Table of Intervals, "Diminished" column

Question

I found the following table of Intervals in the Harvard Dictionary of Music (re-created by me in MS Word):

(Correction to the above: It is "Harvard Dictionary", not "Oxford Dictionary". Oops!)

I am wondering why they use the base note of "c" for all the columns, except for the "Diminished" column. Is it simply to avoid the double-flat? I'd rather see the same base note for all columns. But my level of music theory knowledge is not very high, and sometimes things that initially make sense to me turn out to be wrong. Is there anything "wrong" with the following modification to the chart?

Would someone with a great deal of music theory knowledge find the original Oxford one "better" for some reason?

Answer 1

There’s nothing wrong with both what’s in the first table and what’s in your amended version.

The “quality” of a diminished interval simply suggest how many semitones there are between the two notes, ie one semitone smaller than that of a minor interval.

Take the interval of the diminished third for instance, the example given to you is C# to Eb which spans 2 semitones apart. In your modified version, ie C to Ebb, these 2 notes are also 2 semitones apart. In fact, the interval between Cx to E would give you also a diminished third, since, again, it’s 2 semitones apart AND 3 letter names apart. (This last part is important - why we name these 3 intervals as diminished 3rd and not major 2nd, even though a major 2nd interval is also 2 semitones apart.)

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EDIT: The reason why the example given to you was so, was to illustrate the relationship of how the intervals are inflected from a diatonic interval between notes in the major scale.

Eg.

• Major 3rd: C —> E (4 semitones)
• Minor 3rd: C —> Eb (3 semitones, C remains unchanged, E lowered by a semitone making the interval smaller)
• Diminished 3rd: C# —> Eb (2 semitones, Eb remains unchanged, C raised by a semitone making the interval smaller)

You can also choose to illustrate the intervals in this manner:

• Major 3rd: C —> E (4 semitones)
• Minor 3rd: C#—> E (3 semitones, E remains unchanged, C raised by a semitone making the interval smaller)
• Diminished 3rd: Cx —> E (2 semitones, E remains unchanged, C# raised again by a semitone making the interval smaller)

Also, take note that even though C - Ebb is enharmonically equivalent (ie. sounds exactly the same as) to C - D, the intervals are treated differently because of how the notes are spelt:

• C -> Ebb: “C” and “E” are 3 letters apart, hence the interval is a 3rd, and since E is inflected by a double flat, the interval is diminished 3rd.
• C -> D: “C” and “D” are 2 letters apart, hence the interval is a 2nd, and since the D is not inflected at all (a natural), the interval is a major 2nd.

Both the examples listed in the Oxford version and yours essentially try to illustrate the same thing: showing how intervals are inflected one semitone at a time. I personally don’t exactly have a preference for either, but my guess is the first one is more likely to be used in pedagogy since the double-flat and double-sharp are usually introduced much later in theory teaching.

Hope that helps. :)

Answer 2

The C# examples are more likely to occur "in the wild" -- that is, in actual compositions. That is probably why C# were used instead of C.