Each mode or scale was composed of two sets of four notes, called tetrachords, probably derived from the ancient form of the lyre, which in Homer’s time is known to have had four strings.

Leaving the matter of actual pitch out of the question (for these modes might be pitched high or low, just as our major or minor scale may be pitched in different keys), these three modes were constructed as follows: 

Greek Dorian (E F) G A (B C) D E,
that is, semitone, tone, tone.

/
|  Phrygian  D (E F) G   A (B C) D,
|              or F[#] (G[#] A) B   C[#] (D[#] E) F[#],
Asiatic |              that is, tone, semitone, tone.
|
|  Lydian    C D (E F)   G A (B C),
\              that is, tone, tone, semitone.

Thus we see that a tetrachord commencing with a half-tone and followed by two whole tones was called a Dorian tetrachord; one commencing with a tone, followed by a half-tone, and again a tone, constituted a Phrygian tetrachord.  The other modes were as follows:  In the Aeolian or Locrian the semitones occur between the second and third notes, and the fifth and sixth:  [F:  b, (c+ d) e (f+ g) a b] Theraclides Ponticus identifies the Hypodorian with the Aeolian, but says that the name “hypo-” merely denoted a likeness to Doric, not to pitch.  Aristoxenus denies the identity, and says that the Hypodorian was a semitone below the Dorian or Hypolydian.  In the Hypophrygian, the semitones occur between the third and fourth, and sixth and seventh degrees:  [F:  c+ d+ (e+ f+) g+ (a+ b) c+’] In the Hypolydian, the semitones occur between the fourth and fifth, and seventh and eighth:  [F:  e- f g (a b-) c’ (d’ e-’)] The Dorian (E), Phrygian (commencing on F[sharp] with the fourth sharped), and the Lydian (A[flat] major scale) modes we have already explained.  In the Mixolydian, the semitones occur between the first and second, and fourth and fifth degrees:  [G:  (a b-) c’ (d’ e-’) f’ g’ a’]

According to the best evidence (in the works of Ptolemy, “Harmonics,” second book, and Aristides), these were approximately the actual pitch of the modes as compared one to another.

And now the difficulty was to weld all these modes together into one scale, so that all should be represented and yet not be complicated by what we should call accidentals.  This was accomplished in the following manner, by simple mathematical means: 

We remember that the Dorian, which was the most greatly favoured mode in Greece, was divided into two tetrachords of exactly the same proportions, namely, semitone, tone, tone.  By taking the lowest note of the Mixolydian, B, and forming a Dorian tetrachord on it, B C D E were acquired.  Adding to this another Dorian tetrachord, E F G A (commencing on the last note of the first), and repeating the same series of tetrachords an octave higher, we have in all four Dorian tetrachords, two of which overlap the others.  The two middle tetrachords, constituting the original Dorian mode, were called disjunct, the two outer ones which overlap the middle ones were called conjunct or synemmenon tetrachords.