Fifteenth

In music, a fifteenth or double octave, abbreviated 15^ma, is the interval between one musical note and another with one-quarter the wavelength or quadruple the frequency. It has also been referred to as the bisdiapason. The fourth harmonic, it is two octaves. It is referred to as a fifteenth because, in the diatonic scale, there are 15 notes between them if one counts both ends (as is customary). Two octaves (based on the Italian word for eighth) do not make a sixteenth, but a fifteenth. In other contexts, the term two octaves is likely to be used.

For example, if one note has a frequency of 400 Hz, the note a fifteenth above it is at 1600 Hz (15^ma ), and the note a fifteenth below is at 100 Hz (15^mb ). The ratio of frequencies of two notes a fifteenth apart is therefore 4:1.

As the fifteenth is a multiple of octaves, the human ear tends to hear both notes as being essentially "the same", as it does the octave. Like the octave, in the Western system of music notation notes a fifteenth apart are given the same name—the name of a note an octave above A is also A. However, because of the large frequency distance between the notes, it is less likely than an octave to be judged the same pitch by non-musicians. Passages in parallel fifteenths are much less common than parallel octaves. In particular, sometimes an organist will use two stops a fifteenth away (notated as 2′).

Seventh (chord)

In music, the seventh factor of a chord is the note or pitch seven scale degrees above the root or tonal center. When the seventh is the bass note, or lowest note, of the expressed chord, the chord is in third inversion  Play .

Conventionally, the seventh is fourth in importance to the root, fifth, and third, with third inversion being the third strongest inversion and the seventh variably minor or major. In jazz chords and theory, the seventh is required in a seventh chord, and the fifth is often omitted in preference for it and the chord quality determining third, chord extensions, and additions.

The seventh is most commonly minor or major (in C, B♭ or B♮) or less often diminished or augmented (B=A or B♯=C).

Resolution

In the common practice period the "strict resolution" the chord seventh is stepwise downward. For example, the seventh of the dominant seventh chord, resolving to tonic, moves downward to the third of the following chord.

See also

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