I did a music theory test where I was asked the interval between F# and Db. I called the interval a perfect fifth but I was wrong. It was a diminished 6th. Can someone please can explain why this interval is not a perfect fifth since on my guitar, that is what it is!
Intervals have at least two different names for the same sound.
The basic number of an interval is counted from the lower to the higher letter. In your case F-G-A-B-C-D, making it a 6 of some sort. Next, the gap is made smaller by F raising to F#. That would make it minor 6, but it's smaller again as the D is now Db. So it becomes a diminished 6th.
Play those two notes, and call the Db C#, and, yes, there's your P5. Problem is - just by listening to two notes, it's not enough of a clue to what their interval actually is. Even given the key, is not enough. We need to know what the note names are, in other words where they are written on the stave.
Guitarists in particular seem to have problems with this - it may have something to do with the way the frets are laid out, or the fact that the same note (sounding, but named differently) can be played in many places.
Don't confuse Db and C#. They might be on the same fret, but they are spelled differently. In practice they sound the same, but in theory they are different notes. These two notes are called enharmonic notes.
In theory exams, when you have to identify intervals with many accidentals, this is an easy way to identify them:
- First, remove all the accidentals: You have the interval F - D, which is a major sixth.
- Add one of the accidentals: F#-D, which is a minor sixth
- Add the second accidental: F# - Db, which is a diminished sixth.
On the guitar (or piano) a perfect fifth will sound the same as a diminished sixth, but in theory those are two different intervals, and it'd be wrong not to identify them as such, like in your case.
An interval has the following properties:
To determine the interval between 2 notes:
- find the pitch interval: there are 7 semitones between D and F# (counting from F# to D)
- find the interval number: F-G-A-B-C-D -> 6
- find the quality: have a look at the main intervals to see that 7 semitones with interval number 6 is a diminished sixth
For any other interval, perform the same steps. If your interval is too exotic to be on the list of main intervals, adhere to the following rules:
pcan be diminished
pcan be augmented
Further tampering gets fuzzy (citation needed)
dcan be further diminished
Acan be further augmented
...when is a perfect fifth interval a diminished 6th and why?
This mixes up distance with interval names.
A perfect fifth
P5 and a diminished 6th
d6 are the same distance - 7 semi-tones.
But the interval name is a combination of an interval number - like 5 - and then a quality - like perfect.
D is six diatonic steps so its number is 6. But when we account for the accidentals
Db the distance gets smaller by two semi-tones and so it is called diminished. It's a diminished sixth.
If it were renamed to
D is a 5 and with 7 semi-tones distance it is perfect, it's a perfect fifth.
Db are enharmonic equivalent spellings.
You could say a
P5 and a
d6 are enharmonically equal intervals, but technically they are not the same interval.
That particular interval -
d6 - is a bit odd. Two intervals non-diatonic intervals that are relatively common and could be mis-identified are:
- augmented second
A2which is enharmonically a minor third
m3, it is found in the harmonic minor scale between scale steps
- augmented sixth
A6which is enharmonically a minor seventh
m7, it is found usually in minor keys as one of several augemented sixth chords. In
Cminor the basic form of this chord would be
Ab C F#with
Those two example can be a good way to become familiar with these enharmonic spellings with practical examples that you will encounter fairly commonly.