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I'm still trying to wrap my head around time signatures, but I think I'm stuck on where these metrical accents come from. For example, in 4/4, we say the main beats are Strong-Weak-Less Strong-Weak.

What, exactly, is making beats 1 and 3 stronger? I understand that in rock songs and such, the drums can provide rhythmic support, but in general, is the composer doing something that makes us feel a strong beat, similar to how poets carefully choose words with stressed syllables in particular positions for different types of meter? (Are composers typically taught to do something to emphasize strong beats in a piece?) I've seen resources (e.g. Laitz's The Complete Musician) discuss agogic or dynamic accents, but those seem to be described as distinct from metrical accents, i.e., marked changes that go counter to listeners' expectations. I do, however, notice some of these at the beginning of some measures, like durational and harmonic changes, but this isn't something that happens with every piece or even every measure in a piece.

So is it something mostly psychological perceived by listeners due to certain expectations? If so, what would give rise to this perception? I'm trying to imagine a violin or piano just playing a simple melodic line—do we still necessarily perceive or feel a certain time signature or meter, absent non-metrical accents?

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This is a real chicken-and-egg problem. However, the thing that makes the question answerable is that time signatures are placed as the starting point.

Time signatures are, after a fashion, a declaration of convention. A time signature of 2/4 is like saying "there will be emphases of roughly equal value every other beat." 4/4 is like saying "there will be emphases every two beats, but the first of them will generally be stronger than the second." 6/8 is like saying "I want two 'large' beats per measure, in a strong — less-strong pattern, with each 'large' beat subdivided into three smaller beats."

Thus:

[In 4/4] what, exactly, is making beats 1 and 3 stronger?: Convention. And, of course, we see jazz and pop routinely play against this convention by placing emphasis on beats 2 and 4, the back-beat.

And, corollary:

Is the composer doing something that makes us feel a strong beat, similar to how poets carefully choose words with stressed syllables in particular positions for different types of meter? Yes. The composer chooses a time signature not unlike the way a poet chooses, say, a limerick, haiku, or iambic pentameter.

(Are composers typically taught to do something to emphasize strong beats in a piece?) Yes. Leaving aside those who have a natural intuition for meter, meter and its conventions are routine part of elementary instruction for any musician, composer or performer — and this includes musical cultures whose metric structures are not based on the same comparatively rigid principles of Western music.

So is it something mostly psychological perceived by listeners due to certain expectations? Up to a point. Again leave aside those with a natural intuition, many people aren't consciously aware of meter, if aware at all — hence its being part of elementary instruction, and not infrequently a particularly difficult part.

But once one has learned or intuited the musical language, then there is an expectation — one intentionally upset by composers attempting to garner some musical impact, as mentioned in relation to the back-beat in jazz and popular musics.

Do we ... necessarily perceive or feel a certain time signature or meter, absent non-metrical accents? No. If metrical accents were inevitable, then a great deal of music could not exist: unmetered chant, for example.

The heart of the question

Metrical accents, more often than not, are achieved via dynamic emphasis — usually, but not necessarily, subtle emphasis. They can be achieved in other ways as well, but what makes them metrical is their regularity in time.

What differentiates a dynamic accent, even if it corresponds to a metrical emphasis point, is that it's given additional emphasis, beyond what would be expected from the meter alone. At this point, though, we are solidly in the realm of perception and aesthetics, since the question of how loud a metrical accent should be and how much louder a dynamic accent should be are not rigidly defined.

Consider speech. Certain syllables of certain English words are emphasized — typically by way of a "normal" accent, an expected level of emphasis, but a level unique to individual speakers, subjects, situations, etc. But a dynamic or agogic (or both) accent might be added to an already accented syllable for even more emphasis. And this same principle can be applied to (metered) poetry: there's the expected, metrical syllabic stresses, and the additional stresses added by the reader.

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  • Great answer! +1. A lot of the time when I was writing stuff, I only became aware of the metrics of a song after I'd started to actually write it down. So they were rarely the starting point, more an afterthought. Of course, having a time signature then made it easier to compartmentalise the songs.
    – Tim
    Jun 12, 2023 at 8:46
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    Funny, I'd argue the opposite chicken/egg order: "time signatures don't cause metric emphasis, metric emphasis causes time signatures." Of course if we want to talk about historical evolution, I guess we have to go back to mensural notation and etc., and I'm too lazy to do that at the moment. But I'm thinking of how often I have a musical idea, and then have to decide on the best time signature (plenty of questions on here about that). Is it in 6, or in 3 and I'm just hearing phrasing? Meanwhile, I'd argue that the listener often does superimpose perceived meter on unemphasized material: Jun 12, 2023 at 12:34
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    ... Turn on a metronome, and I'd argue that most would subconsciously "feel it in 4," rather than 3 or 5. Maybe that just says something about the predominance of 4 in our music. But it also seems to me that the vast majority of music across cultures and history has been pulsed, and most has been metered as well. Plainchant and shakuhachi are exceptions off the top of my head, but the Indian tala, African rhythms, some indigenous American practices (drums), gamelan... I'm pretty sure even Ancient Greek practice had meter (though I'm not clear on the details at the moment). Jun 12, 2023 at 12:38
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    The fact that verbal poetry has been all about feet and lines for so long probably speaks to the same thing: There's a human urge to organize time into recurring patterns, and to differentiate moments in those cycles with emphasis or de-emphasis. Jun 12, 2023 at 12:39
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    @AndyBonner a fair amount of mensural music is rhythmically organized in a way that confounds expectations if you look for a correspondence between mensuration and meter.
    – phoog
    Jun 12, 2023 at 13:17
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I can answer this:

...do we still necessarily perceive or feel a certain time signature or meter, absent non-metrical accents?

The Musescore.com website plays back close to all of its music with no metrical accents at all - within a given piece, all notes with the same dynamics play at the same volume. This leads to interesting effects when playing back poorly notated music there.

Musical indications as scanty as well-placed chords and patterns of longer and shorter melody notes (e.g. half note-quarter note-half note-quarter note) can force or at least greatly narrow down what time signature this music without metrical accents uses. For example, I have smoked out music written in 4/4 time but actually in 3/4 time based on a chord or drum beat every 3 quarter notes instead of every 2 or 4. Nevertheless, the most common metrical "Necker Cube" I have witnessed on Musescore.com is the same piece/excerpt making just as much sense in 3/4 or 6/8 time (sometimes to the point that I hear a piece notated in 3/4 time as being in 6/8 time instead).

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  • A couple of pieces spring to mind, Bluesette and All Blues, which always get counted in as 123,123. Making me question whether they're actually a quick 3/4 or a slower 6/8 (ref. your last sentence).
    – Tim
    Jun 12, 2023 at 9:15
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    @Tim this is also common in baroque music, where you have the question of hemiola -- a pair of 3/4 measures being treated as one 3/2 measure (or the equivalent in other triple meters). It's very common just before cadences, but sometimes you find pieces where it could be happening more frequently, or in different voices at different times.
    – phoog
    Jun 12, 2023 at 11:19
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    A pet peeve of mine is when a song starts without the drums, starts with an instrument like rhythm guitar that happens to be playing a pattern that leaves out the downbeat, or is syncopated, etc., and it tricks my ear into hearing a different downbeat or different meter altogether, and then the drums finally enter and I'm thrown off. Jun 12, 2023 at 12:41
  • @AndyBonner - the Beatles She's a Woman, for example!
    – Tim
    Jun 12, 2023 at 13:17
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    @AndyBonner the first metronome exercise in my masters program was to set the metronome, take the clicks as the offbeat, and then proceed. It was infuriating before I got the hang of it, but it has proven to be a useful skill indeed.
    – phoog
    Jun 12, 2023 at 13:19
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Well... take this with a heap of salt, but I'll venture an observation.

The most common rhythms in western music quite resemble the stress patterns found in many languages from the same part of the world, only made much more regular. A good number of these languages (though not all) tend to put stress on the first syllable of a word, either as a rule or at least as the most common options; in two-syllable or three-syllable words, this is the only stress there, while words four syllables and longer adopt secondary stresses on the third or fourth syllable (not entirely unlike 4/4 or 6/8).

I don't really think it's just random chance that the most common rhythms found in our poetry and music resemble the most common stress patterns found in our speech. Trocheis, dactyls, four-beat, three-beat and two-beat bars. That's how we're used to express ourselves from our first words. And I also don't think it's just random chance these rhythms are such a rule in Europe... but not so in regions where tonal languages are in use instead.

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Meter and time signatures are conceptual.

They are just categories of accent grouping.

Accents can be realized in various ways:

  • dynamic (loud/soft)
  • duration (longer rhythm is the accent)
  • harmony (chord change coincides with bar line)
  • you could abstract harmony further and just talk about pitch change (arpeggiating a chord can create a rhythmic/metrical pattern)

As long as something is providing accents you have the potential to create a metrical feel.

From a practical point of view, and moving up metrical levels, a common thing is to establish the barline with chord changes, establish some number of pulses per barline in beats, subdivide the beat by either simple 2 or compound 3.

Metrical feel doesn't just automatically happen. The composer needs to use musical elements to make meter emerge. A performer needs to play with good metrical feel. If composing or performing mishandles the musical elements, it can undermine the metrical feel.

Sometimes a composer can deliberately work against meter with devices like hemiola and syncopation, but when done right, those support the meter through contrast. Sort of in the way that dissonance works to support harmony.

Some music is unmetered. Medieval chant is a well known example. I've read that the unmetered aspect of chant was a kind of cultivated, high art endeavor meant to distinguish sacred music from secular music, which presumably at that time was metrical.

The take away is whether music is metered or unmetered musical elements must be controlled properly to achieve it, and not one, but several musical devices can be used to those ends.

...I'm trying to imagine a violin or piano just playing a simple melodic line—do we still necessarily perceive or feel a certain time signature or meter, absent non-metrical accents?

Sure. Just play some nursery rhyme tunes, like Twinkle, Twinkle Little Star or Pop Goes the Weasel. Even if you play those without any chord accompaniment, the metrical feel is clear. The pitch changes of the melody and the harmonic implications of the scale degrees used, and some chord arpeggiation in Pop Goes the Weasel, create the sense of barline, beat, and subdivision.

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Rhythm is intrinsic to humans, so having it in music is natural. We live with a regular heartbeat for most/all of our lives, so get used to regularity. Especially when there are words to a song, where they will, to a great degree, dictate the metric of that song, exactly like poetry, as opposed to prose (as I learned at school...).

It's interesting that nearly all time signatures will be broken down into basic twos and/or threes. 4/4 will usually have two emphasis points per bar, even 5/4 will be split into 2/3, or 3/2. March time will inevitably have a two metric - either 2/4 or 6/8, due to us possessing two legs.

Why 4/4 has become the 'common time' rather than 2/4 escapes me although probably that's where the 3rd beat of 4/4 gets its emphasis.

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is the composer doing something that makes us feel a strong beat, similar to how poets carefully choose words with stressed syllables in particular positions for different types of meter? (Are composers typically taught to do something to emphasize strong beats in a piece?)

With an unadorned melody, generally the composer does this by choosing a meter. The rest is up to the performer.

Other things the composer can do include

  • using rhythmic or melodic patterns that repeat once every measure or every two measures (examples include God Save the King -- a.k.a. America -- and Twinkle, Twinkle, Little Star)

  • changing the harmony in line with the meter (almost every song that has both meter and harmony)

  • when there are words, aligning the text accents with the metrical accents (almost every song that has both meter and text, but beware that text accents frequently appear on non-metrical accents such as syncopation or accented anticipation)

But really, the single most influential thing a composer does is often to write the key signature. Consider the allegro from Handel's Water Music. It starts with several measures of F major in which everyone plays this rhythm repeatedly:

X: 1
M: 3/4
K: F
L: 1/8
zFFFFF|F6|

How do we know that the second and fourth eighth notes receive the metrical accent rather than the third? Because it's not written like this, with a 6/8 time signature:

X: 1
M: 6/8
K: F
L: 1/8
zFFFFF|F6|
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  • If anyone can help me figure out why the musical examples are not displaying correctly, please let me know.
    – phoog
    Jun 12, 2023 at 12:03
  • It's supposed to be an eighth rest followed by five eighth note Fs, beamed together, followed by a dotted half note F, in the first case in 3/4 time and in the second in 6/8.
    – phoog
    Jun 12, 2023 at 13:21
  • Possibly ABCjs: can't set clef in K info field if mode not fully specified and image is cached or one of the linked issues.
    – Aaron
    Jun 12, 2023 at 15:38
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Let's start with your last question.

I'm trying to imagine a violin or piano just playing a simple melodic line—do we still necessarily perceive or feel a certain time signature or meter, absent non-metrical accents?

No, not necessarily. And it's not hard to find music that does just that.

plainchant

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There are several ways to view it. As many wrote and according to Riemann, „Musiklexikon, Sachteil“ there‘s a lot of history to it, including pruning more chaotic approaches. Here are views under the topic „orientation“, „knowing where you are“.

Natural breathing. You breath in (strongly accented 1), out (more silent, 2), in again (3, softer than 1; try breathing with 1=3), and out again (fading 4). Emphasis, next beat (strong 1 again). Consequence: just by listening you know where you are within the current beat.

Poems as a song. From poems we know metrics, i.e. certain schemes to emphasize syllables within a word, a phrase, a sentence. Some of these match the pattern you asked for. To have severe mismatch between the metrics of text and music is possible, which will either sound chaotic (which can be intended) or enticing (polyrhythms etc.).

As a drummer … I more often than not use this scheme to help my band mates along, which they appreciate. Specific to drums it‘s often more effective to translate or augment amplitude (how loud I sound) with a rhythmic pattern, depending on the song: it‘s easier to recognize. Example within a 4/4 beat:

  1. dam (with kick drum for empasise)
  2. dam
  3. dadada
  4. dammmm

There are enough sound options on the drum set to make that feel and hear.

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