Editing Scale (music) (section)

==Note names==
In many musical circumstances, a specific note of the scale is chosen as the [[Tonic (music)|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 (music)|tonic]], [[supertonic]], [[mediant]], [[subdominant]], [[Dominant (music)|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#Movable do solfège|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.<ref>{{Cite web |title=C Major Scale |url=https://www.allaboutmusictheory.com/major-scale/c-major-scale/ |access-date=2022-09-12 |website=All About Music Theory.com |language=en-US}}</ref><!--Who says it is not possible to name notes with letters of the alphabet following G? German nomenclature, at least, uses eight letters, A through H.-->

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]]. The most common binary numbering scheme defines lower pitches to have lower numeric value (as opposed to low pitches having a high numeric value). Thus a single pitch class n in the pitch class set is represented by 2^n. This maps the entire power set of all pitch class sets in 12-TET to the numbers 0 to 4095. The binary digits read as ascending pitches from right to left, which some find discombobulating because they are used to low to high reading left to right, as on a piano keyboard. In this scheme, the major scale is 101010110101 = 2741. This binary representation permits easy calculation of interval vectors and common tones, using logical binary operators. It also provides a perfect index for every possible combination of tones, as every scale has its own number.<ref>Daniel Starr. ‘Sets, Invariance, and Partitions’. In: Journal of Music Theory 22.1 (1978), pp. 1–42</ref><ref>Alexander Brinkman. Pascal Programming for Music Research. University of Chicago Press, 1990.</ref>

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.