Musical mode

From Wikipedia, the free encyclopedia

Jump to: navigation, search

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

  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-like meaning.


[edit] Modes and scales

A "scale" is an ordered series of intervals, which, along with the key or tonic, defines the pitches. However, "mode" is usually used in the sense of "scale" applied only to the specific diatonic scales found below.[citation needed] "Modality" refers to the pitch relationships found in music using modes and contrasted with later tonality. The use of more than one mode makes music polymodal, such as with polymodal chromaticism. While all tonal music may technically be described as modal, music that is called modal often has less diatonic functionality and changes key less often than other music.[citation needed]

[edit] Modern

In the modern conception each mode encompasses the usual diatonic scale but with a different tonic or tonal center. On a keyboard instrument, white-note scales map onto modes as: C:Ionian, D:Dorian, E:Phrygian, F:Lydian, G:Mixolydian, A:Aeolian, B:Locrian. Although many of the names in modern music theory are the same as names used in Greece, the sequence of tones is not the same either in pitch or in interval as in the ancient Greek modes (see below).

The modes can be arranged in the following sequence, where each mode has one more shortened[clarification needed] interval in its scale than the one preceding it.

mode white
Intervals in the modal scales
prime second third fourth fifth sixth seventh octave
Lydian IV F perfect major major augmented perfect major major perfect
Ionian I C perfect
Mixolydian V G minor
Dorian II D minor
Aeolian VI A minor
Phrygian III E minor
Locrian VII B diminished

The first three modes are termed major, the remaining four minor, governed by their third scale degree.

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 (C Ionian.ogg listen ) is identical to a major scale. The Lydian mode (C Lydian.ogg listen ) is a major scale with a raised fourth scale degree. The Mixolydian mode (C Mixolydian.ogg listen ) is a major scale with a lowered seventh scale degree.

Minor modes The Aeolian mode (C Aeolian.ogg listen ) is identical to a natural minor scale. The Dorian mode (C Dorian.ogg listen ) is a natural minor scale with a raised sixth scale degree. The Phrygian mode (C Phrygian.ogg listen )is a natural minor mode with a lowered second scale degree.

Diminished modes Locrian (C Locrian.ogg listen ) is the only mode whose fifth is not perfect. This interval is enharmonically equivalent to the augmented fourth of the Lydian mode. The Locrian's (I)'s seventh chord is naturally a half diminished seventh which is a diminished triad with a minor seventh on top.

[edit] Use

Modes came back into favor some time later with the developments of impressionism, modal jazz, and more contemporary 20th century music.

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."[cite this quote]

The Ionian mode is another name for the major mode, 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.[citation needed]

Besides the Ionian major and modern (harmonic/melodic) minor modes, the other modes have limited use in music today. Folk music is often best analysed in terms of modes. For example, in Irish traditional music the Ionian, Dorian, Aeolian and Mixolydian modes occur (in roughly decreasing order of frequency); the Phrygian mode is an important part of the flamenco sound. The Dorian mode is also found in other folk music, particularly Latin and Laotian music, while Phrygian is found in some Central European or stylized Arab music, whether as natural Phrygian or harmonic Phrygian (Phrygian Dominant), which has a raised third (the so-called "gypsy scale"). Mixolydian mode is quite common in jazz and most other forms of popular music. Because of its dream-like sound, the Lydian mode is most often heard in soundtrack and video game music.[citation needed]

Some works[weasel words] by Beethoven contain modal inflections, and Chopin, Berlioz, and Liszt made extensive use of modes.[citation needed] They influenced nineteenth-century Russian composers, including Mussorgsky and Borodin[citation needed]; many twentieth-century composers drew on this earlier work in their incorporation of modal elements, including Claude Debussy, Leoš Janáček, Jean Sibelius, Ralph Vaughan Williams and others.[citation needed] 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.[citation needed]

They have also been used in popular music, especially in rock music. Some notable examples of songs using modality include Scarborough Fair and Another Brick in the Wall (part II), which use the Dorian mode, and many of the jam-songs of The Grateful Dead[citation needed]. The Dorian and Aeolian modes are also very prevalent in modern punk and post-hardcore music[citation needed].

While remaining relatively uncommon in modern (Western) popular music, the darker tones implied by the flatted 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.[citation needed]

[edit] Chords

In jazz, the modes correspond to and are played over particular chords. (This is not entirely true. For this usage, scale on a chord, the correct term is "chord scale", not mode. Ex: The dorian chord scale is commonly played over the II-7 chord in a major key. Being in the dorian mode signifies that that particular chord is the tonic chord.) The chord examples below are shown for the modes of the key of C. For example, over an Fmaj711 chord, musicians typically play notes from the F Lydian mode (a Lydian chord scale over a IVma7 chord).

Mode Ionian Dorian Phrygian Lydian Mixolydian Aeolian Locrian
Chord Cmaj7 Dm7 Esus9 (or Em7) Fmaj711 G7 Am7 Bø (Bm75)

Although both Dorian and Aeolian can be played over a minor seventh (m7) chord, the Dorian mode is most commonly used in straightahead jazz because the Dorian mode has a whole step between the 5th and 6th scale degrees, in contrast to the more jarring half step in the Aeolian. Also note that the most common jazz cadence or chord progression is a ii-V-I which suggests Dorian mode in the case of the ii chord.

Similarly, over a half-diminished (ø or m7♭5) chord, many jazz musicians will alter the Locrian mode by raising the second degree of the scale by a semitone, in order to form a major ninth over the chord (e.g. C over Bø), rather than the more dissonant minor ninth (e.g. C natural over Bø). This scale is also called the 6th mode of the melodic minor. And over the "sus9" chord, the sixth scale degree of the Phrygian mode is often raised by a semitone, in order to make a major sixth in the chord, rather than the more dissonant minor sixth. This mode is also called the 2nd mode of melodic minor. See Other modes below for more about the melodic minor modes and their associated chords.

[edit] Other types

In modern music theory, scales other than the major scale sometimes have the term "modes" applied to the scales which begin with their degrees. This is seen, for example, in "melodic minor" scale harmony, which is based on the seven modes 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.

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 Emaj5 F711 G713 Aø (or) A-75 B7alt
Name Harmonic Minor Locrian Natural 6th Harmonic Major 5 Dorian 4 Phrygian major 3rd Lydian 2 Super Locrian diminished
Chord C-minmaj7 E-maj75 F-7 G7 A-maj7 (or) A-minmaj7 B-Dim7

Most of these chords and modes are commonly used in jazz; the min/maj chord, 711 and alt were in common use in the bebop era (indeed, the Lydian dominant scale and 711 chord practically defined the bebop sound), while Coltrane-era and later jazz made extensive use of sus9 chords. Maj5 is less common, but appears in Wayne Shorter's compositions. The 67 is rarely seen as such.

Though the term "mode" is still used in this case (and is useful in recognizing that these scales all have a common root, that is the melodic minor scale); it is more common for musicians to understand the term "mode" to refer to Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, or Locrian scales. In everyday speech, this is the most common understanding. But in truth, any scale can be *used* as a mode by establishing its final as the tonal center and emphasizing its characteristic color pitches.

However, strictly speaking, for any possible scale, the number of possible distinct melodic modes is dictated by the pattern of intervals in the scale. For scales built of a pattern of intervals that only repeats at the octave, the number of modes is the number of notes in the scale: such 6-note scales have 6 modes, 5-note scales have 5 modes, etc. Scales that repeat their interval pattern at some subdivision of the 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 on the whole step) and all even-numbered modes are equivalent to the second (starting on the half step). These scales are sometimes referred to as modes of limited transposition. 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.

While most scales (a defined number of notes occurring in defined intervals) have commonly accepted names, most of the modal variations of the more obscure scales do not, and are instead referred to as "3rd mode of [your-scale-name-here]", etc.

[edit] 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—the latter subsuming 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 Minor (Lydia, Phrygia). Some of these 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)).

[edit] 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′)

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)).

Because scales were constructed from one of three different genera of tetrachords, the intervals in each of the seven octave species were variable. These were (1) the diatonic genus (ascending semitone–tone–tone), (2) the chromatic genus (ascending semitone–semitone–minor third, and (3) the enharmonic genus (ascending diesis–diesis–major third, where a diesis is approximately a quarter-tone) (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: mid chromatic (with small semitones and large minor third dividing the fourth in proportions of 4:4:22), hemiolic chromatic (intermediate intervals of 4.5:4.5:21), and tonic chromatic (large semitones and small minor third, 6:6:18), and mid (soft) and intense (syntonic) diatonic, the former with a small and large whole tone (6:9:15), the latter with equal whole tones (6:12:12) (Cleonides 1965, 39–40; Mathiesen 2001a, 6(iii)(c)).

[edit] 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).

[edit] Harmoniai

In music theory the Greek word harmonia can signify the enharmonic genus, the seven octave species, or a style of music associated with one of the ethnic types or the tonoi named by them (Mathiesen 2001b).

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.[citation needed] Plato believed that a change in the musical modes of the state would cause a wide-scale social revolution.[citation needed]

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, this quote from Aristotle's Politics (viii:1340a:40–1340b:5):

The musical modes [harmoniôn] differ essentially from one another, and those who hear them are differently affected by each. Some of them make men sad and grave, like the so called Mixolydian; others enfeeble the mind, like the relaxed modes; another, again, produces a moderate or settled temper, which appears to be the peculiar effect of the Dorian; and the Phrygian inspires enthusiasm. (Jowett 1943,[page number needed])

Plato and Aristotle describe the modes to which a person listened as molding the person's character. The modes even made the person more or less fit for certain jobs. The effect of modes on character and mood was called the "ethos of music".[citation needed]

[edit] Western Church

There is a common misconception that the church modes (also called ecclesiastical modes) of medieval European music were directly descended from the Greek notion of modality mentioned above.[citation needed] In fact, the church modes originated in the 9th century.[citation needed] 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. 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.

The pairs are organized so that the modes sharing a final note are numbered together, with the odd numbers used for the authentic modes and the even numbers for the plagal modes.

In addition, each mode has a "dominant" or "reciting tone", which is the tenor[clarification needed] of the psalm tone[clarification needed]. 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, p.67).

Only one accidental is used commonly in Gregorian chant—si (B) may be lowered by a half-step. 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).

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 the 16th century, the Swiss theorist Henricus Glareanus published Dodekachordon, in which he solidified the concept of the church modes, and added four additional modes: the Aeolian, Hypoaeolian, Ionian, and Hypoionian.

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"[1] 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 (τετράρδος), in practice used as: protus authentus / plagalis.

The eight musical modes. f indicates "final"[citation needed].

[edit] Use

Early music made heavy use of the Church modes. 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 (ie, emotional effect). Liane Curtis (1998) 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,"[cite this quote] in Medieval and Renaissance music. While it is true that other technical features such as reciting tones, cadences, and expressive qualities have roles in modal theory, it was nevertheless the scalar aspect of mode—in authentic and plagal forms—that was most universally described by theorists, and which has the greatest use in Renaissance polyphony.[citation needed] The use of cadences on important modal steps (especially the modal final) greatly helps to establish the sound of the mode, and once that has taken place, it is natural that the inherent expressive sounds of the modes are heard.[citation needed] The different orders of tones and semitones were widely recognized[who?] as creating the expressive qualities of the modes. Although today the significance of mode in Renaissance polyphony is being debated,[who?] most Renaissance theorists refer to the use of mode in polyphonic composition, and the principles of diatonic scale and practice of composing music around central pitches are so common in the music of this period that it is probable that composers did directly apply the modes to their compositions.[citation needed]

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),[citation needed] Adam of Fulda (1445-1505),[citation needed] and Juan de Espinoza Medrano (1632-1688),[citation needed] follow:

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

Most of the theoretical writings on Gregorian chant modes postdate the composition of the early Gregorian chant repertoire, which was not composed with the intention of conforming to particular modes.[citation needed] As a result, for these chants, the application of a mode number can be only approximate. Later chants, however, were written with a conscious eye on the eight modes.[citation needed]

[edit] Analogues in different musical traditions

[edit] See also

[edit] Notes

  1. ^ Knighton, Tess; Fallows, David (1998). Companion to Medieval and Renaissance Music. University of California Press. ISBN 0520210816. 

[edit] References

  • Barbera, André (1984). "Octave Species". The Journal of Musicology 3, no. 3 (Summer): 229–41.
  • Barker, Andrew (ed.) (1984–89). Greek Musical Writings. 2 vols. Cambridge & New York: Cambridge University Press. ISBN 0521235936 (v. 1) ISBN 052130220X (v. 2)
  • Bower, Calvin M. (1984). "The Modes of Boethius". The Journal of Musicology 3, no. 3 (Summer): 252–63.
  • 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.
  • 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.
  • Curtis, Liane. "Mode".[verification needed]
  • Dahlhaus, Carl (1990). Studies on the origin of harmonic tonality. trans. Robert O. Gjerdingen. Princeton, New Jersey: Princeton University Press. ISBN 0-691-09135-8. OCLC 59809840. 
  • Hoppin, Richard H. (1978). Medieval Music. New York City: W. W. Norton & Company. ISBN 0-393-09090-6. OCLC 3843431. 
  • 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.
  • Judd, Cristle Collins (1998). Tonal Structures in Early Music. Criticism and Analysis of Early Music 1; Garland Reference Library of the Humanities 1998. New York City: Garland Pub. ISBN 0-8153-2388-3 0-8153-3638-1. OCLC 43500621. 
  • 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.
  • Palisca, Claude V. (1984). "Introductory Notes on the Historiography of the Greek Modes". The Journal of Musicology 3, no. 3 (Summer): 221–28.
  • Powers, Harold S. (2001). "Mode". The New Grove Dictionary of Music and Musicians, edited by Stanley Sadie and John Tyrrell. London: Macmillan.
  • Solomon, Jon (1984). "Towards a History of Tonoi". The Journal of Musicology 3, no. 3 (Summer): 242–51.

[edit] Further reading

  • Apel, Willi (1968). Harvard Dictionary of Music. Cambridge, MA: Belknap Press. 2nd edition.
  • Grout, Donald; Palisca, Claude; and Burkholder, J. Peter (2006). A History of Western Music. New York: W. W. Norton. 7th edition. ISBN 0-3939799-1-1.
  • Levine, Mark (1989). The Jazz Piano Book. Petaluma, CA: Sher Music Co. ISBN 0-9614701-5-1.
  • 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.
  • Miller, Ron (1996). Modal Jazz Composition and Harmony, Vol. 1. Rottenburg, Germany: Advance Music.
  • Powers, Harold S. (1980). "Mode", in The New Grove Dictionary of Music and Musicians, ed. Stanley Sadie. London: Macmillan. (The classic treatment of mode in the English language.)
Personal tools