귀도, 존, 마르케토의 선법 이론에 대한 연구

이귀자 이화여자대학교 음악연구소 2006 이화음악논집 Vol.10 No.1

본 연구의 목적은 11세기 초 이태리의 이론가인 아렛조의 귀도의 논서 "미크로로구스"와 그로부터 거의 1세기 후반에 저술된 존의 "음악서" 그리고 14세기 초반에 또 다른 이태리의 이론가 마르케토에 의해 저술된 단성성가 예술에 대한 "루치다리움"에서 논의된 선법이론을 연구하는데 있다. 귀도의 "미크로로구스"는 다성 음악과 단성 성가를 논하는 음악 실습에 대한 최초의 논서로 중세기의 수도원 성가대를 훈련시키는데 사용하기 위한 논서였다. 위의 세 논서들은 선법 이론의 기본 틀에서 공통점을 지니지만 더 구체적인 면에서 차이점들을 보여준다. 귀도는 음들의 유사성 이론을 통하여 선율의 이도가 가능함을 보여 준다. 존은 정격과 변격 선법이 가지는 공통 음들과 그렇지 않은 음들을 구별하며, 각 선법에 따른 테노르 음 지정을 특징적으로 보여준다. 그리고 마르케토는 선법의 종류를 음역에 따라 더 세분화하며, 각 선법에서 성가를 시작할 수 있는 음들과 종지할 수 있는 음들을 제시한다. 그리고 성가 선율은 특정 음들의 관계에 따라 선법을 판단할 수 있다는 이론에 따라 각 선법의 음계 중 처음 다섯 음 중 어떤 음이 생략되어도 선법 결정에는 이상이 없음을 선율의 중단(interruption)이론을 통하여 전개해 나간다. 이 세 이론가들은 선법의 기능을 설명하기 위하여 실제 문헌에서 예들을 발췌했으며, 따라서 중세의 성가 구조를 이해하고 분석하는데 좋은 자료를 제공한다. The present study aims at an investigation of modal theories presented in Guido's "Micrologus(1026)", John's "De Musica(1100)", and Marchetto's "Lucidarium(1317 or 1318)". The modal theories descussed in these treatises are based on the modal theories used from the 9th century. The modes used in the medieval period are called Protus, Deuterus, Tritus and Tetrardus, and each mode is divided into authentic and plagal modes, thus making 8 modes all together. Marchetto divides the modes further into perfect, imperfect, mingled and mixed modes according to the melodic range. Guido and John also talk about the extension of melodic range, but their treatises do not contain detailed explanations. In Guido's treatise, the theory of the affinities of notes in which the possibility of melodic transpositions up a 5th are described, takes much space. This idea was initially presented in Hucbald's De Harmonica Institutione in early 10th century. John and Marchetto also agree that the lower ranged melodies can be transposed up a 5th without ruining the interval relations of the melody. But they do not discuss the affinities of notes based on theoretic relations. All three theorists examined for the present research deal with modal functions and thus refer actual chants in order to make their theoretic points clear. Therefore, their treatises are useful for understanding and analyzing medieval chants.

리듬 이론에 관한 연구

이귀자 이화여자대학교 음악연구소 2000 이화음악논집 Vol.4 No.-

The present study aims at an examination of two treatises on rhythm, which were written in ancient Greece : ‘Elementa Rhythmica' by Aristoxenus and ‘Peri Musike^s’ by Aristides Quintilianus. The former was written in the 4th century B.C. and the latter around the 3rd or 4th century A.D. Although the two treatises were written at a great interval in time, they resemble each other in their contents. ‘Elementa Rhythmica’ is only a part of the whole treatise (probably in 3 books), of which, only chapters 1 through 36 from book Ⅱ have come down to us. Even with such a small portion from the treatise, one can notice the importance of the rhythmic elements discussed by Aristoxenus. The theory of rhythm discussed by Aristides Quintilianus is found in chapters 13-21 of the 1st book and in chapter 15 of the second book of his whole treatise, ‘Peri Mousikes.’Especially, the 2nd book is concerned with the use of rhythm in relation to education which aims at enhancing virtue by using properly rhythmicized music. The two treatises are parallel in the definition of rhythm, perception of rhythm, in distinguishing rhythm and rhythmicized substance, and composite and incomposite durations, in discussing the primary time unit called chronos protos, in the exposition of the seven differences of the feet and the rhythmic genera. However, even in the similar content, Aristides Quintilianus discusses the subjects in much more detail and gives numerous rhythmic patterns combined by basic metric feet. Especially, his discussions on the nature and use of these rhythmic patterns are worthwhile and should be considered for use even today.

T. Campion과 G. Coperario의 作曲理論에 관한 比較硏究

李貴子 이화여자대학교 한국문화연구원 1985 韓國文化硏究院 論叢 Vol.46 No.-

The purpose of this study lies on the examination and comparison of the two early 17th century English treatises, "A New Way of Making Four-parts in Counterpoint," and "Rules How to Compose" written by Thomas Campionand Giovanni Coperario. These two theorists lived between the 1560's and 1620's, and were close enough to collaborate in writing certain songs. Although Thomas Morley's treatise, "A Plain and Easy Introduction to Practical Music," written in 1957, represents the early 17th century theoretical writings in England, the auther discusses the compositional rules in the concept of the Renaissance period which emphasizes the tenor part as the basis of a composition. However, both Campion and Coperario take the bass part as the foundation of music. This concept made an important change in the history of music theory. The Present study examined the contents of the two treatises with some historical and theoretical notes and compared the two in regard to their mutual influences and rules especially in the discussion of 4-part writing. The following results are drawn from the study: 1. The two theorists take the bass as the foundation of 4-part writing and discuss the setting of 40part songs in terms of harmonic concepts rather than the contrapuntal techniques practiced until the 16th century. 2. They both use full triads, mostly doubling the root, and 1st inversion of the triads. The examples shown in their treatises show the V-I cadential ideas in the bass line. 3. Cadential formulas always have suspensions in the upper most voice. 4. Harmonic progressions are very close to those of the common practice period of the later years, although there are some rules of progressions which do not agree with the later rules. 5. Both Campion and Coperario try to explain the most essential elements of composition but 4-part(contrapuntal) setting and suspensions (in Coperario's treatise) seem to be the most thoroughly discussed elements. 6. There are some differences in the rules of voice-leading. However, common rules appear more often than the different ones. They even used the same wording in describing their work, such as regarding the cadences.

리듬 이론에 관한 연구(2) : 12-13세기 이론을 중심으로 centered on the 12^th and 13^th century theories

이귀자 이화여자대학교 음악연구소 2001 이화음악논집 Vol.5 No.-

The present study is the second of a research series on the theory of rhythm. The first study was about the ancient Greek theory in which the poetic feet and the musical rhythm showed close relationship. Also the Greek rhythm theory showed relationship with ethos so that composers could choose the appropriate rhythmic patterns for their works. With the development of a new kind of polyphonic music during the 12^th and 13^th centuries, composers needed to have some method to control the rhythmic proportions between the voices. Magisters Leoninus and Perotinus, the two leading composers of the Notre Dame School at Paris during the second half of the 12^th century created a repertory of polyphonic music and a system of rhythm. Although the original manuscripts of Leoninus' works do not come down to us, Leoninus is known to have written many organum and conductus in which he shows a coherent rhythmic system. A new rhythmic theory which is called rhythmic mode or modal rhythm is discussed in several treatises written in the 13^th century. Some of the representative treatises are 「Discantus positio vulgaris」 (Anonymous), 「De musica libellus」(Anonymous Ⅶ), 「De Mensurabili Musica」 (Johannes de Garlandia), 「De Musica Mensurabili positio」 (Johannes de Garlandia). During the second quarter of the 13^th century, some of the theorists began to use different note shapes to indicate exact rhythmic values. This idea was led to the theory of mensural notation. 「Ars Cantus Mensurabili」(Franco of Cologne), 「Tractatus Musica」(Lambertus) and 「De Speculatione Musicae」(Walter Odington) all discuss about mensural notation although they use the same neumes as in the modal theory. Theoretically speaking, there are different opinions concerning the origin of a modal rhythm and its association with the classical poetic feet. Some theorists say that the rhythmic modes are closely related to the classical metrics and some other theorists say that the rhythmic modes are something that have to do with the accent. Also there are differences of opinions about the species of the rhythmic mode and the species of consonance and dissonance. Even the durational value of the ‘long’ had different meanings in the early and later parts of the 13^th century. At the early stage, half-note long was called a correct long (or true long) but later a dotted half-note was called a perfect long, thus the perfect long contained three breves. It is the 13^th century theory which includes major and minor thirds as imperfect consonances and perfect 5^th and 4^th, which have been considered as consonances from the ancient world, are now only classified as intermediate consonances. Although the notation system was not examined in detail, the present study sees that the 12^th and 13^th century literature and treatises provide good sources for the theory and practice of the rhythmic modes and mensural notation.

스크리아빈 음악의 화성어법과 선율작법에 관한 연구 : 후기 소나타를 중심으로 based on the Later Sonatas

이귀자 이화여자대학교 음악연구소 1997 이화음악논집 Vol.1 No.-

Alexander Scriabin(1872∼1915) was known as a revolutionary composer whose innovations were many-sided. His harmonic language and melodic idioms have been the subject of many analyses since his death in 1915. However, Scriabin's techniques can not be understood clearly unless one goes through his works by careful analysis. The purpose of this study is to examine Scriabin's later sonatas in order to find out his harmonic vocabulary and methods of melodic construction so typical of these works. Examination of the plentiful articles and books on his music preceeded the analysis of the harmonic and melodic structure of sonatas 6 through 10. A detailed analysis was made in order to prove that his methodology for harmonic usage and melodic structure show common traits in all his later sonatas. The results of the study can be summarized as follows. First, Scriabin's harmony is rooted in traditiona chord structure. Many people thought his harmonies were newly invented by him, and especially, the so-called mystic chord was something quite new. But it is found that his basic methods for his harmony are basically altered dominant sonorities, such as ??, ??, ??, ??, etc. Second, he uses enharmonic respellings in melodies very often in all his later sonatas. Third, his chords are also spelled enharmonically so that a tritone link which suggests dual modality can be made possible. Fourth, he uses 3rds as basic intervals for connecting chords and melodies. Fifth, he works basically with short motives and develops them by repetition, sequence, transposition-repetition, altered repetition, and so on. Sixth, Scriabin uses whole-tone or octatonic scales for his melodic resources. Seventh, sonata 9 shows all the musical techniques typical of his later piano works.

L. Dallapiccola 가곡에 나타난 작곡기법 연구

李貴子 이화여자대학교 한국문화연구원 1989 韓國文化硏究院 論叢 Vol.55 No.-

The purpose of this study lies on an analysis of 4 songs by Luigi Dallapiccola. The 4 songs are "Cinque Frammenti di Saffo", "Due Liriche di Anacreonte", "Goethe-Lieder", and "Cinque Canti". The 1st two are written in 1940 's and the other two in 1950 's. All of them employ 12-tone method. Born in listria in 1904, Dallapiccola is known as an Italian composer who has adopted Viennese 12-tone techniques in most of his compositions. He began musical studies by playing piano and writing some pieces, but due to the political reasons, his family had to leave hometown and was sent to concentration camp in Austria. During the 30 's, Dallapiccola had chances to encounter the Viennese 12-tone composers ' works. This has made an important change in his musical development. Especially, studies on Alban Berg and Anton Webern 's music have become turning points in his musical style. However, he has always kept Italian traditional concepts in his scores, and thus, he is known as a 20th century composer whose compositions rooted in romanticism and traditional Italian style. One of the main reasons for his adoption of dodecaphony was to increase the warmth to his melodies. He was not interested in exploiting the principle of variations as utilized by the Viennese composers. In his early works, Dallapiccola mixed pure diatonic scales with 12-tone row. This was done in the "Canti di Prigionia" written in 1938~41. Complete dodecaphonic pieces began to appear in early 40 's. in the early works, Dallapiccola used the technique very loosely. In the "Cinque Frammenti di Saffo", for instance, he uses more than one row in each song. The 12-tone row here does not predominate the whole song. It can be said that he uses different tone rows to express different melodic ideas. He often use tow rows simultaneously. As the technique matures, however, his pieces show more of the typical atonal characteristics found in Anton Webern 's works. For example, the songs in "Goethe-Lieder" show much of the Webernian traits in melodic construction such as large leaps and segmentation of the rows into 2 or 3 notes, thus resulting Klangfarben-melodic. The present study analyzed the 4 selected compositions in terms of their celodic structure, text setting, harmonic aspects and rhythmic characteristics, in relation to the whole structure of each song. Briefly considered also is come of the characteristic features found in his 12-tone rows and methods of using the rows. Following are some of the characteristics found from the analysis: 1) Interval class 1,3,5 and 6 appear as frequent intervals in his rows. Among these, interval class 5 and 6 are used more chordally and the rest more linearly. 2) Melodic and chordal construction by superimposition of 3rds resulted triads, 7th and 9th chords. 3) Choice of different variants of the row has some relation to the formal structure. 4) In many instances, only part of the row was used. Trichordal segmentations appear most frequently and the hexachord, next. Large leaps and melodic segmentation appear more in the 2 works written in 1950 's. 5) In the two compositions in 1940 's, he is not confined to strict use of the row. He sometimes changes the order of the row in order to obtain desired melodic contour. 6) Syllabic setting predominates, but there are some melismatic lines. Also, there are some symbolic expressions of the text. 7) In chordal construction, dyads, trichords, tetrachords, quintachords, hexachords and all 12-tone chord are used. But trichords and hexachords appear most frequently. 8) Dynamics also seem to have some relation to the structure. Some of the songs have mostly p or f, but in several songs, the dynamic change coincides with the structural division. 9) Rhythm is the least related element to the formal structure. Dallapiccola 's rhythm frequently features irregular division of the beats and accentless down beat. 10) In general, contrapuntal texture dominates. Expecially, conoic writing is noticeable in Goethe-Lieder and Cinque Canti. Canon between voice and accompaniments, canon in contrary motion, and paired canonic accompaniment ase found often.

15세기 대위법의 이론과 실제 : Tinctoris의 대위법 이론을 중심으로

李貴子 이화여자대학교 한국문화연구원 1993 韓國文化硏究院 論叢 Vol.62 No.1

The theory of counterpoint has emerged from the theory of discant of the 12th and 13th centuries. The term "Counterpoint", however, was first used in "Compendium", a treatise written by Petrus dictus Palma ociosa in 1336. This treatise mainly discussed the simple discant concentrating on interval successions, and used the term "punctus contra punctum" only once. Therefore, the term "counterpoint", in the true sense, can be said to have began to be used approximately from 1350 after Petrus dictus Palma ociosa. In the 13th century, a new theory of consonance and dissonance was developed in the treatises by Johannes de Garlandia, France of Cologne, and several other anonymous theorists. These theorists divided the consonances into three classes, namely perfect, imperfect, and intermediate ones. Now the 3rds were considered consonances and gradually the 6ths also came to be included in the domain of consonance. Thus, the interval successions discussed in the treatises of this period emphasized how each interval can move to another. The compositions were based on the tenor above which discant voices were added, each forming consonances with the tenor. Johannes Tinctoris, one of the most important theorists in the 15th century, wrote a treatise, "Liber de Arte Contrapuncti" in which contrapunctal theories were discussed in detail. Compared to the 13th and 14th century contrapunctal theories which mainly dealt with voice leading according to the rules of interval successions, Tinctoris theories exposed diverse possibilities of voice leading, and thus, his rules were adapted and applied in compositions by the later theorists. More important than the theory of consonance and dissonance, was the content in chapter 23 through 34 of "Liber de Arte Contrapuncti". These chapters discussed the rules concerning the placement of dissonances. Tinctoris explained the placement of dissonances according to the rhythmic and melodic positions. His theory was based on the mensuration theory popularly practiced in the 15th century. The present study lies in an investigation of the theory and application of the contrapunctal theories explained in the "Liber". A thorough examination of the treatise and an analysis of arbitrarily chosen compositions by Tinctoris compose the main body of this thesis. Some of the findings which have resulted from the study are as follows. In the theory of interval connections, Tinctoris showed some differences when compared to the earlier theorists. He did not limit the number of continuous progressions of the imperfect consonances to 3 or 4 times. In his compositions, continuous 3rds or 6ths sometimes appear more than 4 times. In the melodic progressions, Tinctoris emphasized step progressions, but he mentioned that wide skips are sometimes used to give a special character to the melody. Skips of 3rd, 4th, and 5th from a dissonance appear frequently, especially at the cadential points forming Landini cadence. Dissonances used are passing tones, auxiliary tones, anticipations and suspensions. Passing tones appear to be the most frequently used non-chord tones, and suspensions are mostly used at the cadences. Dissonances have minima, semiminima or fusa rhythmic value, and in any case, they do not exceed the rhythmic value of half the measuring unit. Dissonances using the rhythmic value of minima or semiminima appear in the works in major or minor prolation but fusa dissonances appear only in the works of minor prolation using minima as a measuring unit. Also explained in relation to major or minor prolations are 7-6, 4-3, or 2-3 suspensions. Tinctoris explained the positions of dissonances in several different occasions depending on the rhythmic value and melodic lines of the penultimate note or notes in penultimiate measure. Tinctoris also discussed the 3 basic rules for dissonance usage in binary and ternary proportions. However, rhythmic positions of the dissonances seem to be the same, except that in triple proportion, the 3rd minima should be consonance at least on its first half. To sum up the study, it can be said that Tinctoris had exercised his rules in practice.

귀도, 존, 마르케토의 선법 이론에 대한 연구

이귀자 이화여자대학교 음악연구소 2006 이화음악논집 Vol.10 No.2

The present study aims at an investigation of modal theories presented in Guido's "Micrologus(1026)", John's "De Musica(1100)", and Marchetto's "Lucidarium(1317 or 1318)". The modal theories descussed in these treatises are based on the modal theories used from the 9th century. The modes used in the medieval period are called Protus, Deuterus, Tritus and Tetrardus, and each mode is divided into authentic and plagal modes, thus making 8 modes all together. Marchetto divides the modes further into perfect, imperfect, mingled and mixed modes according to the melodic range. Guido and John also talk about the extension of melodic range, but their treatises do not contain detailed explanations. In Guido's treatise, the theory of the affinities of notes in which the possibility of melodic transpositions up a 5th are described, takes much space. This idea was initially presented in Hucbald's De Harmonica Institutione in early 10th century. John and Marchetto also agree that the lower ranged melodies can be transposed up a 5th without ruining the interval relations of the melody. But they do not discuss the affinities of notes based on theoretic relations. All three theorists examined for the present research deal with modal functions and thus refer actual chants in order to make their theoretic points clear. Therefore, their treatises are useful for understanding and analyzing medieval chants. 본 연구의 목적은 11세기 초 이태리의 이론가인 아렛조의 귀도의 논서 "미크로로구스"와 그로부터 거의 1세기 후반에 저술된 존의 "음악서" 그리고 14세기 초반에 또 다른 이태리의 이론가 마르케토에 의해 저술된 단성성가 예술에 대한 "루치다리움"에서 논의된 선법이론을 연구하는데 있다. 귀도의 "미크로로구스"는 다성 음악과 단성 성가를 논하는 음악 실습에 대한 최초의 논서로 중세기의 수도원 성가대를 훈련시키는데 사용하기 위한 논서였다. 위의 세 논서들은 선법 이론의 기본 틀에서 공통점을 지니지만 더 구체적인 면에서 차이점들을 보여준다. 귀도는 음들의 유사성 이론을 통하여 선율의 이도가 가능함을 보여 준다. 존은 정격과 변격 선법이 가지는 공통 음들과 그렇지 않은 음들을 구별하며, 각 선법에 따른 테노르 음 지정을 특징적으로 보여준다. 그리고 마르케토는 선법의 종류를 음역에 따라 더 세분화하며, 각 선법에서 성가를 시작할 수 있는 음들과 종지할 수 있는 음들을 제시한다. 그리고 성가 선율은 특정 음들의 관계에 따라 선법을 판단할 수 있다는 이론에 따라 각 선법의 음계 중 처음 다섯 음 중 어떤 음이 생략되어도 선법 결정에는 이상이 없음을 선율의 중단(interruption)이론을 통하여 전개해 나간다. 이 세 이론가들은 선법의 기능을 설명하기 위하여 실제 문헌에서 예들을 발췌했으며, 따라서 중세의 성가 구조를 이해하고 분석하는데 좋은 자료를 제공한다.

음열 확대 기법에 관한 연구 : Babbitt의 연가곡 "Du"를 중심으로 Centered on Babbitt's song cycle, "Du"

李貴子 이화여자대학교 음악대학 1991 音樂藝術論壇 Vol.- No.1

The twelve­tone technique of the second Viennese school rapidly spread out to other countries after World War Ⅱ, and by the late 1950's, it had influenced many composers in Europe and America. Particularly, many American composers or composers who have been active in America have extended and developed the twelve­tone technique by using diverse methods. Some of the representative twelve­tone composers are Ernst Krenek, Igor Stravinsky (in his later period), Milton Babbitt and Luigi Dallapiccola, an Italian twelve­tone composer who has done some work in the United States. These composers not only used the twelve­tone row in the conventional method as did the Viennese composers, but also extended the row in various ways, thus creating new orderings of the pitches originally set for the basic series. Some examples of the frequently utilized methods for set extensions are the use of rotation of the pitches in a certain order, the use of a derived set generated by a segment of a basic set, and the use of a secondary set formed by combinatorial principle of the series. The above­mentioned composers have utilized these techniques as a means of set extensions. The purpose of this study lies in an investigation of various methods used for set extensions and an analysis of Babbitt's song cycle "Du" in terms of the above­mentioned extended set procedures. For this, a brief discussion on the technical procedures for rotation, formation of the derived set and the secondary set and a detailed analysis of Babbitt's "Du" in regard to pitch structure have been made. Some of the characteristic features found by the analysis are as follows : the basic set used for "Du" has several characteristic elements possible for set extensions : i.e., it consists of two all­combinatorial hexachords, each of which contains four different types of trichord which becomes the basis for derived sets, and the set is an all­interval set which creates a palindrome centering on the tritone between the order number 5 and 6. In "Du" there exsist six derived sets and three secondary sets, and the use of these sets are closely related to the overall structure of the work. In addition to these extended set procedures, Babbitt also uses a four­part symmetrical array for the greater part of the song cycle. The lynes for the four­part array are distinguished by the difference in register and the melodic line of the voice part has four distinctive contours continuously existing in each twelve­tone row, except for two cases. As a whole, "Du" presents various techniques for set extension and foreshadows the more systematic organization of serial technique found in Babbitt's later compositions.

13세기 디스칸트 이론에 관한 연구

이귀자 이화여자대학교 한국문화연구원 1986 韓國文化硏究院 論叢 Vol.51 No.-

The purpose of this study lies on an examination of the well known treatises concerning the theory of discant in the 13th century. Although discant emerged as a new form in the 12th, more theoretical writings on discant were written during the 13th century. The present study will, therefore, look through representative treatises dealing with polyphonic writing from the 9th century to the 13th century. The term "discant" came from the Latin "discantus" which was a translation of "diaphony" meaning a sweet song. "Diaphony" appears in Musica Enchiriadis, the earliest source for polyphonic writing and is used to refer parallel organum in diatessaron and diapente. Thus, diaphony and organum had the same meaning. In the earliest manifestations, the organum meant a note-against-note style in parallel or oblique motion. With the St. Martial period, however, more elaborate type of organum which had a long sustained tenor part and a melismatic upper voice emerged. And along with this changing style of organum, there appeared a new type of polyphony in note-against-note style. This was called discant. In the beginning, however, "discant" was referred to the polyphonic style in general just as the organum did. One can find that the theorists in the 13th century used the terms without clearly distinguishing their meaning. Some theorist talks about the species of organum in general, namely discant, copula and organum in specific sense, and some theorist talks about the species of discant, namely pure discant, organum, conductus, motel and hocket. Although the theorists seem to have used the terms in a mixed way, close examinations of the treatises reveal that triple meaning of the term "discant" was used by the theorists: the voice part of a polyphonic composition, a diaphonic style of composition, and the motet-conductus category. Discussed in the treatises were the various elements of music necessary for the writings in discant style. The rhythmic mode was considered as the basis of every type of discant and all the theorists discussed this in detail. Appeared as the especially important were the discussions by Johannes de Garlandia and Anonymous Ⅳ. They divided the 6 rhythmic modes into proper modes(1,2,6) and modes beyond measure(3,4,5). Combinations of these modes were discussed in detail along with musical examples in Johannes de Garlandias treatise, De Mensurabili Musica. The use of rhythmic modes contributed to the development of rhythmic aspects of music in the later periods. Also discussed were the consonances and their use in melodic progressions. The concept of consonances has changed during the course of polyphonic development from the 9th century. In the beginning, only the 4th, 5th and 8th were regarded as consonances, and then John Cotton recognized the the 13rds (both major and minor) as consonant intervals. In the 13th century, the theorists divided the consonances into 3 groups; namely, the perfect, imperfect and intermediate ones. Unison and octave were considered as the perfect consonances, 3rds and 6ths as the imperfect consonances, and 4th and 5th as the intermediate consonances. In discussing the discant, theorists talked about the consonances only and not much about the dissonances, although dissonances were found in literature as passing or neighboring notes especially when the diminution was practiced. Concerning the rules for voice-leading, there appear certain rules that govern the counterpoint principles in the later periods. Prohibition of the parallel movements of perfect concords and continuous use of imperfect concords already appeared in the treatises. The melodic progression of the discant voice was determined according to the rise and fall of the tenor part and main concern was given to the formation of certain intervals one after the other. The types of discant compositions mentioned by the theorists were discant, organum, copula, hocket, conductus and motet. However, these mention only in terms of stylistic characteristics using discant techniques.