page_title: Interval (music)
section_title: Interval root
hierarchical_section_title: Interval (music) / Interval root
caption_attribution_description: English: Harmonic series with intervals labeled. Blue notes differ significantly from equal temperament, though all notes (but 1, 2, 4, 8, and 16) differ some. Source for image with only subminor third, supermajor second, and greater and lesser tone labels: Leta E. Miller and Fredric Lieberman (Summer, 1999). "Lou Harrison and the American Gamelan", p.162, American Music, Vol. 17, No. 2, pp. 146-178. Other labels added by Hyacinth (talk). Created by Hyacinth (talk) using Sibelius. External use: http://www.sengpielaudio.com/calculator-harmonics.htm
context_page_description: In music theory, an interval is the 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 differences between notes of a diatonic scale. 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.
context_section_description: Although intervals are usually designated in relation to their lower note, David Cope and Hindemith both suggest the concept of interval root. To determine an interval's root, one locates its nearest approximation in the harmonic series. The root of a perfect fourth, then, is its top note because it is an octave of the fundamental in the hypothetical harmonic series. The bottom note of every odd diatonically numbered intervals are the roots, as are the tops of all even numbered intervals. The root of a collection of intervals or a chord is thus determined by the interval root of its strongest interval.
  As to its usefulness, Cope provides the example of the final tonic chord of some popular music being traditionally analyzable as a "submediant six-five chord" (added sixth chords by popular terminology), or a first inversion seventh chord (possibly the dominant of the mediant V/iii). According to the interval root of the strongest interval of the chord (in first inversion, CEGA), the perfect fifth (C–G), is the bottom C, the tonic.
caption: Intervals in the harmonic series.
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