What the heck is a diminished second?

So, here I am working on the score for Tchaikovsky’s Swan Lake Suite in my Dorico notation app when I come across some strange looking notes in the clarinets. Accidentals in places where they should not be or missing in places where they should be. This wasn’t just accidentals arbitrarily hidden or cautionarily revealed, the notes were wrong as well These things will catch your eye when visually scanning a transcribed score and boy did they ever.

Right away I knew I had several things I needed to check on here; no clef changes I’m unaware of, there’s a key change from G♭ Major to C Major, and the clarinets are transposed in B♭ instead of the usual A Major. In fact, the entire score is in transposed pitch (for those instruments that transpose) rather than in concert pitch.

Visually scanning from the start of the score, the clarinets were shown to be correct until the last ten bars of the flow, where things got janky and where my eyes originally saw things as suspect. Visually, the notes appear to be off by one diatonic (staff) position, but simply moving things up one position (Major second) on the musical staff screws things up. This is turning into a real head scratcher for me.

I thought I’d try transposing the errant notes up a minor second (instead of a major second) to see what that would look like – but no dice, the result was still wrong. So, out of frustration and feeling that I am getting nowhere fast, I tried transposing up a diminshed second. Voila! – all is looking mostly correct now, but what the heck did I just do? I simply tried a diminished second transposition because it was an option in my music software, and I’d never even considered encountering such an interval before.

Turns out a diminished second is indeed a thing. From Wikipedia:

“In modern Western tonal music theory, a diminished second is the interval produced by narrowing a minor second by one chromatic semitone.[1] In twelve-tone equal temperament, it is enharmonically equivalent to a perfect unison;[3] therefore, it is the interval between notes on two adjacent staff positions, or having adjacent note letters, altered in such a way that they have no pitch difference in twelve-tone equal temperament. An example is the interval from a B to the C♭ immediately above; another is the interval from a B♯ to the C immediately above.”

Ok. So for twelve-tone equal temperament scales (and that’s us by the way), the diminished second is simply the enharmonic equivalent of the current note using the next scale letter. (For Pythagorean-type tunings, it’s that comma difference between a sharp and a flat of two adjacent staff position – something not important in modern equal temperament tuning and a story for another day.)

Fixing the strange notes I had discovered looked to be a straight-forward job, but there were some catches encountered. The notes that needed to be fixed were digitally imported from an A Major clarinet and transposed automatically to a B flat clarinet. I’m using a B flat clarinet because that’s what the 1900 first edition printing print of Swan Lake Suite has.

Now even though I source a lot of music digitally, I always verify that ‘digital transcription’ against an urtext edition, or a copy of a first edition or authoritative printing. It’s a bit of work, but you get to know the piece of music you’re working with intimately, you might fix a few of that prior transcription’s errors, and learning is my joy here. I always try to get things from free sources; I usually can get what I need from the Petrucci Music Library, an awesome resource for classical music.

It turned out that the person who did the transcription only altered ‘some’ of the notes when switch from B♭ to A, because if I blindly transposed everything up a diminished second, a few notes would wind up with double flats. Those were no big deal for me since double flats are easily respelled to the previous staff position, and then all is good again. There were some notes that weren’t right at all, instead of being an enharmonic diminished second down, they were down a minor second (a semitone), but I caught them. I can see somebody making that mistake in this instance.


I learned something today. Actually several ‘somethings’. For instance, it’s important to note the difference between physical intervals (i.e. semitones) and the scale intervals used by the musical staff. The example below from Wikipedia illustrates this. Each pair of notes shown is exactly four semitones apart, yet there are three different scale intervals, there are four spellings, and they are the exact same two tones.


Remember, F♯ and G♭ are enharmonically equivalent – they are the exact same tone. So is A♯ and B♭. Something to consider.

Number
of semitones
Interval nameStaff positions
1234
4major thirdF♯ A♯ 
4major third G♭ B♭
4diminished fourthF♯  B♭
4doubly augmented second G♭A♯ 

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