How many notes does it take to state the key? To Have "Tonality"?

Question

I'm referring to "tonal dominant function" as this gentleman is talking about in this video.

How many notes in a "melody" do you need to state the key? Do the ideas of root progressions and the fundamental bass coincide with what I'm inquiring? And can a key also be stated in a ONE chord (or does it take two?).

Also, I'm having trouble understanding the fundamental structure. Is it the fundamental line or the bass arpeggiation that states the key. OR, is it something about both that supposedly works together to state the key?

And so lastly, which theory is true or false. "The Yavorsky Model" or "The Ursatz" (Schenkers Model).

I hope this doesn't seem to be multiple questions in one. My main point is that I want to know which of these theories/methods is most true. My perception of it is that they are all speaking on the same concept but with differing opinions.

If my understanding of any of these theories is actually completely off, please correct me. I'm an amateur theorist, and its possible a lot of these theories go directly over my head.

Answer 1

How many notes does it take to state the key? To Have "Tonality"?

Tonality is the theory that describes what it is to be in a key. Thus being "in a key" and "Tonality" are more or less synonymous.

The "how many notes" issue is the sort of question that music theorists debate without necessarily coming to a definitive answer. The video presents two models of tonality and clearly makes the case that the video author prefers the Yavorsky model.

The Yavorsky model presents a four-pitch minimum, and the Schenkerian model (as presented here) requires six. Thus, within the context of the video, it takes four pitches to establish Tonality/a key.

How many notes in a "melody" do you need to state the key?

Here, too, there is ambiguity, and it depends on the restrictions placed on "melody". In the most strict sense, a melody is not sufficient to define tonality. Establishing a key requires more context than single notes presented sequentially.

However, there is an idea of "compound melody" in which a single melodic line functions as though there were two separate melodies intertwined. In that case, it would again take four notes, according to the Yavorskian model.

Do the ideas of root progressions and the fundamental bass coincide with what I'm inquiring?

Root progressions and fundamental bass are both concepts that can be understood independently of tonality. However, in the Schenkerian model as shown in the video, we see a root progression of I-V-I.

Fundamental bass is a pre-tonality concept that proved an important idea as the theory of tonality developed. But the core of "fundmental bass" is just the idea that, given several simultaneous pitches, there is one pitch that serves as what today we would call the "root" of the chord.

And can a key also be stated in a ONE chord (or does it take two?)

At least two chords must be present, because given only a single chord, there's no way to establish that it is a I chord in the sense of Tonality.

Also, I'm having trouble understanding the fundamental structure. Is it the fundamental line or the bass arpeggiation that states the key. OR, is it something about both that supposedly works together to state the key?

It's the two notes in each of the two chords, working together, that these theories claim defines Tonality.

And so lastly, which theory is true or false. "The Yavorsky Model" or "The Ursatz" (Schenkers Model)?

Neither is true or false. They are two models to describe a certain musical vocabulary. One can choose the theory that best reflects one's experience of the music or that best illuminates a particular aspect of the music.

Answer 2

The speaker in the embedded video* starts with the following definition of tonality: "Without tonal-dominant function, you don't have tonality." This assumption is presented without evidence or reference.

He then demonstrates how the "Yavorsky model" aligns with this definition, while Schenker's "Ursatz" does not.†

While the speaker's tone suggests there is a "right" and "wrong" here‡, the question "What is tonality?" fails Alder's Razor and can't be meaningfully given a definitive answer.

I think it's much more interesting to think of such things as thought experiments of the form: 'If I consider this to be the definition of "Tonality", then what are the consequences? What music is included? What music is excluded?

Another way to think about the question of tonality is, "I'll know it when I hear it." This acknowledges the messiness of the neuro-acoustic systems that allow us to judge whether a sound is tonal or not on listening.

So back to your headline question: How many notes does it take to state the key? To Have "Tonality"?

Maybe one. Probably more. Keep listening until you're sure.

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*For future reference in case it goes dead, "The Ursatz is NOT TONAL" by Joshua Broyles.

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†I reserve comment on the validity of this analysis. I have only a passing knowledge if Schenker and none of Yavorsky.

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‡This is a bit like the controversy over whether Pluto is a planet or not:

To an outsider, it might have looked like a schoolyard fight between the Pluto fans and the Pluto haters, saying "Not a planet!" "Is too!" "Is not!"... The real debate was over the definition of "planet". Whether Pluto, previously considered a planet, fit this definition or not was a side effect.

Answer 3

It's a difficult question. For one thing, how strong does the "key feeling" need to be? A single note by itself (as suggested in a comment) by be enough to hint at a key. However, I have read (or heard) somewhere that if a single note is repeated several times in a row, it can begin to sound like the dominant note of a key.

To truly establish a key, one needs a pattern that would be rare in another key. Ratner suggests that notes 4, 7, and 1 (preferably in that order) are enough to suggest a key (locally at least.) By adding some harmony, one can do better: IV-V-I adds some root movement (classical music prefers ii-V-I as two roots move by fifths) and this should be enough to locally establish kay. (I use the term locally because one can have excursions to a second key without totally losing touch with the first key.)

One can use steps 4 and 7 simultaneously with ii-V7-I. A ninth chord on the dominant note (G-B-D-F-A, in the key of C major) only exists in that key (though it can be created harmonically in any key.) Similarly the dominant minor ninth indicates a minor key unambiguously (G-B-D-F-Ab, in C minor.)

One tricky point is that some chords apply to more than one key if treated enharmonically: Ab-C-Eb-Gb is a dominant seventh in the key of Db but Ab-C-Eb-F# is a German-Sixth in the key of C major or C minor. Ab7 resolves to Db but the German Sixth in C resolves to G or G7 or C64 and then some form of G. Actually, the pattern Augmented-Sixth followed by the dominant chord may more strongly imply a key than even the ii-V-I pattern. (Ab-C-Eb-F# then G-C-E(b)-G followed by G-B-D-G strongly implies either C major or C minor.)

Setting a key can be tricky; composers like to delay such things at times. Establishing and then moving away (and maybe back) from a key is an important element in composition.