Tritone: Difference between revisions
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{{Infobox interval region|Name=Tritone, augmented fourth, diminished fifth|Cents lower=570|Cents lower wide=540|Cents upper=630|Cents upper wide=660|JI intervals=7/5, 10/7|MOSes=[[2L 5s]], [[2L 7s]]|Complement=[[Tritone]]|Lower region=[[Semi-augmented fourth]] <br> [[Perfect fourth]]|Higher region=[[ | {{Infobox interval region | ||
| Name = Tritone, augmented fourth, diminished fifth | |||
| Cents lower = 570 | |||
| Cents lower wide = 540 | |||
| Cents upper = 630 | |||
| Cents upper wide = 660 | |||
| JI intervals = 7/5, 10/7 | |||
| MOSes = [[2L 5s]], [[2L 7s]] | |||
| Complement = [[Tritone]] | |||
| Lower region = [[Semi-augmented fourth]] <br> [[Perfect fourth]] | |||
| Higher region = [[Semidiminished fifth]] <br> [[Perfect fifth]] | |||
}} | |||
{{Wikipedia}} | |||
A '''tritone''' is an interval that spans six steps of a 12-tone [[chromatic]] scale. In [[just intonation]], an interval may be classified as a tritone if it is reasonably mapped to [[24edo|12\24]]. The use of 24edo's 12\24 as the mapping criteria here rather than [[12edo]]'s 6\12 better captures the characteristics of many intervals in the [[11-limit|11-]] and [[13-limit]]. Functionally, tritones come in octave-complementary pairs, called '''augmented fourth''' ('''A4''') and '''diminished fifth''' ('''d5''') based on their number of steps in the [[5L 2s|diatonic]] scale. | A '''tritone''' is an interval that spans six steps of a 12-tone [[chromatic]] scale. In [[just intonation]], an interval may be classified as a tritone if it is reasonably mapped to [[24edo|12\24]]. The use of 24edo's 12\24 as the mapping criteria here rather than [[12edo]]'s 6\12 better captures the characteristics of many intervals in the [[11-limit|11-]] and [[13-limit]]. Functionally, tritones come in octave-complementary pairs, called '''augmented fourth''' ('''A4''') and '''diminished fifth''' ('''d5''') based on their number of steps in the [[5L 2s|diatonic]] scale. | ||
As a concrete [[interval region]], it is typically near 600 [[cent]]s in size. A rough tuning range for the tritone is about 560 to 640 cents according to [[Margo Schulter]]'s theory of interval regions. ''Tritone'' in this sense can also refer to the semi-octave, a tritone of exactly 600 cents found in every even [[edo]], due to the fact that it is [[2edo|1\2edo]]. | As a concrete [[interval region]], it is typically near 600 [[cent]]s in size. A rough tuning range for the tritone is about 560 to 640 cents according to [[Margo Schulter]]'s theory of interval regions. ''Tritone'' in this sense can also refer to the semi-octave, a tritone of exactly 600 cents found in every even [[edo]], due to the fact that it is [[2edo|1\2edo]]. | ||
For the sake of fully covering the range of intervals within the octave, this page also covers '''semiaugmented fourths''' of about 550 cents, and '''semidiminished fifths''' of about 650 cents. Note that these are not conventionally considered tritones, and are included here for simplicity | For the sake of fully covering the range of intervals within the octave, this page also covers '''semiaugmented fourths''' of about 550 cents, and '''semidiminished fifths''' of about 650 cents. Note that these are not conventionally considered tritones, and are included here for simplicity and for having more than one pair of simple ratios to use in the edo section. More info may be found at [[semiaugmented fourth]] and [[semidiminished fifth]]. | ||
As such, this article covers intervals from 560 to 640 cents, but intervals between 540-560 and 640-660 cents have been "grandfathered in" due to the fact that superfourths and subfifths were not originally given their own articles. | As such, this article covers intervals from 560 to 640 cents, but intervals between 540-560 and 640-660 cents have been "grandfathered in" due to the fact that superfourths and subfifths were not originally given their own articles. | ||
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* The 11-limit '''superfourth''' and '''subfifth''' are ratios of 11/8 and 16/11 respectively, and are about 551{{c}} and 649{{c}} respectively; they are listed here because they barely do not make the cutoff (550{{c}} and 650{{c}}) 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{{c}} and 649{{c}} respectively; they are listed here because they barely do not make the cutoff (550{{c}} and 650{{c}}) to be included in the pages on fourths and fifths. | ||
== In | == In edos == | ||
The following table lists the tunings of 11/8, 7/5, and their octave complements, as well as other tritones if present, in various significant [[ | The following table lists the tunings of 11/8, 7/5, and their octave complements, as well as other tritones if present, in various significant [[edo]]s. Note that many edos map 7/5 and 10/7 to the semioctave. | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! | ! Edo | ||
! 11/8 | ! 11/8 | ||
! 7/5 | ! 7/5 | ||
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=== Temperaments that use 7/5 as a generator === | === Temperaments that use 7/5 as a generator === | ||
{{todo|complete section|inline=1|text=(see [[ | {{todo|complete section|inline=1|text=(see [[List of rank two temperaments by generator and period #Generator .7E7.2F5]])}} | ||
== In | == In mos scales == | ||
Intervals between 545 and 654 cents generate the following [[ | Intervals between 545 and 654 cents generate the following [[mos]] scales: | ||
These tables start from the last monolarge [[ | These tables start from the last monolarge [[mos]] generated by the interval range. | ||
Scales with more than 12 notes are not included. | |||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! Range | ! Range | ||
! colspan="6" | | ! colspan="6" | Mos | ||
|- | |- | ||
| 545–654{{c}} | | 545–654{{c}} | ||
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| [[2L 9s]] | | [[2L 9s]] | ||
|} | |} | ||
{{Navbox intervals}} | {{Navbox intervals}} | ||
[[Category:Tritone]] | [[Category:Tritone]] <!-- Main article --> | ||