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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|730}}
{{ED intro}}


== Theory ==
== Theory ==
730edo is a very strong 5-limit system, but is also [[consistency|distinctly consistent]] up to the [[15-odd-limit]]. The equal temperament [[tempering out|tempers out]] the {{monzo| -69 45 -1 }} ([[counterschisma]]), {{monzo| -16 35 -17 }} (minortone comma), {{monzo| -53 10 16 }} ([[kwazy comma]]), {{monzo| 37 25 -33 }} (whoosh comma), and {{monzo| -90 -15 49 }} (pirate comma). In the 7-limit it tempers out [[4375/4374]] and {{monzo| -21 0 3 5 }}, so that it [[support]]s the [[mitonic]] temperament. In the 11-limit, [[3025/3024]] and {{monzo| 4 -3 -6 4 1 }}, so that it supports the [[deca]] temperament. In the 13-limit, [[1001/1000]] and [[4225/4224]], supporting 13-limit deca.
730edo is a very strong 5-limit system, but is also [[consistency|distinctly consistent]] up to the [[15-odd-limit]]. As an equal temperament, it [[tempering out|tempers out]] the {{monzo| -69 45 -1 }} ([[counterschisma]]), {{monzo| -16 35 -17 }} (minortone comma), {{monzo| -53 10 16 }} ([[kwazy comma]]), {{monzo| 37 25 -33 }} (whoosh comma), and {{monzo| -90 -15 49 }} (pirate comma). In the 7-limit it tempers out [[4375/4374]] and {{monzo| -21 0 3 5 }}, so that it [[support]]s the [[mitonic]] temperament. In the 11-limit, [[3025/3024]] and {{monzo| 4 -3 -6 4 1 }}, so that it supports the [[deca]] temperament. In the 13-limit, [[1001/1000]] and [[4225/4224]], supporting 13-limit deca.


{{W|W. S. B. Woolhouse}} proposed 730edo as a [[interval size measure|logarithmic measure of interval size]]<ref name="summary">[https://www.webcitation.org/5zxZzQ3eS A summary of W. S. B. Woolhouse's Essay on musical intervals], 1999 by [[Joseph Monzo]]</ref>, sometimes called the '''Woolhouse unit'''. While 730 is divisible by 2, 5, 10, 73, 146 and 365, it is not divisible by 12 and it is also deficient, with [[abundancy index]] of 0.82, which limits its application as an interval size measure.
{{W|W. S. B. Woolhouse}} proposed 730edo as a [[interval size measure|logarithmic measure of interval size]]<ref name="summary">[https://www.webcitation.org/5zxZzQ3eS A summary of W. S. B. Woolhouse's Essay on musical intervals], 1999 by [[Joseph Monzo]]</ref>, sometimes called the '''Woolhouse unit'''. While 730 is divisible by 2, 5, 10, 73, 146, and 365, it is not divisible by 12 and it is also deficient, with [[abundancy index]] of 0.82, which limits its application as an interval size measure.


=== Prime harmonics ===
=== Prime harmonics ===
{{Harmonics in equal|730|columns=11}}
{{Harmonics in equal|730}}


=== Subsets and supersets ===
=== Subsets and supersets ===
Since 730 factors into {{factorization|730}}, 730edo has subset edos {{EDOs| 2, 5, 10, 73, 146, and 365 }}. 1460edo, which doubles it, gives alternative approximations to harmonics 7, 11, and 13. [[2190edo]], which triples it, corrects these harmonics to near-just levels of accuracy. [[4380edo]] gives a possible full 31-limit system.  
Since 730 factors into 2 × 5 × 73, 730edo has subset edos {{EDOs| 2, 5, 10, 73, 146, and 365 }}. 1460edo, which doubles it, gives alternative approximations to harmonics 7, 11, and 13. [[2190edo]], which triples it, corrects these harmonics to near-just levels of accuracy. [[4380edo]] gives a possible full 31-limit system.


== Intervals ==
== Intervals ==
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== Regular temperament properties ==
== Regular temperament properties ==
{{comma basis begin}}
{| class="wikitable center-4 center-5 center-6"
|-
! rowspan="2" | [[Subgroup]]
! rowspan="2" | [[Comma list]]
! rowspan="2" | [[Mapping]]
! rowspan="2" | Optimal<br>8ve stretch (¢)
! colspan="2" | Tuning error
|-
! [[TE error|Absolute]] (¢)
! [[TE simple badness|Relative]] (%)
|-
|-
| 2.3
| 2.3
| {{monzo| -1157 730 }}
| {{Monzo| -1157 730 }}
| {{mapping| 730 1157 }}
| {{Mapping| 730 1157 }}
| +0.0117
| +0.0117
| 0.0117
| 0.0117
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|-
|-
| 2.3.5
| 2.3.5
| {{monzo| -53 10 16 }}, {{monzo| -16 35 -17 }}
| {{Monzo| -53 10 16 }}, {{monzo| -16 35 -17 }}
| {{mapping| 730 1157 1695 }}
| {{Mapping| 730 1157 1695 }}
| +0.0096
| +0.0096
| 0.0100
| 0.0100
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| 2.3.5.7
| 2.3.5.7
| 4375/4374, 2100875/2097152, {{monzo| 12 -3 -14 9 }}
| 4375/4374, 2100875/2097152, {{monzo| 12 -3 -14 9 }}
| {{mapping| 730 1157 1695 2049 }}
| {{Mapping| 730 1157 1695 2049 }}
| +0.0612
| +0.0612
| 0.0899
| 0.0899
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| 2.3.5.7.11
| 2.3.5.7.11
| 3025/3024, 4375/4374, 391314/390625, 2100875/2097152
| 3025/3024, 4375/4374, 391314/390625, 2100875/2097152
| {{mapping| 730 1157 1695 2049 2525 }}
| {{Mapping| 730 1157 1695 2049 2525 }}
| +0.0856
| +0.0856
| 0.0940
| 0.0940
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| 2.3.5.7.11.13
| 2.3.5.7.11.13
| 1001/1000, 3025/3024, 4225/4224, 4375/4374, 2100875/2097152
| 1001/1000, 3025/3024, 4225/4224, 4375/4374, 2100875/2097152
| {{mapping| 730 1157 1695 2049 2525 2701 }}
| {{Mapping| 730 1157 1695 2049 2525 2701 }}
| +0.0951
| +0.0951
| 0.0884
| 0.0884
| 5.38
| 5.38
{{comma basis end}}
|}


=== Rank-2 temperaments ===
=== Rank-2 temperaments ===
{{rank-2 begin}}
{| class="wikitable center-all left-5"
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>ratio*
! Temperaments
|-
|-
| 1
| 1
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| 162.74
| 162.74
| 1125/1024
| 1125/1024
| [[Kwazy]]
| [[Crazy]]
|-
|-
| 1
| 1
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| 113\730
| 113\730
| 185.75
| 185.75
| {{monzo| 24 4 -13 }}
| {{Monzo| 24 4 -13 }}
| [[Pirate]]
| [[Pirate]]
|-
|-
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|-
|-
| 10
| 10
| 192\730<br />(27\730)
| 192\730<br>(27\730)
| 315.62<br />(44.38)
| 315.62<br>(44.38)
| 6/5<br />(40/39)
| 6/5<br>(40/39)
| [[Deca]]
| [[Deca]]
{{rank-2 end}}
|}
{{orf}}
<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


== Scales ==
== Scales ==
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