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Encyclopedia of Microtonal Music Theory

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[John Chalmers, Divisions of the Tetrachord]

A cyclic permutation of the intervals of a scale, equivalent to Octave Species.

The tonic of a Mode is not necessarily the starting note.

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[Joe Monzo]

The various diatonic modes are today known by Greek names. See their individual entries for details:

In the earliest music-theory treatises describing the church modes, dating from the late 800s, the modes were categorized as four pairs with Greek numerical names, an "authentic" and a "plagal" version each of "protus" ("1st"), "deuterus" ("2nd"), "tritus" ("3rd") and "tetrardus" ("4th"), determined by the "final" (the note on which a chant ends). Chant melodies were each assigned to a particular mode, and the difference between "authentic" and "plagal" concerns primarily which other notes besides the final are structurally important and which notes are covered by the range of the melody. Psalms chants recite most syllables on one particular note, the "reciting note". The 8 church modes are listed below, with the Greek, Boethian, and Alia Musica names, and with reciting notes in bold and finals in italic.

                           Boethius      Alia musica

1. Protus authentus       phrygian       dorian                D E F G a b c d
2. Protus plagis          hypodorian     hypodorian      A B C D E F G a
3. Deuterus authentus     dorian         phrygian                E F G a b c d e
4. Deuterus plagis        mixolydian     hypophrygian      B C D E F G a b
5. Tritus authentus       hypolydian     lydian                    F G a b c d e f
6. Tritus plagis          lydian         hypolydian          C D E F G a b c
7. Tetrardus authentus    hypophrygian   mixolydian                  G a b c d e f g
8. Tetrardus plagis           --         hypermixolydian       D E F G a b c d
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