Interval Progressions Ear Training

Interval classification

Intervals can be described, classified, or compared with each other according to various criteria.

Melodic and harmonic

An interval can be described as

• Vertical or harmonic if the two notes sound simultaneously
• Horizontal, linear, or melodic if they sound successively.^[2]

Diatonic and chromatic

The table above depicts the 56 diatonic intervals formed by the notes of the C major scale (a diatonic scale). Notice that these intervals, as well as any other diatonic interval, can be also formed by the notes of a chromatic scale.

The distinction between diatonic and chromatic intervals is controversial, as it is based on the definition of diatonic scale, which is variable in the literature. For example, the interval B–E♭ (a diminished fourth, occurring in the harmonic C-minor scale) is considered diatonic if the harmonic minor scales are considered diatonic as well.^[9] Otherwise, it is considered chromatic. For further details, see the main article.

By a commonly used definition of diatonic scale^{[lower-alpha 4]} (which excludes the harmonic minor and melodic minor scales), all perfect, major and minor intervals are diatonic. Conversely, no augmented or diminished interval is diatonic, except for the augmented fourth and diminished fifth.

The distinction between diatonic and chromatic intervals may be also sensitive to context. The above-mentioned 56 intervals formed by the C-major scale are sometimes called diatonic to C major. All other intervals are called chromatic to C major. For instance, the perfect fifth A♭–E♭ is chromatic to C major, because A♭ and E♭ are not contained in the C major scale. However, it is diatonic to others, such as the A♭ major scale.

Consonant and dissonant

Consonance and dissonance are relative terms that refer to the stability, or state of repose, of particular musical effects. Dissonant intervals are those that cause tension and desire to be resolved to consonant intervals.

These terms are relative to the usage of different compositional styles.

• In 15th- and 16th-century usage, perfect fifths and octaves, and major and minor thirds and sixths were considered harmonically consonant, and all other intervals dissonant, including the perfect fourth, which by 1473 was described (by Johannes Tinctoris) as dissonant, except between the upper parts of a vertical sonority—for example, with a supporting third below ("6-3 chords").^[10] In the common practice period, it makes more sense to speak of consonant and dissonant chords, and certain intervals previously considered dissonant (such as minor sevenths) became acceptable in certain contexts. However, 16th-century practice was still taught to beginning musicians throughout this period.
• Hermann von Helmholtz (1821–1894) theorised that dissonance was caused by the presence of beats.^[11] von Helmholtz further believed that the beating produced by the upper partials of harmonic sounds was the cause of dissonance for intervals too far apart to produce beating between the fundamentals.^[12] von Helmholtz then designated that two harmonic tones that shared common low partials would be more consonant, as they produced less beats.^[13][14] von Helmholtz disregarded partials above the seventh, as he believed that they were not audible enough to have significant effect.^[15] From this von Helmholtz categorises the octave, perfect fifth, perfect fourth, major sixth, major third, and minor third as consonant, in decreasing value, and other intervals as dissonant.
• David Cope (1997) suggests the concept of interval strength,^[16] in which an interval's strength, consonance, or stability is determined by its approximation to a lower and stronger, or higher and weaker, position in the harmonic series. See also: Lipps–Meyer law and #Interval root

All of the above analyses refer to vertical (simultaneous) intervals.

Simple and compound

A simple interval is an interval spanning at most one octave (see Main intervals above). Intervals spanning more than one octave are called compound intervals, as they can be obtained by adding one or more octaves to a simple interval (see below for details).^[17]

Steps and skips

Linear (melodic) intervals may be described as steps or skips. A step, or conjunct motion,^[18] is a linear interval between two consecutive notes of a scale. Any larger interval is called a skip (also called a leap), or disjunct motion.^[18] In the diatonic scale,^{[lower-alpha 4]} a step is either a minor second (sometimes also called half step) or major second (sometimes also called whole step), with all intervals of a minor third or larger being skips.

For example, C to D (major second) is a step, whereas C to E (major third) is a skip.

More generally, a step is a smaller or narrower interval in a musical line, and a skip is a wider or larger interval, where the categorization of intervals into steps and skips is determined by the tuning system and the pitch space used.

Melodic motion in which the interval between any two consecutive pitches is no more than a step, or, less strictly, where skips are rare, is called stepwise or conjunct melodic motion, as opposed to skipwise or disjunct melodic motions, characterized by frequent skips.

Intervals in chords

Chords are sets of three or more notes. They are typically defined as the combination of intervals starting from a common note called the root of the chord. For instance a major triad is a chord containing three notes defined by the root and two intervals (major third and perfect fifth). Sometimes even a single interval (dyad) is considered a chord.^[20] Chords are classified based on the quality and number of the intervals that define them.

Chord qualities and interval qualities

The main chord qualities are major, minor, augmented, diminished, half-diminished, and dominant. The symbols used for chord quality are similar to those used for interval quality (see above). In addition, + or aug is used for augmented, ° or dim for diminished, ^ø for half diminished, and dom for dominant (the symbol − alone is not used for diminished).

Deducing component intervals from chord names and symbols

The main rules to decode chord names or symbols are summarized below. Further details are given at Rules to decode chord names and symbols.

1. For 3-note chords (triads), major or minor always refer to the interval of the third above the root note, while augmented and diminished always refer to the interval of the fifth above root. The same is true for the corresponding symbols (e.g., Cm means C^m3, and C+ means C⁺⁵). Thus, the terms third and fifth and the corresponding symbols 3 and 5 are typically omitted. This rule can be generalized to all kinds of chords,^{[lower-alpha 5]} provided the above-mentioned qualities appear immediately after the root note, or at the beginning of the chord name or symbol. For instance, in the chord symbols Cm and Cm⁷, m refers to the interval m3, and 3 is omitted. When these qualities do not appear immediately after the root note, or at the beginning of the name or symbol, they should be considered interval qualities, rather than chord qualities. For instance, in Cm^M7 (minor major seventh chord), m is the chord quality and refers to the m3 interval, while M refers to the M7 interval. When the number of an extra interval is specified immediately after chord quality, the quality of that interval may coincide with chord quality (e.g., CM⁷ = CM^M7). However, this is not always true (e.g., Cm⁶ = Cm^M6, C+⁷ = C+^m7, CM¹¹ = CM^P11).^{[lower-alpha 5]} See main article for further details.
2. Without contrary information, a major third interval and a perfect fifth interval (major triad) are implied. For instance, a C chord is a C major triad, and the name C minor seventh (Cm⁷) implies a minor 3rd by rule 1, a perfect 5th by this rule, and a minor 7th by definition (see below). This rule has one exception (see next rule).
3. When the fifth interval is diminished, the third must be minor.^{[lower-alpha 6]} This rule overrides rule 2. For instance, Cdim⁷ implies a diminished 5th by rule 1, a minor 3rd by this rule, and a diminished 7th by definition (see below).
4. Names and symbols that contain only a plain interval number (e.g., “seventh chord”) or the chord root and a number (e.g., “C seventh”, or C⁷) are interpreted as follows:
   • If the number is 2, 4, 6, etc., the chord is a major added tone chord (e.g., C⁶ = C^M6 = C^add6) and contains, together with the implied major triad, an extra major 2nd, perfect 4th, or major 6th (see names and symbols for added tone chords).
   • If the number is 7, 9, 11, 13, etc., the chord is dominant (e.g., C⁷ = C^dom7) and contains, together with the implied major triad, one or more of the following extra intervals: minor 7th, major 9th, perfect 11th, and major 13th (see names and symbols for seventh and extended chords).
   • If the number is 5, the chord (technically not a chord in the traditional sense, but a dyad) is a power chord. Only the root, a perfect fifth and usually an octave are played.