A musical ratio of 15:8.
In classical music from Western culture, a seventh is a musical interval encompassing seven staff positions (see Interval for more details), and the major seventh is one of two commonly occurring sevenths. It is qualified as major because it is the larger of the two. The major seventh spans eleven semitones, its smaller counterpart being the minor seventh, spanning ten semitones. For example, the interval from C to B is a major seventh, as the note B lies eleven semitones above C, and there are seven staff positions from C to B. Diminished and augmented sevenths span the same number of staff positions, but consist of a different number of semitones (nine and twelve). Wikipedia, Major Seventh
Ramsay
Starting again at C major and A minor and going round by the keys in ?s, we come first to D minor and F major. The major gets its ? fourth from the ? sixth of the relative minor; and as the interval between D-E, the major sixth and seventh, must be a 9-comma interval, and its own D-E is only an 8-comma one, it must take the D of A minor, which is a comma lower, and this will correctly show the 9-comma interval between D and E. This is the way of their mutual providing in the region of ?s; the ? sixth of the minor is given to be the ? fourth of the relative major; and the comma-lower fourth of the sub-relative minor becomes the correct sixth of the major. The arrows indicate the source from which, and the place to which; the new notes come and go. [Scientific Basis and Build of Music, page 113]
Hughes
ALTHOUGH only twelve notes of a keyed instrument develope perfect minor harmonics, there are fifteen different chords, the double tones D#-E?, E#-F?, A#-B? all sounding as roots. The fifteen roots are written in musical clef. A major and a minor fifth embrace the same number of key-notes, but the division into threefold chords is different. In counting the twelve, a major fifth has four below the third note of its harmony, and three above it; a minor fifth has three below the third note of its harmony, and four above it. A major seventh includes twelve key-notes, a minor seventh only eleven. As an example of the minor chords in the different keys, we may first examine those in the key of A, written in musical clef. The seven of its harmony have two threefold chords, and two of its ascending scale. If we include the octave note, the highest chord of the descending scale is a repetition (sounding an octave higher) of the lowest chord of the seven in its harmony, and the second chord of the descending scale is a repetition of the first chord of its ascending scale. These two repetition chords are only written to the key of A: the chords of the other eleven keys will all be found exactly to agree with those of A in their mode of development. We may again remark on the beautiful effect which would result if the colours of the minor chords could be seen, with the tones, as they develope. [Harmonies of Tones and Colours, Diagram XII - The Chords of the Twelve Minor Keys, page 37a]
See Also
7.16 - Seventh
Interval
major
Major Scale
Major Second
Major Sixth
Major Third
Scale
Seven
Seventh