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34edo: Difference between revisions

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}}
}}
{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|34}}
{{ED intro}}
{{Wikipedia| 34 equal temperament }}
{{Wikipedia| 34 equal temperament }}


Line 21: Line 21:
! Cents
! Cents
! Approx. ratios<ref group="note">{{sg|limit=2.3.5.11.13.17.23 [[subgroup]]}}</ref>
! Approx. ratios<ref group="note">{{sg|limit=2.3.5.11.13.17.23 [[subgroup]]}}</ref>
! Ratios of 7<br>Using the 34 Val
! Ratios of 7 <br />Using the 34 Val
! Ratios of 7<br>Using the 34d Val
! Ratios of 7 <br />Using the 34d Val
! colspan="3" | [[Ups and Downs Notation]]
! colspan="3" | [[Ups and Downs Notation]]
! colspan="2" | [[Solfege|Solfeges]]
! colspan="2" | [[Solfege|Solfeges]]
Line 65: Line 65:
| [[15/14]], [[21/20]]
| [[15/14]], [[21/20]]
| vA1, ^m2
| vA1, ^m2
| downaug 1sn, <br>upminor 2nd
| downaug 1sn, <br />upminor 2nd
| vD#, ^Eb
| vD#, ^Eb
| fru
| fru
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|  
|  
| ^M2, vm3
| ^M2, vm3
| upmajor 2nd, <br>downminor 3rd
| upmajor 2nd, <br />downminor 3rd
| ^E, vF
| ^E, vF
| ru/no
| ru/no
Line 329: Line 329:
|  
|  
| ^M6, vm7
| ^M6, vm7
| upmajor 6th, <br>downminor 7th
| upmajor 6th, <br />downminor 7th
| ^B, vC
| ^B, vC
| lu/tho
| lu/tho
Line 514: Line 514:
! rowspan="2" | [[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
|-
|-
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|+ Rank-2 temperaments by period and generator
|+ Rank-2 temperaments by period and generator
|-
|-
! Periods<br>per 8ve
! Periods <br />per 8ve
! Generator
! Generator
! Cents
! Cents
Line 579: Line 579:
| 3\34
| 3\34
| 105.88
| 105.88
| [[11L 1s]]<br> [[11L 12s]]
| [[11L 1s]] <br />[[11L 12s]]
|  
|  
|-
|-
| 5\34
| 5\34
| 176.471
| 176.471
| [[6L 1s]]<br> [[7L 6s]] <br> [[7L 13s]] <br> 7L 20s
| [[6L 1s]] <br />[[7L 6s]] <br />[[7L 13s]] <br />7L 20s
| [[Tetracot]], [[bunya]] (34d), [[modus]] (34d), [[monkey]] (34), [[wollemia]] (34)
| [[Tetracot]], [[bunya]] (34d), [[modus]] (34d), [[monkey]] (34), [[wollemia]] (34)
|-
|-
| 7\34
| 7\34
| 247.059
| 247.059
| [[5L 4s]] <br> [[5L 9s]] <br> [[5L 14s]] <br> [[5L 19s]] <br>Pathological 5L 24s
| [[5L 4s]] <br />[[5L 9s]] <br />[[5L 14s]] <br />[[5L 19s]] <br />Pathological 5L 24s
| [[Immunity]] (34), [[immunized]] (34d)
| [[Immunity]] (34), [[immunized]] (34d)
|-
|-
| 9\34
| 9\34
| 317.647
| 317.647
| [[4L 3s]]<br> [[4L 7s]]<br> [[4L 11s]]<br> [[15L 4s]]
| [[4L 3s]] <br />[[4L 7s]] <br />[[4L 11s]] <br />[[15L 4s]]
| [[Hanson]], [[keemun]] (34), [[catalan]] (34d), [[catakleismic]] (34d)
| [[Hanson]], [[keemun]] (34), [[catalan]] (34d), [[catakleismic]] (34d)
|-
|-
| 11\34
| 11\34
| 388.235
| 388.235
| [[3L 7s]]<br> [[3L 10s]]<br> [[3L 13s]]<br> [[3L 16s]]<br> [[3L 19s]] <br>[[3L 22s]]<br> Pathological [[3L 25s]] <br> Pathological 3L 28s
| [[3L 7s]] <br />[[3L 10s]] <br />[[3L 13s]] <br />[[3L 16s]] <br />[[3L 19s]] <br />[[3L 22s]] <br />Pathological [[3L 25s]] <br />Pathological 3L 28s
| [[Würschmidt]] (34d), [[worschmidt]] (34)
| [[Würschmidt]] (34d), [[worschmidt]] (34)
|-
|-
| 13\34
| 13\34
| 458.824
| 458.824
| [[3L 2s]]<br> [[5L 3s]]<br> [[8L 5s]]<br> [[13L 8s]]
| [[3L 2s]] <br />[[5L 3s]] <br />[[8L 5s]] <br />[[13L 8s]]
| [[Petrtri]]
| [[Petrtri]]
|-
|-
| 15\34
| 15\34
| 529.412
| 529.412
| [[2L 3s]]<br> [[2L 5s]]<br> [[7L 2s]]<br> [[9L 7s]] <br> 9L 16s
| [[2L 3s]] <br />[[2L 5s]] <br />[[7L 2s]] <br />[[9L 7s]] <br />9L 16s
| [[Mabila]]
| [[Mabila]]
|-
|-
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| 3\34
| 3\34
| 105.882
| 105.882
| [[2L 6s]]<br>[[2L 8s]]<br> [[10L 2s]]<br> [[12L 10s]]
| [[2L 6s]] <br />[[2L 8s]] <br />[[10L 2s]] <br />[[12L 10s]]
| [[Srutal]] (34d), [[pajara]] (34d), [[diaschismic]] (34)
| [[Srutal]] (34d), [[pajara]] (34d), [[diaschismic]] (34)
|-
|-
| 4\34
| 4\34
| 141.176
| 141.176
| [[2L 6s]]<br> [[8L 2s]]<br> [[8L 10s]] <br> 8L 16s
| [[2L 6s]] <br />[[8L 2s]] <br />[[8L 10s]] <br />8L 16s
| [[Fifive]], [[crepuscular]] (34d), [[fifives]] (34)
| [[Fifive]], [[crepuscular]] (34d), [[fifives]] (34)
|-
|-
| 5\34
| 5\34
| 176.471
| 176.471
| [[6L 2s]]<br> [[6L 8s]]<br> [[14L 6s]]
| [[6L 2s]] <br />[[6L 8s]] <br />[[14L 6s]]
| [[Stratosphere]]
| [[Stratosphere]]
|-
|-
| 6\34
| 6\34
| 211.765
| 211.765
| [[4L 2s]] <br> [[6L 4s]] <br> [[6L 10s]] <br> [[6L 16s]] <br> Pathological 6L 22s
| [[4L 2s]] <br />[[6L 4s]] <br />[[6L 10s]] <br />[[6L 16s]] <br />Pathological 6L 22s
| [[Antikythera]]
| [[Antikythera]]
|-
|-
| 7\34
| 7\34
| 247.059
| 247.059
| [[4L 2s]] <br> [[4L 6s]] <br> [[10L 4s]] <br> [[10L 14s]]
| [[4L 2s]] <br />[[4L 6s]] <br />[[10L 4s]] <br />[[10L 14s]]
| [[Tobago]]
| [[Tobago]]
|-
|-
| 8\34
| 8\34
| 282.353
| 282.353
| [[2L 2s]] <br> [[4L 2s]] <br> [[4L 6s]] <br> [[4L 10s]] <br> [[4L 14s]] <br> 4L 18s <br> 4L 22s <br> Pathological 4L 26s
| [[2L 2s]] <br />[[4L 2s]] <br />[[4L 6s]] <br />[[4L 10s]] <br />[[4L 14s]] <br />4L 18s <br />4L 22s <br />Pathological 4L 26s
| [[Bikleismic]]
| [[Bikleismic]]
|}
|}
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{| class="commatable wikitable center-all left-3 right-4 left-6"
{| class="commatable wikitable center-all left-3 right-4 left-6"
|-
|-
! [[Harmonic limit|Prime<br>limit]]
! [[Harmonic limit|Prime <br />limit]]
! [[Ratio]]<ref group="note">{{rd}}</ref>
! [[Ratio]]<ref group="note">{{rd}}</ref>
! [[Monzo]]
! [[Monzo]]
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