I wouldn't work too hard to derive "truths" from this website. It has a point to make, and there are some good aspects to that point, but it's a very simple point and it makes it in a conversational, not-very-careful way (and not entirely clearly either). It makes one indefensible overstatement (or "under-explanation"?), which you disprove by your question. The website itself isn't very valuable as a source for learning about music; people have been thinking (better) and writing (better) about these ideas for centuries. But it's worth discussing if only to clear up some of these limitations.
First, definitions. The website is using informal, conversational definitions, so let's use them as well. This is what most people in most contexts mean by these words:
- note: This is a note: . We could get really complicated and scientific about our definition, and talk about fundamentals and harmonics, but conversationally, we can talk about "a single note." A "tone," or "pitch," that we understand as a single unit. Many instruments play only one note at a time—as the human voice usually does (aside from some unusual techniques).
- chord: This is a chord: . Several "notes," happening at once—at the same moment in time. Chances are, they fit some recognized pattern, like say a major triad.
- melody: Most people use "melody" to mean "a series of 'notes' happening one after the other." Where chords look vertically, melody looks horizontally. It "connects the dots" from one note to another, across time, to make a recognizable "tune" (motif, theme, riff, lick...). "Melody" is often contrasted with "harmony":
- harmony: In this clip: I've added "harmony" to the "melody." The treble clef still holds single notes—"the melody"—while the bass clef accompanies it with "chords," a.k.a. "the harmony." This kind of conception differentiates between notes by role—why didn't we call the series of lowest notes a "melody"? Because that's how we're thinking of it, that's why. This analysis started by identifying a string of notes as "melodic," and then relegated other notes to a supporting role. This system makes analytic statements and assumptions. And it works for some music. (And even for "that kind of music," these words are only useful in casual talk; for in-depth analysis we might require more careful words like "voice," "harmonic," "tonal," "function," etc.)
Now, let's cut straight to the most problematic bit of the quote:
A note will have no characteristic when played on its own. However, when a chord is formed from a group of notes then this will form a certain feel of mood (E.g. happy, sad, bright or dark).
There are many problems with these two sentences. The second sentence makes assumptions about how certain chords make us feel. This kind of simple discussion can be useful when talking to kids—"How does this chord make you feel? happy? sad?"—but it doesn't hold up to a broader view of "all music." The ancient Greeks had a lot to say about how certain combinations of notes made people feel—warlike, amorous, peaceful, etc—and so do many other music-cultures. The problem is, they don't all agree. A given musical construct might carry an emotional payload, but that's culturally construed. There's nothing about the scientific distances between these pitches that is actually "sad."
Furthermore, it's pretty easy to argue with even within a music-culture. There are plenty of "happy" pieces in minor and vice versa. Even an overall "sad song" uses major chords as well as minor; it's what it does with them. There's are many, many posts on these topics already on this stack exchange; here's a search for "happy minor", and others could be just as fruitful.
But now let's assault the biggest mistake: "... a note will have no characteristic when played on its own." In fairness, I think the author is having trouble expressing what they really mean, and has also overstated their case. A more defensible (but clunkier) rewrite might be: "Within the Western tonal tradition, it's hard (although possible) for a single note to convey much emotion. You can do much more emotively by choosing how you harmonize it." That's fair. But I'm sorry, no, a single note does have "characteristics." Even setting aside hair-splitting arguments, we could stay with the author's intended meaning of "expressive impact," and still pack that into one note.
I could get out a violin and play you a single note—in fact, maybe I'll edit this post to prove it on video later—and I could make it "angry," "wistful," "playful," "tentative," "plaintive," etc. I can change the overall volume of the note and how long it lasts. I'm cheating a bit by picking an instrument that can do a lot to shape the note even after starting it—I can get louder and softer during the note; I can change the timbre by altering the weight or speed of the bow, making it "growly" or "breathy." I can use "vibrato," wiggling the pitch around but still counting it as the same "note."
So no, a note by itself is not helpless to convey meaning. You then extrapolate from the author's point about "notes" to what we can say about "melody." If an individual note carries no emotion, does that mean melodies can't convey emotion either? And your question proves the author's error, because yes, of course, there are many (memorably, famously) moving melodies. Maybe some of these rely for their power on the chords that they imply, but that's not the whole picture. You could play the theme from Schindler's List unaccompanied and make people cry, but you could also take the underlying chords and write a new, boring, banal melody to go with them. It's the large leaps in the theme that make it work.
And frankly, it's just insulting to monophony ("melody") to suggest that it's incomplete or incapable on its own. With apologies to Goria Steinem and Irene Dunn, a melody needs harmony like a fish needs a bicycle. First of all, if we step back and look at music across the globe, and across time, much of it is music in which we can't talk about this "harmony" thing anyway, or at least not in the same language. The vast majority of music across human experience has been monophonic—that is, one note at a time, a.k.a. "melody." We can't talk about "chords" with the traditional musics of much of Eastern Europe, Asia, Africa, indigenous Americas, etc. You can't talk about them in medieval chant. Even when European classical music started using "multiple notes at once," they didn't think about "chords" in the renaissance, or even all the time in the baroque, and even later. Instead they thought about "counterpoint," "voices," i.e. multiple "melodies happening at once. You can't talk about "chords" in a lot of art music from the twentieth century and ongoing—atonal music is often contrapuntal, or it's easier to talk about "pitch clusters" than chords. And the whole assumption that music does or should convey or cause a "mood" is not an underlying assumption of a lot of work.
So... where does that leave us? If the logic suggested by the website was:
- notes can't convey mood
- chords can
- but melodies can convey mood
- therefore... melodies must have chords in them?
... then we've reached a problematic conclusion because we started with a fallacy. A better flow might be:
- notes can too convey mood
- so can chords
- melodies sure as heck can
- and adding chords to them can help
- and yes, as other answers here have shown, melodies can imply chords, or even yes, "contain" chords by sounding the notes of the chord one at a time.
But we should be careful about making any statements about what's true "of music" without defining how our conversation is limited, and very careful about drawing conclusions from writing that is not careful.