of the Medieval Ideal of Music as Rational
By Joseph J. Mullen
The Rational Musical Scale
Guido D’Arezzo, also known as Guido the Monk is the man who not only innovated music by introducing the solmization syllables used to this day for the reading and understanding of music. He also, by inventing the musical staff, transformed the art of music from an aural/memory based tradition to a literary one. As Dr. Thomas Forrest Kelly acknowledged in his book on Medieval musical notation ‘Capturing Music:’
“With a single stroke Guido achieved one of the simplest but most radical technological breakthroughs in the history of writing music: he made it possible to sing a song you have never heard before!” 
He also summarized and clarified for the medieval man the ideal of the musical scale as rational, as put forth in his foundational work on choir pedagogy “Micrologus” in the 11th century. The Micrologos also goes into great detail on what is known as the “liberal art” of music. Guido demonstrates how to construct the musical scale on the mono-chord. The musical scale is based on the pure ratios of 1:1 (unison), 1:2 (octave), 2:3 (perfect fifth), 3:4(perfect fourth) and 8:9 (major second).
Micrologos is not only a foundational work on music theory but also on composing simple organum. It is, along with the works of Boethius, a seminal work on western musical theory. It was dedicated to Theodaldus, the bishop of Arezzo, and was written in regard to the education of choir boys for singing in the liturgy.
The medieval ideal of music was that of the pure ratio. The word rational is derived from ratio. The ability of man to abstract concepts from his memory by means of the agent intellect and to recognize a one to one (ratio) relationship with reality is the very definition of rational being.
The solmization syllables of Guido were: ut, re, mi, fa, sol, la and were taken from the divine office hymn “Ut queant Laxis.” A hymn to St. John the Baptist as sung on his feast day; the 24th of June. The six notes of his scale have come to be known as the hexachord. His system of rational music was actualized in seven overlapping hexachords. The first note of his system was the Greek letter gamma. ( Γ )  The Guidonian solmization of this note was the syllable “ut.” Thus the term “Gamut” was used to describe not only his scale, but also has come to mean any hierarchical scale, stepwise construction or completion in a discipline or body of knowledge.
Thus the music of the Gamut was rational, that is, built on pure ratio and recognized as harmonic parts of the whole. These parts had due proportion or beauty. The mind could abstract the universals of proportionality, beauty and hierarchical order and recognize them in the rational musical scale as defined in the Gamut of Guido. Thus it was considered rational or “true” music because it was part of Guido’s Gamut. 
The western understanding of rational proportionality is the foundational principle upon which the entire western musical tradition originated. The development of the medieval rudimentary polyphony of Guido to that of the Renaissance ideal of Palestrina were not contrary in essence. They were one in perfecting the understanding of the nature of music as rational. Palestrina was the culmination of the tradition that began in the medieval ideal of a rational musical scale. This scale or framework was the structure upon which the liturgical chant and polyphony of the Catholic Church was built. As Knud Jeppeson summarized in his work “ The Style of Palestrina and the Dissonance:”
Palestrina’s “works might appropriately be called a vast summary of the musical development of the preceding centuries. In them are united all the various currents,–some that spring from sources in a deeply-buried past, traceable through the more primitive phases of polyphony back to the Gregorian age.”
The musical staff, invented by Guido, and the rational scale are the material causes upon which the various forms of polyphony developed. Using these material causes composers through the Middle Ages and early Renaissance perfected the polyphonic form. The culmination of this high art was particularly manifest in the works of Giovanni Pierluigi da Palestrina. In his work “Music in the History of the Western Church” Edward Dickinson states:
“The contrapuntal chorus music of the Middle Age reached its maturity in the middle of the sixteenth century. For five hundred years this art had been growing, constantly putting forth new tendrils, which interlaced in luxuriant and ever- extending forms until they overspread all Western Christendom. It was now given to one man, Giovanni Pierluigi, called Palestrina from the place of his birth, to put the finishing touches upon this wonder of medieval genius, and to impart to it all of which its peculiar nature was capable in respect to technical completeness, tonal purity and majesty, and elevated devotional expression.
Palestrina was more than a flawless artist, more than an Andrea del Sarto; he was so representative of that inner spirit which has uttered itself in the most sincere works of Catholic art that the very heart of the institution to which he devoted his life may be said to find a voice in his music.”
One of the ways in which the style of Palestrina was perfected was that it lived completely in the rational bounds of the Gamut. His beautifully tempered chromaticism was the harmonious servant of the rational proportional scale of Guido. In a musical display of the virtue of temperance, never is there found in his music a disordered chromatic novelty, either in melodic line or harmonic structure. Again Jepperson states:
“The use he makes of chromatic alterations does not substantially exceed what was valid in plainsong.”
It always served the rationality of the proportioned scale. Jepperson:
While “madrigal writers were employing chromatic notes in their eagerness to lend new life and brilliancy to music, Palestrina alone stood firm and steady in the midst of all these currents. He knew his own mind and was but little concerned for chromatic alterations”
In his music we have a reflection of a virtuous soul who composed for the glory of God and the pious edification of his neighbor. Its appeal is to the intellect and soul of man.
A Mirroring of the Rational Mind
It seems to me that one of the most profound attributes of the Catholic polyphonic style, developed through medieval simple harmony and perfected by Palestrina, is that of imitation. Gioseffo Zarlino, a Renaissance composer and well known theorist of the day, in his book “L’istitutioni harmoniche” describes imitation :
“in this type of melody what is consequently sung can be repeated by another.”
According to Zarlino “Fugue, imitation and consequence” are the three specific types of imitative devices that a composer could employ. A detailed explanation of the characteristics of each of these devices does not serve our purpose at this time. Suffice it to say that the imitative style takes the form of musical dialogue.
In Dialogue we have the root of philosophy. The great Brazilian Catholic thinker Professor Plinio Corrêa de Oliveira properly understood it thus:
“ ‘Dialogue’ is used in Socrates and Plato to designate the form of intellectual elaboration that two or more speakers, proceeding by questions and answers, use to distinguish things according to their genus.”
In the works of Plato we see Socrates engaging in dialogue to get to the essence of things. Let us see if we can discover, by means of dialogue, the essence of this music. Its nature as not only rational and dialectical, but we can also see it as a participation in the music of heaven. Take, for example, some of the texts and Gregorian melodies from the Ordinary of the Catholic mass. For brevity’s sake we will consider the Kyrie, Gloria, and Sanctus:
The Kyrie consists of three acclamations, Kyrie eleison, Christe eleison, and Kyrie eleison, each of which is sung three times, so that the entire melody consists of nine distinct phrases. This ancient ninefold plea for mercy’s number is evocative of the nine choirs of angels, whose harmonious echoes fill the heavens. We know from scripture that the angels do indeed plea for mercy:
“And the angel of the Lord answered, and said: O lord of hosts, how long wilt thou not have mercy on Jerusalem, and on the cities of Juda, with which thou hast been angry?” (Zech 1:12)
By its very nature, construction and execution the Kyrie is a call and response in dialectical form. The most ancient of the Kyrie melodies suggest, by their simplicity, a congregational participation and dialogue with the priest. It has perhaps developed from the ancient litanies sung on certain feasts and Rogation days.
Gloria in excelsis Deo is the second item of the Ordinary. It is the Hymnus Angelicus also called the greater doxology. Along with the “Te Deum” it is a chant written like the “Psalmi idotici” that is, non biblical texts in the style of the psalms. The psalms from antiquity until the present day are sung in choir, alternating one side with the other. Again, this is a dialectical unfolding of the psalm and antiphon.
The text “Glory to God in the highest and peace to men of good will,” (Luke 2:14) is taken from the hymn the vast multitude of angels sang on the night of Christ’s birth. Scripture says elsewhere of the glory of God in Proverbs:
“it is the glory of God to conceal the word, and the glory of kings to search out the speech.” (Prov. 25:2)
The concealed “Word,” the Son of God, born lowly and hidden in the stable at Bethlehem enters the world, incarnate to live and converse with men. To “search out this word,” that is: to ponder, dialogue, meditate and contemplate upon Him is the “glory of kings.” Not just the three kings who sought out the hidden word, but every Catholic in the state of sanctifying grace who seeks Him out somehow participates in the kingly nature of Christ.
Again, ideally, when sung in Gregorian chant choral style alternating the phrases from one side of the choir stall to the other, it is evocative of a reciprocal dialectic unfolding which gives a greater understanding and elucidation of the sacred text.
The Sanctus is preceded in the preface of the Mass with a plea to unite our song with that of the angels in heaven. These are the six winged seraph spoken of in the book of Isaiah. It is in the angelic “trisagion” that we have special insight into the dialectical and polyphonic nature of the music of heaven.
In sacred scripture we find:
“and they cried one to another, and said: Holy, holy, holy, the Lord God of hosts, all the earth s full of his glory.” (Isa. 6:2)
“And they rested not day and night, saying: Holy, holy, holy, Lord God Almighty, who was, and who is, and who is to come.” (Rev. 4:8)
From these texts at least two things can be deduced about the nature of the heavenly Sanctus
1. It takes dialectic form: “they cried one to another
2. It is unceasing: “they rested not day and night”
Upon further reflection one may ask, what is the nature of this eternal repetition? Does it forever remain the same in essence as well as accidents? Or are the accidental attributes forever changing to eternally elaborate the holiness of God? Are they repeated one after the other, each awaiting their turn or are they layered in harmonic construction one upon the other? Is it like the snowflake, always beautiful, proportional yet never being replicated? One only needs to ponder the almost infinite variety that is found in the vast creation of our visible world, to perhaps realize that an ever progressive eternal flowering of beauty is congruent with the nature of Almighty God. I suspect, though we have a small glimpse from sacred scripture into the nature of this trifold Sanctus, its real essence has not “entered into the heart of man.” (1 Cor. 2:9, Isa. 64:9)
In the polyphonic choral art of the Renaissance we can see a mirroring of the heavenly style as found in sacred scripture. The style serves and develops the texts of the liturgy. These texts are elucidated and intensified through a dialectical syllogism of musical phraseology. So it is not only a manifestation of the classical ideal of thesis, antithesis and synthesis but much more. Each new idea, as taken by a different species of the human voice, is united to the texts in dialectical development that intensify or magnify the words of praise and pleas for mercy offered unto Almighty God.
This compositional polyphonic style is reminiscent of the classical dialogue of the Socratic method as found in the works of Plato. Yet this dialectical classical ideal, although having a perfection in Socrates, does not find its origin in Greek Philosophy. It is from our creation and built into the human psyche.
Was it not Almighty God Himself in dialogue with Himself who said:
“Let us make man in Our image, according to Our likeness?” (Gen. 1:26)
Who was Almighty God speaking to if not Himself? Is not the image and likeness of God manifested in the immaterial powers of the soul? As St. Thomas affirms:
“Since man is said to be the image of God by reason of his intellectual nature, he is most perfectly like God according to that in which he can best imitate God in his intellectual nature.”
Also he states:
“The image of God, in its principal signification, namely the intellectual nature, is found both in man and in woman.”
Of all mankind, from the highest intellect to the most simple soul, we all participate in this intellectual nature of God to “self reflect.” Our ability to inner dialogue is a light that we have in order to see ourselves as we are.
“In reflection and self-consciousness it [the intellect] turns back on itself in such a manner that there is perfect identity between the knowing subject and the object known.”
This light every man has received from God: “This was the true light which, coming into the world, enlightens every man.” (John 1:9)
This inner dialogue is manifest simply in what every Catholic should know as the “examination of conscience.” What is the subject of the examination if not yourself? Who is doing the examination? Not only does the intellect have the ability to examine itself but it can also examine its own examination as to quality, motive and sincerity. Then it can even examine this examination, which results in a greater striving toward a more perfect knowledge of self in seeking to conform to the image and likeness of Almighty God within the soul. “Be you therefore perfect, as also your heavenly Father is perfect.” (Matt: 5-48)
This example of examination of conscience can be applied to any conceptual phantasm abstracted from the memory by the agent intellect. Whereby one’s awareness can become extraneous to one’s very own thoughts, look back at them and exercise judgment upon them. So in one sense this inner dialogue of self reflecting is a kind of zooming in, if you will. An inner inquiry or magnifying glass whereby knowledge can come to a greater perfection within the soul.
Perfect Example of the Blessed Virgin Mary
What creature better exemplifies this inner dialogue of the soul than the Blessed Virgin Mary? We know from scripture that she:
“kept all these words in her heart” (Luke 2:51)
“kept all these words, pondering them in her heart.” (Luke 2:19)
What is the nature of this inner pondering?
In Sacred Scripture, the book of Wisdom gives us some insight on these “words” and her “pondering them in her heart:”
“When I go into my house, I shall repose myself with her: for her conversation hath no bitterness, nor her company any tediousness, but joy and gladness. Thinking these things with myself, and pondering them in my heart, that to be allied to wisdom is immortality, and that there is great delight in her friendship, and inexhaustible riches in the works of her hands, and in the exercise of conference with her, wisdom, and glory in the communication of her words: I went about seeking, that I might take her to myself.” (Wisdom 16:18)
This passage can plainly be understood as inner dialectic and self reflection:
“pondering them in my heart” (direct reference to the BVM in Luke chapter 2 verses 19 and 51)
“seeking” (inquiry, questioning which implies someone being asked, which implies dialogue)
By this inner self reflecting dialectic the knowledge of the things we ponder is perfected. By inquiry upon inquiry we magnify what is known in order to see it in a more detailed analysis or different perspective. This greater magnification will aid the intellect to specify particulars and resolve conflicts. The Blessed Virgin Mary proclaims the fruits of her inner pondering and reflection:
“And Mary said: My soul doth magnify the Lord. And my spirit hath rejoiced in God my Savior.” (Luke 1:46-47)
If her Magnificat can be understood as an inner dialogue of self reflection toward perfection; the fruits of which are to “rejoice in God” her Savior; then it must follow that we find in her the greatest most edifying example of a Christian soul to be imitated.
In the 1903 Motu Proprio: “Tra le Pius X, Tra le sollecitudini” Pope St. Pius X wrote that the polyphonic choral style had:
“Reached its greatest perfection in the fifteenth century, owing to the works of Pierluigi da Palestrina.”
This perfection was contingent upon the understanding of the rationality of music and the musical scale. This understanding grew out of the ideals that flourished throughout Medieval Christendom.
The Roman polyphonic style, as perfected in the imitative works of Palestrina, is an aurally perceived type of the immaterial power of the human soul to “self reflect.”
This ability to “self reflect” is a participation in the Divine nature. Because this music is structured upon musical dialectics that reflect the divine nature, it appeals to the highest attributes of the human rational mind and soul. It magnifies and elucidates the sacred texts of the Catholic Liturgy that tend toward the contemplation of the good, true and beautiful.
The musical phrases as stated in one voice, then restated in another differing in melodic and rhythmic expression, are one in harmonic union. This union augments, intensifies and magnifies texts of the liturgy. In this dialogue one can hear the echo of heaven. Not a dialogue of argument or polemics but an ever elucidating and unfolding of perfection.
Benetictine monk and medieval musical theorist. Inventor of the tonal solfege and the western musical staff. Otten, J. (1910). “Guido of Arezzo.” The Catholic Encyclopedia. (New York, NY, Robert Appleton Company.
“Solmization. General term for systems of designating the degrees of the scale by syllables instead of letters. The syllables mostly used today are: do (doh), re, mi, fa, sol, lat, si(ti).” Randal, Don Michael, Harvard Concie Dictionary of Music, (Cambridge, MA, Belknap Press, 1978), 470.
Kelly, Thomas Forrest, Capturing Music, (New York, NY, London, Norton,2015) 62.
Liberal Art of music comes out of the seven Liberal Arts summarized in the Trivium and Quadrivium. In the Trivium are contained the Arts of the mind: Grammar, Logic and Rhetoric. The Quadrivium consists of the Arts of matter: Arithmetic, Geometry, Music and Astronomy. The Liberal Art of Music is different from that of the Fine Art of Music in that the Fine Art of Music is concerned with mastery in performance and the liberal Art is concerned with the causes of music as understood through ratio and proportion. Pythagoras is said to have discovered that the harmonious relationships of the notes of the musical scale were caused by pure ratios. Boethius further elaborated on this in his work: De Istitutione Musica.
 “Monochord. A device consisting of a single string stretched over a long wooden resonator to which a movable bridge is attached so that the vibrating length of the string can be varied. The monochord was widely used in antiquity (under the name Kanon) and in the Middle Ages for the investigation and demonstration of the laws of the musical acoustics, a purpose for which it is still used today.” Randal, Don Michael, Harvard Concise Dictionary of Music, (Cambridge, MA, Belknap Press, 1978) 316.
 The four ratios of 1:1, 1:2, 2:3 and 3:4 were visualized by the Pythagoreans as ten points in a triangle. This was know as the “Tetraktys.” -(it is from the Greek, tretras, four). “Fourness”…The Tetraktys symbolizes the perfection of number and the elements that comprise it. The Tetraktys also contains the symphonic ratios which make possible the musical scale.”Gurthrie, Kenneth Sylvan, The Pythagorean Sourcebook and Library, (Grand Rapids, MI, Phanes Press 1987) 334.
“Organum. (2) The earliest type of preserved polyphonic music, from the ninth-century (the treatise Music enchiriadis) through the thirteenth-century…” Randal, Don Michael, Harvard Concise Dictionary of Music, (Cambridge, MA, Belknap Press, 1978) 360.
Henry, H. (1912). “Ut Queant Laxis Resonae Fibris.” In the catholic Encyclopedia. (New York, N.Y. Robert Appleton Company)
Wilson, David Fenwick: Music in the Middle Ages, (New York, N.Y. Schirmer Books, 1990) 90.
Mead, Sarah: “Renaissance Theory.” A Performer’s Guide to Renaissance Music, Editors: Mc-crow, Michael: Gellespie, Wendy (Blooming, IN, Indiana University Press, 2007) 606.
Jeppesen, Knud, The Style of Palestrina and the Dissonance, (New York, NY, Dover, 1946). 3.
The rationality of the musical scale’s discovery is attributed to Pythagoras (circ. 495-570 BC) but written about by Guido in his Micrologus. Babb, Warren. Hucbald, Guido and John on Music: Three Medieval Treatises, (New Haven CT and London, Yale University Press, 1978) 32.
“Adrea del Sarto (Italian: [an’drea del’ sarto]; 1486-1530) was an Italian painter from Florence, whose career flourished during the High Renaissance and early Mannerism.”…”highly regarded during his lifetime as an artist senza errori (“without errors”)” http://en.wikipedia.org/wiki/Andrea_del_Sarto
Dickenson, Edward, Music in the History of the Western Church, (New York, NY. Haskel House, 1969) 145.
Jeppesen, Knue, The Style of Palestrina and the Dissonance, (New York, NY. Dover, 1946) 32.
Haar, James, The Science and Art of Renaissance Music, (Princeton, NJ, Princeton University Press, 1970), 122.
Oliveria, Plinio de Correa, Unperceived Idiological Transshipment and Dialogue, (York, PA, York Press, 1970) Chapter IV Legitimate Meanings of Dialogue.
Apel, Willi, Gregorian Chant, (Bloomington, IN, Indiana University Press, 1958) 406.
Ibid, 409. In distinction from the Gloria Patri, aka. Lesser doxology.
1 Pete 2:9 “But you are a chosen generation, a kingly priesthood, a holy nation, a purchased people. That you may declare his virtues, who hath called you out of darkness into his marvelous light.”
Apel, Willi, Gregorian Chant, (Bloomington IN, Indiana University Press, 1958) 415.
Ibid, 415.(Greek: thrice Holy) “The Sanctus is the only item of the Mass Ordinary whose text is derived from the Old Testament. Isaiah’s Sanctus survives in the Jewish liturgy in its original language, as the ‘kadusha,’ the threeforld ‘kadosh, kadosh, kadosh.’ Its Greek counterpart is the ‘trishagion, ‘hagios, hagios, hagios.”
J. Mullen: Apel is mistaken about the text being derived from the Old Testament only, it is also found in the book of the Apocalypse of St. John as quoted above.
“But, as it is written: That eye has not seen, nor ear heard, neither hath it entered into the heart of man, what things God hath prepared for them that love Him.” (1 Cor. 2:9)
“From the beginning of the world they have not heard, nor perceived with the ears: the eye hath not seen, O God, besides Thee, what things thou hast prepared for them that wait for thee.” (Isa. 64:9
Aquinas, Thomas, Summa Theologica 1.93.4 “Respondeo.”
Ibid. Reply to Obj. 1.
Maher, M. (1910). “Intellect.” In the Catholic Encyclopedia. (New York, NY, Robert Appleton Company)
Ripperger, Chadd, Introduction to the Science of Mental Health, Vol. 1 Philosophical Psychology, (Lincoln NE. Sensus Traditionis Press, 2013) 51.
Pius X, Moto Proprio, Tra le sollecitudini (1903) paragraph 3.