The Hypoaeolian mode, literally meaning "below Aeolian", is the name assigned by Henricus Glareanus in his Dodecachordon (1547) to the musical plagal mode on A, which uses the diatonic octave species from E to the E an octave above, divided by the final into a second-species fourth (semitone–tone–tone) plus a first-species fifth (tone–semitone–tone–tone): E F G A + A B C D E.  The tenor or reciting tone is C, mediant B, the participants are the low and high Es, the conceded modulations are G and D, and the absolute initials are E, G, A, B, and C. 
For his plainchant examples Glarean proposed two important and well-known Gregorian melodies normally written with their finals on A: the antiphon Benedicta tu in mulieribus (traditionally designated as transposed Hypophrygian) and the gradual Haec dies—Justus ut palma (traditionally designated as transposed Hypodorian). 
A polyphonic example of the Hypoaeolian mode is motet 19 from Palestrina's Liber quartus of five-voice motets on the Song of Solomon. 
In music theory, a diatonic scale is any heptatonic scale that includes five whole steps and two half steps (semitones) in each octave, in which the two half steps are separated from each other by either two or three whole steps, depending on their position in the scale. This pattern ensures that, in a diatonic scale spanning more than one octave, all the half steps are maximally separated from each other.
In the theory of Western music, a mode is a type of musical scale coupled with a set of characteristic melodic and harmonic behaviors. Musical modes have been a part of western musical thought since the Middle Ages, and were inspired by the theory of ancient Greek music. The name mode derives from the Latin word modus, "measure, standard, manner, way, size, limit of quantity, method".
In music theory, a scale is any set of musical notes ordered by fundamental frequency or pitch. A scale ordered by increasing pitch is an ascending scale, and a scale ordered by decreasing pitch is a descending scale.
Dorian mode or Doric mode can refer to three very different but interrelated subjects: one of the Ancient Greek harmoniai, 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.
Mixolydian mode may refer to one of three things: the name applied to one of the ancient Greek harmoniai or tonoi, based on a particular octave species or scale; one of the medieval church modes; a modern musical mode or diatonic scale, related to the medieval mode.
The Aeolian mode is a musical mode or, in modern usage, a diatonic scale also called the natural minor scale. On the white piano keys, it is the scale that starts with A. Its ascending interval form consists of a key note, whole step, half step, whole step, whole step, half step, whole step, whole step. That means that, in A aeolian, you would play A, move up a whole step to B, move up a half step to C, then up a whole step to D, a whole step to E, a half step to F, a whole step to G, and a final whole step to a high A.
The Phrygian mode can refer to three different musical modes: the ancient Greek tonos or harmonia sometimes called Phrygian, formed on a particular set of octave species or scales; the Medieval Phrygian mode, and the modern conception of the Phrygian mode as a diatonic scale, based on the latter.
In music, transposition refers to the process or operation of moving a collection of notes up or down in pitch by a constant interval.
The shifting of a melody, a harmonic progression or an entire musical piece to another key, while maintaining the same tone structure, i.e. the same succession of whole tones and semitones and remaining melodic intervals.
The modern Lydian mode is a seven-tone musical scale formed from a rising pattern of pitches comprising three whole tones, a semitone, two more whole tones, and a final semitone.
In the musical system of ancient Greece, Genus is a term used to describe certain classes of intonations of the two movable notes within a tetrachord. The tetrachordal system was inherited by the Latin medieval theory of scales and by the modal theory of Byzantine music; it may have been one source of the later theory of the jins of Arabic music. In addition, Aristoxenus calls some patterns of rhythm "genera".
The Locrian mode is either a musical mode or simply a diatonic scale. On the white piano keys, it is the scale that starts with B. Its ascending form consists of the key note, a half step, two whole steps, a further half step, and three more whole steps.
Scientific pitch notation is a method of specifying musical pitch by combining a musical note name and a number identifying the pitch's octave.
Modes of limited transposition are musical modes or scales that fulfill specific criteria relating to their symmetry and the repetition of their interval groups. These scales may be transposed to all twelve notes of the chromatic scale, but at least two of these transpositions must result in the same pitch classes, thus their transpositions are "limited". They were compiled by the French composer Olivier Messiaen, and published in his book La technique de mon langage musical.
The Hypolydian mode, literally meaning "below Lydian", is the common name for the sixth of the eight church modes of medieval music theory. The name is taken from Ptolemy of Alexandria's term for one of his seven tonoi, or transposition keys. This mode is the plagal counterpart of the authentic fifth mode.
The Hypophrygian mode, literally meaning "below Phrygian ", is a musical mode or diatonic scale in medieval chant theory, the fourth mode of church music. This mode is the plagal counterpart of the authentic third mode, which was called Phrygian. In the Middle Ages and Renaissance this mode was described in two ways: the diatonic scale from B to B an octave above, divided at the mode final E ; and as a mode with final E and ambitus from the A below to the C above. The note A above the final had an important melodic function. The melodic range of the ecclesiastical Hypophrygian mode therefore goes from the perfect fourth or fifth below the tonic to the perfect fifth or minor sixth above.
The Hypodorian mode, a musical term literally meaning 'below Dorian', derives its name from a tonos or octave species of ancient Greece which, in its diatonic genus, is built from a tetrachord consisting of a semitone followed by two whole tones. The rising scale for the octave is a single tone followed by two conjoint tetrachords of this type. This is roughly the same as playing all the white notes of a piano from A to A: A | B C D E | (E) F G A. Although this scale in medieval theory was employed in Dorian and Hypodorian, from the mid-sixteenth century and in modern music theory they came to be known as the Aeolian and Hypoaeolian modes.
Ionian mode is a musical mode or, in modern usage, a diatonic scale also called the major scale.
Diatonic and chromatic are terms in music theory that are most often used to characterize scales, and are also applied to musical instruments, intervals, chords, notes, musical styles, and kinds of harmony. They are very often used as a pair, especially when applied to contrasting features of the common practice music of the period 1600–1900.
The Hypolocrian mode is an almost entirely theoretical mode, introduced into chant theory in the 19th century by the editors of the Pustet-Ratisbon, Mechlin, and Rheims-Cambrai Office-Books, who designated it mode 12. It is the plagal counterpart to the authentic Locrian mode, mode 11 in that system of numbering, in which the Ionian and Hypoionian become modes 13 and 14. The ambitus of the mode lies between F and the F an octave higher, divided at the final, B. Its reciting tone, is E, and its mediant is D. It has two participants, G and C. Although a few plainchant melodies, as well as polyphonic compositions, have been attributed to this mode by some writers, it will generally be found that they are really derived, by transposition, from some other tonality.
The musical system of ancient Greece evolved over a period of more than 500 years from simple scales of tetrachords, or divisions of the perfect fourth, to The Perfect Immutable System, encompassing a span of fifteen pitch keys