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4349edo: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|4349}}
{{ED intro}}


== Theory ==
== Theory ==
4349edo is [[consistent]] to the [[29-odd-limit]], [[temper out|tempering out]] [[12376/12375]], 10241/10240, 13377/13376, 89376/89375, 25025/25024, [[123201/123200]], 76545/76544, 47125/47124 and 25840/25839. It [[support]]s [[counterquectismic]], [[chalmersic]], [[tritomere]] and [[girardic]]. [[Essentially tempered chords]] available in 4349et include [[vicetertismic chords]].
4349edo is a fairly strong [[29-limit]] system, [[consistent]] to the [[29-odd-limit]]. We may note it is a [[counterquectismic]], [[fortune]], and [[euzenius]] system. Some of the simpler commas in [[tempering out|tempers out]] in the higher limits include [[151263/151250]] and [[1771561/1771470]] in the 11-limit; [[123201/123200]] in the 13-limit; [[12376/12375]] in the 17-limit; 10241/10240, 13377/13376, 89376/89375 in the 19-limit; [[12168/12167]], 25025/25024, 76545/76544 in the 23-limit; 47125/47124 and 25840/25839. Since it tempers out 12168/12167, it allows [[vicetertismic chords]] in the [[23-odd-limit]].


=== Prime harmonics ===
=== Prime harmonics ===
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=== Subsets and supersets ===
=== Subsets and supersets ===
4349edo is the 594th [[prime EDO]].
4349edo is the 594th [[prime edo]].


== 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|-6893 4349}}
| {{monzo| -6893 4349 }}
| {{mapping|4349 6893}}
| {{mapping| 4349 6893 }}
| +0.0002
| +0.0002
| 0.0002
| 0.0002
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|-
|-
| 2.3.5
| 2.3.5
| {{monzo|-107 47 14}}, {{monzo|-35 -79 69}}
| {{monzo| -107 47 14 }}, {{monzo| -35 -79 69 }}
| {{mapping|4349 6893 10098}}
| {{mapping| 4349 6893 10098 }}
| +0.0027
| +0.0027
| 0.0036
| 0.0036
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|-
|-
| 2.3.5.7
| 2.3.5.7
| 78125000/78121827, {{monzo|-1 -18 -3 13}}, {{monzo|-52 17 12 -1}}
| 78125000/78121827, {{monzo| -1 -18 -3 13 }}, {{monzo| -52 17 12 -1 }}
| {{mapping|4349 6893 10098 12209}}
| {{mapping| 4349 6893 10098 12209 }}
| +0.0066
| +0.0066
| 0.0074
| 0.0074
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| 2.3.5.7.11
| 2.3.5.7.11
| 151263/151250, 21437500/21434787, 246071287/246037500, 369140625/369098752
| 151263/151250, 21437500/21434787, 246071287/246037500, 369140625/369098752
| {{mapping|4349 6893 10098 12209 15045}}
| {{mapping| 4349 6893 10098 12209 15045 }}
| +0.0064
| +0.0064
| 0.0067
| 0.0067
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|-
|-
| 2.3.5.7.11.13
| 2.3.5.7.11.13
| 123201/123200, 196625/196608, 151263/151250, 492128/492075, 5175625/5174928
| 123201/123200, 151263/151250, 196625/196608, 492128/492075, 5175625/5174928
| {{mapping|4349 6893 10098 12209 15045 16093}}
| {{mapping| 4349 6893 10098 12209 15045 16093 }}
| +0.0079
| +0.0079
| 0.0070
| 0.0070
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|-
|-
| 2.3.5.7.11.13.17
| 2.3.5.7.11.13.17
| 12376/12375, 123201/123200, 37180/37179, 194481/194480, 221221/221184, 1328125/1328096
| 12376/12375, 37180/37179, 123201/123200, 194481/194480, 221221/221184, 1328125/1328096
| {{mapping|4349 6893 10098 12209 15045 16093 17776}}
| {{mapping| 4349 6893 10098 12209 15045 16093 17776 }}
| +0.0104
| +0.0104
| 0.0089
| 0.0089
| 3.23
| 3.23
{{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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| 8388608/7381125
| 8388608/7381125
| [[Fortune]]
| [[Fortune]]
{{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
 
== Music ==
; [[Francium]]
* "Naughty Girl Era" from ''Naughty Girl Era'' (2024) – [https://open.spotify.com/track/0ulmRt6G21G2X5RyxHLYHT Spotify] | [https://francium223.bandcamp.com/track/naughty-girl-era Bandcamp] | [https://www.youtube.com/watch?v=gJ9ZAKfgigA YouTube] – girardic in 4349edo
Retrieved from "https://en.xen.wiki/w/4349edo"