Minor third

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Minor third
Inverse major sixth
Name
Other namessesquitone
Abbreviationm3
Size
Semitones 3
Interval class 3
Just interval 6:5, 19:16, 32:27 [1]
Cents
Equal temperament 300
Just intonation 316, 298, 294
Minor third Play (help*info)
equal tempered or just (help*info)
(6:5). Minor third on C.png
Minor third Loudspeaker.svg Play   equal tempered or Loudspeaker.svg just   (6:5).
19th harmonic (19:16), E Play (help*info)
. 19th harmonic on C.png
19th harmonic (19:16), E Loudspeaker.svg Play  .
Comparison, in cents, of intervals at or near a minor third Comparison of minor thirds.png
Comparison, in cents, of intervals at or near a minor third
Jazz and rock bassist Joseph Patrick Moore introducing a cycle of minor thirds

In music theory a minor third is a musical interval that encompasses three half steps, or semitones. Staff notation represents the minor third as encompassing three staff positions (see: interval number). The minor third is one of two commonly occurring thirds. It is called minor because it is the smaller of the two: the major third spans an additional semitone. For example, the interval from A to C is a minor third, as the note C lies three semitones above A. Coincidentally, there are three staff positions from A to C. Diminished and augmented thirds span the same number of staff positions, but consist of a different number of semitones (two and five). The minor third is a skip melodically.

Contents

Notable examples of ascending minor thirds include the opening two notes of "Greensleeves" and of "Light My Fire".

The minor third may be derived from the harmonic series as the interval between the fifth and sixth harmonics, or from the 19th harmonic.

The minor third is commonly used to express sadness in music, and research shows that this mirrors its use in speech, as a tone similar to a minor third is produced during sad speech. [2] It is also a quartal (based on an ascendance of one or more perfect fourths) tertian interval, as opposed to the major third's quintality. The minor third is also obtainable in reference to a fundamental note from the undertone series, while the major third is obtainable as such from the overtone series. (See Otonality and Utonality.)

The minor scale is so named because of the presence of this interval between its tonic and mediant (1st and 3rd) scale degrees. Minor chords too take their name from the presence of this interval built on the chord's root (provided that the interval of a perfect fifth from the root is also present or implied).

A minor third, in just intonation, corresponds to a pitch ratio of 6:5 ( Loudspeaker.svg play  ) or 315.64 cents. In an equal tempered tuning, a minor third is equal to three semitones, a ratio of 21/4:1 (about 1.189), or 300 cents, 15.64 cents narrower than the 6:5 ratio. In other meantone tunings it is wider, and in 19 equal temperament it is very nearly the 6:5 ratio of just intonation; in more complex schismatic temperaments, such as 53 equal temperament, the "minor third" is often significantly flat (being close to Pythagorean tuning ( Loudspeaker.svg play  )), although the "augmented second" produced by such scales is often within ten cents of a pure 6:5 ratio. If a minor third is tuned in accordance with the fundamental of the overtone series, the result is a ratio of 19:16 or 297.51 cents (the nineteenth harmonic Loudspeaker.svg Play  ). [3] The 12-TET minor third (300 cents) more closely approximates the nineteenth harmonic with only 2.49 cents error. [4] M. Ergo mistakenly claimed that the nineteenth harmonic was the highest ever written, for the bass-trumpet in Richard Wagner's WWV 86 Der Ring des Nibelungen (1848 to 1874), when Robert Schumann's Op. 86 Konzertstück for 4 Horns and Orchestra (1849) features the twentieth harmonic (four octaves and major third above the fundamental) in the first horn part three times. [5]

Other pitch ratios are given related names, the septimal minor third with ratio 7:6 and the tridecimal minor third with ratio 13:11 in particular.

The minor third is classed as an imperfect consonance and is considered one of the most consonant intervals after the unison, octave, perfect fifth, and perfect fourth.

The sopranino saxophone and E♭ clarinet sound in the concert pitch ( C ) a minor third higher than the written pitch; therefore, to get the sounding pitch one must transpose the written pitch up a minor third. Instruments in A – most commonly the A clarinet, sound a minor third lower than the written pitch.

Pythagorean minor third

Semiditone (32:27) on C Play (help*info)
. Semiditone on C.png
Semiditone (32:27) on C Loudspeaker.svg Play  .
Semiditone as two octaves minus three justly tuned fifths. Semiditone.png
Semiditone as two octaves minus three justly tuned fifths.

In music theory, a semiditone (or Pythagorean minor third) [6] is the interval 32:27 (approximately 294.13 cents). It is the minor third in Pythagorean tuning. The 32:27 Pythagorean minor third arises in the C major scale between D and F. [7] Loudspeaker.svg Play  

It can be thought of as two octaves minus three justly tuned fifths. It is narrower than a justly tuned minor third by a syntonic comma.

See also

Related Research Articles

Equal temperament The musical tuning system where the ratio between successive notes is constant

An equal temperament is a musical temperament or tuning system, which approximates just intervals by dividing an octave into equal steps. This means the ratio of the frequencies of any adjacent pair of notes is the same, which gives an equal perceived step size as pitch is perceived roughly as the logarithm of frequency.

Just intonation Musical tuning based on pure intervals

In music, just intonation or pure intonation is the tuning of musical intervals as whole number ratios of frequencies. Any interval tuned in this way is called a just interval. Just intervals consist of members of a single harmonic series of a (lower) implied fundamental. For example, in the diagram, the notes G and middle C are both members of the harmonic series of the lowest C and their frequencies will be 3 and 4 times, respectively, the fundamental frequency; thus, their interval ratio will be 4:3. If the frequency of the fundamental is 50 Hertz, the frequencies of the two notes in question would be 150 and 200.

Musical tuning Terms for tuning an instrument and a systems of pitches

In music, there are two common meanings for tuning:

Pythagorean tuning

Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are based on the ratio 3:2. This ratio, also known as the "pure" perfect fifth, is chosen because it is one of the most consonant and easiest to tune by ear and because of importance attributed to the integer 3. As Novalis put it, "The musical proportions seem to me to be particularly correct natural proportions." Alternatively, it can be described as the tuning of the syntonic temperament in which the generator is the ratio 3:2, which is ≈702 cents wide.

Meantone temperament

Meantone temperament is a musical temperament, that is a tuning system, obtained by slightly compromising the fifths in order to improve the thirds. Meantone temperaments are constructed the same way as Pythagorean tuning, as a stack of equal fifths, but in meantone each fifth is narrow compared to the perfect fifth of ratio 3:2.

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.

Perfect fifth musical interval

In music theory, a perfect fifth is the musical interval corresponding to a pair of pitches with a frequency ratio of 3:2, or very nearly so.

Semitone musical interval

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. For example, C is adjacent to C; the interval between them is a semitone.

Major sixth musical interval

In music from Western culture, a sixth is a musical interval encompassing six note letter names or staff positions, and the major sixth is one of two commonly occurring sixths. It is qualified as major because it is the larger of the two. The major sixth spans nine semitones. Its smaller counterpart, the minor sixth, spans eight semitones. For example, the interval from C up to the nearest A is a major sixth. It is a sixth because it encompasses six note letter names and six staff positions. It is a major sixth, not a minor sixth, because the note A lies nine semitones above C. Diminished and augmented sixths span the same number of note letter names and staff positions, but consist of a different number of semitones.

The intervals from the tonic (keynote) in an upward direction to the second, to the third, to the sixth, and to the seventh scale degrees (of a major scale are called major.

Minor sixth musical interval

In Western classical music, a minor sixth is a musical interval encompassing six staff positions, and is one of two commonly occurring sixths. It is qualified as minor because it is the smaller of the two: the minor sixth spans eight semitones, the major sixth nine. For example, the interval from A to F is a minor sixth, as the note F lies eight semitones above A, and there are six staff positions from A to F. Diminished and augmented sixths span the same number of staff positions, but consist of a different number of semitones.

Minor chord

In music theory, a minor chord is a chord that has a root, a minor third, and a perfect fifth. When a chord has these three notes alone, it is called a minor triad. For example, the minor triad built on C, called a C minor triad, has pitches C–E–G:

A schismatic temperament is a musical tuning system that results from tempering the schisma of 32805:32768 to a unison. It is also called the schismic temperament, Helmholtz temperament, or quasi-Pythagorean temperament.

Comma (music)

In music theory, a comma is a very small interval, the difference resulting from tuning one note two different ways. The word comma used without qualification refers to the syntonic comma, which can be defined, for instance, as the difference between an F tuned using the D-based Pythagorean tuning system, and another F tuned using the D-based quarter-comma meantone tuning system. Intervals separated by the ratio 81:80 are considered the same note because the 12-note Western chromatic scale does not distinguish Pythagorean intervals from 5-limit intervals in its notation. Other intervals are considered commas because of the enharmonic equivalences of a tuning system. For example, in 53TET, B and A are both approximated by the same interval although they are a septimal kleisma apart.

Quarter-comma meantone, or 14-comma meantone, was the most common meantone temperament in the sixteenth and seventeenth centuries, and was sometimes used later. In this system the perfect fifth is flattened by one quarter of a syntonic comma (81:80), with respect to its just intonation used in Pythagorean tuning ; the result is , or a fifth of cents. This fifth is then iterated to generate the diatonic scale and other notes of the temperament. The purpose is to obtain justly intoned major thirds. It was described by Pietro Aron in his Toscanello de la Musica of 1523, by saying the major thirds should be tuned to be "sonorous and just, as united as possible." Later theorists Gioseffo Zarlino and Francisco de Salinas described the tuning with mathematical exactitude.

Twelve-tone equal temperament is the musical system that divides the octave into 12 parts, all of which are equally-tempered (equally-spaced) on a logarithmic scale, with a ratio equal to the 12th root of 2. That resulting smallest interval, ​112 the width of an octave, is called a semitone or half step.

Pythagorean interval Musical interval

In musical tuning theory, a Pythagorean interval is a musical interval with frequency ratio equal to a power of two divided by a power of three, or vice versa. For instance, the perfect fifth with ratio 3/2 (equivalent to 31/21) and the perfect fourth with ratio 4/3 (equivalent to 22/31) are Pythagorean intervals.

Music and mathematics Relationships between music and mathematics

Music theory has no axiomatic foundation in modern mathematics, although some interesting work has recently been done in this direction, yet the basis of musical sound can be described mathematically and exhibits "a remarkable array of number properties". Elements of music such as its form, rhythm and metre, the pitches of its notes and the tempo of its pulse can be related to the measurement of time and frequency, offering ready analogies in geometry.

Musical temperament A tuning system that slightly compromises the pure intervals of just intonation to meet other requirements

In musical tuning, a temperament is a tuning system that slightly compromises the pure intervals of just intonation to meet other requirements. Most modern Western musical instruments are tuned in the equal temperament system. Tempering is the process of altering the size of an interval by making it narrower or wider than pure. "Any plan that describes the adjustments to the sizes of some or all of the twelve fifth intervals in the circle of fifths so that they accommodate pure octaves and produce certain sizes of major thirds is called a temperament." Temperament is especially important for keyboard instruments, which typically allow a player to play only the pitches assigned to the various keys, and lack any way to alter pitch of a note in performance. Historically, the use of just intonation, Pythagorean tuning and meantone temperament meant that such instruments could sound "in tune" in one key, or some keys, but would then have more dissonance in other keys.

A[n anomalous chord is,] A chord containing an interval which has been made very sharp or flat in tempering the scale for instruments of fixed pitches.

Regular diatonic tuning

A regular diatonic tuning is any musical scale consisting of "tones" (T) and "semitones" (S) arranged in any rotation of the sequence TTSTTTS which adds up to the octave with all the T's being the same size and all the S's the being the same size, with the 'S's being smaller than the 'T's. In such a tuning, then the notes are connected together in a chain of seven fifths, all the same size which makes it a Linear temperament with the tempered fifth as a generator.

Five-limit tuning

Five-limit tuning, 5-limit tuning, or 5-prime-limit tuning (not to be confused with 5-odd-limit tuning), is any system for tuning a musical instrument that obtains the frequency of each note by multiplying the frequency of a given reference note (the base note) by products of integer powers of 2, 3, or 5 (prime numbers limited to 5 or lower), such as 2−3·31·51 = 15/8.

References

  1. Haluska, Jan (2003). The Mathematical Theory of Tone Systems, p.xxiv. ISBN   0-8247-4714-3. 19th harmonic, overtone minor tone.
  2. Curtis ME, Bharucha JJ (June 2010). "The minor third communicates sadness in speech, mirroring its use in music". Emotion. 10 (3): 335–48. doi:10.1037/a0017928. PMID   20515223.
  3. Dowsett, Peter (2015). Audio Production Tips: Getting the Sound Right at the Source, p.3.6.3. CRC. ISBN   9781317614203. "The minor third, however, does not appear in the harmonic series until the nineteenth harmmonic. Your ear almost expects to hear the major third ([on A:] C), and when that is replaced with a more distantly related note, this makes the listener feel more 'unpleasant', 'tense', or 'sad'."
  4. Alexander J. Ellis (translating Hermann Helmholtz): On the Sensations of Tone as a Physiological Basis for the Theory of Music, page 455. Dover Publications, Inc., New York, 1954. "16:19...The 19th harmonic, ex. 297.513 [cents]". Later reprintings: ISBN   1-150-36602-8 or ISBN   1-143-49451-2.
  5. Prout, Ebenezer (December 1, 1908). "In the Forecourts of Instrumentation", The Monthly Musical Record . p.268.
  6. John Fonville. "Ben Johnston's Extended Just Intonation- A Guide for Interpreters", p.124, Perspectives of New Music, Vol. 29, No. 2 (Summer, 1991), pp. 106-137.
  7. Paul, Oscar (1885). A manual of harmony for use in music-schools and seminaries and for self-instruction , p.165. Theodore Baker, trans. G. Schirmer.