Exploring the Harmonies and Frequencies of Music in a Physics Perspective

[InfPerf000]

I'll just leave this open for anyone to discuss about note frequencies, harmonies, chords etc

Y do notes complement each other in chords, do the frequencies complement each other and how can this b put into a general equation?

 

[GENIERE]

I’m neither a musician nor a programmer but perhaps thirty years ago I read a technical article that included waveforms from a bow being drawn across violin strings. The waveform was a near saw-tooth in appearance. In 1977 I purchased an Atari 800 computer for my kids that came with assembler and Basic plug-in cartridges. I bought the Atari as it had on-board sound and graphics chips which Apple, etc. lacked. The sound chip had four channels and could play four notes at once. I wrote a simple program where notes were entered one at a time (melody only); each note required inputting several variables. It took forever to enter a single pop tune. Most of the program was in non-compiled (interpreted) Basic, but 6502 code was used to achieve the speed required to alter the rise and decay times of the note being played as well as duration. To my untrained ear, I was able to duplicate various instruments by changing parameters. I recall that stringed instruments were the easiest to mimic while I had no success with a trumpet.

 

[Janitor]

I recall that stringed instruments were the easiest to mimic while I had no success with a trumpet.

From having played around with a two-year-old Yamaha electronic keyboard, I can tell you that the brass instruments remain unconvincing.

 

[Galileo]

Y do notes complement each other in chords, do the frequencies complement each other and how can this b put into a general equation?

There's some subjectivity in what I have to say, so take it as a general idea:

When the ratio of the frequencies of two notes is (approximately) a 'simple' fraction, the note will sound consonant and pleasing to us.
For example, if you play a middle A on your piano, it will have a fundamental frequency of 440 Hz. If you play the A one octave higher, it will have a fundamental frequency of 880 Hz, which is twice as high as the frequency of the middle A. (Ratio 2:1)
For a perfect fifth, the ratio is 3:2
For a perfect fourth it's 4:3
For a major third / minor sixth it's 5:4 / 8:5

For a less consonent interval like a minor second, the ratio is 16:17 (or close to that, due to tuning problems)

So when you play an A Major chord in root position, the frequencies will be (approx): 440 HZ, 550 Hz and 660 Hz
So these have a nice realtion to each other, that's why they sound nice to us.

To the question WHY nice ratios sound nice to us: I don't know (and I don't care)

 

[Erus]

Modes, music theory, all a system! I am a musician myself and get into the system of music.. Last summer I was bored and decided to 'shape' music with a frequency/progression axis. For example: C E G make up 3 points on an axis X = Progression and Y = Frequency. It is easiest to use low frequencies, so I will use 8.17 (Low C note). E is our next note, at 10.30 and G is our final note at 12.14. Let us do some simple math just to show that when these 3 frequencies are plotted, they will no appear to be linear.

C = 8.17
E = 10.30
G = 12.14

E - C = 2.13
G - E = 1.84
G - C = 3.97

If you draw the shortest straight line to each plot, you will see you form a shape. A 3 sided shape. A triangle, and this triangle is a Major Triad Triangle C to G is the base, and C to E/E to G are your two other sides. You can make many different shapes out of music and using frequency measurements. I really only got into it for a few days. Try using a different Major Triads and see if you get the same results.

Most likely you won't, which is curious because many will argue that there is no difference between C major scale or D major scale except the pitch and frequency.

Anyway, music has a long history of 'evolution'. Music began as a singular note rang over an event/ritual. It then was systemized by a scale, where 3 notes were used (the key, the sub-dominant 4th and the dominant 5th), then 5 notes, then 7 notes, which is what is called 'diatonic scale', or western music. Over a long period of time music became popular, after thousands of years of listeners and understanding.

Music can be put into formulas or equations. Sound (frequency) can be made into intervals, thereby making a measurement. A wholetone consists of two semitones, and 4 quartertones. A scale in westernized music is made up of Wholetones and Semitones. There are formulas to every scale. You get a formula by working out the intervals between each note in the scale. Example: C to D is a wholetone (W), for C to C# or C# to D is a semitone(H).

C - D = W
D - E = W
E - F = H
F - G = W
G - A = W
A - B = W
B - C = H

So the formula for a major scale is WWHWWWH.

 

[InfPerf000]

Thank you Galileo. Very helpful. I've been wondering for a while

To the question WHY nice ratios sound nice to us: I don't know (and I don't care)

LOL That would be an interesting experiment