Knowing that the interval between A and B (within one octave) is a whole step and that the interval between B and C-sharp is also a whole step, is the interval between B and C-natural also considered a whole step ?

Doesn't seem to be, considering a half-step back from a C-natural is a C-flat, which also happens to be a B-natural.

But, staying within the ABCDEFG octave progression, how could the interval between B-natural and C-natural not also be considered a whole step...?

Confused...

Thanks,
AC

On a piano, the distance between two adjacent keys is a half step.

The diatonic scale, which you're thinking of, is a pattern of whole and half steps, totaling 7 tones, before repeating the sequence. For major tonalities, the intervals are whole steps except for two half step intervals, between the 3rd and 4th tone, and between the 7th and 8th (or 1st) tone. The pattern differs for other modes.

Have your teacher go through this with you in more detail.

Definition – Whole Step – is an interval comprised of 2 half steps. A half step is the distance between 1 pitch and the very next pitch either up or down. On the piano it can be a white key to a black key if they are next to each other or 2 white keys if there is no black key between them. There are only 2 places that 2 white keys are next to each other with no black key between. “C & B” and “E & F”.

It makes no difference what you call them. Example – C or B# is the same pitch. That is called the enharmonic spelling of the same pitch. Don’t get bogged down with the diatonic scale (ABCDEFG). It has nothing to do with whole and half steps.

The formula for a Major scale is whole, whole, half, whole, whole, whole, half. The only time you need to worry about the diatonic order of the scale is in this formula (or minor and modal scales) Example – you cannot have 2 steps of a scale with the same letter name in a row. (Cb and C in the same scale. It would have to be B and C)

I hope this helps.

You're actually talking about different things: steps
and intervals. A step, in the context, of piano (and
there are only two types, whole and half steps) is
simply a way of talking about moving up or down the
keyboard in a very small way: either from one
key to the adjacent black or white key
(a half step), or from one key to the next one
by hopping over the adjacent one (a whole step).
For example, the following are half steps: A to A#,
A to Ab, A# to A, Ab to A, A# to B, B to C, C
to C#, Cb to C, C# to C, C to Cb, etc.--in all
of these you're just going from one key to
the adjacent one.

The following are whole steps: A to B, B to A, A to
G, G to A, G# to A#, Bb to Ab, A# to C, B to C#,
etc.--in all of these you've hopped over the
adjacent key to the next one up or down the keyboard.
Another way of saying it is that you've gone up
or down two half steps (2 half steps equals a whole
step).

That's all there is to steps, and the application
of the term is very limited. And this is where
intervals come in. An interval is a way of measuring
distance on the keyboard or between notes on a score.
For example, you could say that the distance between
A and D is 5 half steps, or 2 whole steps plus
a half step, but that quickly becomes awkward.
There's a better way of doing it, which is by intervals.

Hundreds of years ago, musicians faced this very problem:
how to measure distances on a keyboard or between notes
on a score in a convenient and uniform way. The system
of measurement they came up with was intervals. Note
that all systems of measurement are arbitrary. For
example, the unit of length, the foot, could have just
as easily been longer or shorter than it is, but hundreds
of yrs. ago people saw that they needed a way to specify lengths
uniformly, and so they settled on what we now know
as the standard ft. Similary, the system of measuring
distances between notes in music is entirely arbitrary.
The system that musicians devised hundreds of years ago
was that the measurement of distance between notes would
be based on the major scale only.

The standard that was set up was that the distance between
the first and second notes of a major scale would be
called a maj. second (C to D in C maj., A to B in
A maj., etc.). The distance between the first and third
notes of a maj. scale would be called a maj. third
(C to E in C maj., A to C# in A maj., etc.). The
distance between the first and fourth notes of a maj.
scale would be called a perfect fourth (C to F, A to D,
etc.). From the first to the fifth, a perf. fifth
(C to G, A to E, etc.). From the first to the sixth,
a maj. sixth (C to A, A to F#, etc.). From the first to
the seventh, a maj. seventh (C to B, A to G#, etc.).

The other intervals are based on these: any maj.
interval decreased by a half step is called a min.
interval (C to D is a maj. second, C to Db a min.
second, C to E is a maj. third, C to Eb a min.
third, etc.), and so forth.

Note that intervals are only defined in terms of a maj.
scale, no matter if we are talking about a min. scale,
or a blues scale, or a min. triad, etc. There is no
such thing, for example, as an interval defined in
terms of a min. scale.

For example, what is the interval between Bb and
G? To answer this we refer to the Eb maj. scale. By
definition, the distance between the first and sixth
notes of a maj. scale (Eb to G in Eb maj.) is a maj.
sixth. So Eb to G is a maj. 6th.

What is the interval between C# and B? We refer to
the C# maj. scale. The distance between the first
and 7th notes of a maj. scale (C# to B# in C# maj.)
is by definition a maj. seventh. A maj. interval
decreased by a half step is by definition a min.
interval. And so C# to B is a min. 7th.

And so forth.

That doesn't seem strictly accurate; it sounds as if they all got together, held a convention and voted on the matter. I suspect this account is as fanciful as last year's fractured history lesson about how the piano originated.

Steven

??????
Typo Gyro?

Maybe he's counting backwards. If you play a descending Eb scale, G will be the 6th note

It's just a typo. Eb up to G is a Major 3rd. Eb down to G is a minor 6th.

So a whole tone = a whole step and semitone = a half step? I'm working in a theory workbook that explained that a major scale was made up of two tetrachords (tetrachords = whole tone, whole tone, semitone) joined by a whole tone. That's the same as whole step, whole step, half step, whole step, whole step, whole step, half step, right?

The steps make more sense to me because in C major, they match the black keys. But then when I try to visualize it in another scale, it confuses me.

Susan, major scales are: W W H W W W H. I think that's what you're asking. Minor scales on the other hand, have a different pattern.

You can start on any key, white or black, and find the major scale by using that pattern.



I'm not sure what you mean by "matching the black keys".
No matter where you start on the keyboard, the black keys fit into the pattern.

What I meant by "matching the black keys" is that on the piano, there's a set of two black keys and a set of three black keys. So in C Major, the first half step between E and F follows the first set of two black keys, then there's a set of three black keys (the three Ws) and then another half step between B and C.

I think that's what's been messing me up. For EVERYTHING scale and chord related, I used C major as the anchor and just now from reading your post, I'm realizing that I need to "unlearn" all the inside out and upside down mechanations I made up to cope with the stress of piano lessons as a child. For example, I can't figure out key signatures unless I know where they are related to C major. I can see now that just knowing W W H W W W H makes it significantly easier, no matter what key I start on.

Little by little, the theory is making sense. On a side note, I also want to thank you for your little tag line "It is better to be kind than to be right." It is such a good reminder and it put me in my place two weeks ago, when I had made an appointment at the doctor's office but the clerks didn't honor the appointment. I was so upset, and they knew that they'd messed up but I just wouldn't let it go. Unfortunately, I was unkind, because being "right" meant more to me at the time than being kind.

So thank you, twice!

You're welcome twice
Thanks for the thanks!

In general (to all):

Half step means go to the right or left, one key, no matter the color of the key.

Whole step means go to the right or left, two keys, no matter the color of the keys.

A whole tone=a whole step.

For those who want to know more about tetrchords, there have been long discussions of this subject.

Notating intervals is a lot more tricky. There have been many threads about that.

For my students this little formula for "constructing a major scales" seems to work best AFTER we have explored two or three scales simply by sound.

In other words, C is a gimme. All white. Key of G sharps the F, and you can explore how the scale sounds without that sharp. Key of F flats the B, and again listening is important.

People who think mathematically will grab onto the ideas of tetrachords immediately, but others will link to how the scales are formed in other ways. Leaning style plays a huge role.

I stopped teaching tetrachords a long time ago. I prefer the WWHWWWH method for major scales and WHWWHWW method for natural minor scales. That, and memorizing the key signatures of all major and minor scales. Makes theory a lot easier.

I don't have a preference for teaching scales or theory except what works at the moment.

But a lot of people don't relate well to tetrachords.

Some people work best with the idea of just flipping. For instance, F major is Bb. F# major is B natural. The flat turns to natural, all the naturals turn to sharps.

Different strokes for different folks.

Can you explain this a bit more? I don't quite follow.

Like Eb has 3 flats, E has four naturals.

Eb = Bb, Eb and Ab

E = B, E, A, the others are sharped.

Also, "companion keys" always add up to 7.

E=4#, Eb=3b

Useful for the keys with lots of flats and sharps.

D=2#, Db=5b.

D has F# and C#. Db has ONLY F and C natural, all others flat.

I know you know this. I must be communicating badly.

Gary:

One of my student's mother learned it this way when she took lessons EONS ago. She tried explaining the same thing to me. I told her there's a much easier way.

I prefer memorizing the order of sharps and order of flats and go from there. Everything else can be figured out from the order of sharps and flats.

Careful. The "easier" way is easier for you, and it may be easier for many of your students, even the majority.

I have many ways of explaining things like this to different people, depending on their age and learning styles. The moment you think you have found the best way to teach anything, someone will come into your life who will pick up the same info using an alternate method.

By the way, I have NO idea how I remember key signatures. I could tell you how I was taught, but somehow I jumped and internalized them in a very different way. I see complete scales as "key sets". For instance, if someone mentions E, I see F, G, C, D, all sharped. I don't ever think about those sharps being in the order in which they appear in the key signature. However, when WRITING the signature, I do. Then I see a zig-zag.

Ha! This is a part I've never seen mentioned - the shape that the sharps and flats take on. As part of recognizing key signatures, isn't this part of what we do? It's like a roll of dice - here you instantly see "5" and "6". In fact, couldn't you buy a set of blank dice and draw key signatures on them for a "signature recognition" game?:

(Addendum: Every time I wanted to look at the Invention in E major, I was flipping to no. 4 instead of no. 6. I finally realized the E strongly associates with "4" in my mind, i.e. 4 #'s)

I taught this only once, and only to one person, with the purpose of theory only, but because my own learning was only a few years ago, I can say the how and why of it. To set it up: my student had played piano self-taught for 10 years but wanted to know the rudiments of how music worked. We began with note names and values, right at the beginning.

The first thing we did was understand what an interval was, and combine senses and impressions. So: press adjacent keys for half step (we used "semitone") and observe this, and also hear it, and also hear the discord of both played at once. Ditto for whole step. Understanding that 2 semitones = 1 (whole) tone. The mistake I'd made the first time around was to learn it all intellectually and not connect the theory to real experiences.

The same was with WWHWWWH. Because of what she could already do, I had her slowly play every scale in the order of the circle of fifths. Do so while observing the half steps and whole steps and listening for them so it becomes real. Write down what you did and write the intervals in between. It looks like:
C w D w E h F w G wA w B h C
G w A w B h C wD w E w F# h G
D w E w F# h Gw A w B w C# h D

If you have a page of this, then WWHWWWH jumps out at you. It becomes real.

The next thing was to focus on the idea of "leading note". If you stop at B in C major, you are itching to play the C, and the fact that it's a semitone makes it want to tip over to C. For me, when I was learning, that "pull" helped me remember the new sharp for the new key signature, like a feeling that I didn't think about.

After that it was a matter of learning the signatures. I'm only teaching theory and am definitely not qualified to teach piano playing so this part isn't the same. It has to be better when people learn to play, and get the theory as they go along. However, for a fellow adult student, when we tend to want to understand things, this seemed to work well. We also tend to intellectualize and I thought actually experiencing it to understand would be good.

The "leading note" idea was also to set up minor keys later, because we began with the natural (relative) minor, and you can notice that the "pull" of a leading note is missing. We sharp the note, presto the "pull" is there, and that seemed a good way of making sense out of harmonic minor.

For myself as an adult student, the more meaningful it is, the easier it is to remember. When I was a self-learning child I just explored. I fell in love with major 6ths and played tons of them just to hear that vibration, but I never knew there was such a thing as "minor 6th" or "interval". But as an adult, that experience helped me understand the idea of intervals.

This does not connect with my mind at all.

The problem is seeing Ws and Hs. They actually interfere with what I see in mind.

I need this:

CxDxE FxGxAxB C

I need the concept that the letters go to keys and that all the white keys are the same distance apart (approximately) but there are "things" inside some of them, the black keys. I don't have the patience to color the letters (say in red), and even so it is a poor replacement, in my mind, for an actual keyboard.

Obviously the keyboard itself is my link. If you are teaching another instrument, maybe your way would make more sense to me. And since your way connected with your student, it is obviously useful for that person.

Which emphasizes, again, that no way of getting anything across is enough for all people. What works is as many strategies as possible, then you pick the one the connects best with the student you are teaching.

I probably do something similar, but in reverse. I play a scale, descending, both with and without black keys. I start with G.

Then I ask students which one sounds right when they think of "Joy to the World". Most students will say, "That one," when I get to F, in the G scale, or to B, in the F scale.

But everything reinforces everything else. If you have to learn to play a scale, then write the scale, then read the scale, then play with the scale notes in pieces using that scale, each step adds another level of solidarity to the concept or skill.

I once heard a memory expert say this, although it sounds a bit disgusting:

If you harpoon a whale, no matter how good the harpoon and the rope (and so on), you don't have the whale. If you hit it with 100 harpoons, you have the whale. Learning is all about connections. The more you have, the more solidly you have things in your mind/body. No offence meant to whales.

I would hope that anyone who CAN learn to play and do it with a good teacher would learn the theory as part of playing, not as something separate.

In some ways I'm teaching under ideal circumstances since it's volunteer. My student is working with me because her purpose is to understand what lies beneath music at a rudimentary level and she does everything I suggest and more to make it happen - How many times do teachers get that? You guys get students who don't want to be there, don't want to be learning to play the instrument, couldn't care less about theory, and since it's how you make a living you have little choice.

I think you've pointed out something important: our physical learning style. Although I'm primarily a student, I am also a trained (academic) teacher so I naturally use what I learned. The person I teach paints and is visual so it's natural to use vision. Since this is distance learning we are limited to visuals and some audio files and also audial assignments.

But Gary, something intrigues me about what you wrote. I know that you play a brass instrument too. Now supposing that you play a melody that starts G Bb which is a minor 3rd. Do you hear these as separate pitches since you have perfect pitch, or do you also hear them as a "minor 3rd sound"? Supposing that you play with others where you improvise, which I think you've done (?), consciously or subconsciously are you not aware of intervals on some level? Or are you sitting inside a chord? I hope my question makes sense to you.

I suppose that we have something similar here.

Yes, but what is the reality? Do we get the concept deeply enough, or is it utilitarian just to get by with the playing? When people start doing formal theory, can they connect it, or do they end up with two separate bodies of knowledge?

Actually on the last point, I have been connecting this to something I learned from a master teacher in second language learning. Grammar and vocabulary is like music theory. She told us that if a student learns these separately, but cannot then apply them fluidly in actually writing and speaking, then it is useless academic knowledge. She called this "integrating". In the same way our music theory has to be "integrated" into our music. When it comes to spoken language then there is some similarity to music. We are in real time, improvising, and using our physical apparatus to produce sounds. Even pitch, pauses, and phrasing cross over.