There's another way to look at the way תלמוד תורה expresses our relationship with ה׳.
<blockquote lang=he><p><b>מט</b> זכר דבר לעבדך על אשר יחלתני׃<br/>
<b>נ</b> זאת נחמתי בעניי; כי אמרתך חיתני׃<br/>
<b>נא</b> זדים הליצני עד מאד; מתורתך לא נטיתי׃<br/>
<b>נב</b> זכרתי משפטיך מעולם ה׳; ואתנחם׃<br/>
<b>נג</b> זלעפה אחזתני מרשעים עזבי תורתך׃<br/>
<b>נד</b> זמרות היו לי חקיך בבית מגורי׃<br/>
<b>נה</b> זכרתי בלילה שמך ה׳; ואשמרה תורתך׃<br/>
<b>נו</b> זאת היתה לי; כי פקדיך נצרתי׃</p>
<footer class=source>תהילים פרק קיט</footer></blockquote>
The volta here is זמרות היו לי חקיך; "your laws were music to me". This is a new metaphor. What does it mean to call Torah "music"?
<blockquote lang=he><p>ועתה כתבו לכם את השירה הזאת ולמדה את בני ישראל שימה בפיהם; למען תהיה לי השירה הזאת לעד בבני ישראל׃</p>
<footer class=source>דברים לא:יט</footer></blockquote>
One understanding is that there are many ways to learn Torah, all of which harmonize to create a greater whole:
<blockquote lang=he><p>וכל התורה כולה נקראת
שירה, וחפארת השיר היא כשהקולות משונים זה מזה וזהו עיקר הנעימות. ומי שמשוטט בים התלמוד יראה נעימות
משונות בכל הקולות המשונות זה מזה.</p>
<footer class=source>ערוך השלחן חושן משפט, הקדמה</footer></blockquote>
Now, the gemara finds fault with David for this metaphor, in explaining how he could get his attempt to move the ארון to Jerusalem so wrong:
<blockquote lang=he><p>דרש רבא: מפני מה נענש דוד? מפני שקרא לדברי תורה זמירות דכתיב ”זמירות היו לי חקיך“, אמר לו הקדוש ברוך הוא דברי תורה שכתוב בהן (משלי כג:ה) ”התעיף עיניך בו ואיננו“ אתה קורא אותם זמירות? הריני מכשילך בדבר שאפילו תינוקות של בית רבן יודעים, דכתיב ”ולבני קהת לא נתן כי עבודת הקדש עליהם בכתף ישאו“, ואיהו אתיה בעגלה.</p>
<footer class=source>סוטה לה,א</footer></blockquote>
But at the level of פשט, it's a nice metaphor. Rabbi Jacob Neusner develops that idea into something profound. Rabbi Neusner was a graduate of JTS and a professor at multiple institutions who published over 900 books on a wide variety of Jewish topics. He was brilliant and strongly opinionated, and I think under-appreciated.
<blockquote lang=en><p>The sad irony about Jacob Neusner is that he is arguably one of the most influential voices in American Jewish intellectual life in the past half-century—yet outside of the academy, and more specifically outside the academic study of Judaism, while many people know his name, few are actually familiar with his work. He is perhaps most widely known for his irascible, sometimes quite nasty, and often pugnacious personality, his famous excoriating reviews, sometimes book-length critiques, and his fallings-out with almost every institution he worked in, almost every teacher who taught him, many of his students—as well as the errors that scar his many translations and publications. He sued institutions he worked for and individuals who attacked his work...There is a joke that in 200 years when scholars study Neusner they will think Neusner was a “school” and not a person.</p>
<footer class=source>Shaul Magid, <a href="https://www.tabletmag.com/jewish-arts-and-culture/books/211209/take-jacob-neusner-seriously"><cite>Is It Time to Take the Most-Published Man in Human History Seriously?</cite></a></footer></blockquote>
He argued with everything he read, including his own opinions. In the 1980's, sociologists of American Judaism discovered Orthodoxy and realized that it wasn't fading away. People actually started looking at the Orthodox community seriously. One study published in 1983 was by Samuel Heilman, and he wrote:
<blockquote lang=en><p>From early on I realized that, for many of the Jews I was observing, this experience was more than the assimilation of knowledge. For one thing, many...seemed unable to review the texts on their own...For another, even those who had <i lang=yi>lernt</i> a lot and displayed an erudite familiarity with the texts took apparent great pleasure in repeating what they had already studied rather than looking for the new and yet unknown. The best questions to ask were those the texts themselves asked; and the best if not the only true answers were those already written on the pages before one. Finally...they often spent more time in class getting their feelings about Judaism off their chests. Clearly much more than learning or the accumulation of knowledge of information about Jewish texts we going on.</p>
<footer class=source><a href="https://books.google.com/books?isbn=1351477579">Samuel Heilman, <cite>The People of the Book: Drama, Fellowship, and Religion</cite></a>, p. 2</footer></blockquote>
In 1984 Rabbi Neusner took that study and criticised what the Orthodox called "learning Torah":
<blockquote lang=en><p>Study of the Torah turns out to constitute a ritual of little study and virtually no torah...</p>
<p>Learning thus forms a labor, not of discovery and testing, but of repetition and revalidation...Learning becomes a process not of discovery but of renewal, not of inquiry and the testing of possibilities but of displaying, in intellectual form, one's loyalty and devotion to the revealed truths of the faith...</p>
<p>To state matters simply, <i lang=yi>lernen</i> and learning have little to do with one another. We teachers aim through teaching to make ourselves obsolete. We want our students to be able to do things on their own...If my students could only repeat what I say, without critical examination and renewal, I should regard my teaching as hopeless...therefore, I have to judge the so-called traditional setting for Jewish learning as worthless, hopeless, and pointless.</p>
<footer class=source>Rabbi Jacob Neusner (1984), <cite>Lehrnen and Learning</cite>, chapter 10 in <a href="https://www.amazon.com/Israel-America-Jacob-Neusner/dp/0807036021"><cite>Israel in America</cite></a>, pp. 133-150 <i lang=la>passim</i></footer></blockquote>
Ten years later, he wrote a book extolling the wonder of the way we learn Torah. He discovered that a "labor...of repetition and revalidation" has inherent value. And that value is exactly the way we experience music.
<blockquote lang=en><p>G-d sings to Israel. The Torah is G-d's song. In secular, descriptive language, in Judaism, G-d is made manifest in the Torah, and it is in the Torah that Israel meets G-d.</p>
...
<p>This act of self-revelation and, therefore, encounter in the Torah takes place before living Israel in two places, synagogue and academy. In both meetings the Torah is not read but sung, and the singing serves to transform secular study into sacred service. Thus--in line with these facts of the faith as practiced every day and everywhere--the theology of Judaism finds its voice in the singing of the Torah. Israel sings G-d's song on its way across the ages--song without end--through eternity, to Heaven.</p>
...
<p>How do we encounter Sinai at one time in the past and the giving of the Torah in the here-and-now? What chemistry of the present moment unites them so as to surpass the paradox of past and present in one and the same moment? Music comes into being at the moment of performance; written-out notes are not music. Music is intensely present; that is its only used tense. That is why music forms the sole right medium for that message, because G-d's self-manifestation in the Torah takes place in the immediate and acutely present sense.</p>
...
<p>If the written part of the Torah is G-d's statement in the synagogue, what of the other, oral part of the Torah?...[W]hat makes the oral part of the Torah equal in importance to the written is, in the careful study of the writings of our sages of blessed memory, through which the Torah, oral and written, joins together and comes to us, we hear G-d's word and respond to it--and talk back. </p>
...
<p>Go to an academy and stand against the wall and listen to the cacophony, as men young and old shout at each other in animated (also ritualized) argument, and you will soon hear the inner rhythm of the shouts and grasp that they are not yelling at one another but singing to one another. In fact, there is a pattern, a sing-song, not an array of civil arguments, calmly put forth for reasoned argument and decision, but an explosion of violent sound, crescendos of phrases, rivers of words, all of them flowing in a powerful current, deeply felt, sincerely meant: the stakes are high. So the men shout at each other, singing to one another, the chant bearing the signals of the sort of argument that is being mounted, the conventions of thought that are being replayed.</p>
<footer class=source><a href="http://press.uchicago.edu/ucp/books/book/chicago/J/bo3613874.html">Rabbi Jacob Neusner, (1995) <cite>Judaism's Theological Voice: The Melody of the Talmud</cite></a>, pp. 1-10 <i lang=la>passim</i></footer></blockquote>
We can appreciate music even if we can't play or sing. Hearing the same themes, the same songs over and over again gives us pleasure. Sometimes we get new insights, but even without that we value it.
תלמוד תורה is not academic research, it is "the theology of Judaism find[ing] its voice in the singing of the Torah". זמרות היו לי חקיך. And that is why David says, כי אמרתך חיתני.
<blockquote lang=he><p>ואמר רבי ירמיה בן אלעזר: כל בית שנשמעין בו דברי תורה בלילה שוב אינו נחרב, שנאמר (איוב לה:י) וְלֹא אָמַר אַיֵּה אֱ־לוֹהַּ עֹשָׂי; נֹתֵן זְמִרוֹת בַּלָּיְלָה׃</p>
<footer class=source>ערובין יח,ב</footer></blockquote>