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The question says it all. I'm assuming 12-tone equal temperament.

To give a more familiar example, we hear a minor third and an augmented second differently, for one is a consonance and the other is a dissonance. Similarly, we would hear a perfect fourth and an augmented third differently, if we could indeed construct a harmonic-melodic context in which an augmented third would be heard.

I'm not challenging the conceptual relevance of the distinction between enharmonic intervals in equal temperament, I'm just curious to find out if there are situations in which those specific intervals would arise in a tonal composition, opposed to more radical enharmonics like the doubly augmented octave, which I would bet are impossible to realize in practice.

phoog
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Felipe Martins
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  • I understand this question the same way Tim has. Felipe, maybe you can confirm: My paraphrase of the question is: "Why would you ever use, say, an augmented 3rd instead of a perfect 4th? I'm not arguing that it's never needed, I just want to know why you would choose it." (The mention of temperaments is just because one of the first answers to "what's the difference between X and Y" is "Well, barring equal temperament, the intonation is different...", but we're not hashing out that discussion here.) – Andy Bonner Oct 19 '21 at 15:14
  • Related question: [How can an augmented 3rd interval be considered dissonant?](https://music.stackexchange.com/q/102162/70803). – Aaron Oct 19 '21 at 18:25

2 Answers2

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Augmented third

1. A key change

Imagine a piece in the key of G major that modulates to F# major. In that case, we might encounter the chord progression D7 - C#7 - F#. Within that, one voice might move from C (in the D7 chord) to E# in the C#7 chord.

X: 1
T: Augmented third example
M: none
L: 1/1
K: G
[V:V1] [Fc] [^G^e] [^A^f]
[V:V2 clef=bass] [D,A,] [^C,B,] [^F,,^C]

2. Chromatic chords

A piece that embellishes its tonic chord with a common-tone diminished chord, then moves to the dominant chord could create an augmented third. The chord progression would be I - C.T.o7 - V7 - I with the fifth of the common-tone chord moving to the third of the dominant chord.

In the key of F, this would be F - Fdim - C7 - F, with the Fdim's Cb moving the the C7's E.

X: 1
T: Augmented third example #2
M: none
L: 1/1
K: F
[V:V1] [FAc] [F_A_c] [GBe] [Acf]
[V:V2 clef=bass] C, __E, C, F,,

Enharmonic perfect fifth

Enharmonic equivalents to a perfect fifth — a doubly-augmented fourth or a diminished sixth — I have never encountered and seem unlikely. However, in theory were an augmented third from the above inverted (e.g., C moves down to E# rather than up), then the diminished sixth scenario would occur.

Aaron
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  • I really like the first example, thanks! I'm aware that many theories regard the second chord of the second example as a Fdim, but I tend to disagree. The "Cb" will most likely be heard as a leading tone to C, and therefore as a B, not a Cb. That is the case in the example, where the chord is in fact a Bdim, a dominant (with omitted root) of the dominant C in F. – Felipe Martins Oct 19 '21 at 19:03
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    @FelipeMartins Agreed regarding the second example, which is a bit forced. Even the first example could be respelled such that rather than V in D major, it's an augmented sixth chord in F# minor. However, when played, I do find both examples sound like an augmented third rather than a perfect fourth, so I let myself get away with both. – Aaron Oct 19 '21 at 19:21
2

Trying hard to understand the question.

I think what you're asking is, in 12tet, say key C, using an augmented third note (e.g.E♯) as opposed to a P4 (F), or a diminished 6th note (e.g.A♭♭) as opposed to P5 (G) in a piece.

If that's the essence, there are two basic considerations when writing out music. One is getting the notes technically correct, two is making the piece as easy as possible to read and play. They usually align, but if not, then the second will usually take precedence.

Once in a while, I come across this dilemma, and question why the writer has favoured the first - especially when there's the dots and the accompanying chord name doesn't follow them. Sometimes it's sloppy writing, sometimes ignorance, sometimes pedantry! Most would agree simplicity of reading, thus playing, is of more importance, I think. Downvoters - please give your reasons for disagreeing..!

Tim
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    Ah, now I'm getting what the question is about. Chromatic ornamentation is where unusual accidentals often occur, and the piece still might be tonal. – user1079505 Oct 19 '21 at 15:51