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I play ukulele and can't read notes very well, so I play with tabs. Luckily, the arrangement am asking about is duplicated in standard notation as well.

This is a line from the Christmas carol "Angels we have heard on high", or "Hört, der Engel helle Lieder" in German, or "Les Anges Dans Nos Campagnes" in French. I noticed that the notes highlighted in this picture produce a distinct feeling that amounts to much more than just completing (part of the) chord.

Together with the melody itself it sounds like the song is going up and down at the same time, though if you look closely, it only goes down.

Angels we have heard on high

Is there a special name for what's happening here? I would also be very thankful for some examples of the same thing in other songs, as I find it really beautiful in a mathematical kind of way.

I guess I am looking for an answer that explains the feelings that the music creates, similar to "this kind of chord usually feels like suspension, this one like resolution". And explaining contrast between bass and melody notes is important to me.

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I think that you are getting a first sense of the venerable art of counterpoint, that is, making different melodies sound good together. You have circled some notes in the ukulele part; these are in fact the notes of the alto part in the standard-notation score. It is very similar to the alto part of the common 4-part choral harmonization of the tune.

Some alto parts fill out the chords in an unassuming way, staying mainly on one or two notes, or following the melody at the 3rd below. Not so with this part. It maintains its own interest through the use of contrary motion, that is, having one voice go up while one goes down. If we strip away all but the important notes on the 1st and 3rd beats of every measure, you'll see that the motion is all contrary until the end. This is rather impressive.

The remaining notes of the part are added with an eye to rhythmic independence: when the melody has a sustained note, the alto is moving, and vice versa. This creates a flowing texture without the fits and starts that the melody by itself would possess.

Composers of the Baroque era, such as Bach and Handel, cultivated the art of counterpoint to the extent of having three or four independent singing parts, each with its own rhythm and directional drive. If you're interested in the genre, see if there's a Messiah sing-along in your area this holiday season. :)

  • coconochao explained it very well already, but you nailed it! Counterpoint, choral harmonization and rhythmic independence are the terms I was looking for. – gingergenius Dec 17 '18 at 22:19
  • Indeed the counterpoint appears to play a more central role in the passage than the harmony and the circle of fifths! +1 – coconochao Dec 18 '18 at 12:02
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This is a hard question to answer, because no one can know how exactly how it feels to you. What Tim said is true, what we see is a sequence of the Circle of Fifths. This means that the next chord is always a fifth apart from the previous one. I think this may be what creates this sensation that the song is going up an down as the same time. Sometimes it feels like rest, but the next chord comes and it feels like it was a suspension. It's a circle after all, it's not going up nor down.

I noticed that the notes highlighted in this picture produce a distinct feeling that amounts to much more than just completing (part of the) chord.

I disagree. I think it's exactly that. By playing the upper notes alone you don't feel the chords. When you add the lower ones, you are able to perceive the harmony and experience what I talked about in the first paragraph. There is nothing special with those lower notes, they just play along with the melody in a friendly diatonic (this means with notes that belong to the scale) way. Actually, the timing may have it's merit, because it fits the melody very well, completing the descents while the melody holds, and holding while the melody initiates another descent. Maybe it makes it feel more complete...

As for examples, Tim already provided more than I could give. You should check them and see if this is the sensation you are looking for. As for understanding why these I-IV / V-I movements sound nice, I feel like this involves a lot of things, but reading about cadences might help...? And to know what I IV and V, it's Roman Numeral Analysis.

  • Totaly agree about the timing. It didn't occur to me to think about it this way. Would you say that most modern pop/rock music is too simple, and this is why ears not used to classical music perceive that timing pattern as very distinct? – gingergenius Dec 17 '18 at 22:15
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From the D, it goes sequentially to the Gm. landing on the 3. D>G (V>I). (or if you like, I>IV). is a very common move. Then it does the same move again, from C to F. V>I or I>IV. Then almost the same again, but getting back to C. It's all a pattern found in the cycle/circle of 4s/5s. D>G>C>F>Bb.

Sweet Georgia Brown, Autumn Leaves, Fly Me to the Moon are among many, many that use a similar sequence, not always in the same key, or with maj/min., but count letter names, and you'll be going up in fourths throughout the sequences. At some point, generally, there's a stop, getting back to the root. I don't know of any tune that cycles through all twelve, but there probably is one. Come on guys, help us out !

  • Unfortunately, am not familiar enough with definitions of V, I, IV and so on. It seems to me like you are only speaking of the notes I highlighted (bass notes), but I still don't understand why bass notes and melody notes combine in a way that feels unique. Maybe I didn't play enough classical music, otherwise it wouldn't be so new to my ears. – gingergenius Dec 16 '18 at 11:39
  • Also, when you say D, do you mean D7? There is no D chord in there, only D7. This difference is enough to confuse a beginner like me. – gingergenius Dec 16 '18 at 11:48
  • The bass notes reflect the root of each chord. I, IV and V are the 1st, 4th and 5th chords in a key, so in D, I=D, IV=G, V=A. They run down slowly, from root to 7 to 6. That 6 is the next chord root The melody notes (at least the first and fourth in each run down) are from root to fifth notes. D and D7, for the purposes of explanation, are not important in this example. Your first task is to find 'Circle of 5ths'! – Tim Dec 16 '18 at 11:52
  • You explain the maths behind the music. I am curious about interpretation of that, i. e. why it creates the feeling it does. – gingergenius Dec 16 '18 at 12:05
  • That's subjective and as such is out of the remit for questions and answers on this site. – Tim Dec 16 '18 at 12:11
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It's pretty straight forward. There is a harmonic sequence, but even if you don't identify it, the harmony is very standard...

F F7 D7|Gm C|F Bb|C

With Roman numerals and the sequence in brackets...

I (passing I7) [V/ii | ii] [V | I] IV | V

Two other things to point out are 1) root progressions by descending fifth are important and we have that, but its a bit out of alignment with the bracketed sequence...

I (passing I7) [V/ii | ii] ↓5 [V ↓5| I] ↓5 IV | V

And finally the Bb to C may seem to not fit the pattern, but it's really just breaking out to end the phrase with a half cadence with is when the phrase ends on a V chord...

| I IV | V

@Mirlan already explain some of the counterpoint in the music so I won't repeat that.

...an answer that explains the feelings that the music creates...

Applying adjectives and emotions like 'heavenly' or 'uplifting' are subjective, but we can try to assess music with generic perceptive words like push/pull, tension/release, expectation/surprise, etc.

While you don't (yet) understand the mean of the Roman numerals you can understand that chords labeled V have a strong sense of resolution when resolving to their tonics or temporary tonics. Notice in this music the use of the V chords in the sequence. That regular resolution of the V and the tension/release produced is very satisfying.

The concept of repetition with variation is important in music. It sort of plays with patterns and expectations. The harmonic sequence satisfies that concept. We don't just get V resolving to the same tonic twice. We get that V resolution on two different tonics. The Gm happens to be a temporary tonic while the F is the real tonic.

  • It would be really helpful to know what you mean by tonic, since as you know I am still a beginner with a small vocabulary for music. But I can look it up myself. Nice perspective. Those are the generic perceptive words I meant. – gingergenius Dec 18 '18 at 8:58
  • You're on the right path to look up the meanings. If you want to analyze, you need to gain a grasp of the vocabulary. Tonic is the first note of a scale or the chord built on that first scale note. – Michael Curtis Dec 18 '18 at 14:49

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