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Exactly. And I think this is an important enough point that I felt it was worthwhile (and still do, for that matter) to stress that octaves aren't defined by the number of white and black keys on a piano keyboard.

In fairness, the piano keyboard IS probably the best visual representation available for pitches though. It illustrates why some notes have unique sharps and flats- whereas raising others results in notes that are effectively the same. I'm aware that string players will tend to play an f sharp slightly differently to a g flat say, but we're not talking almighty differences.

There's nothing absolute about the idea that sharps or flats relate to black notes on a piano, but it certainly is a convenient way of 'seeing' pitches in a way that illustrates intervals. The 12 pitches don't have to laid out that way, but when I think about the logic of sharps and flats (which are used for all standard instruments), I can see how it does illustrate something rather important about the nature of those.

I seem to recall that my teacher communicated sharps and flats to me by just saying something like sharping a note pushes it up a half-step, and flatting it pushes it down a half-step. It was all just relative to the note you were talking about. It seemed to make things easier.

That, plus playing scales, seemed to set things in my head so that I never struggled to remember what notes were sharp or flat in a key signature. When I had to play something in C#, I just knew the notes of which that scale was composed, so I never had to look back at the clef and find out whether a certain printed note was sharp or flat. When you play something in C#, for instance, you know that when one of the notes is parked on the G line, it's a sharped G because that's the one that's in the scale for that key. I can't imagine having a hard time keeping track of sharps and flats once you know scales.

But sharps and flats weren't told to me in any sort of a concrete way, I don't think. It was just pushing a note up or down by a half-step, and a certain number of pushes one way or another starting from C moved you up a fifth each time.

I'm actually having a tough time thinking about how I learned all this now that I'm approaching it again. It's like asking which way is up. This stuff REALLY sank in deep.

Monica says: ".....this is an important enough point that I felt it was worthwhile (and still do, for that matter) to stress that....octaves aren't defined by the number of white and black keys on a piano keyboard."

The "Essential Dictionary of Music - Alfred Publishing Company" defines octave:

The interval of eight diatonic steps or from one note to it's nearest note of the same name.

Common usage in piano teaching also includes the understanding that there are 7 white key letter names within an octave and 5 black notes along with the duplicated octave note.

There is also an "octave hand span" - the distance that most teen and adult hands can easily span.

Within the two matching notes of an octave it is understood there are 12 half step; From these 12 half steps, the tetrachord formula determines the major scale.

So, how ever many times Monica says this, and no matter what inflection given to the word, I cannot agree with Monica. Nor do I understand what she is trying to say.

"...OCTAVES aren't defined by the number of white and black keys on a piano keyboard."
"...octaves AREN'T defined by the number of white and black keys on a piano keyboard."
"...octaves aren't DEFINED by the number of white and black keys on a piano keyboard."
"...octaves aren't defined BY the number of white and black keys on a piano keyboard." etc., ad naseum.

Furthermore on an acoustic piano:
There are 8 octaves of A
There are 8 octaves of B
There are 8 octaves of C
There are 7 octaves of D
There are 7 octaves of E
There are 7 octaves of F
There are 7 octaves of G

Can this be agreed upon?

Yes it does. But that is a PIANO teaching book. I think what some of these folks are saying (not just Monica) is that octaves are not solely defined by a piano keyboard. Of course they are if you are teaching piano.

Octaves are not white and black keys on instruments.
Nor are there as many octaves on instruments.

Sorry. I feel like I shot the horse myself. :-) It went off while I was cleaning it, honest ...

I think this is a (not the whole truth) true statement:

The piano has 8 white keys that, in the key of C major, represent a diatonic scale from one C to the next, called an octave because of the definition of a diatonic scale. (I don't think a piano has to have its keys colored black and white in the scheme we are used to - even tho most of them these days do.) (The Alfred's definition does take in to account that one can play only 2 pitches and be playing an octave, leaving out the steps in between.)

I think this is a false statement:

An octave has 8 diatonic steps because a piano has 7 white notes, represented by letter names, that span an octave.

It's the use of the word because that makes the difference.

So I agree with Monica.

Cathy

J. Cortese -

I believe you, ma'am. We all just do the best we can.



Cathy

My two Eurocents:

An octave is indeed named because it contains 8 steps. Octa = 8 in several languages.

But an octave is defined as a 2:1 ratio of frequencies. This predates the piano by several thousand years. The octave was known to the ancient Greeks, who determined frequency ratios with monochords. They also defined other simple integral ratio intervals like the third, fourth, fifth, etc. And they knew in Pythagoreus's day that a circle of fifths would not close, missing by a comma.

I have never seen a convincing explanation for why an octave sounds like a repetition of the same note. It's a neurological mystery, or at least was the last time I researched it.

Thank you Tim

Yea, Tim.

Cathy

There are not 8 steps in an octave. There are 8 (diatonic) notes, with 7 steps between them. I feel so strongly about this that I made a new topic.

For me fingering is always going to be determined, in the end, by what works best. When scales are taught and practiced, hands together, up and down four octaves, this may or may not have much to do with what we need to to when actually playing music.

If I'm playing a one or two octave A scale, LH, starting and ending on A, of course I will start with the 5th finger and use the default fingering. On the other hand, if a run starts on F#, LH only, and ascends to C#, an octave and a 5th, the fingering I choose will be totally according to which makes my LH feel most comfortable. This is a simplistic example. I can't give you a better one taken from a famous passage by composer A or B, though I'm sure they exist. Regardless of the chord structure, this would feel like a modal movement using the notes of the A scale and so could be thought of either that way or as an ascending natural minor scale, F#. I could honestly flip a coin, I think, between one fingering and the other, and I have to admit that I don't have a clear preference just for ripping up and down the natrual minor scale. So I'll give that point to you. Fair?

Introducing an E# into the scale still does not give me a really solid preference. But when the D# is added, so that now there is a melodic minor, I want 4 on F#, because the feel is more like that an F# major scale, with a lowered 3rd.

But this gets away from some solid principles for scale AND passage playing that I think are rather solid.

The number of thumb turns needed in a run are weighed against the ease of the thumb turns. In the keys of C, D, E, and G the RH fingering is set up so that both are true. You start on thumb, end on 5, and there is no better way to do it, assuming you are starting on the tonic.

The left hand, in contrast, is set up for least number of thumb turns, but G, D and A do not utilize optimum black to white thumb turns. This does make these scales marginally more "bumpy" for the LH than the RH, although the difference is very small. For intance, starting on F#, but thinking modally for a moment:

F# G A B C# D E F# G A B, ascending in the LH, only LH, in a passage, would surely put 4 on F# and 3 on C#. To you this is so obvious that you would not even think about it. For a very good student, the same would be true. A less advanced student might not immediately think it through. This is where the theory behind how scaled fingerings are chosen should become interesting to people who are learning.

I doubt it. I slipped into a bit of rhetorical posturing for a moment.

I utterly dispute your utter dispute, or something. My father can beat up your father. This is going to get REALLY stupid fast.

I was saying that there is good reason to study the reasons why the conventional fingerings were chosen. To mindlessly follow ANY fingering system without adjusting for any number of reasons would be so rigid that some music would never be played will. Fingering is not a science. It's an art.

No more than it is "uncomfortable" to play a C scale. But most people acknowledge immediately that a scale like B major is much faster and smoother for the LH than C. Do you disagree with that? Db should theoretically be easiest for the LH because of the half step thumb turns from white to black.

On the other hand, the kind of patterns used often by people such as Mozart are easier in C because we can set up a pattern. It's not a clear matter of what is easiest or hardest, in all cases. The first scale patterns in the RH in K545, first movement, is a perfect example. There you go up 34, using your abbreviation, but come down 44 because the downward pattern is 9 notes, not 8. This is effortless to do in C, much harder in Gb. There are always tradeoffs.

But that happens in F# melodic minor, ascending. There too you want to turn to B with your 4th finger?

True for natural and harmonic, not for melodic. And that means potentially changing the fingering descending in both hands as they return with 6 and 7 lowered.

For the others, natural and harmonic, frankly, I would most likely present both fingerings, yours and the conventional one. But I would explain why.

Which MAY mean we actually agree. Because for me, as a teacher, the WHY is the important part. This gives a student the opportunity to think flexibly and does not leave him/her boxed in by limited thinking.

"F# G A B C# D E F# G A B, ascending in the LH, only LH, in a passage, would surely put 4 on F# and 3 on C#. To you this is so obvious that you would not even think about it. For a very good student, the same would be true. A less advanced student might not immediately think it through. This is where the theory behind how scaled fingerings are chosen should become interesting to people who are learning."

Quite honestly, I would take three on the F sharp without a shade of doubt. As I said earlier, I find 4 on the B to be an excellent means of preparing for 2 and 3 on C sharp and D. I find it slightly more uncomfortable to lead straight into this position direct from the thumb. There's very little in it, but I would certainly be more inclined to start on 3. I would likely then take 4 on the second F sharp, to finish on the thumb,

"I doubt it. I slipped into a bit of rhetorical posturing for a moment. :)"

Well, with respect, the entirety of your previous post seemed quite unequivocally damning of the notion that my alternative fingering might possibly be considered valid. The explicit statement you made about picking fingerings for convenience of coordination implying sloppy teaching did not come across as to me being a slip.

"I was saying that there is good reason to study the reasons why the conventional fingerings were chosen. To mindlessly follow ANY fingering system without adjusting for any number of reasons would be so rigid that some music would never be played will. Fingering is not a science. It's an art."

Well, having played it myself conventionally for years (before I decided that the conventional pattern was not optimal) I can safely say that my hand is marginally more comfortable with the A major- despite the years I had spent playing it with a normal fingering. The difference is certainly slight. However, that's precisely why I see no reason to divert from the A major fingering to a unique coordination that is found in no other scale. This is the single case where I believe the logic of the standard fingering is flawed. Even for those who might find 4 more comfortable, I believe that any benefits are unlikely to be sufficient for it to be worth teaching such an awkward coordination as the norm. I think that should be the variant for those who wish to use it, not the standard.


"No more than it is "uncomfortable" to play a C scale. But most people acknowledge immediately that a scale like B major is much faster and smoother for the LH than C. Do you disagree with that? Db should theoretically be easiest for the LH because of the half step thumb turns from white to black."

Not at all. These do lie very nicely. However, standard F sharp minor fingering is nowhere near that level of comfort. It doesn't offer much difference to my hand. I have never felt an inherent problem with going to a white note on my fourth finger. It's no D flat major in terms of comfort, but neither is F sharp minor- however you finger it. If this ought to be considered a problem, the conventional F sharp minor ought to be regarded as 'easier' than A major- as, on your principle, every left hand finger turns to land on a black note. Do you think this is this the case? Perhaps it's just me, but it's not of the most natural fits imaginable. I honestly find the A major lies better under my hand. Have you tried practising it that way? So, why do we usually teach kids something so complex- merely in order to solve a 'problem' that they will inevitably encounter and have to master in A major scales?


"But that happens in F# melodic minor, ascending. There too you want to turn to B with your 4th finger?"

Especially there. It involves a simple thumbs always together going up and 343 back down. Physically I encounter no problems whatsoever. A regular 343 turns the single most accident-prone scale into a fairly straightforward one.

"True for natural and harmonic, not for melodic. And that means potentially changing the fingering descending in both hands as they return with 6 and 7 lowered."

Just an in C sharp minor/E major yes. The principle is identical. It's actually quite easy, when you do the same in both.

"Which MAY mean we actually agree. Because for me, as a teacher, the WHY is the important part. This gives a student the opportunity to think flexibly and does not leave him/her boxed in by limited thinking."

Indeed. I always explain both pairs of scales together- showing how simple the principle is. They can use four if they wish, but nobody has ever complained that my simpler alternative is uncomfortable in any sense. Even if it were less optimal- where do you draw the line? After all, we don't tell beginners to use 4 on B flats in chromatic scales. It's too complex when the hands come together. So why not start simple for F sharp minor- and let them try more complex coordinations later, if they feel it fits their hand more? To my mind, it seems clear that what is standard ought to be the variant, not the rule.