What's the Reason for Naming Major Second a Diminished Third?

Question

I know that interval between those is identical, but very often I see that instead of typing CM2, people use Cd3 to indicate the interval. Isn't simpler to simply use fewer accidentals and make the score cleaner?

Does calling notes a diminished third can mean something different in a specific context than the major second?

Answer 1

You've picked an extreme example! Outside a theory test paper, a diminished 3rd is more likely to look like this. Maybe within a dom7+5 chord.

Answer 2

Sometimes diminished thirds are respelled to make reading easier, but here's why it can be important to call a diminished third a diminished third.

This post contains three parts: 1) Helping to hear the intervals, 2) some examples of how they arise, and 3) some examples from compositions.

Notice that in all cases (shown here, at least), the diminished third arises from surrounding a target pitch with the notes a half-step above and below. That is, a diminished third follows the "rule" that diminished intervals resolve inward to a unison.

Hearing the difference

Try playing these three exercises. All three, in their penultimate measures, use the same two pitches -- Ab and Bb, enharmonically speaking -- but sound quite different. Repeat the scale measures a few times to orient your ear to the key, then play the ending. (Note: These are not constructed to be realistic examples; just ways to hear the contextual differences in sound.)

Major Second

X:0
T:Major second
K:Eb
M:2/4
L:1/8
[|: EFGA | BAGF :|] [AB]4 | [GB]4|]

Diminished Third

X:0
T:Diminished Third
K:A
M:2/4
L:1/8
[|: ABcd | edcB :|] [^G_B]4 | A4|]

Augmented Unison (Special Bonus Interval)

X:0
T:Augmented Unison
K:G
M:2/4
L:1/8
[|: GABc | dcBA :|] [_A^A]4 | [GB]4|]

Those context-dependent differences in sound are the reason for the distinction of the intervals in theory and when notating.

In Context

Diminished thirds don't occur naturally in diatonic scales; they arise from chromatic alterations. For a sufficiently experienced reader, alerting them to the alteration gives information about what's happening in the music and what may be coming.

In LaurencePayne's F7#5 example, the C# indicates a likelihood that pitch will proceed (resolve) to D.

X:0
T:F7#5 resolution (d3)
K:Bb
M:4/4
L:1/1
[V:V1] e  | d |
[V:V2] ^c | d |
[V:V3] A  | B |
[V:V4] "_F7#5"F  | "_Bb"F |

Respelling the chord to use Db suggests a different resolution (and renames the chord). (Note: I've displaced the b13 by an octave for the illustration).

X:0
T:F7b13 resolution (M2)
K:Bb
M:4/4
L:1/1
[V:V1] e  | d |
[V:V2] _d | c/2 B/2 |
[V:V3] A  | A/2 B/2 |
[V:V4] "_F7b13"F  | "_Bb"F |

Another respelling (and revoicing) of the chord gives an inverted augmented sixth chord and, again, another resolution.

X:0
T:Faug6 resolution (d3)
K:Amin
M:4/4
L:1/1
[V:V1] a  | a | ^g | a |
[V:V2] f | e | e | e |
[V:V3] ^d | e | d | c |
[V:V4] "_Faug6"c  | "_Amin"c | "_E7"B | "_Amin"A |

In the wild

Schubert

A melodic diminished third is found in Schubert's “Der Müller und der Bach” from Die Schöne Müllerin (D795/19), measures 8-9.¹

mm. 7-9²

Bach

Bach's Fugue in D minor (BWV 851) from WTC I contains a diminished third in m. 12.³

Fugue in D minor m. 12⁴

Brahms

In Brahms's German Requiem, a diminished third (one of many diminished and augmented intervals in the piece) can be found in the Alto part at m. 72.⁵

Ein Deutsches Requiem m. 72, vocal parts⁶

Note that were Brahms resolving to Gb Major rather than F major, he would have written the Alto B as a Cb; i.e., a minor third with the tenor.

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¹_{Adapted from https://milnepublishing.geneseo.edu/fundamentals-function-form/chapter/31-the-neapolitan-chord/}

²_{Mandyczewski edition from IMSLP}

³_{Adapted from https://www.teoria.com/en/articles/2017/BWV851/01.php}

⁴_{J.S. Bach, Das Wohltemperierte Klavier, Teil I Urtext (1997, Henle), p. 28.}

⁵_{Adapted from Ouida Clemons, "TYPICAL ELEMENTS OF BRAHMS'S CHORAL STYLE AS FOUND IN THE GERMAN REQUIEM", M.A. Thesis, North Texas State Teachers College (1942). See PDF page 52.}

⁶_{Mandyczewski edition from IMSLP.}