It's All Greek To Me...
While Pythagoras is widely regarded as the founding father of 'Musical Science', it was Aristoxenus through his texts Harmonic Elements and Rhythmic Elements who sought to expand the boundaries of this science beyond the mere mathematical elements of the properties of sound.
It should be remembered that 'Musical Art' existed long before 'Musical Science' came onto the scene. This is to say that there already existed preferences of compositional style, performance methods for these, construction of instruments for this performance, and the habits formed by these preferences were passed on through instruction. Musical artists used diagrams and superficial generalizations in order to facilitate instruction and aid memory but they weren't interested in principles for their own sake. It is with principles for their own sake that science begins and where Pythagoras and his disciples enter the picture. (The Harmonics of Aristoxenus - Macran: 1902)
Pythagoras brought an empirical sensibility to the study of sound and a mathematical logic to the numerical relationships in the sensations of hearing pitch. The hypotheses of Pythagoras proved to be 'good science' and continue to underpin modern study and research of acoustical phenomena. However, as Macran goes on to note, "For if the artists were musicians without science, the physicists and mathematicians (Pythagoras et.al.) were men of science without music." (p 88)
Where Aristoxenus differs from the Pythagorean school is he broadened the scope of musical science. He theorized musical science should include other elements of music beyond its purely physical acoustic properties - conceptions of voice, interval, high, low, concord, discord, etc. - and sought to reduce the complex phenomena of music to these simple forms and to ascertain general laws with regards to their interconnectedness. In short, what Aristoxenus could see (and what the Pythagoreans failed to see) was that the essense of musical sounds lies in their dynamic relationship to each other. Furthermore, Aristoxenus conceived a notion of music as a system or organic whole of sounds, each member of which is essentially what it does, and that no sound can be a part of that system simply because there's room for it, but only if there's a function it can discharge.
The conception then of a science of music which will accept its material from the ear, and carry its analysis no further than the ear can follow; and the conception of a system of sound functions, such and so many as the musical understanding may determine them to be, are the two principle contributions of Aristoxenus to the philosophy of music.
Aristoxenus was concerned with the philosophical definitions and categories necessary to establish a complete and correct view of the musical reality of scales and tonoi (accent), two primary elements of musical composition. In Harmonic Elements he defines seven "technical" categories (not necessarily in this order) in his theoretical system:
Notes. Aristoxenus's definition is both economical and sophisticated: "a falling of the voice on one pitch is a note; then, it appears to be a note as such because it is ordered in a melos and stands harmonically on a single pitch." This subtle definition destinguishes among a voice, which is articulate sound; a single pitch, which is the position of a voice; and a note, which is a production of sound at a single relative ordered position within a musical composition, a melos.
Intervals. Intervals are defined as bounded by two notes of differing pitch, distinguished by magnitude, by consonance or dissonance, as rational or irrational, by genus, and as simple or compound (the first four distinctions also apply to scales). For Aristoxenus, the fourth and the fifth, not the octave, were the primary scalar components of music and music theory.
Genera. Aristoxenus recognized three basic genera of tetrachords: the enharmonic (also known as harmonia), the chromatic (also known as color), and the diatonic; the last two of which exhibited various shades. The intonations were created by the two middle notes of the tetrachord, which were "movable", in relation to the two outer notes of the tetrachord, which were "immovable".
Scales. Aristoxenus rejected the closely packed scales of the Harmonicists (Pythagoreans) because by ignoring the principles of synthesis and continuity and consecution, they failed to accord with musical logic. Scales, Aristoxenus asserts, must always follow "the nature of melos": an infinite number of notes cannot simply be strung together; and if a melos ascends or descends, the intervals formed by notes separated by four or five consecutive degrees in the scale must form the consonant intervals of a fourth or fifth. Scales larger than the tetrachord are assembled by combining tetrachords, either by conjunction (eg., E F G A and A B C D) or disjunction (eg., E F G A and B C D E). Relying on the aforestated principles, Aristoxenus formulates a detailed set of possible progressions.
Tonoi and harmoniai. This section of Harmonic Elements hasn't survived, but it's clear from other sections of the treatise that Aristoxenus associated the tonoi with "position of the voice." Harmoniai is the collective name given to the seven Greek modes (not to be confused with the seven Church modes of the Middle Ages). Both Plato and Aristotle considered that the harmoniai could have an impact on human character, but in their use of the term, they almost certainly are referring to a full complex of musical elements, including register, characteristic rhythmic pattern, textual subject, etc.
Modulation. Since the functions of the notes in a scale would change in the course of a modulation, a full comprehension of musical logic would be impossible without determining the nature of a modulation. This section of Aristoxenus's treatise hasn't survived, but Cleonides articulates four types of modulation: in scale, genus, tonos, and melic composition.
Melic composition. This subject, Aristoxenus's final category, remains obscure in the surviving treatises. Aristides Quintilianus refers to choice, mixing, and usage as three parts of melic (and rhythmic) composition. He goes on to remark that the particular notes used will indicate the ethos of the composition. Cleonides identified three types: diastalic, or elevating, which conveyed a sense of magnificance (mainly elevation of the soul, and heroic deeds, especially appropriate to tragedy); systaltic, or depressing, which expressed dejection and unmanliness, suitable to lamentation and eroticism; and hesychastic, or soothing, which evoked quietude and peacefulness, suitable to hymns and paens.
Because the Aristoxian tradition lent itself to the construction of musical "rules", it came to be viewed as a practical tradition, distinct from the ideal or purely theoretical traditions of the Pythagoreans and the Harmonicists. Yet this is a misleading and simplistic dichotomy. While Aristoxenus's followers may often have failed to grasp his larger epistemological concerns, it is clear that he was trying to develop an idealized phenomenology of music, based not on the abstraction of number but rather on a careful definition of the separable elements of musical sound that became music only when they combined to create something the intellect would comprehend. It is one of the ironies of history that the Aristoxian tradition, especially as it was adopted and adapted by later Western theorists, forgot the interests of its founder and instead became mired in fruitless practical controversies, especially in the areas of tuning.
It should be remembered that 'Musical Art' existed long before 'Musical Science' came onto the scene. This is to say that there already existed preferences of compositional style, performance methods for these, construction of instruments for this performance, and the habits formed by these preferences were passed on through instruction. Musical artists used diagrams and superficial generalizations in order to facilitate instruction and aid memory but they weren't interested in principles for their own sake. It is with principles for their own sake that science begins and where Pythagoras and his disciples enter the picture. (The Harmonics of Aristoxenus - Macran: 1902)
Pythagoras brought an empirical sensibility to the study of sound and a mathematical logic to the numerical relationships in the sensations of hearing pitch. The hypotheses of Pythagoras proved to be 'good science' and continue to underpin modern study and research of acoustical phenomena. However, as Macran goes on to note, "For if the artists were musicians without science, the physicists and mathematicians (Pythagoras et.al.) were men of science without music." (p 88)
Where Aristoxenus differs from the Pythagorean school is he broadened the scope of musical science. He theorized musical science should include other elements of music beyond its purely physical acoustic properties - conceptions of voice, interval, high, low, concord, discord, etc. - and sought to reduce the complex phenomena of music to these simple forms and to ascertain general laws with regards to their interconnectedness. In short, what Aristoxenus could see (and what the Pythagoreans failed to see) was that the essense of musical sounds lies in their dynamic relationship to each other. Furthermore, Aristoxenus conceived a notion of music as a system or organic whole of sounds, each member of which is essentially what it does, and that no sound can be a part of that system simply because there's room for it, but only if there's a function it can discharge.
The conception then of a science of music which will accept its material from the ear, and carry its analysis no further than the ear can follow; and the conception of a system of sound functions, such and so many as the musical understanding may determine them to be, are the two principle contributions of Aristoxenus to the philosophy of music.
Aristoxenus was concerned with the philosophical definitions and categories necessary to establish a complete and correct view of the musical reality of scales and tonoi (accent), two primary elements of musical composition. In Harmonic Elements he defines seven "technical" categories (not necessarily in this order) in his theoretical system:
Notes. Aristoxenus's definition is both economical and sophisticated: "a falling of the voice on one pitch is a note; then, it appears to be a note as such because it is ordered in a melos and stands harmonically on a single pitch." This subtle definition destinguishes among a voice, which is articulate sound; a single pitch, which is the position of a voice; and a note, which is a production of sound at a single relative ordered position within a musical composition, a melos.
Intervals. Intervals are defined as bounded by two notes of differing pitch, distinguished by magnitude, by consonance or dissonance, as rational or irrational, by genus, and as simple or compound (the first four distinctions also apply to scales). For Aristoxenus, the fourth and the fifth, not the octave, were the primary scalar components of music and music theory.
Genera. Aristoxenus recognized three basic genera of tetrachords: the enharmonic (also known as harmonia), the chromatic (also known as color), and the diatonic; the last two of which exhibited various shades. The intonations were created by the two middle notes of the tetrachord, which were "movable", in relation to the two outer notes of the tetrachord, which were "immovable".
Scales. Aristoxenus rejected the closely packed scales of the Harmonicists (Pythagoreans) because by ignoring the principles of synthesis and continuity and consecution, they failed to accord with musical logic. Scales, Aristoxenus asserts, must always follow "the nature of melos": an infinite number of notes cannot simply be strung together; and if a melos ascends or descends, the intervals formed by notes separated by four or five consecutive degrees in the scale must form the consonant intervals of a fourth or fifth. Scales larger than the tetrachord are assembled by combining tetrachords, either by conjunction (eg., E F G A and A B C D) or disjunction (eg., E F G A and B C D E). Relying on the aforestated principles, Aristoxenus formulates a detailed set of possible progressions.
Tonoi and harmoniai. This section of Harmonic Elements hasn't survived, but it's clear from other sections of the treatise that Aristoxenus associated the tonoi with "position of the voice." Harmoniai is the collective name given to the seven Greek modes (not to be confused with the seven Church modes of the Middle Ages). Both Plato and Aristotle considered that the harmoniai could have an impact on human character, but in their use of the term, they almost certainly are referring to a full complex of musical elements, including register, characteristic rhythmic pattern, textual subject, etc.
Modulation. Since the functions of the notes in a scale would change in the course of a modulation, a full comprehension of musical logic would be impossible without determining the nature of a modulation. This section of Aristoxenus's treatise hasn't survived, but Cleonides articulates four types of modulation: in scale, genus, tonos, and melic composition.
Melic composition. This subject, Aristoxenus's final category, remains obscure in the surviving treatises. Aristides Quintilianus refers to choice, mixing, and usage as three parts of melic (and rhythmic) composition. He goes on to remark that the particular notes used will indicate the ethos of the composition. Cleonides identified three types: diastalic, or elevating, which conveyed a sense of magnificance (mainly elevation of the soul, and heroic deeds, especially appropriate to tragedy); systaltic, or depressing, which expressed dejection and unmanliness, suitable to lamentation and eroticism; and hesychastic, or soothing, which evoked quietude and peacefulness, suitable to hymns and paens.
Because the Aristoxian tradition lent itself to the construction of musical "rules", it came to be viewed as a practical tradition, distinct from the ideal or purely theoretical traditions of the Pythagoreans and the Harmonicists. Yet this is a misleading and simplistic dichotomy. While Aristoxenus's followers may often have failed to grasp his larger epistemological concerns, it is clear that he was trying to develop an idealized phenomenology of music, based not on the abstraction of number but rather on a careful definition of the separable elements of musical sound that became music only when they combined to create something the intellect would comprehend. It is one of the ironies of history that the Aristoxian tradition, especially as it was adopted and adapted by later Western theorists, forgot the interests of its founder and instead became mired in fruitless practical controversies, especially in the areas of tuning.
Labels: Music Essay
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