Claire,
I think perhaps more fundamental aspect of this question involves an understanding how we perceive consonances and dissonances, with the understanding that dissonances plead for resolution.
Informally speaking we can say that consonances (such as perfect fifths) are intervals that rest easy. That is to say, they seem to require little or no resolution. Consider the octave or even the unison to take a more extreme/obvious example. I think this notion would be challenged by few, and I believe it is in part why much early music was written in unison. From there, everything was an experiment that led to our contemporary ears. For instance, consider that many early music ears (for instance in the 11th or 12th century) avoided writing music that incorporated parallel thirds and sixths, instead preferring fifths and even fourths. Thirds and sixths were dissonances that required resolution (if you were to dare to use them at all). That all changed very rapidly by the Renaissance, where the number of acceptable consonances began to expand.
And yes, there are mathematical underpinnings to all this. Remember, intervals can be defined by a ratio of two frequencies. Fifths and fourths belong to the most fundamental group of these with a 3:2 ratio. Because (simplistically speaking) our Western scale is based on a stacked series of this particular interval, it follows that the further we go from it, the more dissonant the resulting interval when heard against the tonic. Now, while some might disagree with some of the ramifications of this statement (not all of us would necessarily agree about what the hierarchy of dissonances is), but I think there is an underlying truth to it.
So, getting to your question, the dominant chord features the major seventh tone of the scale, which is about as far as it gets from the tonic given the math I just mentioned (and in a diatonic world). Assuming that the tonic has been established in our ear, the mere presence of that note begs for resolution. But there are cases where this can happen where we don't even need to have previously heard the tonic. The dominant seventh chord, with it's signature tri-tone can not be mistaken for any other four note chord built from a diatonic scale, so our Western ears immediately assume what it is and its major 7th tone (or leading tone) becomes implied, again begging for resolution.
Re: major and minor -- Great question. While I think I have some understanding of it, it is mostly speculation. I would be curious to hear someone else's reply.
Dear Mark,
Thanks a lot for your explanation, I hadn't noticed the presence of the 7th tone of the tonic scale in the dominant chord, I understand better the need for resolution now. Basically, what you say it that this need of resolution would come mainly from ear education of our western scales. Do you think that someone who has never heard western music would not expect this resolution, or let's put the question differently, don't you think he would feel good to hear the resolution? Is dissonance recognition cultural or physiologic?
I read a bit on the subject and found that dissonance seems to be recognised by non-human primates as well as be 1 to 3 days old infants tending to show that there is a physiological component to dissonance recognition. Was my little walz dictated by evolution? and I thought I had been creative...
In the sense that there are mathematical underpinnings to how the scale is constructed, Absolutely. Consider non-Western scales that have 17 or even 19 notes. Many of their tones are similar to, or even identical to the traditional Western scale, and most of their extra notes are just that ..extra. Clearly one who possesses and ear for those scales is hearing many of the harmonies that we hear, with an extra layer of subtlety, especially in melodies. The down side of having such a rich scale is that layered tones, for instance chords with more than 4 or 5 different notes, start to become overly complex and it is difficult to parse harmonic function This, of course is my personal opinion. I am by no means an expert on non-western scales.
Let's turn the idea around. (I'm going to assume that like me, you are even less familiar with non-western scales but have nonetheless heard them before) I will guess that you recognize a haunting beauty in these scales. Surely much of this arises from the use of these aforementioned additional scale tones.
So the simple answer to your question is a qualified yes, we all hear dissonances the same, not unlike the way we perceive red as red and yellow as yellow and agree on their qualities. (By the way, colors are waves that can be defined by frequency too. Surely this is not a coincidence).
