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B to C and E to F?

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(@antonio43)
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After starting to get into a little bit of theoryand scale progression, and with all the excellent articles here I have epiphenies weekly. But I can't figure out why there is no #/b between B and C or E and F? just wondering. This is one of the most helpful pages out there thanks for all the help from everyone who contributes, it is appreciated. J

I don't beleive in beatles, I only beleive in myself - Jon Lennon


   
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(@nicktorres)
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It may seem a bit odd or obvious, but there is nothing between them because they are only 1 half step apart.


   
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 Mike
(@mike)
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Cb is in-between B & C (although Cb = B)

&

Fb is in-between E & F (although Fb =E)


   
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(@nicktorres)
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Well no, they aren't in between. They are the same note, different name or in other words, enharmonic spelling.


   
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(@slydog)
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It may seem a bit odd or obvious, but there is nothing between them because they are only 1 half step apart.

That's the obvious answer, and I know we'd probably have to bring a few monks back from the middle ages to answer this question, but why are they only a half step apart? It's really a two part question - why are scales laid out the way they are - WWHWWWH - and why are they labeled the way they are, with sharps, flats, etc. Why not just call them A thru L?

Did the standard intervals arise because of some innate preference by our human ear, or have we been conditioned to them over the centuries? Just curious.

Blame it on the lies that killed us, blame it on the truth that ran us down.


   
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(@nicktorres)
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From "Gin and Diatonic"

Sound waves… who remembers the scene in Jurassic park where the scientist looks into the puddle and sees the ripples?
The Tyrannosaurus was on his way. Time to go.

The ripples were caused by the sound wave created by the dinosaur's footstep. They traveled through the ground and created the ripples in the puddle.

So let's consider the T-Rex our root note frequency. Wherever he is stepping he is going to cause the ripples to move through the water at the same speed.

If you used the T-Rex ripple frequency as a base, you could figure out any other kind of dinosaur's approach by comparing the ripples.

Now if instead of the T-Rex, it had been the dreaded "Octave-asaurus", the ripples would move exactly twice as fast. Doubling the frequency of ripples in other words.

The "Fifth-asaurus" would send out 3 ripples in the same time as 2 T-Rex ripples.

The "Fourth-asaurus" would create 4 ripples in the same time it took for 3 T-Rex ripples.

Remember Mr. "Square of the Hypoteneuse" Pythagoras? He discovered the ratio for these harmonics, amongst other things, a couple of thousand years before Spielberg was born.

Octave = 2/1
Fifth = 3/2
Fourth =4/3

Pythagoras, who was a mathematician, came up with all of the combinations of these ratios to get numeric values for the scale.

For example:

A perfect fifth (3/2) plus a perfect fourth (4/3)
3*4 = 12/6 or 2/1= an octave
2*3

If you look at all the combinations of these ratios, you get the aforementioned and dreaded Pythagorean diatonic scale. In the line below big "C" is the root note and little "c" is the octave.

C=1; D=9/8; E=81/64; F= 4/3; G=3/2; A=27/16; B=243/128; c=2/1.

This is an exact ratio scale.


   
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(@hummerlein)
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Ancient greece and rome never cease to amaze me.


   
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(@slydog)
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Thanks for that answer, Nick. I'm a numbers guy, so I'm going to have to contemplate those ratios a bit so I can understand it all. Now I understand why my guitar-playing neighbor said a mathematically inclined person like me should be able to understand theory. We'll see.

Thanks again.

Blame it on the lies that killed us, blame it on the truth that ran us down.


   
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(@slydog)
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From "Gin and Diatonic"

C=1; D=9/8; E=81/64; F= 4/3; G=3/2; A=27/16; B=243/128; c=2/1.

This is an exact ratio scale.

OK, I had to find the pattern, and here's what I see:

C (1) x 3/2 = G (3/2)
D (9/8 ) x 3/2 = A (27/16)
E (81/64) x 3/2 = B (243/128)
F (4/3) x 3/2 = C (2/1) - two times the frequency of root C
G (3/2) x 3/2 = D (9/4 or 18/8 - which is exactly 2 times the frequency of our original D)
A (27/16) x 3/2 = E (81/32 or 162/64 which is double our original E)
B (243/128) x 3/2 = 729/256 = pattern breaks down, because it's the only interval that's not 3 1/2 steps from the lower note, it's only 3 steps.

So what does it all mean? That I have way too much time on my hands. And that I still don't quite understand why WWHWWWH sounds pleasing to the ear - or how this ever ended up in Beginner's Q&A. :?

Blame it on the lies that killed us, blame it on the truth that ran us down.


   
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 hh83
(@hh83)
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please excuse my english, alright?

here's a simple way to understand the scale.
if you take the major-C scale, its

C D E F G A B C, right?

imagine your sitting there with a chromatic harmonica or something fretless, like a violin, and you play something that is harmonic, while rising in pitch. the "cleanest" is the major, right? if you play C D E F# G#
the F# sounds a bit to high, so you would by ear alone, make a scale that goes WWHWWWH, and since you just invented the tones, you name them, from low too high, from the alphabet. some time later,you try some more (again, on the violin, starting from a different position) you just invented transposing, and you now need sharps/flats to make a major scale starting at a different spot. cause if you play the C scale from a different place, you are in modes. remeber, knowledge is like 4-wheel drive. you just get stuck in more remote places;)

simple answer: the major scale is what the notes are named after, and there are two tones that are only a half step apart, therefor have no b/# between them.

Never call a shovel "an ingenious hole-digging instrument"


   
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 sirN
(@sirn)
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Gin, Tonic, Ripple? Dang, I'm gonna go get drunk.

check out my website for good recording/playing info


   
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(@slydog)
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imagine your sitting there with a chromatic harmonica or something fretless, like a violin, and you play something that is harmonic, while rising in pitch. the "cleanest" is the major, right? if you play C D E F# G#, the F# sounds a bit to high, so you would by ear alone, make a scale that goes WWHWWWH...

This is why I drove my teachers nuts back in school. I'm not satisfied with knowing how things are ( that major scale intervals are WWHWWWH), I want to know WHY they're that way.

Why does it bother us if a scale goes unresolved? Scott Houston, PBS's Piano Guy, used to torment his profesional musician parents by running scales for seven notes and stopping - do-re-mi-da-so-la-ti - and ending there. They'd scream at him, "Finish it!!" Why does that bother us so? Why does the F# sound wrong to our ear in a C major scale?

Based on the Pythagorean calculations laid out by Nick, for some reason we have come to prefer - expect - major scales that do not progress in a constant, steady mathematical pattern, with identical changes in frequencyfrom note to note along the scale. The only pattern is that the frequency increases by fifty percent from I to IV, II to V, III toVI, IV to VII and V to I (octave higher), but the relative change in frequency is not equal from note-to-note. Why does that please us more than a constant increase in ratio? Is it innate or is it learned? Is this unique to Western music? Do other cultures have different scales? Do they cringe when they hear a western major scale?

To quote the title of a book my parents gave me when I was six or seven - "Why, Why, Why - Tell Me More".

See why I drove my teachers nuts?

Blame it on the lies that killed us, blame it on the truth that ran us down.


   
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(@paul-donnelly)
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Do other cultures have different scales? Do they cringe when they hear a western major scale?
Are these just rhetorical? To answer them regardless:

Yes, other cultures do have other scales. Indonesian Gamelan orchestras use the Pelog and Slendro scales (sometimes both at the same time), and Indian music uses a 22 note scale. You'd have to ask them if they cringe. :)


   
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(@painthorses)
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To put it in simple terms , as I would need to understand it, there isnt a frett between B & C or E & F , therefore there cannot be a Cb because thats the frett that B is on nor can there be an Fb cause thats the frett that E is on. And C is on the frett that B# would need to be on and F is on the frett that E# would need to be on. All other tones have a frett inbetween them making it possible for the other tones to be sharped or flatted. Hope this helps ,


   
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(@greybeard)
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In modern western music, we use the tempered scale, that is there is an equal relationship between the frequencies of notes, which is equivalent to 1/12th of the root of 2 or 1.05946309436.
Open 1 2 3 4 5 6 7 8 9 10 11 12
E 329,6 349,2 370,0 392,0 415,3 440,0 466,2 493,9 523,3 554,4 587,3 622,3 659,3
B 246,9 261,6 277,2 293,7 311,1 329,6 349,2 370,0 392,0 415,3 440,0 466,2 493,9
G 196,0 207,7 220,0 233,1 246,9 261,6 277,2 293,7 311,1 329,6 349,2 370,0 392,0
D 146,8 155,6 164,8 174,6 185,0 196,0 207,7 220,0 233,1 246,9 261,6 277,2 293,7
A 110,0 116,5 123,5 130,8 138,6 146,8 155,6 164,8 174,6 185,0 196,0 207,7 220,0
E 82,4 87,3 92,5 98,0 103,8 110,0 116,5 123,5 130,8 138,6 146,8 155,6 164,8

Look at the A string. The 5th should be at a ratio of 1.5 to the root (110Hz), which would make it 165Hz. In the tempered system it is actually a little flat, at 164.8Hz.
To put it in simple terms , as I would need to understand it, there isnt a frett between B & C or E & F , therefore there cannot be a Cb because thats the frett that B is on nor can there be an Fb cause thats the frett that E is on. And C is on the frett that B# would need to be on and F is on the frett that E# would need to be on.

But this is where the notion of enharmonics comes in. We are able to give two names to each of the accidentals. C is enharmonic to B#. By definition, B# is the note B raised by a semitone - the fact that it coincides with C is irrelevant in music theory (until you get to intervals and then it becomes extremely important). Reversely, B is enharmonic to Cb.
B is also enharmonic to Ax, or A double sharp, and C is enharmonic to Dbb. D is enharmonic to Cx.

I started with nothing - and I've still got most of it left.
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