I've observed that the harmonic series which are the most consonant pitches of the fundamental such as the note A for this example, with A's first harmonic series being (A) E and C#.. Do not correlate with the consonance to dissonance ratios. In the ratios it would be A,E and D..
- Harmonic Series - A (root) E (fifth) C# (Third)
- Interval Ratios - A (root) E (fifth) D (Fourth)
It is also worth mentioning that the following harmonic after the third (C#) is a 7th (G).. While in interval ratios the order would be Unison, Octave, Fifth, Fourth and a Major Sixth.
What is going on here?
Also, could you folks confirm the validity of this interval ranking shown in the image below? Image Source: https://www.pnas.org/content/112/36/11155