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Let's solve Harmony! The first scientific experiment was conducted by 5th century BC Pythagoreans. They wanted to show that the basis for musical consonance wa

Let's solve Harmony! The first scientific experiment was conducted by 5th century BC Pythagoreans. They wanted to show that the basis for musical consonance was math. From that, they inferred that harmony in math accounted for the harmony of the cosmos. This integration of math+physics was very forward thinking. But, if we fast forward to the present, we still don't have a complete scientific explanation for the basis of consonance and dissonance. Really! To make my own contribution, I've been running psychophysical experiments to investigate why consonant chords that are mathematically slightly dissonant actually sound much better than chords with perfect mathematical consonance. I've been gathering data with sounds but also with haptic vibrations and with visual flicker frequencies. This multisensory approach is fun because it produces visible rhythmic entrainment in the brain, as seen with EEG. My goal is to contribute to a general theory of neural resonance and harmony in human experience. Why does this matter? Happiness is great, but I'd argue that what we really want is personal and global harmony. Note that harmony isn't sameness, it is unity in variety -- the resolution of conflict and dissonance into an integrated wholeness. We want inner harmony with our selves, harmony in our relationships with others, harmony in society, harmony with technology and harmony with nature. Happiness is individualistic but harmony involves the pleasure of virtue. I hypothesize that harmony can help set a better objective function for the future of humanity. Harmony was also the objective function for the first deep learning neural network, Paul Smolensky's Harmonium. Finally, harmony is also a central theme in classical philosophy. The concept had a massive influence in the Italian Renaissance and in the English Scientific Revolution. I recently put together a reader for understanding Plato's views on Harmony. Comments are welcome: https://docs.google.com/document/d/1lqXpXgWI5YMBCz1O0gCmrEwzfw65MD7-WZG1FL0fPPU/edit?usp=drivesdk https://docs.google.com/document/d/1lqXpXgWI5YMBCz1O0gCmrEwz...

dr_dshiv 6y ago
> Harmony was also the objective function for the first deep learning neural network, Paul Smolensky's Harmonium. Here is the 1986 work in Parallel Distributed Processing, along with G. Hinton and Rummelhart. Don Norman wrote a chapter, too! http://93.174.95.29/main/3C9F2A7AEF5BE7461DECE4AE766F94B1 http://93.174.95.29/main/3C9F2A7AEF5BE7461DECE4AE766F94B1
ShamelessC 6y ago
I got a little lost when you tried to compare musical harmony to societal harmony. With regards to musical harmony, is it possible that it's more or less random? I know multiple cultures have different definitions of musical harmony. I suspect the evolution of hearing also contains random elements. Similar to language, it's not so much about an inherent universality, just a universality we can all learn and agree on. Thoughts?
- sova 6y ago
  The human ear has an intimate relationship with the octave 2:1 and its ratios, so its very hard to believe the convergence of appreciation globally to be random. More dramatically, visualizing the harmonious ratios on objects such as Chladni plates (a field called Cymatics) reveals that there is something deeper to consonance and harmony than meets the number line.
  - marzell 6y ago
    "visualizing the harmonious ratios on objects such as Chladni plates (a field called Cymatics) reveals that there is something deeper to consonance and harmony than meets the number line" Ok I'll bite. What does it reveal? There's nothing inherently meaningful here. We know that 'dissonant' sounds (those that create interference patterns) create wavelets that are smaller and with less contrast than the more 'coherent' patterns from ratios that are closer to whole numbers. But in what way is this meaningful or useful?
    - megameter 6y ago
      It means we find consonance pleasurable and see a distinct "signal" in it. At least, that's the information-theoretical way of looking at it. When dealing with cosmology one often seeks to make a big deal out of a simple concept like a duality, a cycle, or a ratio. These are concepts recurring through the world, and looking for them in more places sometimes reveals knowledge.
  - walleeee 6y ago
    There is some evidence that ratio/octave recognition and preferences for consonant sound are culturally contingent http://mcdermottlab.mit.edu/papers/McDermott_etal_2016_consonance.pdf http://mcdermottlab.mit.edu/papers/McDermott_etal_2016_conso... http://mcdermottlab.mit.edu/papers/Jacoby_etal_2019_Bolivia_sung_reproduction.pdf http://mcdermottlab.mit.edu/papers/Jacoby_etal_2019_Bolivia_... Preferences vary individually as well: modern music may feature or favor dissonance (e.g., some forms of metal, electronic)
PaulDavisThe1st 6y ago
I worry from this brief description that you may be ignoring cultural aspects to our perception of consonance and dissonance. Also, harmony itself is a distinctly western concept whose musical role expanded dramatically with the advent of polyphony. Many (most!) musical cultures around the world don't give harmony much, if any role, and place higher importance on melodic structure. Also, music harmony and the other kinds of harmony you mention seem to me to be related only by the language used for this particular metaphor. There seems to me to be no likelihood of there being any interesting relationship between musical consonsance and "harmony with technology and harmony with nature".
- dr_dshiv 6y ago
  I agree that the central scientific question is whether harmony is a metaphor or mechanism, e.g., for psychological constructs like Cognitive Dissonance. My guess is that harmony is so pervasive that it ceases to have original meaning -- like in the manner that every atom is a harmonic oscillator or how brainwaves are based on an "octave" structure (e.g., Beta is double Alpha, Gamma is double Beta, etc). However, this question of metaphor or mechanism should be resolvable with science, eh? However, I disagree that harmony is primarily a western phenomena. It is a central feature to Confucianism and Daoism. It also plays a major role in Native American philosophy.
  - PaulDavisThe1st 6y ago
    I was talking specifically about harmony in a musical context as being very western.
    - dr_dshiv 6y ago
      Well, the point still applies. The small integer ratios of harmony apply even to the rhythms of gamelan. And, of course, octaves are more-or-less universal across cultures.
      - PaulDavisThe1st 6y ago
Nav_Panel 6y ago
> why consonant chords that are mathematically slightly dissonant actually sound much better than chords with perfect mathematical consonance. Probably because we're used to hearing music in equal temperament, so we associate it with "correct" harmony, whereas something like just intonation sounds a little weird and off (but I ultimately find myself preferring it? Wtf?)
082349872349872 6y ago
You may be interested in de Waal, Peacemaking Among Primates. An under-appreciated aspect to our educational system is that school desks are shared between two children, so people grow up learning how to interact relatively harmoniously with at least one other small child. Absent a vaccine, Covid may alter that to the one-child-per-desk model, so I may discover in another 20-30 years how important shared desks were or weren't.
ttctciyf 6y ago
Regards Plato, I'm curious if you've looked at Ernest McClain's book The Pythagorean Plato? (See my other comment[1] here for some details if not.) 1: https://news.ycombinator.com/item?id=23746057 https://news.ycombinator.com/item?id=23746057

dr_dshiv 6y ago

> Harmony was also the objective function for the first deep learning neural network, Paul Smolensky's Harmonium. Here is the 1986 work in Parallel Distributed Processing, along with G. Hinton and Rummelhart. Don Norman wrote a chapter, too! http://93.174.95.29/main/3C9F2A7AEF5BE7461DECE4AE766F94B1 http://93.174.95.29/main/3C9F2A7AEF5BE7461DECE4AE766F94B1

ShamelessC 6y ago

I got a little lost when you tried to compare musical harmony to societal harmony. With regards to musical harmony, is it possible that it's more or less random? I know multiple cultures have different definitions of musical harmony. I suspect the evolution of hearing also contains random elements. Similar to language, it's not so much about an inherent universality, just a universality we can all learn and agree on. Thoughts?

sova 6y ago
The human ear has an intimate relationship with the octave 2:1 and its ratios, so its very hard to believe the convergence of appreciation globally to be random. More dramatically, visualizing the harmonious ratios on objects such as Chladni plates (a field called Cymatics) reveals that there is something deeper to consonance and harmony than meets the number line.
- marzell 6y ago
  "visualizing the harmonious ratios on objects such as Chladni plates (a field called Cymatics) reveals that there is something deeper to consonance and harmony than meets the number line" Ok I'll bite. What does it reveal? There's nothing inherently meaningful here. We know that 'dissonant' sounds (those that create interference patterns) create wavelets that are smaller and with less contrast than the more 'coherent' patterns from ratios that are closer to whole numbers. But in what way is this meaningful or useful?
  - megameter 6y ago
    It means we find consonance pleasurable and see a distinct "signal" in it. At least, that's the information-theoretical way of looking at it. When dealing with cosmology one often seeks to make a big deal out of a simple concept like a duality, a cycle, or a ratio. These are concepts recurring through the world, and looking for them in more places sometimes reveals knowledge.
- walleeee 6y ago
  There is some evidence that ratio/octave recognition and preferences for consonant sound are culturally contingent http://mcdermottlab.mit.edu/papers/McDermott_etal_2016_consonance.pdf http://mcdermottlab.mit.edu/papers/McDermott_etal_2016_conso... http://mcdermottlab.mit.edu/papers/Jacoby_etal_2019_Bolivia_sung_reproduction.pdf http://mcdermottlab.mit.edu/papers/Jacoby_etal_2019_Bolivia_... Preferences vary individually as well: modern music may feature or favor dissonance (e.g., some forms of metal, electronic)

PaulDavisThe1st 6y ago

I worry from this brief description that you may be ignoring cultural aspects to our perception of consonance and dissonance. Also, harmony itself is a distinctly western concept whose musical role expanded dramatically with the advent of polyphony. Many (most!) musical cultures around the world don't give harmony much, if any role, and place higher importance on melodic structure. Also, music harmony and the other kinds of harmony you mention seem to me to be related only by the language used for this particular metaphor. There seems to me to be no likelihood of there being any interesting relationship between musical consonsance and "harmony with technology and harmony with nature".

dr_dshiv 6y ago
I agree that the central scientific question is whether harmony is a metaphor or mechanism, e.g., for psychological constructs like Cognitive Dissonance. My guess is that harmony is so pervasive that it ceases to have original meaning -- like in the manner that every atom is a harmonic oscillator or how brainwaves are based on an "octave" structure (e.g., Beta is double Alpha, Gamma is double Beta, etc). However, this question of metaphor or mechanism should be resolvable with science, eh? However, I disagree that harmony is primarily a western phenomena. It is a central feature to Confucianism and Daoism. It also plays a major role in Native American philosophy.
- PaulDavisThe1st 6y ago
  I was talking specifically about harmony in a musical context as being very western.
  - dr_dshiv 6y ago
    Well, the point still applies. The small integer ratios of harmony apply even to the rhythms of gamelan. And, of course, octaves are more-or-less universal across cultures.
    - PaulDavisThe1st 6y ago

Nav_Panel 6y ago

> why consonant chords that are mathematically slightly dissonant actually sound much better than chords with perfect mathematical consonance. Probably because we're used to hearing music in equal temperament, so we associate it with "correct" harmony, whereas something like just intonation sounds a little weird and off (but I ultimately find myself preferring it? Wtf?)

082349872349872 6y ago

You may be interested in de Waal, Peacemaking Among Primates. An under-appreciated aspect to our educational system is that school desks are shared between two children, so people grow up learning how to interact relatively harmoniously with at least one other small child. Absent a vaccine, Covid may alter that to the one-child-per-desk model, so I may discover in another 20-30 years how important shared desks were or weren't.

ttctciyf 6y ago

Regards Plato, I'm curious if you've looked at Ernest McClain's book The Pythagorean Plato? (See my other comment[1] here for some details if not.) 1: https://news.ycombinator.com/item?id=23746057 https://news.ycombinator.com/item?id=23746057