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Tonality Is God

15K views 129 replies 29 participants last post by  millionrainbows 
#1 · (Edited)
It's possible to construe that the system of tonality itself, based on an hierarchy of sonance in relation to a single tonic note, as the harmonics of a fundamental note relate, is a "sacred" concept, since it relates every diverse harmonic function to a tonic, which becomes the "great note,' metaphorically representing God, "the one." These harmonic functions of Western tonality are based on the division of the octave into 12 notes, which was derived from Pythagoras' (imperfect) cycling of the 2:3 perfect fifth, with its inverted counterpart, the 4:5 perfect fourth.

Fifths are a value of 7 semitones, and fourths are 5 semitones. These are the only two intervals which do not coincide within the octave or divide it evenly until many cycles of projection are completed; in the case of fifths, 12 x 7 = 84, and for fourths this is 12 x 5 = 60. These are the main harmonic stations of traditional tonality, which is based on root movement by fifths as being most closely related.

12 is not divisible by either of these intervals, so an 'outside the octave' common denominator must be used. This makes these intervals "outgoing" by nature.

The other basic intervals (of the 6 possible basic intervals, not counting inversional counterparts) can be divided into 12:
1 (m2)
2 (M2)
3 (m3)
4 (M3)
6 (tritone)

These are intervals which coincide in their cycles or projections within the octave, and divide it symmetrically, so I call these "inward-going" intervals.

Conversely, systems which are not tonal (based on harmonic models), but use local tone-centers and small divisions of the octave (geometric systems), like Bartok and most modern systems which diverge from harmonic-based hierarchies, are "inner-directed."

These two different systems represent what I have earlier called "Western" (outward-directed, objective), and "Eastern" (inward-directed, subjective).

If we continue to stretch this metaphor, we can see that each system represents a different way of conceiving a religious system, or approach to the sacred.

The Western represents an objective, outer system which must be approached in a receptive (and many times literal) belief in a God 'out there' which is part of the objective scheme of things. If anything, we are merely small extensions of this great oneness, if that. Until we establish a connection, we are separated.

The Eastern represents a 'going within,' a diametric reversal, where we are connected internally with the sacred. For me, this is a more inclusive model, as every being is assumed to have an inner connection with the sacred, with no recognition of external symbols necessary. For me, this precludes the establishment of 'objective' belief systems of religion.

On a number line, these two approaches, the inner and outer, can be seen as two directions to infinity (God): The Western going to the right, in ever-increasing numbers, from 1 into infinity; The Eastern going to the left, from 1 towards zero, in ever-decreasing degrees of fractions.

Both are based on the starting point of "1," the big note, or the octave.

Taking this metaphor further, tonality can be seen as the embodiment of a Newtonian universe, a universe based on "gravity" and in keeping with a church-based view of Man, that God is the center of all things.

Atonality, or serialism, can be metaphorically seen as the dissolution of the Newtonian universe, and of gravity, into a relativistic, Einsteinian universe, in which Man is insignificant by comparison to the stars. Historically, this reflects the diminishing power of the church, ans increasing secularism and a new scientific realism which now pervades.
 
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#3 ·
Fascinating post. :cool:

I don't accept the Eastern \ Western or inner \ outer dichotomy except as reflecting different approaches to spirituality - the contemplative \ active dichotomy which reflects the Christian belief that God is out there but his life (of grace) is within us.

Neither do I accept that atonality or serialism represents the dissolution of the Newtonian universe rather it represents a dissatisfaction with the increasingly formal structures of counterpoint and harmony much as Gödel and Turing showed that mathematics and computing had become so complex as to be unprovable. Even within scientific realism there is room for the divine. As Einstein said - God does not play dice - a comment on aleatory music perhaps? We can also see this in the work of Musica Facta on syntonic temperament where the Pythagorean tuning is one among many just as Euclidean Geometry is also one among many.

I wouldn't consider that composers who have moved away from tonality whether into modes or into folk themes are inner directed or subjective. Vaughan Williams and others of the English folk song revival are focused on the outward reality of the English folk culture.
 
#8 ·
I don't accept the Eastern \ Western ... dichotomy
This is crucial. I wouldn't have expected in 2014 to run into this colonialist reduction of half the globe's people to stereotypes of sub-rationality. Anyone who believes this stuff about the mystical Eastern mind needs to spend a few months abroad - and not in places where people will tell him anything he wants to hear in exchange for cash.
 
#7 ·
I've seen the same associations made to suggest that music since Schoenberg has sucked because it was implicitly atheistic. With either spin, I suspect hyperactive pattern recognition.

What would, say, Richard Taruskin say of this analysis? Or Bruno Nettl? I'll take it seriously when I find out that they do.
 
#15 ·
When I read something like this, someone using terms like "Western" and "Eastern" in this manner, I never think that it refers to actual, living people. It's all metaphysical to me, completely unconnected to actual present reality and I'm sure that MR intended it that way.
 
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#18 ·
Maybe not connected to present reality, but apparently to past:

Western tonality . . . can be construed to metaphorically embody the conquering, dominating Western colonial mindset (which would include Spain, France, Germany, and Britain), which feels compelled to constantly 'modulate' or conquer new harmonic territory (invade and dominate foreign countries).
 
#17 ·
Could you explain just what you're trying to get at in simpler terms? From what I see you're mixing around some straightforward group theory (implicitly, anyhow; the quotient groups of Z/12Z and some of their properties) with some Pythagorean mysticism, some sort of odd usage of the field dependence/field independence concept from psychology, and some theological musings to top it all off. It's not really making much sense to me, I have to say.
 
#25 · (Edited)
The Church doctrine of privatio boni says that 'evil' is simply the absence of good. In this sense, atonality and serialism are 'evil' only insofar as they embody a state in which a tonal center is absent. In this sense, they are a 'diseased' form of music, in that for a disease or virus to exist, it must have a 'host' to feed on.

In this view, without tonality, atonality would not exist, and as such, atonality and serialism do not exist except as 'absenses' of healthy, tonal musical processes. In this sense, atonality is an 'unnatural' state of music, in that it removes music from its aural, sensually-based, and Human roots.

Therefore, since in this view atonality is a deficient form of 'healthy,' tonal, God-centered music, in order for it to exist as anything other than an 'absence,' we must create a new category for serialism.

Let's call it 'structural sound' and remove it from 'music' altogether.
 
#23 · (Edited)
Umm... I think you are taking too seriously certain properties of 12-tone temperament (not necessarily equal temperament, but some kind of temperament system that allows you to play in different keys whether white or black notes). The fact that twelve fifths circle around from C back to C is solely a feature of our western chromatic scale. It isn't even strictly true from a just intonation standpoint.

You know, in 19-tone temperament (which if not for historical accident could have been western music's standard) no interval neatly divides the octave, for example you need to stack 19 major thirds in order to get from C back to C. This feature of 19 tones is just an artifact of using 19 tones, nothing fundamental. And the feature that 3 major thirds give an octave in 12 tones is also an artifact.
 
#24 · (Edited)
Umm... I think you are taking too seriously certain properties of 12-tone temperament (not necessarily equal temperament, but some kind of temperament system that allows you to play in different keys whether white or black notes). The fact that twelve fifths circle around from C back to C (No, they don't; this is called the Pythagoran comma-Ed.) is solely a feature of our western chromatic scale. (Yeah, that's where "12" came from-Ed.) It isn't even strictly true from a just intonation standpoint.

You know, in 19-tone temperament (which if not for historical accident could have been western music's standard) no interval neatly divides the octave (I assume you mean "divide the octave in half equally"...that's because 19 is an odd number and can't be divided evenly; 12 can.-Ed.) for example you need to stack 19 major thirds in order to get from C back to C. This feature of 19 tones is just an artifact of using 19 tones, nothing fundamental. And the feature that 3 major thirds give an octave in 12 tones is also an artifact. (because 4x3=12.-Ed.)
19-tone is an equal temperament. It's arbitrary, in that it is a numerical division rather than one based on small number ratios.

When Pythagoras stacked his 3:2 fifths, he wanted to preserve the acoustic purity of the interval, as well as preserving the octave. He stopped at 12 because the coincidence was so close; but not perfect, as it will never be. An octave cannot be evenly divided (acoustically) using small-ratio intervals. With the compromise of arithmetic and the 12-division, it can (at the tritone).

Read my blogs; you are confusing arithmetic with ratios.
 
#32 ·
Tonality is God?
I would have guessed "white noise". I suspect God to be more incorporative.
But since I also adhere to Buddha's definition of God -- "God both is and is not, neither is nor is not" -- I suppose He/She/It/Them could equally be "silence" ... simultaneously with being "white noise".
I'm only confused by what "sound" is the Devil. But if it's true that there's a lot of harp music going on in Heaven, I'm quite willing to find out about Beelzebub. If he is indeed atonality, I won't be so disappointed ... as long as the music does not come by way of harps. I hate harps.
 
#33 ·
Getting back to serious metaphor, tonality is God because the scale is derived from, and is related to the 'key' note as "1". All other divisions of the "1" octave are ratios: 2:3, 3:4, 4:5, etc.

Really, the Devil only exists within tonality's purview, so the tritone is really the Devil (diabolus in music), because the tritone embodies the undoing of tonality, being related to the whole-tone scale (which is tonally neutral) and the diminished scale (which is a form of 'vagrant chord').
 
#41 · (Edited by Moderator)
Meanwhile: Christianity has died a slow, painful death, due to Dvorak and Schubert mixing the major and minor modes, thus increasing chromaticism and further degrading tonality's connection to 'the drone.' We then witness tonality spiraling into chromaticism, harmonic ossification, and loss of meaning and purpose...with music becoming, finally, what it is at its essence, a constructed language of sound, serving no other human purpose. At last, the separation of church and state!!
 
#46 ·
Tonality provides the soul to real art music. Pure and simple. :)
 
#48 ·
Tonality is the institutional language of Western classicism, which was powered by Church, state, and a wealthy upper class. Thus, "tonality is God" also has a political/social/historical meaning, which adds to the metaphor. In musical terms, the relation of all notes to "1" is a very easy metaphor to grasp.

12-tone music and serialism conveniently represents and reflects the dissolution of tonality, being slowly replaced by Enlightenment logic, scientific reason, and a "democratic humanism," because the tonal center is gone, and all notes relate only to their adjacent notes.

The metaphor is so obvious that I couldn't resist using it; in fact it practically invented itself.

Of course, to really get the significance of it, you have to understand "why" tonality is tonal, and how intervals are expressed as ratios, and lots of other givens.
 
#50 ·
So why did the Catholic church use modal music without a tonal centre? Surely it was the abandonment of Gregorian chant and the move to harmonised ditties after the Second Vatican Council that saw a decline in the influence of the church. In other words a move to tonality not its abandonment.
 
#53 · (Edited)
There is also a mathematical basis to my "ridiculous metaphor" that tonality is God:

"1" is the basis of tonality, and is subdivided into fractions to derive the scale steps.

Atonality, by contrast, operates on a number line with a zero point, since it is measuring interval-distances.

Tonality uses number as "identity" rather than quantity, as all scale notes are given a place in relation to "1" or the key note. This is an identity-relationship in an hierarchy, not a quantity of distance.

Tonality is congruent with the Western idea of measurement,in which Time=Being=Identity. These terms are all equivalent, and reveal the religious bias against the use of "zero" until much later, when we got it back from the Arabs, who had preserved many of the Greek mathematical treatises which the Church fathers had destroyed as heresy. The explanation follows:

We all know what quantity is. Let's say I have 53 sheep. If I trade you one sheep for your Suhr guitar (because you can't get any jobs playing fusion and need to feed your family), I have 52 sheep left. Easy enough.

However, if I number each sheep 1-53 in order to keep track of them, then they have been given a number identity. For example, if I trade you sheep number 52 for your '67 Marshall 50-watt head, then I will have 52 sheep left, although sheep #52 is gone. So now we can see the difference between number as quantity and as identity.

These two ideas used to get mixed up in the olden days; we had no "zero" because people tended to see numbers as representing actual objects, and when they counted their sheep, for instance, each number corresponded to an actual sheep. There was no "zero sheep;" the concept was useless to these lamb-eaters and traders, who dealt in concrete terms.

This is part of the reason time is usually measured in numbers without zero; there are 7 days in a week, but there is no "zero" day of the week; they are 1 thru 7, as identities. There is no "zero year;" Christ was crucified in the year 1 A.D., and the year before that was I B.C., not "zero." Clocks have no zero, they go from 12 to 1, except in military time, which does have a "zero hour," but the military is the Devil's tool.

From WIK: Astronomical year numbering, used by astronomers, includes a year zero (0). Consequently, the first century in these calendars may designate the years 0 to 99 as the first century, years 100 to 199 as the second etc. However, in order to regard 2000 as the first year of the twenty-first century according to the astronomical year numbering, the astronomical year 0 has to correspond to the Gregorian year 1 BC.


According to WIK:
Start and end in the Gregorian Calendar

According to the Gregorian calendar, the 1st century A.D./C.E. started on January 1, 1 and ended on December 31, 100. The 2nd century started at year 101, the third at 201, etc. The n-th century started/will start on the year 100×n-99 and ends in 100×n . A century will only include one year, the centennial year, that starts with the century's number (e.g. 1900 is the final year in the 19th century).

1st century CE and BCE

There is no "zeroth century" in between the first century BCE and the first century AD. Also, there is no 0 AD[1]. The Julian calendar "jumps" from 1 BC to 1 AD. The first century BC includes the years 100 BCE to 1 BCE. Other centuries BC follow the same pattern.


Arthur C. Clarke gave this analogy (from a statement received by Reuters): "If the scale on your grocer's weighing machine began at 1 instead of 0, would you be happy when he claimed he'd sold you 10 kg of tea?" This statement illustrates the common confusion about the calendar. If one counts from the beginning of A.D. 1 to the ending of A.D. 1000, one would have counted 1000 years. The next 1000 years (millennium) would begin on the first day of 1001. So the calendar has not 'cheated' anyone out of a year. In other words, the argument is based on the fact that the last year of the first two thousand years in the Gregorian Calendar was 2000, not 1999.


So, in our non-zero system, the first century consisted of the years 1 B.C. thru 100; the second century was 101-200; and so on, until we get to the eighteenth century, 1701 to 1800, and the twentieth century, 1901 to 2000. That's why many experts were telling us that the "millenium" was not actually the year 2000, but January 1, 2001.

Part of the reason for avoidance of zero was religious, and goes back to the Church doctrine of "privatio boni"... Look it up if you're interested.
 
#54 ·
#71 ·
The whole tone scale is an 6-tone based on the projection of the major second. The scale's interval content is M2s, M3s, and tritones. It repeats symmetrically; no matter which note you begin on, the resulting intervals are the same. It divides evenly at the tritone.

Tonality uses the 7-note diatonic scale, and its "dividing point" is the fifth.

That's because the 12-note chromatic scale was derived from the projection of the fifth; thus the circle of fifths. This is an acoustically-based method.

But actually, the 12-note scale is an anomaly, an approximation, based on the attempt to close the octave after 12 cycles of 3:2 fifths.

Thus, "12" is the resulting mathematical result of this error or approximation; there is no acoustic ("tonal") reason for its existence, other than that it approximates fifths. In ET, all these fifths are 2 cents flat, to compensate for this error, and to close the octave, which would otherwise spiral onward into irrational values. No ratio, such as the 3:2 fifth, can be divided into "1" (the octave) as a whole number (such as 12).

Thus, all the resulting symmetries created by "12" are mathematical in nature, and thus have a way of degrading tonality's supposed "acoustic" nature of ratios, and turning it into a mathematically/geometrically based system. Thus, the "undoing" of tonality was always inherent in the "12" based scale of Pythagoras.
 
#74 ·
...a nefarious force called Man.

Yes, tonality is based on a harmonic model of one note and its harmonics;

...but its hubris is that it desired to "stray" from the "one note" and seek the "fruit of excessive modulation" in distant areas of chromaticism. This is called "the fall."

Thusd, Man becomes lost in chromaticism, wandering aimlessly.

What did always exist, and always will, is "the Big Note." It is Man who has strayed....
 
#81 ·
That was before tonality had developed. However, you have a point there; early chant used tetrachords and combined them, so unless you consider the starting notes, or possibly the ending notes (finals), of a tetrachord or phrase to be indicative of a tone-centric unit, then it's true that it's not tonal; but pre-tonal.

Does this mean "atheistic?" I think that's an exaggeration. Even the scriptures were not compiled until the Nicene Council of 300 A.D., and even at that point certain doctrinal questions were still not definitive, until declared so by the fathers.

On the other hand, since chant is so drone-like and does not modulate, it can be said to be closer to 'the Big Note' than later tonality, where it began to stray into new territory, further from the home note.
 
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