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Mode (from Latin modus, "measure, standard, manner, way") is a term from Western music theory having three definitions (Powers 2001, introduction):

  1. the rhythmic relationship between long and short values in the late medieval period;
  2. in early medieval theory, interval;
  3. most commonly, a concept involving scale and melody type.


In addition, from the end of the eighteenth century, the term began to be used in ethnomusicological contexts to describe pitch structures in non-European musical cultures, sometimes with doubtful compatibility (Powers 2001, §V,1).

This article addresses the scale and melody-type meaning.

Modes and scales

A "scale" is an ordered series of intervals, which, along 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 next. The use of more than one mode makes music polymodal, such 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 ).

Greek

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 (in the simultaneous combination of tones) the corresponding tonoi but not necessarily the converse (Mathiesen 2001a, 6(iii)(e)). These were named after one of the Ancient Greek subgroups (Dorians), one small region in central Greece (Locris), and certain neighboring (non-Greek) peoples from Asia Minormarker (Lydia, Phrygia).

Greek Scales

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 Minormarker (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)).

Tonoi

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 Ptolomy'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 harmony correspond with the intervals of the familiar moder Major and Minor. See Pythagorean_tuning and Pythagorean_interval..

Harmoniai

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):

In The Republic Plato describes the music to which a person listened as molding the person's character.

The word ethos 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).

Melos

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:

Western Church

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 Boethius, a scholar from the 6th century who had translated Greek music theory treatises by Nicomachus and Ptolemy into Latin (Bower 2001 ), in order to defend and explain the mode of plainchant, 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 took Boethius’s terms tropus and modus and applied them (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 ambitus, or ranges. If the "scale" is completed by adding three higher notes, the mode is termed authentic, while if the scale is completed by adding three lower notes, the mode 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 is substituted 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 ).

Mode I II III IV V VI VII VIII
Name Dorian Hypodorian Phrygian Hypophrygian Lydian Hypolydian Mixolydian Hypomixolydian
Final (note) D D E E F F G G
Final (solfege) re re mi mi fa fa sol sol
Dominant (note) A F B-C A C A D C
Dominant (solfege) la fa si-do la do la re 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 (Powers 2001 §III.4(ii)(a) & §III.5(i) ).

In the late-eighteenth and nineteenth centuries, some chant reformers (notably the editors of the Mechlinmarker, Pustet-Ratisbon (Regensburgmarker), and Rheimsmarker-Cambraimarker 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, to which they gave the names 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).
)


Use

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:

Name Mode D'Arezzo Fulda Espinoza Example chant
Dorian I serious any feeling happy, taming the passions Veni sancte spiritus ()
Hypodorian II sad sad serious and tearful Iesu dulcis amor meus ()
Phrygian III mystic vehement inciting anger Kyrie, fons bonitatis ()
Hypophrygian IV harmonious tender inciting delights, tempering fierceness Conditor alme siderum ()
Lydian V happy happy happy Salve Regina ()
Hypolydian VI devout pious tearful and pious Ubi caritas ()
Mixolydian VII angelical of youth uniting pleasure and sadness Introibo ()
Hypomixolydian VIII perfect of knowledge very happy Ad cenam agni providi ()


Modern

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 used by 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 (2 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 there are only seven diatonic notes that 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:

Mode Tonic relative
to major scale
White
note
Interval sequence
Ionian I C T-T-s-T-T-T-s
Dorian II D T-s-T-T-T-s-T
Phrygian III E s-T-T-T-s-T-T
Lydian IV F T-T-T-s-T-T-s
Mixolydian V G T-T-s-T-T-s-T
Aeolian VI A T-s-T-T-s-T-T
Locrian VII B s-T-T-s-T-T-T


where "piano white-note scale" indicates the starting note for a scale of "white notes" on the piano that provides an example of the mode.

Note that mode 'VI' (Aeolian) is identical to the natural minor scale.

The modes can be arranged in the following sequence, which follows the cycle 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.
Mode White

note
Intervals in the modal scales
prime second third fourth fifth sixth seventh octave
Lydian F perfect major major augmented perfect major major perfect
Ionian C perfect
Mixolydian G minor
Dorian D minor
Aeolian A minor
Phrygian E minor
Locrian B diminished


The first three modes are sometimes termed 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 modesThe Ionian mode ( ) corresponds to the major scale. Scales in the Lydian mode ( ) are major scales with the fourth degree raised a semitone. The Mixolydian mode ( ) corresponds to the major scale with the seventh degree lowered a semitone.

Minor modesThe Aeolian mode ( ) is identical to the natural minor scale. The Dorian mode ( ) corresponds to the natural minor scale with the sixth degree raised a semitone. The Phrygian mode ( ) corresponds to the natural minor scale with the second degree lowered a semitone.

Diminished modesLocrian ( ) is the only mode whose fifth is not perfect. This interval is enharmonically equivalent to the augmented fourth found in the Lydian mode.

Use

The use and conception of modes or modality today is different from their use and conception 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 the modes were revived by 19th-century composers it was necessary, in order to make their qualities distinct from the prevailing major-minor system, to render them more strictly than had been the case in the Renaissance, when leading tones were routinely sharped at cadences and the fourth scale degree lowered in the Lydian mode (Carver 2005, 74 n4).

The Ionian (or Iastian) mode is another name for the major scale, in which much Western music is composed. The Aeolian forms the base of the most common Western minor scale; however, a true Aeolian mode composition will use only the seven notes of the Aeolian scale, while nearly every minor mode composition of the common practice period will have some accidentals on the sixth and seventh scale degrees in order to facilitate the cadences of western music.

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.

Other types

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.

Mode I II III IV V VI VII
Name Melodic minor Dorian 2 Lydian augmented Lydian dominant Mixolydian 6 or "Hindu" half-diminished (or) Locrian Natural 2nd altered (or) diminished whole-tone (or) Super Locrian
Chord C-maj7 D- 9 E maj 5 F7 11 G7 13 Aø (or) A-7 5 B7alt


Mode I II III IV V VI VII
Name Harmonic minor Locrian Natural 6th Harmonic Major 5 Ukrainian minor Phrygian major 3rd Lydian 2 Super Locrian diminished
Chord C-minmaj7 E -maj7 5 F-7 G7 A -maj7 (or) A -minmaj7 B-Dim7


Mode I II III IV V VI VII
Name Double harmonic scale Lydian 2 6 Phrygian 4 7 Hungarian gypsy scale Locrian Nat6 3 Harmonic Major 5 2 Locrian 3 7
Chord Cmaj7 Dbmaj7 Edim7nat5 F-maj7 G7flat5 Abmaj7#5 Bdim7flat3


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 wit 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



See also



References

  1. * Powers, Harold S. (2001). "Mode". The New Grove Dictionary of Music and Musicians, edited by Stanley Sadie and John Tyrrell. London: Macmillan.
  2. Winnington-Ingram, Reginald Pepys. 1936. Mode in Ancient Greek Music. Cambridge Classical Studies. Cambridge: Cambridge University Press. Reprinted, Amsterdam: Hakkert, 1968.
  3. Thomas J. Mathiesen, "Greece, §I: Ancient". The New Grove Dictionary of Music and Musicians, edited by Stanley Sadie and John Tyrrell (London: Macmillan), 6(iii)(e).
  4. Barbera, André (1984). "Octave Species". The Journal of Musicology 3, no. 3 (Summer): 229–41.
  5. Cleonides, "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, 1965). The reference is on pp. 35–36.
  6. Cleonides, "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, 1965). The reference is on pp. 39–40
  7. Cleonides, "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, 1965). The reference is on p. 44.
  8. * Solomon, Jon (1984). "Towards a History of Tonoi". The Journal of Musicology 3, no. 3 (Summer): 242–51.
  9. * Mathiesen, Thomas J. (2001c). "Tonos". The New Grove Dictionary of Music and Musicians, edited by Stanley Sadie and John Tyrrell. London: Macmillan.
  10. * Mathiesen, Thomas J. (2001b). "Harmonia (i)". The New Grove Dictionary of Music and Musicians, edited by Stanley Sadie and John Tyrrell. London: Macmillan.
  11. Cleonides, "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, 1965). The reference is on p. 35.
  12. http://www.scribeserver.com/medieval/byzantin.htm#music
  13. * Bower, Calvin (2001). "Boethius [Anicius Manlius Severinus Boethius]". The New Grove Dictionary of Music and Musicians, edited by Stanley Sadie and John Tyrrell. London: Macmillan.
  14. * Palisca, Claude V. (1984). "Introductory Notes on the Historiography of the Greek Modes". The Journal of Musicology 3, no. 3 (Summer): 221–28.
  15. * Bower, Calvin M. (1984). "The Modes of Boethius". The Journal of Musicology 3, no. 3 (Summer): 252–63.
  16. * Apel, Willi (1969). Harvard Dictionary of Music. Cambridge, MA: Belknap Press. 2nd edition.
  17. Liane Curtis, "Mode" in Companion to Medieval and Renaissance Music, edited by Tess Knighton and David Fallows (Berkeley: University of California Press). ISBN 0520210816.
  18. * Dahlhaus, Carl (1990). Studies on the origin of harmonic tonality. Princeton, New Jersey: Princeton University Press. ISBN 0691091358.
  19. Jim Samson, Music in Transition: A Study of Tonal Expansion and Atonality, 1900-1920 (Oxford & New York: Oxford University Press, 1977), 148. ISBN 0460861506.


  • 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.
  • Barbera, André (1984). "Octave Species". The Journal of Musicology 3, no. 3 (July): 229–41. 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 0521235936 (v. 1) ISBN 052130220X (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. 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.
  • 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 0945996047
  • 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.
  • Cott, Jonathan. 1973. Stockhausen: Conversations with the Composer. New York: Simon and Schuster. ISBN 0671214950
  • Curtis, Liane (1997). "Mode". In Companion to Medieval and Renaissance Music, edited by Tess Knighton and David Fallows. Berkeley: University of California Press. ISBN 0520210816.
  • Dahlhaus, Carl (1990). Studies on the Origin of Harmonic Tonality. Princeton, New Jersey: Princeton University Press. ISBN 0691091358.
  • Hoppin, Richard (1978). Medieval Music. The Norton Introduction to Music History. New York: Norton. ISBN 0393090906.
  • Jowett, Benjamin (1937). The Dialogues of Plato, translated by Benjamin Jowett, 3rd ed. 2 vols. New York: Random House.
  • 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 0803230796
  • 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.
  • Mathiesen, Thomas J. (2001c). "Tonos". The New Grove Dictionary of Music and Musicians, edited by Stanley Sadie and John Tyrrell. London: Macmillan.
  • 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. http://www.jstor.org/stable/763812 (Subscription access)
  • 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.
  • Sabine, David (2006). " Pythagoras: Mathematical Theorum in Music". davesabine.com website (Accessed 7 November 2009)
  • Samson, Jim (1977). Music in Transition: A Study of Tonal Expansion and Atonality, 1900-1920. Oxford & New York: Oxford University Press. ISBN 0460861506.
  • Smith, Charlotte (1989). A Manual of Sixteenth-century Contrapuntal Style. Newark: University of Delaware Press; London: Associated University Presses. ISBN 978-0874133271 http://books.google.co.uk/books?id=usc74SGmrf8C&pg=PA14&lpg=PA14&dq=dominant+reciting+tone+tenor&source=bl&ots=WJY8oaf5WU&sig=SzGikjFrIoRCV7xMdfWv_YQ-F9k&hl=en&ei=FsG7Sp3iGJ-UjAfRioSpCw&sa=X&oi=book_result&ct=result&resnum=6#v=onepage&q=dominant%20reciting%20tone%20tenor&f=false
  • Solomon, Jon (1984). "Towards a History of Tonoi". The Journal of Musicology 3, no. 3 (July): 242–51. http://www.jstor.org/stable/763814 (Subscription access)
  • Vieru, Anatol (1985). "Modalism-A 'Third World'". Perspectives of New Music 24, no. 1 (Fall–Winter): 62–71.
  • Winnington-Ingram, Reginald Pepys (1936). Mode in Ancient Greek Music. Cambridge Classical Studies. Cambridge: Cambridge University Press. Reprinted, Amsterdam: Hakkert, 1968.


Further reading

  • 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; Palisca, Claude; and Burkholder, J. Peter (2006). A History of Western Music. New York: W. W. Norton. 7th edition. ISBN 0393979911.
  • Judd, Cristle (ed) (1998). Tonal Structures in Early Music: Criticism and Analysis of Early Music, 1st ed. New York: Garland. ISBN 0815323883.
  • Levine, Mark (1989). The Jazz Piano Book. Petaluma, CA: Sher Music Co. ISBN 0961470151.
  • 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
  • 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 (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
  • Miller, Ron (1996). Modal Jazz Composition and Harmony, Vol. 1. Rottenburg, Germany: Advance Music.
  • 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.
  • 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 (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.


External links

  • Neume Notation Project, "is principally an exploration of data representations for medieval music notations and data streams" http://www.scribeserver.com/medieval/index.html#contents
  • Booklet on the modes of ancient greece with detailed examples of the construction of Aolus (reed pipe instruments) and monochord with which the intervals and modes of the greeks might be reconstructed http://www.nakedlight.co.uk/pdf/articles/a-002.pdf
  • Division of the Tetrachord is a methodical overview of ancient greek musical modes and contemporary use, including developments to Xenakis - http://eamusic.dartmouth.edu/~larry/published_articles/divisions_of_the_tetrachord/index.html
  • Delahoyd notes on ancient greek music http://www.wsu.edu/~delahoyd/greek.music.html
  • Hammel on modes,"We are not quite sure what a Greek mode really was.", with other useful glosses on music theory http://graham.main.nc.us/~bhammel/MUSIC/Gmodes.html
  • A Pathologist and pianist http://www.pathguy.com/modes.htm with some examples of 7 string tunings showing modes for popular songs and a collection of links.
  • An interactive demonstration of many scales and modes http://www.looknohands.com/chordhouse/piano/
  • Nikolaos Ioannidis musician, composer has attempted to reconstruct ancient greek music from a combination of the ancient texts (to be performed) and his knowledge of greek music. http://homoecumenicus.com/ioannidis_music_ancient_greeks.htm
  • relatively concise overview of ancient Greek musical culture and philosophy http://arts.jrank.org/pages/258/ancient-Greek-music.html
  • mid 19th century, 1902 edition, Henry S. Macran, The Harmonics of Aristoxenus, http://www.archive.org/stream/aristoxenouharm00arisgoog
  • analysis of Aristoxenus from Joe Monzo http://www.tonalsoft.com/monzo/aristoxenus/aristoxenus.aspx



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