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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|574}}
{{ED intro}}


== Theory ==
== Theory ==
574 = 14 × 41, and 574edo shares the [[harmonic]] [[3/1|3]] with [[41edo]]. Unfortunately, it is only [[consistent]] to the [[5-odd-limit]], and the [[patent val]] and the 574d [[val]] are about equally viable.  
574edo shares the [[harmonic]] [[3/1|3]] with [[41edo]]. Unfortunately, it is only [[consistent]] to the [[5-odd-limit]], and the [[patent val]] and the 574d [[val]] are about equally viable.  


The 574d val [[tempering out|tempers out]] 4375/4374 ([[ragisma]]), 29360128/29296875 (quasiorwellisma), and 40500000/40353607 in the 7-limit; [[3025/3024]], [[5632/5625]], [[9801/9800]], and [[19712/19683]] in the 11-limit; [[676/675]], [[4225/4224]], and [[10648/10647]] in the 13-limit.  
The 574d val [[tempering out|tempers out]] 4375/4374 ([[ragisma]]), 29360128/29296875 (quasiorwellisma), and 40500000/40353607 in the 7-limit; [[3025/3024]], [[5632/5625]], [[9801/9800]], and [[19712/19683]] in the 11-limit; [[676/675]], [[4225/4224]], and [[10648/10647]] in the 13-limit.  


The patent val tempers out 2100875/2097152 ([[rainy comma]]), 67108864/66976875 ([[vishnuzma]]), 49009212/48828125, and 78125000/78121827 ([[euzenius comma]]) in the 7-limit; 5632/5625, 42875/42768, 117649/117128, [[131072/130977]], 160083/160000, 161280/161051, 166698/166375, 391314/390625, and [[532400/531441]] in the 11-limit; 676/675, [[1001/1000]], [[2080/2079]], [[4096/4095]], and 4225/4224 in the 13-limit.  
The patent val tempers out 2100875/2097152 ([[rainy comma]]), 6115295232/6103515625 ([[vishnuzma]]), 49009212/48828125, and 78125000/78121827 ([[euzenius comma]]) in the 7-limit; 5632/5625, 42875/42768, 117649/117128, [[131072/130977]], 160083/160000, 161280/161051, 166698/166375, 391314/390625, and [[532400/531441]] in the 11-limit; 676/675, [[1001/1000]], [[2080/2079]], [[4096/4095]], and 4225/4224 in the 13-limit.  


=== Prime harmonics ===
=== Prime harmonics ===
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=== Subsets and supersets ===
=== Subsets and supersets ===
Since 574 factors into 2 × 7 × 41, 574edo has subset edos {{EDOs| 2, 7, 14, 41, 82, and 287 }}.  
Since 574 factors into 2 × 7 × 41, 574edo has subset edos {{EDOs| 2, 7, 14, 41, 82, and 287 }}.


== Regular temperament properties ==
== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
{| class="wikitable center-4 center-5 center-6"
|-
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve Stretch (¢)
! rowspan="2" | Optimal<br />8ve stretch (¢)
! colspan="2" | Tuning Error
! colspan="2" | Tuning error
|-
|-
! [[TE error|Absolute]] (¢)
! [[TE error|Absolute]] (¢)
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| {{monzo| 23 6 -14 }}, {{monzo| 42 -47 14 }}
| {{monzo| 23 6 -14 }}, {{monzo| 42 -47 14 }}
| {{mapping| 574 910 1333 }}
| {{mapping| 574 910 1333 }}
| -0.1658
| −0.1658
| 0.1260
| 0.1260
| 6.03
| 6.03
|-
|- style="border-top: double;"
| style="border-top: double;" | 2.3.5.7
| 2.3.5.7
| style="border-top: double;" | 4375/4374, 29360128/29296875, 40500000/40353607
| 4375/4374, 29360128/29296875, 40500000/40353607
| style="border-top: double;" | {{mapping| 574 910 1333 1612 }} (574d)
| {{mapping| 574 910 1333 1612 }} (574d)
| style="border-top: double;" | -0.2320
| −0.2320
| style="border-top: double;" | 0.1583
| 0.1583
| style="border-top: double;" | 7.57
| 7.57
|-
|-
| 2.3.5.7.11
| 2.3.5.7.11
| 3025/3024, 4375/4374, 5632/5625, 40500000/40353607
| 3025/3024, 4375/4374, 5632/5625, 40500000/40353607
| {{mapping| 574 910 1333 1612 1986 }} (574d)
| {{mapping| 574 910 1333 1612 1986 }} (574d)
| -0.2202
| −0.2202
| 0.1435
| 0.1435
| 6.87
| 6.87
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| 676/675, 3025/3024, 4225/4224, 4375/4374, 41600/41503
| 676/675, 3025/3024, 4225/4224, 4375/4374, 41600/41503
| {{mapping| 574 910 1333 1612 1986 2124 }} (574d)
| {{mapping| 574 910 1333 1612 1986 2124 }} (574d)
| -0.1786
| −0.1786
| 0.1607
| 0.1607
| 7.69
| 7.69
|-
|- style="border-top: double;"
| style="border-top: double;" | 2.3.5.7
| 2.3.5.7
| style="border-top: double;" | 10976/10935, 2100875/2097152, 49009212/48828125
| 10976/10935, 2100875/2097152, 49009212/48828125
| style="border-top: double;" | {{mapping| 574 910 1333 1611 }} (574)
| {{mapping| 574 910 1333 1611 }} (574)
| style="border-top: double;" | -0.0459
| −0.0459
| style="border-top: double;" | 0.2347
| 0.2347
| style="border-top: double;" | 11.23
| 11.23
|-
|-
| 2.3.5.7.11
| 2.3.5.7.11
| 5632/5625, 10976/10935, 131072/130977, 166698/166375
| 5632/5625, 10976/10935, 131072/130977, 166698/166375
| {{mapping| 574 910 1333 1611 1986 }} (574)
| {{mapping| 574 910 1333 1611 1986 }} (574)
| -0.0713
| −0.0713
| 0.2160
| 0.2160
| 10.33
| 10.33
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| 676/675, 1001/1000, 4096/4095, 10976/10935, 166698/166375
| 676/675, 1001/1000, 4096/4095, 10976/10935, 166698/166375
| {{mapping| 574 910 1333 1611 1986 2124 }} (574)
| {{mapping| 574 910 1333 1611 1986 2124 }} (574)
| -0.0544
| −0.0544
| 0.2007
| 0.2007
| 9.60
| 9.60
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=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
! Periods<br>per 8ve
|-
! Periods<br />per 8ve
! Generator*
! Generator*
! Cents*
! Cents*
! Associated<br>Ratio*
! Associated<br />ratio*
! Temperaments
! Temperaments
|-
|-
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| [[Vishnu]] (574d)
| [[Vishnu]] (574d)
|}
|}
<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
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