Concept
Interval (music)
Overview
In music theory, an interval is a difference in pitch between two sounds. An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or harmonic if it pertains to simultaneously sounding tones, such as in a chord.
In Western music, intervals are most commonly differencing between notes of a diatonic scale. Intervals between successive notes of a scale are also known as scale steps. The smallest of these intervals is a semitone. Intervals smaller than a semitone are called microtones. They can be formed using the notes of various kinds of non-diatonic scales. Some of the very smallest ones are called commas, and describe small discrepancies, observed in some tuning systems, between enharmonically equivalent notes such as C♯ and D♭. Intervals can be arbitrarily small, and even imperceptible to the human ear.
In physical terms, an interval is the ratio between two sonic frequencies. For example, any two notes an octave apart have a frequency ratio of 2:1. This means that successive increments of pitch by the same interval result in an exponential increase of frequency, even though the human ear perceives this as a linear increase in pitch. For this reason, intervals are often measured in cents, a unit derived from the logarithm of the frequency ratio.
In Western music theory, the most common naming scheme for intervals describes two properties of the interval: the quality (perfect, major, minor, augmented, diminished) and number (unison, second, third, etc.). Examples include the minor third or perfect fifth. These names identify not only the difference in semitones between the upper and lower notes but also how the interval is spelled. The importance of spelling stems from the historical practice of differentiating the frequency ratios of enharmonic intervals such as G–G♯ and G–A♭.
Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).
In the original texts
Passages from public-domain books where Interval (music) is discussed.
This takes us to space-time. We have already seen that, in the special theory of relativity, the square of the interval is found by subtracting the square of the distance between the events from the square of the distance that light would travel in the time between them. In the general theory, we do not assume this special form of interval, except at a great distance from matter. Elsewhere, we assume to begin with a…
Bertrand Russell, The A B C of Relativity
names the idea; a chapter is titled for it; states what it is; opens on it
If such a journey is physically impossible, the interval will be the same as the distance as estimated by an observer to whom the two events are simultaneous. But the interval is only definite when the two events are very near together; otherwise the interval depends upon the route chosen for travelling from the one event to the other. Four numbers are needed to fix the position of an event in the world; these…
Bertrand Russell, Philosophy
names the idea; states what it is; opens on it
The close frequently of each of those intervals, but always of every second interval, is marked by a distinct accent. This accent may frequently, with great grace, fall upon the beginning of the first interval; after which, it cannot, without spoiling the verse, fall any where but upon the close of an interval. The syllable or syllables which come after the accent that closes the fifth interval are never accented…
Adam Smith, The Essays of Adam Smith
names the idea; states what it is
And this breadth was to the breadth of the bright Light of the second Fringe as seven to four, and to the dark Interval of the first and second Fringe as three to two, and to the like dark Interval between the second and third as two to one. For the breadths of the Fringes seem'd to be in the progression of the Numbers 1, sqrt(1/3), sqrt(1/5), and their Intervals to be in the same progression with them; that is, the…
Isaac Newton, Opticks
names the idea; opens on it
Life is short, not so much because of the short time it lasts, but because we are allowed scarcely any time to enjoy it. In vain is there a long interval between the hour of death and that of birth; life is still too short, if this interval is not well spent. We are born, so to speak, twice over; born into existence, and born into life; born a human being, and born a man.
Jean-Jacques Rousseau, Emile
states what it is; names the idea
Philosophers who discussed Interval (music)
Related ideas
- Internet Archive
- Latin
- Western culture
- Octave
- Harmony
- Oxford University Press
- Hermann von Helmholtz
- Symmetry
- Ratio
- Melody
- Logarithmic scale
Place in the tradition
Part of Pythagoreanism.