\\override Score.TimeSignature #'stencil = ##f

\\relative c' {

  \\clef treble \\time 7/4  c4 d es fis g aes b c2

} }

|width=300|caption=The Hungarian minor scale starting on C, ascending}}A large variety of other scales exists, some of the more common being:

• The Phrygian dominant scale (a mode of the harmonic minor scale)
• The Arabic scales
• The Hungarian minor scale
• The Byzantine music scales (called echoi)
• The Persian scale

Scales such as the pentatonic scale may be considered gapped relative to the diatonic scale. An auxiliary scale is a scale other than the primary or original scale. See: modulation (music) and Auxiliary diminished scale.

Note names

In many musical circumstances, a specific note of the scale is chosen as the tonic—the central and most stable note of the scale. In Western tonal music, simple songs or pieces typically start and end on the tonic note. Relative to a choice of a certain tonic, the notes of a scale are often labeled with numbers recording how many scale steps above the tonic they are. For example, the notes of the C major scale (C, D, E, F, G, A, B) can be labeled {1, 2, 3, 4, 5, 6, 7}, reflecting the choice of C as tonic. The expression scale degree refers to these numerical labels. Such labeling requires the choice of a "first" note; hence scale-degree labels are not intrinsic to the scale itself, but rather to its modes. For example, if we choose A as tonic, then we can label the notes of the C major scale using A = 1, B = 2, C = 3, and so on. When we do so, we create a new scale called the A minor scale. See the musical note article for how the notes are customarily named in different countries.

The scale degrees of a heptatonic (7-note) scale can also be named using the terms tonic, supertonic, mediant, subdominant, dominant, submediant, subtonic. If the subtonic is a semitone away from the tonic, then it is usually called the leading-tone (or leading-note); otherwise the leading-tone refers to the raised subtonic. Also commonly used is the (movable do) solfège naming convention in which each scale degree is denoted by a syllable. In the major scale, the solfège syllables are: do, re, mi, fa, so (or sol), la, ti (or si), do (or ut).

In naming the notes of a scale, it is customary that each scale degree be assigned its own letter name: for example, the A major scale is written A–B–C{{music|sharp}}–D–E–F{{music|sharp}}–G{{music|sharp}} rather than A–B–D{{music|flat}}–D–E–E{{music|doublesharp}}–G{{music|sharp}}. However, it is impossible to do this in scales that contain more than seven notes, at least in the English-language nomenclature system.{{Citation needed|date=March 2016}}

Scales may also be identified by using a binary system of twelve zeros or ones to represent each of the twelve notes of a chromatic scale. It is assumed that the scale is tuned using 12-tone equal temperament (so that, for instance, C{{Music|sharp}} is the same as D{{Music|flat}}), and that the tonic is in the leftmost position. For example, the binary number 101011010101, equivalent to the decimal number 2773, would represent any major scale (such as C–D–E–F–G–A–B). This system includes scales from 100000000000 (2048) to 111111111111 (4095), providing a total of 2048 possible species, but only 351 unique scales containing from 1 to 12 notes.^[9]

A more mathematically flexible schema for binary representation, espoused by theorist Ian Ring in his study of musical scales,^[10] has bits representing ascending tones, with the smaller bits representing lower pitches and higher bits representing higher pitches. This causes the bits to appear reversed compared with Duncan's system. Under this schema, a major scale is 101010110101 = (2741), a single root tone is 1, and a chromatic scale is still 111111111111 (4095). All the tone possibilities that begin with a root tone, and are thus scale-like, are odd-numbered.

Scales may also be shown as semitones from the tonic. For instance, 0 2 4 5 7 9 11 denotes any major scale such as C–D–E–F–G–A–B, in which the first degree is, obviously, 0 semitones from the tonic (and therefore coincides with it), the second is 2 semitones from the tonic, the third is 4 semitones from the tonic, and so on. Again, this implies that the notes are drawn from a chromatic scale tuned with 12-tone equal temperament. For some fretted string instruments, such as the guitar and the bass guitar, scales can be notated in tabulature, an approach which indicates the fret number and string upon which each scale degree is played.

Transposition and modulation

Composers transform musical patterns by moving every note in the pattern by a constant number of scale steps: thus, in the C major scale, the pattern C–D–E might be shifted up, or transposed, a single scale step to become D–E–F. This process is called "scalar transposition" or "shifting to a new key" and can often be found in musical sequences and patterns. (It is D-E-F# in Chromatic transposition). Since the steps of a scale can have various sizes, this process introduces subtle melodic and harmonic variation into the music. In Western tonal music, the simplest and most common type of modulation (or changing keys) is to shift from one major key to another key built on the first key's fifth (or dominant) scale degree. In the key of C major, this would involve moving to the key of G major (which uses an F#). Composers also often modulate to other related keys. In some Romantic music era pieces and contemporary music, composers modulate to "remote keys" that are not related to or close to the tonic. An example of a remote modulation would be taking a song that begins in C major and modulating (changing keys) to F# major.

Jazz and blues

  \\clef treble \\time 6/4  c4 es f fis g bes c2