Editing Diatonic scale (section)

==Theory==
[[File:Piano-keyboard.jpg|thumb|right|300px|The modern [[piano keyboard]] is based on the interval patterns of the diatonic scale. Any sequence of seven successive white keys plays a diatonic scale.]]
Of Glarean's six natural scales, three have a major third/first triad: ([[Ionian mode|Ionian]], [[Lydian mode|Lydian]], and [[Mixolydian mode|Mixolydian]]), and three have a minor one: [[Dorian mode|Dorian]], [[Phrygian mode|Phrygian]], and [[Aeolian mode|Aeolian]]). To these may be added the seventh diatonic scale, with a diminished fifth above the reference note, the [[Locrian mode|Locrian]] scale. These could be transposed not only to include one flat in the signature (as described by Glarean), but to all twelve notes of the [[chromatic scale]], resulting in a total of eighty-four diatonic scales.

The modern [[musical keyboard]] originated as a diatonic keyboard with only white keys.<ref>Meeùs, Nicolas (2001). "Keyboard." ''[[Grove Music Online]]''. {{doi|10.1093/gmo/9781561592630.article.14944}}. Retrieved 9 May 2018.</ref> The black keys were progressively added for several purposes:

* improving the consonances, mainly the thirds, by providing a major third on each degree;
* allowing all twelve transpositions described above;
* and helping musicians to find their bearings on the keyboard.{{Citation needed|date=May 2018}}

The pattern of elementary intervals forming the diatonic scale can be represented either by the letters T ([[whole tone|tone]]) and S ([[semitone]]) respectively. With this abbreviation, a major scale, for instance, can be represented as

:T–T–S–T–T–T–S

===Major scale===
{{Main|Major scale}}
The [[major scale]] or [[Ionian mode]] is one of the diatonic scales. It is made up of seven distinct [[Musical note|note]]s, plus an eighth that duplicates the first an [[octave]] higher. The pattern of seven intervals separating the eight notes is T–T–S–T–T–T–S. In [[solfège]], the syllables used to name each [[Degree (music)|degree]] of the scale are ''Do–Re–Mi–Fa–Sol–La–Ti–Do''. A sequence of successive [[natural note]]s starting from C is an example of major scale, called [[C-major]] scale.

{| border=0 cellspacing=0 cellpadding=3
|-
| &nbsp; || Notes in C major: || C || &nbsp; || D || &nbsp; || E || &nbsp; || F || &nbsp; || G || &nbsp; || A || &nbsp; || B || &nbsp; || C
|-
| &nbsp; || Degrees in solfège: || ''Do'' || &nbsp; || ''Re'' || &nbsp; || ''Mi'' || &nbsp; || ''Fa'' || &nbsp; || ''Sol'' || &nbsp; || ''La'' || &nbsp; || ''Ti'' || &nbsp; || ''Do''
|-
| &nbsp; || Interval sequence: || &nbsp; || T || &nbsp; || T || &nbsp; || S || &nbsp; || T || &nbsp; || T || &nbsp; || T || &nbsp; || S || &nbsp;
|}
The seen degrees of the scale are also known by traditional names, especially when used in a tonal context:
:*1st – [[Tonic (music)|Tonic]] (key note)
:*2nd – [[Supertonic]]
:*3rd – [[Mediant]]
:*4th – [[Subdominant]]
:*5th – [[Dominant (music)|Dominant]]
:*6th – [[Submediant]]
:*7th – [[Leading-tone|Leading tone]]
:*(8th – [[Tonic (music)|Tonic]])

===Natural minor scale===
{{Main|Minor scale}}
For each major scale, there is a corresponding [[minor scale#Natural minor scale|natural minor scale]], sometimes called its [[relative key|relative minor]]. It uses the same sequence of notes as the corresponding major scale but starts from a different note. That is, it begins on the sixth degree of the major scale and proceeds step-by-step to the first octave of the sixth degree. A sequence of successive [[natural note]]s starting from A is an example of a natural minor scale, called the A natural minor scale.

{| border=0 cellspacing=0 cellpadding=3
|-
| &nbsp; || Notes in A minor: || A || &nbsp; || B || &nbsp; || C || &nbsp; || D || &nbsp; || E || &nbsp; || F || &nbsp; || G || &nbsp; || A
|-
| &nbsp; || Interval sequence: || &nbsp; || T || &nbsp; || S || &nbsp; || T || &nbsp; || T || &nbsp; || S || &nbsp; || T || &nbsp; || T || &nbsp;
|}
The degrees of the natural minor scale, especially in a tonal context, have the same names as those of the major scale, except the seventh degree, which is known as the [[subtonic]] because it is a whole step below the tonic. The term [[leading tone]] is generally reserved for seventh degrees that are a ''half step'' (semitone) below the tonic, as is the case in the major scale.

Besides the natural minor scale, five other kinds of scales can be obtained from the notes of a major scale, by simply choosing a different note as the starting note. All these scales meet the definition of diatonic scale.

===Modes===
{{Main|Mode (music)}}
The whole collection of diatonic scales as defined above can be divided into seven different scales.

As explained above, all [[major scale]]s use the same interval sequence T–T–S–T–T–T–S. This interval sequence was called the ''Ionian mode'' by Glarean. It is one of the seven modern modes. From any major scale, a new scale is obtained by taking a different [[degree (music)|degree]] as the tonic. With this method it is possible to generate six other scales or modes from each major scale. Another way to describe the same result would be to consider that, behind the diatonic scales, there exists an underlying diatonic system which is the series of diatonic notes without a reference note; assigning the reference note in turn to each of the seven notes in each octave of the system produces seven diatonic scales, each characterized by a different interval sequence:

{| class="wikitable" style="margin-left: auto; margin-right: auto; border: none; text-align: center;"
! Mode
! Also known as
! Starting note relative<br/>to major scale
! Interval sequence
! Example with white keys
! Example with tonic C
|-
| [[Ionian mode|Ionian]] || Major scale
| align="center" | C
| align="center" | T–T–S–T–T–T–S
| colspan=2 | C–D–E–F–G–A–B–C
|-
| [[Dorian mode|Dorian]] ||
| align="center" | D
| align="center" | T–S–T–T–T–S–T
| D–E–F–G–A–B–C–D
| C–D–E♭–F–G–A–B♭–C
|-
| [[Phrygian mode|Phrygian]] ||
| align="center" | E
| align="center" | S–T–T–T–S–T–T
| E–F–G–A–B–C–D–E
| C–D♭–E♭–F–G–A♭–B♭–C
|-
| [[Lydian mode|Lydian]] ||
| align="center" | F
| align="center" | T–T–T–S–T–T–S
| F–G–A–B–C–D–E–F
| C–D–E–F♯–G–A–B–C
|-
| [[Mixolydian mode|Mixolydian]] ||
| align="center" | G
| align="center" | T–T–S–T–T–S–T
| G–A–B–C–D–E–F–G
| C–D–E–F–G–A–B♭–C
|-
| [[Aeolian mode|Aeolian]] || [[Minor scale#Natural minor scale|Natural minor scale]]
| align="center" | A
| align="center" | T–S–T–T–S–T–T
| A–B–C–D–E–F–G–A
| C–D–E♭–F–G–A♭–B♭–C
|-
| [[Locrian mode|Locrian]] ||
| align="center" | B
| align="center" | S–T–T–S–T–T–T
| B–C–D–E–F–G–A–B
| C–D♭–E♭–F–G♭–A♭–B♭–C
|}

The first column examples shown above are formed by [[natural note]]s (i.e. neither sharps nor flats, also called "white-notes", as they can be played using the white keys of a [[piano keyboard]]). But any [[transposition (music)|transposition]] of each of these scales (or of the system underlying them) is a valid example of the corresponding mode. In other words, transposition preserves mode. This is shown in the second column, with each mode transposed to start on C. 

The whole set of diatonic scales is commonly defined as the set composed of these seven natural-note scales, together with all of their possible transpositions. As discussed [[diatonic and chromatic#Diatonic scales|elsewhere]], different definitions of this set are sometimes adopted in the literature.

[[File:Modes.svg|thumb|center|700px|[[Pitch constellation]]s of the modern musical modes]]

===Diatonic scales and tetrachords===
A diatonic scale can be also described as two [[tetrachord#Romantic era|tetrachords]] separated by a [[whole tone]]. For example, under this view the two tetrachord structures of C&nbsp;major would be:
:[C–D–E–F] – [G–A–B–C]
each tetrachord being formed of two tones and a semitone, T–T–S,

and the natural minor of A would be:
:[A–B–C–D] – [E–F–G–A]
formed two different tetrachords, the first consisting in a semitone between two tones, T–S–T, and the second of a semitone and two tones, S–T–T.

The medieval conception of the tetrachordal structure, however, was based on one single tetrachord, that of the D scale,
:[D–E–F–G] – [A–B–C–D]
each formed of a semitone between tones, T–S–T. It viewed other diatonic scales as differently overlapping disjunct and conjunct tetrachords:
:E scale: E–F–G | A–B–C–D = D–E
:F scale: F–G | A–B–C–D = D–E–F
:G scale: G | A–B–C–D = D–E–F–G
:A scale: A–B–C–D = D–E–F–G | A
:B scale: B–C–D = D–E–F–G | A–B
:C scale: C–D = D–E–F–G | A–B–C
(where G | A indicates the disjunction of tetrachords, always between G and A, and D = D indicates their conjunction, always on the common note D).