|Posted on August 16, 2012 at 1:40 PM|
As stated in RobertCogan and Pozzi Escot's enlightening book, SonicDesign: "The European tonal system . . . has been regarded by itstheorists, from Rameau to Hindemith, as a natural order. Certain of themproclaimed the eighteenth and nineteenth centuries as the 'common-practice'period, an astonishing conception when one compares its two centuries of commonideals, with the proceeding thousand years of the European modal system, not tomention the several millennia of the Indian raga systems. Since it ignoredthese, as well as the music of other cultures, and cannot apply to thetwentieth-century music of the entire world, how common can it be?"1
Constructing aseven-note scale by using a series of successive intervals of a fifth, iscommon in the history of music. It has been the basis for scaler structure frombefore Pythagorean times (c. 550 B.C.E.) to the present (The Lydian ChromaticConcept). Examples of this can be found in the music of Eastern civilizations.Slabs of stones, used as instruments tuned in sets, are still found in China,Korea, and Samoa. The Chinese sets were originally tuned by a Pythagorean-likesystem several hundred years before the "Pythagorean school"developed in Greece.
Chinese musicaltreatises from the eleventh through the sixteenth centuries were consistent indescribing the use of a cycle of fifths for scale construction. Theeleventh-century Chinese (Sonq Dynasty) treatise, Twujih, by Roan Yih and Hwa Yuan, explains in detailed terms theuse of a fundamental tone, over which a scale of twelve semitones is producedby a cycle of fifths. It was this same process that was used by Prince Ju TzayYeh (1596) in an early form of the equal-tempered scale.
Two hundred yearsafter Twujih, Chern Yuanjing includeda circular diagram in his ShyhlinGoangjih, (c.1270), assembling the twelve semitones of a chromatic scale bymeans of a succession of fifths. He explained that by doing so, the basicscale, "gong-diaw" (C,D,E,F#,G,A,B) was obtained. According to the Shyhlin Goangjih, any note of the scalecould serve as the "tonic" of a melody, and a mode was defined bythis tonic pitch on which the scale was constructed. Because there were twelvepitches in that chromatic scale and seven notes in each basic scale,eighty-four modes were theoretically possible.
Both the traditionalmusic of Japan and Hindusthani music are based on scales derived from a seriesof fifths. The two basic scales in Japanese music are the Ryo (D,E,F#,G#,A,B,C#) and the Ritsu(D,E,F,G,A,B,C). They coincide with a D Lydian scale and its"parallel" Lydian minor scale (on the sixth degree of F). In the bookHindusthani Music, An Outline of ItsPhysics and Aesthetics, author, G.H. Ranade states that, ". . . eversince the days of the sage Bharata (prior to 300 B.C.) it was a wellestablished practice to obtain the various notes of the scale by a chain ofsuccessive fifths."2
The question arisesthen; if these ancient and advanced cultures derived scales from successions offifths to arrive at what we refer to as Lydian scales, why did Westernmusicians move so predominantly toward the major-minor scale system?
Leonard Meyer in hisbook Music, The Arts, And Ideas,discusses the idea of teleology inmusic.3 Teleological music, in thissense, refers to "goal-oriented” music (comparable in part, to Russell’sidea of Horizontal Tonal Gravity) that represents the large majority of Westernmusic (referring to European and European-influenced music). By reflecting thebasic philosophy of goal-orientation, the major-minor scale system (a resolvingor Horizontal idea) is manifested. It seems logical then, that Zen and otherEastern philosophies, which refer more often to a vertical, a blending, non, orat least less, goal-oriented idea, should originate in cultures reflecting thisthought in musical scale choice.
The choice of themajor-minor scale system is completely consistent with the teleology, andtechnologically-oriented Western mind. It is a mind set of the Written Tradition. The phenomenon of tension and release,goal-oriented organized Western religion and philosophies, climbing the socialladder, getting ahead, planning for tomorrow; all fit easily with WesternEuropean music, the music of the commonpractice era. Would music based uponthe idea of modality structured on the scale derived from a series ofsuccessive perfect fifths, assuming the lowest of that series as tonal or modalcenter, the fundamental, have a different sound? Would a music coming from amore vertically-oriented philosophy and culture lead to a different musicalphilosophy?
William Thomson, inhis in-depth article Emergent‘Dissonance’ and the Resolution of a Paradox, discusses and questionsnumerous ideas regarding the perfect fourth as it has been perceived throughmusic history, from consonance to dissonance.4 He points to the Grove’s Dictionary definition of Dissonance. A discord, or any sound which, in the context of theprevailing harmonic system, is unstable, and must therefore be resolved to aconsonance. Perhaps those changesare in direct relationship to the contrast of fundamental approach to scalerconstruction; the use of the subdominant, and, the continuing perfect fifthsabove a fundamental.
Examples of Westernmusical thought regarding the construction of the Pythagorean scale, resultingin the major scale, are discussed below. In both instances, the resultant(major scale) appears to have been reached by manipulated means. The methodsused in each example (varied from that used in the previous examples) seem tohave been guided toward the desired end the major scale.
John Backus explainsthe construction of the Pythagorean scale in his widely used (and certainlyauthoritative) book, The AcousticalFoundation of Music. Beginning on the pitch C, Mr. Backus progresses to aperfect fourth above (to F), moves back to C, then proceeds by fifths: G,D,A,E,and B to "...avoid black notes...”5 Black notes only come into play, of course, with keyboards. The idea of subdominant is acceptable andwith great purpose in Western music. Itcertainly proceeds the use of black and white notes on a keyboard.
A second example isfrom the Harvard Dictionary of Music,edited by Willi Apel in which the Pythagorean scale is described as a"diatonic" scale with one fifth below the fundamental (C to F),followed by five fifths above (C down to F, then C,G,D,A,E,B). This group ofpitches is combined to form a scale within one octave; the resultant scalebeing a major scale on C (C,D,E,F,G,A,B).
By examining thesetwo examples, one might ask the question; if a real construction of a series ofsuccessive fifths has occurred, is the pitch F not the true fundamental and theF Lydian Scale (F,G,A,B,C D,E,) the resultant as supported by the Easterntreatises? The two differinginterpretations offer the possibilities of Horizontal (major and minor tonalsystem) and Vertical (Lydian and modal system).
Historically, thereis evidence describing sources of influence which led Western musicians in thedirection of the resolving major scale. Along with the idea of teleology wasthe powerful influence of the Christian Church. The Church influenced much ofthe music from well before the eleventh century to the eighteenth, when thatinfluence began to diminish. By the tenth century, after many centuries ofdevelopment, the Church recognized eight modes:
AUTHENTIC MODES PLAGALMODES
and relative pitches
d, e, f, g, a, b, c a, b, c, d, e, f,g
e, f, g, a, b, c, d b, c, d, e, f, g,a
f, g, a, b, c, d, e c, d, e, f, g, a,b
g, a, b, c, d, e, f d, e, f, g, a, b,c
The final (similar to tonic) note for eachof the Plagal modes was that of the corresponding Authentic mode (example boththe Phrygian and Hypophrygian had finals of E.The Plagal mode was constructed on the pitch a perfect fourth below the finalnote of the Authentic mode and considered to be grouped in a pair with thecorresponding Authentic mode. Modes built upon notes equivalent to A, B, and C, while appearing in practice for centuries, were not recognizedby theoretical treatise until the middle of the sixteenth century (1547) whensystems of twelve modes containing the Ionian, Hypoionian, Aeolian, (later thenatural minor scale), and Hypoaeolian were described by Glareau. Previously,modes of this nature were used often and constructed when notes were altered atcadences and to avoid the tritone by means of "musica ficta"(accidentals added by performers). As the practice of avoiding the tritone(occasionally referred to as the Devil'sinterval) particularly in choral music, was common and offered associationwith the declaration of "impurity,” the use of modes containing theperfect fourth were given an added emphasis. Of course, this also was connected to the growing popularity of usingthe perfect fourth above the final/tonic in a decorative, passing way with theperfect fifth above, and later, to the Dominant 7th chord.
This time period(1547) coincided with the formation of the Council of Trent. This body of high-ranking clergy within the Roman Catholic Church, met on an irregular basisbetween 1545 and 1563, and was responsible for the establishment of a reformedMass. The Council was formed out of a need for "purifying" and desecularizing the sacred service, as dissension was rising from England,Germany, The Netherlands, and other European areas within the realm of the Roman Catholic Church.
In exploring thefoundation upon which certain scales are founded,we discover, as Mr. Russellpoints out, that the Lydian Scale is based on a series of successive fifths andto a degree, on the overtone series. It is the product of a physically naturalacoustical phenomenon. The naturalness of the Lydian Scale is confirmed too, bythe symmetry of its construction. By including the sharped fourth, the exactcenter-point of the octave interval is present (C to F# is an interval of threewhole steps; from F# to C is also three whole steps).
Perhaps the logic of using the major and minor tonal system as so exclusive a foundation of ourtheoretical and compositional approach to music, is questionable. Evidence ofthe fact that advanced cultures took the circle of fifths as the basis forscaler structure, deriving differing and beautifully valid scale results, isnumerous and strong. By inclusively attuningourselves to other cultures and musics; their origins and philosophies, webecome aware of the some of the associations between the Lydian Scale andnatural symmetry and order.