'Consciousness Ignored' — Wayfarer

'Consciousness Explained Away" is better.

This has to do specifically with eliminating the "Pythagorean comma" in tuning keyboard instruments to enable transposition to all keys, because the tones cannot be sharpened or flattened by slight adjustments of finger position or breath on keyboard instruments. Hence the title of his 48 Preludes and Fugues: "The Well-Tempered Clavier". Other methods utilizing slight flattening or sharpening of fifths were used prior to Bach's invention.

:up: Interesting - I knew it was something like that, but not the specifics.

Modern tuning of the twelve tone scale is usually "equal temperament", in which the octave is divided into twelve equal parts.The Pythagorean tuning of the 12 tone scale is called pure temperament, or just temperament, because the designated notes are derived from the 3:2 ratio which gives the perfect fifth, pure consonance. With the numerous octaves required to produce the twelve notes of the scale in the Pythagorean method, a slight gap opens up, called the Pythagorean comma. This creates a slight difference between the same note, played in a different key. So modern musicians have turned to equal temperament to avoid this problem, making modulations smooth.

Incidentally, the problem of the Pythagorean comma is a function of the relation between frequency and time. There is no starting point, no base unit or fundamental frequency. So divisions or multiplications may proceed infinitely. Therefore your harmonies are always determined by your starting point, which due to the nature of time cannot be well-defined. I believe it is this same inability to define perfect harmony, because there is no base unit, which produces the infamous uncertainty principle from the Fourier transform. You might say that the Pythagorean comma and the uncertainty principle are symptoms of the very same problem.

They probably worked it out by trial and error until they got something that sounded good to them. — Bitter Crank

Well, you cannot keep drilling holes in the same piece of wood, in the process of trial and error, because your instrument would be ruined. So measurement would be necessary, to ensure that the errors were not repeated, and the successes were maintained. I think therefore, that the holes in your 40,000 year old instrument were measured. Otherwise it wouldn't be an instrument at all, it would be a stick with random holes.

you cannot keep drilling holes in the same piece of wood — Metaphysician Undercover

You are obsessed with these old holes.

This creates a slight difference between the same note, played in a different key. So modern musicians have turned to equal temperament to avoid this problem, making modulations smooth. — Metaphysician Undercover

How very interesting. I had read about this before but not had it explained so clearly. :

I actually haven’t thought about the question of why we laugh - that’s one to ponder, for sure.

‘Survival of the fittest’ is an extrapolation (or a broad generalisation) of the theory of natural selection. It explains a prevalence of certain forms of diversity in certain environments, but it doesn’t satisfactorily explain the emergence of all traits. Especially not human cognitive or social evolution. I find attempts to make it explain these developments to be unsatisfactory at best. At worst, their apologist-style conclusions have actually been holding people back from developing the capacity that we have. This suggests there is more to evolution than natural selection - just as Copernicus recognised his calculation errors as suggesting there was more to the structure of our solar system than everything revolving around the Earth.

I will admit in this discussion that I’m reluctant to use the term ‘metaphysical’ myself, because of the perception of a dichotomy it creates between physical/metaphysical that I don’t believe is either accurate or helpful. In my view there is a dimensional difference between our capacity to experience ‘actual’ events in time and our capacity to experience (predict, plan for, recall, respond to, etc) events that occur in a different spacetime to ‘this/here/now’. It’s more complex, granted, but still a dimensional increase in information processing, not much different from that between an animal’s capacity to locate an objective in space and its capacity to recognise an object’s change or movement in time.

Actually, I don't know if I quite got it right. I learned a lot (from jamalrob I think) on the old forum, and followed up study of some of the principles on my own, being a musician and composer who was always lost in the theory. I believe the basic issue is that division starts from an assumed unit, which is divided, while multiplication starts from an assumed multiplicity. So, despite the fact that we look at division as a simple inversion of multiplication, it is not, there is a fundamental inconsistency between the two. One presupposes a unit, while the other presupposes a multiplicity. Since a conclusion always follows the principles of the premises, an act of division will always produce a specified unit, while an act of multiplication will always produce a specified multiplicity.

I think that resolving the problem of the Pythagorean comma will produce the universal key (the key to the universe), because it requires a determination of the fundamental unit of time, and producing a scale based in something real rather than an arbitrary frequency. This is where the wave theory of modern physics is currently lost. I am obsessed

Thank you for that...I didn't want to get into any Dualism debate either.

Anyway, just another little detour of sorts. I'm liking the all the discussion thus far... !!!!

Just in case you are interested in more detail, and since MU has given what I think is a somewhat confusing/ confused and/ or incorrect account of the issue:

There are 8 'C' keys on an 88 key keyboard. The frequency of the lowest is 32 hertz. Since the ratio of frequencies between successive octaves is 2:1, then the frequencies of the 7 successive C keys is 64, 128, 256, 528, 1056, 2112, 4224. So the frequency of the top C key is 4224 hertz.

If you go through the cycle of fifths from the lowest to the highest C key, applying the ration 3:2, you get: C:32, G:48, D:72, A:108, E:162, B:243, F SHARP; 364.5, C SHARP; 546.75, A FLAT: 820.125, E FLAT: 1230.1875, B FLAT: 184.28125, F: 2767.921875, C: 4151.8828125

The discrepancy in frequency between 4224 hertz and 4151.8828126 hertz is the so-called "Pythagorean Comma".

Interesting. I'd never heard that expression before.

.I didn't want to get into any Dualism debate either. — 3017amen

Actually I have begun to make sense out of dualism, but it takes a ton of reading to understand it. I might create an OP on 'matter-form' dualism, which is a predecessor to, but very distinct from, Cartesian dualism.

Sure! I hope it's lucid enough for me to contribute.

Very good description. I see why you say that my description is confused. I see the importance of the problem in a slightly different way.

We produce perfect harmony with the octave, doubling the frequency. But every time the frequency is doubled, there are many frequencies, notes, in between. These in between notes must be determined, in order to scale the octave. This requires division of frequency. The Pythagorean method proceeds by using only divisions of half. Half way between one and two is one and a half. Half way between two and four is three, half way between four and eight is six. Notice, that the only division employed is the half, though the half is always taken three times, each time it produces another in between note to scale the octave. The half is always in harmony with the unit that it is half of (as an octave) and that is why the Pythagorean method of scaling the octave is considered to be more truly harmonic. That the Pythagorean method produces the Pythagorean comma is a problem which has not been resolved. Going to a less harmonic system of division, equal temperament, is not a real solution. It's a simple fix which lowers the quality.

That the Pythagorean method produces the Pythagorean comma is a problem which has not been resolved. Going to a less harmonic system of division, equal temperament, is not a real solution. It's a simple fix which lowers the quality. — Metaphysician Undercover

Yes, it is always going to be a compromise. I love the harmonic versaltility of keyboards, though!

Here's a thought provoking phenom of sorts. It relates to the math/music interval known as the devil's interval. Which, is a third up, but of course a flat 5th away from tonic.

Here's the sort short irony:

"The number three is used in the Torah to mediate between two opposing or contradictory values. The third value mediates, reconciles, and connects the two. Three is the number of truth."

All that makes me think of the survival value of music. It's proof again that Darwinism has holes. But it begs a salient point/question: why were we born with knowledge of dissonance and/or tension and relief (like root and fifth)?

Sounds have certain 'procreation' benefit to animals of course, yet I believe even animals don't even like dissonance... .

Interesting I thought….

If the positioning of the holes was not random, it was measured. And it couldn't have been random or the sound wouldn't be musical. Don't you agree? — Metaphysician Undercover

You could (and probably still do) have limitless fun with identifiable melodies on scales of randomly spaced pitches that were nonetheless identifiable: as e.g. low-high (a 2-note scale) or low-medium-high (3 notes). (You could use randomly spaced holes in a flute, or randomly sized bongos etc.)

Don't be in too much of a hurry for society to learn to identify performances of melodies on one of the particular spacings... requiring them to access a particular flute / bongo-set, or to produce new instruments the same size and with the same particular spacing... or... where the new identification of melody according to spacing were indifferent to choice of starting pitch: access new instruments with the same spacing relative (scaled in proportion) to the size of the whole instrument.

Even then, when spacing is scaled in proportion for each instrument, don't expect many of the proportions to have gravitated to producing arithmetically nice frequency ratios. More likely they combine one or two arbitrary (and arithmetically non-nice) pitch intervals (frequency ratios).

Yes, the sequence of proportions (step-intervals) might eventually repeat at the octave on the same instrument, but even then there is no reason for the musician or instrument maker or musicologist to assume that any arithmetically nice ratios are crucial to their art, in any obvious way.

A lot of them have done so, of course, ever since Pythagoras. With the result that we are taught to assume the octave to be aesthetically more fundamental than other strikingly consonant intervals. Or that perception of consonance depends on approximation to nice ratios - a notion somewhat challenged by equal temperament, to say nothing of folk traditions.

So I would guess the 40,000 year-old flute was crafted in careful imitation of previous models, with a keen sense of proportion but also in enviable ignorance of theories of arithmetically nice ratios.

Here's a thought provoking phenom of sorts. It relates to the math/music interval known as the devil's interval. Which, is a third up, but of course a flat 5th away from tonic. — 3017amen

I don't want to be pedantic, but I think you are confusing the fact that the so-called "devil's interval" is also called a tritone, with the interval known as a third (which can be major or minor). A tritone can be understood as either a sharp fourth or a flatted fifth.

Tritones are (literally) pivotal in musical harmony. For example the most common harmonic movement, in music: from dominant (fifth) to tonic (first) is often transformed by means of tritone substitution. Tritone substitution is where a dominant seventh chord is substituted by the other dominant seventh chrod that shares the two notes (in reverse order, of course) of the tritone.

For example the movement from G dominant 7 to C major 7 is transformed to be a movement form D flat dominant 7 to C major 7. The commonality that forms a tritone in both chords are the notes B and F. G dominant 7 is G B D F and D flat dominant 7 is D flat F A flat B (note that tritones are such bi-directionally).

Here's the sort short irony:

"The number three is used in the Torah to mediate between two opposing or contradictory values. The third value mediates, reconciles, and connects the two. Three is the number of truth." — 3017amen

Having to deal with the number three is what messes up the Pythagorean scale, causing the occurrence of the comma. For example, If we start with "one" unit of frequency, a designated length of string or whatever, as the base unit, then we double to two units, this gives us the harmony of the octave. If we double again, we have four, as the next octave. Now three is excluded, but we want to fit it in, as the half way point of the octave, halfway between two and three, thinking that the halfway point ought to be harmonic. The halfway point of the first octave is one and a half (3:2), and of second octave it is 3.

The problem is that the first set of octaves produced, 1, 2, 4, 8, etc., is fundamentally incompatible with the second set which is produced at the halfway point, 11/2, 3, 6, etc. However, if we take the base unit, 1, and cut that in half to get 1/2, this is compatible. So we can always take a designated frequency, cut it in half and produce a perfect harmony of an octave. But we cannot take a designated octave and cut it in half, to find the midpoint, without producing dissonance.

Very awesome fellow Philosophers!!!

At least one point to made viz. Evolution; it's hard to see how diatonic music theory confers survival advantages in the Jungle!!!

At least one point to made viz. Evolution; it's hard to see how diatonic music theory confers survival advantages in the Jungle!!! — 3017amen

Should it?

That's a great question! I'm thinking that if it was part of Darwinism, perhaps it would evolve into something different... like a whole different set of frequencies. But that would assume we could aquire the ability to hear those frequencies.

But that would assume we could aquire the ability to hear those frequencies. — 3017amen

If the ability to hear an expanded range of frequencies conferred a survival advantage, I imagine we could evolve to hear more than we do now. But that would be an expansion of our existing sense. To add the ability to 'hear' radio frequencies, for example, might be more of a challenge. :wink:

Not to detour the subject matter too much, but that reminds me of electromagnetic waves transporting sounds and images in the atmosphere, then appearing in our smartphones, TV's , etc..

Could similar electromagnetic waves produced from our consciousness, be a spiritual medium that travels too...

Could similar electromagnetic waves produced from our consciousness, be a spiritual medium that travels too... — 3017amen

Many things are possible.... :smile:

I've experienced a similar phenomenon at times performing music. I'm not conscious of it all the time when it happens, but when 'I snap out of it' I come to realize it.

To describe it would be more or less an out-of-body experience. I'm not even aware that I'm playing guitar. It's almost as if I feel the audience's electromagnetic waves from their consciousness...

I tried to google the connection, but was unsuccessful in finding any theories. Why do you think we have musical and mathematical abilities ?

If neither confer any survival value (eg: we don't have to compute the laws of gravity in order to dodge falling objects) are there any plausible explanations out there as to why we have these abilities? — 3017amen

We don't have the data nor the tools to give you a good answer.

The dynamics of evolution work at multiple levels. Which biological entity evolves? Is it the individual, the group? Do other species and groups exert an influence? What about the totally random element of geography and climate? I don't think we can, given the complex nature of evolution, get a fix on the single cause or effector of a particular trait evolving in a given species. Random chance can't be eliminated as a possibility.

That said evolution is usually understood in terms of survival advantages: Does a species have a trait x? If yes then it gives an edge to the species. If no then it was harmful to the species.

Why should music and math be different then? It must surely help a small group of 5 primitive humans to realize that it stands zero chance of survival against a group of 20.

I don't have a theory on musical ability but we can safely bet, ceteris paribus, that it too must have a hitherto undiscovered reproductive advantage.

One more thing about mathematical ability. Comparing objects is an essential feature of understanding our world - the tiger is bigger than me, the pig is smaller than me, she loves me more, etc. All these comparisons we make involve quantification which even though at first were non-numerical soon evolved into the exactitude and precision of numbers. Mathematics did confer an evolutionary advantage.

I don't have a theory on musical ability but we can safely bet, ceteris paribus, that it too must have a hitherto undiscovered reproductive advantage. — TheMadFool

...because, as we know, everything about h. sapiens can be explained with reference to evolutionary biology, so musical ability *must* have biological implications.

...because, as we know, everything about h. sapiens can be explained with reference to evolutionary biology, so musical ability *must* have biological implications. — Wayfarer

I'm toeing the official line. I keep an open mind but accepted wisdom is a safe bet. Don't you think?

I really don't have an evolutionary explanation for music. How does it help survival? I have one theory though and it has to do with battle music. If I'm not mistaken fiddlers, bagpipes and drums played a role in battle and war. Music fosters bonding between tribe/clan members making for a more cohesive group which is an edge over other groups that were more loosely bonded.

:rofl:

"We don't have the data nor the tools to give you a good answer."

As far as making perfect sense of it, that's basically it. However, the tenants of Darwinism and theories thereof do not account for music and math.

Accordingly, two additional questions could be added to the mix:

1. Why do we have this dual capacity to know the world; one mathematical, the other spacial. (It doesn't require computation of gravity to dodge falling objects in the jungle.)

2. What biological value does music theory hold (discussing the diatonic scale, modes, tension and release, dominant chord structure, major and minor scales, etc. etc.).

The abstract reasoning or capability in our cognition is largely part of the issue. Some say these are just 'extra' unexplained features that we have. I believe they are metaphysical languages.

Now there's a leap of faith!! LOL

‘Survival of the fittest’ is an extrapolation (or a broad generalisation) of the theory of natural selection. It explains a prevalence of certain forms of diversity in certain environments, but it doesn’t satisfactorily explain the emergence of all traits. — Possibility

Not only that, but the slogan is not a good representation of the theory of natural selection.

At least one point to made viz. Evolution; it's hard to see how diatonic music theory confers survival advantages in the Jungle!!! — 3017amen

You are still stuck on the idea of hyper-adaptationism - the idea that all and only those traits that confer survival advantage will emerge as a result of evolution by natural selection. This was never part of the theory of evolution, not even in Darwin's original works (and we have come a long way from there in the last century and a half).