What is an interval called which is greater than augmented? For example, what is C to E double sharp? And what is C to F double sharp? If there aren't names for these intervals, why not? There are names for intervals which include double flats. I felt really embarrassed yesterday when my student asked me, and I promised him I'd find out. Thank you for any helpful answers.

Welcome to the forums!! There was a similar question a while back - quite an interesting read! Here it is!

I think it would be a double augmented, going by the respones to that thread.

Hi, Rosemary. Thank you for your answer and for the guide to a similar question with its answers. I really appreciate what you wrote.

No problem

Why isn't C to E double sharp simply an augmented fourth? (i.e the same as C to F#?)

Similarly, I'd have thought that C to F double sharp( C to G, really) was a Perfect 5th?

Please forgive my ignorance here!

They sounds the same when played, but naming the intervals is about the way they are spelt ie the letter names of the notes. You start by counting the gap between the notes by their letter names so C to E is a 3rd. Then you fiddle about with the sharps and flats etc to decide if it's diminished, perfect or whatever. Does that make sense?

There are lots of ways of writing the same sound! The different ways crop up because you are writing in different keys, or to make the music easier to read.

Fx and G sound the same on the piano, which has only 12 notes per octave, but there has been at least one experimental keyboard* that gives you different pitches for them. Organs were built in the 16th and 17th centuries, some still in existence, with split (fore and aft) black keys so that e.g. you played the front key for C#, Eb, F#, G# and Bb, and the back keys for Db, D#, Gb, Ab and A#. They would have been tuned in one of the mean tone systems, giving more accurate tuning of thirds, compared to equal temperament, at the expense of slightly less accurate perfect fifths, and the splits extended the range of keys that could be used without horribly sour intervals.

On orchestral strings, woodwind and brass, in tonal music, good players instinctively play different pitches for enharmonic equivalents, so as to make the chords sound right. The standard fingering of the upper strings in a given position is to use forward extension for sharps and backward extensions for flats. Think of the sequences G A Bb in G minor and G A# B in B minor, playing the G with first finger on the D string: Bb gets 3 and A# gets 2.

* It has 53 keys per octave, and used to be on display in the Kensington Science Museum, but I haven't seen it lately.

53??! Goodness!

I've been trying to think of a way of explaing this for ages! Pupils just dont understnad why double sharps exist and when I try to explain it in terms of keys they get confused.

Mine have tended to be happy with the explanation that it depends what the function of the note is (what job it's doing).

Hmmm... Mine are all quite young at the moment, well, the ones doing exams are...

It depends a bit on the context, but sometimes with younger ones the fact that a scale (or key) must have one of each letter along the way is a handy reason - eg in D major your C# can't be Dflat because you've already got a D and you can't have two Ds and no C.

Depending on the level of the pupil and their understanding you can translate the same idea into more complex keys.

Now thats a good way of putting it!

Oh thank you ! glad if it helps.

Thanks - I get the bit about naming the notes, it just never occurred to me that it also applies to intervals.

I guess I thought interval names were meant to be "key-less" and could therefore be universally applied.

For example a Perfect 5th could be applied to any scale whereas a double augmented fourth can't.

The thing with naming intervals is that it's just a pair of notes taken out of context.
Put them back in context and how you spell the note is dependant on the prevailing key.

The short response to all of the questions in this thread is 'Pythagoras'. If you'll pardon a bit of mathematics...

We ended up with a scale of 7 different notes because that's what you sort of get using the ratio of 3:2 (the ratio of 2:1 is a PERFECT octave, 3:2 is a PERFECT 5th) seven times: F C G D A E B. (Re-arrange into a familar pattern ... ah yes the scale of C major.)

Lots of complicated(ish) maths later, and you realise that if you carry on, you end up finding that a B# ain't the same as a C ... it's different by what's called a 'Pythagorean comma' (a B# is sharp of a C by that amount).

ANYWAY, suffice to say that a piano is a totally compromised instrument (as is any instrument with fixed tuning), in that NONE of the intervals you play are actually acoustically pure or conform to the laws of nature. You can prove this with maths ... or you can prove it with your ears.

The ear-proof is that intervals that sound fine on the piano (e.g Ab-B) actually sound extremely unpleasant (or at least very odd) if tuned accurately (i.e if the Ab is a true Ab and the B is a true B, not the type of 'average tuning' that is equal temperament).

And to return to the original question, I guess that the main reason that these odd intervals haven't really got proper names is that they are so far way from the natural root of how tonal relationships work that you hardly ever get them in any sort of tonal music, or at least in music which has a meaningful relationship with the laws of nature.

If you are interested in this area, and are mathematically and computorially adept, find the free program 'Scala' (easily findable via Google) and have a play. (You'll be able to try 'virtual keyboards' with hundreds of different tunings with Scala.) Otherwise, listen to some recordings of Bach's 48 made using harpsichords tuned in unequal temperament ... and you might discover what an incredibly fascinating area of study this is.

The saddest thing about the ubiquity of pianos and equal temperament is that they have deafened us to the amazing power of intervals and the interest of studying them.

Brian

Fab post - thank you, briantrumpet!

*Goes to look for scala*