In music

Music

Music is an art form whose medium is sound and silence. Its common elements are pitch , rhythm , dynamics, and the sonic qualities of timbre and texture...

 a common tone is a pitch class

Pitch class

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...

 that is a member of, or common to, a musical scale

Musical scale

In music, a scale is a sequence of musical notes in ascending and descending order. Most commonly, especially in the context of the common practice period, the notes of a scale will belong to a single key, thus providing material for or being used to conveniently represent part or all of a musical...

 and a transposition

Transposition (music)

In music transposition refers to the process, or operation, of moving a collection of notes up or down in pitch by a constant interval.For example, one might transpose an entire piece of music into another key...

 of that scale, as in modulation

Modulation (music)

In music, modulation is most commonly the act or process of changing from one key to another. This may or may not be accompanied by a change in key signature. Modulations articulate or create the structure or form of many pieces, as well as add interest...

 (Johnson 2003, p.42). Six of seven possible common tones are shared by closely related key

Closely related key

In music, a closely related key is one sharing many common tones with an original key, as opposed to a distantly related key...

s, though keys

Key (music)

In music theory, the term key is used in many different and sometimes contradictory ways. A common use is to speak of music as being "in" a specific key, such as in the key of C major or in the key of F-sharp. Sometimes the terms "major" or "minor" are appended, as in the key of A minor or in the...

 may also be thought of as more or less closely related according to their number of common tones.
In diatonic set theory

Diatonic set theory

Diatonic set theory is a subdivision or application of musical set theory which applies the techniques and insights of discrete mathematics to properties of the diatonic collection such as maximal evenness, Myhill's property, well formedness, the deep scale property, cardinality equals variety, and...

 the common tone theorem explains that scales possessing the deep scale property

Deep scale property

In diatonic set theory, the deep scale property is the quality of pitch class collections or scales containing each interval class a unique number of times. Examples include the diatonic scale...

 share a different number of common tones for every different transposition of the scale. However many times an interval class

Interval class

In musical set theory, an interval class , also known as unordered pitch-class interval, interval distance, undirected interval, or interval mod...

 occurs in a diatonic scale is the number of tones common both to the original scale and a scale transposed by that particular interval class. For example, then, modulation to the dominant (transposition by a perfect fifth

Perfect fifth

In classical music from Western culture, a fifth is a musical interval encompassing five staff positions , and the perfect fifth is a fifth spanning seven semitones, or in meantone, four diatonic semitones and three chromatic semitones...

) includes six common tones between the keys as there are six perfect fifths in a diatonic scale, while transposition by the tritone

Tritone

In classical music from Western culture, the tritone |tone]]) is traditionally defined as a musical interval composed of three whole tones. In a chromatic scale, each whole tone can be further divided into two semitones...

 includes only two common tones (for indeed there are two tritone intervals in a diatonic scale

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...

). (ibid)

Source

• Johnson, Timothy (2003). Foundations of Diatonic Theory: A Mathematically Based Approach to Music Fundamentals. Key College Publishing. ISBN 1-930190-80-8.