The foundation of formal analysis is segmenting a work into spans of time (at multiple levels) and assessing the relationship between those spans. Groups are typically discussed in following four domains:
Below I'll provide an overview of the grouping process and describe each of the four domains of grouping in detail.
In musical form, the grouping process is the act of dividing up a musical span into smaller parts based upon perceived changes and/or repetitions. This is the first step in the analytical process and it is done at multiple levels. I like to think of this process like the process of traveling and describing directions. In that case, the largest group is from the starting point to the final destination. Below that, you might think of the main roads required to get where you're going. For example, if the destination is the university, you can get there by taking highway 1, transferring to highway 2, and getting off at a particular exit. However, that doesn't fully describe the actual details of the trip. A big portion might be just getting to the highway, and the distance from the highway exit to the university is also an important part of the trip. When doing the actual traveling, there are smaller concerns that are part of the trip and important to the driver but aren't regularly specified because they're too detailed (e.g., changing lanes and using blinkers). This is similar to how we group aspects of music at different levels. We can either think big and describe the large sections only (equivalent so only describing the highways used), or when get really detailed and divide the work into phrases and subphrases as well (equivalent to the more nuanced way the navigation system on your phone gives directions).
The grouping process should be done multiple times, and at multiple levels. You might find it easiest to start at the largest level and break the work down in 2, 3, or 4 large groups. From there, you might just work on each of those sections individually. The difference between one group and another may be really obvious, but it can also be rather ambiguous. In particularly ambiguous situations, you might have to some less conventional symbols or even words to convey your personal understanding of the music's grouping structure.
Placing things in groups seems to be a very natural activity for humans. We tend to have names and categories for most things and ideas in our world. The naming and categorization of animals is a great example of this. Your individual dog has a name, and to you, that name refers to a single animal, even if there are other dogs with that same name. But you probably categorize your dog by breed (or you categorize it as not being a known breed with the term "mutt"). At a higher level, you consider it to be part of the category of "dog" which can mean many things, but just as well, it excludes many things. You think of your dog as being a dog because it checks off several features that you've seen other dogs have. It's not the same as any other particular dog, but you feel comfortable putting it in the same general category with other dogs, instead of saying your dog seems more like a hammer, for example. From the dog category, you can categorize it even more generally as a mammal, and above that an animal, and above that as "life," and maybe above that as "matter."
The example represents a single way to categorize something, but we also could consider completely different perspectives as well. For example, we could consider it's physical attributes like height and length which could then be directly compared with even inanimate objects, or we could put them in a group that contains the types of things that are a regular part of human culture.
Grouping is such a natural and intuitive phenomenon, that our brains attempt to categorize things in the wrong way like when a cloud looks like a face. We know it's not a face, but our brains are constantly putting things in groups and then comparing those groups to our existing knowledge.
The grouping aspect of musical form is just like that. When you listen to a piece of music, your brain recognizes change and repetition without you having to think about it very much. The grouping process is simply following what you hear and dividing a span of musical time into groups. The analytical part is comparing those groups and considering them from the perspective of the domains below.
This mode of inquiry focuses on trying to describe the group's role in the work. It's difficult to provide hard criteria for each function because there's an aspect of relatively within the work and within any given genre, but I think you'll find that you already have a sense of what they mean intuitively. Also while you will generally feel comfortable placing a single label on each section, you'll also find sections that seem to start as one function and then change to another, so you'll want to keep that in mind in order to handle those situations, otherwise it might feel like you're trying to fit a square peg in a round hole, and accurate categorization doesn't usually feel like that.
Core sections typically introduce and repeat a work's primary musical ideas and you can think of them as the sections of music that you might sing for someone, if they asked you how the work "went." You can also consider core sections to contain the work's "themes" though usage of that word tends to range from very broad to incredibly specific. Core sections also tend to repeat which is another reason they will often make a stronger impression on your memory. See the page on Core Sections for a more in-depth description.
Auxiliary sections are those that are described in relation to core sections and they are considered less essential in some way though this distinction is unrelated to emotional affect or your appreciation of its value. For example, you can have a piece that only has core sections, but you won't find one (or at least I haven't) that only has auxiliary sections. The auxiliary sections either serve to introduce, follow, or come between core sections. See the page on Auxiliary Formal Sections for a more in-depth description.
Describing a formal section in terms of its thematic material is a very common mode of formal analysis. For the most part, this is a same-different test. If a section is a repeated version of a previous section then it gets the same label, if it's different then it gets a different one. While it's intuitive and common to label sections using letters starting with A and moving alphabetically for each different section, I recommend that you follow my general procedure for formal analysis described on the Approaching Formal Analysis in General page where I advocate for using color or texture first, then find the section's function, and only after that add letters or other labels.
While it's often quite clear whether a section is the same or different than a previous section, it's also possible for the distinction between two section to be ambiguous. Either it sounds somewhat like a previous section but it's really quite different in substantial ways, or it sounds like the blending of two previous section. It could also start like one section but end like a different one. See the section Denoting Same, Similar, and Different on the Approaching Formal Analysis in General page for more information.
The experience of time in a piece of music is powerful way to engage with form. In much music, but certainly not all (see the section below called "Static Stability"), there is an experience of time akin to that of storytelling. In general terms, most stories you encounter have a beginning, middle, and end. If you walked into a movie theater and a movie was already playing, after a short period, you could probably guess where in the story was in terms of temporal function even though you hadn't seen the whole thing. There are usually similarities between a story's beginning, middle, and end that your brain intuitively recognizes based upon your experience with the genre.
The same experience is common with many, though not all, styles of music. If you repeated the example above but with a Beethoven symphony, you'd have a pretty good idea of the temporal function you were hearing, that is, does it sound like a beginning, middle, or end? Like determining primary function, it's difficult to provide hard criteria for each temporal function because there's an aspect of relatively within the work and within any given genre, but I also think you'll find that you already have a sense of what they mean intuitively.
A musical beginning is often relatively stable, has a relatively clear melody that you might sing to someone if they asked you a piece "goes." In classical-style, European music, a saturation of tonic harmony can often be found in beginnings.
Middles tend to be relatively unstable, have less clear melodies (or shorter ones), and are less likely to stick in your memory due their higher degree of variety than a work's beginnings and endings.
Endings often have a clear point of arrival or the drive toward the conclusion of some musical tension. In classical-style, European music, endings are associated with cadences. Endings in many styles, however, are juxtaposed with the beginning of the next section (either a repeat or a new section). This boundary of change is an important perceptual marker between ends and beginnings. The boundary between beginning & middle and middle & end, however, is typically less obvious though these boundaries can typically be argued by the analyses but noting changes in particular (usually more than one) musical domain.
William Caplin is one of the key music theorists championing this this temporal domain in European Classic-era music. He also describes music as having a before-the-beginning character and an after-the-end character. While at first this may sound odd to have music before the beginning, it again relates to what most would call the core formal sections of the work. For example, many popular songs open with minimal music that sets the tempo, key, or affect for the actual song to come. Again, if someone asked you to sing the beginning of a song, most are unlikely to sing the music that occurs before the vocalist begins singing. The music before the vocalist begins, is typically the temporal function of before-the-beginning. Musical endings also typically display a clear point in time where the ending occurred, but in many cases there is still music that follows that ending point before the piece ends or moves on to the beginning of another musical beginning. The storytelling equivalent is the point in the story after, the protagonist resolves their primary goal and overcomes the main problem in the story that needed resolution. For example, many action films have endings where the protagonists defeats the villain and is subsequently reunited with their loved one. At that point, you likely feel resolved in parallel with them. What follows is typically a state of comfort where the energy of the story comes way down relative to the height of tension that led up to the ending point. This space is after-the-end. The story could have ended as soon as the protagonist was reunited with their loved one and still felt complete (and some stories do this, see the end of The Karate Kid for example). Music, especially heavily goal-directed or theological music, does this often as well and it is distinct temporal experience.
Groups are often compared based on their relative stability. Stability can be defined in relation to the piece, section, or phrase, and it can also be compared externally to other pieces in the same or even different genres. In the context of a formal analysis, most of these comparisons are done relative to the piece being analyzed. Regarding core formal section, main sections of a work are most-often characterized by their relative stability, while contrasting sections range more widely from stable (e.g., a sonata's secondary theme) to unstable (e.g., a sonata's development section). Regarding auxiliary sections, connective sections are relatively unstable while external sections are relatively stable. These stability expectations are based on what is common and are not rigid requirements.
Within a section, the relative stability level will rise and fall so there's no need to expect that a stable section needs to exert the same level of stability throughout. In most cases, it changes. It is very common for the stability within a section to follow the beginning-middle-end paradigm where the beginning is stable, the middle is less stable, and the end ends with a return to stability through its conclusion of various musical tensions.
Though most music can be readily approached from the perspective of changing stability, some music does not engage with this domain and instead pursues a more static affect. This approach can be found in some minimalist music, "Lo-Fi," and so-called "elevator music" and "muzak." Music like this doesn't project a strong sense of temporal function either. It's not changing from beginning to middle to end, and instead is more focused on maintaining a single temporal state with no aspirations of teleology or temporal goals.