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Rescue the table of approximations of the semioctave; fix "cents" (including 'c')
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== In just intonation ==
== In just intonation ==
Due to being close to 600 cents, tritones come in octave-complementary pairs. For low-limit harmony, these pairs are often referred to as "augmented fourth" (A4) and "diminished fifth" (d5) based on their function in diatonic harmony, but in higher limits, the tritones are usually just distinguished by size.
Due to being close to 600{{cent}}, tritones come in octave-complementary pairs. For low-limit harmony, these pairs are often referred to as "augmented fourth" (A4) and "diminished fifth" (d5) based on their function in diatonic harmony, but in higher limits, the tritones are usually just distinguished by size.


Historically, the term "tritone" referred to the '''Pythagorean augmented fourth,''' the ratio of 729/512 reached by stacking three Pythagorean whole tones (hence "tri-tone"), or equivalently, six [[3/2]]<nowiki/>s, which is an interval of about 612 cents. There is also the octave complement, the '''Pythagorean diminished fifth''' of 1024/729, which is about 588 cents in size.
Historically, the term "tritone" referred to the '''Pythagorean augmented fourth,''' the ratio of 729/512 reached by stacking three Pythagorean whole tones (hence "tri-tone"), or equivalently, six [[3/2]]<nowiki/>s, which is an interval of about 612{{cent}}. There is also the octave complement, the '''Pythagorean diminished fifth''' of 1024/729, which is about 588{{cent}} in size.


Much [[Odd limit|simpler]] tritones exist in higher [[Prime limit|limits]], however, for example:
Much [[Odd limit|simpler]] tritones exist in higher [[Prime limit|limits]], however, for example:


* The 5-limit '''ptolemaic augmented fourth''' and '''ptolemaic diminished fifth''' are ratios of 45/32 and 64/45 respectively, and are about 590 and 610 cents respectively.
* The 5-limit '''ptolemaic augmented fourth''' and '''ptolemaic diminished fifth''' are ratios of 45/32 and 64/45 respectively, and are about 590{{cent}} and 610{{cent}} respectively.
** There are also the '''classical augmented fourth''' and '''classical diminished fifth,''' which are ratios of 25/18 and 36/25 respectively, and are about 569 and 631 cents respectively.
** There are also the '''classical augmented fourth''' and '''classical diminished fifth,''' which are ratios of 25/18 and 36/25 respectively, and are about 569{{cent}} and 631{{cent}} respectively.
* The 7-limit '''narrow tritone''' and '''wide tritone''' are ratios of 7/5 and 10/7 respectively, and are about 583 and 617 cents respectively.
* The 7-limit '''narrow tritone''' and '''wide tritone''' are ratios of 7/5 and 10/7 respectively, and are about 583{{cent}} and 617{{cent}} respectively.
* The 11-limit '''superfourth''' and '''subfifth''' are ratios of 11/8 and 16/11 respectively, and are about 551 and 649 cents respectively; they are listed here because they barely do not make the cutoff (550 and 650 cents) to be included in the pages on fourths and fifths.
* The 11-limit '''superfourth''' and '''subfifth''' are ratios of 11/8 and 16/11 respectively, and are about 551{{cent}} and 649{{cent}} respectively; they are listed here because they barely do not make the cutoff (550{{cent}} and 650{{cent}}) to be included in the pages on fourths and fifths.


== In EDOs ==
== In EDOs ==
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|-
|-
|12
|12
| colspan="4" |600c
| colspan="4" |600{{cent}}
|
|
|-
|-
|15
|15
| colspan="2" |560c
| colspan="2" |560{{cent}}
| colspan="2" |640c
| colspan="2" |640{{cent}}
|
|
|-
|-
|16
|16
|525c
|525{{cent}}
|600c
|600{{cent}}
|675c
|675{{cent}}
|600c
|600{{cent}}
|
|
|-
|-
|17
|17
| colspan="2" |565c
| colspan="2" |565{{cent}}
| colspan="2" |635c
| colspan="2" |635{{cent}}
|
|
|-
|-
|19
|19
| colspan="2" |568c
| colspan="2" |568{{cent}}
| colspan="2" |632c
| colspan="2" |632{{cent}}
|
|
|-
|-
|22
|22
|545c
|545{{cent}}
|600c
|600{{cent}}
|655c
|655{{cent}}
|600c
|600{{cent}}
|
|
|-
|-
|24
|24
|550c
|550{{cent}}
|600c
|600{{cent}}
|650c
|650{{cent}}
|600c
|600{{cent}}
|
|
|-
|-
|25
|25
|*
|*
|576c
|576{{cent}}
|*
|*
|624c
|624{{cent}}
|
|
|-
|-
|26
|26
|554c
|554{{cent}}
|600c
|600{{cent}}
|646c
|646{{cent}}
|600c
|600{{cent}}
|
|
|-
|-
|27
|27
|*
|*
|578c
|578{{cent}}
|*
|*
|622c
|622{{cent}}
|
|
|-
|-
|29
|29
|*
|*
|579c
|579{{cent}}
|*
|*
|621c
|621{{cent}}
|
|
|-
|-
|31
|31
|542c
|542{{cent}}
|581c
|581{{cent}}
|658c
|658{{cent}}
|619c
|619{{cent}}
|
|
|-
|-
|34
|34
|565c
|565{{cent}}
|600c
|600{{cent}}
|635c
|635{{cent}}
|600c
|600{{cent}}
|
|
|-
|-
|41
|41
|556c
|556{{cent}}
|585c
|585{{cent}}
|644c
|644{{cent}}
|615c
|615{{cent}}
|
|
|-
|-
|53
|53
|543c
|543{{cent}}
|589c
|589{{cent}}
|657c
|657{{cent}}
|611c
|611{{cent}}
|634c ≈ 36/25, 566c ≈ 25/18
|634{{cent}} ≈ 36/25, 566{{cent}} ≈ 25/18
|}
|}
[[Category:Tritone]]
[[Category:Tritone]]
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* TBD
* TBD
== Tritones as approximations of the semioctave ==
The following table compares selected JI tritone pairs that approximate the half-octave and the commas separating them:
{| class="wikitable sortable center-all right-3"
! class="unsortable" | Ratios
! Prime<br>limit
! Distance<br>from 600{{cent}}
! Comma
|-
| [[729/512]], [[1024/729]]
| 3
| 11.730
| [[Pythagorean comma|531441/524288]]
|-
| [[45/32]], [[64/45]]
| 5
| 9.776
| [[Diaschisma|2048/2025]]
|-
| [[7/5]], [[10/7]]
| 7
| 17.488
| [[50/49]]
|-
| [[99/70]], [[140/99]]
| 11
| 0.088
| [[9801/9800]]
|-
| [[13/9]], [[18/13]]
| 13
| 36.618
| [[169/162]]
|-
| [[24/17]], [[17/12]]
| 17
| 3.000
| [[289/288]]
|-
| [[27/19]], [[38/27]]
| 19
| 8.352
| [[729/722]]
|-
| [[23/16]], [[32/23]]
| 23
| 28.274
| [[544/529]]
|-
| [[41/29]], [[58/41]]
| 41
| 0.515
| [[1682/1681]]
|}


{{Navbox intervals}}<!-- main article -->
{{Navbox intervals}}<!-- main article -->
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