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I can't figure out where the phrases are in this piece of music and I am expected to draw brackets over them. There is no real rest or pause so I looked at where there is an end on the tonic note and made that the end of the phrase but I am not sure about it. In a piece like this how does one tell?

Brahms-excerpt

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    I'd be worried if the person marking your answer considers yours wrong because it doesn't exactly match theirs. More than one correct answer is possible! Commented Oct 20, 2021 at 13:21

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I'll focus on "written theory" concerns first, before approaching it in a different (but more helpful) way later. In this particular example, I would argue that there are two issues at play: parallelism and harmony.

By "parallelism," I mean something that is the same. Notice that m. 6 is exactly the same as m. 1; this suggests that, since m. 1 is obviously the very beginning, that m. 6 could also be a beginning in its own right. So let's work with this hypothesis for now.

And by harmony, I mean that phrases often end with V or I and often begin with I. As we look through the example, our hypothesized m. 6 phrase opening fits within a I chord in the tonic B♭. Furthermore, the end of m. 5 aligns with a V chord. (Technically, the entire measure is dominant, albeit it with a cadential six-four on the downbeat.) Thus m. 5 fits within a common phrase-ending harmony, and m. 6 begins with a common phrase-beginning harmony. Based on these two aspects, we can assume that the first phrase is mm. 1–5 and the second phrase is mm. 6–10.

(This is a little interesting, by the way, because these are five-measure phrases as opposed to the more common four-measure phrases. But that's one of the many things that makes this little piece famous.)

But as I said, these were just the "written theory" concerns. The single best way to identify phrase endings is to actually listen to the piece. Not only to the parallelism and harmony become more clear this way, but we also notice that the sixteenth notes at the end of m. 5 are really just a handful of instruments; the majority of the orchestra rests right there to clearly demarcate the phrase ending.

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    (Highlighting takeaways: 1) Phrase structure often hinges on harmony, so in a melody-only example like this you have to extrapolate the harmonic structure, 2) It's not just about rests. Leroy Anderson's "Sleigh Ride" has a big old interruption for a whip-crack in the middle of a melodic phrase. 3) Theory describes actual music by observation. Any rules and procedures that can be codified ultimately derive from observation. Don't work backwards on music you haven't heard/played yet! Commented Oct 20, 2021 at 14:25
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As a trumpet player I'd look at the line and if there are no written rests (as in the Haydn example provided) I'd ask myself:

When I play this, where can I breathe without spoiling the line? What would be the least disruptive point?

You can often phrase the line convincingly in several different ways. The thing to take away is: there's often no single, unique answer. As long as you can justify your choices musically you're OK.

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    See my answer! I think we're both reaching the same conclusion - it's a 10-bar phrase, but wind players might have to work out how to do least damage to it by their choice of breathing spot! The performances I've just consulted are pretty successful in disguising any breaks.
    – Laurence
    Commented Oct 20, 2021 at 12:58
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Just sing the melody to yourself, the phrasing will usually be apparent.

Though this particular example is a tricky one, and there may not be an obvious 'right' answer. Brahms dovetails his musical elements together so ingeniously that I wouldn't count 'one 10-bar phrase' as a wrong answer!

What else could we say? There's a reiteration of the opening figure at bar 6, so that could be considered the start of a new phrase. But do we count the little 3-note run into it as the start of a new phrase or the end of the previous one? Or do we cop out of the decision by making bars 5-9 a single 5-bar phrase? We're probably on firmer ground counting the first 3 bars as a phrase, and the last 2.

This is the sort of question that I really wish asked for the sort of discussion I've just offered, rather than a definite answer to be judged as right or wrong! If I was singing this, or playing it on a wind instrument, I'd not be recognising obvious places to take a breath. It would be more a matter of 'where can I snatch a breath in these 10 bars and do least harm!

I wondered if the complete score would give any clues. IMSLP has various versions available. Here's the Oboe 1 part. Some slurs, but no phrase marks. However, the sudden 'f' marking at bar 6 suggests that that, rather than the three lead-in notes might be intended as the boundary. (Also note Variation III. Brahms wasn't afraid to write a single, legato 10-bar phrase when he wanted it!)

There's a wide selection of performances on YouTube and elsewhere. Have a listen. I'm coming more and more to the opinion that it's one 10-bar phrase. Great music often DOES fall into long phrases. That may or may not be the answer your test is looking for though!

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This is how I did it before reading any of the other answers and before looking up the actual harmonization. Perhaps some illustration of process will be helpful.

First upon playing the melody, actually upon first glance, I notice elements of repetition and can see a musical period structure...

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...mm. 1-3 and the first beat of m. 4 are repeated exactly in mm. 6-8 and the first beat of m. 9, those parts highlighted in blue. Then second beat of m. 4 and m. 5 for a "first ending" and second beat of m.9 and m. 10 for the second ending.

So, there is a clear 5+5 phrase structure. Mm. 1-5 is phrase one and mm. 6-10 is phrase two, and because of the repetition and alternate endings you can call the whole 10 measures a period.

I also start thinking of how it can be harmonized. I didn't know this music so I tried to demark what seemed sensible points for primary chords I IV V. I sort of sketch out the essential outline of the melody at the keyboard. This is a bit of trial and error, but I'm looking at the strong one beats especially, and then omit certain less essential notes. It's sort of like asking myself "how much can I omit while still being able to hear the essence of the melody?" I came up with something like this...

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...at that sketching level I'm not trying to indicate chord inversions or other details just what are the primary harmonies. Also, keep in mind there are "levels" of harmony to consider. I could have super simplified the first two bars are just I. That is not as important as noting what seems like obligatory I for mm. 1 and 6 and dominant (or some non-tonic) at mm. 4 and 9, and that the second beat of m. 5 which ends phrase 1 is not tonic, while the final beat of m. 10 should clearly be tonic.

Based on the harmony you could say the two 5 measure phrase could each be further divided in to segments (sub-phrases, whatever you want to call them) of 3+2 bars. So the phrasing could be describe as (3+2) + (3+2).

To be clear Brahms didn't harmonize the melody this way. The tones FA and RE can be alternately harmonized as subdominant or dominant harmony. In mm. 4-5 and 9-10 instead of treating it as plain vanilla V harmony Brahms essentially used ii V. Neither choice is right or wrong. The key point is those parts would be non-tonic harmony and that has implications for phrasing.

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Starting or finishing on particular notes can be clues as to where phrases start/end.

A better clue, here, is to spot patterns of notes. It may be certain note directions, but here, it's patterns of rhythm. Often pieces have 'question/answer' motifs, and the rhythmic patterns are a giveaway.

Sometimes the two ideas will combine, making the job easier.

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