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1 Simple diatonic intervals
Below are listed the most commonly used harmonic function, ratio, integer, cents, and relative consonance or dissonance of common diatonic simple intervals. There are many other intervals and ratios, some of which follow.
1.1 Common simple intervals
- Unison: The ratio of 1:1 is a unison, two notes playing the same pitch. In integer notation it is a 0 and is also zero cents. It is the simplest and most consonant of intervals.
- Octave: The ratio of 2:1 is an octave, two notes, one of which is double or half the pitch of the other. It is 1200 cents and in integer notation it is a 0, like the unison. Octave equivalency describes the perception that octaves are the same note, that the same notes repeat throughout the pitch range. Thus C and C', C5 and C3, and C and any C any number of octaves above or below, are all the same note or pitch class. Thus the octave is slightly less or just as consonant as the unison.
- Perfect fifth & perfect fourth: The ratio of is a perfect fifth, two pitches, one note 1.5 times the pitch of another. In integer notation it is 7 and is 700 cents in equal temperament, which is a ratio two (1.955) cents flat of 3:2. The inverse of a perfect fifth is a perfect fourth. A perfect fourth is the ratio , 5 in integer notation, and 500 cents in equal temperament, which is two cents sharp of 4:3. The unison, octave, fifth, and fourth are considered "perfect intervals" and thus the most consonant, in that order.
- Major third & minor sixth: The ratio of is a major third. In integer notation it is 4 and is 400 cents, which is 13.686 cents sharp of 5:4. Its inverse is a minor sixth, 8:5, which is 8 in integer notation and 800 cents in equal temperament, 13.686 cents flat of 8:5. The thirds and sixths are considered the most dynamic and interesting of the consonant intervals, and are thus the least consonant, in the following order: major third, major sixth, minor third, minor sixth.
- Minor third & major sixth: The ratio of is a minor third. In integer notation it is 3, and is 300 cents in equal temperament, which is 15.641 cents flat of 6:5. Its inverse is a major sixth, 5:3, which is 9 in integer notation and 900 cents in equal temperament, which is 15.641 cents sharp of 5:3.
- Major second & minor seventh: The ratio of is a major second. In integer notation it is 2 and is 200 cents, which is 3.91 cents flat of 9:8. Its inverse is a minor seventh, 16:9, which is 10 in integer notation and is 1,000 cents or 3.91 cents sharp of 16:9. It is the first dissonant interval and is commonly used between chord tones such as in the dominant seventh chord, which features the minor seventh between the fifth and second degress of a major scale. A non-equal tempered minor seventh is also one of the blue notes used in the blues and jazz. The major second is also know as a whole tone or whole step.
- Minor second and major seventh: Like the above intervals, many ratios are used for the minor second, but 16:15 is the most common. In integer notation it is 1 and is 100 cents, which is 11.731 cents flat of 16:15, but fairly close to . Its inverse is the major seventh, commonly 15:8, which is 11 in integer notation and 1,100 cents. The minor second and minor seventh are the most dissonant intervals with the possible exception of the tritone, below. The minor second is also known as a semitone, half tone, or half step.
1.2 Augmented and diminished intervals
Along with all seconds and sevenths, all augmented and diminished intervals are considered dissonant. However, in twelve tone equal temperament, most intervals, when augmented or diminished, are enharmonically equivalent to another interval. For example, a diminished minor second is a unison and thus only the fourth and fifth are commonly altered.
- Tritone: The tritone, which may be a diminished fifth or augmented fourth, is 6 in integer notation and 600 cents. It can be approximated by the ratio 17:12, whose inverse is 24:17 and is 6 cents flatter than 17:12. (Ideally, the tritone should equal its own inverse.) It is called "tritone" because it spans three whole steps. It exactly, symmetrically, divides the octave in half and was considered the most dissonant interval, literally "the devil's interval" (diabolus in musica). It plays an important role in the dominant seventh chord.
