Yes there are.
Yes there are.
Please summarize them.Originally Posted by josejherring
I'm not sure these rate as laws, so much as Pyscho-acoustic phenomena (I love that phrase) but there is a thing called the overtone series and looking at intervals as they occur within the series can lend a lot of insights as to why they are considered resolved or not.
For example the series has 16 partials. From C1 it would go like:
13th partial=G#4 (or A)
c1 to c2 is an octave or 2:1 (ie partial 2 against 1)
c2 to g2 is a 5th or 3:2
g2 to c3 is a 4th or 4:3
In this way we find that the intervals of the 8va, 5th 4th are the lowest partials and therefore have the greatest "strength" or "fusion".
Following the same procedure you get the following intervals in order of occurance:
1. 8va, 5th, 4th, ma 6th, ma 3rd, (more harmonic than melodic)
2. m7th, m3rd, dim5, m6th, (both)
3. ma2nd, ma7th, m2nd. (more melodic than harmonic)
Further, partial numbers 456 spell out a major triad.
It is this reason why the major triad is so easily heard as a tonic sound and 5th and 4ths suggest a key.
If you follow the history of music you'll also see an ascension of partial numbers from monk chants with 4ths and 5ths and octaves as the initial harmony (all low partial numbers) up to modern jazz with chords like Cma7#11 (which has tons of upper partials).
>Are there natural laws of music?
There are laws of physics of sounds.
There are theories of music.
Sorry, I'm just being picky....
Kentaro Sato (Ken-P)
Since we use an equal tempered system our scale no longer follows the overtone series except for perfect 5ths and octaves…. Our system is now artificial.
Trent P. McDonald
If so, then we are all under a rest for breaking them!
The problem with the overtone theory, is that any brass player can tell you that the upper overtones begin to get slightly out of tune.
Hindemith proposed another set of the order of consonances and dissonances.
Here in order from most consonant to most dissonant:
This is where he gets his system of quartal harmony that actually can be quite pleasing to most people's ears.
Just another theory, but neither can be conclusively proven.
DMA Student and Teaching Asst in Music Theory/ Composition at the University of Miami
Music as we know it in western culture is a deductive process... After 100s of years of evolution, people basically have taken note of what works and what doesn't work, and what works becomes an established technique ... So, after all this time, we've developed a very complex system which has been found to work over time, but only through trial and error and experimentation, not through any "natural laws"... As has been mentioned, the only natural laws, are the laws of physics, and the overtone series...
True enough about the out of tune qualites, but nevertheless, it is the actual physical process of sound.Originally Posted by jesshmusic
As far as Hindemith goes, he believed in the invertability of intervals so that ma3rd and m6th essentially occured at the same time, as too with the m3rd ma6th. Doing that ends up with ratios that seem to conflict with the concept of first occurance.
An ex: a ma6 interval is 5:3 whereas a m3 interval is 6:5. Because 6 and 3 are the same note he figures the intervals occur at the same time. They are however different frequencies. The actual occurance of a m3 is after a m7.
Like a lot of Hindemith's theory, it is spurious. When he is creating his chromatic scale based on acoustic roots being in the lower partials, a lot of times he foregos his own system just to get the note he wants.
His theory does have some neat aspects though: the fact he catagorizes chords as having (or not) the tri-tone is handy.
"Here in order from most consonant to most dissonant (according to Hindemith):
I think the list is actually:
uni 8va, 5th 4th, ma3 m6, m3 ma6, ma2 m7, m2 ma7, TT