It is said that Pythagoras, the founder of an ancient mystery cult, and arguably, the father of both mathematics and music theory, took his own life, out of guilt for discovering irrational numbers.
Pythagoras had discovered universal truths about music, by first observing that dividing a vibrating string into different proportions yielded the entire series of harmonics for the notes of the diatonic musical scale. The pitch of a musical note corresponds to an exact mathematical proportion between the length of the string being played and the length of the segment of the string created by touching a node. Thus, touching nodes positioned at various intervals on the string creates pitches that correspond with all the notes of the scale.
Pythagoras had discovered a connection between the quality of experience and the reality of numbers. The more perfect the actual mathematical proportion of the node to the entire length, the more harmonious and satisfying our experience when the two notes are sounded together. We call that satisfying relationship - harmony, and the feeling of dissatisfaction - dissonance.
The interesting thing about music is its dynamics. It gets its power from the way that it plays with our expectations and feelings, building tension and release via elements of tempo, rhythm, dynamic volume, the degree of dissonance and harmony, and the movement of a tonal centre further or closer to the key signature. Put in the context of a song, some dissonance is necessary in order to produce tension and make the music more compelling.
The judgement of quality in musical experience appears to be both due to subjective impressions and to objective reality. Individual musicians who do not adhere to the standards of pitch, tonality, tempo, dynamics, etc., are judged to be bad musicians. It would seem that there exists something universal about musical standards that leads to a better quality of music when these standards are closely adhered to.
Music also gives rise to powerful sensations of mood. Music embodies human nature, in its understanding of life’s goals and hardships. The experience of music is considered so desirable that the most popular musical pieces are constantly being re-created by musical groups.
Musicians re-create songs, producing music by collective adherence to standards. I want to argue that in moral systems there is something similar going on - the group re-creates society every time it collectively acknowledges and enforces moral standards.
The issue is this: we expect others to act morally and not take advantage or abuse their power but we always have to do more than this.
Because, if we do not collectively exclude those who consistently disrespect moral law, they will undermine and ultimately destroy society from within.
Because, if we do not collectively exclude those who consistently disrespect moral law, they will undermine and ultimately destroy society from within.
Moral standards are ultimately about differentiating people who support the group from people who undermine the group. People who commit wrongs can be said to fail the moral standards. They are excluded from the group temporarily, through forms of punishment, or permanently via banning or executing. In the past, those who refused to play by the rules were eventually selected out of the gene pool by the rest of the group.
By accepting universal standards for our social conduct we are also implying that there is something objective about reality that leads to some forms of conduct being better and some forms of conduct being worse than others. But at the same time, there is something irreducibly subjective about morality because it is such a powerful motivator for judgement and action.
In today’s world we take a jaundiced view of “morality”. People believe in the value of privacy to override almost everything else, and they see religious extremists insisting on strict “moral” codes of conduct as dangerously divisive.
But notice that moral standards can sometimes trump religious standards. Priests, cardinals, even popes can be held accountable for moral failings.
My intuition is that moral systems long pre-dated religion, but I wouldn’t be surprised if music is also of ancient pedigree, perhaps originating about the same time as morality, because they both have similar structures, but vastly different functions.
Music, like morality has standards that are exclusive. Bands can be very picky who they let in to become band members, and this often has to do with the prospect’s ability to reliably adhere to musical standards. Adhering to high standards is what distinguishes a good band from a mediocre band. Generally speaking, the higher the musical standards that a band or orchestra can achieve, the better the quality of experience supplied to the audience and greater the number of people drawn into their music’s orbit.
Musical scales, melodies, favourite harmonies, and songs can vary from one culture to another, but in every case, musicians have to play in tune, with appropriate instruments, in the same tempo, and the same key as the other musicians. In order to play music together they must follow the same musical standards.
The singer who sings off key undermines the song and harms the collective musical experience; and, if she consistently sings off key she can be kicked out of the band. Both the audience and the musicians together uphold standards of excellence that pertain to the quality of the musical experience.
Fortunately, there’s lots of room in modern society for musicians of different age, abilities, and tastes to form bands and play music, sometimes in public, sometimes not. It doesn’t undermine society for this to be the case.
But we make a mistake if we think that the fact that there are so many different groups and cultures with different rules of conduct - different moralities, if you will, means that there are no universal moral principles that we all should adhere to.
Living in groups demands much more from us than playing music in a group. For one thing, with music we always have the option of not playing music. Nor do we have to play music with other musicians, nor even to an audience. But moral choices are always about social situations. We do not have the option of opting out, unless we leave the group, and this was probably not an option when morality first originated.
Both music and morality show the importance of cooperation in human conduct. Music draws in other musicians, singers, dancers, innkeepers, as well as an audience, but morality makes human cooperation possible in the first place. Music draws people together and its re-creation makes life more meaningful and enjoyable. Morality is ultimately what makes it possible for people to live together. That’s what I mean by the “re-creation of society”.
II
Unity, diversity, coherence, dissonance, harmony, and universal rules. All these elements can be loosely conceived as the basis for both music and morality. We can see that dissonance, while sometimes unpleasant, is actually an essential part of the musical experience because of its contribution to musical tension and sense of movement.
Conflict and disagreement, as unwanted and unpleasant as they can be, are probably essential in human groups too, as a challenging impetus that leads to better fairer agreements that are more satisfying and sustainable over the long haul.
If all we ever did was just to get along with everyone else we would never have gotten out of the state of nature. By having to deal with conflict we got better at living together. Animals deal with conflicts with dominance hierarchies. The bigger and stronger animal has more say. Humans have added a crucial innovation - rules that apply to everyone, backed up by negative consequences that are collectively instituted against rule breakers.
The thing about rules, which is different from nature, is that rules are not self-organizing. They are based on prior agreements about how to behave. In nature any “rule” is more automatic, instinctual and genetically wired-in, or, it’s part of a developmental process.
Nature is self-organized in this important sense: there is no viewpoint that understands the whole. In self-organized systems, the parts of the system, if they have awareness, only have awareness of their immediate environment. There is no consciousness in charge of everything.
These kinds of systems are ubiquitous in nature. Think of the organ systems in our own bodies. Each of our bodies is said to be made up of thirty-seven trillion individual cells, all interacting in multiple organ systems. None of these individual cells have awareness of what their particular system is doing. We are certainly not aware of the vast majority of things going on with the thirty-seven trillion cells in our own bodies, although our minds exert control over our actions and our brains exert unconscious control over our body systems.
Music is not self-organized. Musicians have to learn how to play instruments, how to play in key, and according to musical scales, and to remember melody and chord changes. Conductors and band leaders need to be aware of how all the playing fits together to re-create a piece of music. Musicians and audiences have all learned how to hear a piece of music as a whole, rather than just as a random series of sounds.
In order for a song to be composed, the composer must be able to conceive of the song as a whole, not just the individual parts. In nature there is no composer, so natural systems tend to be self-organized and the parts only need to be aware of their immediate surroundings. Rules pull us out of the state of nature, by substituting conscious organization for self-organization.
We see self-organization when the scale of human activity gets so large, that no-one has a handle on it or can predict where it’s going. This is certainly true of business cycles, where economists often cannot predict what will happen next. It’s instructive to consider that the actors in business cycles, are often tagged as either “bulls” or “bears” because of their herd impulse to buy or sell.
This is also true of language. Language involves so many speakers, so many words and grammatical rules, that it also is a self-organized system. No single speaker is aware of all the uses and changes in pronunciation and meaning that are constantly occurring in any language. Nor do we normally have any awareness of a system-wide goal. There is no one who understands the whole thing, not even Noam Chomsky. There seem to be an infinite number of different goals involved in the use of language, although cooperation and sharing information seems to be the main ones.
There is very powerful evidence that humans are distinct from all other living things, and that evidence is in our ubiquitous use of rules. When we agree together to follow rules we are also demonstrating our understanding of and commitment to system-wide goals. This is where music and morality meet.
In hindsight, it turns out that irrational numbers got a bad rap. They are actually quite useful, and they haven’t led to the erosion of mathematics from within, as, I guess, tragically, Pythagoras was so concerned about. In human society everything depends on adherence to rules and standards. Both music and morality can only survive if the collectivity has the means and ultimately the will to exclude rule-breakers.
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