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Inverse | major third |
---|---|

Name | |

Other names | minor hexachord, hexachordon minus, lesser hexachord |

Abbreviation | m6 |

Size | |

Semitones | 8 |

Interval class | 4 |

Just interval | 8:5, 11:7, 128:81 |

Cents | |

Equal temperament | 800 |

24 equal temperament | 800 |

Just intonation | 814, 782, 792 |

In classical music from Western culture, a **sixth** is a musical interval encompassing six staff positions (see Interval number for more details), and the **minor sixth** 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 (seven and ten).

**Classical music** is art music produced or rooted in the traditions of Western culture, including both liturgical (religious) and secular music. While a more precise term is also used to refer to the period from 1750 to 1820, this article is about the broad span of time from before the 6th century AD to the present day, which includes the Classical period and various other periods. The central norms of this tradition became codified between 1550 and 1900, which is known as the common-practice period.

**Western culture**, sometimes equated with **Western civilization**, **Occidental culture**, the **Western world**, **Western society**, and **European civilization**, is a term used very broadly to refer to a heritage of social norms, ethical values, traditional customs, belief systems, political systems and specific artifacts and technologies that have some origin or association with Europe. The term also applies beyond Europe to countries and cultures whose histories are strongly connected to Europe by immigration, colonization, or influence. For example, Western culture includes countries in the Americas and Australasia, whose language and demographic ethnicity majorities are European. The development of western culture has been strongly influenced by Christianity.

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 equal temperament, the minor sixth is enharmonically equivalent to the augmented fifth. It occurs in first inversion major and dominant seventh chords and second inversion minor chords.

In classical music from Western culture, an **augmented fifth** is an interval produced by widening a perfect fifth by a chromatic semitone. For instance, the interval from C to G is a perfect fifth, seven semitones wide, and both the intervals from C♭ to G, and from C to G♯ are augmented fifths, spanning eight semitones. Being augmented, it is considered a dissonant interval.

A minor sixth in just intonation most often corresponds to a pitch ratio of 8:5 or 1.6:1 (^{ [1] }^{ [2] }^{ [3] } in 12-tone equal temperament, a minor sixth is equal to eight semitones, a ratio of 2^{2/3}:1 (about 1.587), or 800 cents, 13.7 cents smaller. The ratios of both major and minor sixths are corresponding numbers of the Fibonacci sequence, 5 and 8 for a minor sixth and 3 and 5 for a major.

In music, **just intonation** or pure intonation is the tuning of musical intervals as (small) whole number ratios of frequencies. Any interval tuned in this way is called a **just interval**. Just intervals and chords are aggregates of harmonic series partials and may be seen as sharing a (lower) implied fundamental. For example, a tone with a frequency of 300 Hz and another with a frequency of 200 Hz are both multiples of 100 Hz. Their interval is, therefore, an aggregate of the second and third partials of the harmonic series of an implied fundamental frequency 100 Hz.

An **equal temperament** is a musical temperament, or a system of tuning, in which the frequency interval between every pair of adjacent notes has the same ratio. In other words, the ratios of the frequencies of any adjacent pair of notes is the same, and, as pitch is perceived roughly as the logarithm of frequency, equal perceived "distance" from every note to its nearest neighbor.

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.

The 11:7 **undecimal minor sixth** is 782.49 cents.^{ [4] } (^{ [5] }

**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.

See also the subminor sixth, which includes ratios such as 14:9 and 63:40.^{ [6] } of 764.9 cents^{ [7] }^{ [8] } or 786.4 cents,

The minor sixth is one of consonances of common practice music, along with the unison, octave, perfect fifth, major and minor thirds, major sixth and (sometimes) the perfect fourth. In the common practice period, sixths were considered interesting and dynamic consonances along with their inverses the thirds, but in medieval times they were considered dissonances unusable in a stable final sonority; however in that period they were tuned very flat, to the Pythagorean minor sixth of 128/81. In just intonation, the minor sixth is classed as a consonance of the 5-limit.

In music, **unison** is two or more musical parts sounding the same pitch or at an octave interval, usually at the same time.

In music, an **octave** or **perfect octave** is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems". The interval between the first and second harmonics of the harmonic series is an octave.

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.

Any note will only appear in major scales from any of its minor sixth major scale notes (for example, C is the minor sixth note from E and E will only appear in C, D, E, F, G, A and B major scales).

Inverse | supermajor third |
---|---|

Name | |

Abbreviation | m6 |

Size | |

Semitones | 8 |

Interval class | 4 |

Just interval | 14:9^{ [9] } or 63:40 |

Cents | |

Equal temperament | 800 |

24 equal temperament | 750 |

Just intonation | 765 or 786 |

- ↑ Hermann von Helmholtz and Alexander John Ellis (1912).
*On the Sensations of Tone as a Physiological Basis for the Theory of Music*, p.456. - ↑ Partch, Harry (1979).
*Genesis of a Music*, p.68. ISBN 0-306-80106-X. - ↑ Benson, David J. (2006).
*Music: A Mathematical Offering*, p.370. ISBN 0-521-85387-7. - ↑ International Institute for Advanced Studies in Systems Research and Cybernetics (2003).
*Systems Research in the Arts*: Music, Environmental Design, and the Choreography of Space, Volume 5, p.18. ISBN 1-894613-32-5. "The proportion 11:7, obtained by isolating one 35° angle from its complement within the 90° quadrant, similarly corresponds to an undecimal minor sixth (782.5 cents)." - ↑ Benson (2006), p.163.
- ↑ Jan Haluska (2003).
*The Mathematical Theory of Tone Systems*, p.xxiii. ISBN 0-8247-4714-3. - ↑ Duckworth & Fleming (1996).
*Sound and Light: La Monte Young & Marian Zazeela*, p.167. ISBN 0-8387-5346-9. - ↑ Hewitt, Michael (2000).
*The Tonal Phoenix*, p.137. ISBN 3-922626-96-3. - ↑ Haluska, Jan (2003).
*The Mathematical Theory of Tone Systems*, p.xxiii. ISBN 0-8247-4714-3. Septimal minor sixth.

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In the music theory of Western culture, 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. 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, and (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. The minor third is a skip melodically.

In classical music from Western culture, a **seventh** is a musical interval encompassing seven staff positions, and the **major seventh** is one of two commonly occurring sevenths. It is qualified as *major* because it is the larger of the two. The major seventh spans eleven semitones, its smaller counterpart being the minor seventh, spanning ten semitones. For example, the interval from C to B is a major seventh, as the note B lies eleven semitones above C, and there are seven staff positions from C to B. Diminished and augmented sevenths span the same number of staff positions, but consist of a different number of semitones.

In music theory, a **minor seventh** is one of two musical intervals that span seven staff positions. It is *minor* because it is the smaller of the two sevenths, spanning ten semitones. The major seventh spans eleven. For example, the interval from A to G is a minor seventh, as the note G lies ten semitones above A, and there are seven staff positions from A to G. Diminished and augmented sevenths span the same number of staff positions, but consist of a different number of semitones.

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.

In classical music from Western culture, an **augmented sixth** is an interval produced by widening a major sixth by a chromatic semitone. For instance, the interval from C to A is a major sixth, nine semitones wide, and both the intervals from C♭ to A, and from C to A♯ are augmented sixths, spanning ten semitones. Being augmented, it is considered a dissonant interval.

In music theory, a **comma** is a minute 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

In classical music from Western culture, an **augmented second** is an interval that, in equal temperament, is sonically equivalent to a minor third, spanning three semitones, and is created by widening a major second by a chromatic semitone. For instance, the interval from C to D is a major second, two semitones wide, and the interval from C to D♯ is an augmented second, spanning three semitones.

The **diaschisma** is a small musical interval defined as the difference between three octaves and four perfect fifths plus two major thirds. It can be represented by the ratio 2048:2025 and is about 19.5 cents. The use of the name diaschisma for this interval is due to Helmholtz; earlier Rameau had called that interval a "diminished comma" or **comma minor**.

In music, the **septimal semicomma**, a seven-limit semicomma, is the ratio 126/125 and is equal to approximately 13.79 cents. It is also called the *small septimal comma* and the *starling comma* after its use in starling temperament.

In classical music from Western culture, a **diminished third** is the musical interval produced by narrowing a minor third by a chromatic semitone. For instance, the interval from A to C is a minor third, three semitones wide, and both the intervals from A♯ to C, and from A to C♭ are diminished thirds, two semitones wide. Being diminished, it is considered a dissonant interval.

In classical music from Western culture, a **diminished fourth** is an interval produced by narrowing a perfect fourth by a chromatic semitone. For example, the interval from C to F is a perfect fourth, five semitones wide, and both the intervals from C♯ to F, and from C to F♭ are diminished fourths, spanning four semitones. Being diminished, it is considered a dissonant interval.

In music, the **septimal whole tone**, **septimal major second**, or **supermajor second** *septimal* refers to the fact that it utilizes the seventh harmonic. It can also be thought of as the octave inversion of the 7/4 interval, the harmonic seventh.

In music theory and tuning, the **kleisma** (κλεισμα), or **semicomma majeur**, is a minute and barely perceptible comma type interval important to musical temperaments. It is the difference between six justly tuned minor thirds (each with a frequency ratio of 6/5) and one justly tuned *tritave* or *perfect twelfth* (with a frequency ratio of 3/1, formed by a 2/1 octave plus a 3/2 perfect fifth). It is equal to a frequency ratio of 15625/15552 = 2^{−6} 3^{−5} 5^{6}, or approximately 8.1 cents (

A **neutral sixth** is a musical interval wider than a minor sixth

In classical music from Western culture, a **diminished sixth** is an interval produced by narrowing a minor sixth by a chromatic semitone. For example, the interval from A to F is a minor sixth, eight semitones wide, and both the intervals from A♯ to F, and from A to F♭ are diminished sixths, spanning seven semitones. Being diminished, it is considered a dissonant interval, despite being equivalent to an interval known for its consonance.

A **septimal 1/3-tone** is an interval with the ratio of 28:27, which is the difference between the perfect fourth and the supermajor third. It is about 62.96 cents wide. The septimal 1/3-tone can be viewed either as a musical interval in its own right, or as a comma; if it is tempered out in a given tuning system, the distinction between these two intervals is lost. The septimal 1/3-tone may be derived from the harmonic series as the interval between the twenty-seventh and twenty-eighth harmonics. It may be considered a diesis.

In music theory, a **neutral interval** is an interval that is neither a major nor minor, but instead in between. For example, in equal temperament, a major third is 400 cents, a minor third is 300 cents, and a neutral third is 350 cents. A neutral interval inverts to a neutral interval. For example, the inverse of a neutral third is a neutral sixth.