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| 4
| 4
| 252.63
| 252.63
| Augmented second<br>Diminished third
| Augmented second<br />Diminished third
| [[7/6]], [[8/7]], [[15/13]]
| [[7/6]], [[8/7]], [[15/13]]
| Ri/Ma
| Ri/Ma
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| 9
| 9
| 568.42
| 568.42
| Augmented fourth<br>(Small [[tritone]])
| Augmented fourth<br />(Small [[tritone]])
| [[7/5]], [[18/13]], [[25/18]]
| [[7/5]], [[18/13]], [[25/18]]
| Fi
| Fi
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| 10
| 10
| 631.58
| 631.58
| Diminished fifth<br>(Large [[tritone]])
| Diminished fifth<br />(Large [[tritone]])
| [[10/7]], [[13/9]], [[36/25]]
| [[10/7]], [[13/9]], [[36/25]]
| Se
| Se
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| 15
| 15
| 947.37
| 947.37
| Augmented sixth<br>Diminished seventh
| Augmented sixth<br />Diminished seventh
| [[7/4]], [[12/7]], [[26/15]]
| [[7/4]], [[12/7]], [[26/15]]
| Li/Ta
| Li/Ta
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|-
|-
! [[5L 2s|Diatonic Interval Names]]
! [[5L 2s|Diatonic Interval Names]]
! Note Names<br>on D
! Note Names<br />on D
|-
|-
| 0
| 0
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| 1
| 1
| 63.16
| 63.16
| Augmented unison (A1)<br>Diminished second (d2)
| Augmented unison (A1)<br />Diminished second (d2)
| D#<br>Ebb
| D#<br />Ebb
|-
|-
| 2
| 2
| 126.32
| 126.32
| Doubly augmented unison (AA1)<br>Minor second (m2)
| Doubly augmented unison (AA1)<br />Minor second (m2)
| Dx<br>Eb
| Dx<br />Eb
|-
|-
| 3
| 3
| 189.47
| 189.47
| '''Major second (M2)'''<br>Doubly diminished third (dd3)
| '''Major second (M2)'''<br />Doubly diminished third (dd3)
| '''E'''<br>Fbb
| '''E'''<br />Fbb
|-
|-
| 4
| 4
| 252.63
| 252.63
| Augmented second (A2)<br>Diminished third (d3)
| Augmented second (A2)<br />Diminished third (d3)
| E#<br>Fb
| E#<br />Fb
|-
|-
| 5
| 5
| 315.79
| 315.79
| Doubly augmented second (AA2)<br>'''Minor third (m3)'''
| Doubly augmented second (AA2)<br />'''Minor third (m3)'''
| Ex<br>'''F'''
| Ex<br />'''F'''
|-
|-
| 6
| 6
| 378.95
| 378.95
| '''Major third (M3)'''<br>Doubly diminished fourth (dd4)
| '''Major third (M3)'''<br />Doubly diminished fourth (dd4)
| '''F#'''<br>Gbb
| '''F#'''<br />Gbb
|-
|-
| 7
| 7
| 442.11
| 442.11
| Augmented third (A3)<br>Diminished fourth (d4)
| Augmented third (A3)<br />Diminished fourth (d4)
| Fx<br>Gb
| Fx<br />Gb
|-
|-
| 8
| 8
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| 9
| 9
| 568.42
| 568.42
| Augmented fourth (A4)<br>Doubly diminished fifth (dd5)
| Augmented fourth (A4)<br />Doubly diminished fifth (dd5)
| G#<br>Abb
| G#<br />Abb
|-
|-
| 10
| 10
| 631.58
| 631.58
| Doubly augmented fourth (AA4)<br>Diminished fifth (d5)
| Doubly augmented fourth (AA4)<br />Diminished fifth (d5)
| Gx<br>Ab
| Gx<br />Ab
|-
|-
| 11
| 11
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| 12
| 12
| 757.89
| 757.89
| Augmented fifth (A5)<br>Diminished sixth (d6)
| Augmented fifth (A5)<br />Diminished sixth (d6)
| A#<br>Bbb
| A#<br />Bbb
|-
|-
| 13
| 13
| 821.05
| 821.05
| Doubly augmented fifth (AA5)<br>Minor sixth (m6)
| Doubly augmented fifth (AA5)<br />Minor sixth (m6)
| Ax<br>Bb
| Ax<br />Bb
|-
|-
| 14
| 14
| 884.21
| 884.21
| '''Major sixth (M6)'''<br>Doubly diminished seventh (dd7)
| '''Major sixth (M6)'''<br />Doubly diminished seventh (dd7)
| '''B'''<br>Cbb
| '''B'''<br />Cbb
|-
|-
| 15
| 15
| 947.37
| 947.37
| Augmented sixth (A6)<br>Diminished seventh (d7)
| Augmented sixth (A6)<br />Diminished seventh (d7)
| B#<br>Cb
| B#<br />Cb
|-
|-
| 16
| 16
| 1010.53
| 1010.53
| Doubly augmented sixth (AA6)<br>'''Minor seventh (m7)'''
| Doubly augmented sixth (AA6)<br />'''Minor seventh (m7)'''
| Bx<br>'''C'''
| Bx<br />'''C'''
|-
|-
| 17
| 17
| 1073.68
| 1073.68
| Major seventh (M7)<br>Doubly diminished octave (dd8)
| Major seventh (M7)<br />Doubly diminished octave (dd8)
| C#<br>Dbb
| C#<br />Dbb
|-
|-
| 18
| 18
| 1136.84
| 1136.84
| Augmented seventh (A7)<br>Diminished octave (d8)
| Augmented seventh (A7)<br />Diminished octave (d8)
| Cx<br>Db
| Cx<br />Db
|-
|-
| 19
| 19
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! rowspan="2" | [[Comma list|Comma List]]
! rowspan="2" | [[Comma list|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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{| 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|10}}</ref>
! [[Ratio]]<ref group="note">{{rd|10}}</ref>
! [[Monzo]]
! [[Monzo]]
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| Triaphonisma
| Triaphonisma
|}
|}
<references/>


=== Linear temperaments ===
=== Linear temperaments ===
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| M2
| M2
| [[1L 5s]], [[6L 1s]], [[6L 7s]]
| [[1L 5s]], [[6L 1s]], [[6L 7s]]
| [[Deutone]]<br>[[Spell]]
| [[Deutone]]<br />[[Spell]]
|-
|-
| 4
| 4
| 252.63
| 252.63
| A2, d3
| A2, d3
| [[1L 3s]], [[4L 1s]], <br>[[5L 4s]], [[5L 9s]]
| [[1L 3s]], [[4L 1s]], <br />[[5L 4s]], [[5L 9s]]
| [[Godzilla]]
| [[Godzilla]]
|-
|-
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| 315.79
| 315.79
| m3
| m3
| [[3L 1s]], [[4L 3s]], <br>[[4L 7s]], [[4L 11s]]
| [[3L 1s]], [[4L 3s]], <br />[[4L 7s]], [[4L 11s]]
| [[Cata]] / [[keemun]]
| [[Cata]] / [[keemun]]
|-
|-
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| 378.95
| 378.95
| M3
| M3
| [[3L 1s]], [[3L 4s]], [[3L 7s]], <br>[[3L 10s]], [[3L 13s]]
| [[3L 1s]], [[3L 4s]], [[3L 7s]], <br />[[3L 10s]], [[3L 13s]]
| [[Magic]] / [[muggles]]
| [[Magic]] / [[muggles]]
|-
|-
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| 568.42
| 568.42
| A4
| A4
| [[2L 3s]], [[2L 5s]], [[2L 7s]], <br>[[2L 9s]], [[2L 11s]], [[2L 13s]], <br>[[2L 15s]]
| [[2L 3s]], [[2L 5s]], [[2L 7s]], <br />[[2L 9s]], [[2L 11s]], [[2L 13s]], <br />[[2L 15s]]
| [[Liese]] / [[pycnic]]<br>[[Triton]]
| [[Liese]] / [[pycnic]]<br />[[Triton]]
|}
|}


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