Missing intervals in chord ratios?

Good hour folks,

Here are a selection of chord ratios..

Minor Chord - 10:12:15

Root (1:1) - Major 3rd (4:5) - Perfect 5th (2:3)

Major 7th Chord - 8:10:12:15

Root (1:1) - Major 3rd (4:5) - Perfect 5th (2:3) - Major 7th (8:15)

Major 9th Chord - 8:10:12:15:18

Root (1:1) - Major 3rd (4:5) - Perfect 5th (2:3) - Major 2nd (8:9) - Major 9th (8:18/4:9)

If we look at the Major 7th Chord.. according to the chord ratios, it holds the intervals Major 3rd, Perfect 5th and Major 7th.

But yet, there are more intervals within the Major 7th than what the chord ratio 8:10:12:15 represents. The intervals are the following..

• Major 3rd - C - E - (4:5)
• Perfect 5th - C - G - (2:3)
• Major 7th - C - B - (8:15)
• Minor 3rd - E - G - (5:6)
• Perfect 5th - E - B (2:3)
• Major 3rd - G - B - (4:5)

1. Why are those intervals not represented in the chord and it's ratios?
2. By those intervals not being included in the chord ratio, does that make the chord ratio inaccurate given that the Major 7th chord holds a Minor 3rd which is not accounted for in the ratio?
3. There are duplicates of the Major 3rd and Perfect 5th, does that make the chord that much dissonant as opposed to if there were only 1 Major 3rd and Perfect 5th?

Many thanks guys!

3 minutes ago, Seery said:

• Why are those intervals not represented in the chord and it's ratios?
• By those intervals not being included in the chord ratio, does that make the chord ratio inaccurate given that the Major 7th chord holds a Minor 3rd which is not accounted for in the ratio?

They are represented. They're just multiplied by a certain factor to preserve the relationship between the two. 2:3, the perfect fifth is equal to 8:12 and 10:15. 

4 minutes ago, Seery said:

There are duplicates of the Major 3rd and Perfect 5th, does that make the chord that much dissonant as opposed to if there were only 1 Major 3rd and Perfect 5th?

No. They're all individual and considered together at the same time.

1 hour ago, Monarcheon said:

They are represented. They're just multiplied by a certain factor to preserve the relationship between the two. 2:3, the perfect fifth is equal to 8:12 and 10:15. 

Could you elaborate on this as i don't quite understand it and it would be of great help to understand?

1 hour ago, Monarcheon said:

No. They're all individual and considered together at the same time.

So even though they are duplicated, it's not accounted for in the chord ratio because they're the same interval, which as a result signifies that duplicate intervals are as good as single intervals?

Thanks.

That's how ratios work. They divide and reduce like fractions do. It's just basic math.

8:12 divide both sides by 4, you get 2:3, perfect fifth.

10:15 divide both sides by 5 you get 2:3, perfect fifth.

The fact that they're off by a factor of 4 or 5 doesn't mean anything as far as the ratios are concerned. It's just a bigger form of 2:3. They need to be that big so that the other intervals also work with it.

I appreciate your explanation but i will tell you that although i may appear to have a decent amount of knowledge revolving around this, it is bits and pieces, so i get lost. If i understand what you're saying, the ratio for the minor 3rd is present in the chord ratio of  8:10:12:15. I guess my follow up question is, where is the minor 3rd ratio involved in the math? Again, i need the explanation to be detailed as i don't have the sufficient knowledge to understand your current explanation.

This isn't really music anymore. It's just math that you'd learn in school.

The minor third ratio is from E to G, or the second and third places in the ratio. That's 10:12. 10:12 dividing both sides by 2 gets you 5:6 which is the proper ratio for the minor third.

In the math it says the 10:12 stems from the B and C which pertain to the Maj 3rd and Perfect 5th. I guess in the B of 4:5 the B represents the note E and the 4 is note C (root). In the C of 2:3, the 3 represents the note G and the 2 is note C (root). Between E and G is a minor 3rd.

Is this what you're describing?

Major 7th Chord Ratios: 4:5, 2:3, 8:15

A1 = 4
B = 5
A2 = 2
C = 3
A3 = 8
D = 15

(A1 x (A2 x A3)): 4 x (16) = 64
(B x (A2 x A3)): 5 x (16) = 80
(A2 x (A1 x A3)): 2 x (32) = 64
(C x (A1 x A3)): 3 x (32) = 96
(A3 x (A1 x A2)): 8 x (8) = 64
(D x (A1 x A2)): 15 x (8) = 120

64:80, 64:96, 64:120

Merge: 64:80:96:120

Common factor: 8

64/8 = 8
80/8 = 10
96/8 = 12
120/8 = 15

Combined Ratio: 8:10:12:15

I don't know what this whole A1 A2 business is. Their math is right but I don't know how they got there.

So the math regarding the presence of the minor 3rd as i described is correct?

Here is the formula simplified.

That seems to be a somewhat long-winded way of doing it, but it works, I guess. It doesn't specifically tackle how to deal with the minor third, but it does get you the correct intervals. But that's only how to calculate it; it doesn't really explain anything in and of itself.

This stems from my work the last few months regarding producing music from physics as opposed to more "conventional" forms. I wanted to learn how to build chords from interval ratios as to give me the position to dictate a chords desired level of consonance/dissonance. I got quite a bit of backlash from far older musicians than myself at the start of approaching composition this way but as I've progressed with the research, I've gotten positive feedback and aroused their curiosity towards this approach. Thank you for your patience and knowledge.

You should research the concept of "dissonant counterpoint". You'll need basic knowledge of tonal counterpoint to understand some of it, but it's a type of counterpoint that consonant notes end up sounding dissonant because of the flipping of rules.
"Dissonance" is not an audioacoustic term. It's a very relative term that varies from person to person (or culture to culture, though I personally dislike talking about music in terms of overarching cultures). What one person find extremely dissonant may be very consonant for another.

I cant listen to the audio now but I'll check it shortly. Most if not everybody has said to me that consonance/dissonance is subjective but I'm set on the logic that pitches in their purest source are sound waves and when two pitches sound waves crests align frequently, they are in harmony and produce consonance and when their crests dont align that much they produce beating which is dissonance. So with that being said, I can understand that people can enjoy bland food or spicy food but in my mind the fact that they're bland or spicy still remains regardless of taste preference. I wish to produce music from science and not cultural taste or expectations.

Just heard the piece. Its extraordinarily composed, by making the significant consistent dissonance so beautiful to hear. I'd go as far as to say that i can enjoy this style of composition just as much or slightly more (depending on my current mood) than regular music but at the same time i gravitate towards dissonance in many aspects of life. The section at 2:25 where it builds up is very beautiful. I'll listen to more of this dissonant counterpoint music.