Dorian mode

Dorian mode or Doric mode can refer to three very different but interrelated subjects: one of the Ancient Greek "harmoniai" (characteristic melodic behaviour, or the scale structure associated with it), one of the medieval musical modes, or, most commonly, one of the modern modal diatonic scales, corresponding to the piano keyboard's white notes from D to D, or any transposition of this.
\override Score.TimeSignature #'stencil = ##f
\relative c' { 
 \clef treble \time 7/4
 c4^\markup { Modern C Dorian mode } d es f g a bes c2
</score>
Greek Dorian mode.
The Dorian mode (properly "harmonia" or "tonos") is named after the Dorian Greeks. Applied to a whole octave, the Dorian octave species was built upon two tetrachords (four-note segments) separated by a whole tone, running from the "hypate meson" to the "nete diezeugmenon".
In the enharmonic genus, the intervals in each tetrachord are quarter tone–quarter tone–major third.
\override Score.TimeSignature #'stencil = ##f
\relative c' { 
 \clef treble \time 4/4
 e4^\markup { Greek Dorian tonos (enharmonic genus) on E } feh geses a b ceh deses e
</score>
In the chromatic genus, they are semitone–semitone–minor third.
\override Score.TimeSignature #'stencil = ##f
\relative c' { 
 \clef treble \time 4/4
 e4^\markup { Greek Dorian tonos (chromatic genus) on E } f ges a b c des e
</score>
In the diatonic genus, they are semitone–tone–tone.
\override Score.TimeSignature #'stencil = ##f
\relative c' { 
 \clef treble \time 4/4
 e4^\markup { Greek Dorian tonos (diatonic genus) on E } f g a b c d e
</score>
In the diatonic genus, the sequence over the octave is the same as that produced by playing all the white notes of a piano ascending from E to E, a sequence equivalent to the modern Phrygian mode.
Placing the single tone at the bottom of the scale followed by two conjunct tetrachords (that is, the top note of the first tetrachord is also the bottom note of the second), produces the Hypodorian ("below Dorian") octave species: A | B C D E | (E) F G A. Placing the two tetrachords together and the single tone at the top of the scale produces the Mixolydian octave species, a note sequence equivalent to modern Locrian mode.
Medieval Dorian mode.
The early Byzantine church developed a system of eight musical modes (the octoechos), which served as a model for medieval European chant theorists when they developed their own modal classification system starting in the 9th century. The success of the Western synthesis of this system with elements from the fourth book of "De institutione musica" of Boethius, created the false impression that the Byzantine octoechos was inherited directly from ancient Greece.
Originally used to designate one of the traditional "harmoniai" of Greek theory (a term with various meanings, including the sense of an octave consisting of eight tones), the name was appropriated (along with six others) by the 2nd-century theorist Ptolemy to designate his seven "tonoi", or transposition keys. Four centuries later, Boethius interpreted Ptolemy in Latin, still with the meaning of transposition keys, not scales. When chant theory was first being formulated in the 9th century, these seven names plus an eighth, Hypermixolydian (later changed to Hypomixolydian), were again re-appropriated in the anonymous treatise "Alia Musica". A commentary on that treatise, called the "Nova expositio", first gave it a new sense as one of a set of eight diatonic species of the octave, or scales.
In medieval theory, the authentic Dorian mode could include the note B "by licence", in addition to B. The same scalar pattern, but starting a fourth or fifth below the mode final D, and extending a fifth above (or a sixth, terminating on B), was numbered as mode 2 in the medieval system. This was the plagal mode corresponding to the authentic Dorian, and was called the Hypodorian mode. In the untransposed form on D, in both the authentic and plagal forms the note C is often raised to C to form a leading tone, and the variable sixth step is in general B in ascending lines and B in descent.
Modern Dorian mode.
The modern Dorian mode (also called "Russian minor" by Balakirev), by contrast, is a strictly diatonic scale corresponding to the white keys of the piano from D to D (shown below)
\override Score.TimeSignature #'stencil = ##f
\relative c' { 
 \clef treble \time 7/4
 d4^\markup { Modern D Dorian mode } e f g a b c d2
</score>
or any transposition of its interval pattern, which has the ascending pattern of whole steps and half steps as follows:
Thus, the Dorian mode is a symmetric scale, since the pattern of whole and half step is the same ascending or descending.
The modern Dorian mode can also be thought of as a scale with a minor third and seventh, a major second and sixth, and a perfect fourth and fifth, notated relative to the major scale as:
It may be considered an "excerpt" of a major scale played from the pitch a whole tone above the major scale's tonic , i.e., a major scale played from its second scale degree up to its second degree again. The resulting scale is, however, "minor" in quality, because, as the D becomes the new tonal centre, the F a minor third above the D becomes the new mediant, or third degree. Thus, when a triad is built upon the tonic, it is a minor triad.
The modern Dorian mode is equivalent to the natural minor scale (or the Aeolian mode) but with a major sixth. The modern Dorian mode resembles the Greek Phrygian "harmonia" in the diatonic genus.
It is also equivalent to the ascending melodic minor scale with a minor seventh.