But going through all of it will give you a perspective on how classical and pop music is constructed and the importance of practicing certain etudes focused on broken intervals and chord progressions.
If you have any urge to compose, or perhaps explore improvisation with other music genres, like folk or jazz, that website will give you a solid foundation.
If you want to learn elementary music theory from a book there are many options. You can look at the syllabi of courses at universities, which list the textbooks they use. For example, the Eastman school of music used The Complete Musician by Laitz in their TH 101 course a few years back.
For decades Harmony by Walter Piston was the standard music theory text.
You may be more adventurous and would like a different text. Schoenberg wrote several texts on harmony. There are also older texts by c h Parry, and a multitude of others.
You may want an historical text. Rameau’s treatise in harmony is a place to start.
You mention harmonics and tuning types. You may wish to explore books on acoustics such as classics by Benade, or books on temperament.
Now you may not be interested in books at all. There are many online resources. Juilliard has an online introduction to music theory. There are also many websites, such as open music theory. Many of these resources are free.
Sometime later you may start to play in multi-part ensemble with other people and start to find that some notes that are "in tune" are "out of tune." What is happening? This is when you will need to look at books on Harmony and temperament as Michael Berger has suggested. As a physicist I think of this as the "Real Music Theory" because it relates to music of all cultures, not just those based on 12-tone scales.
I think that as an adult player (even as a beginner) it is good to be aware of both these aspects of "music theory." I was taught "Western Music Theory" for 2 years between ages 9 and 11 at MSM for an hour every Saturday morning. I think it helped me with my violin playing - at least later if not at the time. (Even then I knew it was "rules" not "theory.")
"Real Music Theory" comes into play for a violinist when you start to play chords and double-stops and find the challenges of different tuning systems, which can be the source of argument when trying to get a string quartet to sound "in tune" - or playing string instruments with a piano. Getting further - into the part that harmonics ("partials") play in optimizing vibrato actually gets pretty deeply into the physics and neurology of sound perception. I think this too should be part of "Music Theory."
As was noted above about piston being difficult to understand, topics such as fast fourier transforms etc would be incomprehensible to a beginner.
I do not think we can change the established* terminology nor would it be worth doing even if there were a chance of success.
* you may think "incorrectly established" if you like.
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