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For instance, the above-mentioned C major scale contains the tritones F–B (from F to the B above it, also called augmented fourth) and B–F (from B to the F above it, also called diminished fifth, semidiapente, or semitritonus); [2] the latter is decomposed as a semitone B–C, a whole tone C–D, a whole tone D–E, and a semitone E–F ...
Chapter 8 (The solution of equations of the fifth degree at the Wayback Machine (archived 31 March 2010)) gives a description of the solution of solvable quintics x 5 + cx + d. Victor S. Adamchik and David J. Jeffrey, "Polynomial transformations of Tschirnhaus, Bring and Jerrard," ACM SIGSAM Bulletin, Vol. 37, No. 3, September 2003, pp. 90–94.
The Lydian scale can be described as a major scale with the fourth scale degree raised a semitone, making it an augmented fourth above the tonic, e.g., an F-major scale with a B ♮ rather than B ♭. This mode's augmented fourth and the Locrian mode's diminished fifth are the only modes to have a tritone above the tonic.
Its tonic chord is a diminished triad (B dim = B dim 5 min 3 = B D F, in the Locrian mode using the white-key diatonic scale with starting note B, corresponding to a C major scale starting on its 7th tone). This mode's diminished fifth and the Lydian mode's augmented fourth are the only modes that contain a tritone as a note in their modal scale.
Augmented fifth on C. In Western classical music, an augmented fifth (Play ⓘ) is an interval produced by widening a perfect fifth by a chromatic semitone. [1] [3] For instance, the interval from C to G is a perfect fifth, seven semitones wide, and both the intervals from C ♭ to G, and from C to G ♯ are augmented fifths, spanning eight semitones.
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) Play ⓘ.
Pythagorean interval. Pythagorean perfect fifth on C ⓘ: C-G (3/2 ÷ 1/1 = 3/2). In musical tuning theory, a Pythagorean interval is a musical interval with a frequency ratio equal to a power of two divided by a power of three, or vice versa. [ 1 ] For instance, the perfect fifth with ratio 3/2 (equivalent to 3 1 / 2 1) and the perfect fourth ...
A tritone substitution is the substitution of one dominant seventh chord (possibly altered or extended) with another that is three whole steps (a tritone) from the original chord. In other words, tritone substitution involves replacing V 7 with ♭ II 7[7] (which could also be called ♭ V 7 /V, subV 7, [7] or V 7 / ♭ V [7]).