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The diminished fifth is often called a tritone in modern tonal theory, but functionally and notationally it can only resolve inwards as a diminished fifth and is therefore not reckoned a tritone—that is, an interval composed of three adjacent whole tones—in mid-renaissance (early 16th-century) music theory. [19]
diminished fifth (6 semitones), and; augmented fifth (8 semitones). After the unison and octave intervals, the perfect fifth is the most important interval in tonal harmony. It is highly consonant. Its implementation in equal temperament tuning is highly accurate, unlike the major third interval, for example.
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.
Conversely, no augmented or diminished interval is diatonic, except for the augmented fourth and diminished fifth. A ♭-major scale. The distinction between diatonic and chromatic intervals may be also sensitive to context. The above-mentioned 56 intervals formed by the C-major scale are sometimes called diatonic to C major.
The table shows from which notes some of the above listed intervals can be played on an instrument using a repeated-octave 12-tone scale (such as a piano) tuned with D-based symmetric Pythagorean tuning. Further details about this table can be found in Size of Pythagorean intervals. Pythagorean perfect fifth on D Play ⓘ: D-A+ (27/16 ÷ 9/8 ...
This, as shown above, implies that only eleven just fifths are used to build the entire chromatic scale. The remaining interval (the diminished sixth from G ♯ to E ♭) is left badly out-of-tune, meaning that any music which combines those two notes is unplayable in this tuning. A very out-of-tune interval such as this one is known as a wolf ...
The diatonic circle of fifths is the circle of fifths encompassing only members of the diatonic scale. Therefore, it contains a diminished fifth, in C major between B and F. See structure implies multiplicity. The circle progression is commonly a circle of fifths through the diatonic chords, including one diminished chord.
The extremes of the meantone systems encountered in historical practice are the Pythagorean tuning, where the whole tone corresponds to 9:8, i.e. (3:2) 2 / 2 , the mean of the major third (3:2) 4 / 4 , and the fifth (3:2) is not tempered; and the 1 ⁄ 3-comma meantone, where the fifth is tempered to the extent that three ...
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