In music theory Music theory is the field of study that deals with how music works. It examines the language and notation of music. It seeks to identify patterns and structures found in composers' techniques, across or within genres, styles, or historical periods. In a grand sense, music theory distills and analyzes the fundamental parameters or elements of music, the term interval describes the relationship between the pitches Pitch represents the perceived fundamental frequency of a sound. It is one of the four major auditory attributes of sounds along with loudness, timbre and sound source location. When the actual fundamental frequency can be precisely determined through physical measurement, it may differ from the perceived pitch because of overtones, also known as of two notes Notes are the "atoms" of much Western music: discretizations of musical phenomena that facilitate performance, comprehension, and analysis.
Intervals may be described as:
- vertical (or harmonic In music, harmony is the use of simultaneous pitches , or chords. The study of harmony involves chords and their construction and chord progressions and the principles of connection that govern them. Harmony is often said to refer to the "vertical" aspect of music, as distinguished from melodic line, or the "horizontal" aspect) if the two notes sound simultaneously
- linear (or melodic A melody , also tune, voice, or line, is a linear succession of musical tones which is perceived as a single entity. In its most literal sense, a melody is a sequence of pitches and durations, while, more figuratively, the term has occasionally been extended to include successions of other musical elements such as tone color), if the notes sound successively.[1]
Interval class In musical set theory, an interval class , also known as unordered pitch-class interval, interval distance, undirected interval, or (completely incorrectly) interval mod 6 (Rahn 1980, 29; Whittall 2008, 273–74), is the shortest distance in pitch class space between two unordered pitch classes. For example, the interval class between pitch is a system of labelling intervals when the order of the notes is left unspecified, therefore describing an interval in terms of the shortest distance possible between its two pitch classes In music, a pitch class is a set of all pitches that are a whole number of octaves apart, e.g., the pitch class C consists of the Cs in all octaves. "The pitch class C stands for all possible Cs, in whatever octave position." Thus, using scientific pitch notation, the pitch class "C" is the infinite set.[2]
Frequency ratios
Intervals may be labelled according to the ratio In mathematics, a ratio is a relationship between two numbers of the same kind , usually expressed as "a to b" or a:b, sometimes expressed arithmetically as a dimensionless quotient of the two, which explicitly indicates how many times the first number contains the second of frequencies Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency. The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency. Loosely speaking, 1 year is the period of the Earth's orbit around the Sun, and the Earth's rotation on its axis has of the two pitches. Important intervals are those using the lowest integers, such as 1:1 (unison Unison may refer to the pseudo-interval formed by a tone and its duplication , for example c-c, as differentiated from the second, c-d, etc. In the unison the two pitches have the ratio of 1:1 or 0 half steps and zero cents. Although two tones in unison are considered to be the same pitch, they are still perceivable as coming from separate sources, or prime), 2:1 (octave In music, an octave ( Play ) is the interval between one musical pitch and another with half or double its frequency. Using notes, this would be the same note up or down 12 semi-tones on the chromatic scale. For example, an A4 note would be one octave lower than an A5 note, and one octave higher than an A3 note. The octave relationship is a), 3:2 (perfect fifth The perfect fifth is the musical interval between a note and the note seven semitones above it on the musical scale. For example, the note G lies a perfect fifth above C; D is a perfect fifth above G, C is a perfect fifth above F. The perfect fifth may be derived from the harmonic series as the interval between the second and third harmonics), 4:3 (perfect fourth The perfect fourth ( Play ) is a musical interval which spans four scale degrees. It consists of the note and the note five semitones above it on the musical scale. For example, the interval between a C and the next F above it is a perfect fourth; similarly the interval between a G and the next C above it, between an F and the B flat above it, and), etc. This system is frequently used to describe intervals in both Western and non-Western music. This method is also often used in just intonation In music, just intonation is any musical tuning in which the frequencies of notes are related by ratios of small whole numbers. Any interval tuned in this way is called a just interval. The two notes in any just interval are members of the same harmonic series. Arbitrary frequency ratios such as 1024:927 are not generally said to be justly tuned, and in theoretical explanations of equal-tempered intervals used in European tonal music, to explain them through their approximation of just intervals.
Interval number and quality
Number
Interval namesIn Western harmonic theory, intervals are labeled according to the number of scale steps In music theory, a scale degree is the name of a particular note of a scale in relation to the tonic . The degrees of the traditional major and minor scales may be identified several ways: or staff positions In standard Western musical notation, the staff or stave is a set of five horizontal lines and four spaces, each of which represents a different musical pitch, or, in the case of a percussion staff, different percussion instruments. Appropriate music symbols, depending upon the intended effect, are placed on the staff according to their they encompass, as shown at right.
Intervals larger than an octave In music, an octave ( Play ) is the interval between one musical pitch and another with half or double its frequency. Using notes, this would be the same note up or down 12 semi-tones on the chromatic scale. For example, an A4 note would be one octave lower than an A5 note, and one octave higher than an A3 note. The octave relationship is a are called compound intervals; for example, a tenth is known as a compound third.[3] The quality of the compound interval is determined by the quality of the interval on which it is based. For example, a perfect eleventh is the same as a compound perfect fourth.
Intervals larger than a thirteenth seldom need to be spoken of, most often being referred to by their compound names, for example "two octaves plus a fifth"[4] rather than "a 19th".
The name or the label of an interval is determined by counting the number of diatonic degrees between the two notes Notes are the "atoms" of much Western music: discretizations of musical phenomena that facilitate performance, comprehension, and analysis beginning with one for the lower note. The number of degrees between C and G for example is 5, therefore the interval is a fifth.
Quality
The name of any interval is further qualified using the terms perfect, major In music, the adjectives major and minor can describe a scale, key, chord, or interval, minor In music, the adjectives major and minor can describe a scale, key, chord, or interval, augmented In music and music theory augmentation is the lengthening or widening of rhythms, melodies, intervals or chords. The opposite is diminution, and diminished Diminution, from Italian diminuimento, is a musical term used to mean different things in the context of intervals, scales, chords or note values. This is called its interval quality.
It is possible to have doubly-diminished and doubly-augmented intervals, but these are quite rare.
The name of an interval cannot, in general, be determined by counting semitones alone. For example, there are four semitones between A and C♯, between B and E♭, and between C♭ and D♯, but the first is a major third, the second a diminished fourth, and the third a doubly augmented second. The diminished fourth is an interval found between the seventh and third degrees of the harmonic minor scale, while the doubly augmented second only occurs in entirely chromatic contexts. In equal-tempered tuning Equal temperament is a musical temperament, or a system of tuning in which every pair of adjacent notes has an identical frequency ratio. In equal temperament tunings, an interval — usually the octave — is divided into a series of equal steps . For classical music, the most common tuning system is twelve-tone equal temperament, inconsistently, as on a piano, these intervals are indistinguishable by sound when played in isolation, but in musical context the diatonic function A diatonic function, in tonal music theory, is the specific, recognized role of each of the 7 notes and their chords in relation to the key. "Role" in this context means the degree of tension produced by a moving away to a note, chord or scale other than the tonic; and at the same time "how" this musical tension would be eased ( of the notes incorporated is very different.
- Major/minor:
Major and minor intervals are so-called because certain diatonic intervals (seconds, thirds, sixths, sevenths, and their compounds) may occur in two sizes in the diatonic scale. The larger of the two versions is called major, the smaller one minor. For example, the third occurs both as three semitones away from Re, Mi, La, and Ti in the major scale (or in the C Ionian Diatonic scale, three semitones above D, E, A, and B), and four semitones away from Do, Fa, and Sol, (or C, F, and G). The smaller, three-semitone version is called the "minor third" and the larger, four-semitone one is called the "major third". Major intervals invert to minor ones, and vice-versa. For example, a major second inverts to a minor seventh, and the reverse.
- Perfect:
Perfect intervals are so-called because of their high levels of consonance, and because the inversion of a perfect interval is also perfect. Within the diatonic scale all fourths and fifths are perfect, with five and seven semitones respectively, except for one occurrence each of six semitones: the fourth between Fa and Ti, and the fifth between Ti and Fa—an augmented fourth and a diminished fifth, respectively
- Augmented/diminished:
Augmented and diminished intervals are so called because they exceed or fall short of either a perfect interval, or a major/minor pair by one semitone, while falling on the same scale degrees (letter-names). Except for the augmented fourth and diminished fifth, they do not appear in the diatonic scale. For instance, there is no three-semitone interval in the diatonic scale that functions as a second, and the augmented second (e.g., E♭–F♯) is three semitones wide.
Diatonic and chromatic intervals
The intervals contained in the table are diatonic Diatonic and chromatic are terms in music theory that are most often used to characterize scales, and are also applied to intervals, chords, notes, musical styles, and kinds of harmony. They are very often used as a pair, especially when applied to contrasting features of the common practice music of the period 1600–1900 to C major. All other intervals are chromatic to C major.A diatonic interval is an interval formed by two notes of a diatonic scale In music theory, a diatonic scale is a seven note octave-repeating musical scale comprising five whole steps and two half steps for each octave, in which the two half steps are separated from each other by either two or three whole steps. This pattern ensures that, in a diatonic scale spanning more than one octave, all the half steps are maximally. The table on the right depicts all diatonic intervals for C major.
Shorthand notation
Intervals are often abbreviated with a P for perfect, m for minor, M for major Major is a rank of commissioned officer, with corresponding ranks existing in almost every military in the world, d for diminished, A for augmented, followed by the diatonic interval number. The indication M and P are often omitted. The octave In music, an octave ( Play ) is the interval between one musical pitch and another with half or double its frequency. Using notes, this would be the same note up or down 12 semi-tones on the chromatic scale. For example, an A4 note would be one octave lower than an A5 note, and one octave higher than an A3 note. The octave relationship is a is P8, and a unison Unison may refer to the pseudo-interval formed by a tone and its duplication , for example c-c, as differentiated from the second, c-d, etc. In the unison the two pitches have the ratio of 1:1 or 0 half steps and zero cents. Although two tones in unison are considered to be the same pitch, they are still perceivable as coming from separate sources, is usually referred to simply as "a unison" but can be labeled P1. The tritone The tritone ( Play , tri- "three" and tone) is a musical interval that spans three whole tones. The tritone, sometimes known as the "Diabolus in Musica", refers to either the augmented fourth or the diminished fifth, which in 12-tone equal temperament are enharmonic equivalents. It is often used as the main interval of, an augmented fourth or diminished fifth is often TT. Examples:
- m2: minor second
- M3: major third
- P5: perfect fifth
- m9: minor ninth.
For use in describing chords Chord notation refers to the written notation for musical chords and chord-like intervals using chord symbols. Although these symbols are used occasionally in classical music, they are "universally used in jazz and popular music" to specify the harmony of compositions, usually inside lead sheets and fake books, the sign + is used for augmented and ° for diminished. Furthermore the 3 for the third is often omitted, and for the seventh, the plain form stands for the minor interval, while the major is indicated by maj. So for example:
- m: minor third (with perfect fifth)
- 7: minor seventh (with major third and perfect fifth, dominant seventh Of all the seventh chords, perhaps the most important to understand is the 'dominant seventh' play , a major triad with a minor seventh. It was the first seventh chord to appear regularly in Western music. The name comes from the fact that it occurs naturally in the seventh chord built on the dominant (fifth) scale degree of a given major key)
- m7: minor seventh (with minor third and perfect fifth)
- °7: diminished seventh (with minor third and diminished fifth)
- ø7: half-diminished seventh (minor seventh with minor third and diminished fifth)
- maj7: major seventh (with major third and perfect fifth)
- +5: augmented fifth (with major third)
- °5: diminished fifth (with minor third).
Enharmonic intervals
Two intervals are considered to be enharmonic In modern music and notation, an enharmonic equivalent is a note , interval (enharmonic interval), or key signature which is equivalent to some other note, interval, or key signature, but "spelled", or named, differently. Thus, the enharmonic spelling of a written note, interval or chord is an enharmonic equivalent to the way that note,, or enharmonically equivalent, if they both contain the same pitches Pitch represents the perceived fundamental frequency of a sound. It is one of the four major auditory attributes of sounds along with loudness, timbre and sound source location. When the actual fundamental frequency can be precisely determined through physical measurement, it may differ from the perceived pitch because of overtones, also known as spelled in different ways; that is, if the notes in the two intervals are themselves enharmonically equivalent. Enharmonic intervals span the same number of semitones A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically. It is defined as the interval between two adjacent notes in a 12-tone scale . This implies that its size is exactly or approximately equal to 100 cents, a. For example, as shown in the matrix below, F♯–A♯ (a major third), G♭–B♭ (also a major third), F♯–B♭ (a diminished fourth), and G♭–A♯ (a double augmented second) are all enharmonically equivalent — and they all span four semitones.
| step | 1 | 2 | 3 | 4 |
|---|---|---|---|---|
| major third | F♯ | A♯ | ||
| major third | G♭ | B♭ | ||
| diminished fourth | F♯ | B♭ | ||
| double augmented second | G♭ | A♯ |
|
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Q. I need help with intervals. I need 5 examples of intervals for a group class at my piano school. This was the first group class I actually went to so I don't know a lot about intervals. I need 5 examples and the answers. Also I need to know WHY they are a 'minor whatever' or a 'perfect whatever.'
Asked by iluvcocoa23 - Thu Apr 23 15:25:22 2009 - - 1 Answers - 0 Comments
A. C to D Major second because it moves a 2 half steps C to E Major third because it moves 4 half steps and A to C Minor third because it moves 3 half steps and E to F Minor second because it moves 1 half step A to E Perfect fifth because it moves 7 half steps
Answered by ilovestrawberry.com - Thu Apr 23 15:33:44 2009
