I am a student at the conservatory, CMU university. I am a classical pianist. My teacher asked me this question and I am having problems finding the answer online. Her question is "why did Beethoven laugh at the rule of forbidding parallel fifths"? I need detailed explanations and am very willing to search for this if you could direct me. Thank you very much.

     Your teacher's question is, in a way, a loaded one and we will try to sort out the parts gradually. One thing seems certain, you will not find a satisfactory answer anywhere on the web.
     1. This question seems to be a specific case of the more general "why did (and still do) all composers laugh at (or at least disrespect) all the rules of (traditional and academic) music theory?" One could even go beyond composers and ask what teachers (including yours) think about these numerous rules (and their equally numerous exceptions), including parallel fifths. Maybe you should look into this.
     The answer to this general question is fairly simple. Traditional academic theory has never been of any appreciable use to composers who have composed by intuition and cultural custom (which varies with time and styles) without the help of any form of map or compass.. Some cases are particularly interesting and well documented. Spitta speaks at length of how Bach (J.S.) taught composition to his students, but all these rules had nothing to do with the way Bach composed his polyphony, including his fugues, which corresponded much more closely with the principles proposed by Rameau in 1722 that harmony was at the base of all melody, including polyphony. Beethoven seems to have been more aware of his disregard for traditional theory than Bach was, but in both cases, they did not use it.
     2. Now, why does the question specify parallel fifths and not some other equally arbitrary and insufficiently studied interdiction ?
     Number of cases of parallel fifths are of common usage, generally accepted, and used by numerous composers (including those who teach) - (a) When the movement is completely operated on the same chord and not during a progression. On a chord of Dm7 (or F6) the parallel fifths between D-A and F-C are perfectly acceptable, merely the result of displacement and not of progression voice-leading. (b) When the parallel fifths are between the secondary notes (third and seventh) of one (or both) of the chords of the progression. In the progression from Cmaj7 to F6, the fifths between E-B and D-A are perfectly acceptable when the tetrads are complete, with the dissonance of the B with the C and the dissonance of the D with the C. (c) When the progressions are between an alternation of dominant 7th and dominant 7thb5b9 with the b5 in the bass, such as E7, A7b5b9/Eb, D7, G7b5b9/Db, C (often erroneously written E7, Eb7, D7, Db7, C) the fifths E-B, Eb-Bb, D-A, Db-Ab, C-G (preferably in the Bass and Tenor voices) are truly common usage.
     Unpleasant parallel fifths are usually the result of faulty voice-leading. When a triad of F is followed by a triad of G (in the IV-V progression) the parallel fifths F-C, G-D are faulty because the triad of F is really part of the Dm7 tetrad and the C being a seventh has a normal voice-leading down to the B rather than up to the D.
     We hope that this explanation has been useful, but you must understand that we are not Beethoven's psychiatrist, nor have we ever had access to his medical file. The culprit seems to be the unjustified interdictions of traditional academic theory. If Beethoven really did laugh at this interdiction, it must have been one of the few joyful moments in a generally sad and painful existence.
     You seem to have come to MusicNovatory as part of a web search for your specific question. We are sure that you will find our site useful for all sorts of problems including truly reliable procedures of Voice-leading (in Harmony/Transformations) with which you will never have to think or worry about parallel fifths. You might also have a look at Incompleteness (also in Harmony/Transformations) in which Real and Deceptive Triads are clearly defined. Good luck, let us know if you need more help.

     I can't thank you enough for your letter, and advice. Your so very right saying it was a loaded question, that is my piano teacher. :) You we're also correct in saying I wouldn't find it on the web. But, I did write to other web sites and the responses I received, were very inaccurate. Your explanation was detailed and complete, thank you! I will use your web site often.
     Also, I asked my teacher her opinion about the numerous rules, etc. I also submitted my reply based on your information and she was very impressed. From what you say and what my piano teacher tells me it is confusing! I have a very dear friend at CMU who is going to be a Theorist. Laughingly, she told me that "if you don't know theory they won't let you go shopping" :) Of course, thats just my dear friend Marcie's reaction lol.
     If I may, I would like to ask another quetion. I am a performer, classical piano. Right now, im in the middle of harmonic interpretation, before I am permitted to interpret any given work on the piano. (thinks how to phrase this:) So, as you have said and my teacher agrees, I follow the composer and of course my soul to interpret. I shouldn't be so concered about theory? Please know, that I know you cannot break the laws, Beethoven (my favorite great composer) seemed more to bend the rules but they cannot be broken. I just don't think im making sense here. It goes one direction then another lol. But it my choosen path, I just desire to learn and perform. Again, your letter to me was the BEST. Thank you very very much!

     Your reply to ours was very heart-warming and appreciated. We are happy to see that your piano teacher seems to agree with what we sent you.
     As far as your second question is concerned, the problem seems to be your use of the words "laws" and "rules". We prefer to avoid the word "laws" in our explanations because the scientific use of the word means definite, unchanging and real, whereas the legal use of the word means arbitrary, temporary, and changeable, and this creates confusion right from the start. What we have is a natural phenomenon based on natural principles, just like motion is based on the natural principle of gravity. You can disregard it if you wish but it always applies anyway. Disregarding it might also not be the best thing to do as you may hurt yourself, yet, you most probably would not get arrested for it, as it is not against the law. Natural principles govern the operation of natural phenomena and ignoring or disregarding these principles can lead to accidents, not illegal behavior. Human laws and rules are arbitrary, they can be changed, and they are not necessarily efficient (such as the old French rule of priority on the right which fills traffic circles rather than empty them). MusicNovatory defines Music as a natural intuitive phenomenon, and also presents and explains the natural principles that govern it, "what makes Music tick".
     Now, as far as Beethoven (or any other composer) is concerned, they do not bend the natural principles of Music, because they cannot be bent. As for the arbitrary rules of traditional theory, they may be squarely disregarded. Do composers occasionally have accidents ? The answer is unfortunatlely "yes" for the simple reason that composing music is a complex and subtle task and that even the greatest of us are still human. Of course, this is completely another issue which we might undertake a little later. In the meantime, enjoy the site and let us know if we can help you.
     If what you call "harmonic interpretation" is what we would call analysis, we strongly recommend that you look into establishing "Level 0" first so that you are sure that chords are in the "right place". Again, let us know if you need help.

     Thank you very much for your informative letter! Please forgive me for not replying sooner but with school starting I've had my hands full. I agree completly about your definition of "rules" and "laws". I hope I can explain this.. I'm a junior at a musical conservatory. MOST of my professors use the term "Laws". Also, I'm at, like most of my friends, a position in my education, where I seem to find most educated people have some VERY different ideas! Its terribly frustrating. One class I have for example if I used the term "rules", it wouldn't go over very well. :) Oh! Please, may I use your example of "laws" and "rules"?? My friends would applaud till the roof comes down. I'm very close with my principle piano teacher and I've talked to her about this and everything else. She hugs me tight, whispers in my ear "give it time". I'm trying. :)
     I've told my friends (musicians and others in the same field) though why anyone wouldn't want to be a performer is beyond me. I told them of your web sight with glowing praise.
     Your explanation that Beethoven didn't bend the laws or rules staggered me. I have always, been taught this. Yet again, as I learn more .. its almost like a conflict in me! Thank you again for your kindness and wisdom.

Of course you may use our definitions and examples of laws and rules, that's what they are there for.