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A septimal tritone is a An unorthodox look at consonance
, ''The Bohlen-Pierce Site''. Depending on the temperament used, "the" tritone, defined as three whole tones, may be identified as either a lesser septimal tritone (in
A septimal tritone is a tritone
In music theory, the tritone is defined as a musical interval composed of three adjacent whole tones (six semitones). For instance, the interval from F up to the B above it (in short, F–B) is a tritone as it can be decomposed into the three a ...
(about one half of an octave) that involves the factor seven. There are two that are inverses. The lesser septimal tritone (also Huygens' tritone) is the musical interval with ratio 7:5 (582.51 cents). The greater septimal tritone (also Euler's tritone), is an interval with ratio 10:7 (617.49 cents). They are also known as the sub-fifth and super-fourth, or subminor fifth and supermajor fourth, respectively.
The 7:5 interval (diminished fifth) is equal to a 6:5 minor third plus a 7:6 subminor third.
The 10:7 interval (augmented fourth) is equal to a 5:4 major third plus an 8:7 supermajor second, or a 9:7 supermajor third plus a 10:9 major second.
The difference between these two is the septimal sixth tone (50:49, 34.98 cents) .
12 equal temperament and 22 equal temperament do not distinguish between these tritones; 19 equal temperament does distinguish them but doesn't match them closely. 31 equal temperament
In music, 31 equal temperament, 31-ET, which can also be abbreviated 31-TET (31 tone ET) or 31- EDO (equal division of the octave), also known as tricesimoprimal, is the tempered scale derived by dividing the octave into 31 equal-sized steps (equ ...
and 41 equal temperament both distinguish between and closely match them.
The lesser septimal tritone is the most consonant
In articulatory phonetics, a consonant is a speech sound that is articulated with complete or partial closure of the vocal tract. Examples are and pronounced with the lips; and pronounced with the front of the tongue; and pronounced wit ...
tritone when measured by combination tone
A combination tone (also called resultant or subjective tone)Combination Tone
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harmonic entropy
Paul Erlich (born 1972) is a guitarist and music theorist living near Boston, Massachusetts. He is known for his seminal role in developing the theory of regular temperaments, including being the first to define pajara temperament Accessed 2013 ...
, and period length., ''The Bohlen-Pierce Site''. Depending on the temperament used, "the" tritone, defined as three whole tones, may be identified as either a lesser septimal tritone (in
septimal meantone
In music, septimal meantone temperament, also called ''standard septimal meantone'' or simply ''septimal meantone'', refers to the tempering of 7-limit musical intervals by a meantone temperament tuning in the range from fifths flattened by the am ...
systems), a greater septimal tritone (when the tempered fifth is around 703 cents), neither (as in 72 equal temperament
In music, 72 equal temperament, called twelfth-tone, 72-TET, 72-EDO, or 72-ET, is the tempered scale derived by dividing the octave into twelfth-tones, or in other words 72 equal steps (equal frequency ratios). Each step represents a frequency r ...
), or both (in 12 equal temperament only).
References