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= Theory =
The '''540 equal divisions of the octave''' ('''540edo'''), or the '''540(-tone) equal temperament''' ('''540tet''', '''540et'''), divides the [[octave]] in 540 [[equal]] steps of about 2.22 [[cent]]s each.  
'''540 tone equal temperament''', also called '''540-EDO''' divides the octave in 540 equal steps. Since 540 = 2 * 270 and 540 = 45 * 12, it contains [[270edo]] and [[12edo]] as subsets, both belonging to [[The Riemann Zeta Function and Tuning#Zeta EDO lists|the ''zeta peak edos'', ''zeta integral edos'' and ''zeta gap edos'' sequences]]. The [[31-limit]] [[patent val]] for 540-EDO is <540 856 1254 1516 1868 1998 2207 2294 2443 2623 2675|.


= Divisors =
== Theory ==
The prime factorization of 540 is
Since 540 = 2 × 270 and 540 = 45 × 12, it contains [[270edo]] and [[12edo]] as subsets, both belonging to [[The Riemann Zeta Function and Tuning #Zeta EDO lists|the ''zeta peak edos'', ''zeta integral edos'' and ''zeta gap edos'' sequences]].
<math>540 = 2^{2} \cdot 3^{3} \cdot 5</math>


Its divisors are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, 270, 540.
=== Prime harmonics ===
{{Primes in edo|540|columns=11}}


= Intervals =
=== Divisors ===
540 is a very composite number. The prime factorization of 540 is 2<sup>2</sup> × 3<sup>3</sup> × 5. Its divisors are 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, and 270.


== Harmonic primes ==
[[Category:Equal divisions of the octave]]
{| class="wikitable sortable"
|+
!Prime
!Closest step
!Error (steps)
!Error (cents)
|-
|2
|540
|0.000000000
|0.000000000
|-
|3
|856
|0.120249611
|0.267221357
|-
|5
|1254
|0.158828761
|0.352952802
|-
|7
|1516
|0.028342089
|0.062982420
|-
|11
|1868
| -0.093074064
| -0.206831254
|-
|13
|1998
| -0.237447796
| -0.527661769
|-
|17
|2207
| -0.229934275
| -0.510965056
|-
|19
|2294
|0.119142740
|0.264761645
|-
|23
|2443
|0.276543729
|0.614541620
|-
|29
|2623
| -0.309737369
| -0.688305264
|-
|31
|2675
| -0.266007609
| -0.591128020
|}
== Patent val mapping ==
{| class="wikitable"
|+
!Size (steps)
!Size (extended 12-edo notation)
!Size (cents)
!______
!Just (ratio)
!Just (factorization)
!Just ([[Functional Just System|FJS]] notation)
!Just (cents)
!______
!Error (steps)
!Error (cents)
!______
!Comments
|-
|0
|
|  0.000
|
|
|
|
|
|
|
|
|
|
|-
|1
|
|  2.222
|
|
|
|
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|
|
|
|-
|2
|
|  4.444
|
|
|
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|
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|
|
|-
|3
|
|  6.667
|
|
|
|
|
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|
|
|
|
|-
|4
|
|  8.889
|
|
|
|
|
|
|
|
|
|
|-
|5
|
| 11.111
|
|
|
|
|
|
|
|
|
|
|-
|6
|
| 13.333
|
|
|
|
|
|
|
|
|
|
|-
|7
|
| 15.556
|
|
|
|
|
|
|
|
|
|
|-
|8
|
| 17.778
|
|
|
|
|
|
|
|
|
|
|-
|9
|
| 20.000
|
|
|
|
|
|
|
|
|
|
|-
|10
|
| 22.222
|
|
|
|
|
|
|
|
|
|
|-
|11
|
| 24.444
|
|
|
|
|
|
|
|
|
|
|-
|12
|
| 26.667
|
|
|
|
|
|
|
|
|
|
|-
|13
|
| 28.889
|
|
|
|
|
|
|
|
|
|
|-
|14
|
| 31.111
|
|
|
|
|
|
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|
|
|-
|15
|
| 33.333
|
|
|
|
|
|
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|
|
|-
|16
|
| 35.556
|
|
|
|
|
|
|
|
|
|
|-
|17
|
| 37.778
|
|
|
|
|
|
|
|
|
|
|-
|18
|
| 40.000
|
|
|
|
|
|
|
|
|
|
|-
|19
|
| 42.222
|
|
|
|
|
|
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|
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|-
|20
|
| 44.444
|
|
|
|
|
|
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|
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|-
|21
|
| 46.667
|
|
|
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|
|
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|
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|-
|22
|
| 48.889
|
|
|
|
|
|
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|
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|-
|23
|
| 51.111
|
|
|
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|
|
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|-
|24
|
| 53.333
|
|
|
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|
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|-
|25
|
| 55.556
|
|
|
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|
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|-
|26
|
| 57.778
|
|
|
|
|
|
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|
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|-
|27
|
| 60.000
|
|
|
|
|
|
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|
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|-
|28
|
| 62.222
|
|
|
|
|
|
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|
|
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|-
|29
|
| 64.444
|
|
|
|
|
|
|
|
|
|
|-
|30
|
| 66.667
|
|
|
|
|
|
|
|
|
|
|-
|31
|
| 68.889
|
|
|
|
|
|
|
|
|
|
|-
|32
|
| 71.111
|
|
|
|
|
|
|
|
|
|
|-
|33
|
| 73.333
|
|
|
|
|
|
|
|
|
|
|-
|34
|
| 75.556
|
|
|
|
|
|
|
|
|
|
|-
|35
|
| 77.778
|
|
|
|
|
|
|
|
|
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|-
|36
|
| 80.000
|
|
|
|
|
|
|
|
|
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|-
|37
|
| 82.222
|
|
|
|
|
|
|
|
|
|
|-
|38
|
| 84.444
|
|
|
|
|
|
|
|
|
|
|-
|39
|
| 86.667
|
|
|
|
|
|
|
|
|
|
|-
|40
|
| 88.889
|
|
|
|
|
|
|
|
|
|
|-
|41
|
| 91.111
|
|
|
|
|
|
|
|
|
|
|-
|42
|
| 93.333
|
|
|
|
|
|
|
|
|
|
|-
|43
|
| 95.556
|
|
|
|
|
|
|
|
|
|
|-
|44
|
| 97.778
|
|
|
|
|
|
|
|
|
|
|-
|45
|
|100.000
|
|
|
|
|
|
|
|
|
|
|-
|46
|
|102.222
|
|
|
|
|
|
|
|
|
|
|-
|47
|
|104.444
|
|
|
|
|
|
|
|
|
|
|-
|48
|
|106.667
|
|
|
|
|
|
|
|
|
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|-
|49
|
|108.889
|
|
|
|
|
|
|
|
|
|
|-
|50
|
|111.111
|
|
|
|
|
|
|
|
|
|
|-
|51
|
|113.333
|
|
|
|
|
|
|
|
|
|
|-
|52
|
|115.556
|
|
|
|
|
|
|
|
|
|
|-
|53
|
|117.778
|
|
|
|
|
|
|
|
|
|
|-
|54
|
|120.000
|
|
|
|
|
|
|
|
|
|
|-
|55
|
|122.222
|
|
|
|
|
|
|
|
|
|
|-
|56
|
|124.444
|
|
|
|
|
|
|
|
|
|
|-
|57
|
|126.667
|
|
|
|
|
|
|
|
|
|
|-
|58
|
|128.889
|
|
|
|
|
|
|
|
|
|
|-
|59
|
|131.111
|
|
|
|
|
|
|
|
|
|
|-
|60
|
|133.333
|
|
|
|
|
|
|
|
|
|
|-
|61
|
|135.556
|
|
|
|
|
|
|
|
|
|
|-
|62
|
|137.778
|
|
|
|
|
|
|
|
|
|
|-
|63
|
|140.000
|
|
|
|
|
|
|
|
|
|
|-
|64
|
|142.222
|
|
|
|
|
|
|
|
|
|
|-
|65
|
|144.444
|
|
|
|
|
|
|
|
|
|
|-
|66
|
|146.667
|
|
|
|
|
|
|
|
|
|
|-
|67
|
|148.889
|
|
|
|
|
|
|
|
|
|
|-
|68
|
|151.111
|
|
|
|
|
|
|
|
|
|
|-
|69
|
|153.333
|
|
|
|
|
|
|
|
|
|
|-
|70
|
|155.556
|
|
|
|
|
|
|
|
|
|
|-
|71
|
|157.778
|
|
|
|
|
|
|
|
|
|
|-
|72
|
|160.000
|
|
|
|
|
|
|
|
|
|
|-
|73
|
|162.222
|
|
|
|
|
|
|
|
|
|
|-
|74
|
|164.444
|
|
|
|
|
|
|
|
|
|
|-
|75
|
|166.667
|
|
|
|
|
|
|
|
|
|
|-
|76
|
|168.889
|
|
|
|
|
|
|
|
|
|
|-
|77
|
|171.111
|
|
|
|
|
|
|
|
|
|
|-
|78
|
|173.333
|
|
|
|
|
|
|
|
|
|
|-
|79
|
|175.556
|
|
|
|
|
|
|
|
|
|
|-
|80
|
|177.778
|
|
|
|
|
|
|
|
|
|
|-
|81
|
|180.000
|
|
|
|
|
|
|
|
|
|
|-
|82
|
|182.222
|
|
|
|
|
|
|
|
|
|
|-
|83
|
|184.444
|
|
|
|
|
|
|
|
|
|
|-
|84
|
|186.667
|
|
|
|
|
|
|
|
|
|
|-
|85
|
|188.889
|
|
|
|
|
|
|
|
|
|
|-
|86
|
|191.111
|
|
|
|
|
|
|
|
|
|
|-
|87
|
|193.333
|
|
|
|
|
|
|
|
|
|
|-
|88
|
|195.556
|
|
|
|
|
|
|
|
|
|
|-
|89
|
|197.778
|
|
|
|
|
|
|
|
|
|
|-
|90
|
|200.000
|
|
|
|
|
|
|
|
|
|
|-
|91
|
|202.222
|
|
|
|
|
|
|
|
|
|
|-
|92
|
|204.444
|
|
|
|
|
|
|
|
|
|
|-
|93
|
|206.667
|
|
|
|
|
|
|
|
|
|
|-
|94
|
|208.889
|
|
|
|
|
|
|
|
|
|
|-
|95
|
|211.111
|
|
|
|
|
|
|
|
|
|
|-
|96
|
|213.333
|
|
|
|
|
|
|
|
|
|
|-
|97
|
|215.556
|
|
|
|
|
|
|
|
|
|
|-
|98
|
|217.778
|
|
|
|
|
|
|
|
|
|
|-
|99
|
|220.000
|
|
|
|
|
|
|
|
|
|
|-
|100
|
|222.222
|
|
|
|
|
|
|
|
|
|
|-
|101
|
|224.444
|
|
|
|
|
|
|
|
|
|
|-
|102
|
|226.667
|
|
|
|
|
|
|
|
|
|
|-
|103
|
|228.889
|
|
|
|
|
|
|
|
|
|
|-
|104
|
|231.111
|
|
|
|
|
|
|
|
|
|
|-
|105
|
|233.333
|
|
|
|
|
|
|
|
|
|
|-
|106
|
|235.556
|
|
|
|
|
|
|
|
|
|
|-
|107
|
|237.778
|
|
|
|
|
|
|
|
|
|
|-
|108
|
|240.000
|
|
|
|
|
|
|
|
|
|
|-
|109
|
|242.222
|
|
|
|
|
|
|
|
|
|
|-
|110
|
|244.444
|
|
|
|
|
|
|
|
|
|
|-
|111
|
|246.667
|
|
|
|
|
|
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|
|
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|-
|112
|
|248.889
|
|
|
|
|
|
|
|
|
|
|-
|113
|
|251.111
|
|
|
|
|
|
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|
|
|
|-
|114
|
|253.333
|
|
|
|
|
|
|
|
|
|
|-
|115
|
|255.556
|
|
|
|
|
|
|
|
|
|
|-
|116
|
|257.778
|
|
|
|
|
|
|
|
|
|
|-
|117
|
|260.000
|
|
|
|
|
|
|
|
|
|
|-
|118
|
|262.222
|
|
|
|
|
|
|
|
|
|
|-
|119
|
|264.444
|
|
|
|
|
|
|
|
|
|
|-
|120
|
|266.667
|
|
|
|
|
|
|
|
|
|
|-
|121
|
|268.889
|
|
|
|
|
|
|
|
|
|
|-
|122
|
|271.111
|
|
|
|
|
|
|
|
|
|
|-
|123
|
|273.333
|
|
|
|
|
|
|
|
|
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|-
|124
|
|275.556
|
|
|
|
|
|
|
|
|
|
|-
|125
|
|277.778
|
|
|
|
|
|
|
|
|
|
|-
|126
|
|280.000
|
|
|
|
|
|
|
|
|
|
|-
|127
|
|282.222
|
|
|
|
|
|
|
|
|
|
|-
|128
|
|284.444
|
|
|
|
|
|
|
|
|
|
|-
|129
|
|286.667
|
|
|
|
|
|
|
|
|
|
|-
|130
|
|288.889
|
|
|
|
|
|
|
|
|
|
|-
|131
|
|291.111
|
|
|
|
|
|
|
|
|
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|-
|132
|
|293.333
|
|
|
|
|
|
|
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|-
|133
|
|295.556
|
|
|
|
|
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|
|
|
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|-
|134
|
|297.778
|
|
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|
|
|
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|-
|135
|
|300.000
|
|
|
|
|
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|-
|136
|
|302.222
|
|
|
|
|
|
|
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|-
|137
|
|304.444
|
|
|
|
|
|
|
|
|
|
|-
|138
|
|306.667
|
|
|
|
|
|
|
|
|
|
|-
|139
|
|308.889
|
|
|
|
|
|
|
|
|
|
|-
|140
|
|311.111
|
|
|
|
|
|
|
|
|
|
|-
|141
|
|313.333
|
|
|
|
|
|
|
|
|
|
|-
|142
|
|315.556
|
|
|
|
|
|
|
|
|
|
|-
|143
|
|317.778
|
|
|
|
|
|
|
|
|
|
|-
|144
|
|320.000
|
|
|
|
|
|
|
|
|
|
|-
|145
|
|322.222
|
|
|
|
|
|
|
|
|
|
|-
|146
|
|324.444
|
|
|
|
|
|
|
|
|
|
|-
|147
|
|326.667
|
|
|
|
|
|
|
|
|
|
|-
|148
|
|328.889
|
|
|
|
|
|
|
|
|
|
|-
|149
|
|331.111
|
|
|
|
|
|
|
|
|
|
|-
|150
|
|333.333
|
|
|
|
|
|
|
|
|
|
|-
|151
|
|335.556
|
|
|
|
|
|
|
|
|
|
|-
|152
|
|337.778
|
|
|
|
|
|
|
|
|
|
|-
|153
|
|340.000
|
|
|
|
|
|
|
|
|
|
|-
|154
|
|342.222
|
|
|
|
|
|
|
|
|
|
|-
|155
|
|344.444
|
|
|
|
|
|
|
|
|
|
|-
|156
|
|346.667
|
|
|
|
|
|
|
|
|
|
|-
|157
|
|348.889
|
|
|
|
|
|
|
|
|
|
|-
|158
|
|351.111
|
|
|
|
|
|
|
|
|
|
|-
|159
|
|353.333
|
|
|
|
|
|
|
|
|
|
|-
|160
|
|355.556
|
|
|
|
|
|
|
|
|
|
|-
|161
|
|357.778
|
|
|
|
|
|
|
|
|
|
|-
|162
|
|360.000
|
|
|
|
|
|
|
|
|
|
|-
|163
|
|362.222
|
|
|
|
|
|
|
|
|
|
|-
|164
|
|364.444
|
|
|
|
|
|
|
|
|
|
|-
|165
|
|366.667
|
|
|
|
|
|
|
|
|
|
|-
|166
|
|368.889
|
|
|
|
|
|
|
|
|
|
|-
|167
|
|371.111
|
|
|
|
|
|
|
|
|
|
|-
|168
|
|373.333
|
|
|
|
|
|
|
|
|
|
|-
|169
|
|375.556
|
|
|
|
|
|
|
|
|
|
|-
|170
|
|377.778
|
|
|
|
|
|
|
|
|
|
|-
|171
|
|380.000
|
|
|
|
|
|
|
|
|
|
|-
|172
|
|382.222
|
|
|
|
|
|
|
|
|
|
|-
|173
|
|384.444
|
|
|
|
|
|
|
|
|
|
|-
|174
|
|386.667
|
|
|
|
|
|
|
|
|
|
|-
|175
|
|388.889
|
|
|
|
|
|
|
|
|
|
|-
|176
|
|391.111
|
|
|
|
|
|
|
|
|
|
|-
|177
|
|393.333
|
|
|
|
|
|
|
|
|
|
|-
|178
|
|395.556
|
|
|
|
|
|
|
|
|
|
|-
|179
|
|397.778
|
|
|
|
|
|
|
|
|
|
|-
|180
|
|400.000
|
|
|
|
|
|
|
|
|
|
|-
|181
|
|402.222
|
|
|
|
|
|
|
|
|
|
|-
|182
|
|404.444
|
|
|
|
|
|
|
|
|
|
|-
|183
|
|406.667
|
|
|
|
|
|
|
|
|
|
|-
|184
|
|408.889
|
|
|
|
|
|
|
|
|
|
|-
|185
|
|411.111
|
|
|
|
|
|
|
|
|
|
|-
|186
|
|413.333
|
|
|
|
|
|
|
|
|
|
|-
|187
|
|415.556
|
|
|
|
|
|
|
|
|
|
|-
|188
|
|417.778
|
|
|
|
|
|
|
|
|
|
|-
|189
|
|420.000
|
|
|
|
|
|
|
|
|
|
|-
|190
|
|422.222
|
|
|
|
|
|
|
|
|
|
|-
|191
|
|424.444
|
|
|
|
|
|
|
|
|
|
|-
|192
|
|426.667
|
|
|
|
|
|
|
|
|
|
|-
|193
|
|428.889
|
|
|
|
|
|
|
|
|
|
|-
|194
|
|431.111
|
|
|
|
|
|
|
|
|
|
|-
|195
|
|433.333
|
|
|
|
|
|
|
|
|
|
|-
|196
|
|435.556
|
|
|
|
|
|
|
|
|
|
|-
|197
|
|437.778
|
|
|
|
|
|
|
|
|
|
|-
|198
|
|440.000
|
|
|
|
|
|
|
|
|
|
|-
|199
|
|442.222
|
|
|
|
|
|
|
|
|
|
|-
|200
|
|444.444
|
|
|
|
|
|
|
|
|
|
|-
|201
|
|446.667
|
|
|
|
|
|
|
|
|
|
|-
|202
|
|448.889
|
|
|
|
|
|
|
|
|
|
|-
|203
|
|451.111
|
|
|
|
|
|
|
|
|
|
|-
|204
|
|453.333
|
|
|
|
|
|
|
|
|
|
|-
|205
|
|455.556
|
|
|
|
|
|
|
|
|
|
|-
|206
|
|457.778
|
|
|
|
|
|
|
|
|
|
|-
|207
|
|460.000
|
|
|
|
|
|
|
|
|
|
|-
|208
|
|462.222
|
|
|
|
|
|
|
|
|
|
|-
|209
|
|464.444
|
|
|
|
|
|
|
|
|
|
|-
|210
|
|466.667
|
|
|
|
|
|
|
|
|
|
|-
|211
|
|468.889
|
|
|
|
|
|
|
|
|
|
|-
|212
|
|471.111
|
|
|
|
|
|
|
|
|
|
|-
|213
|
|473.333
|
|
|
|
|
|
|
|
|
|
|-
|214
|
|475.556
|
|
|
|
|
|
|
|
|
|
|-
|215
|
|477.778
|
|
|
|
|
|
|
|
|
|
|-
|216
|
|480.000
|
|
|
|
|
|
|
|
|
|
|-
|217
|
|482.222
|
|
|
|
|
|
|
|
|
|
|-
|218
|
|484.444
|
|
|
|
|
|
|
|
|
|
|-
|219
|
|486.667
|
|
|
|
|
|
|
|
|
|
|-
|220
|
|488.889
|
|
|
|
|
|
|
|
|
|
|-
|221
|
|491.111
|
|
|
|
|
|
|
|
|
|
|-
|222
|
|493.333
|
|
|
|
|
|
|
|
|
|
|-
|223
|
|495.556
|
|
|
|
|
|
|
|
|
|
|-
|224
|
|497.778
|
|
|
|
|
|
|
|
|
|
|-
|225
|
|500.000
|
|
|
|
|
|
|
|
|
|
|-
|226
|
|502.222
|
|
|
|
|
|
|
|
|
|
|-
|227
|
|504.444
|
|
|
|
|
|
|
|
|
|
|-
|228
|
|506.667
|
|
|
|
|
|
|
|
|
|
|-
|229
|
|508.889
|
|
|
|
|
|
|
|
|
|
|-
|230
|
|511.111
|
|
|
|
|
|
|
|
|
|
|-
|231
|
|513.333
|
|
|
|
|
|
|
|
|
|
|-
|232
|
|515.556
|
|
|
|
|
|
|
|
|
|
|-
|233
|
|517.778
|
|
|
|
|
|
|
|
|
|
|-
|234
|
|520.000
|
|
|
|
|
|
|
|
|
|
|-
|235
|
|522.222
|
|
|
|
|
|
|
|
|
|
|-
|236
|
|524.444
|
|
|
|
|
|
|
|
|
|
|-
|237
|
|526.667
|
|
|
|
|
|
|
|
|
|
|-
|238
|
|528.889
|
|
|
|
|
|
|
|
|
|
|-
|239
|
|531.111
|
|
|
|
|
|
|
|
|
|
|-
|240
|
|533.333
|
|
|
|
|
|
|
|
|
|
|-
|241
|
|535.556
|
|
|
|
|
|
|
|
|
|
|-
|242
|
|537.778
|
|
|
|
|
|
|
|
|
|
|-
|243
|
|540.000
|
|
|
|
|
|
|
|
|
|
|-
|244
|
|542.222
|
|
|
|
|
|
|
|
|
|
|-
|245
|
|544.444
|
|
|
|
|
|
|
|
|
|
|-
|246
|
|546.667
|
|
|
|
|
|
|
|
|
|
|-
|247
|
|548.889
|
|
|
|
|
|
|
|
|
|
|-
|248
|
|551.111
|
|
|
|
|
|
|
|
|
|
|-
|249
|
|553.333
|
|
|
|
|
|
|
|
|
|
|-
|250
|
|555.556
|
|
|
|
|
|
|
|
|
|
|-
|251
|
|557.778
|
|
|
|
|
|
|
|
|
|
|-
|252
|
|560.000
|
|
|
|
|
|
|
|
|
|
|-
|253
|
|562.222
|
|
|
|
|
|
|
|
|
|
|-
|254
|
|564.444
|
|
|
|
|
|
|
|
|
|
|-
|255
|
|566.667
|
|
|
|
|
|
|
|
|
|
|-
|256
|
|568.889
|
|
|
|
|
|
|
|
|
|
|-
|257
|
|571.111
|
|
|
|
|
|
|
|
|
|
|-
|258
|
|573.333
|
|
|
|
|
|
|
|
|
|
|-
|259
|
|575.556
|
|
|
|
|
|
|
|
|
|
|-
|260
|
|577.778
|
|
|
|
|
|
|
|
|
|
|-
|261
|
|580.000
|
|
|
|
|
|
|
|
|
|
|-
|262
|
|582.222
|
|
|
|
|
|
|
|
|
|
|-
|263
|
|584.444
|
|
|
|
|
|
|
|
|
|
|-
|264
|
|586.667
|
|
|
|
|
|
|
|
|
|
|-
|265
|
|588.889
|
|
|
|
|
|
|
|
|
|
|-
|266
|
|591.111
|
|
|
|
|
|
|
|
|
|
|-
|267
|
|593.333
|
|
|
|
|
|
|
|
|
|
|-
|268
|
|595.556
|
|
|
|
|
|
|
|
|
|
|-
|269
|
|597.778
|
|
|
|
|
|
|
|
|
|
|-
|270
|
|600.000
|
|
|
|
|
|
|
|
|
|
|-
|271
|
|602.222
|
|
|
|
|
|
|
|
|
|
|-
|272
|
|604.444
|
|
|
|
|
|
|
|
|
|
|-
|273
|
|606.667
|
|
|
|
|
|
|
|
|
|
|-
|274
|
|608.889
|
|
|
|
|
|
|
|
|
|
|-
|275
|
|611.111
|
|
|
|
|
|
|
|
|
|
|-
|276
|
|613.333
|
|
|
|
|
|
|
|
|
|
|-
|277
|
|615.556
|
|
|
|
|
|
|
|
|
|
|-
|278
|
|617.778
|
|
|
|
|
|
|
|
|
|
|-
|279
|
|620.000
|
|
|
|
|
|
|
|
|
|
|-
|280
|
|622.222
|
|
|
|
|
|
|
|
|
|
|-
|281
|
|624.444
|
|
|
|
|
|
|
|
|
|
|-
|282
|
|626.667
|
|
|
|
|
|
|
|
|
|
|-
|283
|
|628.889
|
|
|
|
|
|
|
|
|
|
|-
|284
|
|631.111
|
|
|
|
|
|
|
|
|
|
|-
|285
|
|633.333
|
|
|
|
|
|
|
|
|
|
|-
|286
|
|635.556
|
|
|
|
|
|
|
|
|
|
|-
|287
|
|637.778
|
|
|
|
|
|
|
|
|
|
|-
|288
|
|640.000
|
|
|
|
|
|
|
|
|
|
|-
|289
|
|642.222
|
|
|
|
|
|
|
|
|
|
|-
|290
|
|644.444
|
|
|
|
|
|
|
|
|
|
|-
|291
|
|646.667
|
|
|
|
|
|
|
|
|
|
|-
|292
|
|648.889
|
|
|
|
|
|
|
|
|
|
|-
|293
|
|651.111
|
|
|
|
|
|
|
|
|
|
|-
|294
|
|653.333
|
|
|
|
|
|
|
|
|
|
|-
|295
|
|655.556
|
|
|
|
|
|
|
|
|
|
|-
|296
|
|657.778
|
|
|
|
|
|
|
|
|
|
|-
|297
|
|660.000
|
|
|
|
|
|
|
|
|
|
|-
|298
|
|662.222
|
|
|
|
|
|
|
|
|
|
|-
|299
|
|664.444
|
|
|
|
|
|
|
|
|
|
|-
|300
|
|666.667
|
|
|
|
|
|
|
|
|
|
|-
|301
|
|668.889
|
|
|
|
|
|
|
|
|
|
|-
|302
|
|671.111
|
|
|
|
|
|
|
|
|
|
|-
|303
|
|673.333
|
|
|
|
|
|
|
|
|
|
|-
|304
|
|675.556
|
|
|
|
|
|
|
|
|
|
|-
|305
|
|677.778
|
|
|
|
|
|
|
|
|
|
|-
|306
|
|680.000
|
|
|
|
|
|
|
|
|
|
|-
|307
|
|682.222
|
|
|
|
|
|
|
|
|
|
|-
|308
|
|684.444
|
|
|
|
|
|
|
|
|
|
|-
|309
|
|686.667
|
|
|
|
|
|
|
|
|
|
|-
|310
|
|688.889
|
|
|
|
|
|
|
|
|
|
|-
|311
|
|691.111
|
|
|
|
|
|
|
|
|
|
|-
|312
|
|693.333
|
|
|
|
|
|
|
|
|
|
|-
|313
|
|695.556
|
|
|
|
|
|
|
|
|
|
|-
|314
|
|697.778
|
|
|
|
|
|
|
|
|
|
|-
|315
|
|700.000
|
|
|
|
|
|
|
|
|
|
|-
|316
|
|702.222
|
|
|
|
|
|
|
|
|
|
|-
|317
|
|704.444
|
|
|
|
|
|
|
|
|
|
|-
|318
|
|706.667
|
|
|
|
|
|
|
|
|
|
|-
|319
|
|708.889
|
|
|
|
|
|
|
|
|
|
|-
|320
|
|711.111
|
|
|
|
|
|
|
|
|
|
|-
|321
|
|713.333
|
|
|
|
|
|
|
|
|
|
|-
|322
|
|715.556
|
|
|
|
|
|
|
|
|
|
|-
|323
|
|717.778
|
|
|
|
|
|
|
|
|
|
|-
|324
|
|720.000
|
|
|
|
|
|
|
|
|
|
|-
|325
|
|722.222
|
|
|
|
|
|
|
|
|
|
|-
|326
|
|724.444
|
|
|
|
|
|
|
|
|
|
|-
|327
|
|726.667
|
|
|
|
|
|
|
|
|
|
|-
|328
|
|728.889
|
|
|
|
|
|
|
|
|
|
|-
|329
|
|731.111
|
|
|
|
|
|
|
|
|
|
|-
|330
|
|733.333
|
|
|
|
|
|
|
|
|
|
|-
|331
|
|735.556
|
|
|
|
|
|
|
|
|
|
|-
|332
|
|737.778
|
|
|
|
|
|
|
|
|
|
|-
|333
|
|740.000
|
|
|
|
|
|
|
|
|
|
|-
|334
|
|742.222
|
|
|
|
|
|
|
|
|
|
|-
|335
|
|744.444
|
|
|
|
|
|
|
|
|
|
|-
|336
|
|746.667
|
|
|
|
|
|
|
|
|
|
|-
|337
|
|748.889
|
|
|
|
|
|
|
|
|
|
|-
|338
|
|751.111
|
|
|
|
|
|
|
|
|
|
|-
|339
|
|753.333
|
|
|
|
|
|
|
|
|
|
|-
|340
|
|755.556
|
|
|
|
|
|
|
|
|
|
|-
|341
|
|757.778
|
|
|
|
|
|
|
|
|
|
|-
|342
|
|760.000
|
|
|
|
|
|
|
|
|
|
|-
|343
|
|762.222
|
|
|
|
|
|
|
|
|
|
|-
|344
|
|764.444
|
|
|
|
|
|
|
|
|
|
|-
|345
|
|766.667
|
|
|
|
|
|
|
|
|
|
|-
|346
|
|768.889
|
|
|
|
|
|
|
|
|
|
|-
|347
|
|771.111
|
|
|
|
|
|
|
|
|
|
|-
|348
|
|773.333
|
|
|
|
|
|
|
|
|
|
|-
|349
|
|775.556
|
|
|
|
|
|
|
|
|
|
|-
|350
|
|777.778
|
|
|
|
|
|
|
|
|
|
|-
|351
|
|780.000
|
|
|
|
|
|
|
|
|
|
|-
|352
|
|782.222
|
|
|
|
|
|
|
|
|
|
|-
|353
|
|784.444
|
|
|
|
|
|
|
|
|
|
|-
|354
|
|786.667
|
|
|
|
|
|
|
|
|
|
|-
|355
|
|788.889
|
|
|
|
|
|
|
|
|
|
|-
|356
|
|791.111
|
|
|
|
|
|
|
|
|
|
|-
|357
|
|793.333
|
|
|
|
|
|
|
|
|
|
|-
|358
|
|795.556
|
|
|
|
|
|
|
|
|
|
|-
|359
|
|797.778
|
|
|
|
|
|
|
|
|
|
|-
|360
|
|800.000
|
|
|
|
|
|
|
|
|
|
|-
|361
|
|802.222
|
|
|
|
|
|
|
|
|
|
|-
|362
|
|804.444
|
|
|
|
|
|
|
|
|
|
|-
|363
|
|806.667
|
|
|
|
|
|
|
|
|
|
|-
|364
|
|808.889
|
|
|
|
|
|
|
|
|
|
|-
|365
|
|811.111
|
|
|
|
|
|
|
|
|
|
|-
|366
|
|813.333
|
|
|
|
|
|
|
|
|
|
|-
|367
|
|815.556
|
|
|
|
|
|
|
|
|
|
|-
|368
|
|817.778
|
|
|
|
|
|
|
|
|
|
|-
|369
|
|820.000
|
|
|
|
|
|
|
|
|
|
|-
|370
|
|822.222
|
|
|
|
|
|
|
|
|
|
|-
|371
|
|824.444
|
|
|
|
|
|
|
|
|
|
|-
|372
|
|826.667
|
|
|
|
|
|
|
|
|
|
|-
|373
|
|828.889
|
|
|
|
|
|
|
|
|
|
|-
|374
|
|831.111
|
|
|
|
|
|
|
|
|
|
|-
|375
|
|833.333
|
|
|
|
|
|
|
|
|
|
|-
|376
|
|835.556
|
|
|
|
|
|
|
|
|
|
|-
|377
|
|837.778
|
|
|
|
|
|
|
|
|
|
|-
|378
|
|840.000
|
|
|
|
|
|
|
|
|
|
|-
|379
|
|842.222
|
|
|
|
|
|
|
|
|
|
|-
|380
|
|844.444
|
|
|
|
|
|
|
|
|
|
|-
|381
|
|846.667
|
|
|
|
|
|
|
|
|
|
|-
|382
|
|848.889
|
|
|
|
|
|
|
|
|
|
|-
|383
|
|851.111
|
|
|
|
|
|
|
|
|
|
|-
|384
|
|853.333
|
|
|
|
|
|
|
|
|
|
|-
|385
|
|855.556
|
|
|
|
|
|
|
|
|
|
|-
|386
|
|857.778
|
|
|
|
|
|
|
|
|
|
|-
|387
|
|860.000
|
|
|
|
|
|
|
|
|
|
|-
|388
|
|862.222
|
|
|
|
|
|
|
|
|
|
|-
|389
|
|864.444
|
|
|
|
|
|
|
|
|
|
|-
|390
|
|866.667
|
|
|
|
|
|
|
|
|
|
|-
|391
|
|868.889
|
|
|
|
|
|
|
|
|
|
|-
|392
|
|871.111
|
|
|
|
|
|
|
|
|
|
|-
|393
|
|873.333
|
|
|
|
|
|
|
|
|
|
|-
|394
|
|875.556
|
|
|
|
|
|
|
|
|
|
|-
|395
|
|877.778
|
|
|
|
|
|
|
|
|
|
|-
|396
|
|880.000
|
|
|
|
|
|
|
|
|
|
|-
|397
|
|882.222
|
|
|
|
|
|
|
|
|
|
|-
|398
|
|884.444
|
|
|
|
|
|
|
|
|
|
|-
|399
|
|886.667
|
|
|
|
|
|
|
|
|
|
|-
|400
|
|888.889
|
|
|
|
|
|
|
|
|
|
|-
|401
|
|891.111
|
|
|
|
|
|
|
|
|
|
|-
|402
|
|893.333
|
|
|
|
|
|
|
|
|
|
|-
|403
|
|895.556
|
|
|
|
|
|
|
|
|
|
|-
|404
|
|897.778
|
|
|
|
|
|
|
|
|
|
|-
|405
|
|900.000
|
|
|
|
|
|
|
|
|
|
|-
|406
|
|902.222
|
|
|
|
|
|
|
|
|
|
|-
|407
|
|904.444
|
|
|
|
|
|
|
|
|
|
|-
|408
|
|906.667
|
|
|
|
|
|
|
|
|
|
|-
|409
|
|908.889
|
|
|
|
|
|
|
|
|
|
|-
|410
|
|911.111
|
|
|
|
|
|
|
|
|
|
|-
|411
|
|913.333
|
|
|
|
|
|
|
|
|
|
|-
|412
|
|915.556
|
|
|
|
|
|
|
|
|
|
|-
|413
|
|917.778
|
|
|
|
|
|
|
|
|
|
|-
|414
|
|920.000
|
|
|
|
|
|
|
|
|
|
|-
|415
|
|922.222
|
|
|
|
|
|
|
|
|
|
|-
|416
|
|924.444
|
|
|
|
|
|
|
|
|
|
|-
|417
|
|926.667
|
|
|
|
|
|
|
|
|
|
|-
|418
|
|928.889
|
|
|
|
|
|
|
|
|
|
|-
|419
|
|931.111
|
|
|
|
|
|
|
|
|
|
|-
|420
|
|933.333
|
|
|
|
|
|
|
|
|
|
|-
|421
|
|935.556
|
|
|
|
|
|
|
|
|
|
|-
|422
|
|937.778
|
|
|
|
|
|
|
|
|
|
|-
|423
|
|940.000
|
|
|
|
|
|
|
|
|
|
|-
|424
|
|942.222
|
|
|
|
|
|
|
|
|
|
|-
|425
|
|944.444
|
|
|
|
|
|
|
|
|
|
|-
|426
|
|946.667
|
|
|
|
|
|
|
|
|
|
|-
|427
|
|948.889
|
|
|
|
|
|
|
|
|
|
|-
|428
|
|951.111
|
|
|
|
|
|
|
|
|
|
|-
|429
|
|953.333
|
|
|
|
|
|
|
|
|
|
|-
|430
|
|955.556
|
|
|
|
|
|
|
|
|
|
|-
|431
|
|957.778
|
|
|
|
|
|
|
|
|
|
|-
|432
|
|960.000
|
|
|
|
|
|
|
|
|
|
|-
|433
|
|962.222
|
|
|
|
|
|
|
|
|
|
|-
|434
|
|964.444
|
|
|
|
|
|
|
|
|
|
|-
|435
|
|966.667
|
|
|
|
|
|
|
|
|
|
|-
|436
|
|968.889
|
|
|
|
|
|
|
|
|
|
|-
|437
|
|971.111
|
|
|
|
|
|
|
|
|
|
|-
|438
|
|973.333
|
|
|
|
|
|
|
|
|
|
|-
|439
|
|975.556
|
|
|
|
|
|
|
|
|
|
|-
|440
|
|977.778
|
|
|
|
|
|
|
|
|
|
|-
|441
|
|980.000
|
|
|
|
|
|
|
|
|
|
|-
|442
|
|982.222
|
|
|
|
|
|
|
|
|
|
|-
|443
|
|984.444
|
|
|
|
|
|
|
|
|
|
|-
|444
|
|986.667
|
|
|
|
|
|
|
|
|
|
|-
|445
|
|988.889
|
|
|
|
|
|
|
|
|
|
|-
|446
|
|991.111
|
|
|
|
|
|
|
|
|
|
|-
|447
|
|993.333
|
|
|
|
|
|
|
|
|
|
|-
|448
|
|995.556
|
|
|
|
|
|
|
|
|
|
|-
|449
|
|997.778
|
|
|
|
|
|
|
|
|
|
|-
|450
|
|1000.000
|
|
|
|
|
|
|
|
|
|
|-
|451
|
|1002.222
|
|
|
|
|
|
|
|
|
|
|-
|452
|
|1004.444
|
|
|
|
|
|
|
|
|
|
|-
|453
|
|1006.667
|
|
|
|
|
|
|
|
|
|
|-
|454
|
|1008.889
|
|
|
|
|
|
|
|
|
|
|-
|455
|
|1011.111
|
|
|
|
|
|
|
|
|
|
|-
|456
|
|1013.333
|
|
|
|
|
|
|
|
|
|
|-
|457
|
|1015.556
|
|
|
|
|
|
|
|
|
|
|-
|458
|
|1017.778
|
|
|
|
|
|
|
|
|
|
|-
|459
|
|1020.000
|
|
|
|
|
|
|
|
|
|
|-
|460
|
|1022.222
|
|
|
|
|
|
|
|
|
|
|-
|461
|
|1024.444
|
|
|
|
|
|
|
|
|
|
|-
|462
|
|1026.667
|
|
|
|
|
|
|
|
|
|
|-
|463
|
|1028.889
|
|
|
|
|
|
|
|
|
|
|-
|464
|
|1031.111
|
|
|
|
|
|
|
|
|
|
|-
|465
|
|1033.333
|
|
|
|
|
|
|
|
|
|
|-
|466
|
|1035.556
|
|
|
|
|
|
|
|
|
|
|-
|467
|
|1037.778
|
|
|
|
|
|
|
|
|
|
|-
|468
|
|1040.000
|
|
|
|
|
|
|
|
|
|
|-
|469
|
|1042.222
|
|
|
|
|
|
|
|
|
|
|-
|470
|
|1044.444
|
|
|
|
|
|
|
|
|
|
|-
|471
|
|1046.667
|
|
|
|
|
|
|
|
|
|
|-
|472
|
|1048.889
|
|
|
|
|
|
|
|
|
|
|-
|473
|
|1051.111
|
|
|
|
|
|
|
|
|
|
|-
|474
|
|1053.333
|
|
|
|
|
|
|
|
|
|
|-
|475
|
|1055.556
|
|
|
|
|
|
|
|
|
|
|-
|476
|
|1057.778
|
|
|
|
|
|
|
|
|
|
|-
|477
|
|1060.000
|
|
|
|
|
|
|
|
|
|
|-
|478
|
|1062.222
|
|
|
|
|
|
|
|
|
|
|-
|479
|
|1064.444
|
|
|
|
|
|
|
|
|
|
|-
|480
|
|1066.667
|
|
|
|
|
|
|
|
|
|
|-
|481
|
|1068.889
|
|
|
|
|
|
|
|
|
|
|-
|482
|
|1071.111
|
|
|
|
|
|
|
|
|
|
|-
|483
|
|1073.333
|
|
|
|
|
|
|
|
|
|
|-
|484
|
|1075.556
|
|
|
|
|
|
|
|
|
|
|-
|485
|
|1077.778
|
|
|
|
|
|
|
|
|
|
|-
|486
|
|1080.000
|
|
|
|
|
|
|
|
|
|
|-
|487
|
|1082.222
|
|
|
|
|
|
|
|
|
|
|-
|488
|
|1084.444
|
|
|
|
|
|
|
|
|
|
|-
|489
|
|1086.667
|
|
|
|
|
|
|
|
|
|
|-
|490
|
|1088.889
|
|
|
|
|
|
|
|
|
|
|-
|491
|
|1091.111
|
|
|
|
|
|
|
|
|
|
|-
|492
|
|1093.333
|
|
|
|
|
|
|
|
|
|
|-
|493
|
|1095.556
|
|
|
|
|
|
|
|
|
|
|-
|494
|
|1097.778
|
|
|
|
|
|
|
|
|
|
|-
|495
|
|1100.000
|
|
|
|
|
|
|
|
|
|
|-
|496
|
|1102.222
|
|
|
|
|
|
|
|
|
|
|-
|497
|
|1104.444
|
|
|
|
|
|
|
|
|
|
|-
|498
|
|1106.667
|
|
|
|
|
|
|
|
|
|
|-
|499
|
|1108.889
|
|
|
|
|
|
|
|
|
|
|-
|500
|
|1111.111
|
|
|
|
|
|
|
|
|
|
|-
|501
|
|1113.333
|
|
|
|
|
|
|
|
|
|
|-
|502
|
|1115.556
|
|
|
|
|
|
|
|
|
|
|-
|503
|
|1117.778
|
|
|
|
|
|
|
|
|
|
|-
|504
|
|1120.000
|
|
|
|
|
|
|
|
|
|
|-
|505
|
|1122.222
|
|
|
|
|
|
|
|
|
|
|-
|506
|
|1124.444
|
|
|
|
|
|
|
|
|
|
|-
|507
|
|1126.667
|
|
|
|
|
|
|
|
|
|
|-
|508
|
|1128.889
|
|
|
|
|
|
|
|
|
|
|-
|509
|
|1131.111
|
|
|
|
|
|
|
|
|
|
|-
|510
|
|1133.333
|
|
|
|
|
|
|
|
|
|
|-
|511
|
|1135.556
|
|
|
|
|
|
|
|
|
|
|-
|512
|
|1137.778
|
|
|
|
|
|
|
|
|
|
|-
|513
|
|1140.000
|
|
|
|
|
|
|
|
|
|
|-
|514
|
|1142.222
|
|
|
|
|
|
|
|
|
|
|-
|515
|
|1144.444
|
|
|
|
|
|
|
|
|
|
|-
|516
|
|1146.667
|
|
|
|
|
|
|
|
|
|
|-
|517
|
|1148.889
|
|
|
|
|
|
|
|
|
|
|-
|518
|
|1151.111
|
|
|
|
|
|
|
|
|
|
|-
|519
|
|1153.333
|
|
|
|
|
|
|
|
|
|
|-
|520
|
|1155.556
|
|
|
|
|
|
|
|
|
|
|-
|521
|
|1157.778
|
|
|
|
|
|
|
|
|
|
|-
|522
|
|1160.000
|
|
|
|
|
|
|
|
|
|
|-
|523
|
|1162.222
|
|
|
|
|
|
|
|
|
|
|-
|524
|
|1164.444
|
|
|
|
|
|
|
|
|
|
|-
|525
|
|1166.667
|
|
|
|
|
|
|
|
|
|
|-
|526
|
|1168.889
|
|
|
|
|
|
|
|
|
|
|-
|527
|
|1171.111
|
|
|
|
|
|
|
|
|
|
|-
|528
|
|1173.333
|
|
|
|
|
|
|
|
|
|
|-
|529
|
|1175.556
|
|
|
|
|
|
|
|
|
|
|-
|530
|
|1177.778
|
|
|
|
|
|
|
|
|
|
|-
|531
|
|1180.000
|
|
|
|
|
|
|
|
|
|
|-
|532
|
|1182.222
|
|
|
|
|
|
|
|
|
|
|-
|533
|
|1184.444
|
|
|
|
|
|
|
|
|
|
|-
|534
|
|1186.667
|
|
|
|
|
|
|
|
|
|
|-
|535
|
|1188.889
|
|
|
|
|
|
|
|
|
|
|-
|536
|
|1191.111
|
|
|
|
|
|
|
|
|
|
|-
|537
|
|1193.333
|
|
|
|
|
|
|
|
|
|
|-
|538
|
|1195.556
|
|
|
|
|
|
|
|
|
|
|-
|539
|
|1197.778
|
|
|
|
|
|
|
|
|
|
|-
|540
|
|1200.000
|
|
|
|
|
|
|
|
|
|
|}

Revision as of 17:50, 21 October 2021

The 540 equal divisions of the octave (540edo), or the 540(-tone) equal temperament (540tet, 540et), divides the octave in 540 equal steps of about 2.22 cents each.

Theory

Since 540 = 2 × 270 and 540 = 45 × 12, it contains 270edo and 12edo as subsets, both belonging to the zeta peak edos, zeta integral edos and zeta gap edos sequences.

Prime harmonics

Script error: No such module "primes_in_edo".

Divisors

540 is a very composite number. The prime factorization of 540 is 22 × 33 × 5. Its divisors are 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 27, 30, 36, 45, 54, 60, 90, 108, 135, 180, and 270.

Retrieved from "https://en.xen.wiki/index.php?title=540edo&oldid=79759"