EARLY CISTERCIAN
POLYPHONY: A NEWLY-DISCOVERED SOURCE *
M ANUEL PEDRO FER REIRA
III. 2. I. The Status of the Major Second
The major second
is included by Guido of Arezzo in his Micrologus among the consonant
intervals, although, if the examples are taken into account, he regards it
only as a secondary, transitional consonance. Short successions of
parallel seconds are allowed; so are the seconds resulting from oblique
movement of the voices, or the second used as an appog- giatura to the
unison. Sustained parallel movement at the second (or the third) is
avoided.
長二度は、Guido of Arezzoの「Micrologus」においては、協和音の中に含められている。しかし、いくつかの例を見てみると、Guidoは、長二度は二次的に一過性に出現した協和音程と考えているようである。各声部の斜行の結果として、あるいはユニゾンへの途中経過（appoggiatura）としてであるならば、平行二度の短い継続は許される。二度（あるいは三度）の継続した平行は禁止されていた。
The tentative transcriptions of the extensive polyphonic sections of the Winchester Troper (Cambridge, Corpus Christi College, MS 473) " and the pieces formerly in Chartres, Bibliotheque de la ville, MS 109, f. 75, ' confirm the secondary consonant status of the major second in the eleventh-century.
Winchester Troperのポリフォニーの不確かなtranscriptionとChartres, Bibliotheque de la
ville, MS 109, f. 75中の古い作品は、11世紀における長二度の二次的協和音の状態の正当性を立証する。
The second is freely handled in
what is possibly the oldest two-voiced versus in folios 202 to 205 of
Troper Paris, Bibliotheque Nationale, lat. 909, from St. Martial de
Limoges. The polyphonic nature of the set, already suspected by Dreves,
was subsequently, and in my opinion wrongly, denied（Is it polyphony? MANUEL PEDRO FERREIRA
参照）. The major second appears mostly as the
result of oblique movement, voice-crossing, or appoggiatura. but also in
contexts where these explanations do not apply (Example 7)
.
長二度は、もっとも古いサンマーシャル楽派の写本、Troper Paris, Bibliotheque Nationale,
lat. 909のfolio
202-205においても、自由に扱われている。（略）長二度は大部分が斜行、反行、途中経過（appoggiatura）の結果として出現する。 （略）
The refrain of “ Annus novus in gaudio” , included in the later Aquitanian
MS Paris, Bibliotheque Nationale, lat. 1139, even goes so far as to allow
a second to start a poetic line. But already “ Prima mundi,” in the same
manuscript, uses the second only as an appoggiatura. 61
後期アキテーヌポリフォニーの写本Paris, Bibliotheque Nationale, lat. 1139に含まれる“
Annus novus in gaudio” では、歌詞の最初部分に長二度が出現する。しかし、同じ写本中の“
Primi mundi,”においては、長二度はわずかにappoggiatura部分でしか出現しない61（Facsimile of “ Annus novus” in Theodore Karp. The Polyphony of Saint-Martial.
plates 6-7. Analysis of “ Prima mundi" in Sarah Fuller. “ Aquitanian
Polyphony of the Eleventh and Twelfth Centuries" (Ph. D diss.. University
California at Berkeley. 1969). pp. 285-88. Transcriptions in Van der Werf.
The Oldest Extant Part Music. 2: 90f., 184ff. ）。
We can therefore suspect that
the major second, around 1100, was beginning to be regarded by some as a
dissonance: this attitude gained currency during the
twelfth-century62.
我々はそれゆえ、1100年頃、否、12世紀全般において、長二度が不協和音程として認められていたという点に関して、疑問を持たざるを得ない。 62Leo
Treitler. based on transcriptions that do not incorporate corrections of
dissonances. pointed out that "M S 1159 has parts frequently rubbing up
against one another and clashing in seconds and sevenths (...) This occurs
less often in the later sources, and hardly at all in the British Museum
manuscript." Leo Treitler. "The Polyphony of Saint-Martial." Journal of
the American Musicolof>ical Society X V II (1964), 39, reprinted in The
Garland Library of the History of Western Music, Ellen Rosand. ed. (New
York: Garland. 1985). 2: 351 -64.
An extreme case of seconds handled as primary consonances, to begin and
end a piece, is found in two musical examples from the twelfth- century
manuscript, Vatican City, Biblioteca Apostolica Vaticana. lat. 9496. An
explicit remark by Anonymous IV (ca. 1300) allows us to identify this feature
as typical from the Lombard area in northern Italy; in the examples of
related archaic Milanese polyphony reported by Franchino Gaffurio (1496)63. it can be concluded that the
style allows also for parallel seconds near the beginning and the end of a
piece. 64 63Reproduced in Joseph Smits van Waesberghe. ed.. Exposinones
in Micrologum Guidonis Aretini (Amsterdam: North-Holland Pub. Co.. 1957).
pp. 29. 57.
作品の最初と最後の部分において、初歩的な協和音程として扱われた極端な”二度”のケースが、12世紀のVatican City, Biblioteca Apostolica Vaticana. lat. 9496写本中の二つの例において見出される。1300年頃、Anonymous IVによる、「この特徴（長二度の多様性）は、北イタリアのロンバール地方においてよく認められる」いう、明白な証言がある。その例は、Franchino Gaffurio (1496)によって報告された古いミラノ風ポリフォニー関連のものである。そのスタイルはまた、作品の最初と最後が、平行二度において終始する、というものである。
Although apparently particular to the north of Italy, this style was certainly
known to the Cistercians, for St. Bernard spent large periods in Milan
and was so popular there that the Milanese unsuccessfully tried to have
him as a bishop.
It should be remembered that the use of seconds and even parallel seconds is found also in European traditional music and in a number of non-European polyphonic traditions; “ it will be seen below that this phenomenon was probably more current in Europe in the Middle Ages than we are generally willing to admit.
The
second as an appoggiatura to the unison is found in a large number of
twelfth-century pieces, for instance: “ Regi regum glorioso" (Lucca,
Biblioteca Capitolare, MS 603. f. 256r); 6７ "Rex immense" from the Codex
Calixtinus; ** “ Arce siderea," "Omnis curet" and "Virga lesse floruit"
from the Aquitanian repertoire; and "Regis cuius potentia” from Cambridge,
University Library, MS Ff. i.17. This can also be seen in Example 8, which
presents "Hoc in solemnio," read directly from the Cambridge M S .
Ornamental and passing seconds are found, for
instance.
ユニゾンへのappoggiatura
としての長二度は12世紀の非常に多数の作品にみられる。（略）
These findings are in accordance
with Johannes dc Garlandia's remark that accented dissonance may be
employed “ for the sake of musical color.” as when a tone precedes a
perfect consonance. 7３
こうした例は、 Johannes dc Garlandiaの「アクセントがある不協和音は、音程が協和音に先立つ時に、音楽のカラーを生み出すために使われる」という命題に結びつく。
While
major seconds followed by thirds are common, minor or major seconds
resolving into a fifth also occur. Theodore Karp has coined the expression
“ compression
dissonance" to refer to the progression from a
minor or major second to a perfect fifth, which he found quite
characteristic of the St. Martial and Compostela repertoires both in
note-against- note and in more florid textures. 74
74 Karp, The Polyphony of Saint
Martial, p.
184.
The
second resolves into a fifth, for instance, in “Noster cetus”/ “ Ad
superni", from the Aquitanian and Compostela repertoires: “ Ave virgo
singularis” from the Norman-Sicilian MS Madrid, Biblioteca National, 19421
(written ca. 1200); and the Notre-Dame clausula Tamquam no. 4 (in
which parallel seconds occupy a whole beat).
Aquitanian と
Compostela のレパートリーである“Noster cetus”や“ Ad
superni",あるいはノートルダム楽派のにTamquam no.
4等において、こうした解決法（短・長二度→完全五度）が見られる。
" Parallel seconds are exceptional
in the twelfth and early thirteenth century; they can also be seen in the
Aquitanian “ Matur dei salus dei” , over paris is and the
Cistercian discant “Nicholai sollempnia” (Example 3 above), discussed
later in this paper.
平行二度は12世紀や13世紀初頭においては例外であるが、Aquitanianの “
Matur dei salus dei”や、シトー派のディスカント “Nicholai
sollempnia”においてもみられる。
It should also be remarked that seconds make
their appearance in the earliest examples of three-part writing: a
previously unreported remake of Guido's example “ Miserere mei” (the
beginning of which is transcribed as Example 9) in Karlsruhe, Badische
Landesbibliothek, MS 504, written ca. 1100; the colophon “Cormacus
scripsit” in an Irish Psalter now in London (British Library, MS Add.
36,929); n the conductus “Congaudet catholici” , by the Parisian Master
Albertus, in the Codex Calixtinus;and “ Verbum patris” from the Cambridge
songbook. x"
”二度”が初期の３声作品にも出現することに注目すべきである。（以下略）。
Anselm
Hughes's analysis of simultaneities in the Codex Calixtinus gives around
5% of seconds, a percentage which is half that found in the
eleventh-century Chartres fragment. 81 Jens Bonderup’s reckoning of
seconds in note-against-note Aquitanian polyphony gives a still lower
number: 2.6%. ８1 Hughes. “Music in the Twelfth Century". 298f. Hughes
gives the figure 4.6%, taking into account both the pieces in the Codex
Calixtinus and two Spanish pieces, but then he states that no seconds are
found in the latter, which implies that their percentage in the Codex
Calixtinus alone is higher than 4.6%.
In spite of the fact that, in the
Aquitanian and Compostela repertoires, the second is clearly more frequent
than the sixth83, these figures confirm that in
the twelfth century, the second has lost its earlier consonant status.
83 Karp. The Polyphony of Saint
Martial, pp. I85f.
こうした事実にもかかわらず、Aquitanian and Compostela repertoiresにおいてはあきらかに、二度は六度よりも頻繁に出現している。こうした形態は、12世紀中に、”二度”は以前の協和音としての地位を失ってしまった、ということを意味する。
There
are. however, exceptions. The Cambridge MS includes a refrain. "Ore del
chanter." in which seconds represent about a third of the intervals formed
against a drone. The style is basically identical to that found today in
the Val di Resia, Udine, in North-East Italy (Example 10). 84 84 Cambridge
University Library. MS Ff. i. 17, f. 4v. For ease of comparison, the
drone-polyphony from the Val di Resia is presented schematically and in
transposition. My two reductions are based on transcriptions presented by
Agemennone and Facci, “II cantare a coppia,” 339f. (tr. 10: Canto di nozze
“Tavana Ruscina”) and Merku. “Polifonia primitiva.“ p. 351 (“Ore li triji
krajave”, A2).
しかしながら、例外もある。Cambridge MS は refrain "Ore del chanter."を含んでいるが、そこにおいては、”二度”はドローンに対しては１/３くらいを占めているのである。そのスタイルは、基本的に、今日において、Val di Resia, Udine, in North-East Italy中のそれと同定されている (Example 10)。
In the early thirteenth century, the author of
Discounts positio vulgaris speaks of the second as the most dissonant among intervals. Later, Johannes
de Garlandia classifies the major second as a “ middle” dissonance, that
is, a more-or-less tolerable discord.Franco speaks of the whole tone as
an “ imperfect discord." a tolerable dissonance.
13世紀初期において、Discounts positio vulgaris の著者は、”二度”に関して、あらゆる音程のうちで、もっとも不協和音的、と述べている。後に Johannes de Garlandiaは、長二度を”中間の”不協和音に分類している。すなわち、ある程度は耐えられる不協和音、ということである。Francoは、whole tone(長二度）を不完全な不協和音、耐えられる不協和音、としている。
As a matter of fact, in the
thirteenth and fourteenth centuries, conservative musicians or genres
continued to allow, in certain contexts, the use of the major second. For
instance. Anonymous IV states that “if the penultimate is a whole tone in
the duplum above the tenor as in organum purum, it will be
excellently concordant, although a whole tone is not a concord."
実際、13〜14世紀においては、保守的な音楽家や分野は、長二度の使用を、音楽内容において、容認していた。たとえば、
Anonymous IV は、「もしもtenor上のduplumの終わりから2番目の音がorganum
purum（オルガヌムの対旋律）として長二度であるならば、長二度は協和音ではないだろうが、きわめて協和する音程として響くだろう、と述べている。
In
the conduclus “Verbum bonum et suave,” 'several syllabic simultaneities of
second are also allowed. In the early moteｔs, major and minor seconds
leading to the fifth are relatively frequent. In the fourteenth century,
the second is used as an appoggiatura in the trope “Ad honorem marie
virginis" (Benevento, Biblioteca Capitolare, MS VI-37). ‘
conduclus “Verbum bonum et suave,においては、"二度”におけるいくつかのシラブルの同時性は許容されている。初期のモテットにおいては、完全五度へと解決する長短二度は、比較的数多い。14世紀では、”二度”は“Ad
honorem marie virginis"において、appoggiatura として使われている。
In Italy, archaic styles survive among the Franciscans: seconds arc conspicuous, including at the start of a poetic line and in parallel movement, in the invitatory “Regi que fecit opera" in Assisi. Biblioteca Comunale. codice no. I (written around 1400).
III. 2. 2.
The Status of Thirds and Sixth In the examples included in the
ninth-century treatises Musica Enchiriadis and Scolica Enchiriadis. the
major second and the major third are the most common, even if
transitional, intervals. ” In the eleventh century, chains of three to
four thirds are found in the Chartres fragment, where the third is the
prominent interval (28%). Chains of up to twelve parallel thirds are found
in the Saint-Martial polyphonic versus copied in Paris. Bibliotheque
Nationale, lat. ９０９); the third is often used to start a phrase. Fourteen
thirds in a row are found in the Aquitanian conductus "Scnescenti
mundano.”
Sixths were
sparingly used in the eleventh century: in the twelfth century, they were
adopted together with the thirds as transitional sonorities, but were used
less often. Around 1100, the Montpellier tract presents three thirds in a
row. But thirds represent already less than 12% of the harmonic intervals
in note-against-note texture in the Aquitanian repertoire99. They
will be more and more regarded as imperfect concords, good only to add
variety and prepare unisons and Fifths. 99 Bonderup, The Saint Martial Polyphony, p. 82. Karp.
The Polyphony of Saint Martial. Appendix A. gives some more
statistics. Typically, in the three Aquitanian MSS analyzed, the interval
content of successions of three or more notae simplices in both the
vox principalis and the vox organalis includes around 9.5% of thirds. In
Paris. Bibliotheque Nationale, lat. 3549, 15% of the simultaneities
produced when two or
more notae simplices are set by an equal
number of binariae
are thirds.
"六度”は、1１世紀には、控えめに使われた。12世紀になると、伝統的響きとして、”三度”とともに、使われるようになった。しかし、それほど頻繁にではない。1100年頃、
Montpellier tractは、三つの”三度”を一列に扱っている。しかし、"三度”はすでに、Aquitanian
repertoireのシラビック形式のharmonic intervalのうちの12％以下しか占めていない。
99 vox principalis とthe vox
organalis両方において、３またはそれ以上のnotae
simplicesの連続したintervalの内容では、だいたい９．５％の”三度”が含まれている。Paris. Bibliotheque
Nationale, lat. 3549写本においては、２またはそれ以上のnotae simplicesが同じ数のbinariaeによってセットされた場合、同時に出来上がる"三度”は15％ある。
変化を付け加えたり、完全五度やユニゾンへ解決していく傾向のみのために、それらはますます不完全音程とみなされるようになるだろう。
Older
practices, possibly rooted in folk traditions, nonetheless survive all
over Europe. Anonymous IV states that “among the best composers of organum
and for example in certain lands like in England, in the region which is
called Westcuntre. [the major third and minor third] are called the best
concords, since among such people they are greatly used." An English
example from the late twelfth century that includes successive thirds
obtained by contrary motion is "Adjuva nos
deus.”
民謡的伝統にもとづくより古い演奏は、ヨーロッパ中に生きている。Anonymous
IVは、「オルガヌムのもっともよい作曲家の間で、そしてたとえばＥｎｇｌａｎｄのような島においては、Westcuntreと呼ばれる地域において、長三度や短三度は、もっともよい協和音程であるとされていた。なぜなら、こうした人々の間では、こうした音程がしばしば使われていたからである」と述べている。反行する動きによって連続三度を含んだ12世紀後半の英語の曲の例として、"Adjuva
nos deus.”がある。
The phenomenon is not. however, specifically
English. From around 1200. the Catalonian conductus “Cedit frigus hiemale"
and the Notre Dame “Salvatoris hodie" also present successive thirds.
“Salvatoris Hodie" and “Amborum sacrum.” from the Cambridge songbook, use
sustained sixths (Example 11).
こうした現象はしかしながら、何も英国だけのことではなかった。1200年頃より、カタロニア語のconductus “Cedit frigus hiemale" とノートルダム楽派の “Salvatoris hodie" にもまた、連続3度が見られた。“Salvatoris Hodie" と “Amborum sacrum.” from the Cambridge songbook, は、連続六度を使っていた。
In
the thirteenth century, short successions of thirds are found, for
instance, in the Gloria trope Spiritus el alme entered in Evreux,
Bibliothcque Municipale, lat. 17; in the two-voice Credo copied in the
early fourteenth century MS Bologna. Civieo Museo Bibliografico Musicale Q
11 and the piece “Virgo solamen desolatorum” copied in Assisi. Archivio
della Cattedrale. codice no. 5. Five sixths in succession can be found in
the English song “Foweles in the frith."But the most striking example of
parallelism - a succession of twenty-four thirds in the hymn
“Nobilis,humilis" - comes from a late thirteenth-century Norwegian MS in
Uppsala.
13世紀においては、短い連続三度が見つかる。（略）。５つの連続六度が英語の歌“Foweles in the frith."において見られる。しかし、なんといっても、連続三度のもっとも典型的な例は、ウプサラ写本にある、hymn
“Nobilis,humilis"である。この曲はなんと、２４連続の三度が続くのである。
Foweles in the frith
Nobilis humilis magne martir
In the theoretical tradition, thirds are admitted at beginnings and middles in the post-Guidonian Berlin B and Montpellier treatises. Later, the third is generally classified as an imperfect concord (in Dahlhaus definition. “ an unstable, dependent consonance supported by an adjoining fifth or unison"); "or. in the case of the tract Discantus positio vulgaris (early thirteenth century) and Marchetus de Padua (early fourteenth century).
as a tolerable discord.
理論的伝統において、”三度”は曲の最初と中間で認められていた。後に”三度”は一般的には不完全協和音程として分類されるようになった。Dahlhausの定義でいえば、「完全五度やユニゾンに接している、不安定で独立していない協和音」ということである。あるいはまた、13世紀初期の論文Discantus positio vulgarisと14世紀初頭のMarchetus de Paduaにおいては、耐えられ得る不協和音として。
As Carl Dahlhaus also points out. “ in the Middle Ages, the determination
of whether thirds and sixths were consonances or dissonances was a problem
that did not admit of an unequivocal solution |...| One could either classify
thirds as dissonances, though they were permissible as simultaneities,
because they did not represent any superparticular numerical proportions;
or one could express the euphony of thirds by the word ≪consonance≫,
but their mathematical imperfection and the lack of autonomy of their sonority
by the additional word ≪imperfect≫” .
Carl Dahlhausはまた、以下のようにも主張している。「中世においては、三度と六度が協和音程なのかあるいは不協和音程なのかという決定は、はっきりとした解決に導かれるべき問題なのである。ある人は、同時に響いて許容され得る範囲ではあるが、”三度”を不協和音として分類する。なぜなら、それらはsuperparticular
numerical proportionsを代表せず、あるいは、ある人は”協和音”という言葉によって三度の心地よさを表現するかもしれないが、他方ある人は、付け加えられた”不完全”と言う言葉によって数学的不完全性や音の自律性の欠如を表現するかもしれない。
Anonymous of St. Emmeram defends the consonant status of the third on
the basis of musical practice: the major or minor third often starts, or
is found in prominent places in both organa and French motets. In the fourteenth
century, the transitional character of the third and sixth is reaffirmed
by Anonymous X III. who nevertheless allows their sonority to be extended
in parallel motion until it reaches a perfect consonance (fifth or octave).
Successions of thirds are also allowed in other treatises.
Anonymous of St. Emmeramは、音楽活動のベースの上に、”三度”の協和音的状況を守った。長短三度は、しばしば、オルガヌムやフランス語モテットにおける目立った場所で見つかるものである。14世紀においては、三度と六度の伝統的な性格は、こうした響きが完全五度やオクターブにまで到達するまで平行で動くことを許容したAnonymous
X III.によって再確認された。”三度”の継続性はまた、他の論文でも許容されている。
Sixths were admitted as imperfect consonances already in the Montpellier tract. In the twelfth century, minor sixths are said by Theinred of Dover to be more frequent than major sixths, because of their closer proximity to the consonance. During the thirteenth century and the first half of the fourteenth century, minor sixths were often, but not always considered to be more dissonant than the major sixth. 117 This has probably to do with the importance of the. then standard, progression of major sixth to octave (in the twelfth century, the major sixth could occur as a passing sonority within the progression of fifth to octave, but was not integral to it).
117 For instance. Anonymous I (Coussemaker. Scriptorum. I: 296-302) considers together the major and minor sixth as imperfect discords, but Anonymous II (ibid., 30319) gives the major sixth the status of an imperfect consonance. See also Richard L. Crocker, “ Discant, Counterpoint, and Harmony." Journal of the American Musicolof>ical Society XV ( 1962). 3-8. reprinted in The Garland library, pp. 29-49.
”六度”は、すでにMontpellier tractにおいて不完全協和音程として認められていた。12世紀には、協和音程に対するそのより近い親和性のために、短六度はTheinred
of Doverにより、長六度よりも使用頻度が高いと言われていた。13世紀を通して、そして１４世紀前半期に、短六度はしばしばしかし、必ずしもいつもではなく、長六度よりも不協和音的であるとされてきた。これはおそらく、長六度からオクターブへの進行の重要さに関係があるからであろう。12世紀においては、長六度は、意図的にではなく、完全五度からオクターブへの進行途中に出現するものと考えられていたのである。
III. 2. 3. The Status of the Perfect
Fourth
Around the year 1000, the fourth is the prevailing organal interval in the Winchester repertoire. In the first half of the eleventh eentury, the Paris treatise and Guido's Micrologus confirm that the perfect fourth was considered to be a primary consonance, and tended
to be preferred to the fifth. In the Chartres fragment, it accounts for 20% of the total number of intervals, while the fifth
occurs less than a third as many times.
Ｉn the two-voice version of the Alleluia "O quant pulchra est” as found in the early twelfth century codex Autun. Bibliotheque de la Ville, MS 46 (olim 40 B), the fourth is the most frequent consonance, closely followed by the octave and the unison; the fifth and the sixth occur just over half as many times. In the two-part "Regi rcgum glorioso” from Lucca, the fourth is still the most frequent interval, but the fifth comes next, two-thirds as frequent.
12世紀初期のcodex Autun. Bibliotheque de la Ville, MS 46 (olim 40 B)にあるAlleluia
"O quant pulchra est” の２声版において、完全四度は、オクターブやユニゾンへと収束していく、もっともしばしば出現する協和音程であった。完全五度と六度はちょうど全部の音程の半分を占めていた。Ｌｕｃｃａ写本中の２声部の"Regi
rcgum glorioso”においては、完全四度はさらにより多い音程となっていた。完全五度がそれにひき続き、長短三度もしばしば出現した。
From the late eleventh century onwards, the fifth is granted an equivalent position to the fourth, and in the twelfth century, the use of the fourth declines drastically: in note-against-note texture in the Aquitanian repertoire, it accounts for a third as many intervals, at most, as the fifth, 123 and tends to be handled as a relatively unstable, secondary consonance;
together, the octave and especially the fifth assume the role of structural
consonances. This may be related to the fact that parallel movement in
fifths (fifthing) was widely adopted, probably as a basic technique for
training singers of polyphony, already before the thirteenth century. Occasionally,
the fourth manages to play a structural role, but this becomes rarer in the thirteenth century.
123 According to Bonderup, The Saint Martial Polyphony, p. 82. the fourth represents only 8.5% of the intervals against 35% for the fifth in note-against-note texture. The comparable figures given by Karp, The Polyphony of Saint Martial, pp. 202f. differ only slightly: in successions of three or more single notes in both voices, the fourth and the fifth represent respectively around 11 % and 33% of the total number of intervals. The total percentage of fourths in the twelfth-century Spanish sources analyzed by Hughes, "Music in the Twelfth Century.” amounts to 12.5%. against 26% for the fifth.
そして完全四度は、比較的不安定、かつ二次的な協和音程として扱われるようになった。それに伴い、オクターブやことに完全五度が、構造的に協和音程の役割を担うようになっていった。こうしたことは、完全五度の平行が広く受け入れられ、すでに13世紀前に。おそらくは（それを歌うことが）ポリフォニーを歌う歌手にとっては基礎的なテクニックであるという事実に関係している。ときとして、完全四度は楽曲の構造的役割を担っていたが、しかし、13世紀にはまれなこととなっている。
126 For instance, in Leonin's discant on Dominus partially reproduced by Richard L. Crocker, A History of Musical Style (New York: Dover Publications. 1986). p. 78.
The practical demise of the fourth is hardly acknowledged in the theoretical
realm before the fourteenth century. To be sure, the fourth is regarded
by the Lafage Anonymous as less consonant than the fifth; and the Discantus positio vulgaris treatise includes it in a completely different category, that of the intervals
which are rather more dissonant than consonant. ' The privileged status
of the fourth in the Pythagorian tradition. however, due to the perfection
of its corresponding proportion (4:3), allows it to be classified together
with the fifth as a "middle” (next-to- basic) consonance in the teaching
of Johannes de Garlandia and other thirteenth century theorists. In the
fourteenth and fifteenth centuries, a number of authors classify it as
a dissonance. '* In actual musical practice, the fourth is in fact treated
as a dissonance between the lower voices of a wor- ked-out three-part composition:
in the second half of the fifteenth century, it is sometimes avoided as
a dissonance between any pair of voices. 1,1
The privileged status of the fourth in the Pythagorian tradition. however,
due to the perfection of its corresponding proportion (4:3), allows it
to be classified together with the fifth as a "middle” (next-to-
basic) consonance in the teaching of Johannes de Garlandia and other thirteenth
century theorists. In the fourteenth and fifteenth centuries, a number
of authors classify it as a dissonance. In actual musical practice, the
fourth is in fact treated as a dissonance between the lower voices of a
worked-out three-part composition: in the second half of the fifteenth
century, it is sometimes avoided as a dissonance between any pair of voices.
４：３のその比に拠っているピタゴラスの伝統を担う完全四度の威厳的地位は、”中間の”協和音程として、Johannes de Garlandiaやその他の13世紀の理論家たちが教えるところにおいては、完全五度と一緒に分類されることを許容されてはいるが、14〜15世紀になると、多くの理論家は完全四度を不協和音とみなすようになった。実際の音楽の実践においては、完全四度は、上等な３声作品のより低いパート間の不協和音程を担うようになった。15世紀後半（訳注；ルネッサンス期の始まり）においては完全四度は、声部間の関係としては不協和音程であり、避けられるべき存在となってしまったのである。
III. 3.
Conclusion
In the Arouca hymn, the major second is not quite used as a secondary
consonance, as in the eleventh century, nor is it avoided as a just-sufferable
dissonance, as it tends to be in the thirteenth. The third seems to retain
the position enjoyed throughout the eleventh century, a position which,
exceptions notwithstanding, seems to have been reaffirmed only from the
fourteenth century onwards.
The fourth is not the basic consonance, as in the eleventh century, nor has it clearly fallen into disfavour, as after the mid-twelfth century. The fifth is not just an alternative primary consonance, as in the eleventh century, nor is it central to the compositional process, as afterwards. The octave is not completely non-existent, as in the early eleventh century, nor is it a structural interval, as in the late twelfth and thirteenth centuries.
Besides the intervallie structure, the Arouca hymn has other interesting
characteristics: the crossing of voices having an equivalent compass; and
the use of voice-exchange technique. The technique of exchanging strains
between the two voices is found in a number of pieces from the Aquitanian
repertoire, including the early "Noster cetus" and "Deus in adiutorium"、 from where it was introduced in the Calixtinus repertoire (“ Ad superni” = "Noster cetus” ) and twelfth century hymnody (“Jam lucis orto sidere” “ Deus in adiutorium"). Later, the technique reappears in northern France (Notre Dame three or four-part organa, two-part conductus. and. outside
Paris, the sequence “ Ave, Virgo" in the Rouen gradual)、 Castile (several “ Bcnedicamus domino" in Las Huelgas) and especially Fngland. "*
音程構造はさておいて、Aroucaヒムは他の興味深い性格も持っている。声部の交叉は相当な幅を持ってなされている、そして声部交換のテクニックもある。そのテクニックは、初期の
"Noster cetus" and "Deus in adiutorium"を含むAquitanian
repertoireの多くの作品において、 Calixtinus repertoire、12世紀のhymnodyにおいて認められる。後にこのテクニックは北フランスやイングランドでも再度見られるようになった。
In conclusion, the style of the Arouca discant corresponds to a transitional
stage that could be chronologically situated around the first third of
the twelfth century, the time when the Cistercian identity became fully
established. This style was already about four generations old when the
hymn was presumably composed. It is, then, a retrospective style that asks
to be understood not in the context of thirteenth-century music, but rather
in the context of the Cistercian conservative ideals.
（略）
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