Good day music lovers!
After the stupendous answers i received recently on this site, i have established the following..
To find the ratio of a chord
- You take two or more intervals
- Multiply each intervals ratios
- Combine the two or more resulting ratios which will supply you the chord ratio you have produced from the intervals selected.
My questions are as follows,
Firstly, are my calculations on the triads mentioned below correct, or have i made errors and if so which?
When you have two intervals or more that you are going to combine into a chord, how do you know how many times to multiply each interval ratio to give you the correct ratio of the chord you are building? e.g. in the major chord, 4:5 x ? - 2:3 x ? = 4:5:6?
When you take the two interval ratios of an augmented chord for example which is a major 3rd (ratio 4:5) and a minor 6th (ratio 5:8), the end result of multiplying those two ratios ends with 16:20:25:40 although the actual chord ratio is 16:20:25.. How do you know which number to omit from the ratio which in the augmented chord is the 40?
Here below are the triad chord ratio formulas in the key of C..
Major Chord (ratio 4:5:6)
Root (C) - Major 3rd (E) ratio 4:5 - Perfect 5th (G) ratio 2:3
Multiply ratio 4:5 x 1 = 4:5 - Multiply ratio 2:3 x 2 = 4:6
As the two intervals merge to produce the major chord so do the ratios, giving us a major chord ratio of 4:5:6
Minor Chord (ratio 10:12:15)
Root (C) - Minor 3rd (D#) ratio 5:6 - Perfect 5th (G) ratio 2:3
Multiply ratio 5:6 x 2 = 10:12 - Multiply ratio 2:3 x 5 = 10:15
As the two intervals merge to produce the minor chord so do the ratios, giving us a minor chord ratio of 10:12:15.
Diminished Chord (ratio 20:24:29)
Root (C) - Minor 3rd (D#) ratio 5:6 - Tritone (F#) ratio 64:77
Multiply ratio 5:6 x 64 = 320:384 - Mutliply ratio 64:77 x 6 = 384:462
As the two intervals merge to produce the diminished chord so do the ratios, giving us a diminished chord ratio of 320:384:462. Given the magnitude of this figure we can shrink it to its smallest figure by dividing it down x16, giving us the diminished chord ratio of 20:24:29.
Augmented Chord (ratio 16:20:25)
Root (C) - Major 3rd (E) ratio 4:5 - Minor 6th (G#) ratio 5:8
Mutiply ratio 4:5 x 4 = 16:20 - Multiply ratio 5:8 x 5 = 25:40
As the two intervals merge to produce the augmented chord so do the ratios, giving us an augmented chord ratio of 16.20:25.
Suspended 2 Chord (ratio 8:9:12)
Root (C) - Major 2nd (D) ratio 8:9 - Perfect 5th (G) ratio 2:3
Mutiply ratio 8:9 x 1 = 8:9 - Mutiply ratio 2:3 x 4 = 8:12
As the two intervals merge to produce the suspended 2nd chord so do the ratios, giving us a suspended 2nd chord ratio of 8.9:12.
Suspended 4 Chord (ratio 6:8:9)
Root (C) - Perfect 4th (F) ratio 3:4 - Perfect 5th (G) ratio 2:3
Mutiply ratio 3:4 x 2 = 6:8 - Mutiply ratio 2:3 x 3 = 6:9
As the two intervals merge to produce the suspended 4th chord so do the ratios, giving us a suspended 4th chord ratio of 6.8:9.
Many many thanks guys!
Seery