In modern Western music, mode (from Latin modus, "measure, standard, manner, way") is a concept that involves scale and melody type.
Historically, it had other meanings. In the early medieval period, it meant interval. In the late medieval period, it meant the rhythmic relationship between long and short values (Powers 2001, Introduction). Since the end of the eighteenth century, the term has also applied—in ethnomusicological contexts—to pitch structures in non-European musical cultures, sometimes with doubtful compatibility (Powers 2001, §V,1).
This article addresses the medieval and modern scale and melody-type meaning.
Modes and scales
A "scale" is an ordered series of intervals that, with the key or tonic (first tone), defines that scale's intervals, or steps. However, "mode" is usually used in the sense of "scale," applied only to the 7 specific diatonic scales (using only the seven tones of the scale without chromatic alterations) that follow the tonic note. The use of more than one mode makes music polymodal, as with polymodal chromaticism. Modern musicological practice has extended the concept of mode to earlier musical systems, such as those of Ancient Greek music and Jewish cantillation, as well as to non-Western musics (Powers 2001, §I, 3; Winnington-Ingram 1936, 2–3).
Early Greek treatises on music do not use the term "mode" (which comes from Latin), but do describe scales (or "systems"), tonoi (the more usual term used in medieval theory for "mode"), and harmoniai (harmony)—the latter subsuming the corresponding tonoi but not necessarily the converse (Mathiesen 2001a, 6(iii)(e);Thomas J. Mathiesen, "Greece, §I: Ancient").
The Greek scales in the Aristoxenian tradition were (Barbera 1984, 240; Mathiesen 2001a, 6(iii)(d)):
- Mixolydian: hypate hypaton–paramese (b–b′)
- Lydian: parhypate hypaton–trite diezeugmenon (c′–c″)
- Phrygian: lichanos hypaton–paranete diezeugmenon (d′–d″)
- Dorian: hypate meson–nete diezeugmenon (e′–e″)
- Hypolydian: parhypate meson–trite hyperbolaion (f′–f″)
- Hypophrygian: lichanos meson–paranete hyperbolaion (g′–g″)
- Common, Locrian, or Hypodorian: mese–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 (Lydia, Phrygia). The association of these ethnic names with the octave species appears to precede Aristoxenos, 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 diesis) (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)).
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 Aristoxenos, 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)). Aristoxenos'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). These tonoi and corresponding harmoniai correspond with the intervals of the familiar modern major and minor scales. See Pythagorean tuning and Pythagorean interval.
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).
In the Republic, Plato 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.
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, "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).
The classification of the requirements we have from Proclus Useful Knowledge as preserved by Photios:
- for the gods—hymn, prosodion, paean, dithyramb, nomos, adonidia, iobakchos, and hyporcheme;
- for humans—encomion, epinikion, skolion, erotica, epithalamia, hymenaios, sillos, threnos, and epikedeion;
- for the gods and humans—partheneion, daphnephorika, tripodephorika, oschophorika, and eutika
According to Mathiesen, music as a performing art was called melos, which in its perfect form (teleion melos) 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, melopoiïa and rhuthmopoiïa) 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; a simple 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 1999, )
The church modes originate in the 8th or 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, but are clearly an intermediary development between the various developments in Greece and the eventual developments in the western, Roman Catholic, church. 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)).
Authors from that period created confusion by trying to use a text by a 6th century scholar named Boethius. Boethius translated Greek music theory treatises by Nicomachus and Ptolemy into Latin (Bower 2001 to defend and 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, used the term "modus"—probably translating the Greek word τρόπος (tropos), which he also rendered as Latin tropus (Bower 1984, 253 )—in connection with the seven diatonic octave species, 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 most important of these writings is the treatise De Musica (or De harmonica institutione) attributed to Hucbald, which 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 later 9th-century treatise known as the Alia musica integrated the seven species of the octave with the eight church modes (Powers 2001, §II.2(ii)). Thus, the names of the modes used today do not actually reflect those used by the Greeks.
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 have different ambituses, or ranges. If the "scale" is completed by adding three higher notes, the mode is termed authentic, if the scale is completed by adding three lower notes, 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). 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).
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).
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 (Powers 2001 §III.4(ii)(a) & §III.5(i)).
In the late-eighteenth and nineteenth centuries, some chant reformers (notably the editors of the Mechlin, Pustet-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), using Roman numeral (I-VIII), rather than using the pseudo-Greek naming system. Contemporary terms, also used by scholars, are simply the Greek ordinals ("first", "second", etc.), usually transliterated into the Latin alphabet: protus (πρῶτος), deuterus (δεύτερος), tritus (τρίτος), and tetrardus (τέταρτος), in practice used as: protus authentus / plagalis.
The eight musical modes. f
indicates "final" (Curtis 1997).
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 in Knighton 1997).
Carl Dahlhaus (1990, 192) lists "three factors that form the respective starting points for the modal theories of Aurelian of Réôme, Hermannus 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 Espinoza Medrano (1632–1688), follow:
||happy, taming the passions
||Veni sancte spiritus (listen)
||serious and tearful
||Iesu dulcis amor meus (listen)
||Kyrie, fons bonitatis (listen)
||inciting delights, tempering fierceness
||Conditor alme siderum (listen)
||Salve Regina (listen)
||tearful and pious
||Ubi caritas (listen)
||uniting pleasure and sadness
||Ad cenam agni providi (listen)
Although many of the names of modes in modern music theory are the same as names used by the ancient Greeks, they do not represent the same sequences of intervals found in the octave species on which the harmoniai were based. In the modern western conception, a mode encompasses the same set of diatonic intervals as the major scale. However, a different "tonic" (central tone) is used, resulting in a different sequence of whole and half steps above it.
By definition, all major scales use the same interval sequence T-T-s-T-T-T-s, where S means a semitone and T means a whole tone (two semitones). From the modal point of view, this interval sequence is called the Ionian or Major mode. It is one of the seven modern modes—seven because only seven diatonic notes can be used as the tonic. Taking any major scale, a new scale is obtained by taking a different degree of the major scale as the tonic. Depending on the degree chosen, this new scale is in one of the other six modes, as follows:
to major scale
where "white note" indicates the starting note for an (upwards) scale of eight white notes on the piano that provides an example of the mode.
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 above the tonic than the one 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 in the modal scales
The first three modes are sometimes called major, the next three minor, and the last diminished, according to the quality of their tonic triads.
The Locrian mode is traditionally considered theoretical rather than practical because the interval between the first and fifth scale degrees is diminished rather than perfect, which creates difficulties in voice leading. However, Locrian is recognized in jazz theory as the preferred mode to play over a iiø7 chord in a minor iiø7-V7-i progression, where it is called a 'half-diminished' scale.
Major modes The Ionian mode ( listen (help·info)) corresponds to the major scale. Scales in the Lydian mode ( listen (help·info)) are major scales with the fourth degree raised a semitone. The Mixolydian mode ( listen (help·info)) corresponds to the major scale with the seventh degree lowered a semitone.
Minor modes The Aeolian mode ( listen (help·info)) is identical to the natural minor scale. The Dorian mode ( listen (help·info)) corresponds to the natural minor scale with the sixth degree raised a semitone. The Phrygian mode ( listen (help·info)) corresponds to the natural minor scale with the second degree lowered a semitone.
Diminished modes Locrian ( listen (help·info)) is the only mode whose fifth is not perfect. This interval is enharmonically equivalent to the augmented fourth found in the Lydian mode.
Use and conception of modes or modality today is different than 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, 74 n4).
The Ionian (or Iastian) 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; however, a true Aeolian mode composition uses only the seven notes of the Aeolian scale, while nearly every minor mode composition of the common practice period has some accidentals on the sixth and seventh scale degrees to facilitate the cadences of western music.
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).
Zoltán Kodály, Gustav Holst, Manuel 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, )
While remaining relatively uncommon in modern (Western) popular music, the darker tones implied by the flattened 2nd and/or 5th degrees of (respectively) the Phrygian and Locrian modes are evident in diatonic chord progressions and melodies of many guitar-oriented rock bands, especially in the late 1980s and early 1990s, as evidenced on albums such as Metallica's "Ride the Lightning" and "Master of Puppets", among others.
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 melodic minor scale, yielding some interesting scales as shown below. The "chord" row lists chords that can be built from the given mode.
||Mixolydian ♭6 or "Hindu"
||half-diminished (or) Locrian Natural 2nd
||altered (or) diminished whole-tone (or) Super Locrian
||Aø (or) A-7♭5
||Double harmonic scale
||Lydian ♯2 ♯6
||Phrygian ♭4 ♭♭7
||Hungarian gypsy scale
||Locrian Nat6 ♯3
||Harmonic Major ♯5 ♯2
||Locrian ♭♭3 ♭♭7
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
- 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.
- Aristotle (1895). Aristotle’s Politics: A Treatise on Government. http://books.google.com/books?id=UHYWAAAAIAAJ&printsec=frontcover&dq=Aristotle+Treatise+Government&cd=3#v=onepage&q=how%20variously%20it%20can%20fascinate%20it&f=false. , translated from the Greek of Aristotle by William Ellis, M.A., with an introduction by Henry Morley. London, Manchester, and New York: 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 http://www.jstor.org/stable/763813 (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 http://www.jstor.org/stable/763815 (Subscription access)
- Carver, Anthony F. (2005). "Bruckner and the Phrygian Mode". Music and Letters 86, no. 1:74–99. doi:10.1093/ml/gci004
- 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: Norton.
- 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 (1990). Studies on the Origin of Harmonic Tonality. Princeton, New Jersey: Princeton University Press. ISBN 0-691-09135-8.
- Hoppin, Richard (1978). Medieval Music. The Norton Introduction to Music History. New York: Norton. ISBN 0-393-09090-6.
- Jowett, Benjamin (1937). The Dialogues of Plato, translated by Benjamin Jowett, 3rd ed. 2 vols. New York: Random House. OCLC 2582139
- Jowett, Benjamin (1943). Aristotle's Politics, translated by Benjamin Jowett. New York: Modern Library.
- 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, edited by Stanley Sadie and John Tyrrell. London: Macmillan.
- Mathiesen, Thomas J. (2001b). "Harmonia (i)". The New Grove Dictionary of Music and Musicians, edited by Stanley Sadie and John Tyrrell. London: Macmillan.
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