Knowledge (XXG)

Tetrachord

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2122: 1283: 1036: 784: 214: 1617: 2374: 2364: 1538: 1676: 1666: 1651: 1636: 1598: 1583: 1568: 1553: 2403: 2111: 553: 537: 521: 477: 461: 409: 393: 248: 545: 529: 485: 469: 453: 401: 385: 240: 353:) with specific tunings were specified. Once the genus and shade of tetrachord are specified, their arrangement can produce three main types of scales, depending on which note of the tetrachord is taken as the first note of the scale. The tetrachords themselves remain independent of the scales that they produce, and were never named after these scales by Greek theorists. 1900:
segment of the chromatic scale, or, in a more historically oriented context, to refer to the six chromatic notes used to fill the interval of a perfect fourth, usually found in descending bass lines. It may also be used to describes sets of fewer than four notes, when used in scale-like fashion to span the interval of a perfect fourth.
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He continues with four other possible genres "dividing the tone in quarters, eighths, thirds, half thirds, quarter thirds, and combining them in diverse manners". Later, he presents possible positions of the frets on the lute, producing ten intervals dividing the interval of a fourth between the
1899:
Theorists of the later 20th century often use the term "tetrachord" to describe any four-note set when analysing music of a variety of styles and historical periods. The expression "chromatic tetrachord" may be used in two different senses: to describe the special case consisting of a four-note
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The number of strings on the classical lyre varied at different epochs, and possibly in different localities – four, seven and ten having been favorite numbers. Larger scales are constructed from conjunct or disjunct tetrachords. Conjunct tetrachords share a note, while disjunct tetrachords are
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are said to also appear particularly in Indian music. In this case, the lower "tetrachord" totals six semitones (a tritone). The following elements produce 36 combinations when joined by halfstep. These 36 combinations together with the 36 combinations described above produce the so-called "72
1937:
Tetrachords based upon equal-tempered tuning were also used to approximate common heptatonic scales in use in Indian, Hungarian, Arabian and Greek musics. Western theorists of the 19th and 20th centuries, convinced that any scale should consist of two tetrachords and a tone, described various
1891:–F, etc.). The 19th-century theorists of ancient Greek music believed that this had also been the case in Antiquity, and imagined that there had existed Dorian, Phrygian or Lydian tetrachords. This misconception was denounced in Otto Gombosi's thesis (1939). 193:
A chromatic tetrachord has a characteristic interval that is greater than about half the total interval of the tetrachord, yet not as great as four-fifths of the interval (between about 249 and 398 cents). Classically, the characteristic interval is a
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All these scales are formed by two complete disjunct tetrachords: contrarily to Greek and Medieval theory, the tetrachords change here from scale to scale (i.e., the C major tetrachord would be C–D–E–F, the D major one
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combinations supposed to correspond to a variety of exotic scales. For instance, the following diatonic intervals of one, two or three semitones, always totaling five semitones, produce 36 combinations when joined by
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The descending tetrachord from tonic to dominant, typically in minor (e.g. A–G–F–E in A minor), had been used since the Renaissance to denote a lamentation. Well-known cases include the ostinato bass of Dido's aria
2471:). It should be mentioned that Al-Farabi's, among other Islamic treatises, also contained additional division schemes as well as providing a gloss of the Greek system as Aristoxenian doctrines were often included. 1473: 134:
as the basic unit for determining tuning, where ancient Greeks used the tetrachord. Ancient Greek theorists recognized that the octave is a fundamental interval but saw it as built from two tetrachords and a
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in an octave, this would create a 25-tone scale. A more inclusive description (where Ottoman, Persian and Arabic overlap), of the scale divisions is that of 24 quarter tones (see also
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An enharmonic tetrachord has a characteristic interval that is greater than about four-fifths the total tetrachord interval. Classically, the characteristic interval is a
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texture, but in contrast to the lament, here the tetrachordal fragment – ascending or descending and possibly reordered – is set in the upper voice in the manner of a
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The Greeks analyzed genera using various terms, including diatonic, enharmonic, and chromatic. Scales are constructed from conjunct or disjunct tetrachords.
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21, no. 1 (Spring 1999): 43–73; Tuire Kuusi, "Subset-Class Relation, Common Pitches, and Common Interval Structure Guiding Estimations of Similarity",
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A diatonic tetrachord has a characteristic interval that is less than or equal to half the total interval of the tetrachord (or approximately 249 
1718:. Given the following vocabulary of tetrachords (the digits give the number of semitones in consecutive intervals of the tetrachord, adding to five): 1609: 560:
In all cases, the extreme notes of the tetrachords, E – B, and A – E, remain fixed, while the notes in between are different depending on the genus.
3383: 271:, meaning "compressed"). This is the case for the chromatic and enharmonic tetrachords, but not the diatonic (meaning "stretched out") tetrachord. 2479:
The tetrachord, a fundamentally incomplete fragment, is the basis of two compositional forms constructed upon repetition of that fragment: the
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of 9/8 (a Pythagorean major second). Alternating conjunct and disjunct tetrachords form a scale that repeats in octaves (as in the familiar
3519: 2773: 1509: 1300: 3476: 1053: 3338: 3293: 3190: 3079: 3071: 2847: 803: 3066:, pp. 1, 18, 68, 70, 73, 87, 88, 21, 119, 123, 124, 125, 138, 143, 171, 174, and 223. New Haven and London: Yale University Press. 2568:
texture, wherein the bass descends through some tetrachord, possibly that of the previous paragraph, but usually one suggesting a
1472: 88: 2807: 3046: 1435: 1398: 1361: 3376: 1701: 2121: 3355: 3320: 3279: 2670: 3024: 2015: 2679:(second ed.). London, UK: Macmillan. 6 Music Theory, (iii) Aristoxenian Tradition, (d) Scales. 3041: 2988: 2964: 2950: 2898: 2093: 2129:
The fourth genre, corresponding to the Greek chromatic, has a tone and a half, a semitone and a semitone, as G–A
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or the kithara, with the implicit understanding that the four strings produced adjacent (i.e., conjunct) notes.
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The first genre, corresponding to the Greek diatonic, is composed of a tone, a tone and a semitone, as G–A–B–C.
1521: 3089: 2603:. Because of the extreme brevity of the theme and number of repetitions required, and free of the binding of 2519:("complaint", "lamentation"), has been used until today. A variant form, the full chromatic descent (e.g. A–G 3529: 3439: 3369: 3007: 2892: 2620: 153: 2873: 3456: 2625: 164:) of tetrachords. These genera are characterized by the largest of the three intervals of the tetrachord: 3281:
Divisions of the Tetrachord: A Prolegomenon [introduction] to the Construction of Musical Scales
2908: 2878: 2504: 2373: 2363: 1926: 1836: 1682: 1541: 177:). This characteristic interval is usually slightly smaller (approximately 200 cents), becoming a 3491: 2919: 258: 3461: 3400: 2725: 3466: 3178: 3124:, 2 vols., translated by John Fenstermaker (Paris: Alphonse Leduc, 1962): 2:35. ASIN: B0006CNH8E. 2761: 569: 345:
As the three genera simply represent ranges of possible intervals within the tetrachord, various
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Reynold Simpson, "New Sketches, Old Fragments, and Schoenberg's Third String Quartet, Op. 30",
2752:, 2 vols., translated by John Fenstermaker. Paris: Alphonse Leduc, 1962, 2:35. ASIN: B0006CNH8E. 213: 1675: 1665: 1650: 1635: 1597: 1582: 1567: 1552: 3427: 3334: 3289: 3186: 3075: 3067: 2843: 2790: 2769: 2604: 2592: 2561: 1711: 1624: 2107:
The second genre is composed of a tone, three quarter tones and three quarter tones, as G–A–B
3486: 2979: 2959: 2914: 2835: 2645: 2533: 2011: 1715: 1616: 1325:, created in such a manner from the diatonic genus), but this was not the only arrangement. 44: 544: 528: 484: 468: 452: 400: 384: 239: 3481: 3002: 2903: 2737: 2608: 2600: 2402: 2110: 1929:, the term may have the special sense of any consecutive four notes of a twelve-tone row. 552: 536: 520: 476: 460: 408: 392: 247: 181:. Classically, the diatonic tetrachord consists of two intervals of a tone and one of a 3361: 3275: 3020: 2983: 2969: 2955: 2923: 2887: 2640: 2545: 1917: 1322: 274:
Whatever the tuning of the tetrachord, its four degrees are named, in ascending order,
111: 97: 48: 36: 28: 198:(approximately 300 cents), and the two smaller intervals are equal semitones, e.g. A–G 3513: 3412: 3351: 3316: 2945: 2937: 2815: 2666: 2492: 2468: 1621: 1271: 1263: 1255: 1247: 1024: 1016: 1008: 1000: 772: 764: 756: 748: 207: 188: 168: 148: 56: 2118:
The third genre has a tone and a quarter, three quarter tones and a semitone, as G–A
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Joanny Grosset, "Inde. Histoire de la musique depuis l'origine jusqu'à nos jours",
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Brent Auerbach, "Tiered Polyphony and Its Determinative Role in the Piano Music of
2941: 2883: 2464: 2417: 1545: 231: 178: 174: 136: 52: 20: 2906:'s 'Construction of Twelve Verticals': An Aspect of Harmony in the Serial Music", 1537: 1069:
Here is a representative Pythagorean tuning of the enharmonic genus attributed to
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The second note of the tetrachord (in descending order) is the first of the scale.
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The third note of the tetrachord (in descending order) is the first of the scale.
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Two Greek tetrachords in the enharmonic genus, forming an enharmonic Dorian scale
3396: 3392: 3269:] (reprint) (in French). Translated by Rodolphe d'Erlanger. Paris: Geuthner. 3244:, 2 vols., translated by John Fenstermaker (Paris: Alphonse Leduc, 1962): 2:110. 3059: 2896:
38, no. 1 (Spring 1994): 21–41; Ian Quinn, "Listening to Similarity Relations",
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If one considers that the interval of a fourth between the strings of the lute (
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music divides the interval of a fourth differently than the Greek. For example,
1908: 227: 195: 3231:, 2 vols., translated by John Fenstermaker. Paris: Alphonse Leduc, 1937): 1:14. 2972:: Tonality, Motivic Sets and the Referential Pitch-Class Specific Collection", 3446: 3185:, translated by Laurie Schwartz. (Portland, Oregon: Amadeus Press, 1996): 19. 1939: 1766: 815: 47:. In traditional music theory, a tetrachord always spanned the interval of a 3451: 3326: 3258: 2596: 2565: 2097: 257:
When the composite of the two smaller intervals is less than the remaining (
3498: 3422: 2021: 1628: 1070: 182: 60: 2930:, With Notes on Narrative, Symmetry, Quantitative Flux and Heraclitus", 2463:) corresponds to a tetrachord, and that there are two tetrachords and a 1765:
the following scales could be derived by joining two tetrachords with a
1603:(b–a–g–f). This tetrachord spans a tritone instead of a perfect fourth. 1097:                  2512: 360:
The first note of the tetrachord is also the first note of the scale.
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Benedict Taylor, "Modal Four-Note Pitch Collections in the Music of
2576:, is repeated again and again over the length of the composition. 1615: 1536: 294:
and, for the second tetrachord in the construction of the system,
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are fixed, and a perfect fourth apart, while the position of the
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Ellen Rosand, "The Descending Tetrachord: An Emblem of Lament",
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4, no. 2 (Spring–Summer 1966): 14–22; Annie K. Yih, "Analysing
123:, originally in reference to harp-like instruments such as the 2460: 3082:(pbk). Allen Forte (1985). "Pitch-Class Set Analysis Today". 3229:
Cours complet d'improvisation a l'orgue: Exercices preparées
1281: 1034: 782: 3333:. Longman Music Series. New York and London: Longman Inc.. 3135:
Encyclopédie de la musique et Dictionnaire du Conservatoire
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17, In Celebration of Arnold Schoenberg (1) (1992): 85–101.
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Mathiesen, Thomas J. (2001). "Greece §I: Ancient". In
2515:'s Mass in C minor, KV 427, etc. This tetrachord, known as 1921:
or simply a "4-element set" – a set of any four pitches or
63:, not necessarily related to a particular tuning system. 55:)—but in modern use it means any four-note segment of a 850:              2579:
Another musical form, of the same time period, is the
2902:
39, no. 2 (Summer 2001): 108–158; Joseph N. Straus, "
2768:, 2 vols. (New York: Carl Fischer, 1941), 1:112–114. 2100:
describes four genres of the division of the fourth:
83:—"string" or "note"). In ancient Greek music theory, 2842:(Boston: Northeastern University Press, 1993): 120. 2840:
The "Style hongrois" in the Music of Western Europe
3040:Nors S. Josephson, "On Some Apparent Sketches for 2922:, "An Imagined Drama of Competitive Opposition in 16:Series of four notes separated by three intervals 3095:Conference 1984): 29–58, citations on 48–51, 53. 2607:to tetrachord in the lament, the breadth of the 3347:The New Grove Dictionary of Music and Musicians 3312:The New Grove Dictionary of Music and Musicians 2676:The New Grove Dictionary of Music and Musicians 2544:There exists a short, free musical form of the 261:) interval, the three-note group is called the 43:) is a series of four notes separated by three 3088:4, nos. 1 & 2 (March–July: Special Issue: 3023:, "Beethoven's Interrupted Tetrachord and the 3377: 2766:The Schillinger System of Musical Composition 8: 2572:. This tetrachord, treated as a very short 1548:(also known as the upper minor tetrachord): 3288:. Hanover, New Hampshire: Frog Peak Music. 572:of the diatonic and chromatic tetrachords: 3384: 3370: 3362: 2936:28, no. 2/3 (July–October 2009): 373–422; 51:, a 4:3 frequency proportion (approx. 498 3170: 3158: 3146: 3137:, vol. 1, Paris, Delagrave, 1914, p. 325. 2954:11, no. 2 (Spring–Summer 1973): 204–209; 2861:Tonarten und Stimmungen der Antiken Musik 2789:(Pacific, Missouri: Mel Bay, 2010): 111. 2591:(OE spur). It is also a set of harmonic 3202: 2713: 2701: 2689: 2027: 1944: 1771: 1720: 1330: 1293:Enharmonic tetrachord pythagorean tuning 3242:Cours complet d'improvisation a l'orgue 3122:Cours Complet d'Improvisation a l'Orgue 2992:2, no. 1 (Autumn–Winter 1963): 102–113. 2750:Cours Complet d'Improvisation a l'Orgue 2657: 1046:Chromatic tetrachord pythagorean tuning 3175:Das Arabische Tonsystem im Mittelalter 1685:: i–v6–iv6–V in C minor (bassline: c–b 813: 794:Diatonic tetrachord pythagorean tuning 598:          592:          2948:: String Quartet (1967): Two Views", 2863:, Kopenhagen, Ejnar Munksgaard, 1939. 2808:"Double harmonic scale and its modes" 2560:. It is typically a set of harmonic 1524:divisions by Chalmers after Hofmann. 75:(from Greek—"four of something") and 7: 2962:: A Few Observations of His Music", 2531:–F–E in A minor), has been known as 2507:'s Mass in B minor, BWV 232, or the 230:, and the two smaller intervals are 3173:, pp. 165–179; Liberty Manik, 1714:tuning were used to explain common 1371:Eratosthenes’ chromatic tetrachord 2918:25, no. 1 (September 2007): 1–11; 1915:to mean what he elsewhere calls a 89:greater and lesser perfect systems 14: 3177:(Leiden, E. J. Brill, 1969): 42; 2006:Indian-specific tetrachord system 3344:Roeder, John. 2001. "Set (ii)". 2978:19, no. 2 (July 2000): 203–229; 2882:32, no. 1 (Spring 2010): 44–59; 2401: 2372: 2362: 2120: 2109: 1698: 1674: 1664: 1649: 1634: 1627:creates a descending tetrachord 1604: 1596: 1581: 1566: 1551: 1506: 1469: 1432: 1395: 1358: 1297: 1050: 814:Problems playing this file? See 798: 551: 543: 535: 527: 519: 483: 475: 467: 459: 451: 407: 399: 391: 383: 246: 238: 105:); the notes between these were 3309:Anonymous. 2001. "Tetrachord". 3011:52, no. 2 (Fall 2008): 273–320. 2986:'s Composition for Orchestra", 1520:This is a partial table of the 3218:65, no. 3 (1979): 346–59. 2611:in litany is usually notable. 1334:Didymos’ chromatic tetrachord 1: 3274:Chalmers, John H. Jr (1993). 3064:The Structure of Atonal Music 2787:Advanced Lead Guitar Concepts 499:Diatonic: C–B | A–G–F–E | D–C 426:Diatonic: D–C–B | A–G–F–E | D 130:Modern music theory uses the 3350:, second edition, edited by 3315:, second edition, edited by 3047:Archiv für Musikwissenschaft 2890:and Intervallic Weighting", 1445:Ptolemy’s intense chromatic 2020:Tetrachords separated by a 1911:occasionally uses the term 1869:1 2 2 : 2 : 1 3 1 1858:2 1 2 : 2 : 2 2 1 1847:2 2 1 : 2 : 1 2 2 1833:1 3 1 : 2 : 1 3 1 1822:2 1 2 : 2 : 1 3 1 1811:2 2 1 : 2 : 1 3 1 1800:2 1 2 : 2 : 1 2 2 1789:2 2 1 : 2 : 2 2 1 363:Diatonic: E–D–C–B | A–G–F–E 156:theory distinguishes three 87:signified a segment of the 3546: 3520:Ancient Greek music theory 3042:Sibelius's Eighth Symphony 2016:Hindustani classical music 2009: 146: 143:Ancient Greek music theory 3408: 2989:Perspectives of New Music 2965:Perspectives of New Music 2951:Perspectives of New Music 2899:Perspectives of New Music 1885:–G, the C minor one C–D–E 1408:Ptolemy’s soft chromatic 1277: 1078: 1030: 829: 778: 577: 568:Here are the traditional 115: 101: 32: 3278:; Carter Scholz (eds.). 3263:Kitābu l-mūsīqī al-kabīr 3050:61, no. 1 (2004): 54–67. 3008:Journal of Music Theory 2893:Journal of Music Theory 2859:Otto Johannes Gombosi, 2785:Joshua Craig Podolsky, 2621:All-interval tetrachord 2489:When I am laid in earth 1710:Tetrachords based upon 3240:Marcel Dupré, (1962). 3183:The Music of the Arabs 2726:"Phrygian Progression" 2626:Diatonic and chromatic 1866:Upper minor + harmonic 1707: 1613: 1286: 1039: 787: 218: 119:). It literally means 40: 3216:The Musical Quarterly 3090:King's College London 2909:Music Theory Spectrum 2879:Music Theory Spectrum 2876:'s American Period", 2505:Johann Sebastian Bach 1895:20th-century analysis 1837:Double harmonic scale 1775:Component tetrachords 1683:Phrygian half cadence 1619: 1542:Descending tetrachord 1540: 1482:Archytas’ enharmonic 1285: 1038: 786: 216: 3358:. London: Macmillan. 3323:. London: Macmillan. 2886:and Jack Douthett, " 2730:Classical Music Blog 502:Chromatic: C–B | A–G 71:The name comes from 3331:Basic Atonal Theory 3106:Theory and Practice 2475:Compositional forms 1844:Major + upper minor 1830:Harmonic + harmonic 1797:Minor + upper minor 570:Pythagorean tunings 564:Pythagorean tunings 154:Ancient Greek music 3179:Habib Hassan Touma 2762:Joseph Schillinger 2736:2011-10-06 at the 2609:harmonic excursion 2534:Passus duriusculus 2034:Upper tetrachords 1951:Upper tetrachords 1933:Non-Western scales 1927:twelve-tone theory 1708: 1614: 1287: 1040: 788: 219: 3507: 3506: 3477:"Ode-to-Napoleon" 3149:, pp. 56–57. 3031:5 (1991): 77–100. 2920:Joshua B. Mailman 2795:978-0-7866-8236-2 2605:chord progression 2457: 2456: 2086: 2085: 2031:Lower tetrachords 2025:karnatic modes". 2003: 2002: 1948:Lower tetrachords 1876: 1875: 1872:Neapolitan minor 1763: 1762: 1716:heptatonic scales 1712:equal temperament 1704: 1610: 1518: 1517: 1512: 1475: 1438: 1401: 1364: 1314: 1313: 1303: 1067: 1066: 1056: 825: 824: 804: 3537: 3386: 3379: 3372: 3363: 3299: 3270: 3267:La musique arabe 3245: 3238: 3232: 3225: 3219: 3212: 3206: 3200: 3194: 3168: 3162: 3156: 3150: 3144: 3138: 3131: 3125: 3118: 3109: 3102: 3096: 3057: 3051: 3038: 3032: 3025:Seventh Symphony 3018: 3012: 2999: 2993: 2915:Music Perception 2870: 2864: 2857: 2851: 2836:Jonathan Bellman 2833: 2827: 2826: 2824: 2823: 2814:. Archived from 2812:docs.solfege.org 2804: 2798: 2783: 2777: 2759: 2753: 2746: 2740: 2723: 2717: 2711: 2705: 2699: 2693: 2687: 2681: 2680: 2662: 2646:Tetratonic scale 2530: 2529: 2524: 2523: 2483:and the litany. 2406: 2405: 2396: 2395: 2388: 2387: 2377: 2376: 2367: 2366: 2357: 2356: 2349: 2348: 2333: 2331: 2330: 2327: 2324: 2316: 2314: 2313: 2310: 2307: 2299: 2297: 2296: 2293: 2290: 2282: 2280: 2279: 2276: 2273: 2265: 2263: 2262: 2259: 2256: 2248: 2246: 2245: 2242: 2239: 2231: 2229: 2228: 2225: 2222: 2214: 2212: 2211: 2208: 2205: 2197: 2195: 2194: 2191: 2188: 2180: 2178: 2177: 2174: 2171: 2163: 2161: 2160: 2157: 2154: 2143: 2142: 2134: 2133: 2125: 2124: 2114: 2113: 2028: 1945: 1890: 1889: 1884: 1883: 1819:Minor + harmonic 1808:Major + harmonic 1781:Resulting scale 1772: 1727:Halfstep String 1721: 1706: 1705: 1696: 1695: 1690: 1689: 1679: 1678: 1669: 1668: 1661: 1660: 1654: 1653: 1646: 1645: 1639: 1638: 1612: 1611: 1601: 1600: 1593: 1592: 1586: 1585: 1578: 1577: 1571: 1570: 1563: 1562: 1556: 1555: 1514: 1513: 1477: 1476: 1440: 1439: 1403: 1402: 1366: 1365: 1331: 1319:disjunctive tone 1305: 1304: 1284: 1238: 1236: 1235: 1232: 1229: 1218: 1216: 1215: 1212: 1209: 1198: 1196: 1195: 1192: 1189: 1176: 1174: 1173: 1170: 1167: 1157: 1155: 1154: 1151: 1148: 1138: 1136: 1135: 1132: 1129: 1119: 1117: 1116: 1113: 1110: 1076: 1075: 1058: 1057: 1037: 991: 989: 988: 985: 982: 971: 969: 968: 965: 962: 951: 949: 948: 945: 942: 929: 927: 926: 923: 920: 910: 908: 907: 904: 901: 891: 889: 888: 885: 882: 872: 870: 869: 866: 863: 838:    827: 826: 806: 805: 785: 739: 737: 736: 733: 730: 719: 717: 716: 713: 710: 699: 697: 696: 693: 690: 677: 675: 674: 671: 668: 658: 656: 655: 652: 649: 639: 637: 636: 633: 630: 620: 618: 617: 614: 611: 586:    575: 574: 556: 555: 548: 547: 540: 539: 532: 531: 524: 523: 513: 512: 507: 506: 488: 487: 480: 479: 472: 471: 464: 463: 456: 455: 446: 445: 440: 439: 434: 433: 412: 411: 404: 403: 396: 395: 388: 387: 377: 376: 371: 370: 253: 251: 250: 243: 242: 203: 202: 118: 117: 104: 103: 34: 3545: 3544: 3540: 3539: 3538: 3536: 3535: 3534: 3525:Music of Greece 3510: 3509: 3508: 3503: 3404: 3390: 3306: 3304:Further reading 3296: 3273: 3257: 3249: 3248: 3239: 3235: 3226: 3222: 3213: 3209: 3201: 3197: 3169: 3165: 3157: 3153: 3145: 3141: 3132: 3128: 3119: 3112: 3103: 3099: 3058: 3054: 3039: 3035: 3019: 3015: 3003:Johannes Brahms 3000: 2996: 2928:Scrivo in Vento 2888:Vector Products 2871: 2867: 2858: 2854: 2834: 2830: 2821: 2819: 2806: 2805: 2801: 2784: 2780: 2760: 2756: 2747: 2743: 2738:Wayback Machine 2724: 2720: 2712: 2708: 2700: 2696: 2688: 2684: 2664: 2663: 2659: 2654: 2617: 2601:chorale prelude 2537:in the Baroque 2527: 2526: 2521: 2520: 2497:Dido and Aeneas 2477: 2400: 2393: 2392: 2385: 2384: 2371: 2361: 2354: 2353: 2346: 2345: 2328: 2325: 2322: 2321: 2319: 2311: 2308: 2305: 2304: 2302: 2294: 2291: 2288: 2287: 2285: 2277: 2274: 2271: 2270: 2268: 2260: 2257: 2254: 2253: 2251: 2243: 2240: 2237: 2236: 2234: 2226: 2223: 2220: 2219: 2217: 2209: 2206: 2203: 2202: 2200: 2192: 2189: 2186: 2185: 2183: 2175: 2172: 2169: 2168: 2166: 2158: 2155: 2152: 2151: 2149: 2131: 2130: 2119: 2108: 2091: 2018: 2008: 1935: 1906: 1897: 1887: 1886: 1881: 1880: 1839:or Gypsy major 1825:Harmonic minor 1814:Harmonic major 1792:Diatonic major 1778:Halfstep string 1699: 1693: 1692: 1687: 1686: 1680: 1673: 1670: 1663: 1658: 1657: 1655: 1648: 1643: 1642: 1640: 1633: 1605: 1602: 1595: 1590: 1589: 1587: 1580: 1575: 1574: 1572: 1565: 1560: 1559: 1557: 1550: 1535: 1530: 1522:superparticular 1507: 1470: 1433: 1396: 1359: 1317:separated by a 1310: 1309: 1308: 1307: 1306: 1298: 1295: 1288: 1282: 1233: 1230: 1227: 1226: 1224: 1213: 1210: 1207: 1206: 1204: 1193: 1190: 1187: 1186: 1184: 1171: 1168: 1165: 1164: 1162: 1152: 1149: 1146: 1145: 1143: 1133: 1130: 1127: 1126: 1124: 1114: 1111: 1108: 1107: 1105: 1063: 1062: 1061: 1060: 1059: 1051: 1048: 1041: 1035: 986: 983: 980: 979: 977: 966: 963: 960: 959: 957: 946: 943: 940: 939: 937: 924: 921: 918: 917: 915: 905: 902: 899: 898: 896: 886: 883: 880: 879: 877: 867: 864: 861: 860: 858: 844:    821: 820: 812: 810: 809: 808: 807: 799: 796: 789: 783: 734: 731: 728: 727: 725: 714: 711: 708: 707: 705: 694: 691: 688: 687: 685: 672: 669: 666: 665: 663: 653: 650: 647: 646: 644: 634: 631: 628: 627: 625: 615: 612: 609: 608: 606: 566: 550: 542: 534: 526: 518: 510: 509: 504: 503: 482: 474: 466: 458: 450: 443: 442: 437: 436: 431: 430: 406: 398: 390: 382: 381:Enharmonic: E–D 374: 373: 368: 367: 342:, are movable. 245: 237: 235: 200: 199: 185:, e.g. A–G–F–E. 151: 145: 110: 96: 69: 17: 12: 11: 5: 3543: 3541: 3533: 3532: 3530:Musical scales 3527: 3522: 3512: 3511: 3505: 3504: 3502: 3501: 3496: 3495: 3494: 3489: 3484: 3479: 3474: 3469: 3464: 3459: 3449: 3444: 3443: 3442: 3432: 3431: 3430: 3420: 3415: 3409: 3406: 3405: 3393:Pitch segments 3391: 3389: 3388: 3381: 3374: 3366: 3360: 3359: 3342: 3324: 3305: 3302: 3301: 3300: 3294: 3284:. foreword by 3276:Larry Polansky 3271: 3247: 3246: 3233: 3227:Marcel Dupré, 3220: 3207: 3195: 3171:Al-Farabi 2001 3163: 3159:Al-Farabi 2001 3151: 3147:Al-Farabi 2001 3139: 3126: 3120:Marcel Dupré, 3110: 3097: 3093:Music Analysis 3085:Music Analysis 3052: 3033: 3021:Robert Gauldin 3013: 2994: 2984:Godfrey Winham 2975:Music Analysis 2956:Milton Babbitt 2933:Music Analysis 2865: 2852: 2828: 2799: 2778: 2774:978-0306775215 2754: 2748:Marcel Dupré, 2741: 2718: 2706: 2704:, p. 103. 2694: 2682: 2656: 2655: 2653: 2650: 2649: 2648: 2643: 2638: 2633: 2628: 2623: 2616: 2613: 2476: 2473: 2455: 2454: 2451: 2448: 2445: 2442: 2439: 2436: 2433: 2430: 2427: 2424: 2421: 2414: 2413: 2410: 2407: 2397: 2389: 2381: 2378: 2368: 2358: 2350: 2342: 2339: 2335: 2334: 2317: 2300: 2283: 2266: 2249: 2232: 2215: 2198: 2181: 2164: 2147: 2137: 2136: 2127: 2116: 2105: 2090: 2087: 2084: 2083: 2080: 2076: 2075: 2072: 2068: 2067: 2064: 2060: 2059: 2056: 2052: 2051: 2048: 2044: 2043: 2040: 2036: 2035: 2032: 2007: 2004: 2001: 2000: 1997: 1993: 1992: 1989: 1985: 1984: 1981: 1977: 1976: 1973: 1969: 1968: 1965: 1961: 1960: 1957: 1953: 1952: 1949: 1934: 1931: 1905: 1902: 1896: 1893: 1874: 1873: 1870: 1867: 1863: 1862: 1861:Melodic minor 1859: 1856: 1852: 1851: 1850:Melodic major 1848: 1845: 1841: 1840: 1834: 1831: 1827: 1826: 1823: 1820: 1816: 1815: 1812: 1809: 1805: 1804: 1803:Natural minor 1801: 1798: 1794: 1793: 1790: 1787: 1783: 1782: 1779: 1776: 1761: 1760: 1757: 1753: 1752: 1749: 1745: 1744: 1741: 1737: 1736: 1733: 1729: 1728: 1725: 1672: 1662: 1647: 1632: 1594: 1579: 1564: 1549: 1544:in the modern 1534: 1531: 1529: 1526: 1516: 1515: 1504: 1501: 1498: 1495: 1492: 1489: 1486: 1483: 1479: 1478: 1467: 1464: 1461: 1458: 1455: 1452: 1449: 1446: 1442: 1441: 1430: 1427: 1424: 1421: 1418: 1415: 1412: 1409: 1405: 1404: 1393: 1390: 1387: 1384: 1381: 1378: 1375: 1372: 1368: 1367: 1356: 1353: 1350: 1347: 1344: 1341: 1338: 1335: 1323:diatonic scale 1312: 1311: 1296: 1291: 1290: 1289: 1280: 1279: 1278: 1275: 1274: 1268: 1266: 1260: 1258: 1252: 1250: 1243: 1242: 1239: 1222: 1219: 1202: 1199: 1182: 1178: 1177: 1160: 1158: 1141: 1139: 1122: 1120: 1102: 1101: 1098: 1095: 1092: 1090: 1087: 1085: 1081: 1080: 1065: 1064: 1049: 1044: 1043: 1042: 1033: 1032: 1031: 1028: 1027: 1021: 1019: 1013: 1011: 1005: 1003: 996: 995: 992: 975: 972: 955: 952: 935: 931: 930: 913: 911: 894: 892: 875: 873: 855: 854: 851: 848: 845: 842: 839: 836: 832: 831: 823: 822: 811: 797: 792: 791: 790: 781: 780: 779: 776: 775: 769: 767: 761: 759: 753: 751: 744: 743: 740: 723: 720: 703: 700: 683: 679: 678: 661: 659: 642: 640: 623: 621: 603: 602: 599: 596: 593: 590: 587: 584: 580: 579: 565: 562: 558: 557: 515: 500: 497: 494: 490: 489: 447: 427: 423: 422: 419: 418:Phrygian scale 415: 414: 379: 366:Chromatic: E–D 364: 361: 358: 255: 254: 211: 210: 205: 191: 186: 171: 147:Main article: 144: 141: 68: 65: 49:perfect fourth 15: 13: 10: 9: 6: 4: 3: 2: 3542: 3531: 3528: 3526: 3523: 3521: 3518: 3517: 3515: 3500: 3497: 3493: 3490: 3488: 3485: 3483: 3480: 3478: 3475: 3473: 3470: 3468: 3465: 3463: 3460: 3458: 3455: 3454: 3453: 3450: 3448: 3445: 3441: 3438: 3437: 3436: 3433: 3429: 3426: 3425: 3424: 3421: 3419: 3416: 3414: 3411: 3410: 3407: 3402: 3398: 3394: 3387: 3382: 3380: 3375: 3373: 3368: 3367: 3364: 3357: 3353: 3352:Stanley Sadie 3349: 3348: 3343: 3340: 3339:0-582-28117-2 3336: 3332: 3328: 3325: 3322: 3318: 3317:Stanley Sadie 3314: 3313: 3308: 3307: 3303: 3297: 3295:0-945996-04-7 3291: 3287: 3283: 3282: 3277: 3272: 3268: 3264: 3260: 3256: 3255: 3254: 3253: 3243: 3237: 3234: 3230: 3224: 3221: 3217: 3211: 3208: 3205:, p. 20. 3204: 3203:Chalmers 1993 3199: 3196: 3192: 3191:0-931340-88-8 3188: 3184: 3180: 3176: 3172: 3167: 3164: 3161:, p. 58. 3160: 3155: 3152: 3148: 3143: 3140: 3136: 3130: 3127: 3123: 3117: 3115: 3111: 3107: 3101: 3098: 3094: 3091: 3087: 3086: 3081: 3080:0-300-02120-8 3077: 3073: 3072:0-300-01610-7 3069: 3065: 3061: 3056: 3053: 3049: 3048: 3043: 3037: 3034: 3030: 3026: 3022: 3017: 3014: 3010: 3009: 3004: 2998: 2995: 2991: 2990: 2985: 2981: 2980:J. K. Randall 2977: 2976: 2971: 2967: 2966: 2961: 2960:Edgard Varèse 2957: 2953: 2952: 2947: 2946:Martin Boykan 2943: 2939: 2938:John Harbison 2935: 2934: 2929: 2925: 2921: 2917: 2916: 2911: 2910: 2905: 2901: 2900: 2895: 2894: 2889: 2885: 2881: 2880: 2875: 2869: 2866: 2862: 2856: 2853: 2849: 2848:1-55553-169-5 2845: 2841: 2837: 2832: 2829: 2818:on 2015-06-18 2817: 2813: 2809: 2803: 2800: 2796: 2792: 2788: 2782: 2779: 2775: 2771: 2767: 2763: 2758: 2755: 2751: 2745: 2742: 2739: 2735: 2731: 2727: 2722: 2719: 2716:, p. 11. 2715: 2714:Chalmers 1993 2710: 2707: 2703: 2702:Chalmers 1993 2698: 2695: 2691: 2690:Chalmers 1993 2686: 2683: 2678: 2677: 2672: 2668: 2661: 2658: 2651: 2647: 2644: 2642: 2639: 2637: 2634: 2632: 2629: 2627: 2624: 2622: 2619: 2618: 2614: 2612: 2610: 2606: 2602: 2598: 2594: 2590: 2586: 2582: 2577: 2575: 2571: 2567: 2563: 2559: 2555: 2551: 2547: 2542: 2540: 2536: 2535: 2518: 2514: 2510: 2506: 2502: 2498: 2494: 2493:Henry Purcell 2490: 2484: 2482: 2474: 2472: 2470: 2469:Arabian maqam 2466: 2462: 2452: 2449: 2446: 2443: 2440: 2437: 2434: 2431: 2428: 2425: 2422: 2419: 2416: 2415: 2411: 2408: 2404: 2398: 2390: 2382: 2379: 2375: 2369: 2365: 2359: 2351: 2343: 2340: 2337: 2336: 2318: 2301: 2284: 2267: 2250: 2233: 2216: 2199: 2182: 2165: 2148: 2145: 2144: 2141: 2128: 2123: 2117: 2112: 2106: 2103: 2102: 2101: 2099: 2095: 2088: 2081: 2078: 2077: 2073: 2070: 2069: 2065: 2062: 2061: 2057: 2054: 2053: 2049: 2046: 2045: 2041: 2038: 2037: 2033: 2030: 2029: 2026: 2023: 2017: 2013: 2012:Carnatic rāga 2005: 1998: 1995: 1994: 1990: 1987: 1986: 1982: 1979: 1978: 1974: 1971: 1970: 1966: 1963: 1962: 1958: 1955: 1954: 1950: 1947: 1946: 1943: 1941: 1932: 1930: 1928: 1924: 1923:pitch classes 1920: 1919: 1914: 1910: 1903: 1901: 1894: 1892: 1871: 1868: 1865: 1864: 1860: 1857: 1855:Minor + major 1854: 1853: 1849: 1846: 1843: 1842: 1838: 1835: 1832: 1829: 1828: 1824: 1821: 1818: 1817: 1813: 1810: 1807: 1806: 1802: 1799: 1796: 1795: 1791: 1788: 1786:Major + major 1785: 1784: 1780: 1777: 1774: 1773: 1770: 1769:(2) between: 1768: 1758: 1755: 1754: 1750: 1747: 1746: 1742: 1739: 1738: 1734: 1731: 1730: 1726: 1723: 1722: 1719: 1717: 1713: 1684: 1677: 1667: 1652: 1637: 1630: 1626: 1623: 1618: 1599: 1584: 1569: 1554: 1547: 1543: 1539: 1532: 1527: 1525: 1523: 1505: 1502: 1499: 1496: 1493: 1490: 1487: 1484: 1481: 1480: 1468: 1465: 1462: 1459: 1456: 1453: 1450: 1447: 1444: 1443: 1431: 1428: 1425: 1422: 1419: 1416: 1413: 1410: 1407: 1406: 1394: 1391: 1388: 1385: 1382: 1379: 1376: 1373: 1370: 1369: 1357: 1354: 1351: 1348: 1345: 1342: 1339: 1336: 1333: 1332: 1329: 1326: 1324: 1320: 1294: 1276: 1273: 1269: 1267: 1265: 1261: 1259: 1257: 1253: 1251: 1249: 1245: 1244: 1240: 1223: 1220: 1203: 1200: 1183: 1180: 1179: 1161: 1159: 1142: 1140: 1123: 1121: 1104: 1103: 1099: 1096: 1093: 1091: 1088: 1086: 1083: 1082: 1077: 1074: 1072: 1047: 1029: 1026: 1022: 1020: 1018: 1014: 1012: 1010: 1006: 1004: 1002: 998: 997: 993: 976: 973: 956: 953: 936: 933: 932: 914: 912: 895: 893: 876: 874: 857: 856: 852: 849: 846: 843: 840: 837: 834: 833: 828: 819: 817: 795: 777: 774: 770: 768: 766: 762: 760: 758: 754: 752: 750: 746: 745: 741: 724: 721: 704: 701: 684: 681: 680: 662: 660: 643: 641: 624: 622: 605: 604: 600: 597: 594: 591: 588: 585: 582: 581: 576: 573: 571: 563: 561: 554: 546: 538: 530: 522: 517:Enharmonic: C 516: 501: 498: 495: 492: 491: 486: 478: 470: 462: 454: 449:Enharmonic: D 448: 428: 425: 424: 420: 417: 416: 410: 402: 394: 386: 380: 365: 362: 359: 356: 355: 354: 352: 348: 343: 341: 337: 333: 329: 325: 321: 317: 313: 309: 305: 301: 297: 293: 289: 285: 281: 277: 272: 270: 266: 265: 260: 249: 241: 233: 232:quarter tones 229: 225: 221: 220: 215: 209: 206: 197: 192: 190: 187: 184: 180: 176: 172: 170: 167: 166: 165: 163: 159: 155: 150: 149:Genus (music) 142: 140: 138: 133: 128: 126: 122: 113: 108: 99: 94: 90: 86: 82: 78: 74: 66: 64: 62: 58: 54: 50: 46: 42: 38: 30: 26: 22: 3457:All-trichord 3440:All-interval 3434: 3356:John Tyrrell 3345: 3330: 3321:John Tyrrell 3310: 3286:Lou Harrison 3280: 3266: 3262: 3251: 3250: 3241: 3236: 3228: 3223: 3215: 3210: 3198: 3182: 3174: 3166: 3154: 3142: 3134: 3129: 3121: 3105: 3100: 3092: 3083: 3063: 3055: 3045: 3036: 3028: 3016: 3006: 2997: 2987: 2973: 2963: 2949: 2942:Eleanor Cory 2931: 2927: 2913: 2907: 2897: 2891: 2884:Steven Block 2877: 2868: 2860: 2855: 2839: 2831: 2820:. Retrieved 2816:the original 2811: 2802: 2786: 2781: 2765: 2757: 2749: 2744: 2729: 2721: 2709: 2697: 2692:, p. 8. 2685: 2675: 2660: 2588: 2584: 2580: 2578: 2553: 2549: 2546:Romantic Era 2543: 2539:Figurenlehre 2538: 2532: 2516: 2508: 2500: 2496: 2488: 2485: 2478: 2458: 2138: 2092: 2019: 1936: 1922: 1916: 1912: 1907: 1904:Atonal usage 1898: 1877: 1764: 1709: 1533:Romantic era 1519: 1327: 1318: 1315: 1068: 567: 559: 493:Lydian scale 429:Chromatic: D 357:Dorian scale 350: 346: 344: 339: 335: 331: 327: 323: 319: 315: 311: 307: 303: 299: 295: 291: 287: 283: 279: 275: 273: 268: 262: 256: 161: 157: 152: 129: 121:four strings 120: 106: 92: 84: 80: 79:(from Greek 76: 72: 70: 41:tetrachordum 24: 21:music theory 18: 3397:cardinality 3060:Allen Forte 2671:Tyrrell, J. 2636:Lament bass 2574:ground bass 2338:Note name: 1909:Allen Forte 1756:Upper Minor 1625:progression 1079:Enharmonic 435:–C–B | A–G 259:incomposite 228:major third 196:minor third 160:(singular: 91:bounded by 33:τετράχορδoν 3514:Categories 3492:Schoenberg 3447:Pentachord 3435:Tetrachord 3327:Rahn, John 2904:Stravinsky 2822:2015-04-12 2652:References 2597:homophonic 2593:variations 2587:(Fr.), or 2570:minor mode 2566:homophonic 2562:variations 2554:complainte 2509:Qui tollis 2501:Crucifixus 2465:major tone 2010:See also: 1940:whole step 1913:tetrachord 1767:whole step 1724:Tetrachord 1528:Variations 830:Chromatic 816:media help 372:–C–B | A–G 318:, and the 208:Enharmonic 179:whole tone 137:whole tone 116:κινούμενοι 85:tetrachord 25:tetrachord 3499:Aggregate 3482:Petrushka 3462:Chromatic 3452:Hexachord 3261:(2001) . 3259:Al-Farabi 2667:Sadie, S. 2556:(Fr.) or 2550:complaint 2548:, called 2481:complaint 2140:strings: 2098:Al-Farabi 1546:B Locrian 1089:parhypate 841:parhypate 589:parhypate 578:Diatonic 328:parhypate 288:hypermese 280:parhypate 189:Chromatic 93:immovable 45:intervals 3467:Diatonic 3428:Viennese 3423:Trichord 3329:. 1980. 3074:(cloth) 3062:(1973). 3029:Intégral 2734:Archived 2673:(eds.). 2615:See also 2528:♯ 2522:♯ 2394:♭ 2386:♭ 2355:♯ 2347:♯ 2132:♯ 2022:halfstep 1888:♭ 1882:♯ 1748:Harmonic 1694:♭ 1688:♭ 1659:♭ 1644:♭ 1629:bassline 1622:Phrygian 1591:♭ 1576:♭ 1561:♭ 1094:lichanos 1071:Archytas 847:lichanos 595:lichanos 525:–B | A–G 511:♭ 508:–F–E | D 505:♭ 465:–B | A–G 444:♭ 441:–F–E | D 438:♭ 432:♭ 397:–B │ A–G 375:♭ 369:♭ 340:paranete 332:lichanos 320:paramese 304:paranete 296:paramese 284:lichanos 201:♭ 183:semitone 169:Diatonic 61:tone row 3252:Sources 2970:Debussy 2589:lytanie 2585:litanie 2517:lamento 2332:⁠ 2320:⁠ 2315:⁠ 2303:⁠ 2298:⁠ 2286:⁠ 2281:⁠ 2269:⁠ 2264:⁠ 2252:⁠ 2247:⁠ 2235:⁠ 2230:⁠ 2218:⁠ 2213:⁠ 2201:⁠ 2196:⁠ 2184:⁠ 2179:⁠ 2167:⁠ 2162:⁠ 2150:⁠ 2146:Ratio: 2094:Persian 2089:Persian 1500:(28:27) 1494:(36:35) 1463:(22:21) 1457:(12:11) 1426:(28:27) 1420:(15:14) 1389:(20:19) 1383:(19:18) 1352:(16:15) 1346:(25:24) 1237:⁠ 1225:⁠ 1217:⁠ 1205:⁠ 1197:⁠ 1185:⁠ 1175:⁠ 1163:⁠ 1156:⁠ 1144:⁠ 1137:⁠ 1125:⁠ 1118:⁠ 1106:⁠ 990:⁠ 978:⁠ 970:⁠ 958:⁠ 950:⁠ 938:⁠ 928:⁠ 916:⁠ 909:⁠ 897:⁠ 890:⁠ 878:⁠ 871:⁠ 859:⁠ 738:⁠ 726:⁠ 718:⁠ 706:⁠ 698:⁠ 686:⁠ 676:⁠ 664:⁠ 657:⁠ 645:⁠ 638:⁠ 626:⁠ 619:⁠ 607:⁠ 290:), and 234:, e.g. 107:movable 102:ἑστῶτες 95:notes ( 81:chordon 67:History 3487:Sacher 3472:Mystic 3337:  3292:  3189:  3078:  3070:  2924:Carter 2874:Dvořák 2846:  2793:  2772:  2641:Tetrad 2581:litany 2558:lament 2513:Mozart 2499:, the 2082:1 1 3 2074:1 2 2 2066:2 1 2 2058:1 3 1 2050:2 2 1 2042:3 1 1 1999:1 1 3 1991:1 2 2 1983:2 1 2 1975:1 3 1 1967:2 2 1 1959:3 1 1 1918:tetrad 1759:1 2 2 1751:1 3 1 1743:2 1 2 1735:2 2 1 1084:hypate 835:hypate 583:hypate 541:–E | D 481:–E | D 351:chroai 347:shades 312:hypate 310:. The 306:, and 276:hypate 269:pyknós 267:(from 264:pyknón 224:ditone 158:genera 132:octave 3413:Monad 3265:[ 2418:Cents 2135:–B–C. 2126:–B–C. 2079:1 2 3 2071:2 1 3 2063:1 3 2 2055:2 2 2 2047:3 1 2 2039:3 2 1 1996:1 1 3 1988:1 2 2 1980:2 1 2 1972:1 3 1 1964:2 2 1 1956:3 1 1 1925:. 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Index

music theory
Greek
Latin
intervals
perfect fourth
cents
scale
tone row
greater and lesser perfect systems
Greek
Greek
lyre
octave
whole tone
Genus (music)
Ancient Greek music
Diatonic
cents
whole tone
semitone
Chromatic
minor third
Enharmonic

ditone
major third
quarter tones
double flat
half flat
incomposite

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