Why is it...?, Two little things that I can't quite explain Options

[linda.ff]

I've never actually been asked "why" about these two phenomena, but it's been bugging me that I can't quite explain them. And they are along the same sort of lines as my brother saying when he was young that he couldn't quite work out how come I had two brothers and he only had one. (IMG:style_emoticons/default/biggrin.gif)

Okay. Number one. When you consider the circle of fifths, and you go round in the flatwards direction, for each step, you get a new flat in the key-signature. Next step - suddenly it's the tonic! That's like going into a school as a new teacher and the next day you're the Head. So how come it happens in that direction and not in the opposite direction. As I say, nobody's ever asked, but I can't quite put my finger on it.

Number two. Fingering in scales with flat keynotes (until you reach Gb anyway). The rule is in the RH going up and the LH coming down, that you go under when you've played the last flat (or the only flat) in the group. For the LH going up, it's 4th finger on the 4th note of the scale, and 3rd finger on the keynote. For the RH coming down, though, it's 4th finger over on to Bb, 3rd finger on to Eb. Now, how come one is about where you are in the scale, but the other is about the name of the note, regardless of its position in the scale? Again, I've never been asked, but the answer just kind of eludes me, I'd like to be able to say why, not just "it just does"

I'm sure the answer is actually something mathematica;l in at least one of these cases.

Next, I shall be wanting to be able to explain why there's only one Monopolies Commission

[owainsutton]

Okay. Number one. When you consider the circle of fifths, and you go round in the flatwards direction, for each step, you get a new flat in the key-signature. Next step - suddenly it's the tonic!

Keep going without switching enharmonics:

C major
Add a B flat = F major
Add an E flat = B flat major
Add an A flat = E flat major
Add a D flat = A flat major
Add a G flat = D flat major
Add a C flat = G flat major
Add an F flat = C flat major
Add a B double flat = F flat major
Add an E double flat = B double flat major
...

[linda.ff]

Okay. Number one. When you consider the circle of fifths, and you go round in the flatwards direction, for each step, you get a new flat in the key-signature. Next step - suddenly it's the tonic!

Keep going without switching enharmonics:

C major
Add a B flat = F major
Add an E flat = B flat major
Add an A flat = E flat major
Add a D flat = A flat major
Add a G flat = D flat major
Add a C flat = G flat major
Add an F flat = C flat major
Add a B double flat = F flat major
Add an E double flat = B double flat major
...

And my question was: ?

[owainsutton]

And my question was: ?

I thought you were asking about why we arrive on B major?

[agricola]

Going flatwards, you go down 5 notes for your next keynote eg C to F, then flatten the 4th note of the new scale (B flat), so when you go down another 5 notes from F you automatically land an octave below the last note you flattened. 4 + 5 = an octave because you're counting the F twice ! Going sharpwards you are always altering the 7th note of the new scale so the same rule doesn't apply.

When you turn under a black note you don't need to think about which finger is on the note because you always turn under with the thumb. Turning over, you have a choice of fingers, so you have to remember whether to turn 3 or 4.

[linda.ff]

Going flatwards, you go down 5 notes for your next keynote eg C to F, then flatten the 4th note of the new scale (B flat), so when you go down another 5 notes from F you automatically land an octave below the last note you flattened. 4 + 5 = an octave because you're counting the F twice ! Going sharpwards you are always altering the 7th note of the new scale so the same rule doesn't apply.

I think I'm still trying to work out why the "interval" (not quite the right word) of the new key is the same as the interval of the new flat, but not the other way in the sharp direction. I don't think I've phrased it well. No matter, I've used and understood the circle for many decades now, but I can't quite explain, if asked, why it's a one-way street where that immediate "follow-on" effect happens

When you turn under a black note you don't need to think about which finger is on the note because you always turn under with the thumb. Turning over, you have a choice of fingers, so you have to remember whether to turn 3 or 4.

That's not what I was asking, though. Why is it that, when going over, in the right hand, the choice (of 3 or 4) depends on the pitch of the note itself, regardless of its position in the scale, but in the left hand it depends on its position in the scle, regardless of its pitch? Bearing in mind I'm talking about keys with flat tonics (or possibly sharp tponics as well, since both of those are enharmonic with flat keys)

And my question was: ?

I thought you were asking about why we arrive on B major?

No, not exactly, it was why is the new "altered note" the next keynote if we're going anti-clockwise (I've never seen a circle of 5ths drawn the other way, though there's probably no logical reason) but not if we're going clockwise

[owainsutton]

No, not exactly, it was why is the new "altered note" the next keynote if we're going anti-clockwise (I've never seen a circle of 5ths drawn the other way, though there's probably no logical reason) but not if we're going clockwise

I suppose we're either pushing the leading note sharp towards the new tonic, or the new submediant down to resolve to the major third?

[Invidia]

I don't really understand what you are asking. But in regards to the cycle of fifths, you have to look beyond any harmony textbook and realise that our tuning is the way it is because that's how we in Europe made it. We invented keys and equal temperament so that we could use all of them on one instrument. The Bach 48 were written to demonstrate "look we have a keyboard instrument that can play in any key and the notes will be in tune with each other".

No non-Western educated musician/instrument has such thing as our keys. They have their own mountain of harmonic laws, don't get me wrong, but the Western way isn't "the way music is" at all.

So basically it is that way because we have made it that way to suit the development of our own rules. The rules aren't there because some genius someday discovered them, they are there because they were put in place at the very roots of our culture. The foundations of what we base our tuning (and much of our harmonic laws) on were laid down by Ancient Greek mathematicians/philosophers and countries that knew nothing of the Greeks didn't know a thing about our laws and traditions until the Christians shoved sacred music down their throats.

That is the "idiot-friendly" explanation. I can't give a more detailed one, not having much knowledge of the mathematics/physics of music.

[anacrusis]

If for a moment you use a string to demonstrate the wavelength, because it's the most easily visualised: the first harmonic of a note, its octave, is made by stopping the string from vibrating in its centre, thus making a node in the middle of the vibrating string: you have nodes at either end, and antinodes (points of maximum vibration) halfway between nodes. If you get a taut string to sound, and gently press it in its centre, you'll hear an octave: it's there, along with the sound of the fundamental, even if you don't stop it, but that's how you can bring it forward to dominate the sound of the fundamental.

The next harmonic occurs if you stop the string a third of the way along: that makes a fifth (the bit two thirds along) and its octave (the bit a third long). The one after that, dividing the string at a quarter, gives you two octaves up, and the next again, dividing the string into five, gives you two octaves plus a major third.

It's this subdividing which makes a dominant what it is - it's the loudest or easiest to pick out of the harmonics (apart from the octave, which in any case has a "sounding the same"-ness about it) , hence its name - and therefore that becomes the basis for the next key we go to in the cycle of fifths: that's why it's always a fifth we move to get to what feels logically like the next key. It's therefore not so much a matter of convention, as a matter of the physics (IMG:style_emoticons/default/smile.gif).

I've forgotten about piano fingerings, and scales are traumatic: I'll defer that one to others to solve (IMG:style_emoticons/default/wink.gif).

[fatar760]

is this the most complicated thread ever? Circle of 5ths and 4th is pretty straight forward really as is the fingering in flat scales...

[owainsutton]

No, not exactly, it was why is the new "altered note" the next keynote if we're going anti-clockwise (I've never seen a circle of 5ths drawn the other way, though there's probably no logical reason) but not if we're going clockwise

Thinking about this further, does it answer your question if you think about the clockwise movement altering the keynote you just departed from to get you to the next step?

[linda.ff]

No, not exactly, it was why is the new "altered note" the next keynote if we're going anti-clockwise (I've never seen a circle of 5ths drawn the other way, though there's probably no logical reason) but not if we're going clockwise

Thinking about this further, does it answer your question if you think about the clockwise movement altering the keynote you just departed from to get you to the next step?

Well, yes, but I'm still trying to work out the answer to why they aren't symmetrical, not how you work out one thing from another.

I'm not losing sleep over it, Owain, don't worry; but I have a couple of young clever pupils who do tend to ask that kind of question (IMG:style_emoticons/default/happy.gif)

[Susie]

Number two. Fingering in scales with flat keynotes (until you reach Gb anyway). The rule is in the RH going up and the LH coming down, that you go under when you've played the last flat (or the only flat) in the group. For the LH going up, it's 4th finger on the 4th note of the scale, and 3rd finger on the keynote. For the RH coming down, though, it's 4th finger over on to Bb, 3rd finger on to Eb. Now, how come one is about where you are in the scale, but the other is about the name of the note, regardless of its position in the scale? Again, I've never been asked, but the answer just kind of eludes me, I'd like to be able to say why, not just "it just does"

I think the short answer to this is because it's comfortable. You don't have to follow the rule. In fact when I was learning scales, I realised that I played one of them (Eb major I think) with different fingering when I played hands together (IMG:style_emoticons/default/wacko.gif) but it was still driven by having the thumb on a white note.

When I was taught double thirds, my teacher had his own invention for fingering - different to the "text book" method, but it was completely logical and quite comfortable.

The main thing with fingering is that it isn't awkward and doesn't involve unnecessarily twisting the thumb under on to a black note - so I think I might challenge a bright pupil to go and find something equally as comfortable and logical and memorable if too many questions were asked! (IMG:style_emoticons/default/wink.gif)

[linda.ff]

is this the most complicated thread ever? Circle of 5ths and 4th is pretty straight forward really as is the fingering in flat scales...

Yes, they are. Until someone asks "why?" to the very specific questions I mentioned - "why is it different, why is it a different rule the other way?" (IMG:style_emoticons/default/biggrin.gif) I've never beieved in "it just is"

[fatar760]

is this the most complicated thread ever? Circle of 5ths and 4th is pretty straight forward really as is the fingering in flat scales...

Yes, they are. Until someone asks "why?" to the very specific questions I mentioned - "why is it different, why is it a different rule the other way?" (IMG:style_emoticons/default/biggrin.gif) I've never beieved in "it just is"

ha why is a horse called a horse? why is a tree called a tree? IT JUST IS (IMG:style_emoticons/default/smile.gif)