If you're referring to the harmonics of a fundamental pitch, then yes, they can certainly be shown pictorially. I avoid talking about harmonics in this series to keep the focus on the basics of melody, but the plan is to explore harmonics and their practical applications in a future series :)
It's a good question that deserves a more thorough answer but for now I think I can address what might be the main confusion.
The names of intervals are labels with a certain logic. The logic in the naming doesn't directly correlate to numbers in the way you'd expect, so a Major Third added to a Major Third won't give you a Major Sixth.
Think of a Major Third as an interval of 4 units and a Minor Sixth as another interval with 8 units. Then you can see that four and four make eight and it makes a lot more sense. A Major Sixth in this system is an interval of 9 units, and four and four don't make nine.
What is the basis for assigning 4 or 8 or 9 units to the above intervals? Well, that's the part that needs a more detailed explanation so I'll leave that for an upcoming article. Hope this helps!
Fascinating read! I’m curious if it’s possible to visualize the harmonics in a pictorial form?
If you're referring to the harmonics of a fundamental pitch, then yes, they can certainly be shown pictorially. I avoid talking about harmonics in this series to keep the focus on the basics of melody, but the plan is to explore harmonics and their practical applications in a future series :)
Great piece again 👏
One question though, how would Major third to Major third become Minor sixth?
It's a good question that deserves a more thorough answer but for now I think I can address what might be the main confusion.
The names of intervals are labels with a certain logic. The logic in the naming doesn't directly correlate to numbers in the way you'd expect, so a Major Third added to a Major Third won't give you a Major Sixth.
Think of a Major Third as an interval of 4 units and a Minor Sixth as another interval with 8 units. Then you can see that four and four make eight and it makes a lot more sense. A Major Sixth in this system is an interval of 9 units, and four and four don't make nine.
What is the basis for assigning 4 or 8 or 9 units to the above intervals? Well, that's the part that needs a more detailed explanation so I'll leave that for an upcoming article. Hope this helps!