Good day guys!
Thanks to the gentleman @willross1 and others contributions, i have now discovered the formula behind turning interval ratios into chord ratios, which allows me to determine the level of consonance/dissonance of a chord based off my choice of intervals. I will demonstrate this formula below for context and reference.
"Formula for forming a chord ratio through interval ratios"
i. Select two or more intervals relative to your level of desired consonance/dissonance. In this example for a Major Chord, we will utilize the intervals Major 3rd (4:5) and Perfect 5th (2:3).
ii. The first ratio (4:5) is multiplied by the second ratios (2:3) first number which is 2.
⦁ 4 x 2 = 8
⦁ 5 x 2 = 10
i. The second ratio (2:3) is multiplied by the first ratios (4:5) first number which is 4.
⦁ 2 x 4 = 8
⦁ 3 x 4 = 12
Our ratios for both intervals after being mutliplied between each other, now go from 4:5 and 2:3 to being 8:10 and 8:12 and since both ratios hold the same first number, we can summarize the combined ratios to 8:10:12 which now becomes our Major Chord ratio.
We can further reduce this chord ratio if possible, by finding a common factor (a single number that can produce each of the three numbers) between the three numbers in our chord ratio (8:10:12) which would be "2" and divide each of the three numbers by it.
⦁ 8 ÷ 2 = 4
⦁ 10 ÷ 2 = 5
⦁ 12 ÷ 2 = 6
Our final chord ratio (Major Chord) has now become 4:5:6.
Here are the following questions..
Question 1 - We know the process for finding the chord ratio of two intervals which equals a triad. How do we approach the formula to deal with more than two intervals (e.g. 3 intervals) when we want to find the chord ratio for example of a Major 6th Chord which contains the intervals Major 3rd (4:5) - Perfect 5th (2:3) and Major 6th (3:5)?
This question revolves around finding the formula of a chord ratio when i utilise not only 2 or 3 intervals but 4,5,6,etc. Also, if you could demonstrate the formula in a similar manner to the one demonstrated in this post, it would be most practical.
Question 2 - If we agree that the consonance of an interval stems from the idea of "the lower the ratio, the more consonant the interval", how does this concept apply to situations where for example a minor chord with the ratio of 10:12:15 would be more consonant than a sus 2 chord with the chord ratio of 16:18:24 based off the minor chord having a smaller ratio, but once you find the common factor of a sus 2 chord ratio, the sus 2 chord ratio now becomes 8:9:12 which is now a smaller ratio than the minor chord?
With these scenarios how can one determine which chord is more consonant than the other based off the chord ratios?
Question 3 - If intervals are composed from root to note relationships such as a root and major 3rd producing a Major 3rd interval, once you add a second interval in the process of building a chord, how do the interval relationships begin to act within that chord.
Allow me to elaborate,
We know when building a Major Triad that the first interval (Major 3rd) level of consonance/dissonance is relative to the root. Now, as shown in the image below, if we now add a perfect 5th on top of the major 3rd, is the perfect 5ths level of consonance/dissonance relative to the root also or the major 3rd below it?
If you would care to elaborate on this concept beyond my initial query, I'm sure it would be of significant use. This information will prove useful once i start stacking intervals and need to understand their consonance/dissonance relationships.
Question 4 - What was the logic or process behind the interval ratios that were selected to build major,minor,diminished,augmented,sus2 and sus4 triads? Why were those specific intervals utilized to build each specific triad?
These are the only question i believe i have on this specific topic but should any others of importance arise, i will include them in the post edit. These questions are of immense value to me so thank you very much for your contribution guys.