I'm tired of rote memorization.
You should not think your choice is between rote memorization (of something, I suppose you mean music theory) versus acoustics which is the science of sound - the hertz, waveforms, etc. you mention.
The acoustics info you put into your question is already more than you need to know to study music theory.
The vast bulk of music theory doesn't require acoustics knowledge. The overtone series is about the only thing comes up to (try) explaining the perception of consonance/dissonance.
The non-rote approach to music theory is all about pattern recognition and relative relationships. Even some things that seem like rote knowledge - key signatures, interval names, etc - can be broken down into categories and patterns.
I want to understand why say a pentatonic is constructed the way it is. TO understand that I need to understand the fundamental blocks.
These kinds of question come up a lot. Stuff like 'why are triads the basic kind of chord', 'why does major sound happy', 'where did the major scale come from', etc.
There are usually two kinds of answers:
- because it sounds good
- the intervals involved are acoustically resonant which is perceived as sounding good
Perfect fifths are very consonant and stable. They are super important in music theory. If you stake up four perfect fifths...
C G D A E
...you get a pentatonic scale.
That would be a typical music theory explanation of why a pentatonic scale is constructed as it is. But, as you can see, that explanation didn't really require any acoustical science.
I want to make an addition after reading this comment on another answer from the OP:
Also, theory is confusing. There are 12 notes in an octave from A to A. But octave is Latin for 8. Most skip the flatts/sharpes. Unless you start in a different key. These then are used to make chords. Chords also span octaves. So it is like level 2 of octaves. Chords are combined in different ways to make songs. Typically I IV V but not always. Then there are scales. Seemingly these can be chords and tones/notes. And these can be subdivided into pentatonics if you remove 4 and 7th or 2nd and 5th depending on major or minor. It is, to me, a confusing mess.
I want to elaborate on just one point to illustrate what seems to me an incomplete, lackadaisical attitude about theory which will not be remedied by applying acoustics.
There are 12 notes in an octave from A to A. But octave is Latin for 8.
You didn't really complete the thought. I think you meant to ask "why doesn't an octave contain 8 tones instead of 12?" The information you need to understand the answer is a combination of music history, etymology, and cardinal versus ordinal numbers.
Historically western musical scales used 7 diatonic tones which repeated "at the octave." Each tone was represented by a letter. In modern English the letters are
A B C D E F G. to show the repeating at the octave let's use scientific pitch notation and write two octaves
A4 B4 C5 D5 E5 F5 G5 | A5 B5 C6 D6 E6 F6 G6 | A6.
In music theory an octave is the distance between
A6. In muisc theory those distances are called intervals and the interval names are based on the ordinal number in the tone series.
A4 is first, there isn't no distance with only one tone, it is called a unison.
B4 is second, the distance from
B4 is called a second. As we continue up the series
A5 is eighth and the Latin word for eighth is octavus from which the name of the interval is derived: octave. (The Latin cardinal for the quantity is octo, etymologically it is not the origin of the word octave.) Octave does not represent 8 as a quantity it represents the ordinal number eighth!
From a quantitative perspective an octave contains 7 tones, 7 pitch classes (heptatonic, Greek origin.) Historically, as music evolved chromatically, tones were added by half step between certain letters and indicated with sharps and flats. There are 12 chromatic tones in an octave. The common tonal system used today can be described as diatonic system modified with chromaticism. The 12 chromatic tones didn't replace the 7 diatonic tone system and music theory reflects that. Many theory concepts are in reference to the 7 tone diatonic system.
Notice that acoustics will provide absolutely nothing helpful to understanding these concepts. The reason is because music theory is it's own field of study! Like any other serious study it requires time to develop deep understanding.