I've just had a totally incomprehensible 'conversation' with my musician-geek ds. He thinks he has explained this to me, but I am just as ignorant as I was before!

[GoodyGoodyGumdrops]

On a piano there are white keys and black keys. The interval between a black key and its neighbouring white keys is always a semitone, but the interval between two white keys or two black keys is not always a whole tone. Why?

Also, is there any instrument that does have all its notes fixed at equal intervals from each other?

There is a semi tone between all notes which are directly adjacent to each other.

Black keys are only ever sandwiched between white keys (i.e. always directly adjacent only to white notes), hence only ever a semi tone between them.

There are two locations when there are no black keys between white notes so the white notes are directly adjacent to each other. That is B to C and E to F.

I'm fairly sure that is right (but happy to be corrected). However I'm not sure if it answers your question!

There is always a semitone between adjacent keys on a piano.

You need to see the white and black notes as a continuous line of notes rather than two height levels of notes. Now they are all 'flat' and in a line, any time you jum] one hop (whether that is to the left or right, white or black, it is a semitone. Every time you do two hops , regardless of what colour you started on or landed on, is a tone.

Tonic sol-fa innit

But then why is there no B sharp or E sharp? Why are the named notes (ie the white keys) not regular intervals apart?

B sharp is the same as the white note C, E sharp is the same as the white note F. to properly understand you have to think of them as pitches not as coloured notes!
You would need B# instead of C if you were playing for example in the key of C# harmonic minor where the 7th is raised to B#

You lost me after "...coloured notes!"

(I scared a pass in Grade 3 piano a few decades ago.)

I mean, I know that B# is the same as C, but why?

It's called an 'enharmonic equivalent' - a note might need a different name depending on what scale it is part of.
So B flat is a b flat in F major and an A sharp in B major.
F major looks like this:
F, G, A, Bflat, C, D, E, F

If you used the name A# instead of B flat it would look like this:
F,G,A,A#,C,D,E,F.

In the second example there are two 'A' pitches named and no 'B' pitch so the 'spelling' is wrong

The pattern created by the layout of the white notes if you go from one C to the next C is TTSTTTS where T=tone and S=semitone. And the only reason for this not-equidistant layout is that it creates the patterns of notes that we are used to hearing in Western music.

The pattern of TTSTTTS is a major scale. If all the white notes were the same distance apart, they would create a different pattern, called a whole tone scale. Do a search for a recording of a major scale and a whole tone scale and I expect you will find the whole tone one sounds a bit odd.

So we don't have to have this pattern, but it helps us to play the music that culturally we are used to hearing. And in some non-Western music (and non-Western instruments) different patterns are used.

I like your questions. They are making me think.

It's just the type of scale that Western music is based on.
A major scale will always have the same sequence of tones & semitones.
If you listen to eastern music (think of Chinese or Indian music) it's based on a different scale pattern.
The note names are just that, names.

I think this is a bit like grammar. If you don't understand the grammar of a language, you may be able to use the language, but not have a full and fluent understanding of it.

Actually B# is not the same a C, but for a piano we have graduated to what is called "equal temperament". In the past, keyboard instruments were tuned to suit the key that the piece to be played was in, but obviously that was a very cumbersome and time consuming process if pieces in different keys were to be played.

The first famous example of equal temperament being used is Bach's "Das Wohltemperierte Clavier" where he wrote as series of Preludes and Fugues in all 24 keys (12 major and 12 minor) to be played on a single instrument.

It's down to the way the Western system of music has developed the Heptatonic scale as the basis of most of it's music, which involves a combination of tones and semitones between notes, which explains the layout of the piano keyboard.

It's to do with physics and how the octave is divided up. Gets a bit technical!

And you are right about the grammar. Which is why it does annoy me when instrumental teachers don't teach any theory.

There are on-line explanations and tutorials for all of that, but it is pretty complicated. As some one else, it's all to do with the PHYSICS and science of sound.

There was recently a BBC couple of documentaries (probably on BBC4) which you should be able to find on 'catch up'.

(I'll give you more information sometime.)

The BBC4 documentary was by Dr Helen Czerski, a couple of months ago, and called Sound Waves: the Symphony of Physics. It may still be on 'iPlayer'.

What level/grade is your DS and what is he planning to do with his musical knowledge?

If he knows anything about the Hammond Organ and Leslie Speaker they will include some aspects of theory of harmonics etc.

I assume he will already have good 'gear' but the US company M-Audio do a lot of hardware at surprisingly reasonable prices.

Thanks for that, Ferguson, I look for it.

Ds is in Y12, just starting Music A-level, also Maths, Further Maths, Computing. He is a music tech, rather than a instrumentalist. No grades, though he plays piano and guitar-family. He's not sure where it will take him ATM. It's more the chance to do an A-level in his hobby.

Thanks for information. Our DS also did Maths, Physics, Music A-level, but got Grade 8 on saxophone, and did some Keyboard, and Drums in school shows.

These days there is so much overlap in Computers, Music Technology, Recording etc that it all kind of merges into one. Though, unfortunately, that doesn't mean the music is worth listening to half the time!

In the 1960s & '70s, as well as playing drums (which I did for over 40 years) I did a few years of Electronic music at evening classes, using multiple Revox tape recorders, with tape loops going all round the room, to give echo effects (in the pre-digital age) and used the 'classic' VCS3 synthesizer, as heard on "Dark Side of the Moon". Even today, some people still like 'analogue'! I give some information here:

www.vintagesynth.com/misc/vcs3.php

Another fascinating modern 'tech' site is the Ivory II grand piano samples. These are high quality digital reproductions of very famous Pianos, including Steinway, Bosendorfer, Yamaha etc, but you need a good computer and VERY GOOD sound system to hear them:

synthogy.com/index.php/demos/grand-pianos

I'll pass those links on to ds, thanks. He has invested in good speakers, so may be able to use that second one.

He has a lot of respect for analogue synth, says that you can get better details (?) in effects, even though it's more work than with digital. I think that's what he said.

"The pattern created by the layout of the white notes if you go from one C to the next C is TTSTTTS where T=tone and S=semitone. And the only reason for this not-equidistant layout is that it creates the patterns of notes that we are used to hearing in Western music. "

Actually no, the reason why the layout of white and black keys is non-equidistant on the keyboard is so that they musician playing it has an idea where the notes are in relation to each other.

How are you supposed to play a keyboard instrument where each White key is followed by a Black key? Where is a C or an F on a keyboard that goes W-B-W-B-W-B-W-B-W-B etc?

There is the familiar pattern W-B-W-B-W-W-B-W etc so that we know in a glance (or even without looking, really) that the White (lower) key to the left of two Black (high) keys is C, for example.

As Alexander said above, there is a semitone between each adjacent key on the piano regardless of whether they are white or black.

Oo interesting.
Somerset has a point, non-Western music has different patterns eg gaps less than a semitone so quarter tones. No 'reason' other than convention. Cote that's true too though, had never occurred to me but yes it would be impossible to know where you are if it was just alternating black/ white. Thinking of those toy instruments for little kids with different brightly coloured keys now!
Whole to be scales are weird

t would be impossible to know where you are if it was just alternating black/ white

Only because of our note-naming convention.

Logic (and ignorance of musical theory) tell me that naming should go like numbering:

Between every tone there is a semitone, thus:

1 - 1.5 - 2 - 2.5 - 3 - 3.5 - 4 - 4.5 etc

In our convention we give names to the notes, starting with 1 = C (why? Why not 1=A?).

Thus
1=C
2=D
3=E

but then
3.5=F
4.5=G
5.5=A
6.5=B

and then
7=C

Why do we have those two semitone steps?

If the naming convention gave the whole tones the names A, B, C etc, and the semitones were always the flats and sharps, than you would know where you were on any incremental instrument.

Why did the naming convention fix on these jumps?

An octave, perfect fifth, and perfect fourth are the first overtones, the first 3 ways a string is divided into waves when it vibrates. Because of the physics of sound, these are important intervals in music, the basis of our musical language. A fifth is 3 whole tones and a semitone (C-G) and a fourth is 2 whole tones and a semitone (G-C). Keyboards are built to reflect how the fifth and the fourth add up to the octave. String instruments are tuned in fifths (the bass in 4ths) to help with resonance and tuning (as well as for other reasons).

clara is right. The 5th note is extremely important in any scale and on the keyboard it makes sense to have it under the 5th finger rather than as a flat or sharp, as it will be heavily used in connection with 1st & 3rd notes (Do-Mi-Sol in C Major, for example).

If anyone is interested, genius French musician & theorist Jean-Philippe Rameau was the person who first wrote about the overtones / harmonic series, and explained that those notes go well together because a string that makes a note also makes its secondary notes at the same time (as if it's dividing in 1/2, than in 1/3s, 1/4s etc) in his book Treatise On Harmony published in 1722. Fascinating stuff.

Other considerations were necessary too, I imagine. You would want the hand to span an octave, so you couldn't put all half notes next to each other - some of them had to be flats/sharps. You can't make the key much narrower than it already is due to the size of the average finger tip. (Most earlier harpsichords are very difficult to play due to their keys that are smaller than the piano's).