Saturday, April 8, 2017

greek musical theory

Mode (music)

From Wikipedia, the free encyclopedia
This article is about modes as used in music. For other uses, see Mode (disambiguation).
Modern Dorian mode on C About this sound Play 
In the theory of Western musicmode (from Latin modus, "measure, standard, manner, way, size, limit of quantity, method") (Powers 2001, Introduction; OED) generally refers to a type of scale, coupled with a set of characteristic melodic behaviours. This use, still the most common in recent years, reflects a tradition dating to the Middle Ages, itself inspired by the theory of ancient Greek music.

Mode as a general concept[edit]

Regarding the concept of mode as applied to pitch relationships generally, Harold S. Powers proposed mode as a general term but limited for melody types, which were based on the modal interpretation of ancient Greek octave species called tonos (τόνος) or harmonia (ἁρμονία), with "most of the area between ... being in the domain of mode" (Powers 2001, §I,3). This synthesis between tonus as a church tone and the older meaning associated with an octave species was done by medieval theorists for the Western monodic plainchant tradition (see Hucbald and Aurelian). It is generally assumed that Carolingian theorists imported monastic Octoechos propagated in the patriarchates of Jerusalem (Mar Saba) and Constantinople (Stoudios Monastery) which meant the eight echoi they used for the composition of hymns (e.g., Wellesz 1954, 41 ff.[page needed]), though direct adaptations of Byzantine chants in the survived Gregorian repertoire are extremely rare.
Since the end of the eighteenth century, the term "mode" has also applied to pitch structures in non-European musical cultures, sometimes with doubtful compatibility (Powers 2001, §V,1). The concept is also heavily used in regard to the Western polyphony before advent of the so-called common-practice music, as for example "modale Mehrstimmigkeit" by Carl Dahlhaus (Dalhaus 1968, 174 et passim) or "Tonarten" of the 16th and 17th centuries found by Bernhard Meier (Meier 1974Meier 1992).

Additional meanings[edit]

The word encompasses several additional meanings, however. Authors from the ninth century until the early eighteenth century (e.g. Guido of Arezzo) sometimes employed the Latin modus for interval. In the theory of late-medieval mensural polyphony (e.g. Franco of Cologne), modus is a rhythmic relationship between long and short values or a pattern made from them (Powers 2001, Introduction); in mensural music most often theorists applied it to division of longa into 3 or 2 breves.

Modes and scales[edit]

A "scale" is an ordered series of pitches that, with the key or tonic (first tone) as a reference point, defines that scale's intervals, or steps. The concept of "mode" in Western music theory has three successive stages: in Gregorian chant theory, in Renaissance polyphonic theory, and in tonal harmonic music of the common practice period. In all three contexts, "mode" incorporates the idea of the diatonic scale, but differs from it by also involving an element of melody type. This concerns particular repertories of short musical figures or groups of tones within a certain scale so that, depending on the point of view, mode takes on the meaning of either a "particularized scale" or a "generalized tune". Modern musicological practice has extended the concept of mode to earlier musical systems, such as those of Ancient Greek music, Jewish cantillation, and the Byzantine system of octoechos, as well as to other non-Western musics (Powers 2001, §I, 3; Winnington-Ingram 1936, 2–3).
By the early 19th century, the word "mode" had taken on an additional meaning, in reference to the difference between major and minor keys, specified as "major mode" and "minor mode". At the same time, composers were beginning to conceive of "modality" as something outside of the major/minor system that could be used to evoke religious feelings or to suggest folk-music idioms (Porter 2001).


Early Greek treatises describe three interrelated concepts that are related to the later, medieval idea of "mode": (1) scales (or "systems"), (2) tonos—pl. tonoi—(the more usual term used in medieval theory for what later came to be called "mode"), and (3) harmonia (harmony)—pl. harmoniai—this third term subsuming the corresponding tonoi but not necessarily the converse (Mathiesen 2001a, 6(iii)(e)).

Greek scales[edit]

Greek Dorian octave species in the enharmonic genus, showing the two component tetrachords About this sound Play 
Greek Dorian octave species in the chromatic genus About this sound Play 
Greek Dorian octave species in the diatonic genus About this sound Play 
The Greek scales in the Aristoxenian tradition were (Barbera 1984, 240; Mathiesen 2001a, 6(iii)(d)):
  • Mixolydianhypate hypaton–paramese (b–b′)
  • Lydianparhypate hypaton–trite diezeugmenon (c′–c″)
  • Phrygianlichanos hypaton–paranete diezeugmenon (d′–d″)
  • Dorianhypate meson–nete diezeugmenon (e′–e″)
  • Hypolydianparhypate meson–trite hyperbolaion (f′–f″)
  • Hypophrygianlichanos meson–paranete hyperbolaion (g′–g″)
  • Common, Locrian, or Hypodorianmese–nete hyperbolaion or proslambnomenos–mese (a′–a″ or a–a′)
These names are derived from Ancient Greek subgroups (Dorians), one small region in central Greece (Locris), and certain neighboring (non-Greek) peoples from Asia Minor (LydiaPhrygia). The association of these ethnic names with the octave species appears to precede Aristoxenus, who criticized their application to the tonoi by the earlier theorists whom he called the Harmonicists (Mathiesen 2001a, 6(iii)(d)).
Depending on the positioning (spacing) of the interposed tones in the tetrachords, three genera of the seven octave species can be recognized. The diatonic genus (composed of tones and semitones), the chromatic genus (semitones and a minor third), and the enharmonic genus (with a major third and two quarter tones or dieses) (Cleonides 1965, 35–36). The framing interval of the perfect fourth is fixed, while the two internal pitches are movable. Within the basic forms, the intervals of the chromatic and diatonic genera were varied further by three and two "shades" (chroai), respectively (Cleonides 1965, 39–40; Mathiesen 2001a, 6(iii)(c)).
In contrast to the medieval modal system, these scales and their related tonoi and harmoniai appear to have had no hierarchical relationships amongst the notes that could establish contrasting points of tension and rest, although the mese ("middle note") may have had some sort of gravitational function (Palisca 2006, 77).


The term tonos (pl. tonoi) was used in four senses: "as note, interval, region of the voice, and pitch. We use it of the region of the voice whenever we speak of Dorian, or Phrygian, or Lydian, or any of the other tones" (Cleonides 1965, 44). Cleonides attributes thirteen tonoi to Aristoxenus, which represent a progressive transposition of the entire system (or scale) by semitone over the range of an octave between the Hypodorian and the Hypermixolydian (Mathiesen 2001a, 6(iii)(e)). Aristoxenus's transpositional tonoi, according to Cleonides (1965, 44), were named analogously to the octave species, supplemented with new terms to raise the number of degrees from seven to thirteen. However, according to the interpretation of at least two modern authorities, in these transpositional tonoi the Hypodorian is the lowest, and the Mixolydian next-to-highest—the reverse of the case of the octave species (Mathiesen 2001a, 6(iii)(e); Solomon 1984, 244–45), with nominal base pitches as follows (descending order):
  • f: Hypermixolydian (or Hyperphrygian)
  • e: High Mixolydian or Hyperiastian
  • e: Low Mixolydian or Hyperdorian
  • d: Lydian
  • c: Low Lydian or Aeolian
  • c: Phrygian
  • B: Low Phrygian or Iastian
  • B: Dorian
  • A: Hypolydian
  • G: Low Hypolydian or Hypoaelion
  • G: Hypophrygian
  • F: Low Hypophrygian or Hypoiastian
  • F: Hypodorian
Ptolemy, in his Harmonics, ii.3–11, construed the tonoi differently, presenting all seven octave species within a fixed octave, through chromatic inflection of the scale degrees (comparable to the modern conception of building all seven modal scales on a single tonic). In Ptolemy's system, therefore there are only seven tonoi (Mathiesen 2001a, 6(iii)(e); Mathiesen 2001c). Pythagoras also construed the intervals arithmetically (if somewhat more rigorously, initially allowing for 1:1 = Unison, 2:1 = Octave, 3:2 = Fifth, 4:3 = Fourth and 5:4 = Major Third within the octave). In their diatonic genus, these tonoi and corresponding harmoniai correspond with the intervals of the familiar modern major and minor scales. See Pythagorean tuning and Pythagorean interval.


Harmoniai of the School of Eratocles (enharmonic genus)
In music theory the Greek word harmonia can signify the enharmonic genus of tetrachord, the seven octave species, or a style of music associated with one of the ethnic types or the tonoi named by them (Mathiesen 2001b).
Particularly in the earliest surviving writings, harmonia is regarded not as a scale, but as the epitome of the stylised singing of a particular district or people or occupation (Winnington-Ingram 1936, 3). When the late 6th-century poet Lasus of Hermione referred to the Aeolian harmonia, for example, he was more likely thinking of a melodic style characteristic of Greeks speaking the Aeolic dialect than of a scale pattern (Anderson and Mathiesen 2001). By the late fifth century BC these regional types are being described in terms of differences in what is called harmonia—a word with several senses, but here referring to the pattern of intervals between the notes sounded by the strings of a lyra or a kithara. However, there is no reason to suppose that, at this time, these tuning patterns stood in any straightforward and organised relations to one another. It was only around the year 400 that attempts were made by a group of theorists known as the harmonicists to bring these harmoniai into a single system, and to express them as orderly transformations of a single structure. Eratocles was the most prominent of the harmonicists, though his ideas are known only at second hand, through Aristoxenus, from whom we learn they represented the harmoniai as cyclic reorderings of a given series of intervals within the octave, producing seven octave species. We also learn that Eratocles confined his descriptions to the enharmonic genus (Baker 1984–89, 2:14–15).
In The RepublicPlato uses the term inclusively to encompass a particular type of scale, range and register, characteristic rhythmic pattern, textual subject, etc. (Mathiesen 2001a, 6(iii)(e)). He held that playing music in a particular harmonia would incline one towards specific behaviors associated with it, and suggested that soldiers should listen to music in Dorian or Phrygian harmoniai to help make them stronger, but avoid music in Lydian, Mixolydian or Ionian harmoniai, for fear of being softened. Plato believed that a change in the musical modes of the state would cause a wide-scale social revolution (Plato, Rep. III.10–III.12 = 398C–403C)
The philosophical writings of Plato and Aristotle (c. 350 BC) include sections that describe the effect of different harmoniai on mood and character formation. For example, Aristotle in the Politics (viii:1340a:40–1340b:5):
But melodies themselves do contain imitations of character. This is perfectly clear, for the harmoniai have quite distinct natures from one another, so that those who hear them are differently affected and do not respond in the same way to each. To some, such as the one called Mixolydian, they respond with more grief and anxiety, to others, such as the relaxed harmoniai, with more mellowness of mind, and to one another with a special degree of moderation and firmness, Dorian being apparently the only one of the harmoniai to have this effect, while Phrygian creates ecstatic excitement. These points have been well expressed by those who have thought deeply about this kind of education; for they cull the evidence for what they say from the facts themselves. (Barker 1984–89, 1:175–76)
Aristotle continues by describing the effects of rhythm, and concludes about the combined effect of rhythm and harmonia (viii:1340b:10–13):
From all this it is clear that music is capable of creating a particular quality of character [ἦθος] in the soul, and if it can do that, it is plain that it should be made use of, and that the young should be educated in it. (Barker 1984–89, 1:176)
The word ethos (ἦθος) in this context means "moral character", and Greek ethos theory concerns the ways in which music can convey, foster, and even generate ethical states (Anderson and Mathiesen 2001).


Some treatises also describe "melic" composition (μελοποιΐα), "the employment of the materials subject to harmonic practice with due regard to the requirements of each of the subjects under consideration" (Cleonides 1965, 35)—which, together with the scales, tonoi, and harmoniai resemble elements found in medieval modal theory (Mathiesen 2001a, 6(iii)). According to Aristides Quintilianus (On Music, i.12), melic composition is subdivided into three classes: dithyrambic, nomic, and tragic. These parallel his three classes of rhythmic composition: systaltic, diastaltic and hesychastic. Each of these broad classes of melic composition may contain various subclasses, such as erotic, comic and panegyric, and any composition might be elevating (diastaltic), depressing (systaltic), or soothing (hesychastic) (Mathiesen 2001a, 4).
According to Mathiesen, music as a performing art was called melos, which in its perfect form (μέλος τέλειον) comprised not only the melody and the text (including its elements of rhythm and diction) but also stylized dance movement. Melic and rhythmic composition (respectively, μελοποιΐα and ῥυθμοποιΐα) were the processes of selecting and applying the various components of melos and rhythm to create a complete work. Aristides Quintilianus:
And we might fairly speak of perfect melos, for it is necessary that melody, rhythm and diction be considered so that the perfection of the song may be produced: in the case of melody, simply a certain sound; in the case of rhythm, a motion of sound; and in the case of diction, the meter. The things contingent to perfect melos are motion-both of sound and body-and also chronoi and the rhythms based on these. (Mathiesen 1983, 75).

Western Church[edit]

Tonaries, which are lists of chant titles grouped by mode, appear in western sources around the turn of the 9th century. The influence of developments in Byzantium, from Jerusalem and Damascus, for instance the works of Saints John of Damascus (d. 749) and Cosmas of Maiouma (Nikodēmos ’Agioreitēs 1836, 1:32–33; Barton 2009), are still not fully understood. The eight-fold division of the Latin modal system, in a four-by-two matrix, was certainly of Eastern provenance, originating probably in Syria or even in Jerusalem, and was transmitted from Byzantine sources to Carolingian practice and theory during the 8th century. However, the earlier Greek model for the Carolingian system was probably ordered like the later Byzantine oktōēchos, that is, with the four principal (authentic) modes first, then the four plagals, whereas the Latin modes were always grouped the other way, with the authentics and plagals paired (Powers 2001, §II.1(ii)).
The 6th century scholar Boethius had translated Greek music theory treatises by Nicomachus and Ptolemy into Latin (Powers 2001). Later authors created confusion by applying mode as described by Boethius to explain plainchant modes, which were a wholly different system (Palisca 1984, 222). In his De institutione musica, book 4 chapter 15, Boethius, like his Hellenistic sources, twice used the term harmonia to describe what would likely correspond to the later notion of "mode", but also used the word "modus"—probably translating the Greek word τρόπος (tropos), which he also rendered as Latin tropus—in connection with the system of transpositions required to produce seven diatonic octave species (Bower 1984, 253, 260–61), so the term was simply a means of describing transposition and had nothing to do with the church modes (Powers 2001, §II.1(i)).
Later, 9th-century theorists applied Boethius’s terms tropus and modus (along with "tonus") to the system of church modes. The treatise De Musica (or De harmonica institutione) of Hucbald synthesized the three previously disparate strands of modal theory: chant theory, the Byzantine oktōēchos and Boethius's account of Hellenistic theory (Powers 2001, §II.2). The late 9th-/early 10th-century compilation known as the Alia musica imposed the seven octave transpositions, known as tropus and described by Boethius, onto the eight church modes (Powers 2001, §II.2(ii)), but its compilator also mentions the Greek (Byzantine) echoi translated by the Latin term sonus. Thus, the names of the modes became associated with the eight church tones and their modal formulas, but this medieval interpretation does actually not fit to the concept of the Ancient Greek harmonics treatises. The understanding of mode today does often not reflect that it is made of different concepts which cannot fit altogether.
The introit Jubilate Deo, from which Jubilate Sunday gets its name, is in Mode 8.
According to Carolingian theorists the eight church modes, or Gregorian modes, can be divided into four pairs, where each pair shares the "final" note and the four notes above the final, but they have different intervals concerning the species of the fifth. If the octave is completed by adding three notes above the fifth, the mode is termed authentic, but if the octave is completed by adding three notes below, it is called plagal (from Greek πλάγιος, "oblique, sideways"). Otherwise explained: if the melody moves mostly above the final, with an occasional cadence to the sub-final, the mode is authentic. Plagal modes shift range and also explore the fourth below the final as well as the fifth above. In both cases, the strict ambitus of the mode is one octave. A melody that remains confined to the mode's ambitus is called "perfect"; if it falls short of it, "imperfect"; if it exceeds it, "superfluous"; and a melody that combines the ambituses of both the plagal and authentic is said to be in a "mixed mode" (Rockstro 1880, 343).
Although the earlier (Greek) model for the Carolingian system was probably ordered like the Byzantine oktōēchos, with the four authentic modes first, followed by the four plagals, the earliest extant sources for the Latin system are organized in four pairs of authentic and plagal modes sharing the same final: protus authentic/plagal, deuterus authentic/plagal, tritus authentic/plagal, and tetrardus authentic/plagal (Powers 2001, §II, 1 (ii)).
Each mode has, in addition to its final, a "reciting tone", sometimes called the "dominant" (Apel 1969, 166; Smith 1989, 14). It is also sometimes called the "tenor", from Latin tenere "to hold", meaning the tone around which the melody principally centres (Fallows 2001). The reciting tones of all authentic modes began a fifth above the final, with those of the plagal modes a third above. However, the reciting tones of modes 3, 4, and 8 rose one step during the tenth and eleventh centuries with 3 and 8 moving from B to C (half step) and that of 4 moving from G to A (whole step) (Hoppin 1978, 67).
After the reciting tone, every mode is distinguished by scale degrees called "mediant" and "participant". The mediant is named from its position between the final and reciting tone. In the authentic modes it is the third of the scale, unless that note should happen to be B, in which case C substitutes for it. In the plagal modes, its position is somewhat irregular. The participant is an auxiliary note, generally adjacent to the mediant in authentic modes and, in the plagal forms, coincident with the reciting tone of the corresponding authentic mode (some modes have a second participant) (Rockstro 1880, 342).
Kyrie "orbis factor", in mode 1 (Dorian) with B on scale-degree 6, descends from the reciting tone, A, to the final, D, and uses the subtonium (tone below the final).
Only one accidental is used commonly in Gregorian chant—B may be lowered by a half-step to B. This usually (but not always) occurs in modes V and VI, as well as in the upper tetrachord of IV, and is optional in other modes except III, VII and VIII (Powers 2001, §II.3.i(b), Ex. 5).
Final (note)DDEEFFGG
Final (solfege)reremimifafasolsol
Dominant (note)AFB-CG-ACADB-C
Dominant (solfege)lafasi-dosol-ladolaresi-do
In 1547, the Swiss theorist Henricus Glareanus published the Dodecachordon, in which he solidified the concept of the church modes, and added four additional modes: the Aeolian (mode 9), Hypoaeolian (mode 10), Ionian (mode 11), and Hypoionian (mode 12). A little later in the century, the Italian Gioseffo Zarlino at first adopted Glarean's system in 1558, but later (1571 and 1573) revised the numbering and naming conventions in a manner he deemed more logical, resulting in the widespread promulgation of two conflicting systems. Zarlino's system reassigned the six pairs of authentic–plagal mode numbers to finals in the order of the natural hexachord, C D E F G A, and transferred the Greek names as well, so that modes 1 through 8 now became C-authentic to F-plagal, and were now called by the names Dorian to Hypomixolydian. The pair of G modes were numbered 9 and 10 and were named Ionian and Hypoionian, while the pair of A modes retained both the numbers and names (11, Aeolian, and 12 Hypoaeolian) of Glarean's system. While Zarlino's system became popular in France, Italian composers preferred Glarean's scheme because it retained the traditional eight modes, while expanding them. Luzzasco Luzzaschi was an exception in Italy, in that he used Zarlino’s new system (Powers 2001, §III.4(ii)(a), (iii) & §III.5(i & ii)).
In the late-eighteenth and nineteenth centuries, some chant reformers (notably the editors of the MechlinPustet-Ratisbon (Regensburg), and Rheims-Cambrai Office-Books, collectively referred to as the Cecilian Movement) renumbered the modes once again, this time retaining the original eight mode numbers and Glareanus's modes 9 and 10, but assigning numbers 11 and 12 to the modes on the final B, which they named Locrian and Hypolocrian (even while rejecting their use in chant). The Ionian and Hypoionian modes (on C) become in this system modes 13 and 14 (Rockstro 1880, 342).
Given the confusion between ancient, medieval, and modern terminology, "today it is more consistent and practical to use the traditional designation of the modes with numbers one to eight" (Curtis 1997, 256), using Roman numeral (I–VIII), rather than using the pseudo-Greek naming system. Medieval terms, first used in Carolingian treatises, later in Aquitanian tonaries, are still used by scholars today: the Greek ordinals ("first", "second", etc.) transliterated into the Latin alphabet protus (πρῶτος), deuterus (δεύτερος), tritus (τρίτος), and tetrardus (τέταρτος). In practice they can be specified as authentic or as plagal like "protus authentus / plagalis".
The eight musical modes. f indicates "final" (Curtis 1997, 255).


A mode indicated a primary pitch (a final); the organization of pitches in relation to the final; suggested range; melodic formulas associated with different modes; location and importance of cadences; and affect (i.e., emotional effect/character). Liane Curtis writes that "Modes should not be equated with scales: principles of melodic organization, placement of cadences, and emotional affect are essential parts of modal content" in Medieval and Renaissance music (Curtis 1997, 255, in Knighton 1997).
Carl Dahlhaus (1990, 192) lists "three factors that form the respective starting points for the modal theories of Aurelian of RéômeHermannus Contractus, and Guido of Arezzo:
  • the relation of modal formulas to the comprehensive system of tonal relationships embodied in the diatonic scale;
  • the partitioning of the octave into a modal framework; and
  • the function of the modal final as a relational center."
The oldest medieval treatise regarding modes is Musica disciplina by Aurelian of Réôme (dating from around 850) while Hermannus Contractus was the first to define modes as partitionings of the octave (Dahlhaus 1990, 192–91). However, the earliest Western source using the system of eight modes is the Tonary of St Riquier, dated between about 795 and 800 (Powers 2001, §II 1(ii)).
Various interpretations of the "character" imparted by the different modes have been suggested. Three such interpretations, from Guido of Arezzo (995–1050), Adam of Fulda (1445–1505), and Juan de Espinosa Medrano (1632–1688), follow:
NameModeD'ArezzoFuldaEspinosaExample chant
DorianIseriousany feelinghappy, taming the passionsVeni sancte spiritus
HypodorianIIsadsadserious and tearfulIesu dulcis amor meus
PhrygianIIImysticvehementinciting angerKyrie, fons bonitatis
HypophrygianIVharmonioustenderinciting delights, tempering fiercenessConditor alme siderum
LydianVhappyhappyhappySalve Regina
HypolydianVIdevoutpioustearful and piousUbi caritas
MixolydianVIIangelicalof youthuniting pleasure and sadnessIntroibo
HypomixolydianVIIIperfectof knowledgevery happyAd cenam agni providi


The modern Western modes consist of seven scales related to the familiar major and minor keys.
Although the names of the modern modes are Greek and some have names used in ancient Greek theory for some of the harmoniai, the names of the modern modes are conventional and do not indicate a link between them and ancient Greek theory, and they do not present the sequences of intervals found even in the diatonic genus of the Greek octave species sharing the same name.
Modern Western modes use the same set of notes as the major scale, in the same order, but starting from one of its seven degrees in turn as a "tonic", and so present a different sequence of whole and half steps. The interval sequence of the major scale being T-T-s-T-T-T-s, where "s" means a semitone (half step) and "T" means a whole tone (whole step), it is thus possible to generate the following scales:
ModeTonic relative
to major scale
Interval sequenceExample
For the sake of simplicity, the examples shown above are formed by natural notes (also called "white-notes", as they can be played using the white keys of a piano keyboard). However, any transposition of each of these scales is a valid example of the corresponding mode. In other words, transposition preserves mode.
Pitch constellations of the modern musical modes


Each mode has characteristic intervals and chords that give it its distinctive sound. The following is an analysis of each of the seven modern modes. The examples are provided in a key signature with no sharps or flats (scales composed of natural notes).

Ionian (I)[edit]

Ionian mode on C About this sound Play 
Ionian may arbitrarily be designated the first mode. It is the modern major scale. The example composed of natural notes begins on C, and is also known as the C-major scale:
Natural notesCDEFGABC
Interval from CP1M2M3P4P5M6M7P8
  • Tonic triad: C
  • Tonic seventh chord: CM7
  • Dominant triad: G (in modern tonal thinking, the fifth or dominant scale degree, which in this case is G, is the next-most important chord root after the tonic)
  • Seventh chord on the dominant: G7 (a "dominant 7th" chord type, so-called because of its position in this—and only this—modal scale)
  • The major-minor 7th chord ("dominant 7th" type chord) occurs on V, the one mode where the major-minor 7th is actually a dominant 7th chord.

Dorian (II)[edit]

Dorian mode on D About this sound Play 
Dorian is the second mode. The example composed of natural notes begins on D:
Natural notesDEFGABCD
Interval from DP1M2m3P4P5M6m7P8
The Dorian mode is very similar to the modern natural minor scale (see Aeolian mode below). The only difference with respect to the natural minor scale is in the sixth scale degree, which is a major sixth (M6) above the tonic, rather than a minor sixth (m6).
  • Tonic triad: Dm
  • Tonic seventh chord: Dm7
  • Dominant triad: Am
  • Seventh chord on the dominant: Am7 (a "minor seventh" chord type).
  • The major-minor 7th chord ("dominant 7th" type chord) occurs on IV.

Phrygian (III)[edit]

Phrygian mode on E About this sound Play 
Phrygian is the third mode. The example composed of natural notes starts on E:
Natural notesEFGABCDE
Interval from EP1m2m3P4P5m6m7P8
The Phrygian mode is very similar to the modern natural minor scale (see Aeolian mode below). The only difference with respect to the natural minor scale is in the second scale degree, which is a minor second (m2) above the tonic, rather than a major second (M2).
  • Tonic triad: Em
  • Tonic seventh chord: Em7
  • Dominant triad: Bdim
  • Seventh chord on the dominant: Bø, a "half-diminished seventh" chord type.
  • The major-minor 7th chord ("dominant 7th" type chord) occurs on III.

Lydian (IV)[edit]

Lydian mode on F About this sound Play 
Lydian is the fourth mode. The example composed of natural notes starts on F:
Natural notesFGABCDEF
Interval from FP1M2M3A4P5M6M7P8
The single tone that differentiates this scale from the major scale (Ionian mode) is its fourth degree, which is an augmented fourth (A4) above the tonic (F), rather than a perfect fourth (P4).
  • Tonic triad: F
  • Tonic seventh chord: FM7
  • Dominant triad: C
  • Seventh chord on the dominant: CM7, a "major-seventh" chord type.
  • The major-minor 7th chord ("dominant 7th" type chord) occurs on II.

Mixolydian (V)[edit]

Mixolydian mode on G About this sound Play 
Mixolydian is the fifth mode. The example composed of natural notes begins on G:
Natural notesGABCDEFG
Interval from GP1M2M3P4P5M6m7P8
The single tone that differentiates this scale from the major scale (Ionian mode), is its seventh degree, which is a minor seventh (m7) above the tonic (G), rather than a major seventh (M7). Therefore, the seventh scale degree becomes a subtonic to the tonic because it is now a whole tone lower than the tonic, in contrast to the seventh degree in the major scale, which is a semitone tone lower than the tonic (leading-tone).
  • Tonic triad: G
  • Tonic seventh chord: G7 (the "dominant-seventh" chord type in this mode is the seventh chord built on the tonic degree)
  • Dominant triad: Dm
  • Seventh chord on the dominant: Dm7, a "minor-seventh" chord type.
  • The major-minor 7th chord ("dominant 7th" type chord) occurs on I.

Aeolian (VI)[edit]

Aeolian mode on A About this sound Play 
Aeolian is the sixth mode. It is also called the natural minor scale. The example composed of natural notes begins on A, and is also known as the A natural-minor scale:
Natural notesABCDEFGA
Interval from AP1M2m3P4P5m6m7P8
  • Tonic triad: Am
  • Tonic seventh chord: Am7
  • Dominant triad: Em
  • Seventh chord on the dominant: Em7, a "minor-seventh" chord type.
  • The major-minor 7th chord ("dominant 7th" type chord) occurs on VII.

Locrian (VII)[edit]

Locrian mode on B About this sound Play 
Locrian is the seventh mode. The example composed of natural notes begins on B:
Natural notesBCDEFGAB
Interval from BP1m2m3P4d5m6m7P8
The distinctive scale degree here is the diminished fifth (d5). This makes the tonic triad diminished, so this mode is the only one in which the chords built on the tonic and dominant scale degrees have their roots separated by a diminished, rather than perfect, fifth. Similarly the tonic seventh chord is half-diminished.
  • Tonic triad: Bdim or B°
  • Tonic seventh chord: Bm75 or Bø
  • Dominant triad: FM
  • Seventh chord on the dominant: FM7, a major-seventh chord type.
  • The major-minor 7th chord ("dominant 7th" type chord) occurs on VI.


The modes can be arranged in the following sequence, which follows the circle of fifths. In this sequence, each mode has one more lowered interval relative to the tonic than the mode preceding it. Thus taking Lydian as reference, Ionian (major) has a lowered fourth; Mixolydian, a lowered fourth and seventh; Dorian, a lowered fourth, seventh, and third; Aeolian (Natural Minor), a lowered fourth, seventh, third, and sixth; Phrygian, a lowered fourth, seventh, third, sixth, and second; and Locrian, a lowered fourth, seventh, third, sixth, second, and fifth. Put another way, the augmented fourth of the Lydian scale has been reduced to a perfect fourth in Ionian, the major seventh in Ionian, to a minor seventh in Mixolydian, etc.
Intervals with respect to the tonic
The tonic of a transposed mode is at the same number of 5ths down (resp. up) from the natural tonic of the mode as there are flats (resp. sharps) in its signature: e.g. the Dorian scale with 3  is F dorian as F is three 5ths down from D (F - C - G - D) and the Dorian scale with 3  is B dorian as B is three 5ths up from D (D - A - E - B). Or equivalently it is at the same interval from the tonic of the major scale with the same signature (its relative major) as that formed by its natural tonic and C: e.g. the Lydian scale with 2  is E Lydian and the Lydian scale with 2  is G Lydian as E forms with B (relative major) and G forms with D (relative major), the same interval as between F and C.
Conversely the signature of a transposed mode has as many sharps (resp. flats) as there are 5ths up (resp. down) between the tonic of the natural mode and the tonic of the transposed mode: e.g. B Dorian's signature is 4  as B is four 5ths down from D (B - F - C - G - D) and A lydian's signature is 4  as A is four 5ths up from F (F - C - G - D - A). Or again equivalently the signature of a transposed mode is the same as that of its relative major. That forms with the tonic of the transposed mode the same interval as C with the tonic of the natural mode: e.g. B Phrygian's signature is 6  as its relative major is G (C is a major 3rd down from E) and C Mixolydian's signature is 6  as its relative major is F (C is a 5th down from G).
For example the modes transposed to a common tonic of C have the following signatures:
C Ionian (major)CDEFGABC
C MixolydianCDEFGABC
C Aeolian (natural minor)CDEFGABC
The first three modes are sometimes called major, the next three minor, and the last one diminished (Locrian), according to the quality of their tonic triads.
The Locrian mode is traditionally considered theoretical rather than practical because the triad built on the first scale degree is diminished. Diminished triads are not consonant and therefore do not lend themselves to cadential endings. A diminished chord cannot be tonicized according to tonal phrasing practice.

Major modes[edit]

The Ionian mode (About this sound listen ) corresponds to the major scale. Scales in the Lydian mode (About this sound listen ) are major scales with the subdominant (fourth scale degree) raised by a semitone. The Mixolydian mode (About this sound listen ) corresponds to the major scale using the subtonic (the lowered seventh) instead of the leading-tone.

Minor modes[edit]

The Aeolian mode (About this sound listen ) is identical to the natural minor scale. The Dorian mode (About this sound listen ) corresponds to the natural minor scale with the submediant (sixth scale degree) raised a semitone. The Phrygian mode (About this sound listen ) corresponds to the natural minor scale with the supertonic (second scale degree) lowered a semitone.

Diminished mode[edit]

The Locrian (About this sound listen ) is neither a major nor a minor mode because, although its third scale degree is minor, the fifth degree is diminished instead of perfect. For this reason it is sometimes called a "diminished" scale, though in jazz theory this term is also applied to the octatonic scale. This interval is enharmonically equivalent to the augmented fourth found between scale-degrees 1 and 4 in the Lydian mode and is also referred to as the tritone.


Use and conception of modes or modality today is different from that in early music. As Jim Samson explains, "Clearly any comparison of medieval and modern modality would recognize that the latter takes place against a background of some three centuries of harmonic tonality, permitting, and in the nineteenth century requiring, a dialogue between modal and diatonic procedure" (Samson 1977, 148). Indeed, when 19th-century composers revived the modes, they rendered them more strictly than Renaissance composers had, to make their qualities distinct from the prevailing major-minor system. Renaissance composers routinely sharped leading tones at cadences and lowered the fourth in the Lydian mode (Carver 2005, 74n4).
The Ionian, or Iastian (Anon. 1896Chafe 1992, 23, 41, 43, 48; Glareanus 1965, 153; Hiley 2002, §2(b); Powers 2001, §4.ii(a); Pratt 1907, 67; Taylor 1876, 419; Wiering 1995, 25) mode is another name for the major scale used in much Western music. The Aeolian forms the base of the most common Western minor scale; in modern practice the Aeolian mode is differentiated from the minor by using only the seven notes of the Aeolian scale. By contrast, minor mode compositions of the common practice period frequently raise the seventh scale degree by a semitone to strengthen the cadences, and in conjunction also raise the sixth scale degree by a semitone to avoid the awkward interval of an augmented second. This is particularly true of vocal music (Jones 1974, 33).
Traditional folk music provides countless examples of modal melodies. For example, Irish traditional music makes extensive usage not only of the major mode, but also the Mixolydian, Dorian, and Aeolian modes (Cooper 1995, 9–20). Much Flamenco music is in the Phrygian mode.[citation needed]
Zoltán KodályGustav HolstManuel de Falla use modal elements as modifications of a diatonic background, while in the music of Debussy and Béla Bartók modality replaces diatonic tonality (Samson 1977,[page needed])

Other types[edit]

While the term "mode" is still most commonly understood to refer to Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, or Locrian scales, in modern music theory the word is sometimes applied to scales other than the diatonic. This is seen, for example, in "melodic minor" scale harmony, which is based on the seven rotations of the ascending melodic minor scale, yielding some interesting scales as shown below. The "chord" row lists tetrads that can be built from the pitches in the given mode (Levine 1995, 55–[page needed]); see also Avoid note.
NameAscending Melodic MinorPhrygian 6 or Dorian 2Lydian AugmentedLydian DominantMixolydian 6Half-DiminishedAltered dominant
Notes1 2 3 4 5 6 73 4 5 6 71 2 3 5 6 71 2 3 4 5 6 71 2 3 4 5 71 2 3 4 77
NameHarmonic MinorLocrian 6Ionian 5Ukrainian DorianPhrygian DominantLydian 2Altered Diminished
Notes1 2 3 4 5 6 73 4 5 6 71 2 3 4 5 6 71 2 4 5 6 72 3 4 5 72 3 4 5 6 7double flat7
ChordC–ΔDøEΔ5F–7G79AΔ or AΔBo7
NameDouble HarmonicLydian 6Phrygian double flat4Hungarian MinorLocrian 3 or Mixolydian 2Ionian 2Locrian double flatdouble flat7
Notes2 3 4 5 6 72 3 4 5 6 74 5 double flat71 2 4 5 6 72 3 4 5 6 72 3 4 5 6 7double flat3 4 double flat7
ChordCΔDΔ11E–6F–ΔG75AΔ5Bodouble flat3
The number of possible modes for any intervallic set is dictated by the pattern of intervals in the scale. For scales built of a pattern of intervals that only repeats at the octave (like the diatonic set), the number of modes is equal to the number of notes in the scale. Scales with a recurring interval pattern smaller than an octave, however, have only as many modes as notes within that subdivision: e.g., the diminished scale, which is built of alternating whole and half steps, has only two distinct modes, since all odd-numbered modes are equivalent to the first (starting with a whole step) and all even-numbered modes are equivalent to the second (starting with a half step). The chromatic and whole-tone scales, each containing only steps of uniform size, have only a single mode each, as any rotation of the sequence results in the same sequence. Another general definition excludes these equal-division scales, and defines modal scales as subsets of them: "If we leave out certain steps of a[n equal-step] scale we get a modal construction" (Karlheinz Stockhausen, in Cott 1973, 101). In "Messiaen's narrow sense, a mode is any scale made up from the 'chromatic total,' the twelve tones of the tempered system" (Vieru 1985, 63).

Analogues in different musical traditions[edit]

See also[edit]


  • Anderson, Warren, and Thomas J. Mathiesen (2001). "Ethos". The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers.
  • Anon. (1896). "Plain-song". Chambers's Encyclopaedia: A Dictionary of Universal Knowledge, new edition. Volume 8: Peasant to Roumelia. London and Edinburgh: William & Robert Chambers, Ltd.; Philadelphia: J. B. Lippincott Co.
  • Aristotle (1895). Aristotle’s Politics: A Treatise on Government. , translated from the Greek of Aristotle by William Ellis, MA, with an Introduction by Henry Morley. London: George Routledge and Sons, Ltd.
  • Barbera, André (1984). "Octave Species". The Journal of Musicology 3, no. 3 (July): 229–41. doi:10.1525/jm.1984.3.3.03a00020 (Subscription access)
  • Barker, Andrew (ed.) (1984–89). Greek Musical Writings. 2 vols. Cambridge & New York: Cambridge University Press. ISBN 0-521-23593-6 (v. 1) ISBN 0-521-30220-X (v. 2).
  • Barton, Louis W. G. (2009). "§ Influence of Byzantium on Western Chant". The Neume Notation Project: Research in Computer Applications to Medieval Chant.
  • Bower, Calvin M. (1984). "The Modes of Boethius". The Journal of Musicology 3, no. 3 (July): 252–63. doi:10.1525/jm.1984.3.3.03a00040 (subscription required).
  • Carver, Anthony F. (2005). "Bruckner and the Phrygian Mode". Music and Letters 86, no. 1:74–99. doi:10.1093/ml/gci004
  • Chafe, Eric Thomas (1992). Monteverdi’s Tonal Language. New York: Schirmer Books. ISBN 9780028704951.
  • Chalmers, John H. (1993). Divisions of the Tetrachord / Peri ton tou tetrakhordou katatomon / Sectiones tetrachordi: A Prolegomenon to the Construction of Musical Scales, edited by Larry Polansky and Carter Scholz, foreword by Lou Harrison. Hanover, NH: Frog Peak Music. ISBN 0-945996-04-7.
  • Cleonides (1965). "Harmonic Introduction," translated by Oliver Strunk. In Source Readings in Music History, vol. 1 (Antiquity and the Middle Ages), edited by Oliver Strunk, 34–46. New York: W. W. Norton & Co.
  • Cooper, Peter (1995). Mel Bay's Complete Irish Fiddle Player. Pacific, Missouri: Mel Bay Publications. ISBN 0-7866-6557-2.
  • Cott, Jonathan (1973). Stockhausen: Conversations with the Composer. New York: Simon and Schuster. ISBN 0-671-21495-0.
  • Curtis, Liane (1997). "Mode". In Companion to Medieval and Renaissance Music, edited by Tess Knighton and David Fallows. Berkeley: University of California Press. ISBN 0-520-21081-6.
  • Dahlhaus, Carl (1968). Untersuchungen über die Entstehung der harmonischen Tonalität. Kassel.[full citation needed]
  • Dahlhaus, Carl (1990). Studies on the Origin of Harmonic Tonality. Princeton, New Jersey: Princeton University Press. ISBN 0-691-09135-8.
  • Fallows, David (2001). "Tenor §1". The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers.
  • Glareanus, Henricus (1965). Dodecachordon, Volume 1, translated by Clement Albin Miller. Musicological Studies and Documents 6. [Rome]: American Institute of Musicology.
  • Hiley, David (2002). "Mode". The Oxford Companion to Music, edited by Alison Latham. Oxford and New York: Oxford University Press. ISBN 978-0-19-866212-9.
  • Hoppin, Richard (1978). Medieval Music. The Norton Introduction to Music History. New York: Norton. ISBN 0-393-09090-6.
  • Jones, George Thaddeus (1974). Music Theory. Barnes & Noble College Outline Series 137. New York: Barnes & Noble Books. ISBN 0-06-467168-2.
  • Jowett, Benjamin (1937). The Dialogues of Plato, translated by Benjamin Jowett, third edition, 2 vols. New York: Random House. OCLC 2582139
  • Jowett, Benjamin (1943). Aristotle's Politics, translated by Benjamin Jowett. New York: Modern Library.
  • Levine, Mark (1995). The Jazz Theory Book. Petaluma, California: Sher Music Co. ISBN 1-883217-04-0.
  • Mathiesen, Thomas J. (1983). Aristides Quintilianus. On Music. Translated by Thomas J. Mathiesen. New Haven and London: Yale University Press.
  • Mathiesen, Thomas J. (1999). Apollo's Lyre: Greek Music and Music Theory in Antiquity and the Middle Ages. Publications of the Center for the History of Music Theory and Literature 2. Lincoln: University of Nebraska Press. ISBN 0-8032-3079-6.
  • Mathiesen, Thomas J. (2001a). "Greece, §I: Ancient". The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers.
  • Mathiesen, Thomas J. (2001b). "Harmonia (i)". The New Grove Dictionary of Music and Musicians, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers.
  • Mathiesen, Thomas J. (2001c). "Tonos". The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers.
  • Meier, Bernhard (1974). Die Tonarten der klassischen Vokalpolyphonie: nach den Quellen dargestellt. Utrecht.[full citation needed]
  • Meier, Bernhard (1988). The Modes of Classical Vocal Polyphony: Described According to the Sources, translated from the German by Ellen S. Beebe, with revisions by the author. New York: Broude Brothers. ISBN 978-0-8450-7025-3.
  • Meier, Bernhard (1992). Alte Tonarten: dargestellt an der Instrumentalmusik des 16. und 17. Jahrhunderts. Kassel:[full citation needed]
  • Nikodēmos ’Agioreitēs [St Nikodemos of the Holy Mountain] (1836). ’Eortodromion: ētoi ’ermēneia eis tous admatikous kanonas tōn despotikōn kai theomētorikōn ’eortōn, edited by Benediktos Kralidēs. Venice: N. Gluku. Reprinted, Athens: H.I. Spanos, 1961.
  • Palisca, Claude V. (1984). "Introductory Notes on the Historiography of the Greek Modes". The Journal of Musicology 3, no. 3 (Summer): 221–28. doi:10.1525/jm.1984.3.3.03a00010 (subscription required).
  • Palisca, Claude V. (2006). Music and Ideas in the Sixteenth and Seventeenth Centuries. Studies in the History of Music Theory and Literature 1. Urbana and Chicago: University of Illinois Press. ISBN 9780252031564.
  • Porter, James (2001). "Mode §IV: Modal Scales and Traditional Music". The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers.
  • Powers, Harold S. (2001). "Mode". The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers.
  • Pratt, Waldo Selden (1907). The History of Music: A Handbook and Guide for Students. New York: G. Schirmer.
  • Rockstro, W[illiam] S[myth] (1880). "Modes, the Ecclesiastical". A Dictionary of Music and Musicians (A.D. 1450–1880), by Eminent Writers, English and Foreign, vol. 2, edited by George Grove, D. C. L., 340–43. London: Macmillan and Co.
  • Samson, Jim (1977). Music in Transition: A Study of Tonal Expansion and Atonality, 1900–1920. Oxford & New York: Oxford University Press. ISBN 0-460-86150-6.
  • Smith, Charlotte (1989). A Manual of Sixteenth-Century Contrapuntal Style. Newark: University of Delaware Press; London: Associated University Presses. ISBN 978-0-87413-327-1.
  • Solomon, Jon (1984). "Towards a History of Tonoi". The Journal of Musicology 3, no. 3 (July): 242–51. doi:10.1525/jm.1984.3.3.03a00030 (subscription required).
  • Taylor, John (1876). The Student's Text-book of the Science of Music. London and Liverpool: George Philip and Son.
  • Vieru, Anatol (1985). "Modalism – A 'Third World'". Perspectives of New Music 24, no. 1 (Fall–Winter): 62–71.
  • Wellesz, Egon (1954). "Music of the Eastern Churches". The New Oxford History of Music, vol.2:14-57. L., N.Y.: Oxford University Press.
  • Wiering, Frans. 1995. The Language of the Modes: Studies in the History of Polyphonic Modality. Breukelen: Frans Wiering.
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Further reading[edit]

  • Brent, Jeff, with Schell Barkley (2011). Modalogy: Scales, Modes & Chords: The Primordial Building Blocks of Music. Milwaukee: Hal Leonard Corporation. ISBN 978-1-4584-1397-0
  • Fellerer, Karl Gustav (1982). "Kirchenmusikalische Reformbestrebungen um 1800". Analecta Musicologica: Veröffentlichungen der Musikgeschichtlichen Abteilung des Deutschen Historischen Instituts in Rom 21:393–408.
  • Grout, Donald, Claude Palisca, and J. Peter Burkholder (2006). A History of Western Music. New York: W. W. Norton. 7th edition. ISBN 0-393-97991-1.
  • Judd, Cristle (ed) (1998). Tonal Structures in Early Music: Criticism and Analysis of Early Music, 1st ed. New York: Garland. ISBN 0-8153-2388-3.
  • Levine, Mark (1989). The Jazz Piano Book. Petaluma, CA: Sher Music Co. ISBN 0-9614701-5-1.
  • Lonnendonker, Hans. 1980. "Deutsch-französische Beziehungen in Choralfragen. Ein Beitrag zur Geschichte des gregorianischen Chorals in der zweiten Hälfte des 19. Jahrhunderts". In Ut mens concordet voci: Festschrift Eugène Cardine zum 75. Geburtstag, edited by Johannes Berchmans Göschl, 280–95. St. Ottilien: EOS-Verlag. ISBN 3-88096-100-X
  • McAlpine, Fiona (2004). "Beginnings and Endings: Defining the Mode in a Medieval Chant". Studia Musicologica Academiae Scientiarum Hungaricae 45, nos. 1 & 2 (17th International Congress of the International Musicological Society IMS Study Group Cantus Planus): 165–77.
  • Meeùs, Nicolas (1997). "Mode et système. Conceptions ancienne et moderne de la modalité". Musurgia 4, no. 3:67–80.
  • Meeùs, Nicolas (2000). "Fonctions modales et qualités systémiques". Musicae Scientiae, Forum de discussion 1:55–63.
  • Meier, Bernhard (1974). Die Tonarten der klassischen Vokalpolyphonie: nach den Quellen dargestellt. Utrecht.
  • Meier, Bernhard (1988). The Modes of Classical Vocal Polyphony: Described According to the Sources, translated from the German by Ellen S. Beebe, with revisions by the author. New York: Broude Brothers. ISBN 978-0-8450-7025-3
  • Meier, Bernhard (1992). Alte Tonarten: dargestellt an der Instrumentalmusik des 16. und 17. Jahrhunderts. Kassel
  • Miller, Ron (1996). Modal Jazz Composition and Harmony, Vol. 1. Rottenburg, Germany: Advance Music. OCLC 43460635
  • Ordoulidis, Nikos. (2011). "The Greek Popular Modes". British Postgraduate Musicology 11 (December). (Online journal, accessed 24 December 2011)
  • Pfaff, Maurus (1974). "Die Regensburger Kirchenmusikschule und der cantus gregorianus im 19. und 20. Jahrhundert". Gloria Deo-pax hominibus. Festschrift zum hundertjährigen Bestehen der Kirchenmusikschule Regensburg, Schriftenreihe des Allgemeinen Cäcilien-Verbandes für die Länder der Deutschen Sprache 9, edited by Franz Fleckenstein, 221–52. Bonn: Allgemeiner Cäcilien-Verband, 1974.
  • Powers, Harold (1998). "From Psalmody to Tonality". In Tonal Structures in Early Music, edited by Cristle Collins Judd, 275–340. Garland Reference Library of the Humanities 1998; Criticism and Analysis of Early Music 1. New York: Garland Publishing. ISBN 0-8153-2388-3.
  • Ruff, Anthony, and Raphael Molitor (2008). "Beyond Medici: The Struggle for Progress in Chant". Sacred Music 135, no. 2 (Summer): 26–44.
  • Scharnagl, August (1994). "Carl Proske (1794-1861)". In Musica divina: Ausstellung zum 400. Todesjahr von Giovanni Pierluigi Palestrina und Orlando di Lasso und zum 200. Geburtsjahr von Carl Proske. Ausstellung in der Bischöflichen Zentralbibliothek Regensburg, 4. November 1994 bis 3. Februar 1995, Bischöfliches Zentralarchiv und Bischöfliche Zentralbibliothek Regensburg: Kataloge und Schriften, no. 11, edited by Paul Mai, 12–52. Regensburg: Schnell und Steiner, 1994.
  • Schnorr, Klemens (2004). "El cambio de la edición oficial del canto gregoriano de la editorial Pustet/Ratisbona a la de Solesmes en la época del Motu proprio". In El Motu proprio de San Pío X y la Música (1903–2003). Barcelona, 2003, edited by Mariano Lambea, introduction by María Rosario Álvarez Martínez and José Sierra Pérez. Revista de musicología 27, no. 1 (June) 197–209.
  • Street, Donald (1976). "The Modes of Limited Transposition". The Musical Times 117, no. 1604 (October): 819–23.
  • Vieru, Anatol (1980). Cartea modurilor. Bucharest: Editura Muzicală. English edition, as The Book of Modes, translated by Yvonne Petrescu and Magda Morait. Bucharest: Editura Muzicală, 1993.
  • Vieru, Anatol (1992). "Generating Modal Sequences (A Remote Approach to Minimal Music)". Perspectives of New Music 30, no. 2 (Summer): 178–200.
  • Vincent, John (1974). The Diatonic Modes in Modern Music, revised edition. Hollywood: Curlew Music. OCLC 249898056
  • Wiering, Frans (1998). "Internal and External Views of the Modes". In Tonal Structures in Early Music, edited by Cristle Collins Judd, 87–107. Garland Reference Library of the Humanities 1998; Criticism and Analysis of Early Music 1. New York: Garland Publishing. ISBN 0-8153-2388-3.

External links[edit]

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