From your comment:
Would this statement be true? Consonance is created when two or more frequency waves peak and drops are in sync.
I think "are in sync" might not be the best phrasing, because might imply they need to stay in sync to be consonant. That statement would then only be true when talking about waves of the same frequency (which could be seen as consonant, but trivially so).
A better statement might be "consonance is created when waves come into sync at regular intervals", where by "come into sync" we mean they both hit the same given amplitude level (such as both crossing through zero). This would agree with another common description of consonant frequencies as having 'simple ratios' between them; the "coming into sync" happens at the lowest common multiple of those ratios.
You can see that all your waves are in sync at point '0' on your X-axis, and have come back into sync at '1' (one cycle of the fundamental). Then they'll be back together again at '2' and '3' and so on. So in that sense they are all 'consonant' with the fundamental.
(As mentioned in other answers and comments - we don't usually talk about partials being 'consonant' with each other; rather, we talk about them being 'harmonic' (or 'inharmonic'). The word 'consonance' is more usually reserved for talking about the mixing of complex tones that are, themselves, composed of multiple harmonics).
When looking at the harmonic series transverse waves succession, their crests don't line up most of the time at stated degrees
As just mentioned, the fact that they don't line up at all points in time isn't the same as what people mean by the waves being 'in sync' in your statement about consonance.
Two waves will only stay in sync all the time if they are the same frequency (and therefore trivially consonant).
so how would you measure constructive and destructive interference at that point?
Constructive and destructive interference is something that you normally talk about when you have two waves of the same frequency. Depending on the phase difference between them, they may interfere constructively (resulting in a higher overall amplitude) or destructively (lower amplitude than either wave in isolation).
In your diagram, the waves are of different frequencies - any "cancellation" between waves caused by them being on opposite points of their cycle is only going to be momentary - i.e. it isn't akin to the amplitude of the resultant wave 'over time' being the result of constructive or destructive interference. This is because all the waves in your diagram have different frequencies.
I'm trying to figure out the phase degrees within the harmonic series (pictured below) to understand consonance and dissonance within the harmonic series through the phase of constructive/destructive interference.
I honestly don't think that makes much sense! Consonance and dissonance aren't a simple function of phase relationships, because whenever you have waves of different frequencies, their phase relationships are always changing. Likewise, constructive/destructive interference are something that you only observe with waves of the same or very similar frequencies, so it's not of much relevance when talking about waves of different frequencies.
"consonance is created when waves come into sync at regular intervals" is this how consonance is truly produced? Like a root note of a scale and its first octave are at most consonance within the entire scale because of the wave activity of 2:1?
You can look at this either in the frequency domain, or the time domain.
In the frequency domain, two pitches will be consonant if their frequencies have simple ratios.
In the time domain, two pitches will be consonant if their wave periods have simple ratios.
If we plot two consonant pitches (here, 100 and 150 Hz, or 3:2) together....
...we can see that the phases do come into alignment at the same amplitude at regular intervals, but I don't think it's very helpful to think of that as "how consonance is truly produced". I think it's easier to think about simple ratios. The 'phases coming into sync' is a kind of side-effect.
I'm trying to seek the structure of most consonance/dissonance in a scale.... If you could express to me the order of consonance in the 7 pitches of a scale....
If you are most interested in musical notes, rather than sine waves, things get more complicated, because you have to consider the frequency ratios between all harmonics in each note. This produces a curve a bit like this, from http://sethares.engr.wisc.edu/consemi.html:
However, bear in mind that the precise curve, as well as being somewhat subjective, depends on the harmonic structure of each note - see Dissonance: why doesn't the roughness curve have a dip for complex intervals like 7/6?
while confirming the answer stems from wave alignment between pitches
hmmm.... honestly, I don't think that's a helpful way to think about it. Thinking about simple ratios between frequencies will help you much more, I think.