: Can I use a fundamental's harmonics to sustain consonance by making its harmonics the following fundamental? I've been studying music theory from a physics standpoint and want validation on my supposed theories, firstly the

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If C is the fundamental freq, and G and E its harmonics, would i continue the order of consonance across a scale by making G the fundamental and using its harmonics given that G is C's closest harmonic

I'm not quite sure what you mean by "the order of consonance across a scale". But if you are asking how to choose a note that is melodically consonant with the previous note, then yes - choosing a note that is based on one of the previous note's strong harmonics is likely to give you a note that 'fits' with the previous one.

My theory is that if i'm composing a melody, and start with the tonic C, i could travel through the melody in perfect consonance by using fundamental C's harmonics and then using C's harmonic as the following fundamental and then using the second fundamentals harmonics for the following fundamental and so on. Would that be accurate?

I don't think this idea on its own will lead you to perfect melodic consonance.

If you go far enough up the harmonic series, you'll find frequencies similar to all notes in (say) an equal-tempered scale. There's no obvious threshold at which you can disqualify the corresponding note from being considered as a candidate - or at least, you haven't mentioned one in your theory.
People don't only perceive the consonance of a note with respect to the previous note, but also potentially in the context of the tonality established by a whole passage of notes beforehand.
In practical terms, following the frequencies of harmonics can only be done exactly on instruments capable of continuous variation of intonation, such as a violin. You can't do it on a piano or other instrument with fixed note pitches.

Taking another step back,

Your idea as stated here only deal with melodies - and not with harmonic consonance
In general, music is made to sound satisfying by experimenting with different consonances and dissonances. Aiming for consonance only makes it very hard to have any sense of motion and direction in your melody.

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Consonance and dissonance are generally created within one key. Using what you describe, you'll be out of key by the 3rd or 4th note.

Yes, each successive note will be consonant to the last one, but the tune itself will sound contrived, and what about any harmonies? They will, by definition almost, produce dissonance themselves.

As already mentioned, dissonance is an essential part of music, needed for the 'tension and release'. I wonder whether actually you'll be providing that, but more as 'release and tension'!

That apart, the harmonics themselves are sometimes 'out of tune', especially as far as 12tet goes. So. like a lot of theories, great idea, but isn't going to fly in the real world.

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Can consonance be continued by making a fundamentals harmonics, the following fundamental?

Providing an example of your process would eliminate possible confusion about what the resulting set of tones should be. But, following the process as written, our series of tones should be something like...

C C G C E that is fundamental C and the first harmonics up to E. You wording seems to mean use G and E as the next fundamentals...

G G D G B

E E B E G#

If you put that together, you get C D E G G# B.

If we continue with the original C fundamental's harmonics, we eventually get to Bb
and D as the next pitch classes...

Bb Bb F Bb D are the harmonics which gives us an additional Bb to add...

D D A D F#

Giving us C D E F F# G G# A Bb B

if I'm composing a melody... I could travel through the melody in perfect consonance...

The problem isn't necessarily the resulting set of pitches, but you haven't said anything about the sequence of the pitches for your melody. You could make a melody from that set of pitches comprised of either consonant or dissonant intervals.

If you mean to somehow have the melody's pitches follow an order derived from the overtone series, and you follow a logical process, the result would simply be a single melodic possibility. This is what is most unclear in your description. Are you trying to generate a scale, a melody, and theory of consonance?

I've been studying music theory from a physics standpoint and want validation on my supposed theories... create a scale in perfect progressive consonance... if I'm composing a melody... Can consonance be continued...

I think you mean to say hypothesis not theory. You're posing a question not a statement. But either way, I think you are proposing that this procedure will create consonant melodies. Or, maybe you a proposing a general theory of consonance.

What you have written isn't validation for anything like that.

You need to write more. It needs to be more clearly written. And, I think most importantly, you need to give examples of such a theory in practice.

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Since you are talking about "a melody" and not "chords", I think you are trying to invent a tuning system for a scale.

If you are hoping to do this using "exact" intervals derived from the harmonic series, you will find the arithmetic doesn't work out.

Taking the frequency of C as 1, the harmonics G and E are frequencies 3 and 5. Moving G down an octave, you get the G a 5th above C as frequency 3/2.

Now carry on stacking up fifths:

C = 1
G = 3/2
D = 9/4 (i.e. 3/2 × 3/2)
A = 27/8
E = 81/32

… Oops. E was supposed to be 5, which is 80/32, not 81/32.

A book (or several) could be written about the many different ways that have been used to get round that "inconvenient truth". Do a google search for "temperament".

In the end, what "sounds right" is simply what people in a particular culture think is right. The math is interesting, but there is no "one correct way" to make a musical tuning system.