Why are the black notes in groups of 2 and 3?

[m1469]

And, why does this question seem to belong in the theory board?

*stares deeply and intensely at the piano keys*

[nystul]

Probably to put the main notes of the seven note western scales on white keys.  But it also turns out to be pretty efficient and makes it easy to recognize which note is which.

[m1469]

The layout of the groupings seems mathematical on a fundamental level.

[m1469]

It IS mathematical on a fundamental level.  I am not mad or frustrated, I am calm - this is progress.

*takes a couple of steps*

[keypeg]

I think it starts off with the fact that Western music started off with those modes (in the way we think of them these days) and we ended up with the "Ionian mode" i.e. our major scale.  The white keys starting on C are simply the notes of a major scale which has semitones between the notes that are a whole tone apart, and they plugged the holes with black keys. That gives us the pattern that we get.

Thinking about it a bit further - why did we divide the octave into 12 tones, the interval of which is a semitone.  Why not quarter tones?  Why not intervals that are a third of a tone apart or some other fraction?  The answer to that seems to lie in physics and the properties of intervals like a pure perfect fifth, the overtones and such.

[Bob]

Yeah, I thought it was what you end up with after continuing to go up by fifths.  Off a little for tuning, but close enough to see the pattern of a keyboard there.

[pianoplayjl]

I think it starts off with the fact that Western music started off with those modes (in the way we think of them these days) and we ended up with the "Ionian mode" i.e. our major scale.  The white keys starting on C are simply the notes of a major scale which has semitones between the notes that are a whole tone apart, and they plugged the holes with black keys. That gives us the pattern that we get.

Thinking about it a bit further - why did we divide the octave into 12 tones, the interval of which is a semitone.  Why not quarter tones?  Why not intervals that are a third of a tone apart or some other fraction?  The answer to that seems to lie in physics and the properties of intervals like a pure perfect fifth, the overtones and such.

Interesting.

[m1469]

The answer to that seems to lie in physics and the properties of intervals like a pure perfect fifth, the overtones and such.

Would you mind expanding on what you mean, keypeg?

[keypeg]

Would you mind expanding on what you mean, keypeg?

I'll try.   Ok, I explored all this a couple of years ago and went hog wild exploring whenever something came up.  I don't have the formal lingo or knowledge for it.

Ok, so on the physics side you have the way the notes vibrate and behave.  Each note contains all the other notes in various portions as partials, and they vibrate and interact in some way.  On violin, if you play D, then the open string below that note which is tuned to D will also vibrate if you are precisely in tune, and you'll end up with a very rich sound because you have two strings vibrating.   Everything they produce interacts and you get this awesome tone quality.

When you play that D, then the partial that vibrates the most after the unison and octave is A.  If your D string is tuned precisely, and your A string is tuned precisely, then the A string will do a bit of vibrating too.  Again, you get a richer sound.  (It's also a handy way of staying in tune by listening for this, assuming your instrument hasn't gone out of tune.)

Notice that the two notes I've mentioned can be seen as Tonic and Dominant note of the key of D.  It happens one fifth up.  Other people will talk about this in terms of dividing a string into half and quarters etc., and others will talk about ratios and numbers (look up "harmonic series", "overtones" etc.)  I'm going by an ear thing atm. .... This phenomenon exists for other notes within the fundamental note, in lessening amounts.  There are precise points between an octave that this happens.   Therefore the way our notes have been divided up isn't by chance.  Other cultures that use quarter tones, for example, are still going along these divisions afaik, but they might slip up or down from them in order to create an emotional effect.

When I was exploring this with someone else, we came across all kinds of cool stuff.  One involved Barbershop singing and the attempt to get a phantom fifth note to sound for four singers.  If a note consists of a bunch of notes (partials) contained in a single note, then it stands to reason that if you those partials are vibrating in the air waves, they can make you hear another note which contains those notes, if all four notes are very pure harmonically.  That is exactly what the barbershop folks aim for.  There is a mystical element to it.  They have what is known as the "barbershop seventh" which are the notes of the "dominant seventh" or "seventh" (i.e. CEGBb, GBDF etc.) but precisely tuned.  If they do it right, you will hear a fifth note as though there were a phantom singer.  

I first looked this up when someone gave me a score of b.q. music, I sight read it and some of it sounded odd to my ear.  I started exploring.  This music is full of as many seventh chords as possible.

another related thing is "overtone singing".  Here a singer produces a fundamental tone (sings a note) but shapes his oral cavity by making an O, or E etc., and placing his tongue a certain way.  He can bend the notes coming out of his mouth in such a way that the partial separates, and you will hear his voice with the fundamental tone, but also a second note that sounds like someone is whistling.  That "whistling" will be going along those same specific notes of the well tuned seventh chord.  It is obeying the laws of physics.

Pure tones minus the overtones can be heard when a guitarist makes that high pitched crystal "ping", violinists can do it too - it's marked in the music with a diamond and is called "a harmonic".  You lightly touch the string at a very specific point - miss it and nothing sounds - and you get a specific note along this series.

(My mind was blown by all this a few years ago).

Some of the stuff I looked at back then:

If you listen carefully to the high pitch notes above his normal sounding voice, you will hear the notes of a seventh chord (which he also points to).

https://www.youtube.com/user/MiroslavGrosser#p/u/26/LLMQCuaYZPk

Music played only with harmonics (wine glass)    
https://www.youtube.com/watch?v=XKRj-T4l-e8&feature=relmfu

[keypeg]

In case it got confusing - The basic thing I seemed to be seeing is that we end up with some essential notes in an octave starting with those found in a seven chord (so for example G,B,D,F) and other notes added to that which gives us the 12 notes that we have.  when then organize them a certain way and we ended up with what comes out as a natural minor or major scale - We can only get white keys for one of them (C major or its counterpart A minor).  That plunks the black keys in between as they fall.  Maybe?

[m1469]

Hi Keypeg,

I just wanted to thank you for your response - it didn't get confusing, I'm just thoughtful about it. 

Thank you .

[alessandro]

I also read someplace in a funny book (don't remember the name of the book or the author, but someone could maybe refresh my memory) that the organisation of the "klavier" was an invention of one, continental-European guy, and he had to have permission from Catholic Church (well yes).   So he proposed his structure to some Catholic authorities in England (and they contacted Italy, if I remember it well).   Their main concern were the numbers.  That's why it is a system with 7ths and 12s..., because of their biblical connotation.   The Catholic Church could live with a system organised around sevens and twelves.   Did the inventor himself had in mind some physical ideas, I don't know, probably, but it is in some way the Pope that gave his final blessing.

Ave and kind greetings.

[birdbrain]

In my beginner music theory class, we were told that the 12 tone tuning is slightly out of tune, in order that we can modulate(?).
We were told that the Gregorian Chant guys sang in a true tuning, and with true tuning, you were limited in the melodies.