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Musical system of ancient Greece

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1400: 60:, theoretical, philosophical or aesthetic, is fraught with two problems: there are few examples of written music, and there are many, sometimes fragmentary, theoretical and philosophical accounts. The empirical research of scholars like Richard Crocker, C. André Barbera, and John Chalmers has made it possible to look at the ancient Greek systems as a whole without regard to the tastes of any one ancient theorist. The primary genera they examine are those of Pythagoras and the 7154: 4265: 7164: 7174: 4255: 1325: 1313: 1305: 1285: 2037:, 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). 1932:(ἔθος or ἦθος), in this context best rendered by "character" (in the sense of patterns of being and behaviour, but not necessarily with "moral" implications), to describe the ways music can convey, foster, and even generate emotional or mental states. Beyond this general description, there is no unified "Greek ethos theory" but "many different views, sometimes sharply opposed." Ethos is attributed to the 2117:
Such pieces of music were 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, melopoiĂŻa and rhuthmopoiĂŻa) were the processes of
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The elaboration of tetrachords was also accompanied by penta- and hexachords. The joining of a tetrachord and a pentachord yields an octachord, i.e. the complete seven-tone scale plus a higher octave of the base note. However, this was also produced by joining two tetrachords, which were linked by
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recognizes that, if the interval of a fourth goes up from any given note, and then up the interval of a fifth, the final note is an octave above the first note. Thus, the octave is made up of a fourth and a fifth. ... Philolaus's scale thus consisted of the following intervals: 9:8, 9:8, 256:243 ,
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Based on the above, it can be seen that the Aristoxene system of tones and octave species can be combined with the Pythagorean system of "genera" to produce a more complete system in which each octave species of thirteen tones (Dorian, Lydian, etc.) can be declined into a system of seven tones by
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is an American composer and academic; something of a complement to the above Aristoxenus but, dealing with the earlier and arithmetically precise Archytas. An incidental note. Erickson is keen to demonstrate that Archytas' tuning system not only corresponds with Plato's
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The central three columns of the diagram show, first the modern note-names, then the two systems of symbols used in ancient Greece: the vocal symbols (favoured by singers) and instrumental symbols (favoured by instrument players). The modern note-names are given in the
1988:), with implications for the well-being of the State. Many other ancient authors refer to what is nowadays called psychological effect of music and draw judgments for the appropriateness (or value) of particular musical features or styles, while others, in particular 1802:
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
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in considerable ranges. Instead of using discrete ratios to place the intervals in his scales, Aristoxenus used continuously variable quantities: as a result he obtained scales of thirteen notes to an octave, and considerably different qualities of consonance.
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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
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were named analogously to the octave species, supplemented with new terms to raise the number of degrees from seven to thirteen. In fact, Aristoxenus criticized the application of these names by the earlier theorists, whom he called the "Harmonicists".
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Archytas provided a rigorous proof that the basic musical intervals cannot be divided in half, or in other words, that there is no mean proportional between numbers in super-particular ratio (octave 2:1, fourth 4:3, fifth 3:2, 9:8).
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the Hypodorian is the lowest, and the Mixolydian is next-to-highest: the reverse of the case of the octave species. The nominal base pitches are as follows (in descending order, after Mathiesen; Solomon uses the octave between
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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
172:. Note that Greek theorists described scales as descending from higher pitch to lower, which is the opposite of modern practice and caused considerable confusion among Renaissance interpreters of ancient musicological texts. 550:
according to the harmonic theory of that time, which was however quite different from that of the ancient Greeks. Thus the names Dorian, Lydian etc. should not be taken to imply a historical continuity between the systems.
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Cleonides describes "melic" composition, "the employment of the materials subject to harmonic practice with due regard to the requirements of each of the subjects under consideration" — which, together with the scales,
1888:(iii.10–11) Plato describes the music a person is exposed to as molding the person's character, which he discusses as particularly relevant for the proper education of the guardians of his ideal State. Aristotle in the 1918:
From what has been said it is evident what an influence music has over the disposition of the mind, and how variously it can fascinate it—and if it can do this, most certainly it is what youth ought to be instructed
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after a letter indicates an approximately half-flattened version of the named note; the exact degree of flattening intended depending on which of several tunings was used. Hence a three-tone falling-pitch sequence
542:" named after Greek regions and ethnicities – Dorian, Lydian, etc. This association of the ethnic names with the octave species appears to have preceded Aristoxenus, and the same system of names was revived in the 191:, in modern terms. The sub-intervals of the tetrachord were unequal, with the largest intervals always at the top, and the smallest at the bottom. The 'characteristic interval' of a tetrachord is its largest one. 1317:
only as meaning the immediate prior letter in the alphabet. This complication is unnecessary in Greek notation, which had distinct symbols for each pitch, in set of three: half-flat, flat, or natural notes.
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who flourished in the 4th century BC. He introduced a radically different model for creating scales, and the nature of his scales deviated sharply from his predecessors. His system was based on seven "
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construed the intervals arithmetically, allowing for 1:1 = Unison, 2:1 = Octave, 3:2 = Fifth, 4:3 = Fourth. Pythagoras's scale consists of a stack of perfect fifths, the ratio 3:2 (see also
3446:, 2 vols. Amsterdam: Apud Ludovicum Elzevirium. Facsimile reprint in Monuments of Music and Music Literature in Facsimile, Second Series: Music Literature 51. New York: Broude Bros., 1977. 176: 3562:
is a musician and composer who has attempted to reconstruct ancient Greek music using a combination of the ancient texts (to be performed) and his own understanding of ancient music.
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names in the following table are the original Greek ones, followed by later alternatives (Greek and other). The species and notation are built around the template of the Dorian.
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was the first Greek theorist to point out that ethos does not only reside in the individual parameters but also in the musical piece as a whole (cited in Pseudo-Plutarch,
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In sum, it is clear that the Ancient Greeks conceived of a unified system with the tetrachord as the basic structure, but the octave as the principle of unification.
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This article is about the music theory and musical intervals used in ancient Greece. For a discussion of the cultural aspects and history of ancient Greek music, see
7373: 3539:. Gives detailed examples of the construction of Aolus (reed pipe instruments) and monochord, which might help reconstruct the intervals and modes of the Greeks. 2004:), deny that music possesses any influence on the human person apart from generating pleasure. These different views anticipate in some way the modern debate in 1309:
is used to accommodate as far as possible the modern musical convention that demands every note in a scale to have a distinct, sequential letter; so interpret
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As an initial introduction to the principal names and divisions of the Ancient Greek tone system this article will give a depiction of the "perfect system" or
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32: 1142d ff; see also Aristides Quintilianus 1.12). The Greeks were interested in musical ethos particularly in the context of education (so Plato in his
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to Aristoxenus, which represent a transposition of the tones of the Pythagorean system into a more uniform progressive scale over the range of an octave.
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tetrachords. These are shown on the right hand side of the diagram. Octaves were composed from two stacked tetrachords connected by one common tone, the
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is regarded not as a scale, but as the epitome of the stylised singing of a particular district or people or occupation. When the late 6th-century poet
140: 1289:) are used merely to adhere to the modern convention of that all standard pitches in an octave are assigned a distinct, sequential alphabetic letter. 229:, the continuity of the system encounters a boundary (at b-flat, b). To retain the logic of the internal divisions of the tetrachords and avoid the 126: 7545: 7369: 4301: 3427: 3277: 3256: 3235: 2827: 1905:, 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 1869:
uses the term inclusively to encompass a particular type of scale, range and register, characteristic rhythmic pattern, textual subject, etc.
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After the discovery of the fundamental intervals (octave, fourth and fifth), the first known systematic divisions of the octave were those of
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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
1972:, with the original conception of assigning ethos to the various musical parameters according to the general categories of male and female. 3490: 291:. The first two of these are the same as the first two tetrachords of the Greater Perfect System, with a third tetrachord placed above the 3051: 3018: 53:, into several complex systems encompassing tetrachords and octaves, as well as octave scales divided into seven to thirteen intervals. 5901: 3698: 3208:. Publications of the Center for the History of Music Theory and Literature. Vol. 2. Lincoln, NB: University of Nebraska Press. 382:, contemporary and friend of Plato, who explained the use of arithmetic, geometric and harmonic means in tuning musical instruments. 123:, and the system as a whole in one complete map. (Half-sharp and double-sharp notes not used with the depicted notes are omitted.) 515:, a set of five tetrachords linked by conjunction and disjunction into arrays of tones spanning two octaves, as explained above. 3512: 3405:
Musici scriptores graeci: Aristoteles, Euclides, Nicomachus, Bacchius, Gaudentius, Alypius et melodiarum veterum quidquid exstat
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to whom was often attributed the discovery that the frequency of a vibrating string is inversely proportional to its length.
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means of an intermediary or shared note. The final evolution of the system did not end with the octave as such but with the
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Within these basic forms, the intervals of the chromatic and diatonic genera were varied further by three and two "shades" (
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Below is an elaboration of the mathematics that led to the logic of the system of tetrachords just described.
156: 3668:, dedicated to the recreation of ancient Greek and Roman music and playing scores written on inscriptions and 7130: 6687: 6180: 5696: 5616: 5314: 5024: 7566: 7103: 5632: 5086: 3644: 719:) was used in four senses, for it could designate a note, an interval, a region of the voice, and a pitch. 150:. The pitches of the notes in modern notation are conventional, going back to the time of a publication by 3334:
Documents of Ancient Greek Music: The extant melodies and fragments edited and transcribed with commentary
6158: 5766: 5642: 5304: 5258: 5213: 4989: 4678: 4199: 4063: 3436: 3272: 3251: 3230: 2822: 2052: 1430:, the diatonic of Henderson and Chalmers chromatic versions. Chalmers, from whom they originate, states: 598: 6697: 3599:— Full of interesting and insightful mathematical analysis. There are some original hypotheses outlined. 6819: 6692: 5825: 5820: 5796: 5706: 5223: 4321: 2928: 442:) still had variable tunings. Tetrachords were classified into genera depending on the position of the 3313:. Erlanger Beiträge zur Sprach- und Kunstwissenschaft. Vol. 31. Nuremberg, DE: Hans Carl Verlag. 1399: 7177: 7120: 6076: 5879: 5864: 5786: 5721: 5041: 4936: 4410: 4344: 4268: 4159: 4134: 3925: 3684: 3355: 3156:
The Power and Value of Music: Its effect and ethos in classical authors and contemporary music theory
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arose after the framing interval of the tetrachord was fixed, because the two internal notes (called
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Die Hymnen des Dionysius und Mesomedes: Text und Melodieen nach Handschriften und den alten Ausgaben
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In the enharmonic and chromatic forms of some of the harmoniai, it has been necessary to use both a
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selecting particular tones and semitones to form genera (Diatonic, Chromatic, and Enharmonic).
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9:8, 9:8, 9:8, 256:243 . This scale is known as the Pythagorean diatonic and is the scale that
3590: 3535:— Booklet by composer Elsie Hamilton summarizes work of deceased friend and teacher, Dr.  168:. The range is approximately what is now depicted on a modern music staff and is given in the 7576: 7540: 7535: 7527: 7466: 7167: 6396: 6386: 6376: 6361: 6051: 5791: 5761: 5716: 5711: 5342: 5309: 5111: 5016: 5002: 4658: 4529: 4493: 4240: 4104: 3803: 3084: 2246: 1896:
But melodies themselves do contain imitations of character. This is perfectly clear, for the
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d   e   f   g   a   b   c′   d′   d′  
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d   e   f   g   a   b   c′   d′   d′  
398:). He elaborated the acoustics with reference to the frequency of vibrations (or movements). 2118:
selecting and applying the various components of melos and rhythm to create a complete work.
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for the gods and humans—partheneion, daphnephorika, tripodephorika, oschophorika, and eutika
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These three tunings appear to have corresponded to the actual musical practice of his day.
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Barbera, C. AndrĂŠ (Autumn 1977). "Arithmetic and geometric divisions of the tetrachord".
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can be recognized, depending on the positioning of the interposed tones in the component
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According to the interpretation of at least two modern authorities, in the Aristoxenian
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Winnington-Ingram, Reginald P. (1932). "Aristoxenus and the Intervals of Greek Music".
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resemble elements found in medieval modal theory. According to Aristides Quintilianus (
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and individual tones. The most comprehensive treatment of musical ethos is provided by
1523:(d) e   f   g   a   b   c′   d′   e′   1515:(d) e   f   g   a   b   c′   d′   e′   1507:(d) e   f   g   a   b   c′   d′   e′   352: 7282: 7163: 7062: 6649: 6198: 6046: 5998: 5842: 5811: 5756: 5673: 5550: 5422: 5243: 5076: 5029: 4969: 4843: 4825: 4801: 4783: 4738: 4693: 4688: 4339: 4220: 3968: 3728: 3723: 3519: 3481: 3447: 3337: 3314: 3209: 3159: 2978: 2946: 2938: 2013: 1845: 628: 3407:. Bibliotheca scriptorum graecorum et romanorum Teubneriana. Leipzig: B. G. Teubner. 1665:
B   c   d   e   f   (g)   (a)   b  
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f   g   a   b   c′   d′   e′   f′  
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f   g   a   b   c′   d′   e′   f′  
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f   g   a   b   c′   d′   e′   f′  
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d   e   f   g   a   b   c′   d′  
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Divisions of the Tetrachord: A prolegomenon to the construction of musical scales
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B   c   d   d   e   f   g   b  
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B   c   d   d   e   f   g   b  
1462:. The appropriate tunings for these scales are those of Archytas and Pythagoras. 1324: 7517: 7509: 7489: 7481: 7451: 7357: 7236: 7227: 7196: 6889: 6829: 6824: 6780: 6561: 6509: 6499: 6479: 6469: 6213: 6208: 6203: 5056: 4855: 4849: 4837: 4637: 4612: 4385: 4310: 4230: 3943: 3798: 3418:(2 vols.), translated by Benjamin Jowett (3rd ed.), New York: Random House 2009: 914: 904: 539: 499:
the enharmonic genus consists of a major third and two quarter-tones or diesis.
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Archytas was also the first ancient Greek theorist to provide ratios for all 3
202:) was composed of four stacked tetrachords called (from lowest to highest) the 188: 61: 50: 3665: 3473: 3129: 1856:
characteristic of Greeks speaking the Aeolic dialect than of a scale pattern.
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being forced into three whole tone steps (b–a–g–f), an interstitial note, the
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Apollo's Lyre: Greek music and music theory in antiquity and the middle ages
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in the ratio of 1:2, melodic, in place of equal divisions. Ptolemy, in his
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on mood and character formation (see below on ethos). For example, in the
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In contrast to Archytas who distinguished his "genera" only by moving the
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as found in modern musical practice, except for fine-tuning differences.
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Crocker, Richard L. (Spring 1964). "Pythagorean mathematics and music".
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Crocker, Richard L. (Winter 1963). "Pythagorean mathematics and music".
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The earliest such description of a scale is found in Philolaus fr. B6.
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is misleading: The conventional representation as a section (such as
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The superficial resemblance of these octave species with the church
279:. This was considered apart, built of three stacked tetrachords—the 6924: 6914: 6904: 6879: 6657: 6624: 6586: 6529: 6444: 6429: 6286: 6276: 6193: 6188: 5585: 5580: 5540: 5535: 5510: 5490: 5417: 5372: 5362: 5218: 5116: 5051: 4979: 4587: 4045: 4030: 3873: 3848: 3676: 3368: 3064: 3031: 2910: 2877: 2372: 2083: 379: 65: 6677: 3288:
Mountford, James Frederick (1923). "The musical scales of Plato's
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Chalmers, John H. (1993). Polansky, Larry; Scholz, Carter (eds.).
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In the notation above and below, the standard double-flat symbol
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in 1840; in practice the pitches would have been somewhat lower.
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Winnington-Ingram, Reginald P. (1954). "Greek Music (Ancient)".
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The section spanned by a blue brace is the range of the central
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the chromatic genus is composed of semitones and a minor third,
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tetrachord effected a modulation of the system, hence the name
264:('conjunct') tetrachord, shown at the far left of the diagram. 165: 2688: 2449: 699:
were added to these to form associated scales above and below.
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Crocker, Richard L. (April 1966). "The troping hypothesis".
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B   c   d   e   g   a  
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B   c   d   e   g   a  
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B   c   d   e   g   a  
7052: 7027: 6977: 6464: 6454: 3743: 3005:. Vol. 1 Antiquity and the Middle Ages. Translated by 2935:. Cambridge, UK / New York, NY: Cambridge University Press. 2060: 3353:
Solomon, Jon (Summer 1984). "Towards a history of tonoi".
2977:. Harrison, Lou (foreword). Hanover, NH: Frog Peak Music. 2579: 2577: 2488: 2476: 3107:
Henderson, M.I. (October 1942). "The growth of the Greek
2408: 1880:) include sections that describe the effect of different 1877: 139:, and the Greek note symbols are as given in the work of 97: 41:
evolved over a period of more than 500 years from simple
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Mathiesen, Thomas J. (2001a). "Greece, §I: Ancient". In
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Standard in March 2005 with the release of version 4.1.
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because of the non-heptatonic nature of these scales.
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The diatonic genus is composed of tones and semitones,
2628: 2616: 378:
The next notable Pythagorean theorist known today is
1960:, but also others), rhythms, and sometimes even the 1269:" is standard modern notation for the pitch of note 2895:Barbera, C. AndrĂŠ (Summer 1984). "Octave species". 2739: 2420: 2384: 2357: 898: 413:recognized by Archytas have the following ratios: 295:. When all these are considered together, with the 104: 3444:Antiquae musicae auctores septem: Graece et latine 2345: 2333: 2321: 2309: 2297: 2133:Music symbols of ancient Greece were added to the 1719:B   c   d   e   g   1711:c   d   e   f   g   1703:B   c   d   e   g   1695:B   c   d   e   g   527:, the most significant individual system, that of 245:. This procedure gives its name to the tetrachord 169: 3385: 3246:Mathiesen, Thomas J. (2001b). "Harmonia (i)". In 2812: 2709: 2694: 2437: 1840:Particularly in the earliest surviving writings, 7558: 1944:(iii: 398d–399a), attributes "virility" to the " 1852:, for example, he was more likely thinking of a 260:one step up, permitting the construction of the 4515: 3428:The New Grove Dictionary of Music and Musicians 3278:The New Grove Dictionary of Music and Musicians 3257:The New Grove Dictionary of Music and Musicians 3236:The New Grove Dictionary of Music and Musicians 2828:The New Grove Dictionary of Music and Musicians 1781: 450:, which means "the indicator"). For instance a 3178:(1990). "Unity in Euclid's 'Sectio Canonis'". 2129:Ancient Greek Musical Notation (Unicode block) 1807:. Ptolemy preserved Archytas's tunings in his 733:According to Cleonides, these transpositional 179:The central octave of the ancient Greek system 7204: 4295: 3692: 676:certain neighboring (non-Greek) peoples from 3327: 2414: 2218:in every ancient, Medieval, and Renaissance 518: 183:The earliest Greek scales were organized in 3649:— examples of instruments and compositions. 3567: 3518:(Report) (reprint ed.). Archived from 3052:The Journal of Aesthetics and Art Criticism 3019:The Journal of Aesthetics and Art Criticism 2927: 2721: 2458: 386:further developed Archytas's theory in his 130:Depiction of the ancient Greek tonal system 7218: 7211: 7197: 5181: 4302: 4288: 4254: 3699: 3685: 3664:— KĂŠrylos is a music group led by scholar 3267:Mathiesen, Thomas J. (2001c). "Tonos". In 3266: 3245: 3224: 3009:New York, NY: W.W. Norton. pp. 35–46. 2957: 2781: 2769: 2682: 2670: 2532: 2515: 2402: 1174:(Hypermixolydian, Hyperphrygian, Locrian) 1061:(Hypermixolydian, Hyperphrygian, Locrian) 948:(Hypermixolydian, Hyperphrygian, Locrian) 420:The chromatic – 32:27, 243:224, and 28:27; 88:Overview of the first complete tone system 3491:Grove's Dictionary of Music and Musicians 3390:. London, UK: Cambridge University Press. 3287: 3200: 3106: 2993: 2837: 2793: 2757: 2733: 2634: 2622: 2583: 2494: 2482: 1819:and providing his own ratios and scales. 275:, the modulating system, also called the 237:('dividing'), was introduced between the 76:(including his versions of the genera of 3510: 3308: 2970: 2658: 2646: 2610: 2556: 2544: 2470: 2390: 2378: 2366: 2291: 1984:and Aristotle in his eighth book of his 1872:The philosophical writings of Plato and 1786:In marked contrast to his predecessors, 1766:c   e   f   g   174: 108: 3386:Winnington-Ingram, Reginald P. (1936). 3352: 3158:. New York, NY / Bern, CH: Peter Lang. 3153: 3134:The Stanford Encyclopedia of Philosophy 3127: 3081: 3048: 3015: 2894: 2861: 2745: 2595: 2568: 2431: 2351: 2339: 2327: 2315: 2303: 1811:as well as transmitting the tunings of 14: 7559: 6235: 3281:(2nd ed.). London, UK: Macmillan. 3260:(2nd ed.). London, UK: Macmillan. 3239:(2nd ed.). London, UK: Macmillan. 2831:(2nd ed.). London, UK: Macmillan. 1940:or modes (for instance, Plato, in the 1928:The ancient Greeks have used the word 1369:flat: modern "") from the first note, 603:lichanos hypaton–paranete diezeugmenon 417:The enharmonic – 5:4, 36:35, and 28:27 27:Overview of ancient Greek music theory 7192: 7092: 6234: 5663: 5167: 4514: 4334: 4283: 3680: 3588: 3544: 3174: 2443: 1952:" mode), instruments (especially the 1790:'s scales employed a division of the 1415:) listed first for the Dorian is the 703: 6703:Illicitanus Limin/Portus Illicitanus 4335: 3706: 3604: 2997:(1965). "Harmonic Introduction". In 633:lichanos meson–paranete hyperbolaion 593:parhypate hypaton–trite diezeugmenon 474:, were defined in similar fashion. 423:The diatonic – 9:8, 8:7, and 28:27. 367:adopted in the construction of the 328: 252:To bridge the inconsistency of the 24: 5664: 4309: 3396: 2177:is notation for a fully flattened 2106:, sillos, threnos, and epikedeion; 2075:, nomos, adonidia, iobakchos, and 2012:, independent of text, is able to 669:a small region in central Greece ( 623:parhypate meson–trite hyperbolaion 125: 25: 7598: 3503: 7172: 7162: 7153: 7152: 4264: 4263: 4253: 3571:(1902). Macran, Henry S. (ed.). 3003:Source Readings in Music History 2191:that as well as being different 1422:These tables are a depiction of 1398: 1323: 1311: 1303: 1283: 899:The octave species in all genera 462:from the top, defines the genus 256:, the system allowed moving the 39:musical system of ancient Greece 7173: 3498:. New York: St. Martin's Press. 3439:. London: Macmillan Publishers. 3336:. Oxford, UK: Clarendon Press. 3311:Denkmäler altgriechischer Musik 3147:– via plato.stanford.edu. 2147: 2000:(in his sixth book of his work 1829:In music theory the Greek word 1396:(a quarter-tone sharp: modern " 2964:. Berlin, DE: Albert FĂśrstner. 2958:Bellermann, J.F., ed. (1840). 658:These names are derived from: 613:hypate meson–nete diezeugmenon 534:Aristoxenus was a disciple of 307:tetrachords, they make up the 299:tetrachord placed between the 111:. It shows the common ancient 13: 1: 4774: 4761: 4742: 4725: 3550:"Music of the ancient Greeks" 3442:Meibom, Marcus (ed.) (1652). 2710:Anderson & Mathiesen 2001 2272: 2016:on the listener or musician. 1948:," and "relaxedness" to the " 249:, which means the 'divided'. 5902:Funeral and burial practices 5087:Military of Mycenaean Greece 3645:Austrian Academy of Sciences 3574:The Harmonics of Aristoxenus 3431:, second edition, edited by 3403:Jan, Karl von (ed.) (1895). 2140: 2008:whether music on its own or 1822: 1782:Ptolemy and the Alexandrians 107:reproduces information from 7: 4064:History of music publishing 3513:The Modes of ancient Greece 3494:, fifth edition, edited by 3388:Mode in Ancient Greek Music 2240: 1914:Aristotle remarks further: 662:an Ancient Greek subgroup ( 152:Johann Friedrich Bellermann 10: 7603: 7572:Ancient Greek music theory 5826:Greek Revival architecture 5168: 2805: 2126: 2122: 2040:The classification of the 902: 766:also called Hyperphrygian 570:The octave species in the 558:, Aristoxenus varied both 332: 29: 7526: 7508: 7480: 7422: 7356: 7305: 7268: 7235: 7226: 7148: 7099: 7093: 7088: 6933: 6810: 6799: 6726: 6648: 6605: 6552: 6410: 6262: 6253: 6249: 6230: 6179: 6094: 6032: 5994: 5987: 5937: 5897: 5888: 5810: 5687: 5683: 5659: 5625: 5594: 5436: 5323: 5267: 5234:Attalid kings of Pergamon 5189: 5180: 5176: 5163: 5042:Antigonid Macedonian army 5015: 4988: 4960: 4917: 4874: 4865: 4707: 4646: 4543: 4539: 4510: 4409: 4358: 4354: 4330: 4317: 4269:Category:Musical notation 4249: 4213: 4135:Numbered musical notation 4087: 4054: 3934: 3926:Scientific pitch notation 3817: 3714: 3591:"Analysis of Aristoxenus" 3474:10.1017/s0009838800014415 3356:The Journal of Musicology 3154:Kramarz, Andreas (2016). 3128:Huffman, Carl A. (2011). 2898:The Journal of Musicology 1992:(in his fragmentary work 1892:(viii:1340a:40–1340b:5): 1798:, ii.3–11, construed the 777:also called Hyperiastian 519:The system of Aristoxenus 388:The Division of the Canon 7461:descending melodic major 7408:descending melodic minor 3916:Helmholtz pitch notation 3511:Hamilton, Elsie (1953). 3309:PĂśhlmann, Egert (1970). 2844:A Treatise on Government 2415:PĂśhlmann & West 2001 2113:According to Mathiesen: 2019: 1923: 1848:referred to the Aeolian 1480:Perfect Immutable System 1342:, with the second note, 1185:Mixolydian, Hyperdorian 1072:Mixolydian, Hyperdorian 959:Mixolydian, Hyperdorian 882:also called Hypoiastian 861:also called Hypoaeolian 788:also called Hyperdorian 466:. The other two genera, 137:Helmholtz pitch notation 7436:ascending melodic minor 7374:ascending melodic major 4259:List of musical symbols 4130:Nashville Number System 3461:The Classical Quarterly 3295:The Classical Quarterly 3114:The Classical Quarterly 2865:Journal of Music Theory 1321:The superscript symbol 583:hypate hypaton–paramese 225:At the position of the 58:music of ancient Greece 32:Music of ancient Greece 7447:Lydian augmented (III) 7220:Modes in Western music 5268:Artists & scholars 5183:List of ancient Greeks 4820:Second Athenian League 4669:Greco-Bactrian Kingdom 4494:Ancient Greek colonies 3809:Transposing instrument 3609:"Analysis of Archytas" 3416:The Dialogues of Plato 2933:Greek Musical Writings 2695:Winnington-Ingram 1936 2120: 1966:Aristides Quintilianus 1921: 1912: 1464: 1424:Aristides Quintilianus 1404:") from the following 648:mese–nete hyperbolaion 523:Having elaborated the 477:More generally, three 458:from the bottom and a 409:. The three genera of 200:systema teleion meizon 196:Greater Perfect System 180: 131: 56:Any discussion of the 49:, or divisions of the 18:Greek musical notation 7528:Double harmonic scale 7500:Phrygian dominant (V) 7495:Ukrainian Dorian (IV) 6387:Sybaris on the Traeis 5112:Sacred Band of Thebes 4852:(c. 300 BC–c. 300 AD) 4366:Cycladic civilization 3637:"Ancient Greek music" 3425:(2001d). "Alypius ". 3085:The Musical Quarterly 2247:Alypius of Alexandria 2115: 2002:Adversus mathematicos 1916: 1894: 1432: 1240:Hypophrygian, Ionian 1127:Hypophrygian, Ionian 1014:Hypophrygian, Ionian 652:proslambanomenos–mese 277:Lesser Perfect System 178: 129: 7541:Hungarian minor (IV) 7467:Half diminished (VI) 7457:Aeolian dominant (V) 5912:mythological figures 5633:Ancient Greek tribes 4758:Peloponnesian League 3537:Kathleen Schlesinger 3423:Mathiesen, Thomas J. 3098:10.1093/mq/lii.2.183 2817:(2001). "Ethos". In 2161:is a half-flattened 1281:. The double-flats ( 1277:when flattened by a 1251:Hypodorian, Aeolian 1138:Hypodorian, Aeolian 1025:Hypodorian, Aeolian 830:also called Iastian 809:also called Aeolian 726:attributes thirteen 546:as names of musical 349:Pythagorean Interval 335:Pythagorean interval 189:interval of a fourth 105:diagram at the right 7567:Ancient Greek music 7536:Double harmonic (I) 6024:Tunnel of Eupalinos 6019:Theatre of Dionysus 5643:Ancient Macedonians 5259:Tyrants of Syracuse 4771:Amphictyonic League 4371:Minoan civilization 4155:Percussion notation 3589:Monzo, Joe (2004). 3546:Ioannidis, Nikolaos 3138:Stanford University 2931:, ed. (1984–1989). 2559:, ch. 3, pp. 17–22. 2381:, ch. 5, pp. 48–51. 2212:are also different 1735: 1680: 1634: 1585: 1539: 1492: 1156: 1043: 930: 722:The ancient writer 170:graphic below, left 7518:Harmonic major (I) 7490:Harmonic minor (I) 6698:Menestheus's Limin 6352:Pandosia (Lucania) 6240:Greek colonisation 5602:Athenian statesmen 5363:Diogenes of Sinope 5224:Kings of Macedonia 5214:Kings of Commagene 5082:Macedonian phalanx 5062:Hellenistic armies 4810:(c. 424–c. 395 BC) 4674:Indo-Greek Kingdom 4396:Hellenistic Greece 3656:"Ensemble KĂŠrylos" 3554:homoecumenicus.com 2813:Anderson, Warren; 1728: 1674: 1628: 1579: 1533: 1486: 1150: 1037: 924: 507:), respectively . 353:Pythagorean Tuning 311:(or Unmodulating) 181: 132: 62:Pythagorean school 7554: 7553: 7301: 7300: 7186: 7185: 7144: 7143: 7084: 7083: 7080: 7079: 7076: 7075: 6650:Iberian Peninsula 6582:Lipara/Meligounis 6548: 6547: 6226: 6225: 6222: 6221: 6199:Cypriot syllabary 6090: 6089: 5999:Athenian Treasury 5983: 5982: 5655: 5654: 5651: 5650: 5244:Ptolemaic dynasty 5204:Archons of Athens 5159: 5158: 5155: 5154: 5030:Athenian military 5011: 5010: 4844:League of Corinth 4826:Thessalian League 4802:Chalcidian League 4784:Acarnanian League 4694:Ptolemaic Kingdom 4506: 4505: 4502: 4501: 4277: 4276: 4221:Mensural notation 3328:PĂśhlmann, Egert; 3136:. Palo Alto, CA: 2945:; Volume 2: 1846:Lasus of Hermione 1778: 1777: 1723: 1722: 1669: 1668: 1620: 1619: 1574: 1573: 1527: 1526: 1482:described above. 1454:are synonyms for 1258: 1257: 1145: 1144: 1032: 1031: 913:The order of the 896: 895: 879:Low Hypophrygian 869:High Hypophrygian 273:systema metabolon 16:(Redirected from 7594: 7233: 7232: 7213: 7206: 7199: 7190: 7189: 7176: 7175: 7166: 7156: 7155: 7090: 7089: 6808: 6807: 6307:Heraclea Lucania 6260: 6259: 6251: 6250: 6232: 6231: 5992: 5991: 5924:Twelve Olympians 5895: 5894: 5685: 5684: 5661: 5660: 5249:Seleucid dynasty 5229:Kings of Paionia 5178: 5177: 5165: 5164: 5035:Scythian archers 4942:Graphe paranomon 4872: 4871: 4779: 4776: 4766: 4763: 4747: 4744: 4734: 4730: 4727: 4541: 4540: 4512: 4511: 4391:Classical Greece 4376:Mycenaean Greece 4356: 4355: 4332: 4331: 4304: 4297: 4290: 4281: 4280: 4267: 4266: 4257: 4256: 4120:Graphic notation 3784:Rehearsal letter 3708:Musical notation 3701: 3694: 3687: 3678: 3677: 3663: 3648: 3616: 3598: 3582: 3579:Internet Archive 3557: 3534: 3532: 3530: 3524: 3517: 3485: 3468:(3–4): 195–208. 3419: 3412:Jowett, Benjamin 3391: 3380: 3347: 3322: 3303: 3282: 3261: 3240: 3219: 3195: 3169: 3148: 3146: 3144: 3122: 3110: 3101: 3076: 3043: 3010: 2988: 2965: 2936: 2922: 2889: 2856: 2832: 2797: 2791: 2785: 2779: 2773: 2767: 2761: 2755: 2749: 2743: 2737: 2736:, book 8, ch. 5. 2731: 2725: 2722:Barker 1984–1989 2719: 2713: 2707: 2698: 2692: 2686: 2680: 2674: 2668: 2662: 2656: 2650: 2649:, ch. 6, p. 106. 2644: 2638: 2632: 2626: 2620: 2614: 2613:, ch. 6, p. 109. 2608: 2599: 2593: 2587: 2581: 2572: 2566: 2560: 2554: 2548: 2542: 2536: 2530: 2519: 2513: 2498: 2492: 2486: 2480: 2474: 2468: 2462: 2459:Barker 1984–1989 2456: 2447: 2441: 2435: 2429: 2418: 2412: 2406: 2400: 2394: 2388: 2382: 2376: 2370: 2364: 2355: 2349: 2343: 2337: 2331: 2325: 2319: 2313: 2307: 2301: 2295: 2289: 2267:Oxyrhynchus hymn 2257:Seikilos epitaph 2234: 2233: 2230: 2229: 2211: 2210: 2203: 2202: 2184: 2183: 2176: 2175: 2169:, as opposed to 2168: 2167: 2160: 2159: 2151: 2051:as preserved by 2049:Useful Knowledge 2006:music philosophy 1998:Sextus Empiricus 1736: 1733: 1727: 1681: 1679: 1673: 1635: 1633: 1627: 1586: 1584: 1578: 1540: 1538: 1532: 1493: 1491: 1485: 1417:ProslambanĂłmenos 1403: 1402: 1395: 1393: 1391: 1390: 1387: 1384: 1364: 1362: 1360: 1359: 1356: 1353: 1328: 1327: 1316: 1315: 1308: 1307: 1297:in three genera 1288: 1287: 1275: 1274: 1267: 1266: 1157: 1155: 1149: 1044: 1042: 1036: 931: 929: 923: 757: 756: 574:tradition were: 481:of seven octave 392:Katatomē kanonos 329:The Pythagoreans 319:, the adjoined. 317:Proslambanomenos 160: 149: 21: 7602: 7601: 7597: 7596: 7595: 7593: 7592: 7591: 7557: 7556: 7555: 7550: 7522: 7504: 7476: 7418: 7352: 7297: 7264: 7222: 7217: 7187: 7182: 7140: 7095: 7072: 6935: 6929: 6812: 6803: 6795: 6766:Melaina Korkyra 6722: 6644: 6601: 6554:Aeolian Islands 6544: 6406: 6264: 6245: 6244: 6218: 6175: 6086: 6028: 5979: 5933: 5884: 5806: 5797:Wedding customs 5679: 5678: 5647: 5638:Thracian Greeks 5621: 5612:Olympic victors 5590: 5432: 5319: 5263: 5254:Kings of Sparta 5239:Kings of Pontus 5209:Kings of Athens 5185: 5172: 5151: 5047:Army of Macedon 5007: 4984: 4956: 4913: 4861: 4834:(370–c. 230 BC) 4832:Arcadian League 4816:(c. 400–188 BC) 4814:Aetolian League 4808:Boeotian League 4790:Hellenic League 4777: 4764: 4754:(c. 650–404 BC) 4745: 4739:Italiote League 4732: 4728: 4722:Doric Hexapolis 4712: 4703: 4699:Seleucid Empire 4642: 4535: 4534: 4498: 4405: 4381:Greek Dark Ages 4350: 4349: 4326: 4313: 4308: 4278: 4273: 4245: 4209: 4083: 4074:Music publisher 4069:Music engraving 4050: 3930: 3921:Letter notation 3813: 3710: 3705: 3675: 3654: 3635: 3528: 3526: 3522: 3515: 3506: 3501: 3457: 3410: 3399: 3397:Further reading 3394: 3344: 3332:, eds. (2001). 3216: 3202:Mathiesen, T.J. 3166: 3142: 3140: 3108: 2985: 2937:Volume 1: 2815:Mathiesen, T.J. 2808: 2802: 2800: 2792: 2788: 2782:Mathiesen 2001a 2780: 2776: 2770:Mathiesen 2001a 2768: 2764: 2756: 2752: 2744: 2740: 2732: 2728: 2720: 2716: 2708: 2701: 2693: 2689: 2683:Mathiesen 2001b 2681: 2677: 2671:Mathiesen 2001c 2669: 2665: 2661:, ch. 2, p. 10. 2657: 2653: 2645: 2641: 2633: 2629: 2621: 2617: 2609: 2602: 2594: 2590: 2582: 2575: 2567: 2563: 2555: 2551: 2547:, ch. 5, p. 48. 2543: 2539: 2533:Mathiesen 2001a 2531: 2522: 2516:Mathiesen 2001a 2514: 2501: 2493: 2489: 2481: 2477: 2473:, ch. 5, p. 47. 2469: 2465: 2457: 2450: 2442: 2438: 2430: 2421: 2413: 2409: 2403:Bellermann 1840 2401: 2397: 2389: 2385: 2377: 2373: 2365: 2358: 2350: 2346: 2338: 2334: 2326: 2322: 2314: 2310: 2302: 2298: 2294:, ch. 6, p. 99. 2290: 2279: 2275: 2243: 2238: 2237: 2227: 2226: 2223: 2206: 2205: 2198: 2197: 2179: 2178: 2171: 2170: 2163: 2162: 2155: 2154: 2152: 2148: 2143: 2131: 2125: 2022: 2014:elicit emotions 1926: 1837:named by them. 1827: 1784: 1779: 1729: 1725: 1675: 1671: 1629: 1625: 1622: 1580: 1576: 1534: 1530: 1529: 1487: 1397: 1388: 1385: 1382: 1381: 1379: 1378: 1373:, and the same 1357: 1354: 1351: 1350: 1348: 1347: 1322: 1310: 1302: 1299: 1282: 1272: 1271: 1264: 1263: 1259: 1151: 1147: 1038: 1034: 925: 921: 907: 901: 848:High Hypolydian 774:High Mixolydian 763:Hypermixolydian 709: 654:(a′–a″ or a–a′) 525:Systema teleion 521: 513:Systema teleion 446:(thus the name 337: 331: 267:The use of the 154: 143: 109:Chalmers (1993) 94:systema teleion 90: 35: 28: 23: 22: 15: 12: 11: 5: 7600: 7590: 7589: 7587:Musical tuning 7584: 7579: 7574: 7569: 7552: 7551: 7549: 7548: 7543: 7538: 7532: 7530: 7524: 7523: 7521: 7520: 7514: 7512: 7510:Harmonic major 7506: 7505: 7503: 7502: 7497: 7492: 7486: 7484: 7482:Harmonic minor 7478: 7477: 7475: 7474: 7469: 7464: 7454: 7449: 7444: 7442:Dorian ♭2 (II) 7439: 7432:Jazz minor (I) 7428: 7426: 7420: 7419: 7417: 7416: 7411: 7397: 7395:Mixolydian (V) 7392: 7387: 7385:Phrygian (III) 7382: 7377: 7362: 7360: 7354: 7353: 7351: 7350: 7345: 7340: 7335: 7330: 7325: 7320: 7315: 7309: 7307: 7303: 7302: 7299: 7298: 7296: 7295: 7293:Hypomixolydian 7290: 7285: 7280: 7274: 7272: 7266: 7265: 7263: 7262: 7257: 7252: 7247: 7241: 7239: 7230: 7224: 7223: 7216: 7215: 7208: 7201: 7193: 7184: 7183: 7181: 7180: 7170: 7160: 7149: 7146: 7145: 7142: 7141: 7139: 7138: 7133: 7128: 7123: 7118: 7113: 7112: 7111: 7100: 7097: 7096: 7086: 7085: 7082: 7081: 7078: 7077: 7074: 7073: 7071: 7070: 7065: 7060: 7055: 7050: 7045: 7040: 7035: 7030: 7025: 7020: 7015: 7010: 7005: 7000: 6995: 6990: 6985: 6980: 6975: 6970: 6965: 6960: 6955: 6950: 6945: 6939: 6937: 6931: 6930: 6928: 6927: 6922: 6917: 6912: 6907: 6902: 6897: 6892: 6887: 6882: 6877: 6872: 6867: 6862: 6857: 6852: 6847: 6842: 6837: 6832: 6827: 6822: 6816: 6814: 6805: 6797: 6796: 6794: 6793: 6788: 6783: 6778: 6773: 6768: 6763: 6758: 6753: 6748: 6743: 6738: 6732: 6730: 6724: 6723: 6721: 6720: 6715: 6710: 6705: 6700: 6695: 6690: 6685: 6680: 6675: 6670: 6665: 6660: 6654: 6652: 6646: 6645: 6643: 6642: 6637: 6627: 6622: 6617: 6611: 6609: 6603: 6602: 6600: 6599: 6594: 6589: 6584: 6579: 6574: 6569: 6564: 6558: 6556: 6550: 6549: 6546: 6545: 6543: 6542: 6537: 6532: 6527: 6522: 6517: 6512: 6507: 6502: 6500:Megara Hyblaea 6497: 6492: 6487: 6482: 6480:Hybla Gereatis 6477: 6472: 6470:Heraclea Minoa 6467: 6462: 6457: 6452: 6447: 6442: 6437: 6432: 6427: 6422: 6416: 6414: 6408: 6407: 6405: 6404: 6399: 6394: 6389: 6384: 6379: 6374: 6369: 6364: 6359: 6354: 6349: 6344: 6339: 6334: 6329: 6324: 6319: 6314: 6309: 6304: 6299: 6294: 6289: 6284: 6279: 6274: 6268: 6266: 6257: 6247: 6246: 6243: 6242: 6236: 6228: 6227: 6224: 6223: 6220: 6219: 6217: 6216: 6214:Attic numerals 6211: 6209:Greek numerals 6206: 6204:Greek alphabet 6201: 6196: 6191: 6185: 6183: 6177: 6176: 6174: 6173: 6168: 6167: 6166: 6161: 6156: 6151: 6146: 6141: 6136: 6131: 6126: 6116: 6111: 6106: 6100: 6098: 6092: 6091: 6088: 6087: 6085: 6084: 6079: 6074: 6069: 6064: 6059: 6054: 6049: 6044: 6038: 6036: 6030: 6029: 6027: 6026: 6021: 6016: 6011: 6006: 6001: 5995: 5989: 5985: 5984: 5981: 5980: 5978: 5977: 5972: 5967: 5962: 5957: 5952: 5947: 5941: 5939: 5935: 5934: 5932: 5931: 5926: 5921: 5916: 5915: 5914: 5904: 5898: 5892: 5886: 5885: 5883: 5882: 5877: 5872: 5867: 5862: 5861: 5860: 5858:Musical system 5850: 5845: 5840: 5835: 5830: 5829: 5828: 5817: 5815: 5808: 5807: 5805: 5804: 5799: 5794: 5789: 5784: 5779: 5774: 5769: 5764: 5759: 5754: 5749: 5744: 5739: 5734: 5729: 5724: 5719: 5714: 5709: 5704: 5699: 5693: 5691: 5681: 5680: 5677: 5676: 5671: 5665: 5657: 5656: 5653: 5652: 5649: 5648: 5646: 5645: 5640: 5635: 5629: 5627: 5623: 5622: 5620: 5619: 5614: 5609: 5604: 5598: 5596: 5592: 5591: 5589: 5588: 5583: 5578: 5573: 5568: 5563: 5558: 5553: 5548: 5543: 5538: 5533: 5528: 5523: 5518: 5513: 5508: 5503: 5498: 5493: 5488: 5483: 5478: 5473: 5468: 5463: 5458: 5453: 5448: 5442: 5440: 5434: 5433: 5431: 5430: 5425: 5420: 5415: 5410: 5405: 5400: 5395: 5390: 5385: 5380: 5375: 5370: 5365: 5360: 5355: 5350: 5345: 5340: 5335: 5329: 5327: 5321: 5320: 5318: 5317: 5312: 5307: 5302: 5297: 5292: 5290:Mathematicians 5287: 5282: 5277: 5271: 5269: 5265: 5264: 5262: 5261: 5256: 5251: 5246: 5241: 5236: 5231: 5226: 5221: 5216: 5211: 5206: 5201: 5199:Kings of Argos 5195: 5193: 5187: 5186: 5174: 5173: 5161: 5160: 5157: 5156: 5153: 5152: 5150: 5149: 5144: 5139: 5134: 5129: 5124: 5119: 5114: 5109: 5104: 5099: 5094: 5089: 5084: 5079: 5074: 5069: 5064: 5059: 5057:Cretan archers 5054: 5049: 5044: 5039: 5038: 5037: 5027: 5021: 5019: 5013: 5012: 5009: 5008: 5006: 5005: 5000: 4994: 4992: 4986: 4985: 4983: 4982: 4977: 4972: 4966: 4964: 4958: 4957: 4955: 4954: 4949: 4944: 4939: 4934: 4929: 4923: 4921: 4915: 4914: 4912: 4911: 4906: 4901: 4896: 4891: 4886: 4881: 4875: 4869: 4863: 4862: 4860: 4859: 4856:Achaean League 4853: 4850:Euboean League 4847: 4841: 4838:Epirote League 4835: 4829: 4823: 4817: 4811: 4805: 4799: 4793: 4787: 4786:(c. 500–31 BC) 4781: 4768: 4755: 4749: 4736: 4718: 4716: 4714:Confederations 4705: 4704: 4702: 4701: 4696: 4691: 4686: 4681: 4676: 4671: 4666: 4661: 4656: 4650: 4648: 4644: 4643: 4641: 4640: 4638:Lissus (Crete) 4635: 4630: 4625: 4620: 4615: 4610: 4605: 4600: 4595: 4590: 4585: 4580: 4575: 4570: 4565: 4560: 4555: 4549: 4547: 4537: 4536: 4533: 4532: 4527: 4522: 4516: 4508: 4507: 4504: 4503: 4500: 4499: 4497: 4496: 4491: 4486: 4481: 4476: 4471: 4466: 4461: 4456: 4451: 4446: 4441: 4436: 4431: 4426: 4421: 4415: 4413: 4407: 4406: 4404: 4403: 4398: 4393: 4388: 4386:Archaic Greece 4383: 4378: 4373: 4368: 4362: 4360: 4352: 4351: 4348: 4347: 4342: 4336: 4328: 4327: 4325: 4324: 4318: 4315: 4314: 4311:Ancient Greece 4307: 4306: 4299: 4292: 4284: 4275: 4274: 4272: 4271: 4261: 4250: 4247: 4246: 4244: 4243: 4238: 4233: 4228: 4223: 4217: 4215: 4211: 4210: 4208: 4207: 4202: 4197: 4192: 4187: 4182: 4177: 4172: 4167: 4162: 4157: 4152: 4147: 4142: 4137: 4132: 4127: 4122: 4117: 4112: 4107: 4102: 4097: 4091: 4089: 4085: 4084: 4082: 4081: 4076: 4071: 4066: 4060: 4058: 4052: 4051: 4049: 4048: 4043: 4038: 4033: 4028: 4023: 4018: 4017: 4016: 4011: 4006: 4001: 3996: 3991: 3981: 3976: 3971: 3966: 3961: 3956: 3951: 3946: 3940: 3938: 3932: 3931: 3929: 3928: 3923: 3918: 3913: 3908: 3903: 3898: 3893: 3888: 3883: 3882: 3881: 3876: 3871: 3861: 3856: 3851: 3846: 3845: 3844: 3839: 3834: 3823: 3821: 3815: 3814: 3812: 3811: 3806: 3801: 3799:Time signature 3796: 3791: 3786: 3781: 3776: 3771: 3766: 3761: 3756: 3751: 3746: 3741: 3736: 3731: 3726: 3720: 3718: 3712: 3711: 3704: 3703: 3696: 3689: 3681: 3674: 3673: 3651: 3650: 3632: 3631: 3613:ex-tempore.org 3601: 3600: 3585: 3584: 3581:(archive.org). 3564: 3563: 3541: 3540: 3507: 3505: 3504:External links 3502: 3500: 3499: 3486: 3455: 3440: 3420: 3408: 3400: 3398: 3395: 3393: 3392: 3382: 3381: 3369:10.2307/763814 3363:(3): 242–251. 3349: 3348: 3342: 3324: 3323: 3305: 3304: 3284: 3283: 3269:Sadie, Stanley 3263: 3262: 3248:Sadie, Stanley 3242: 3241: 3227:Sadie, Stanley 3221: 3220: 3214: 3197: 3196: 3186:(4): 430–443. 3171: 3170: 3164: 3150: 3149: 3124: 3123: 3121:(3–4): 94–103. 3103: 3102: 3092:(2): 183–203. 3078: 3077: 3065:10.2307/427236 3059:(3): 325–335. 3045: 3044: 3032:10.2307/427754 3026:(2): 189–198. 3012: 3011: 2990: 2989: 2983: 2967: 2966: 2954: 2953: 2924: 2923: 2911:10.2307/763813 2905:(3): 229–241. 2891: 2890: 2878:10.2307/843492 2872:(2): 294–323. 2858: 2857: 2834: 2833: 2809: 2807: 2804: 2799: 2798: 2794:Mathiesen 1999 2786: 2774: 2762: 2758:Cleonides 1965 2750: 2738: 2734:Aristotle 1912 2726: 2714: 2699: 2687: 2675: 2663: 2651: 2639: 2635:Mountford 1923 2627: 2623:Henderson 1942 2615: 2600: 2588: 2584:Cleonides 1965 2573: 2561: 2549: 2537: 2520: 2499: 2495:Cleonides 1965 2487: 2483:Cleonides 1965 2475: 2463: 2448: 2436: 2419: 2407: 2395: 2383: 2371: 2356: 2344: 2332: 2320: 2308: 2296: 2276: 2274: 2271: 2270: 2269: 2264: 2259: 2254: 2249: 2242: 2239: 2236: 2235: 2145: 2144: 2142: 2139: 2127:Main article: 2124: 2121: 2111: 2110: 2107: 2080: 2021: 2018: 2010:absolute music 1925: 1922: 1826: 1821: 1783: 1780: 1776: 1775: 1772: 1768: 1767: 1764: 1760: 1759: 1756: 1752: 1751: 1748: 1744: 1743: 1740: 1721: 1720: 1717: 1713: 1712: 1709: 1705: 1704: 1701: 1697: 1696: 1693: 1689: 1688: 1685: 1667: 1666: 1663: 1659: 1658: 1655: 1651: 1650: 1647: 1643: 1642: 1639: 1618: 1617: 1614: 1610: 1609: 1606: 1602: 1601: 1598: 1594: 1593: 1590: 1572: 1571: 1568: 1564: 1563: 1560: 1556: 1555: 1552: 1548: 1547: 1544: 1525: 1524: 1521: 1517: 1516: 1513: 1509: 1508: 1505: 1501: 1500: 1497: 1484: 1426:'s enharmonic 1298: 1291: 1261:The notation " 1256: 1255: 1252: 1249: 1245: 1244: 1241: 1238: 1234: 1233: 1230: 1227: 1223: 1222: 1219: 1216: 1212: 1211: 1208: 1205: 1201: 1200: 1197: 1194: 1190: 1189: 1186: 1183: 1179: 1178: 1175: 1172: 1168: 1167: 1164: 1161: 1143: 1142: 1139: 1136: 1132: 1131: 1128: 1125: 1121: 1120: 1117: 1114: 1110: 1109: 1106: 1103: 1099: 1098: 1095: 1092: 1088: 1087: 1084: 1081: 1077: 1076: 1073: 1070: 1066: 1065: 1062: 1059: 1055: 1054: 1051: 1048: 1030: 1029: 1026: 1023: 1019: 1018: 1015: 1012: 1008: 1007: 1004: 1001: 997: 996: 993: 990: 986: 985: 982: 979: 975: 974: 971: 968: 964: 963: 960: 957: 953: 952: 949: 946: 942: 941: 938: 935: 919: 915:octave species 905:Octave species 903:Main article: 900: 897: 894: 893: 891: 888: 884: 883: 880: 877: 873: 872: 870: 867: 863: 862: 859: 858:Low Hypolydian 856: 852: 851: 849: 846: 842: 841: 839: 836: 832: 831: 828: 825: 821: 820: 818: 815: 811: 810: 807: 804: 800: 799: 797: 794: 790: 789: 786: 785:Low Mixolydian 783: 779: 778: 775: 772: 768: 767: 764: 761: 708: 702: 701: 700: 689: 674: 667: 656: 655: 636: 626: 616: 606: 596: 586: 540:octave species 520: 517: 501: 500: 497: 494: 425: 424: 421: 418: 396:Sectio Canonis 333:Main article: 330: 327: 141:Egert PĂśhlmann 89: 86: 51:perfect fourth 26: 9: 6: 4: 3: 2: 7599: 7588: 7585: 7583: 7582:Modes (music) 7580: 7578: 7575: 7573: 7570: 7568: 7565: 7564: 7562: 7547: 7544: 7542: 7539: 7537: 7534: 7533: 7531: 7529: 7525: 7519: 7516: 7515: 7513: 7511: 7507: 7501: 7498: 7496: 7493: 7491: 7488: 7487: 7485: 7483: 7479: 7473: 7472:Altered (VII) 7470: 7468: 7465: 7462: 7458: 7455: 7453: 7452:Acoustic (IV) 7450: 7448: 7445: 7443: 7440: 7437: 7433: 7430: 7429: 7427: 7425: 7421: 7415: 7414:Locrian (VII) 7412: 7409: 7405: 7404:natural minor 7401: 7398: 7396: 7393: 7391: 7388: 7386: 7383: 7381: 7378: 7375: 7371: 7370:natural major 7367: 7364: 7363: 7361: 7359: 7355: 7349: 7348:Reciting tone 7346: 7344: 7341: 7339: 7336: 7334: 7331: 7329: 7326: 7324: 7321: 7319: 7316: 7314: 7311: 7310: 7308: 7304: 7294: 7291: 7289: 7286: 7284: 7281: 7279: 7276: 7275: 7273: 7271: 7267: 7261: 7258: 7256: 7253: 7251: 7248: 7246: 7243: 7242: 7240: 7238: 7234: 7231: 7229: 7225: 7221: 7214: 7209: 7207: 7202: 7200: 7195: 7194: 7191: 7179: 7171: 7169: 7165: 7161: 7159: 7151: 7150: 7147: 7137: 7134: 7132: 7129: 7127: 7124: 7122: 7119: 7117: 7114: 7110: 7107: 7106: 7105: 7102: 7101: 7098: 7091: 7087: 7069: 7066: 7064: 7061: 7059: 7056: 7054: 7051: 7049: 7046: 7044: 7041: 7039: 7036: 7034: 7031: 7029: 7026: 7024: 7021: 7019: 7016: 7014: 7011: 7009: 7006: 7004: 7001: 6999: 6996: 6994: 6991: 6989: 6986: 6984: 6981: 6979: 6976: 6974: 6971: 6969: 6966: 6964: 6961: 6959: 6956: 6954: 6951: 6949: 6946: 6944: 6941: 6940: 6938: 6932: 6926: 6923: 6921: 6918: 6916: 6913: 6911: 6908: 6906: 6903: 6901: 6898: 6896: 6893: 6891: 6888: 6886: 6883: 6881: 6878: 6876: 6873: 6871: 6868: 6866: 6863: 6861: 6858: 6856: 6853: 6851: 6848: 6846: 6843: 6841: 6838: 6836: 6833: 6831: 6828: 6826: 6823: 6821: 6818: 6817: 6815: 6809: 6806: 6802: 6798: 6792: 6789: 6787: 6784: 6782: 6779: 6777: 6774: 6772: 6769: 6767: 6764: 6762: 6759: 6757: 6754: 6752: 6749: 6747: 6744: 6742: 6739: 6737: 6734: 6733: 6731: 6729: 6725: 6719: 6716: 6714: 6711: 6709: 6706: 6704: 6701: 6699: 6696: 6694: 6691: 6689: 6686: 6684: 6681: 6679: 6678:Hemeroscopion 6676: 6674: 6671: 6669: 6666: 6664: 6661: 6659: 6656: 6655: 6653: 6651: 6647: 6641: 6638: 6635: 6631: 6628: 6626: 6623: 6621: 6618: 6616: 6613: 6612: 6610: 6608: 6604: 6598: 6595: 6593: 6590: 6588: 6585: 6583: 6580: 6578: 6575: 6573: 6570: 6568: 6565: 6563: 6560: 6559: 6557: 6555: 6551: 6541: 6538: 6536: 6533: 6531: 6528: 6526: 6523: 6521: 6518: 6516: 6513: 6511: 6508: 6506: 6503: 6501: 6498: 6496: 6493: 6491: 6488: 6486: 6483: 6481: 6478: 6476: 6473: 6471: 6468: 6466: 6463: 6461: 6458: 6456: 6453: 6451: 6448: 6446: 6443: 6441: 6438: 6436: 6433: 6431: 6428: 6426: 6423: 6421: 6418: 6417: 6415: 6413: 6409: 6403: 6400: 6398: 6395: 6393: 6390: 6388: 6385: 6383: 6380: 6378: 6375: 6373: 6370: 6368: 6365: 6363: 6360: 6358: 6355: 6353: 6350: 6348: 6345: 6343: 6340: 6338: 6335: 6333: 6330: 6328: 6325: 6323: 6320: 6318: 6315: 6313: 6310: 6308: 6305: 6303: 6300: 6298: 6295: 6293: 6290: 6288: 6285: 6283: 6280: 6278: 6275: 6273: 6270: 6269: 6267: 6261: 6258: 6256: 6255:Magna Graecia 6252: 6248: 6241: 6238: 6237: 6233: 6229: 6215: 6212: 6210: 6207: 6205: 6202: 6200: 6197: 6195: 6192: 6190: 6187: 6186: 6184: 6182: 6178: 6172: 6169: 6165: 6162: 6160: 6157: 6155: 6152: 6150: 6147: 6145: 6142: 6140: 6137: 6135: 6132: 6130: 6129:Arcadocypriot 6127: 6125: 6122: 6121: 6120: 6117: 6115: 6112: 6110: 6107: 6105: 6102: 6101: 6099: 6097: 6093: 6083: 6082:Zeus, Olympia 6080: 6078: 6075: 6073: 6070: 6068: 6067:Hera, Olympia 6065: 6063: 6060: 6058: 6055: 6053: 6050: 6048: 6045: 6043: 6040: 6039: 6037: 6035: 6031: 6025: 6022: 6020: 6017: 6015: 6012: 6010: 6007: 6005: 6002: 6000: 5997: 5996: 5993: 5990: 5986: 5976: 5973: 5971: 5970:Mount Olympus 5968: 5966: 5963: 5961: 5958: 5956: 5953: 5951: 5948: 5946: 5943: 5942: 5940: 5938:Sacred places 5936: 5930: 5927: 5925: 5922: 5920: 5917: 5913: 5910: 5909: 5908: 5905: 5903: 5900: 5899: 5896: 5893: 5891: 5887: 5881: 5878: 5876: 5873: 5871: 5868: 5866: 5863: 5859: 5856: 5855: 5854: 5851: 5849: 5846: 5844: 5841: 5839: 5836: 5834: 5831: 5827: 5824: 5823: 5822: 5819: 5818: 5816: 5813: 5809: 5803: 5800: 5798: 5795: 5793: 5790: 5788: 5785: 5783: 5780: 5778: 5775: 5773: 5770: 5768: 5765: 5763: 5762:Olympic Games 5760: 5758: 5755: 5753: 5752:Homosexuality 5750: 5748: 5745: 5743: 5740: 5738: 5735: 5733: 5730: 5728: 5725: 5723: 5720: 5718: 5715: 5713: 5710: 5708: 5705: 5703: 5700: 5698: 5695: 5694: 5692: 5690: 5686: 5682: 5675: 5672: 5670: 5667: 5666: 5662: 5658: 5644: 5641: 5639: 5636: 5634: 5631: 5630: 5628: 5624: 5618: 5615: 5613: 5610: 5608: 5605: 5603: 5600: 5599: 5597: 5593: 5587: 5584: 5582: 5579: 5577: 5574: 5572: 5569: 5567: 5564: 5562: 5559: 5557: 5554: 5552: 5549: 5547: 5544: 5542: 5539: 5537: 5534: 5532: 5529: 5527: 5524: 5522: 5519: 5517: 5514: 5512: 5509: 5507: 5504: 5502: 5499: 5497: 5494: 5492: 5489: 5487: 5484: 5482: 5479: 5477: 5474: 5472: 5469: 5467: 5464: 5462: 5459: 5457: 5454: 5452: 5449: 5447: 5444: 5443: 5441: 5439: 5435: 5429: 5426: 5424: 5421: 5419: 5416: 5414: 5411: 5409: 5406: 5404: 5401: 5399: 5396: 5394: 5391: 5389: 5386: 5384: 5381: 5379: 5376: 5374: 5371: 5369: 5366: 5364: 5361: 5359: 5356: 5354: 5351: 5349: 5346: 5344: 5341: 5339: 5336: 5334: 5331: 5330: 5328: 5326: 5322: 5316: 5313: 5311: 5308: 5306: 5303: 5301: 5298: 5296: 5293: 5291: 5288: 5286: 5283: 5281: 5278: 5276: 5273: 5272: 5270: 5266: 5260: 5257: 5255: 5252: 5250: 5247: 5245: 5242: 5240: 5237: 5235: 5232: 5230: 5227: 5225: 5222: 5220: 5217: 5215: 5212: 5210: 5207: 5205: 5202: 5200: 5197: 5196: 5194: 5192: 5188: 5184: 5179: 5175: 5171: 5166: 5162: 5148: 5145: 5143: 5140: 5138: 5135: 5133: 5130: 5128: 5125: 5123: 5122:Seleucid army 5120: 5118: 5115: 5113: 5110: 5108: 5105: 5103: 5100: 5098: 5095: 5093: 5090: 5088: 5085: 5083: 5080: 5078: 5075: 5073: 5070: 5068: 5065: 5063: 5060: 5058: 5055: 5053: 5050: 5048: 5045: 5043: 5040: 5036: 5033: 5032: 5031: 5028: 5026: 5023: 5022: 5020: 5018: 5014: 5004: 5001: 4999: 4996: 4995: 4993: 4991: 4987: 4981: 4978: 4976: 4973: 4971: 4968: 4967: 4965: 4963: 4959: 4953: 4950: 4948: 4945: 4943: 4940: 4938: 4935: 4933: 4930: 4928: 4925: 4924: 4922: 4920: 4916: 4910: 4907: 4905: 4902: 4900: 4897: 4895: 4892: 4890: 4887: 4885: 4882: 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4412: 4408: 4402: 4399: 4397: 4394: 4392: 4389: 4387: 4384: 4382: 4379: 4377: 4374: 4372: 4369: 4367: 4364: 4363: 4361: 4357: 4353: 4346: 4343: 4341: 4338: 4337: 4333: 4329: 4323: 4320: 4319: 4316: 4312: 4305: 4300: 4298: 4293: 4291: 4286: 4285: 4282: 4270: 4262: 4260: 4252: 4251: 4248: 4242: 4241:Transcription 4239: 4237: 4236:Sight-reading 4234: 4232: 4231:Perfect pitch 4229: 4227: 4224: 4222: 4219: 4218: 4216: 4212: 4206: 4203: 4201: 4198: 4196: 4193: 4191: 4188: 4186: 4183: 4181: 4178: 4176: 4173: 4171: 4168: 4166: 4165:Ancient Greek 4163: 4161: 4158: 4156: 4153: 4151: 4148: 4146: 4143: 4141: 4138: 4136: 4133: 4131: 4128: 4126: 4123: 4121: 4118: 4116: 4113: 4111: 4108: 4106: 4105:Chord diagram 4103: 4101: 4098: 4096: 4095:Braille music 4093: 4092: 4090: 4088:Other systems 4086: 4080: 4077: 4075: 4072: 4070: 4067: 4065: 4062: 4061: 4059: 4057: 4053: 4047: 4044: 4042: 4039: 4037: 4034: 4032: 4029: 4027: 4024: 4022: 4019: 4015: 4012: 4010: 4007: 4005: 4002: 4000: 3997: 3995: 3992: 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2375: 2368: 2367:Chalmers 1993 2363: 2361: 2353: 2348: 2341: 2336: 2329: 2324: 2317: 2312: 2305: 2300: 2293: 2292:Chalmers 1993 2288: 2286: 2284: 2282: 2277: 2268: 2265: 2263: 2260: 2258: 2255: 2253: 2252:Delphic Hymns 2250: 2248: 2245: 2244: 2231: 2221: 2220:tuning system 2217: 2216: 2209: 2201: 2196: 2195: 2190: 2189: 2182: 2174: 2166: 2158: 2150: 2146: 2138: 2136: 2130: 2119: 2114: 2108: 2105: 2101: 2097: 2093: 2089: 2085: 2081: 2078: 2074: 2070: 2066: 2062: 2059:for the gods— 2058: 2057: 2056: 2054: 2050: 2047: 2044:we have from 2043: 2038: 2036: 2032: 2028: 2017: 2015: 2011: 2007: 2003: 1999: 1995: 1991: 1987: 1983: 1979: 1975: 1971: 1967: 1963: 1959: 1955: 1951: 1947: 1943: 1939: 1935: 1931: 1920: 1915: 1911: 1908: 1904: 1899: 1893: 1891: 1887: 1883: 1879: 1875: 1870: 1868: 1864: 1863: 1857: 1855: 1854:melodic style 1851: 1847: 1843: 1838: 1836: 1832: 1825: 1820: 1818: 1814: 1810: 1806: 1801: 1797: 1793: 1789: 1773: 1771:2nd Diatonic 1770: 1769: 1765: 1763:1st Diatonic 1762: 1761: 1757: 1754: 1753: 1749: 1746: 1745: 1741: 1738: 1737: 1732: 1726: 1718: 1716:2nd Diatonic 1715: 1714: 1710: 1708:1st Diatonic 1707: 1706: 1702: 1699: 1698: 1694: 1691: 1690: 1686: 1683: 1682: 1678: 1677:Syntonolydian 1672: 1664: 1661: 1660: 1656: 1653: 1652: 1648: 1645: 1644: 1640: 1637: 1636: 1632: 1626: 1623: 1615: 1612: 1611: 1607: 1604: 1603: 1599: 1596: 1595: 1591: 1588: 1587: 1583: 1577: 1569: 1566: 1565: 1561: 1558: 1557: 1553: 1550: 1549: 1545: 1542: 1541: 1537: 1531: 1522: 1519: 1518: 1514: 1511: 1510: 1506: 1503: 1502: 1498: 1495: 1494: 1490: 1483: 1481: 1477: 1473: 1469: 1463: 1461: 1457: 1453: 1449: 1445: 1441: 1438:and either a 1437: 1431: 1429: 1425: 1420: 1418: 1414: 1409: 1407: 1401: 1376: 1372: 1368: 1345: 1341: 1337: 1333: 1326: 1319: 1314: 1306: 1296: 1290: 1286: 1280: 1276: 1268: 1253: 1250: 1247: 1246: 1242: 1239: 1236: 1235: 1231: 1228: 1225: 1224: 1220: 1217: 1214: 1213: 1209: 1206: 1203: 1202: 1198: 1195: 1192: 1191: 1187: 1184: 1181: 1180: 1176: 1173: 1170: 1169: 1165: 1162: 1159: 1158: 1154: 1148: 1140: 1137: 1134: 1133: 1129: 1126: 1123: 1122: 1118: 1115: 1112: 1111: 1107: 1104: 1101: 1100: 1096: 1093: 1090: 1089: 1085: 1082: 1079: 1078: 1074: 1071: 1068: 1067: 1063: 1060: 1057: 1056: 1052: 1049: 1046: 1045: 1041: 1035: 1027: 1024: 1021: 1020: 1016: 1013: 1010: 1009: 1005: 1002: 999: 998: 994: 991: 988: 987: 983: 980: 977: 976: 972: 969: 966: 965: 961: 958: 955: 954: 950: 947: 944: 943: 939: 936: 933: 932: 928: 922: 918: 916: 911: 906: 892: 889: 886: 885: 881: 878: 875: 874: 871: 868: 865: 864: 860: 857: 854: 853: 850: 847: 844: 843: 840: 837: 834: 833: 829: 826: 823: 822: 819: 817:High Phrygian 816: 813: 812: 808: 805: 802: 801: 798: 795: 792: 791: 787: 784: 781: 780: 776: 773: 770: 769: 765: 762: 759: 758: 755: 753: 749: 744: 739: 736: 731: 729: 725: 720: 718: 714: 707: 704:Aristoxenian 698: 694: 691:The prefixes 690: 687: 683: 679: 675: 672: 668: 665: 661: 660: 659: 653: 649: 645: 641: 637: 634: 630: 627: 624: 620: 617: 614: 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BC) 4846:(338–322 BC) 4840:(370–168 BC) 4828:(374–196 BC) 4822:(378–355 BC) 4804:(430–348 BC) 4798:(478–404 BC) 4792:(499–449 BC) 4479:Peloponnesus 4401:Roman Greece 4164: 4140:Klavarskribo 4115:Figured bass 3989:Appoggiatura 3936:Articulation 3734:Abbreviation 3662:(home page). 3659: 3640: 3623: 3612: 3606:Erickson, R. 3594: 3577:– via 3573: 3553: 3527:. 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1488: 1479: 1475: 1474:followed by 1471: 1465: 1459: 1455: 1451: 1447: 1443: 1439: 1435: 1433: 1427: 1421: 1416: 1412: 1410: 1405: 1374: 1370: 1367:quarter-tone 1343: 1339: 1335: 1331: 1320: 1300: 1294: 1279:quarter tone 1270: 1262: 1260: 1152: 1146: 1039: 1033: 926: 920: 912: 908: 827:Low Phrygian 751: 747: 742: 740: 734: 732: 727: 721: 716: 712: 710: 705: 696: 692: 657: 651: 647: 632: 629:Hypophrygian 622: 612: 602: 592: 582: 572:Aristoxenian 569: 563: 559: 555: 553: 533: 524: 522: 512: 509: 504: 502: 482: 478: 476: 460:major second 451: 447: 443: 439: 435: 429: 426: 404: 400: 395: 394:, the Latin 391: 387: 377: 372: 357: 338: 324: 321: 316: 312: 308: 305:Diezeugmenon 304: 300: 296: 292: 288: 284: 280: 276: 272: 268: 266: 261: 257: 253: 251: 247:diezeugmenon 246: 242: 238: 234: 230: 226: 224: 219: 216:Hyperbolaion 215: 212:Diezeugmenon 211: 207: 203: 199: 195: 193: 182: 163: 133: 120: 116: 112: 102: 93: 91: 82:Eratosthenes 55: 38: 36: 7390:Lydian (IV) 7380:Dorian (II) 7338:Hypolocrian 7328:Hypoaeolian 7121:Place names 7033:Salmydessus 6855:Kalos Limen 6835:Chersonesus 6825:Borysthenes 6530:Tauromenion 6342:Metapontion 6104:Proto-Greek 6057:Erechtheion 6052:Athena Nike 6014:Philippeion 5843:Mathematics 5814:and science 5697:Agriculture 5561:Stesichorus 5471:Bacchylides 5461:Archilochus 5348:Antisthenes 5338:Anaximander 5310:Seven Sages 5300:Playwrights 5280:Geographers 5275:Astronomers 5102:Pezhetairos 4729: 1100 4709:Federations 4608:Megalopolis 4545:City states 4520:City states 4226:Music stand 4100:Chord chart 4079:Scorewriter 4056:Sheet music 3854:Dotted note 3789:Repeat sign 3764:Ledger line 3666:Annie BĂŠlis 3569:Aristoxenus 3176:Levin, F.R. 2849:alt. title 2823:Tyrrell, J. 2100:epithalamia 2082:for humans— 1974:Aristoxenus 1910:themselves. 1747:Enharmonic 1692:Enharmonic 1646:Enharmonic 1597:Enharmonic 1551:Enharmonic 1504:Enharmonic 1293:The oldest 1229:Hypolydian 1116:Hypolydian 1003:Hypolydian 855:G (and A?) 796:High Lydian 544:Renaissance 529:Aristoxenos 487:tetrachords 456:minor third 411:tetrachords 185:tetrachords 155: [ 144: [ 70:Aristoxenos 47:tetrachords 7561:Categories 7424:Jazz minor 7366:Ionian (I) 7343:Pentatonic 7318:Hypoionian 7288:Hypolydian 7278:Hypodorian 7260:Mixolydian 7023:Polemonion 6900:Phanagoria 6870:Kimmerikon 6865:Kerkinitis 6850:Hermonassa 6840:Dioscurias 6736:Aspalathos 6683:Kalathousa 6658:Akra Leuke 6587:Phoenicusa 6372:Scylletium 6357:Poseidonia 6277:Brentesion 6164:Pamphylian 6159:Macedonian 6077:Samothrace 6062:Hephaestus 6009:Long Walls 5988:Structures 5929:Underworld 5875:Technology 5838:Literature 5772:Philosophy 5737:Euergetism 5626:By culture 5571:Thucydides 5413:Pythagoras 5408:Protagoras 5398:Parmenides 5383:Heraclitus 5368:Empedocles 5358:Democritus 5343:Anaximenes 5333:Anaxagoras 5285:Historians 4778: 595 4765: 550 4746: 800 4731: â€“ c. 4659:Cappadocia 4464:Ionian Sea 4454:Hellespont 4419:Aegean Sea 4200:Shakuhachi 4175:Ekphonetic 4160:Simplified 4125:Lead sheet 3999:Grace note 3864:Note value 3859:Grace note 3827:Accidental 3660:kerylos.fr 3641:oeaw.ac.at 3330:West, M.L. 3302:: 125–136. 3130:"Archytas" 3007:Strunk, O. 2999:Strunk, O. 2461:, 2:46–52. 2444:Levin 1990 2273:References 2077:hyporcheme 1990:Philodemus 1755:Chromatic 1700:Chromatic 1654:Chromatic 1631:Mixolydian 1605:Chromatic 1559:Chromatic 1512:Chromatic 1153:Enharmonic 1040:Chromatic 890:Hypodorian 806:Low Lydian 754:instead): 678:Asia Minor 644:Hypodorian 619:Hypolydian 579:Mixolydian 472:enharmonic 454:that is a 369:world soul 345:Pythagoras 341:Pythagoras 297:Synemmenon 289:Synemmenon 269:Synemmenon 262:Synemmenon 7237:Authentic 7228:Gregorian 7109:in Epirus 7058:Trapezous 7003:Mesambria 6988:Eupatoria 6958:Apollonia 6953:Anchialos 6915:Theodosia 6885:Nymphaion 6875:Myrmekion 6845:Gorgippia 6801:Black Sea 6786:Tragurion 6771:Nymphaion 6756:Epidauros 6751:Epidamnos 6741:Apollonia 6718:Zacynthos 6640:Ptolemais 6634:Apollonia 6607:Cyrenaica 6597:TherassĂ­a 6592:Strongyle 6572:Ereikousa 6495:Leontinoi 6435:Apollonia 6312:Hipponion 6109:Mycenaean 6072:Parthenon 6004:Lion Gate 5907:Mythology 5870:Sculpture 5833:Astronomy 5767:Pederasty 5742:Festivals 5727:Education 5607:Lawgivers 5576:Timocreon 5556:Sophocles 5551:Simonides 5526:Philocles 5521:Panyassis 5516:Mimnermus 5481:Herodotus 5476:Euripides 5446:Aeschylus 5393:Leucippus 5353:Aristotle 5132:Strategos 4998:Synedrion 4952:Ostracism 4932:Areopagus 4884:Free city 4679:Macedonia 4563:Byzantion 4469:Macedonia 4434:Cyrenaica 4411:Geography 4345:Geography 4195:Swaralipi 4185:Kunkunshi 4145:Tablature 4110:Eye music 3994:Glissando 3969:Fingering 3754:Dal segno 3560:Ioannidis 3496:Eric Blom 3482:170375844 3319:0425-2268 3143:25 August 2995:Cleonides 2929:Barker, A 2839:Aristotle 2819:Sadie, S. 2772:, 6(iii). 2262:Mesomedes 2153:That is, 2141:Footnotes 2104:hymenaios 2088:epinikion 2073:dithyramb 2065:prosodion 2031:harmoniai 1994:De musica 1978:De Musica 1938:harmoniai 1907:harmoniai 1903:harmoniai 1898:harmoniai 1882:harmoniai 1874:Aristotle 1824:Harmoniai 1809:Harmonics 1796:Harmonics 1734:(Ionian) 1662:Diatonic 1613:Diatonic 1567:Diatonic 1520:Diatonic 1428:harmoniai 1295:harmoniai 1207:Phrygian 1094:Phrygian 981:Phrygian 724:Cleonides 711:The term 564:parhypate 536:Aristotle 468:chromatic 440:parhypate 375:(36a-b). 360:Philolaus 309:Immutable 254:diazeuxis 235:diazeuxis 113:harmoniai 7358:Diatonic 7250:Phrygian 7158:Category 7136:Theatres 7063:Tripolis 6998:Kerasous 6993:Heraclea 6925:Tyritake 6880:Nikonion 6791:Thronion 6713:Salauris 6668:Emporion 6625:Berenice 6615:Balagrae 6567:Euonymos 6540:Tyndaris 6525:Syracuse 6520:Selinous 6490:Kamarina 6445:Casmenae 6430:Akrillai 6347:NeĂĄpolis 6282:Caulonia 6263:Mainland 6194:Linear B 6189:Linear A 6119:Dialects 6096:Language 5890:Religion 5848:Medicine 5782:Religion 5747:Folklore 5732:Emporium 5707:Clothing 5702:Calendar 5586:Xenophon 5581:Tyrtaeus 5566:Theognis 5541:Polybius 5536:Plutarch 5511:Menander 5491:Hipponax 5418:Socrates 5373:Epicurus 5219:Diadochi 5117:Sciritae 5077:Hetairoi 5052:Ballista 5017:Military 4980:Gerousia 4970:Ekklesia 4937:Ecclesia 4919:Athenian 4867:Politics 4780:–279 BC) 4767:–366 BC) 4748:–389 BC) 4684:Pergamon 4654:Bithynia 4647:Kingdoms 4588:Pergamon 4530:Military 4525:Politics 4322:Timeline 4205:Znamenny 4046:Tonguing 4031:Staccato 3984:Ornament 3959:Dynamics 3911:Interval 3874:Notehead 3849:Cue note 3624:harmonia 3619:Erickson 3529:22 March 3414:(1937), 3290:Republic 3275:(eds.). 3254:(eds.). 3233:(eds.). 3204:(1999). 3109:េρΟονΚιΚ 2852:Politics 2841:(1912). 2825:(eds.). 2497:, 39–40. 2485:, 35–36. 2241:See also 2225:12 tone 2084:encomion 2035:On Music 1986:Politics 1982:Republic 1970:On Music 1956:and the 1942:Republic 1890:Politics 1886:Republic 1876:(c. 350 1862:Republic 1850:harmonia 1842:harmonia 1831:harmonia 1536:Phrygian 1346:, about 927:Diatonic 638:Common, 599:Phrygian 560:lichanoi 556:lichanoi 464:diatonic 452:lichanos 448:lichanos 444:lichanos 436:lichanoi 380:Archytas 239:paramese 227:paramese 66:Archytas 7333:Locrian 7323:Aeolian 7178:Outline 7131:Temples 7068:Zaliche 7048:Thèrmae 7038:Sesamus 7008:Odessos 6983:Cytorus 6978:Cotyora 6728:Illyria 6693:Mainake 6688:Kypsela 6577:Hycesia 6535:Thermae 6515:Segesta 6505:Messana 6460:Helorus 6440:Calacte 6420:Akragas 6382:Sybaris 6367:Rhegion 6322:Krimisa 6272:Alision 6181:Writing 6154:Locrian 6144:Epirote 6114:Homeric 6047:Artemis 6034:Temples 5975:Olympia 5945:Eleusis 5880:Theatre 5865:Pottery 5792:Warfare 5787:Slavery 5722:Economy 5717:Cuisine 5712:Coinage 5689:Society 5674:Culture 5669:Society 5617:Tyrants 5456:Alcaeus 5438:Authors 5388:Hypatia 5378:Gorgias 5315:Writers 5137:Toxotai 5107:Sarissa 5097:Peltast 5092:Phalanx 5072:Hoplite 5067:Hippeis 4990:Macedon 4962:Spartan 4947:Heliaia 4894:Proxeny 4603:Larissa 4598:Kerkyra 4593:Eretria 4583:Miletus 4578:Ephesus 4573:Corinth 4568:Chalcis 4489:Taurica 4359:Periods 4340:History 4214:Related 4180:Gamelan 4170:Chinese 4150:Parsons 4021:Portato 4004:Mordent 3979:Marcato 3964:Fermata 3954:Damping 3949:Caesura 3906:Tremolo 3837:natural 3749:Da capo 3628:kithara 3192:4476778 3001:(ed.). 2806:Sources 2215:pitches 2135:Unicode 2123:Unicode 2096:erotica 2092:skolion 2053:Photios 2046:Proclus 1958:cithara 1859:In the 1817:Didymos 1788:Ptolemy 1731:Iastian 1476:D E F G 1472:C D E F 1392:⁠ 1380:⁠ 1361:⁠ 1349:⁠ 1218:Dorian 1196:Lydian 1105:Dorian 1083:Lydian 992:Dorian 970:Lydian 686:Phrygia 664:Dorians 640:Locrian 635:(g′–g″) 625:(f′–f″) 615:(e′–e″) 605:(d′–d″) 595:(c′–c″) 483:species 373:Timaeus 371:in the 281:Hypaton 220:synaphe 204:Hypaton 119:in all 78:Didymos 74:Ptolemy 7313:Ionian 7270:Plagal 7255:Lydian 7245:Dorian 7168:Portal 7116:People 7104:Cities 7043:Sinope 7028:Rhizos 7018:Phasis 6968:Bathus 6963:Athina 6948:Amisos 6910:Tanais 6905:Pityus 6830:Charax 6781:Pharos 6776:Orikon 6673:Helike 6663:Alonis 6630:Cyrene 6562:Didyme 6475:Himera 6450:Catana 6412:Sicily 6402:Thurii 6397:Terina 6362:Pixous 6317:Hydrus 6292:Croton 6124:Aeolic 6042:Aphaea 5965:Dodona 5950:Delphi 5919:Temple 5595:Others 5546:Sappho 5531:Pindar 5506:Lucian 5501:Ibycus 5486:Hesiod 5423:Thales 5191:Rulers 5170:People 5147:Xyston 5142:Xiphos 5003:Koinon 4909:Tyrant 4899:Stasis 4889:Koinon 4689:Pontus 4664:Epirus 4633:Sparta 4623:Rhodes 4618:Megara 4613:Thebes 4558:Athens 4484:Pontus 4449:Epirus 4439:Cyprus 4424:Aeolis 4036:Tenuto 3974:Legato 3944:Accent 3901:Tuplet 3670:papyri 3480:  3450:  3377:763814 3375:  3340:  3317:  3212:  3190:  3180:Hermes 3162:  3073:427236 3071:  3040:427754 3038:  2981:  2949:  2941:  2919:763813 2917:  2886:843492 2884:  2598:, 250. 2571:, 240. 2029:, and 1996:) and 1950:Lydian 1946:Dorian 1792:pyknon 1742:Tones 1739:Genus 1687:Tones 1684:Genus 1641:Tones 1638:Genus 1592:Tones 1589:Genus 1582:Lydian 1546:Tones 1543:Genus 1499:Tones 1496:Genus 1489:Dorian 1377:about 1160:Tonic 1047:Tonic 934:Tonic 838:Dorian 671:Locris 609:Dorian 589:Lydian 585:(b–b′) 505:chroai 479:genera 432:genera 407:genera 384:Euclid 313:System 166:octave 121:genera 115:, the 72:, and 43:scales 7306:Other 7126:Stoae 7094:Lists 7013:Oinòe 6936:coast 6934:South 6920:Tyras 6890:Olbia 6860:Kepoi 6813:coast 6811:North 6804:basin 6746:Aulon 6708:Rhode 6620:Barca 6510:Naxos 6465:Henna 6425:Akrai 6392:Taras 6377:Siris 6337:Medma 6332:Locri 6297:Cumae 6287:Chone 6265:Italy 6171:Koine 6149:Ionic 6139:Doric 6134:Attic 5955:Delos 5853:Music 5496:Homer 5451:Aesop 5403:Plato 5305:Poets 4975:Ephor 4927:Agora 4904:Tagus 4879:Boule 4628:Samos 4553:Argos 4459:Ionia 4444:Doris 4429:Crete 4190:Neume 4014:Trill 4009:Slide 3896:Tacet 3886:Pitch 3842:sharp 3794:Tempo 3779:Scale 3774:Ossia 3716:Staff 3523:(PDF) 3516:(PDF) 3478:S2CID 3373:JSTOR 3188:JSTOR 3069:JSTOR 3036:JSTOR 2915:JSTOR 2882:JSTOR 2796:, 25. 2760:, 35. 2586:, 44. 2194:notes 2069:paean 2027:tonoi 2020:Melos 1962:genus 1954:aulos 1934:tonoi 1930:ethos 1924:Ethos 1867:Plato 1835:tonoi 1805:tonoi 1800:tonoi 1468:modes 1411:The ( 1394:sharp 1166:Mese 1163:Name 1053:Mese 1050:Name 940:Mese 937:Name 743:tonoi 735:tonoi 728:tonoi 717:tonoi 715:(pl. 713:tonos 706:tonoi 682:Lydia 642:, or 548:modes 365:Plato 301:Meson 293:Meson 285:Meson 231:Meson 208:Meson 159:] 148:] 117:tonoi 7406:and 7372:and 7053:Tium 6820:Akra 6761:Issa 6455:Gela 6327:LaĂźs 6302:Elea 5960:Dion 5812:Arts 5802:Wine 5428:Zeno 5025:Wars 4026:Slur 3891:Rest 3879:stem 3869:beam 3832:flat 3769:Mode 3744:Clef 3531:2024 3448:ISBN 3435:and 3338:ISBN 3315:ISSN 3210:ISBN 3160:ISBN 3145:2014 2979:ISBN 2947:ISBN 2939:ISBN 2784:, 4. 2697:, 3. 2417:, 7. 2204:and 2188:N.b. 2061:hymn 1919:in.) 1815:and 1458:and 1450:and 1363:flat 1177:(d) 1171:(A) 1064:(d) 1058:(A) 951:(d) 945:(A) 750:and 697:hypo 695:and 693:myxo 562:and 470:and 438:and 430:The 351:and 303:and 287:and 258:nete 243:mese 241:and 214:and 194:The 103:The 80:and 37:The 5757:Law 4041:Tie 3739:Bar 3470:doi 3365:doi 3292:". 3184:118 3111:". 3094:doi 3061:doi 3028:doi 2907:doi 2874:doi 1936:or 1878:BCE 1442:or 1365:(a 1254:d′ 1243:c′ 1141:d′ 1130:c′ 1028:d′ 1017:c′ 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Index

Greek musical notation
Music of ancient Greece
scales
tetrachords
perfect fourth
music of ancient Greece
Pythagorean school
Archytas
Aristoxenos
Ptolemy
Didymos
Eratosthenes
BCE
diagram at the right
Chalmers (1993)
Depiction of the ancient Greek tonal system
Helmholtz pitch notation
Egert PĂśhlmann
de
Johann Friedrich Bellermann
de
octave
graphic below, left

tetrachords
interval of a fourth
Pythagorean interval
Pythagoras
Pythagoras
Pythagorean Interval

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