Is it possible that the course of evolution is predetermined? No? Consider the phenomena of Newtonality a while and think again...

 

In the Newtonal system there are ten orders of composition:

 

I Binary (AB or AA)

II Ternary (ABA)

III Rondo (ABACA Coda)

IV Slow Movement form (ABACBA Coda)

V Sonata

VI Binary Sonata Rondo

VII Sonata Rondo

VIII Free

IX Fugue (Tonal/Newtonal/Thomic)

X Newtonal (Circle/Block/Combination

 

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X must be, naturally, exclusively newtonal. But I-IX (inclusive) may be either tonal or newtonal.

 

Newtonal Block and Combination techniques are suitable for adaptation to any order of composition.

 

Examples: For VI, see Euro-Suite, finale (“Tyler Hill”); For VII, see Euro-Suite, 4thmovement (“Dear Franz”). 

Note: the Euro-Suite, though designed for commercial purposes, employs most of the ten orders, and is therefore useful for the purposes of demonstration.

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Please note: Neither Newtonality nor the technique of Thomes & Phases have any connection with the theories of Paul Hindemith, as those who have taken the trouble to examine my own theories will see.

The theory of Newtonality evolved naturally as a result of my earliest exploration of Thomes & Thases - or, as it was originally named, Thomes & Opposites - a compositional technique which attempted to define and then integrate tonal and atonal material into a single language. The initial response from friends and colleagues was, by and large, incomprehension. Though disappointing at the time, this was - with the benefit of hindsight - hardly surprising; it has taken me thirty years to tease out from the original idea three methods for applying the technique in practise.

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NEWTONALITY: EXPOSITION ON THE LAWS, PRINCIPLES AND DEFINITIONS PERTAINING TO THE EVOLUTION OF THE WESTERN MUSICAL LANGUAGE

Originally published and distributed 1983. This edition revised and published by the Tree Shrew Club 2005 © 1983 N Capocci

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http://www.scoreexchange.com/scores/38320.html

 

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The gaining of a full understanding of this article depends upon the acceptance of the fact that, quantitatively, tonality has no fixed condition. The description of: (ex1; fundamental tone with harmonic partials) as "tonal", or "consonant" is meaningless. It might equally be described as "atonal", or "dissonant". None of these terms have any relevance except where they are employed within the context of an evolved language. Tonality is the artificially created condition of an evolved language. It presents the mutable relationship between consonance and dissonance. Special systems define the quality of that relationship, while the rules of the modus oparandi describe how it will manifest in quantity. The methods and terms of classical, tonal analysis are effective provided the subject of the analysis is a classical, tonal work. The emergence of atonality as a significant compositional element requires those methods and terms be fundamentally altered if they are to remain effective for both tonal and atonal conditions. That this must be true is shown as follows: (ex2; a) simple diatonic chords - b) non-triadic chords) .If a) is said to describe tonality according to the diatonic system, all that can be said with regard to b) is that it does not. If b) is said to be atonal, the condition of its atonality is specifically related to a). Atonality, like tonality, has no fixed condition. Again, if b) is said to be atonal, what character does it possess that it can be so named? Tonality and atonality have no fixed condition. Triadic chords, of themselves, are not tonal; they are the servants of the diatonic view of tonality. Correspondingly, the absence of triadic chords, of itself, does not indicate atonality. The atonality of b) is artificially created by its relation to a). It is as meaningless to equate the condition of atonality with non-triadic sounds as it is to equate the condition of tonality with a fundamental tone and its harmonic partials. If there evolved a special system based on the relationship between tonality and atonality, and, if the modus operandi of that system were formulated so that it allowed for the co-existence of a) and b), it would follow that the rules of the modus operandi of a), together with its methods and terms of analysis, would be fundamentally altered. A composition based on such a system would be impossible to analyse using the classical methods only. It should be noted, however, that the application of Newtonal analysis to a tonal passage, though by no means impossible, is, to a large extent academic. In the present article, where the Newtonal view is applied to tonal systems, and conclusions drawn, it is done with the intention of highlighting the difference between the two systems, revealing the “one-way-membrane” that connects them, and of proving, ultimately, the inseparability of tonality and atonality. The tonal and Newtonal systems are not mutually exclusive, but whereas both are valid at all times, only the Newtonal system is valid under all conditions.
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NEWTONALITY
LAWS
1) Consonance and dissonance are inseparable, being simultaneous in quality (system) and non-simultaneous in quantity (modus operandi). 2) The definition of class is constant with respect to all systems contained within that class. 3) Tonality and atonality are inseparable, being simultaneous in quality (system) and non-simultaneous in quantity (modus operandi).
PRINCIPALS
1) The tonal centre is equivalent to the condition of greatest consonance. 2) A modus operandi is effective only with respect to the system it describes. 3) The Newtonal centre is equivalent to the condition of greatest tonality.
DEFINITIONS (of class)
1st. class : Melodic Melodic systems define tonality thus: the tonal centre is that tone which achieves the condition of greatest consonance with respect to all others, which are then relatively dissonant to it, the degree of dissonance being proportional to the interval(s) of pitch.
2nd. class : Harmonic Harmonic systems define tonality thus: the tonal centre is that chord which achieves the condition of greatest consonance with respect to all others, which are then relatively dissonant to it, the degree of dissonance being proportional to the distance of the chord.
3rd. class : Newtonic The Newtonic system is defined thus: the Newtonal centre is that phase which achieves the condition of greatest tonality with respect to all others, which are then relatively atonal to it, the degree of atonality being dependant upon the method and structure of the Newtonal centre.
There are three classes of systems: Melodic, Harmonic and Newtonic. The Melodic class has three subdivisions, the Harmonic two and the Newtonic none, making a total of six systems, each with their respective modus operandi. (ex; chart)
Both the systems and the classes to which they belong are continuative; that is, the successive transition from one class to another or from one system to another is effected by continuation (represented by the Greek delta symbol). Each class or system is composed of one kinetic force, or element - that force or element being equivalent to the class, or system - and at least one potential force, or element. (ex; chart)
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BASE MATERIAL (harmonic & melodic) Harmonic base: sounding of a fundamental tone with its harmonic partials. (ex; fundamental tone with partials)
Melodic base: transposing partials by the octave -
a) transposing the fundamental tone so as to sound as a new fundamental tone with its partials, (ex; as above transposed)
b) general transposition (ex)
There are three potential forces consequent to the establishment of the base material. They are: 1) MELODY 2) HARMONY 3) NEWTONY
ex; chart showing degrees of dissonance
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MELODIC SYSTEMS
1) Monophonic (single melody) (ex)
Modus operandi - chant (plainsong)
The tonal centre is the tone, X, achieving the condition of greatest consonance with respect to all others, which are relatively dissonant to it, the degree of dissonance being proportional to the intervals of pitch.
2) Diaphonic (double melody) (ex)
Modus operandi - (organum)
The tonal centre is the tone, X, achieving the condition of greatest consonance with respect to all others, which are relatively dissonant to it, the degree of dissonance being proportional to the intervals of pitch.
3) Polyphonic (triple, quadruple, etc., melody) (ex)
Modus operandi -
counterpoint
(strict)
The tonal centre is the tone, X, achieving the condition of greatest consonance with respect to all others, which are relatively dissonant to it, the degree of dissonance being proportional to the
intervals of pitch.
(ex; plainsong X...... X1)
To ascribe a condition of superiority (consonance) to tone X is not possible without simultaneously ascribing a condition of “insuperiority” to another, different tone, X 1. X may exist by itself, but if the term "consonance" is attached to it, it cannot. As a consonance it can only exist by relation to a dissonance. If all that exists is X and X1, and X is consonant, then X1 must be dissonant. The qualitative statement can be made: X is consonant to X1. By introducing the other tones, the three melodic systems can be evolved, their (the tone's) relative conditions of consonance or dissonance being regulated by the intervals of their separation from the tonal centre. A melodic system is the qualitative definition of those relationships. A modus operandi is the non-simultaneous, quantitative method by which the system is described. That is to say; tones representing relative conditions of consonance or dissonance are separated in time by the governing rules of the modus operandi.
(ex; plainsong X...... X1 ...... X2 )
If X is the tonal centre, then both X1 and X2 are relatively dissonant to it. Within the melodic class of systems it is incorrect to define the interval of the perfect 5th. as consonant, since, quantitatively, consonance and dissonance are non-simultaneous, separate events in time - they are not fixed conditions. The interval of the 5th. may acquire the status of a consonant only within the harmonic class of systems. Polyphony deals specifically with three or more lines of melody. The correct analysis of the above is: if X is the tonal centre, then both X1 and X2 are relatively dissonant to it, the degree of dissonance being (approx.) equivalent (interval relation) with respect to X. X1 is more dissonant to X2 than to X, and X2 is more dissonant to X1 than to X. Each tone has a separate relation to each of the others. If X2 were to become (fall to) X3, its own relation to X and X1 would change, but the relation of X1 to X would not alter. The establishment of all these relationships is consequent to the existence of the tonal centre. The statement: "X2 is more dissonant to X1 than to X", cannot be true. Whereas the statement: "X2 is more dissonant to X1 than to X, where X is the tonal centre", is entirely correct. The tonal centre is the condition prior to all other conditions.
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HARMONIC SYSTEMS
1) Diatonic (simple chord relation) (ex) Modus operandi - harmonic progression (diatonic)
The tonal centre is the chord, X, achieving the condition of greatest consonance with respect to all others, which are relatively dissonant to it, the degree of dissonance being proportional to the distance of the chord.
2) Chromatic(complex chord relation - Modus operandi - equal temperament)
(ex) modulatory progression (classical harmony &
counterpoint)
The tonal centre is the chord, X, achieving the condition of greatest consonance with respect to all others, which are relatively dissonant to it, the degree of dissonance being proportional to the distance of the chord.
(ex; 3 chords - X, X1, X2 )
1) To ascribe a condition of superiority (consonance) to tone X is not possible without simultaneously ascribing a condition of insuperiority to another, different chord, X 1. X may exist by itself, but if the term "consonance" is attached to it, it cannot. As a consonance it can only exist by relation to a dissonance. If all that exists is X and X1, and X is consonant, then X1 must be dissonant. The qualitative statement can be made: X is consonant to X1. By introducing the other chords, the two harmonic systems can be evolved, their (the tone's) relative conditions of consonance or dissonance being regulated by their distance from the tonal centre. A harmonic system is the qualitative definition of these relationships. A modus operandi is the non-simultaneous, quantitative method by which the system is described.
If X is the tonal centre, then both X1 and X2 are relatively dissonant to it. Within the harmonic class of systems it is incorrect to define major and minor chords as consonant, since, quantitatively, consonance and dissonance are non-simultaneous, separate events in time, not fixed conditions. The correct analysis of the above is: if X is the tonal centre, then both X1 and X2 are relatively dissonant to it, the degree of dissonance being (approx.) equivalent (distance of chord) with respect to X. X1 is more dissonant to X2 than to X, and X2 is more dissonant to X1 than to X. Each chord has a separate relation to each of the others. The establishment of all these relationships is consequent to the existence of the tonal centre. The statement, "X2 is more dissonant to X1 than to X", cannot be true. Whereas the statement, "X2 is more dissonant to X1 than to X, where X is the tonal centre", is entirely correct. The tonal centre is the condition prior to all other conditions.
2) The remarks and analysis of 1) above apply with equal force to extended compositions. Modulation and the establishment of "new" tonal centres is unimportant. That is to say; in the chromatic system, chords maintain their respective relationships to one another and the tonal centre.
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MELODIC & HARMONIC: GENERAL COMMENTS
1) In the melodic class of systems, conditions of consonance or dissonance cannot be ascribed to the vertical alignment of tones. For example : (ex CFG vertically aligned) is not a chord, but the vertical alignment of three tones resulting from the progression of three melodies. The statement, "the simultaneous vertical alignment of G over F is dissonant" is incorrect. The statement, "G is dissonant to F, where C is the tonal centre", is correct.
2) In the harmonic class of systems, conditions of consonance or dissonance can be ascribed to the vertical alignment of tones (chords). For example : (ex; chord of F) is a chord. It does not result from the progression of three melodies.
To describe: (ex; FACGG as chord) as "dissonant" would be incorrect. The statement, " the chord (triad) of C is dissonant to the chord of F, where the chord of F is the tonal centre", is
correct.
3) All modus operandi, whether melodic, harmonic, or Newtonic, are specifically concerned with horizontal, sequential events. In the melodic class, consonance and dissonance are related by the progression of single tones. In the melodic class, consonance and dissonance are related by the progression of single chords. It is incorrect to describe the famous ninth symphony chord (ex Beethoven ) as dissonant, but it is correct to describe it as dissonant relative to another, different chord, within the total relation to a specific tonal centre. The addition of the 7th., 9th., 11th., and 13th. to a chord does not alter its condition (though it may affect the intensity of the condition). The prime consideration is not the structure of the chord, but its condition relative to other chords.
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GENRAL CONCLUSIONS
1) The Newtonal system has not been designed with the intention of changing or altering the accepted, tonal view of tonal composition, but evolved naturally as a consequence of observations made during experiments with Thomes & Phases, a compositional technique involving the amalgamation of tonal and atonal material into a single language. Tonal diaphony says that the perfect 5th. is a consonance; Newtonal diaphony - or, the Newtonal view of diaphony - says that it is not. Both views are true with respect to themselves. The value of the Newtonal view of a tonal work is, as already stated, that - though academic - it furnishes a simple demonstration of the Newtonal concept. In this connection it may be helpful to regard the relation between different classes as an extension of the second principal. For example, the simpler rules of harmonic progression may be absorbed into the more complex modulatory progressions of the chromatic system, yet, despite their common class, they are fundamentally different from each other. To view a chromatic passage diatonically is not possible: to view a diatonic passage chromatically is possible, but rather pointless. Ultimately, a tonal composition is tonally conceived, tonally executed, and only a tonal analysis makes any sense of it. The statement, "a major chord is not a consonance", makes no sense from purely tonal standards. The value of the Newtonal view of tonally conceived passages and compositions is that it provides indisputable evidence to the fact that, quantitatively, within the context of the evolution of the musical language, tonality has no fixed condition, and that as a consequence of the highly evolved nature of tonality within that context, no discussion of atonality can occur except within the same highly evolved context.
2) Schoenberg's "emancipation of the dissonance" is an erroneous concept: neither dissonance nor consonance may be liberated, either from each other, or from tonality, without immediately discharging all three into the realm of non-existence. The transition between the melodic and harmonic systems was accompanied by the emancipation of melody, ("free" counterpoint, passing tones, etc.) while the transition between the melodic and harmonic systems was accompanied by the emancipation not only of harmony, but of tonality itself. In both cases the emancipation was from the role of workhorse - bound by the regulations of the modus operandi - to a Pegasus of extended expressive capability. A melodic composition is both conceived and executed melodically. A harmonic composition is conceived harmonically and executed melodically. A Newtonal composition is conceived Newtonally and executed tonally.
In a harmonic composition, the progression of a melody is not governed by the regulations of the melodic class. It is the freedom of melody which allows: (ex; Chopin) ideally, the listener is unaware of the underlying structure of the chord progression, but of the interplay between two elemental and diametrically opposing forces: consonance and dissonance.
On the scale of a symphonic work, it might have taken Haydn half a movement to effect a modulation from F-sharp minor to F-minor, if F sharp were the tonal centre. In his overture Romeo and Juliet, Tchaikovsky effected the modulation in under thirty bars. The piece ends in B major with the bulk of the work being executed in B minor. If, from this, it is taken that B is the tonal centre, then the opening chord of F sharp minor is relatively dissonant on the scale of the work as a whole. Again, it is futile to argue the relative merits of either the tonal or Newtonal interpretation. What is important is that, from the Newtonal view, the relationship between consonance and dissonance has become more obscure because the condition of the greatest consonance has become more difficult to define; a situation in which that condition is impossible to define, or has ceased to exist, requires a completely new way of viewing the concept of tonality.
The quality of tonality and the quantitative tonal language are two totally different things. Qualitatively, tonality, with its twin poles of consonance and dissonance, is an immutable constant; any state other than the absolute precludes its existence. But its manifestation in quantity is mutable and inconstant; there is no single state with which its presence can be identified.

(ex chart)

 

 

 

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