dodecachordon

Glareanus wrote two publications on music.
The first was 'Isagoge in Musicen' (1516). It handles about
basic rules in music, and was problaby meant for use in music education.
His most important work is the 'Dodecachordon' (literal: 12 stringed instrument), published in 1547 in Basle.
It is a massive work inclucding writings on philisophy, biography and music theory with 120 complete compositions by composers of the preceeding generation.
The first part begins with a study on Boethius, who wrote on music in the 6th century. The middle part examines the use of the modes in the Gregorian chant and monophony. The last part is a study of the use of modes in polyphony.
The most important element of the Dodecachordon is Glareanus' proposal that there are 12 modes and not 8 as had been assumed till that time. See the diagram below for a listing of the modes.

In the Middle Ages there were 8 modal or church scales, divided in 4 main scales (authentic) with each a scale derived from it (plagal). The mode is defined by its last tone (finalis) and its size (ambitus). The names of the modes are (incorrect, because in a different order and not the same tonal system) copied from the ancient Greek echoii. The scales can be found following the white keys within the ambitus

early division	later division	name	ambitus (size)	finalis (final tone)	dominant
1st modeProtus authentic	I	dorian	d-d	d	a
Protus plagal	II	hypo-dorian	a-a	d	f
2nd mode Deuterus authentic	III	phrygian	e-e	e	c
Deuterus plagal	IV	hypo-phrygian	b-b	e	a
3rd modeTritus authentic	V	lydian	f-f	f	c
Tritus plagal	VI	hypo-lydian	c-c	f	a
4th modeTetrardus authentic Tetrardus plagal	VII VIII	mixolydian hypo-mixolydian	g-g d-d	g g	d c
added by Glareanus:
(a-a is equal to the authentic minor scale)	IX X	aeolian hypo-aeolian	a-a e-e	a a	e c
(c-c is equal to the major scale)	XI XII	ionian hypo-ionian	c-c g-g	c c	g e

Besides these 12 modi Glareanus mentioned 2 more scales:

hyper-aeolian	authentic	b-b	b
hyper-phrygian	plagal	f-f	b

Because of the diminished 5th b-f he considered them as being unusable. Later these modes were named locrian and hypo-locrian.
The dominant is the tone leading to the finalis. In our current scales we have this connection between the 5th (dominant) and 1st tone of a scale.
The Dodecachordon was a work with great influence, later theorists took over the system of 12 modes. The distinction between plagal and authentic is no longer in use so the number of modes are reduced to 6 (7 including locrian).