Tritone: Difference between revisions
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The concept started as an interval in the diatonic scale, and is still used this way. The interval region is a later association. You can't just make it the main definition Tag: Undo |
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{{Wikipedia}} | {{Wikipedia}} | ||
A '''tritone''' | 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]]. | |||
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 frankly 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]]. | 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 frankly 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]]. | ||
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Due to being close to 600{{c}}, 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{{c}}, 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]] | 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]]'s, which is an interval of about 612{{c}}. There is also the octave complement, the '''Pythagorean diminished fifth''' of 1024/729, which is about 588{{c}} 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: | ||