BC and EF

[BlakeJustBlake]

Just something I've always wondered, but never really spent too much time looking into the history of. Why exactly is there only a half step between E and F and B and C? G and G#/Ab would give you an even number of evenly spaced and evenly named notes. So, what makes those special?

I tried googling this, but couldn't find a phrase to google that returned useful results.

[MalcolmAmos]

I presume you already understand WWHWWWH is the step pattern for any major scale. If not do a Google on WWHWWWH. In a nut shell -- Take that pattern to a piano keyboard and starting on the middle C note go up a whole step (two notes) to D, up another whole step to E now go up a half step (one note) to F....... keep going. To check that out - start on the D note instead of the C note and apply the WWHWWWH -- D note, go up a whole step (two notes) for E then go up another whole step for F# -- yep F#. Just follow WWHWWWH and all those sharps and flats are put into the correct places.

Now why WWHWWWH? Every scale has a unique step pattern. Why? To identify it's unique sound. The natural minor step pattern is WHWWHWW. For the other step patterns check out http://www.looknohands.com/chordhous.../index_rb.html they refer to it using numbers, I remember them by taking them to phone numbers, i.e. 212 2122.

Have fun.

[JTE]

Two reasons work together...

A. A major scale is W W H W W W H, because that's the SOUND of a major scale.
B. The key of C was chosen at some point to be the one without any sharps or flats.
Therefore, by default the half steps gotta be between B/C and E/F. Why was C chosen? I don't know. There was a post on TB about nine months ago that asserted that originally when this stuff was codified, the natural minor scale (W H W W H W W) was the important scale, not the diatonic major. So, the key of A minor was the one with no sharps or flats (because they started at the first letter of the alphabet), and its relative major is C.

John

[MalcolmAmos]

Interesting analogy about Am.

[Jim Nazium]

Originally Posted by JTE

... There was a post on TB about nine months ago that asserted that originally when this stuff was codified, the natural minor scale (W H W W H W W) was the important scale, not the diatonic major. So, the key of A minor was the one with no sharps or flats (because they started at the first letter of the alphabet)

That might be right. I think the layout of the piano keyboard predates our note naming system, and the lowest note on a piano keyboard is A.

In other words, our note naming system (and standard notation) is mostly just a historical accident, like the QWERTY keyboard.

[251]

Originally Posted by BlakeJustBlake

Just something I've always wondered, but never really spent too much time looking into the history of. Why exactly is there only a half step between E and F and B and C? G and G#/Ab would give you an even number of evenly spaced and evenly named notes. So, what makes those special?

I tried googling this, but couldn't find a phrase to google that returned useful results.

I believe you will hear the answer to your question by listening to birds. Music is structured as it is because it is pleasing to the ear.

There are scales that divide the octave range into even intervals. I don't know enough to get you started on a search. Perhaps someone else has a better answer?

[anonymous101511]

Originally Posted by BlakeJustBlake

Just something I've always wondered, but never really spent too much time looking into the history of. Why exactly is there only a half step between E and F and B and C? G and G#/Ab would give you an even number of evenly spaced and evenly named notes. So, what makes those special?

I tried googling this, but couldn't find a phrase to google that returned useful results.

Luck of the draw, I guess. Whoever decided what to call the notes just made it all up in the beginning. Nothing special at all about them; I suppose they could have just named every half- step by it's own letter, if you think about it.
Google 'history of musical note names' and you'll see a ton of info about how all this came to be. :-)

[JTE]

Originally Posted by Jim Nazium

In other words, our note naming system (and standard notation) is mostly just a historical accident, like the QWERTY keyboard.

Well, not exactly... QWERTY was designed to slow down typists, despite the assertions by the inventor of the typewriter that it was "scientifically" developed to facilitate higher speed. That's because a more logical layout allowed people to pretty quickly learn to type so fast that the early machines jammed...

Sorry for the hijack!

John

[Jim Nazium]

Originally Posted by JTE

Sorry for the hijack!

That's why I like TB - I learn stuff.

[Billnc]

I had to get a bit of a laugh at the thread title. My youngest students I'll always jokingly ask "1/2 steps?" " B/C and E/F" I hope to get as an answer. Kind of a running joke for most of them, but they can very quickly locate any note on any string without ever having looked at a graph.

[BlakeJustBlake]

Originally Posted by JTE

Two reasons work together...

A. A major scale is W W H W W W H, because that's the SOUND of a major scale.
B. The key of C was chosen at some point to be the one without any sharps or flats.
Therefore, by default the half steps gotta be between B/C and E/F. Why was C chosen? I don't know. There was a post on TB about nine months ago that asserted that originally when this stuff was codified, the natural minor scale (W H W W H W W) was the important scale, not the diatonic major. So, the key of A minor was the one with no sharps or flats (because they started at the first letter of the alphabet), and its relative major is C.

John

I guess this makes enough sense.

I already understood the structure of scales and stuff, I just didn't know why they named the notes the way they did. I guess with EF and BC just being half steps it just makes notation and everything easier.

[Chris K]

Okay folks, now for some facts as opposed to wild guesses. The WWHWWWH system, AKA the DIATONIC SYSTEM was known in ancient Mesopotamia (= Iraq) as early as 3000 B.C. They didn't use keyboards in those days

The most commonly accepted theory on the origins of the diatonic system is that it makes it possible to create a CIRCLE OF FIFTHS:

A - E - B - F - C -G - D - (A)

(Note that in this case not all fifths are perfect fifths)

In this circle, the corresponding circle of thirds (to all of the root notes shown above) the corresponding major and minor thirds are all consonants:

c - g - d - A - E - B - f - (c)

Ancient genius, I would say.

[BlakeJustBlake]

Originally Posted by Chris K

Okay folks, now for some facts as opposed to wild guesses.....

The most commonly accepted theory.....

I'm not questioning you or anything, because I definitely don't know, but I just thought this was funny.

[HaVIC5]

Originally Posted by JTE

Well, not exactly... QWERTY was designed to slow down typists, despite the assertions by the inventor of the typewriter that it was "scientifically" developed to facilitate higher speed. That's because a more logical layout allowed people to pretty quickly learn to type so fast that the early machines jammed...

Sorry for the hijack!

John

Totally OT, but that's a popular myth. Just because QWERTY was designed to prevent jams doesn't mean that it was designed to "slow down" typists. It prevented jams by placing common letters on opposite sides - this didn't really do anything to "slow down" typists, it merely prevented jams. It might not be the most efficient system yet designed, but it certainly wasn't designed to be inefficient.

http://en.wikipedia.org/wiki/QWERTY

ANYWAY....

Okay folks, now for some facts as opposed to wild guesses. The WWHWWWH system, AKA the DIATONIC SYSTEM was known in ancient Mesopotamia (= Iraq) as early as 3000 B.C. They didn't use keyboards in those days

The most commonly accepted theory on the origins of the diatonic system is that it makes it possible to create a CIRCLE OF FIFTHS:

A - E - B - F - C -G - D - (A)

(Note that in this case not all fifths are perfect fifths)

In this circle, the corresponding circle of thirds (to all of the root notes shown above) the corresponding major and minor thirds are all consonants:

c - g - d - A - E - B - f - (c)

Ancient genius, I would say.

Well, I certainly wouldn't say that's the "most commonly accepted theory," there's more to it than that. Check your facts yourself.

Our Western system of music, including the diatonic scale, had it's roots in the ancient Greek system of music. The Greeks, being a highly rational and logical people (presumably), organized their scales and their music by dividing the octave into concrete, simple ratios. A perfect fifth had the ratio of 3:2, for example, and a fourth had a ratio of 4:3. These ratios could be arranged in a series of four notes called tetrachords which could be stacked into different arrangements, which have erroneously be referenced as "the Greek modes" (the actual Greek modal system is far different than our system of Lydian, Phrygian, etc).

This particularly smart Greek by the name of Pythagoras (name rings a bell, doesn't it?) had the idea of stacking the most stable interval of the fifth (3:2) on top of itself, thinking that since it was such a stable interval, all the notes based upon that interval above it would also be stable. He would stack what we'd call C, then G, then D, then A, etc. He was right...almost. The first several fifths on top of the first fifth sounded good, but the further out he got, he noticed something very disturbing.

In the typical Greek system, the major third of the scale can be represented by the ratio 6:5, or 1.2. If you stack a just tuned fifth (3:2) four times, you should get the equivalent of a major third, but that's not what the math adds up to. Instead, its noticably sharper than the major third. This discrepancy only gets worse the more fifths you stack on top of each other.

The difference between the 12th fifth and the root, which should be the same, is known today as the "Pythagorean comma." This ticked off a lot of musicians/composers for a long time because it essentially made it impossible to modulate to foreign keys. It also had the added benefit of making certain keys TRULY sound different than others (the intervallic makeup of each key was slightly different, so different keys really did sound noticeably different). It wasn't until the 18th century development of Well/Equal Temperament that the problem of the Pythagorean comma was addressed. My point is that the major/diatonic scale isn't based upon stacked fifths, because that system wasn't viable until a lot later in music history. Instead, it's based upon stable, simple ratios between notes.

For the OP asking why there is not half step between B-C and E-F, let me put it this way. It would be strange to ask why the word "apple" is spelled "A-P-P-L-E." Sure you could get into a lexicographical discussion of the history of the word and how it came to be part of the English language. But the fact of the matter is, the word is spelled "A-P-P-L-E," and no amount of discussion is going to change that fact or help illuminate some deep metaphysical truth about the word. In other words, it doesn't matter why there isn't any half steps between B-C and E-F because that's simply how the sound of a major scale is defined. If there were half steps between them, then it wouldn't sound like a major scale. Simple as that.

[Steady Eddie]

The Major Scale is drawn from the twelve note chromatic scale with even semitone spacing between each note. Where the notes of a major scale fall within the chromatic scale depends upon how these notes relate to each other harmonically.

When a note is played on an instrument it sounds out a fundamental frequency plus overtones. The most audible overtones of any one note are the major third (4 semitones) and perfect fifth (7 semitones) intervals.

The notes which are harmonically most pleasing when played with the tonic are the perfect fifth and the perfect fourth (5 semitones) which has its first overtone equal to the tonic note of the scale it is based on. These notes, the tonic, the fifth and the fourth, relate so closely to each other in terms of shared tones and overtones and sound so harmonically right that they are present in every musical scale known on earth.

If you write out these three notes together with their most audible overtones within the span of an octave, you will get the following:

Tonic C has overtones, C, G, E
Fifth G has overtones, G, D, B
Fourth F has overtones, F, C, A

Giving the scale:

C, D, E, F, G, A, B

And if you do the math with the semitones you will get tonal spacing:

Tone – tone – semitone – tone – tone – tone – semitone.

And that is why there is only a semitone between EF and BC.

[JTE]

All this esoteric discussion of why there' a half-step between 3/4 and 7/octave doesn't in any way answer the question.

That is why is it B/C & E/F instead of any other letters? Would it not seem more likely to make A major the key with no sharps or flats, putting the hal-steps between C/D and G/A? THAT'S the question.

John

[Chris K]

Originally Posted by HaVIC5

Well, I certainly wouldn't say that's the "most commonly accepted theory," there's more to it than that. Check your facts yourself.

I always do before I dare to bother my TB friends.

http://en.wikipedia.org/wiki/Diatonic_scale

of which the part I refer to is:

"There is evidence that the Sumerians and Babylonians used some version of the diatonic scale.[citation needed] This derives from surviving inscriptions which contain a tuning system and musical composition. Despite the conjectural nature of reconstructions of the piece known as the Hurrian hymn from the surviving score, the evidence that it used the diatonic scale is much more soundly based. This is because instructions for tuning the scale involve tuning a chain of six fifths so that the corresponding circle of seven major and minor thirds are all consonant-sounding, and this is a recipe for tuning a diatonic scale. See Music of Mesopotamia."

So if I'm wrong, I'm in good company...

[Chris K]

Hey Blake,

Originally Posted by Chris K

Okay folks, now for some facts as opposed to wild guesses. The WWHWWWH system, AKA the DIATONIC SYSTEM was known in ancient Mesopotamia (= Iraq) as early as 3000 B.C. They didn't use keyboards in those days

The most commonly accepted theory on the origins of the diatonic system is that it makes it possible to create a CIRCLE OF FIFTHS:

I know leaving stuff away can make life easier, but it made you miss my point...

Fact: The diatonic system was already known in ancient Mesopotamia
Theory: It was created this way because it made it possible to create a circle of fifths etc..

Hope this helps.

[Chris K]

Originally Posted by JTE

All this esoteric discussion of why there' a half-step between 3/4 and 7/octave doesn't in any way answer the question.

That is why is it B/C & E/F instead of any other letters? Would it not seem more likely to make A major the key with no sharps or flats, putting the hal-steps between C/D and G/A? THAT'S the question.

John

But they did take the key of A. Only they took A minor.

Well, maybe they just had a bad day...

[ryco]

I always figured that if there wasn't a semitone thrown in the mix, then music would just be whole tone scales - which, if you play them, get old really fast. The half steps create interesting motion.

If one throws in one semitone step, then there has to be another one to even out the scale so it can reach its 8va tone within one octave.

But this may be under thinking things a little...