January 18
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| January 19
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| January 20
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| January 21
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| January 22
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| January 23
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| January 24
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| January 25
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| January 26
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| January 27
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| January 28
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| January 29
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| January 30
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| January 31
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| February 1
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| February 2
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| February 3
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| February 4
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| February 5
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| February 6
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| February 7
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| February 8
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| February 9
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| February 10
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| February 11
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| February 12
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| February 13
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| February 14
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| February 15
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| February 16
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| February 17
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| February 18
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| February 19
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| February 20
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| February 21
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| February 22
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| February 23
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| February 24
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| February 25
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| February 26
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| February 27
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| February 28
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| March 1
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| March 2
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| March 3
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| March 4
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| March 5
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| March 6
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| March 7
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| March 8
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| March 9
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| March 10
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| March 11
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| March 12
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| March 13
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| March 14
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| March 15
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| March 16
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| March 17
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| March 18
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| March 19
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| March 20
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| March 21
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| March 22
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| March 23
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| March 24
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| March 25
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| March 26
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| March 27
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| March 28
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| March 29
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| March 30
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| March 31
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| April 1
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| April 2
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| April 3
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| April 4
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| April 5
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| April 6
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| April 7
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| April 8
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| April 9
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| April 10
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| April 11
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| April 12
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| April 13
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| April 14
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| April 15
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| April 16
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| April 17
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| April 18
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| April 19
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| April 20
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| April 21
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| April 22
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| April 23
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| April 24
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| April 25
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| April 26
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| April 27
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| April 28
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| April 29
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| April 30
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| May 1
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| May 2
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| May 3
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| May 4
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| May 5
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| May 7
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| May 11
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| May 14
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| May 15
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| May 16
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| May 17
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| May 18
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| May 19
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| May 20
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| May 21
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| May 22
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| May 23
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| May 24
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| May 25
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| May 26
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| May 27
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| May 28
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| May 29
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| May 30
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| May 31
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| June 1
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| June 2
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| June 3
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| June 4
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| June 5
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| June 6
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| June 7
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| June 8
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| June 9
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| June 10
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| June 11
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| June 12
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| June 13
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| June 14
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| June 15
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| June 16
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| June 17
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| June 18
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| June 19
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| June 20
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| June 21
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| June 22
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| June 24
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| June 25
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| June 26
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| June 27
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| June 28
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| June 29
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| June 30
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| July 1
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| July 2
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| July 3
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| July 4
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| July 5
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| July 6
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| July 7
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| July 8
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| July 9
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| July 10
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| July 11
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| July 12
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| July 13
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| July 14
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| July 15
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| July 16
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| July 17
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| July 18
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| July 19
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| July 20
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| July 21
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| July 22
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| July 23
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| July 24
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| July 25
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| July 26
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| July 27
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| July 28
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| July 29
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| July 30
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| July 31
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| August 1
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| August 2
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| August 3
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| August 4
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| August 5
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| August 6
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| August 7
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| August 8
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| August 9
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| August 10
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| August 11
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| August 12
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| August 13
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| August 14
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| August 15
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| August 16
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| August 17
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| August 18
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| August 19
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| August 20
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| August 21
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| August 22
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| August 23
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| August 24
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| August 25
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| August 26
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| August 27
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| August 28
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| August 29
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| August 30
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| August 31
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| September 1
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| September 2
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| September 3
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| September 4
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| September 5
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| September 6
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| September 7
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| September 8
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| September 9
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| September 10
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| September 11
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| September 12
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| September 13
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| September 14
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| September 15
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| September 16
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| September 17
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| September 18
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| September 19
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| September 20
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| September 21
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| September 22
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| September 23
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| September 24
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| September 25
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| September 26
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| September 27
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| September 28
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| September 29
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| September 30
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| October 1
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| October 2
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| October 3
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| October 4
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| October 5
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| October 6
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| October 7
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| October 8
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| October 9
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| October 10
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| October 11
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| October 12
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| October 13
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| October 14
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| October 15
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| October 16
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| October 17
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| October 18
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| October 19
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| October 20
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| October 21
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| October 22
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| October 23
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| October 24
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| October 25
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| October 26
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| October 27
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| October 28
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| October 29
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| October 30
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| October 31
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| November 1
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| November 2
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| November 3
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| November 4
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| November 5
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| November 6
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| November 7
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| November 8
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| November 9
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| November 10
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| November 11
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| November 12
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| November 13
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| November 14
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| November 15
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| November 16
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| November 17
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| November 18
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| November 19
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| November 20
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| November 21
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| November 22
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| November 23
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| November 24
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| November 25
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| November 26
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| November 27
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| November 28
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| November 29
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| November 30
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| December 1
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| December 2
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| December 3
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| December 4
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| December 5
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| December 6
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| December 7
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| December 8
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| December 9
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| December 10
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| December 11
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| December 12
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| December 13
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| December 14
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| December 15
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| December 16
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| December 17
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| December 18
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| December 19
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| December 20
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| December 21
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| December 22
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| December 23
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| December 24
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| December 25
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| December 26
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| December 27
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| December 28
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| December 29
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| December 30
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| December 31
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| }}
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| ==Regular temperament properties== | | == Regular temperament properties == |
| ===Rank-2 temperaments === | | === Rank-2 temperaments === |
| {| class="wikitable center-all left-5" | | {| class="wikitable center-all left-5" |
| !Periods<br>per 8ve
| | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator |
| !Generator<br>(reduced)
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| !Cents<br>(reduced)
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| !Associated<br>ratio
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| !Temperaments
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| |- | | |- |
| |1
| | ! Periods<br />per 8ve |
| |119\360
| | ! Generator* |
| |396.67
| | ! Cents* |
| |44/35
| | ! Associated<br />ratio* |
| |[[Squarschmidt]]
| | ! Temperaments |
| |- | | |- |
| |2 | | | 1 |
| |53\360 | | | 119\360 |
| |176.67 | | | 396.67 |
| |448/405 | | | 44/35 |
| |[[Ragismic microtemperaments#Quatracot|Quatracot]] | | | [[Squarschmidt]] |
| |- | | |- |
| |3 | | | 2 |
| |211\360<br>(91\360) | | | 53\360 |
| |703.33<br>(303.33) | | | 176.67 |
| |3/2 | | | 448/405 |
| |[[Misty]] | | | Quatracot |
| |- | | |- |
| |4 | | | 3 |
| |23\360 | | | 149\360<br />(29\360) |
| |76.67 | | | 703.33<br />(303.33) |
| |4302592/4100625 | | | 4/3<br />(135/128) |
| |[[Reenactment]] | | | [[Misty]] |
| |- | | |- |
| |9 | | | 4 |
| |211\360<br>(11\360) | | | 23\360 |
| |703.33<br>(36.67) | | | 76.67 |
| |3/2 | | | 4302592/4100625 |
| |[[Trimisty]] | | | [[Reenactment]] |
| |- | | |- |
| |20 | | | 9 |
| |211\360<br>(13\360) | | | 149\360<br />(29\360) |
| |703.33<br>(43.33) | | | 703.33<br />(36.67) |
| |3/2<br>(45/44) | | | 4/3<br />(135/128) |
| |[[Degrees]] | | | [[Trimisty]] |
| | |- |
| | | 12 |
| | | 73\360<br />(13\360) |
| | | 243.333<br />(43.333) |
| | | 3145728/2734375<br />(?) |
| | | [[Magnesium]] (360d) |
| | |- |
| | | 20 |
| | | 149\360<br />(5\360) |
| | | 703.33<br />(43.33) |
| | | 4/3<br />(126/125) |
| | | [[Degrees]] |
| |} | | |} |
| | <nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct |
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| | == Music == |
| | ; [[User:Eliora|Eliora]] |
| | * [https://www.youtube.com/watch?v=VSKqwJkWu_U ''Idyllic Tribe''] (2022) |
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| ==Music==
| | == Application as a logarithmic scale outside of music == |
| * [https://www.youtube.com/watch?v=VSKqwJkWu_U Idyllic Tribe] by [[User:Eliora|Eliora]]
| | 360edo is used in the {{w|eyeborg}}, which maps its scale degrees onto color hues, thus converting color into sound waves. The device was originally intended to help colorblind individuals. |
| ==References==
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| * [https://www.huygens-fokker.org/docs/measures.html Logarithmic size measures]
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| ==Application as a logarithmic scale outside of music== | |
| 360edo is used in the [[wikipedia:Eyeborg|eyeborg]], which maps its scale degrees onto color hues, thus converting color into sound waves. The device was originally intended to help colorblind individuals. | |
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| [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | | [[Category:Sonifications]] |
| [[Category:Highly composite]]
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| [[Category:Real-life sonifications]]
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| [[Category:Listen]] | | [[Category:Listen]] |
| | {{Todo| cleanup |comment=move trimisty away}} |