# when is a perfect fifth interval a diminished 6th and why? [duplicate]

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!

## marked as duplicate by Tim H, Carl Witthoft, user45266, David Bowling, Dom♦ theory StackExchange.ready(function() { if (StackExchange.options.isMobile) return; \$('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var \$hover = \$(this).addClass('hover-bound'), \$msg = \$hover.siblings('.dupe-hammer-message'); \$hover.hover( function() { \$hover.showInfoMessage('', { messageElement: \$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); May 12 at 6:03

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.

• Comments are not for extended discussion; this conversation has been moved to chat. – Dom May 10 at 11:37

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: `F#-D`

• 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 `d6`

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:

• `m` and `p` can be diminished `d`
• `M` and `p` can be augmented `A`

Further tampering gets fuzzy (citation needed)

• `d` can be further diminished `dd` (doubly diminished)
• or `dd` (2x diminished)
• `A` can be further augmented`dA` (doubly augmented)
• or `AA` (2x augmented)
• What would 'aa' mean? Could it be 'da'? 'There are 7 semitones between D and F#'. Only if it's counted from F#. – Tim May 8 at 8:40
• @Tim What exactly are the notations for doubly and triply diminished/augmented intervals? I cannot seem to find any info on this. I use ddd for triply diminished and AAA for triply augmented. Is this correct? – dfhwze May 8 at 8:51
• Having so rarely met doule, and never treble, I'm not sure. But dd for double diminished should mean da for double augmented, I reckon. Not convinced with caps versus lower case. – Tim May 8 at 11:07
• @dfhwze I'd be very surprised if there were a standard way to write the interval shorthands for doubly diminished or more (same for augmented). I think the way you did it is better than da for doubly augmented, since the d could stand for diminished instead of doubly (even though the case-sensitive nature might help). You could also try 2d5 for a doubly diminished 5th, but I think your way would probably be understood. – user45266 May 10 at 19:11
• @user45266 I have updated the post and added both methods. I am in favor of the dd, ddd, ddd.. and aa, aaa, aaa.. notation. – dfhwze May 10 at 19:20

...when is a perfect fifth interval a diminished 6th and why?

Never.

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. `F` to `D` is six diatonic steps so its number is 6. But when we account for the accidentals `F#` to `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 `Gb` to `Db`, the `G` to `D` is a 5 and with 7 semi-tones distance it is perfect, it's a perfect fifth.

`F#` to `Db` and `Gb` to `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 `A2` which is enharmonically a minor third `m3`, it is found in the harmonic minor scale between scale steps `^6` and `^7`.
• augmented sixth `A6` which is enharmonically a minor seventh `m7`, it is found usually in minor keys as one of several augemented sixth chords. In `C` minor the basic form of this chord would be `Ab C F#` with `Ab` to `F#` being the `A6`.

Those two example can be a good way to become familiar with these enharmonic spellings with practical examples that you will encounter fairly commonly.

• Don't forget d7 and p6 in your list of common non-diatonic mis-identified intervals. Unless you feel this one is considered straight-forward. – dfhwze May 17 at 10:48
• @dfhwze - what's p6? It was a Rover saloon car from the '70s, but was never a musical interval. – Tim May 21 at 20:58
• @Tim woopz, I meant to say d7 equivalence to M6, thx! – dfhwze May 22 at 4:40