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In Music, Mind and Brain: The Neuropsychology of Music they use a technique to find the most "salient" level of grouping.

Link to passage text here

This is important in musicology for making observations on the metrical structure of a piece.

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Row 0 refers to eighth notes, 1 to quarter notes, etc. What I can't understand is what they shows exactly. There are dots marked on row 0 regardless of whether a note coincides with that particular beat or not, and there are extra dots on row 4 for the start of the second bar yet I don't see why.

How do I read this and what can I infer from this?

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Let's talk about the music before we talk about the metric breakdown. The piece is in cut time (2/2) and the first measure is a pickup and starts from the second beat. In cut time you would count this meter as 1 - 2 where beat 1 would be felt as a stronger beat.

What this is showing in a very round about way is the note hierarchy and how it lines up with the meter and a measure. By doing this you also see the importance of each beat and its divisions in the meter. It also seem that the 5th dot seen in the first full more is to indicate the start of the section.

In this example, every place where you see 4 dots you have the first beat which is the strong beat. Every place where you see 3 dots is the second beat of the measure which is weaker than the strong beat. Every place where you see 2 dots is the up beat of that beat. Every place where you see 1 dot is between the up beat and down beat.

Another way to represent this and how it is typically represented in this meter is through counting the meter like this 1 - e - + - a - 2 - e - + - a. If you look at the analysis you have you'll notice the 1 is represented by the four dots, the 2 is represented by the three dots, the + is represented by the two dots, and the e and a are represented by the single dot.

  • I see the pattern. but I don't see how it's possible to read the music notation and infer, for example, 2nd bar row 4 should have a dot vs 3rd bar row 4 should not. Would they not be equally weighed given they indicate the beginning of a measure? Or is this something external to the piece? Sorry if I am not clear. This subject is new to me. – user3168961 Apr 30 '16 at 14:42
  • @user3168961 they are equally weighted. The extra dot in the second measure means its the start of a grouping of measures. – Dom Apr 30 '16 at 15:12
  • @user3168961 indeed, Dom is correct. I would argue that the second full measure should have the dot in row four rather than the first full measure, but whatever grouping of measures one chooses, it is not expressed in the notation. Row 4 therefore represents an interpretation. Rows zero through three, on the other hand, are unambiguously expressed by the notation. – phoog May 1 '16 at 7:21
  • @phoog the second notated bar here is the first full bar, so is seen as the first in a group of 4 (or could be 2, or 8) bars. As such, it is a "strong beat of level three" (according to the parlance of the OP's linked text) and is weighted more strongly than the first beat of the third notated bar, which is a 'weak beat of level three'. From the text: "a beat of L is strong if it is also the beat of a larger metrical level' (level four here). – topo morto May 1 '16 at 7:24
  • @topomorto I am trying to say that the beat with the b in the melody should be stronger than the beat with the d. This is in keeping with the concept of end weight, and with the structure of the piece starting on a weak beat. In other words, I think that the linked text has interpreted the metrical structure incorrectly. – phoog May 1 '16 at 7:32

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