4349edo: Difference between revisions

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Created page with "{{Infobox ET}} {{EDO intro|4349}} == Theory == 4349edo is consistent to the 29-odd-limit, tempering out 12376/12375, 10241/10240, 13377/13376, 8937..."
 
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4349edo is the 594th [[prime EDO]].
4349edo is the 594th [[prime EDO]].


{| class="wikitable center-4 center-5 center-6"
== Regular temperament properties ==
! rowspan="2" |[[Subgroup]]
{{comma basis begin}}
! rowspan="2" |[[Comma list|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
| 0.07
| 0.07
Line 31: Line 24:
| {{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
| 1.30
| 1.30
Line 38: Line 31:
| 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
| 2.68
| 2.68
Line 45: Line 38:
| 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
| 2.43
| 2.43
Line 52: Line 45:
| 123201/123200, 196625/196608, 151263/151250, 492128/492075, 5175625/5174928
| 123201/123200, 196625/196608, 151263/151250, 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
| 2.54
| 2.54
Line 59: Line 52:
| 12376/12375, 123201/123200, 37180/37179, 194481/194480, 221221/221184, 1328125/1328096
| 12376/12375, 123201/123200, 37180/37179, 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 ===
{| class="wikitable center-all left-5"
{{rank-2 begin}}
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>Ratio*
! Temperaments
|-
|-
|1
| 1
|803\4349
| 803\4349
|221.5682
| 221.5682
|8388608/7381125
| 8388608/7381125
|[[Fortune]]
| [[Fortune]]
|}
{{rank-2 end}}
 
{{orf}}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct

Revision as of 02:04, 16 November 2024

← 4348edo 4349edo 4350edo →
Prime factorization 4349 (prime)
Step size 0.275926 ¢ 
Fifth 2544\4349 (701.954 ¢)
Semitones (A1:m2) 412:327 (113.7 ¢ : 90.23 ¢)
Consistency limit 29
Distinct consistency limit 29

Template:EDO intro

Theory

4349edo is consistent to the 29-odd-limit, tempering out 12376/12375, 10241/10240, 13377/13376, 89376/89375, 25025/25024, 123201/123200, 76545/76544, 47125/47124 and 25840/25839. It supports counterquectismic, chalmersic, tritomere and girardic. Essentially tempered chords available in 4349et include vicetertismic chords.

Prime harmonics

Approximation of prime harmonics in 4349edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 -0.001 -0.018 -0.051 -0.019 -0.059 -0.104 -0.065 +0.008 -0.099 +0.055
Relative (%) +0.0 -0.2 -6.5 -18.7 -6.8 -21.2 -37.6 -23.7 +2.9 -35.9 +20.0
Steps
(reduced) 		4349
(0) 		6893
(2544) 		10098
(1400) 		12209
(3511) 		15045
(1998) 		16093
(3046) 		17776
(380) 		18474
(1078) 		19673
(2277) 		21127
(3731) 		21546
(4150)

Subsets and supersets

4349edo is the 594th prime EDO.

Regular temperament properties

Template:Comma basis begin |- | 2.3 | [-6893 4349⟩ | [⟨4349 6893]] | +0.0002 | 0.0002 | 0.07 |- | 2.3.5 | [-107 47 14⟩, [-35 -79 69⟩ | [⟨4349 6893 10098]] | +0.0027 | 0.0036 | 1.30 |- | 2.3.5.7 | 78125000/78121827, [-1 -18 -3 13⟩, [-52 17 12 -1⟩ | [⟨4349 6893 10098 12209]] | +0.0066 | 0.0074 | 2.68 |- | 2.3.5.7.11 | 151263/151250, 21437500/21434787, 246071287/246037500, 369140625/369098752 | [⟨4349 6893 10098 12209 15045]] | +0.0064 | 0.0067 | 2.43 |- | 2.3.5.7.11.13 | 123201/123200, 196625/196608, 151263/151250, 492128/492075, 5175625/5174928 | [⟨4349 6893 10098 12209 15045 16093]] | +0.0079 | 0.0070 | 2.54 |- | 2.3.5.7.11.13.17 | 12376/12375, 123201/123200, 37180/37179, 194481/194480, 221221/221184, 1328125/1328096 | [⟨4349 6893 10098 12209 15045 16093 17776]] | +0.0104 | 0.0089 | 3.23 Template:Comma basis end

Rank-2 temperaments

Template:Rank-2 begin |- | 1 | 803\4349 | 221.5682 | 8388608/7381125 | Fortune Template:Rank-2 end Template:Orf

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