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#988787 - 12/05/07 10:55 AM E Sharp, B Sharp
vayapues Offline
Full Member

Registered: 11/27/07
Posts: 103
Loc: Salt Lake City, Utah, USA
Aside from F and C, which I realize are the sharps for E and B, what is the reason that they do not have their own black keys?

I am wondering about the math behind it.

Thanks kindly
_________________________
There are 10 kinds of people in the world. Those who understand binary numbers, and those who don't.

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#988788 - 12/05/07 11:11 AM Re: E Sharp, B Sharp
Euan Morrison Offline
1000 Post Club Member

Registered: 12/01/05
Posts: 1588
Loc: Edinburgh
One reason is due to note recognition. By having the '3 black keys, then two black keys' setup, we can identify notes quickly. We know that an F is to the left of the 3 black notes.

If the keyboard had black keys beside each white key, it would be alot more difficult to pick (for example) an F straight away.

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#988789 - 12/05/07 11:13 AM Re: E Sharp, B Sharp
Gyro Offline
4000 Post Club Member

Registered: 04/24/05
Posts: 4534
This apparently has something to do with
the temperment system by which a piano
is tuned, which is not exact. But I
think this also has to do with
playability. The arrangement of 7 white
and 5 black keys within an octave fits
neatly under a normal-sized adult hand.
If there were a separate black key for
E# and B#, this would increase the
span of an octave so that it would no longer
fit the average hand. Moreover, the
keyboard would then be totally regular,
with one white key alternating with one
black key throughout, and the
octaves would then be more difficult to
distinguish by touch, as compared to
the present keyboard with the 2
and 3 black key pattern that repeats
itself along the keyboard.

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#988790 - 12/05/07 12:26 PM Re: E Sharp, B Sharp
ted.stanion Offline
Full Member

Registered: 12/15/06
Posts: 278
Loc: Portland, OR
Speculation aside, it has nothing to do with temperament or hand shape. The basic diatonic (seven-note) scale comes about from a simple mathematical derivation.

The most basic relationship between sounds is the unison, or sounds with the same frequency, i.e., the ratio of the frequencies is 1:1. The second most basic relationship is the octave where one sound has a frequency that is double the other, or a ratio of 2:1. The next most basic relationship is the fifth where the ratio of the two frequencies is 3:2.

Now if we start at F and move up a fifth, we are at C. Go up another fifth, and we are at G followed by D and so on until we reach B. The first seven notes generated this way give us the basic diatonic scale. Starting at F, these are the white keys of the piano. Very early music used these seven notes only. Depending on which of these seven notes you used as your base note, you would generate a different mode. The two modes that most of us are familiar with are the one which starts on C and gives us the major scale and the one which starts on A and gives us the minor scale.

The distance between some notes in the diatonic scale is bigger than others. These are called whole steps and half steps respectively. There are five whole steps and two half steps in the diatonic scale. If we add to the diatonic scale by adding more fifths from B, we will generate the notes which divide each of the whole steps into half steps giving us twelve notes in all. This is called the 12-tone or chromatic scale. Adding another fifth brings us back to (approximately) F, so there are no more notes to add in this manner.

Since the diatonic scale came first, these notes got the names A-G. When people started using the half tones between the whole tones, new names were needed, so the terms flat and sharp were invented. I believe the keyboard is laid out in the way it is because of this relationship between the diatonic scale and the chromatic scale.

Ted

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#988791 - 12/05/07 01:23 PM Re: E Sharp, B Sharp
YD Offline
500 Post Club Member

Registered: 12/28/06
Posts: 590
Loc: San Francisco Bay Area
The 12-tone chromatic scale is a compromise between the consonance quality and the difficulty of writing and playing music with too many notes. There is a ton of explanations on the web, here is a good one at Wikipedia:
http://en.wikipedia.org/wiki/Music_and_mathematics
_________________________
Yuri
FWIW; YMMV

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#988792 - 12/05/07 01:32 PM Re: E Sharp, B Sharp
ted.stanion Offline
Full Member

Registered: 12/15/06
Posts: 278
Loc: Portland, OR
Yes, that is why I said the twelfth application of a fifth brings us approximately back to F. When people ask me why there are twelve notes, my glib answer is that it is because 27 is approximately equal to (3/2)12. The difference is called the Pythagorean comma and is what causes all the arguments about temperament and tuning.

Ted

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#988793 - 12/05/07 04:30 PM Re: E Sharp, B Sharp
rockpeter Offline
500 Post Club Member

Registered: 11/08/05
Posts: 607
Loc: Montreal Canada
I think it occured when they built the first piano, There wasn't enough black key material so they built what they could and it stuck.
All a question of material resources \:\)

Peter
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Ok..Ok... If you don't want your Steinway give it to me !!!!

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#988794 - 12/05/07 04:39 PM Re: E Sharp, B Sharp
Eternal Offline
1000 Post Club Member

Registered: 08/21/06
Posts: 1285
Loc: Posts: 80,372
 Quote:
Originally posted by rockpeter:
I think it occured when they built the first piano, There wasn't enough black key material so they built what they could and it stuck.
All a question of material resources \:\)

Peter [/b]
I'm pretty sure the original piano had the colors reversed.

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#988795 - 12/05/07 05:01 PM Re: E Sharp, B Sharp
RhondaLynne Offline
Full Member

Registered: 04/05/07
Posts: 119
Loc: Chicago
Ted, your explanation is one of the most informative, well-written posts I've read here lately - I didn't know that I didn't know that.

Thanks.
_________________________
Rhonda

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#988796 - 12/06/07 02:42 PM Re: E Sharp, B Sharp
ted.stanion Offline
Full Member

Registered: 12/15/06
Posts: 278
Loc: Portland, OR
You're welcome. I'm glad it made sense to someone.

Ted

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#988797 - 12/06/07 05:47 PM Re: E Sharp, B Sharp
John Citron Offline
3000 Post Club Member

Registered: 07/15/05
Posts: 3925
Loc: Haverhill, Massachusetts
 Quote:
Originally posted by Eternal:
 Quote:
Originally posted by rockpeter:
I think it occured when they built the first piano, There wasn't enough black key material so they built what they could and it stuck.
All a question of material resources \:\)

Peter [/b]
I'm pretty sure the original piano had the colors reversed. [/b]
It goes back further than that.

http://www.denzilwraight.com/florentine.htm

To over come the differences caused by the Pythagorian comma, the builders had the split sharps through out the range of the keyboard.

Mean tone tuning makes keys signatures with fewer sharps and flats sound okay, but when you add in the extra sharps, that's when it begins to sound "wild". The split sharps tuned to their corresponding position in the scale was an attempt to smooth out the wildness of the tunings. So the split sharps have a G-sharp in the front, and an A-flat in the back.

With the development of equal temperment tuning later in the 17th century, this became obsolete as these notes are enharmonic to each other.

Listen to the sound clip of this instrument. It's pretty cool sounding.

This did not create the 'reverse' keyboard as we call it today. That was a decorative feature of the instruments. If you notice in the other links, a lot of the keyboards have light colored naturals and dark colored sharps just like a modern keyboard. The only difference here is the naturals are boxwood or some other light colored wood.

On this site, by the way, is a picture of the original instrument that my own Virginal is based on. It's the one with the crosses done in different inlayed panels.

John
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