A septimal tritone is a

tritone In music theory, the tritone is defined as a interval (music), musical interval spanning three adjacent Major second, 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 ...

(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 In music theory, an interval is a difference in pitch (music), pitch between two sounds. An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and v ...

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 12 equal temperament (12-ET) is the musical system that divides the octave into 12 parts, all of which are Equal temperament, equally tempered (equally spaced) on a logarithmic scale, with a ratio equal to the Twelfth root of two, 12th root of 2 ...

and

22 equal temperament In music, 22 equal temperament, called 22-TET, 22- EDO, or 22-ET, is the tempered scale derived by dividing the octave into 22 equal steps (equal frequency ratios). Each step represents a frequency ratio of , or 54.55 cents (). When composing wi ...

do not distinguish between these tritones;

19 equal temperament In music, 19 equal temperament, called 19 TET, 19 EDO ("Equal Division of the Octave"), 19-ED2 ("Equal Division of 2:1) or 19 Equal temperament, ET, is the musical temperament, tempered scale derived by dividing the octave into 19 equal steps ...

does distinguish them but doesn't match them closely.

31 equal temperament In music, 31 equal temperament, which can also be abbreviated (31 tone ) or (equal division of the octave), also known as tricesimoprimal, is the tempered scale derived by dividing the octave into 31 equally-proportioned steps (e ...

and

41 equal temperament 41 may refer to: * 41 (number) * one of the years 41 BC, AD 41, 1941, 2041 Art and entertainment * 41 (film), ''41'' (film), a 2007 documentary about Nicholas O'Neill, the youngest victim of the Station nightclub fire * ''41'', an Australian award ...

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, except for the h sound, which is pronounced without any stricture in the vocal tract. Examples are and pronou ...

tritone when measured by

combination tone A combination tone (also called resultant tone or subjective tone)Combination Tone
, ''Britanni ...

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.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

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 a ...

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 ste ...

), or both (in

only).

References

Augmented fourths Diminished fifths Tritones 7-limit tuning and intervals {{music-theory-stub