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Enharmonically Equivalent Intervals: Augmented Second Or Minor Third?

 

    

triply a1In the entry On How Musical Intervals Are Built it was already mentioned that besides major, minor and perfect intervals, there also exist diminished and augmented ones. One could ask what the reason for that is since our table covers intervals containing every possible number of available semitones. This is exactly what enharmonic is about, and has been mentioned in an earlier entry entitled Enharmonic - Does It really Complicate Our Lives?

Enharmonic makes it possible to use various names for one sound distance between two notes. Why do so? And why not? ;) In the minor third (F-A flat) each note can be exchanged for its enharmonic equivalent. This results in different versions of the mentioned interval, which, however, sounds always identical and is built of 3 semitones. The name of the interval will vary depending on the "enharmonic equivalent" used.

3 or 2v2

The question is, what difference it actually makes to call an interval augmented second or minor third? Subtle as it may be, though, a difference is there.

While getting familiar with intervals we spoke of interval definition, where interval has been described as distance between degrees of a scale! This is where differences come from, for:

  • the sounds F and A flat might belong to e.g. A flat major, E flat major, D flat major, or f minor scale,
  • the sounds E sharp and G sharp might belong to e.g. C sharp major, F sharp major, d sharp minor scale,
  • and the sounds F and G sharp could belong to the harmonic A minor scale (the notion of "harmonic minor" will be explained in our next entry)

It DOES matter - and why?

It is important because augmented second (which sounds exactly like minor third) is an interval found in a minor scale variant and is the reason for this scale's particular melody. Between two neighboring degrees (here between the 6th and the 7th degree), the distance is larger than whole tone.

While it does not matter in interval recognition, for all we hear are 3 semitones in any case, it could mean pretty much while composing of a piece. Therefore, one should remember to always check distances between basic sounds (white piano keys) without taking into consideration of sharp or flat symbols. The distance between basic sounds informs us on the interval size, i.e. it tells us whether we should speak of e.g. a third or of a seventh. Thus:

F - A = M3

F sharp – A = m3

F sharp – A sharp = M3

F - A flat = m3

F flat - A flat = M3

E sharp - A sharp = 4

E flat - A = a 4

E A flat = d 4

If there are no chromatic signs, it is an easy task, just like in our entry Intervals. If chromatic signs for both sounds are the same, the situation is as shown above. If we have only one sign, the result is augmentation or diminution of the original interval. If some other combination comes into question, i.e. different types of chromatic signs by each sound, first we have to see whether they augment or diminish the original interval, and then augment or diminish the interval as many times as it results from the chromatic signs. Let us check how it looks like using our example interval:

F - A – M3 – basic interval (white keys)

F sharp - A – we diminish the M3 (our basic interval) by one semitone, thus changing the interval size from major to minor and receiving a m3

F sharp - A flat - the third F sharp - A is diminished one more time. Basic sounds remain the same all the time, but chromatic signs are opposite. As a result we receive double diminution of the M3, where the first diminution changes it from major to minor, while the second diminution produces a diminished third (F sharp - A flat).

Most frequently described enharmonically equivalent intervals are a4 and d5: they are used practically as mutual substitutes, but once one variant has been chosen, it determines musical notation.

tritones

As we already

  1. know that enharmonically equivalent intervals sounds identical but are written down differently,
  2. and can give proper names to intervals written with notes,

only one question is left:

Why do we call a distance of three semitones minor third, and not double diminished fourth or augmented second?

Of course, we simply choose the simplest and easiest to memorize piece of information, which means the version with just as few chromatic signs as possible ;)

 

    

 


 

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