The Cross: Its History and Symbolism (Dover Books on Western Philosophy)

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The psychological effect of various musical modes was an important part of the theories of music. For example, some rhythms were considered to lead people more easily into lustful sins, while other rhythms were deemed appropriate for the education of young people. The earliest example of the effects of music was the story of Pythagoras allegedly calming a drunk adolescent simply by making the youth listen to a certain melody in Hypophrygian mode.

Music could influence the soul of human beings; therefore, the type of music people could hear had to be the sort that would positively influence them. The same principles of harmony and proportion applied to all the arts, although there were differences in the way they were applied. The numerical ratios, however, were the same because mathematical values are immutable. For example, the Golden Section, considered to be the most aesthetically pleasing proportion, was often the basis of proportions in architecture and painting.

Even though they were concerned with form, it should be stressed that the medievals were not advocates of form over function. The purpose of the building or painting was the most important thing for an artisan to consider. The form was manipulated in such a way to fulfill the purpose of the work. Medieval scientists, such as Robert Grosseteste, were interested in discovering the nature of light.

The effects of light became more important to the medieval artisans, particularly in architecture, and they frequently associated light with their theories of color. Light and color affected the thoughts of medieval thinkers on certain characteristics of beauty, such as radiance and clarity. One of the motivations for the medieval philosophers to pursue the notion of light developed from the belief that God is Light.

Though Plotinus was not a Christian, the seeds of this idea that God is Light can be seen in his writings. Light is what allows the beauty of objects, especially their color, to become illuminated, in order to display their beauty to the fullest. Light comes from the Good, and light is an image of this archetypal Good. The light of the sun is a mere reflection and symbol of the divine light. Light, for the medieval philosophers, is an important condition for there to be beauty.

Light illuminates the colors, which led the medieval thinkers to construct theories about color. There is a sense in which color causes beauty, since everything has color. Hence, more radiant colors will cause the object to be more radiant and, therefore, more beautiful. Symbolism was employed, first, as a tool to give meaning to artworks, and, second, it was used in a hermeneutical sense, to discover the deeper meaning of texts especially the Bible. Medieval symbolism derives from a particular view of the world. The main idea is that the universe revealed God, its author or creator, through its beauty.

This belief was influenced by the Platonic notion that things on earth are shadows of things from the realm of Forms. Therefore, medieval artists wanted to construct their art in a symbolic manner, which would, likewise, help point to God. To put it differently, God revealed Himself to human beings through general revelation nature and special revelation the Bible.

Therefore, medieval artists tried to create art for those who did not have literary access to the Bible by using symbols. Augustine set the stage for medieval Christian philosophers, drawing heavily from the Platonist and Neo-Platonist traditions. As a result, Platonic philosophy dominated the Christian medieval thought until Thomas Aquinas helped to popularize the writings of Aristotle.

Augustine made a sharp distinction between the creation of God ex nihilo and the creation of artists ex materia. The framework for this idea had its source in Neoplatonic philosophers, particularly Plotinus. The earth occupies the lowest form of beauty, and things become more beautiful as they possess more form, and less of the void. God is supremely beautiful, since only God possesses perfect form.

Augustine, therefore, believes in a hierarchy of beautiful things, based on how much form they possess or lack. Augustine developed ideas about rhythm that are pertinent to his aesthetic theory, especially the belief that rhythm originates with God. For Augustine, rhythm is immutable and eternal because its source is God. Augustine demonstrates this by pointing out how people through usage can change how certain words are pronounced, since pronunciation is conventional. However, mathematical truths cannot be determined by convention; they have already been determined. They can only be discovered by human beings.

Augustine then claims that rhythm is like math; it can only be discovered by people. Rhythm is already determined in God, and human beings cannot invent it. Beardsley points out that Augustine does not systematically present these characteristics of beauty, but they can be found, often in relation to one another, throughout his writings.

First, everything exists as a separate whole unit; therefore, each thing has unity. Simply put, something cannot have the potential to be beautiful, unless it exists. And if it has existence, it will also be a unified whole. Thus, unity is a necessary element of beauty. Further, the more unified something is the more beautiful it will be. Number, for Augustine, measures rhythm.

Since rhythm is based on number, which Augustine believes is immutable, then it follows that rhythm is likewise immutable. In other words, the degree to which things are in their proper place is the degree in which they are beautiful. About the sixth century, the writings of the anonymous author Pseudo-Dionysius , emerged and influenced philosophers, most notably Thomas Aquinas. His main work that has relevance for aesthetics is The Divine Names , in which he refers to God as Beautiful.

The beautiful, which is God, is unchangeably beautiful; therefore, the beautiful cannot cease to be beautiful. This immutable beauty would have to truly exist, if the beautiful is the source of all beauty. Two main points can be taken from these statements. First, beauty is the cause of any beautiful thing that exists; and, second, the beautiful and the good are the same. Since beauty is the source of all things that exist, everything has a degree of beauty.

Accordingly, everything has a desire and drive to move back toward the Beautiful and Good, that is, the source of the beauty of everything. In terms of aesthetics, Thomas Aquinas focused his comments mostly on the notion of beauty. However, he did not say enough to have a detailed system; his views are extracted from what he did say. The discussion here will deal with his definition of beauty, the standards of beauty, and the question of whether beauty is a transcendental. This definition, at first glance, seems to suggest a subjective understanding of beauty for Thomas.

One might be tempted to equate seen with glance or notice ; however, these possibilities are incomplete because they imply a passive account of seeing. Jacques Maritain offers some helpful explanation,. Beauty is essentially the object of intelligence , for what knows in the full meaning of the word is the mind, which alone is open to the infinity of being. The natural site of beauty is the intelligible world: thence it descends. Knowing beauty is not the result of a discursive process, nevertheless it is an activity of the mind.

Knowledge in general, for Thomas, occurs when the form of an object, without its matter, exists in the mind of the knower De Trinitate , q. For example, suppose someone is gazing at a flower. The same form, which is immaterial, of the flower in extra-mental reality is received by the senses and begins to exist in the mind of the knower. Then, the knower can contemplate the form of the object and discover its beauty. This process could transpire quickly. The knower or beholder receives data from the sensible world through the senses, but the senses do not recognize something as beautiful.

The mind is responsible for recognizing the beauty of a given object. Consequently, knowledge has two aspects: passive and active. The passive aspect receives data from extra-mental reality; the active aspect gives the abstracted forms new existence in the mind of the knower. The details of this process are not relevant here; it is mainly important to see that the form of the object in reality begins to exist in the mind of the knower. Since beauty, for Thomas, is caused by the form of the object, then this process explains how the apprehension of beauty is the result of cognition.

More specifically, the senses of sight and hearing are those through which the beholder receives the form of the object. For Thomas, these senses are the most important ones for cognition; therefore, they are the ones employed in perceiving the beautiful. Thomas maintains the objectivity of beauty, in the sense that beauty resides in the object. In other words, beauty is not a concept in the mind of the beholder imposed onto a given object. If beauty is objective, then there must be some criteria by which we discover whether something is in fact beautiful.

The criteria of beauty are not precise formulae for discovering or labeling beautiful things with absolute certainty. These criteria are more like guideposts to help finite minds apprehend beauty. They do not have to all be present for an object to be considered beautiful, and the presence of one does not guarantee that the object is beautiful.

For Thomas, beauty has four primary standards: actuality, proportion, radiance, and integrity ST , I. The original context of this list is centered on the relationship of the three persons of the trinity, specifically in reference to the Son. However, for Thomas, everything has its ultimate source in actuality or being ; therefore, actuality or being is the basis of beauty. According to Maurer, actuality is used in three ways when referring to beauty: existence, form, and action Maurer, 6ff.

Beauty is grounded in the actual existence of the object. For Thomas, everything that has being will also have a degree of beauty, regardless of how small that degree appears. In other words, an object must exist, in some sense, in order for it to be beautiful; otherwise, it would be nothing. Therefore, actuality is the ground of beauty.

For without existence there is no being; there is simply nothing. The second aspect of actuality is form. Form separates the existence of different things. For example, a dog and a tree both exist, but the dog exists as a dog and the tree exists as a tree. In the words of St. This interpretation of Thomas can be gleaned from his account of the relationship between goodness and form ST I. To summarize this passage, everything is what it is because of its form; therefore, a thing has more goodness [and beauty] when it achieves a higher level of perfection in its form.

A tree is beautiful to the degree in which it perfectly attains to the form of a tree and, likewise, a dog would be beautiful according to the form of a dog. The third aspect of actuality is action. A clear illustration of the notion of action is a dancer. A dancer sitting and drinking coffee is still a dancer, in the sense that she possesses the skill required for dancing.

Yet she is most completely a dancer when she performs the act of dancing. Strictly speaking, actuality is not a characteristic of beautiful things; more precisely, it is the necessary condition for grounding beauty in anything. Plotinus had already dismissed the notion of proportion or symmetry or harmony as the only qualification of beauty; however, the medieval philosophers still believed proportion had some importance for beauty. The object may actually be symmetrical, but it is more important that it is well-balanced.

The parts of the whole are in harmony with one another. Proportion is twofold. In one sense it means a certain relation of one quantity to another, according as double, treble and equal are species of proportion. In another sense every relation of one thing to another is called proportion. And in this sense there can be a proportion of the creature to God, inasmuch as it is related to Him as the effect of its cause, and as potentiality to its act; and in this way the created intellect can be proportioned to know God ST I.

Following Eco, proportion, according to this statement, could be reduced to relationships of quantity and relationships of quality Eco, , Radiance is a bit more difficult to pinpoint than the other standards. Radiance signifies the luminosity that emanates from a beautiful object, which initially seizes the attention of the beholder.

This trait is closely related to the medieval notions concerning light. For example, in terms of natural light, there is a sense in which the paintings in a gallery lose some of their beauty when the lights are turned off because they are no longer being perceived. However, Thomas also connects beautiful things with the divine light. This quote provides another account of Thomas connecting all beauty to the beauty of God, as the cause of all beauty. The last standard of beauty for Thomas is wholeness or integrity. Thomas, is existential: it expresses the primal perfection of a thing, which is found in its existence esse.

In a second sense a thing is integral when it is perfect in its operation. If some particular thing was perfectly beautiful, then it would have to be completely actualized, lacking nothing essential to its nature. In other words, anything that is imperfect in some way is lacking some thing or ability necessary for its completion. Whether or not beauty is a transcendental property of being will be the last topic in this entry. The notion of transcendentals has its origins in Aristotle, specifically the Metaphysics.

Aristotle claimed, as quoted earlier, that being and unity are implied in one another Metaphysics , b From this beginning, the medieval philosophers developed a broader notion of transcendentals; the three most mentioned transcendentals are one, true, and good. Aquinas' main presentation of the transcendentals is found in his Questiones Disputatae de Veritate , Question 1. A predicate can add to being in two ways. First, the predicate may express a special mode of being. For example, in itself expresses a special mode of being, namely a substance, but it fails to be a transcendental because it does not apply to being as such.

It applies only to individual beings. Second, a predicate may express a mode of being that is common to every being in general. This second mode can be understood in two ways: 1 absolutely — referring to a being as it relates to itself; 2 relatively — referring to a being as it relates to other beings. A predicate can express being in reference to itself or being-absolutely either affirmatively or negatively.

Affirmatively, Aquinas claims that the predicate thing is a transcendental, since each being is a unified whole. Negatively, Aquinas claims that the predicate one is a transcendental, since each being is undivided with reference to itself. Moving to the predicates that express a relative mode of being, Aquinas claims that there are two ways. The first way refers to the idea that each being is separate from all other beings, so Aquinas refers to something or otherness as a transcendental property of being.

The second way is based on the correspondence that one being has with another, which also has two facets. Such a being is the soul, which, as is said in The Soul, 'in some way is all things. In terms of the knowing power, true is a transcendental property because all knowing is an assimilation of the thing known by the knower.

To summarize, transcendentals are properties of being as such that is, every being. Each transcendental is convertible with being. In other words, the transcendentals are present wherever being is present. However, just like being can be found in varying degrees, the transcendentals can also be found in degrees. For example, every being is not perfectly or completely good, but every being is good to a degree. Audio: Ne oryol li s lebedem kupalisia, lyrical Cossack song, Southern Russia. In a few equintervallic diatonic subsets, elasticity is minimal: i. Minimal tonal tension from ascending motion through 3 equintervallic trichords.

Larger size subsets, such as tetrachordal and pentachordal, common in Georgian traditional music, increase functionality of PCs, inducing substantially greater instability—which is handled by more elaborate hierarchic organization. Audio: Kakhuri nana. The unstable functionality prevails over the stable one. Non-octave hypermodes presented a window for expression for the strictly controlled amounts of tension see Appendix 2 in Supplementary Material for details that was compartmentalized in different registers.

A noticeable affiliation of hypermodal organization with the Christean plainchant, which subsequently shaped the folk music of many Eastern Orthodox nations and ethnicities, expressed rejection of the cultural heritage of the Greco-Roman philosophy of music and an attempt to restore the older Sumero-Babylonian cosmology on new theological ground see Appendix 3. Unlike the hypermode, the diatonic MPS did not restrict degrees to sustain their pitch values throughout the music work. The need to temporarily increase tension was handled by alteration and modulation.

When this happens, listeners familiar with this PCS become surprised by its deviation from the norm. The impulse to restore familiar IS is what is responsible for momentary increase in tension associated with the alteration, when the listener experiences intense expectation for it to comply to the norm Margulis, Alteration is a form of cognitive dissonance. As people realized the limitations of words in reference to real objects, the dialectic method of defining opposites began to make an imprint at first on the manner of conducting scholarly research and legal matters, then on the discipline of rhetoric in general, and finally on tonal organization.

Neither unfixed ekmelic degrees, nor expressively tuned multitonal degrees of pre-MPS musics involved cognitive dissonance. Audio: Shelkovoya travushka, Nekrasov Cossacks. Audio: Alilo, Georgian ritual Christmas song. The melodic rule: in the middle voice, every time B goes to C , it sharpens, but every time it descends to A in the opening of every strophe—it stays natural.

Alteration does not possess such permanence and logic. By its nature, it is accidental. Alteration is relatively rare in oral traditions 30 reserved to technically advanced professional music with fully fledged music theory Improvisation on a ghazal by Hafiz. The stanza starts with the altered degree C , creating a dissonance in relation to the accompaniment—and then resolves into B, restoring the initial non-altered mode: E-F -G -A-A -B-C-D. Such modes can contain their own micro-alterations.

Audio: Falak-I Badakshani, Pamir. Modulation has been theorized exclusively within the framework of Western music. Similar devices are known in other advanced music systems Indian, Arabic, Chinese —although without receiving much attention in their music theory. Modulation in folk music presents a novel and controversial object of study. Intra-modal mutability in pentatonic mode from C to Eb and finally to F. Intra-modulation a step up, from Eb to F, in a heptatonic mode. Mutability of multitonal mode see Part-1 restricts intra-modulation to only anchor-tones, making gravitational shifts predictable and regular.

Audio: Ocarina solo, Bulgaria. Each sentence provided sample starts in A, in major inclination, but ends in F , in minor inclination. Helladic music probably featured simple diatonic modulations Franklin, As time progressed, the set size grew—ultimately reaching an octave species, allowing for inter-tetrachordal enharmonism. Despite their size, all MPSs are treated in the same way: music users remember the normative sets, and upon detecting modulation, hypothesize a new set from what they already know Raman and Dowling, In reality, their pitches are not exactly retained, since each PCS imposes its own expressive tuning: certain degrees are slightly sharpened or flattened, depending on their function in the PCS Sundberg et al.

Although, this adjustment is not as drastic as a single tone mutation in a folk multitonal mode, it nevertheless does occur In the polymodal system, the music user remembers modes by their IS, including their characteristic expressive tuning Brattico et al. Absence of expressive tuning is perceived as faulty performance Sundberg, Every time music modulates from mode to mode, the melodic ISC switches, causing reassignment of expressive tuning values—all at once, as in switching from one tuning table to another.

Listeners take expressive tuning as a prompt in detecting the most stable immutable tuning and unstable most mutable degrees. They estimate modulation in terms of gradations in tension determined by the intervallic value of the modulation — the interval between the old and new tonics. Thus, modulation from minor dominant to minor tonic appears different than modulation from minor subdominant to minor tonic.

The emotional reaction to modulation proves to be one of the most exciting stimuli in music listening experience Korsakova-Kreyn and Dowling, We shall see later how this emotionality is important for the emergence of chromatic system. Modulation usually involves alteration—their combination pioneered in Ancient Greece. Audio: Mesomedes—Hymn to the Muse, second century AD, brief modulation from Lydian to chromatic Hypolydian mode by the end of the hymn Hagel, , p.

Hellenic listeners identified melodies by intervallic differences Lippman, , p. Interval-tracking habit was responsible for non-formulaic composition as opposed to contour-tracking habit of earlier folk-musicians. Both, Babylonian and Assyrian songs fit a single song into a single mode Franklin, , p. In Classical Greek music, a song often contained a nexus of tetrachords, each bearing its own modal organization West, , p. Professionalized folk cultures can come close to what might appear as a chromatic modulation either by emulating MPS music or forming composite mode-a compound of 2 or more stand-alone modes Belaiev, Audio: Duma about Marussia of Bohuslav, Ukraine.

Modulation from E to B that appears to be influenced by the Western classical modulation from tonic to dominant. When folk musicians learn a diatonic PCS, they begin to transpose it by degree. Eventually, they come to connect two tunes, each associated with its own mode, into a medley. Then, one mode becomes transposed so that it would start on the same I degree as another. As the performer gets used to this juxtaposition, he can combine intonations from both modes within the same song.

Even pentatonic modes acquire quasi-chromaticism in this way. Thus, two pentatonic modes built from the same tone i. Even when a folk musical instrument includes the entire chromatic scale, as in Chinese shen or pipa Riemann, , p. This is what must have happened in the Hellenic culture. Pleasantness of alteration was responsible for the quick popularization of lute in Greece from the fourth century BC: unlike lyre, lute allowed to comfortably produce chromaticism Higgins and Winnington-Ingram, Essentially, this composition presents spare use of chromatic alterations shading of the Phrygian tetrachord West, , p.

Most of the melodic content of this lamentation in chromatic Lydian mode is made of altered degrees. Chromatic alteration became affiliated with aesthetic emotion after the practice of connecting certain modes with certain affects was established through the temple culture of Sumerian and Egyptian cults, some time around the 2nd millennium BC Farmer, see Appendix 3 in Supplementary Material. Earlier agricultural civilizations heavily depended on the calendar, which boosted the development of astronomy and math, but carried no mystic and esoteric implications to entitle numerology to a governing status delegated to the elite Frolov, , p.

Babylonian music theory was first to link the arithmetic definitions of musical tones to cosmology. Cosmology empowered music with the status of natural law, equating music's influence with the sun or the moon. Just as excess or shortage of sunlight can cause problems, so presence or absence of certain modal qualities in music was believed to be beneficial or hazardous for a person. In the 6th century BC, Sakadas of Argos started combining different ethea in a single composition by employing intra-modulations between different verses of his song.

Then, Aristoxenus' Perfect System rationalized the means for the composer to generate his individual map of tonal tension suitable for a particular composition. The music is built on the Lydian tetrachord, alternating between Hypolydian and chromatic Lydian modes—which seems to be reserved as means of a peculiar compositional arrangement, unlike the modal stereotypicity of folk music. Rising standard of authorship incorporated modal creativity. Greek civilization championed cultivation of melopoeia , art of composing music, put forth by Plato Kholopov, , p.

From the fifth century BC until the Dark Ages, authorship guided expression in the arts. Distinguished authors' names were perpetuated, encouraging other artists to either follow their steps or to compete with them. Growing popularity of chromatic style in the fifth century Athens reflected the antithesis of diatonic conventionality vs.

For the next half-millennium, enharmonic and chromatic genera made the diatonic genus look too predictable and unimpressive Franklin, Thereby, diatonic system provided the skeleton for all modulations and alterations—very much like in a modern key. However, not all musicians followed the rules Franklin, This accusation should be understood in the context of dithyramb contests and theatrical plays becoming exceedingly popular to the extent of introduction of entrance fees for the first time in Greek history Csapo, Theater musicians made lavish profit and enjoyed enormous popularity—this, together with the growing market 18 theatrical festivals per year, fourth century BC unleashed fierce economic competition Csapo, The immediate reason for the split of public opinion, and voices for its condemnation was its break of conventional ties between mode and genre, and its inter-strophic modulation—which could be rather abrupt, even a semitone apart Hagel, , p.

Modulation from Hyperaeolian to Hyperphrygian mode by common tone. Chromatic music grew out of older enharmonic music that was cultivated in Dyonisiac dithyramb, and became related to theater and symposium drinking parties , both of which involved aesthetic appreciation.

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Athenian chromaticism replaced cosmogonic consonance admiration with admiration for realistic impersonation of humanistic character traits, interwoven into dramatic development. Remarkable is the commonality of Aristoxenian and Euclidian approaches to the infinitely smallest magnitude, setting a conceptual and a terminological correspondence between musical and physical spaces Barbera, Chromatic tetrachords reflected the contemporary advance in the irrational numbers, presenting breakthrough from Pythagorean ratios Scriba, , p. In contrast, Greek geometry sought methods for inferring the relations between objects based on empirical proof.

To minimize the inconvenience of retuning the lyre, which remained a reference instrument for theory, musicians had to find as many common tones between different modes as possible. And seven principal modes, when built from the open string E, mark the E-A-B core of immutable tones, thereby forming the axis for categorization and hierarchical organization Gombosi, Just as ekmelic and mesotonal modes, chromatic modes were crystallized by the permanence of tuning: the least frequently retuned tones acquired the status of stability, while the most alterable tones ended up at the bottom of the tonal hierarchy.

The description of the chromatic system might sound extremely complex, but in practice, the overall number of PSCs in the MPS was not exorbitant There was little distinction between the chromatic and enharmonic genera Greek notation did not distinguish between them at all West, , p.

In reality, musicians had to deal with no more than 14 different types of tetrachords: 2 types of each of the 7 principal keys. This is the register where melodies show the greatest modal complexity. The peculiarity of Greek system is that all alterations are descending This trichord became a melodic frame, where extra tones could be placed in between E and A, forming two oldest heptatonic genera, diatonic and enharmonic, circa seventh century BC, credited to Olympus Barker, , p.

Chromatic genus evolved later, as a simplification of enharmonic genus, and gained in popularity—up until AD: surviving musical fragments from the Roman period are almost wholly diatonic, and both, Gaudentius and Macrobius reported that chromatic and enharmonic genera were obsolete by fifth century AD West, , p.

Chromatic music was ousted in the West, but not in the East of Roman Empire. Greek chromatic MPS impacted all the territories between Greece and India—conquered by Alexander during the heydays of chromatic music. Hemiolic mode differs from diatonic by its chromaticism: recoloration chroma of ICs due to their inequality—most prominent in microtonal varieties of hemiolic modes, i. Audio: B'utho, Syrian Orthodox chant, Tminoyo mode. Hemiolic modes are decidedly non-diatonic : their tones cannot be positioned in a circle of perfect 5ths.

Gapped tones represent discrete—and not altered—degrees of the mode: the entire music work might be based on the stationary gapped tones, without any modification. Such mode differs from pentatony by contrast of gap and semitone, where expansion of one causes shrinking of another, inducing tonal tension.

Instability of both gapped tones is responsible for their flexibility in expressive tuning, which enables them to come closer to a target stable tone, thereby exaggerating tension and relaxation Marcus, The emotional expression of hemiolic gaps also opposes that of pentatonic trichords: related to heightened pleasure and even ecstasy ibid. The traditional monodic implementation, on the other hand, has preserved the microtonal adjustments, especially those of the hemiolic gap, supporting the tonal organization that is distinctly different from Western tonality Marcus, The Mediterranean implementation of chromatic recoloring shares affective aspirations with Western musica ficta Westrup, , but follows a different modal order.

Western chromaticism was accidental in nature, and followed the trichordal scheme, where the chromatic degree would be jammed between two diatonic degrees. Mediterranean chromaticism was regular, modally driven by melodic inflections, following the tetrachordal scheme, where two chromatic degrees would be encapsulated between two diatonic degrees. This difference determined polarly opposite paths of their development.

Mediterranean chromaticism fueled melodic complexity, serving as the primary expressive means for the composer in organizing horizontal harmony by means of intra-tetrachordal alterations and modulations. This important distinction has led to completely different spatial connotations for Western tonal key and Mediterranean tonality. Western spatio-tonal design went towards incremental geometric projection of ever growing complexity, while Eastern Mediterranean focused on ornamental patterning the nexus of small size modules al Faruqi, This contrast seems to reflect more fundamental opposition of philosophies, where Western Christian and Eastern Islamic cultures appear to form the core for the divergence between Western and Mediterranean tonalities see Appendix- 4.

Such organization evolved from the diatonic MPS through standardization of intervallic relations by means of counterpoint techniques which every composer was expected to know. Ability to hear equivalent concords triads between multiple parts, and recognize them as a single typological percept was set in place during the Renaissance Nutting, Subsequently, psychological representations of tonality in terms of chords, for Western listeners, became as real as hearing the tones themselves Vuvan and Schmuckler, Tones, intervals, and chords are processed through imagery representation, and the representation of chords is derived from the representation of tones Hubbard and Stoeckig, Therefore, chords should be regarded as common chunks of pitches, remembered by music users to facilitate tonal navigation across the music work.

The 3-part vertical harmony is based on a few triads: 1 chord on the VI degree, 3—on the V, and 1—on the IV. Audio: Odola, Megrelian work song. The 3-part harmony contains plentiful variety of chords—in stark contrast to the example above. Tonal tension here plays no role in vertical organization, and is reserved to horizontal harmony alone: it is not chords that resolve into one another, but tones of the principal melody. Audio: Ompeh, Efufu area of Ghana. In fact, penetration of Western chordal mentality in non-Western music systems has had detrimental impact on their original tonal organization.

Native performers start thinking musically in terms of Western triads and functions—which then remaps their modal intonations and produces new hybrid modes. This solo song features unmistakable tonic, subdominant, and dominant functions in the melody—noticeably different from pentatonic organization that is traditional to neighboring Tatar ethnicities in Eastern Europe and Central Asia. Intelligibility of pitch alphabets embedded in a tonal key must be the immediate cause for the steady pattern of global Westernization, observable since the introduction of tonal keys in the eighteenth century.

Categorizing melody in terms of implied chords is a form of chunking—a way of compressing information Processing music in terms of standardized progressions of implied chords is another method of chunking, enabling even greater compression. Furthermore, both compression methods allow implicit learning of tonal regularities by mere exposure Tillmann et al.

Ease of implicit learning must be the underlying reason why many non-Western musicians tend to either switch to Western tonality or hybridize their native systems with tonality Nettl, Adoption of tonality in the Third World countries essentially is the same as adoption of banking system or electrification. Technically, what made Western tonality cognitively special was the crystallization of purely intervallic hierarchic typology, where vertical ISC came to replace melodic ISC as the basis of categorization in auditory perception.

If early Medieval polyphony had all its parts share the same PS Atkinson, , p. Compositionally, polyphonic harmony was constructed as a sum of monophonic harmonies, different parts in different species of 4ths and 5ths—until tonality of the early seventeenth century brought all parts to a common denominator of a single fixed IS, defined in semitones Atcherson, So, the tonal composer conceived the entire texture as a single tonal construct which he had decided precompositionally —in contrast to the modal composer who could only discover the actual harmonic results after summing up all the parts Mangani and Sabaino, Nomothetic centripetal hierarchy of tones, fixed in their subordination and coordination relations, is quite analogous to the astronomic model of planets orbiting the sun, discovered during the Renaissance—as well as to the organization of depicted images in linear perspective Cook, Tonality, heliocentricity, and perspective, all implement the same idea of harmonious arrangement of numerous peripheral objects in relation to a centered object.

And this is not a coincidence. Their connection comes naturally: sound and light are waves, subject to the same laws of reflection, dispersion, absorption, diffraction, and interference—differing mostly in wavelength: a musical sound-wave is about the size of a human, while optical wave is microscopic Nazajkinskij, , p.

The laws of physical space that rule audio and optic transmission prototype laws of virtual space constructed by art-works—and, here, musical texture becomes the cross-modal equivalent of visual depth Visual objects populate the visual space , whereas musical tones fill up the musical texture comprised of simultaneous sounding parts and voices. Percepts of pitch and visual size are cross-modally intertwined Bien et al. Melodic layer in musical texture serves as an equivalent of the visible surface—that is closest to the observer. In the pitch domain, discretization occurs in terms of intervals; in the visual domain—by formation of contours.

Visual contour equates melodic contour Terhardt, —both, outline the object of perception. The correspondence between the two has been known in musical literature since Jean-Jacques Rousseau Galeyev, It also finds confirmation in experimental research Weinstein and Gridley, We relate one polyphonic part to another by estimating the vertical intervals between them in terms of their harmonicity, rhythmic simultaneity of tones, and contrast in melodic contour—once we identify the concurrent parts, we track them by their vertical order Palmer and Holleran, Cardinality of vertical order is confirmed by long-standing compositional practice of avoidance of part-crossing in voice-leading Huron, Despite dividing our attention between all the registered parts Demany and Semal, , pitch is best detected in the upper part—and this is disregarding whether or not the upper part contains more semantically important material Palmer and Holleran, Moreover, the ERP studies of perception of polyphonic music indicate that formation of parallel audio information streams is pre-attentive and involves better encoding in the higher part, and even years of experience playing a low-range instrument does not reverse this bias Trainor et al.

The high part superiority effect was found in 7-month-old infants, suggesting automatic ordering of segregated audio streams Marie and Trainor, A similar effect occurs in visual perception of direct motion: we receive more information about the motion of closer objects, whereas optical invariants of distant motion are not picked up by the observer: closer motion is processed faster and with greater accuracy DeLucia, Observers can estimate trajectories of up to eight simultaneously moving objects DeLucia and Novak, —quite on par with melodic motion in polyphonic parts of Italian Renaissance music, where five parts were the norm for sophisticated style, and 3-part writing was considered a sign of simple folk style Dubravskaya, , p.

Although experimental studies demonstrated that non-musicians are only able to count up to three concurrent parts, and musicians—four concurrent parts Stoter et al. Interestingly, the tendency of the upper part in a multi-part setting to be the most busy in contrast to the lowest part that tends to house slower rhythm Broze and Huron, remarkably resembles the motion parallax, sensitivity and awareness of which is found in 6-month-old infants Condry and Yonas, , raising questions about the genetic roots of greater acuity of perception of proximal data.

Everyone knows from experience of vocalizing that raising of the voice involves activation of higher part of the vocal folds Nazajkinskij, , p. For dynamic stimuli, ascending pitch is congruent with growing in size, whereas descending pitch—with shrinking in size—in accordance with the visual illusion of an approaching object growing in size Eitan et al. Just like Renaissance painters went into experimentation with projective geometry to develop an eye for perspective, their music colleagues employed an empirical technology.

At first, composers used tablets as visual aids in configuration of pitches in a single part, but by entire multi-part compositions were drafted on a larger cartella Owens, , p. Visual representation of music on tablet became mentalized. By , composers religiously followed the established technique of a simultaneous conception of all parts in a prescribed order Dahlhaus, , p. Audio: Josquin—Ave Maria , 4-part motet. Graphic visualization by Stephen Malinowsky demonstrates the role of spatiality in the distribution of musical phrases, evoking the state of equilibrium—corroborated by the dominance of C major triad throughout its tonal plan.

Image 1. Piero della Francesca—Brera Madonna One of the first generation works that employed precise linear perspective, characterized by strong sense of harmonicity and proportionality of composition, contributing to the impression of serenity. Rise of tonality accompanied the rise of perspective—in the same cities, sharing the same user base, artistic ideals, and similar organizational principles. Perspective made the first public impression in Edgerton, , p. It flourished in the genre of frottola, popular since s Prizer, Similar homophonic unity characterized uni-syllabic delivery of the multi-part arrangements.

Audio: Josquin—El Grillo , frottola for 4 vocal parts. Eventually, chordal thinking led to the establishment of general bass Schulenberg, : a practice of improvising a progression of chords to a given bass line—which can be viewed as an auditory equivalent of scaling 3D objects onto a 2D plain.

Here, the bass acts as a ground line, whereas a vertical slice of texture is projected onto it by every beat, so that harmony controlled by a certain chord covers a specific number of beats aligned in relation to the bass. This constant projection of the vertical parameter onto horizontal time-line is what every keyboard player was supposed to do while accompanying an ensemble or a solo instrument Bach, Audio: Monteverdi—Zefira Torno , madrigal for 2 parts and basso continuo.

Here, complex harmonic pulse is set by the repetitive formula in the bass. Toward the end, repetitions are disrupted before the movement resumes and marks the end with a flourishing cadenza. General bass discloses harmonic pulse that serves has been serving as an important compositional means, equal to time signature in its formative power, in post-Renaissance music for most part of the Common Practice Period.

Audio: Pachelbel—Canon in D Graphic visualization by Stephen Malinowski demonstrates the formula of 8 chords that is consistently repeated in the bass, forming the progression of 5 vertical harmonies that unite the melodic material of all three melodic parts. Pioneers of both, perspective and chordal textures, found their inspiration in Ancient Greece.

Renaissance theorists of perspective were heavily drawing on treatises by Euclides and Ptolemy Edgerton, Music theorists were equally heavily leaning on Aristoxenus and Ptolemy Galilei, He believed that in doing so, he was restoring the venerated principles of Greek composition by creating perceptual analogs to Greek tonos and modo. Just as much as visual artists invested into projective gadgets, Renaissance musicians went into calculating optimal ratios for tuning in order to maintain the purity of chords while keeping the melodic line expressive.

From the very beginning, Renaissance perspective was bound to proportionality Wittkower, Perspective rules strikingly resemble centripetal gravity in tonality. Correspondence of principles of canonic linear perspective and principles of eighteenth century Western tonality.

Three main principles that distinguish the basic one-point linear perspective find close match in the standards of tonal organization in the music composed according to the functional tonality theory that was formulated by Rameau Horizontal unification originated from vertical unification in Renaissance polyphony: Renaissance triadic tonality was born out of polyphonic texture, by satisfying the counterpoint rules in 4-part cadences Randel, The modern day consensus of historic musicologists holds that compositional process of 14—15th century polyphony was based on expansion of 2-part into multi-part counterpoint Moll, Renaissance mode essentially determined the melodic composition through cadential plan of the soprano and tenor parts—in a way similar to classical tonality Meier, , pp.

Most of the Renaissance went into attempts to forge the meantone temperament with optimal sonance of triads on the degrees critical for most common keys Lindley, : thereby, the idea of optimal division of octave was interconnected to the idea of better sounding chord, which is essentially the same idea that governed logarithmic intervallic distribution between parts Huron, Tri-unification of centrality, ratio and vectorization is specific to Western civilization. Neither China nor Arabia, although technologically ahead of Europe by the fifteenth century, generated a culture based on the theoretical realization of mathematically ordered world, designed for practical production of utilities.

Arabic scholars of the eleventh century knew Euclid and linear perspective Belting, , yet despite their contact with artists, perspective made zero impression on Arabic visual composition Raynaud, , not going any further than affecting depiction of details in architectural design Yazar, Solely in the West the artist adhered to the model of Divine emanation: God creates Man, and Man creates art, which is Divine.

Christianity was a viable force in promoting perspective and tonality. Not only perspective was sanctified by the Quattrocento theologians as a faithful representation of Divine light reflected from an object Edgerton, , p. Hierarchic unification opened doors to compression of information, which enabled great complexity, unparalleled in other cultures.

Audio: Tallis—Spem in alium c. Extremely thick polyphonic texture, with complex division in groups. Image 2. Bruegel the Elder—The Procession to Calvary Extensive landscape is filled up with detailed rendition of over a characters, subdivided in multiple concurrent events—all integrated in a single bird's view perspective. Tonal organization, just like pictorial perspective, establishes a particular model of symbolic representation of reality, shared by majority of the members of the same socio-cultural formation.

Such model sustains over a period of time, instilling the same approach to reality in old and new generations—until the time when, for some reason, the socio-economic change renders this approach inadequate. Then, the old model of symbolic representation is abandoned and replaced by a new one. Just as the shaded line can inform whether the drawing engages the depth parameter, performance of a single melodic line can indicate the vertical and horizontal harmony. A string player or singer, brought up with Western tonality, tunes each melodic tone according to its membership in the chord implied by the vertical harmony Friberg et al.

Tonal performance presents an ongoing challenge of constant mediation between melodic and harmonic tuning. The pre-MPS folk music does not involve such intricacies. The archaic folk singer, raised in monodic music culture, is unaware of implied chords, following only the melodic aspect of tuning. Representatives of any primordial polyphonic folk traditions are likely to combine melodic and harmonic tuning of their respective polyphonic system.

Each melodic interval slightly varied in zonal width: from 24 cents for unison to 76 cents for minor 2nd Garbuzov, , p. Each pitch zone can be viewed as part of representation of a traditionally established set of frequencies, remembered as a repertoire of standard intonations. A pitch zone is the aggregate value of all the expressive tunings for a given degree of a PS across all intonations that characterize this mode, afforded by the music-users Garbuzov, , p.

Narrowing of all the pitch zones would signal of the performer's concern with the vertical harmony. The culprit here is the same—centering on a single aspect of organization due to lack of integrative experience. And just as folk musicians can be taught tonal music, non-Westernized people can learn to draw in linear perspective Mshelua and Lapidus, He employs fissure—isolation of a presumably important sound signal from unimportant ones. Musical listening, in contrary, requires integration of simultaneous sounds, calling for application of an adequate scheme of tonal coding.

There is experimental evidence that pitch is mapped to height for isolated tones differently than for melodic intervals—by non-musicians, while musicians process pitch automatically Lidji et al. This suggests that spatial representation of tonal organization has to be learned. Each scheme of tonal organization abstracts those perceptual features of the living environment that are crucial for the success of the typical representative of a given culture in pursuing his life goals.

Sophistication of a scheme is only an answer to the sophistication of socio-cultural conditions for survival: 2-dimensional representation with indefinite intervallic values sufficed the earliest schemes, whereas later schemes required more dimensions and greater precision. Similar dimensional conversion characterizes literature, where perceptual reality is described from an angle of the speaker, in 2D fashion, word-per-time Uspensky, , p.

Noteworthy, the onset of naturalistic depiction, literature, and harmonic theory all concur in Mesopotamian urban culture.

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The next landmark, invention of perspective, paralleled chromatic music and lyric poetry that became means of individual self-identification. Here, the cognitive centerpiece that supported them all was concise definition of one's position in relation to something: be it a depicted object, a composed melody in a certain mode, or a subject of a poem.

Crystallization of linear perspective c. The musical equivalent here would be the style of musica reservata where, in the polyphonic texture, the listener had to track a theme that expressed a particular emotion related to the lyrics—shaded tonally with the help of chromaticism Meier and Dittmer, There, orientation occurred by triadic sonority and melodic diatonicity guiding the listener in mapping spots of tension and relaxation. Polyphony, tonality, and perspective, each in its own way, all faceted the same sense of individualism that flourished circa fifteenth century Hyer, Their symbiosis did not fall apart after homophony replaced polyphony as the dominant compositional method during mid-eighteenth century Tonal organization is more likely to prototype pictorial representation than vice versa.

The archetype could be the Central Asian tradition of carpet weaving, where weavers use chants to aid memorization of ornamental patterns—possibly dating to an older Indo-European tradition, mentioned by Homer and Bacchylides Tuck, Music behaviors are more widespread than drawing behaviors—especially in egalitarian-oriented folk cultures.

Despite intense professionalization, levels of public engagement in music-making stayed high even in the industrial West congregational and amateur music —until the s Rothstein, ; Chybowski, Nothing comparable in scale is known in art history: neither in prehistoric 49 Curtis, , p. Relatively clear public consensus on what constitutes excellence in music vs. Drawing adheres to a theory only in religious applications, such as iconography, or in professional institutions, such as academy of arts—where such theory noticeably lacks uniformity, with different schools adhering to different techniques and methods of drawing.

Hockney informs about the multiplicity of technical gadgets utilized by artists throughout ages, starting from Euclid Producing and reproducing a tune does not require any comparable technology. Copying a tune by ear is much more intuitive than copying an object by eye. Unlike ubiquitous acquisition of singing skills Hargreaves, , pp.

Their knowledge of what to draw typically interferes with their choice of depicting strategy Tallandini and Morassi, The effective solution becomes abstraction of a graphic-motor schemata adopted per object type Phillips et al. The entire development of pictorial skills throughout childhood is shaped by this goal Morra, Noteworthy, children are more prone to copy each other's pictures than to infer from life Wilson and Wilson, Reproducing a tune is nowhere near as technical, intellectual, problematic, and cognitively demanding as depicting an object.

Children of around that age can infer a tune from a polyphonic folk-song by themselves without any assistance Naumenko, , p. Flattening of a polyphonic song into a monophonic version is a common trait in many ethnic cultures Jordania, , pp. Conversion of musical texture seems to present no obstacle comparable to 3D-2D conversion. No wonder, musicality is considered a biological trait of Homo Morley, , p. Music occupies a prominent position in children development, only magnifying toward adolescence.

In contrast, drawing attracts children at the age of 2—3 years, waning afterwards Winner, An adolescent at large becomes estranged to drawing, once so favored at a younger age—in polar opposition to his musical interests Vygotsky, , p. Modern 8—18 year olds spend on average 2. The underlying reason must be affiliation of music with cognitive consonance. Vygotsky , p. And nothing answers this call better than music itself. Existence of 14 schemes of tonal organization see Appendix 8 in Supplementary Material suggests that tonal order in music manifests a general mental organizational scheme, which serves as a cultural adaptation of human perceptive apparatus to a life style optimal in a certain environment Lomax, , p.

Younger generations in a socio-cultural formation keep reproducing the same schemata as long as the same life style pertains. Music appears to act as a principal enforcer of this mental enculturation.

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The emotional nature of music, its affinity with entrainment, and its capacity to reduce cognitive conflict, all make tonal organization a powerful tool in shaping a methodology of thinking within a given community. Gravitational laws of musical virtual reality reflect perception of physical laws of phenomenological reality, and link the navigation strategies for both of them. The rigorous and systematic organization of music is a product of pressure imposed by natural selection to adequately collect information about the kinds of objects that exist in the environment, what they do, and how they can possibly be used Terhardt, Through a complex process of conversion of frequency data into pitch information, the brain exercises an organizational scheme that is archetypical for majority of music users in a given community.

Capacity to make emotional judgments about imagined music Halpern, makes music a par excellence tool for social engineering. Pitch presents a perfect medium for exercising discretization: human hearing is inherently zonal—it cannot distinguish between different pitches in a clear-cut manner; there is a zone between frequencies of tones in a familiar PS, upon hearing of which the listener cannot reliably tell which pitch it is. Even extremely gifted and well-trained soloists observe cent inter-zonal threshold Garbuzov, , p.

Parncutt and Cohen also specify the 10—20 cent threshold Jordan demonstrated that listeners can discriminate intervals of cents, but categorize them in terms of diatonic IS, and musicians do so more than non-musicians. Models of tonal organization can be viewed exactly as algorithms designed to minimize indiscretion in detection and production of pitches in a given socio-cultural formation. Similar mechanisms must be at play in the perception of other important attributes of musical sound. Garbuzov experimentally identified the zonal nature of perception of dynamics Garbuzov, , timbre Garbuzov, , tempo, and rhythm Garbuzov, Garbuzov's pupil, Rags , p.

It appears that during the passed century the zones and zonal thresholds have shrunken in perception of Western classical music Rags, , p. For non-tempered intervals, inter-zonal thresholds are about 2—2. Moran and Pratt confirmed this ratio for the tempered scale. Comparative investigation of how Western and native Java musicians estimate intervals in Western and gamelan music demonstrate that Javanese listeners have wider zones of pitch uncertainty in auditioning Western music than Western listeners do in Javanese music Perlman and Krumhansl, Another trend, noticeable throughout the evolution of tonal organization, is the progressive increase of the number of pitch zones within an ambitus of a mode Rags, , p.

Pitch zone discrimination throughout the evolution of tonal organization in low voice vocal music. The compass of an average singing voice is taken as 2 octaves Kob et al. For the khasmatonal music the compass is an octave wider because of inclusion of falsetto singing Heylen et al. Oligotonal music engages no more than 4 degrees, some of which are fixed in pitch, while others variable.

Ancient Greek chromatic system contains 16 discrete PCs within A2-A4, 11 of which are octave-equivalent. That leaves 27 available pitch slots in the range reserved for vocal composition. The critical width of chromatic semitone can be assessed based on discussions of chromatic shading in period treatises Hagel, , p. Vocal solo music in Western tonality contains 17 PCs and 35 slots in 2-octave range since it tends to adhere to the Pythagorean model Ghrab, , especially for non-professional singers Devaney et al.

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Ten stages of tonal evolution are mostly cumulative — Figure 5 Alekseyev illustrates how archaic principles of pitch organization are still present in modern music. Khasmatonal principle manifests itself in folk yodeling or rock music growling. Ekmelic principle comes out in gliding inflections and half-spoken pitches of blues or rap.

Stages 1—6 are cumulative until the divergence between pentatony and heptatony. Second divergence occurred between chromatic and diatonic MPSs, bringing to life hypermode. Chromatic MPS produced yet another divergence between hemiolic modality and tonality.

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Divergence, on the other hand, requires learning of a scheme that is diverged in relation to the music user's native system. A music-user from a later stage of tonal development possesses apparatus to decode the representational schemata of earlier cultural formations, but a listener raised exclusively on music of earlier stages cannot adequately decode spatial aspects in music of a later stage. This is most obvious in the communication of motherese: Western mothers have no problems reserving to the khasmatonal organization in their singing despite their competence in tonality see Presentation-3 from Part-I , while for their babies khasmatonal music remains the only form of tonal organization that they seem to be able to fully follow.

Their perception of tonality is severely limited Trehub, Zemtsovsky considers the very concept of musical tone to carry a signature of tonal organization. Artificiality of periodic oscillation in musical vocalization calls for justification. Hearing a single pitched tone generates expectation, and hence, induces gravitational projection toward the following pitched tone. In order to make sense, a tone must proceed to another tone or be repeated , forming an intonation. And a melodic intonation becomes not only a brick in the melody, but a quantum of gravity in the virtual reality of music.

It appears that progressive increase in tonal acuity is the result of evolution in melodic complexity. Crystallization of melodic contour typology brought to life ekmelic pitch regions to replace much wider and less definite khasmatonal registers. Forging of absolute intervals of 2nd, 3rd, and 4th between the anchored tones replaced ekmelic regions with oligotonal pitches. Triad induction caused variable tuning of unstable degrees to recede to bi-optional tuning. Transposition-by-degree of pentatonic and hemitonic motives fixed unstable degrees in tuning, and narrowed the pitch zone to a semitone.

Institution of chromatic alterations further narrowed the zones below a semitone. Parallel increase in PCs and establishment of complex tonal hierarchy within a mode made encoding of tonal relations effective enough to support simultaneous data transmission via multiple sound streams, up to 7-componental music texture. Each of the components simultaneously encodes information by means of idioms of pitch, rhythm, meter, and harmony, plus the contribution of expressive parameters of dynamics, tempo, articulation, timbre, and music form Such unprecedented density of information makes music a par excellence tool for abstraction of important features in a living environment, and mediation of their schemata between the members of the same social group in the best interests of each individual.

Language is an important factor that shaped melodic intonation and its tonal organization. People sing together to share the same experience, but talk one after another—usually to resolve an issue. Listeners routinely engage into musical behaviors for relaxation or recreation, which is less common for speech that normally cannot run in a semi-automatic regime, unlike music.

Less stressful manner of experiencing music is likely the result of different strategies preferred in comprehension of music vs. The tendency to fuse spectral content dominates the perception of music, while the tendency to segregate phonemes prevails in the perception of pitch Bregman, , pp. Then, the need to differentiate between the spectral elements greatly promotes the realization of opposition and discrepancy within the sound material, whereas the need to integrate partials into musical tones, and tones into chords, promotes the realization of similarity.

It looks like both forms of communication co-evolved from some primordial animal-like vocalization, defining each other through the different treatment of pitch—each forging its dedicated processing system Zatorre and Baum, The ethnomusicological evidence leads one to believe that melodic intonation was formed by borrowing and exaggerating the pitch contour of the conventional verbal intonations, while contrasting the verbal timbral organization and articulation style.

Stabilization of pitch in oligotonal music led to reduction in timbral complexity, changing the manner of its opposition to speech. However, overall, music tends to contrast speech in pitch organization—most evident in tonal languages, where the musical pitch contour of traditional songs often violates the normative intonation contours of the lyrics List, In a compensatory manner, cardinal stages in the development of language tend to concur with shifts in the method of tonal organization.

Development of sentence syntax conditioned transition from khasmatonal to ekmelic mode. Emergence of epic poetry promoted oligotonal music. Introduction of literacy boosted the emergence of philosophy, law, and science—promulgating prescriptive theory of harmony and diatonic music. Any ensemble attempt to sing a melody with fixed pitches would contain asynchrony, when one performer produces a new pitch while the other still carries the previous pitch—thereby converting melodic interval into harmonic.

Just as a single pitch is prone to generate a 2-tone intonation, it is prone to generate a 2-tone vertical harmony. And this is where spatial representation comes into play: 2-tone vertical harmony is cross-modally equivalent to 2D pictorial representation, and 3-tone harmony chord —to 3D. In the same way it takes at least three objects to hint to three distinct levels of pictorial depth Cook et al. Upgrade from dyadic thinking constitutes the greatest achievement of human civilization 57 , underlying all the technological achievements. Possibly, tetradic thinking is there to follow. By cross-modal implication, musical intonation differs from verbal.

Speech is not heard in terms of visualizing auditioned tones the way music is. The bifurcation point must have occurred during the oligotonal stage:. Melodic intonation is immensely important for human culture of thinking. Once generated, melodic intonation receives life of its own. It can be adopted by many music users and embedded into a mode It can be developed: by contribution of each of them. Historic development of intonation resembles epistemology and historic changes in syntax of language. Analysis of intonations in a song enables reconstruction of the gravitational system observed by the creator of that song—in a way similar to a paleontologist's reconstruction of a fossil from a bunch of bones.

Mode is capable of showing which intonations have stayed popular within a community of users over an extended period of time This makes it possible to generalize a gravitational scheme exercised in the music of that culture, and to formulate the cognitive style peculiar to a given historical socio-cultural formation. Understanding this cognitive style allows for extrapolating a method of musical order in organization of other cultural activities. Overall, music appears as a naturally formed testing ground for various principles of representation of reality, conscious and unconscious Hubbard, , used to prime emotional reactions to music idioms, thereby establishing and cultivating conventional standards of intellectual and emotional intelligence.

The author confirms being the sole contributor of this work and approved it for publication. The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. My special thanks go to Sheila Bazleh for editing the text of my manuscript. Sacredness of number 9 in Antiquity stemmed from the Babylonian Lunar calendar Wiltse and Palmer, Babylonian proportions were perpetuated in the Parthenon Kappraff, Such effect seems to be universal Larson and McAdams, ; Deutsch, ; Larson, and therefore applicable to the Ancient Greek music.

The difference between perfect 5th cents and 4th produces major 2nd Specialization required expertise from the musicians—to prepare music ahead of time, and their performance could score varying degrees of success, reflected by difference in wage Ziegler, The Old Babylonian tablet CBS postulated heptatonic tuning Dumbrill, in the eighteenth century BC Friberg, , likely descending from the older tradition, perhaps the twenty sixth century, when the Lyre of Ur was made Rowan, The influence of obykhod on Russian folk music is tracked to the fifteenth century Rudneva, , p.

Correct spelling of pitches can be verified by computer analysis of the frequency of each discrete musical tone within a song, then defining its PS by mediating between the average values received by incrementing the degrees in the ambitus and the melodic intonations established by morphological analysis of a song see Presentation-1 for an example. Lack of precise instrumental reference aulos could not support didactic descriptions of microtonal tuning due to its construction West, , p.

That still keeps in place about textural components. National Center for Biotechnology Information , U. Journal List Front Psychol v. Front Psychol. Published online Mar Author information Article notes Copyright and License information Disclaimer. This article was submitted to Cognition, a section of the journal Frontiers in Psychology. Received Dec 16; Accepted Feb 3. The use, distribution or reproduction in other forums is permitted, provided the original author s or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice.

No use, distribution or reproduction is permitted which does not comply with these terms. This article has been cited by other articles in PMC. Associated Data Supplementary Materials Presentation1. Abstract This paper reveals the way in which musical pitch works as a peculiar form of cognition that reflects upon the organization of the surrounding world as perceived by majority of music users within a socio-cultural formation. Introduction Part-1 of this paper presented the framework for study of tonal organization 1 in any kind of music.

Genesis of modal family and the role of tetrachord What separates prehistoric and historic forms of music is the emergence of math-based music theory and notation. Open in a separate window. Figure 1. Figure 2. Formulation of the mega-pitch-set The next development occurred when the triad induction see Part-I caused to re-conceptualize the lower tetrachord plus a tone above it as pentachord , forging a concept of melodic intonation of 5th as a modal unit 13 , and introducing a new hierarchic layer I-III-V into a mode.

Figure 3. Figure 4. Alteration and modulation Unlike the hypermode, the diatonic MPS did not restrict degrees to sustain their pitch values throughout the music work. The most common form of gravitational shift in folk music is intra-modal mutability. Renaissance polyphony and perspective: parallels in organization Just like Renaissance painters went into experimentation with projective geometry to develop an eye for perspective, their music colleagues employed an empirical technology.

Table 1 Correspondence of principles of canonic linear perspective and principles of eighteenth century Western tonality. Principles of Linear Perspective Principles of Vertical Harmony Principles of Horizontal Harmony Centrality principles The single viewpoint principle: ideally, a spectator is supposed to stand where the artist stood while drawing—at the equidistant point where all the rays that are reflected from the depicted objects join together, marking the center of projection.

Observation from any other point is regarded as inferior, ought to be avoided Greene, Single part principality: The composer, the performer, and the listener all are supposed to focus attention on one part voice at a time—determined by placement of the theme: which can be defined as a distinct characteristic progression of motifs, reused in a music work in the capacity of a discrete unit of expression Mazel, , p.

The tonicity principle: A particular tone ought to be recognized by the composer, performer, and listener as the strongest in stability amongst all tones used within a music work—thereby setting a single point where all the vectors of resolution for all unstable tones in the key would meet.

If related keys were engaged in a composition, their tonics would be regarded as secondary. Single ratio principles The principle of single scale of proportions: Certain unit of measurement has to be selected, and then applied consistently to the entirety of the picture to measure and arrange intervals of space between the depicted objects in order of their position towards the spectator, representing their distance from him. The principle of logarithmic intervallic spacing: The parts voices at the top of the texture must be closer to each other as compared to the parts voices at the bottom of the texture—ideally, staying close to logarithmic ratio, similar to intervallic distances between the partials in a harmonic series Huron, The lower the register, the wider the intervals.

The principle of equal temperament: The entire MPS has to consist of tones that are equally spaced from one another by the interval of the well-tempered semitone, defined by division of an octave into 12 parts—so that the same piece of music would maintain its intervallic integrity precisely, if transposed to a different key. Vectorization principles The principle of single horizon: All the lines directed toward the depth of a depicted space, away from the spectator, must converge and vanish at the rational horizon line, defined by imagining an infinite horizontal plane.

Only a slight deviation from the direct angle is afforded for the vantage point: the line that joins the vantage and the vanishing points sets the direction for viewing. The principle of key recapitulation: All tones of the composition must comply with the IS model of major or minor keys, and follow the tonal plan suitable for a given genre and music form, where the music work has to start and end in the same key, securing tonal integrity Kholopov, , p. Melodic line, geometric line and environmental topography: their connection Just as the shaded line can inform whether the drawing engages the depth parameter, performance of a single melodic line can indicate the vertical and horizontal harmony.

The course of tonal evolution Existence of 14 schemes of tonal organization see Appendix 8 in Supplementary Material suggests that tonal order in music manifests a general mental organizational scheme, which serves as a cultural adaptation of human perceptive apparatus to a life style optimal in a certain environment Lomax, , p. Table 2 Pitch zone discrimination throughout the evolution of tonal organization in low voice vocal music.

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Figure 5. General summary Zemtsovsky considers the very concept of musical tone to carry a signature of tonal organization. Author contributions The author confirms being the sole contributor of this work and approved it for publication. Conflict of interest statement The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

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Evidence from traditional singing pitch transcriptions. Music Stud. Berlin: Springer. Moscow: Prosvesheniye. Perceptual dynamics in musical expression. Tbilisi: Tbilisi State Conservatoire; , — Key and mode in seventeenth-century music theory books. Music Theory 17 , — Oxford: Oxford University Press; New York, NY: Norton. The prehistory of chinese music history , in Proceedings of the British Academy , Vol.

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