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What is the quality of the interval B♯ to F?

If you count from B to F, you get the generic interval 5th. So it must be some kind of 5th.

B ♮ to F♯ is a P5.

By lowering the upper note to F♮, it becomes a d5.

Then changing B to B♯, it becomes a P4, because the interval becomes smaller.

But B♯'s P4 is E♯, not F.

I can't find the answer anywhere. Software programs I tried don't even give me the option to check it, because if I try to check the possible intervals from B♯, it never shows an F♮.

Is this interval impossible?

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    Highly related: music.stackexchange.com/questions/15430/… – Dom May 7 at 0:49
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    Hi Fulgencio, I just sat down at the piano and played these two notes together. It turns out it's not impossible. I also tried B# and Fv, and B## to Fbb, a quadrouple dimiinished fifth. It might be better to spell it as C to F, tho. – AJFaraday May 7 at 9:23
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    Your 5th para. - it cannot becoe a P4 - any B to any F (in the same octave) will always be a fifth. – Tim May 7 at 13:08
  • Dumb question: what's an "impossible" interval? I'm assuming it doesn't mean literally physically impossible... – Eric Dand May 8 at 1:57
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How about "double-diminished fifth".

As you noted, some-B to some-F is a fifth, but in this case it's two semitones lower than a perfect fifth. If it were one semitone lower (e.g. B-F) it would be a diminished fifth. And if it's two semitones lower, I'd call it a double-diminished fifth.

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  • Just to cover the part about the perfect fourth P4, a double-diminished 5th dd5 is enharmonically a perfect fourth. – Michael Curtis May 7 at 16:20
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    "Doubly-diminished fifth" is the term I was taught in college, so I suspect it is in pretty general use. – BobRodes May 8 at 3:44
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The interval exists, it just tends to be more theoretical than practical. In general when make an augmented distance bigger or diminished interval smaller, you get into the "doubly" interval range. B♯ to F would be a doubly diminished 5th (labeled dd5) and the inverse interval would be a double Augmented 4th (AA4).

For practical applications of these intervals, see this question.

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  • Agreed about this interval being more theoretical than practical. I can't imagine any harmonic context where it would be the best way to spell the interval. It either makes more sense as B♯ - E♯ or C - F. – Scott Wallace May 7 at 13:34
  • It can happen when there are chromatacisms that move around and a bass note that stays the same, but yes as long as you are not deviating from the scale a B# which only happens in one major scale (C# major) should always have a F#. – Neil Meyer May 7 at 13:55
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Any B to any F is a fifth, of some sort. B - C - D - E - F. B >F♯ is called P5, as there is a space of 7 semitones between them.

That space in made smaller by one semitone because the B has moved closer to the F. So now, we call the B B♯, (but it's not called C). So now, that P5 has shrunk, and becomes known as a diminished fifth (d5).

But, the F♯ has also moved, towards the B(♯). So now, the interval gets diminished once more. Thus it's now a DOUBLE DIMINISHED FIFTH. An interval that's pretty rare - but in theory it can and does exist. Normally, if there was an F note played, the preceding note would be called C - unless there was a particularly good technical reason to call it B♯ - but even then, it's likely to be written as C, one of the main points of written music is to make it easy to read.

All this assumes from the question that the B♯ is the lower of the two notes.

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  • The quality of being perfect is not just a product of semitones, it has to do with the purity of the tone and the fact that the F# fits in both the major and minor key of the root – Neil Meyer May 7 at 13:57
  • @NeilMeyer - Ah, as far as P5 is concerned, it is 7 semitones from the other note - which may or may not be the root of a key. A So is a dim6, but that's another story. I understand and agree with purity of tone to a degree, although I think it's more to do with divisions of the octave, but fitting into both major and minor key of that root is erroneous. Using that criterion, a 2nd would also be perfect - P2 - but that gets called M2 even in a minor key, so it can't be a good or accurate way to determine its label. – Tim May 7 at 14:42
  • @Tim: In a normal diatonic scale, five of the seconds and two of the sevenths are large than the rest. Three of the thirds and four of the sixths are larger than the rest. There's an even enough balance between the two sizes that they're called "major" and "minor". On the other hand, only one of the fourths has a different size from the rest, and likewise only one of the fifths. Thus, the ones that share a common size are "perfect". – supercat May 7 at 15:11
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    @supercat - I don't think Pythagoras spoke English. He was clever, but not that clever! – Tim May 7 at 16:01
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    @supercat: major and minor are 16th century inventions. (From around the 9th to the 16th centuries, the only modes were Phrygian, Dorian, Lydian, and Mixolydian.) The Ancient Greeks did not use our modes or scales, and our understanding of what their music actually sounded like is incomplete. The names for our modes are a Medieval attempt to lend respect to their music by pretending it was theoretically similar to that of the Ancient Greeks. – Alexander Woo May 7 at 19:51

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