Hi guys. I've started this book over quite a few times now, cause I usually skip the parts I don't understand, but I always get to a point where I don't feel content having not understood everything I've read.

So, here I am on my 5th start over, and I'm at a point labled Exercise 2.5, and in this exercise I'm to work out all the notes of the major and minor scales of G, D and F. That's easy enough. But then it says 'can you find all the diatonic and chromatic intervals mentioned so far, on each of these notes?'

This is where I'm confused. From what I understand, diatonic intervals are simply the notes within the key signature for any given note, right? So for F major for example, F,G,A,Bb,C,D,E. And for F minor, F,G,Ab,Bb,C,Db,E (natural, as you sharpen then 7th, right?), then back to F. Now in each major or minor scale for each note, arn't all the notes just diatonic anyway? If so, how am I to find chronmatic intervals within G/D/F major and minor?

Any help much appreciated!

A scale is made up of intervals or steps, the inverval between notes, C to C#, is a half step, C to D is a whole step. The chromatic scale is entirely half steps. A chromatic interval would be a interval that is only a half step apart. In the F Major scale the Bb to C would be a chromatic interval, in the F minor the C to Db would be chromatic. The C Major scale the chromatic interval would be between the E and F (a half step). Does this Help?

I guess half steps in the UK are called semitones, and steps are called tones. Is that right?

Walt

I would answer the question differently from wj3. I would say that, given a scale, the diatonic intervals are all the intervals between two notes of the scale. For example, in the key of G, the following are all diatonic intervals:

G to A (major second)
B to C (minor second)
G to F# (major seventh)
C to F# (augmented fourth)
and so on.

The chromatic intervals built on the notes of the scale are all the intervals that start from a note of the scale and go to a note not in the scale. For example, in the key of G, the intervals built on E are

diatonic:
E to E, perfect unison
E to F#, major second
E to G, minor third
E to A, perfect fourth
E to B, perfect fifth
E to C, minor sixth
E to D, minor seventh
E to E, perfect octave

chromatic:
E to F, minor second
E to G#, major third (or E to Ab, diminished fourth)
E to A#, augmented fourth (or E to Bb, diminished fifth)
E to C#, major sixth (or E to Db, diminished seventh)
E to D#, major seventh

You can do this starting from any note of the given scale. There will always be five chromatic intervals built on any note of a diatonic scale. Note that the interval is not just the size of the interval (e.g. minor second) but also the names of the two notes it's between.

Oh, yeah I'm aware of whole notes/half notes etc. The impression I got was that the step from B to C within the scale of G major, for example, was still diatonic because despite the interval, it's still within the key of G Major. Know what I mean?

Here, the book says 'Intervals that fit the intervals in major or minor scales are called diatonic intervals. But sometimes that doesn't work. In these cases we treat the interval as an alteration of one of the normal intervals: as a chromatic interval.'

Having read your reply, and read that section again, is the book simply saying that any half step within a major or minor scale is not diatonic, but instead considered an alteration to keep up with the ratio of whole notes to half notes needed for the given scale, and is then a chromatic interval?

I'm probably over-complicating something very simple here, bare with me! And thanks for the reply

Here are two links:
Diatonic and Chromatic
Intervals

Taking "C" as the example:

Major Scale: C,D,E,F,G,A,B,C.

Minor (natural, relative major is Eb): C,D,Eb,F,G,Ab,Bb,C.
Minor (harmonic): C,D,Eb,F,G,Ab,B,C.
Minor (melodic): C,D,Eb,F,G,A,B,C,Bb,Ab,etc.)

As for the intervals,

C,C: unison
C,C#/Db: augmented unison/diminished second
C,D: major second
C,D#/Eb: augmented second/minor third
C,E: major third
C,F: perfect fourth
C,F#/Gb: augmented fourth/diminished fifth (tritone)
C,G: perfect fifth
C,G#/Ab: augmented fifth/diminished sixth
C,A: major sixth
C,A#/Bb: augmented sixth/minor seventh
C,B: major seventh
C,C: (perfect) octave.

As wj3 said, the intervals contained in the scale are diatonic, all others are chromatic.

Half-steps/semitones contained in the scale, i.e. between 3 and 4 in major, and 2 and 3 in minor ARE diatonic.

I think wj3's answer is wrong in focusing on half-steps for chromatic interval. Any given interval name (like minor second, major third, etc.) can be diatonic or chromatic based on which scale you're in and which two notes the interval is between. For example, in the key of C:

The interval from E to F is a minor second and is diatonic.
The interval from G to Ab is a minor second and is chromatic.
The interval from C to E is a major third and is diatonic.
The interval from D to F# is a major third and is chromatic.

The diatonic intervals have both notes within the scale. The chromatic intervals have at least one note not in the scale. For example, in the key of C the interval from Gb to Bb is a major third and is chromatic.

PianoStudent88, you've seriously confused me.



So, for this first part. G to A being a major second, easy to understand. B or C being a minor second? not so much. For starters, B is the third in G major, so how does B to C = a second? Also this book mentions minor seconds, but it says 'Note that the intervals of a minor 2nd and minor 7th from the keynote do not appear in the minor scale,' later saying 'The minor 2nd funtions more like a chromatic interval: that's why it's more common to refere to it as a semitone.' And I just find the whole minor second thing a bit confusing. G to F# = major 7th, I get it. C to F# = augmented 4th though? within C major, I just about understand, but you're talking about G major here arn't you?



So you mean, a chromatic interval would only be the interval between the first note and second note of any given scale, as long as the second note is a note not belonging to the scale?



And here, do you mean the scale of G, but starting on E withing G major? (E,F#,G,A,B,C,D?) Wouldn't that be E minor? (E minor being the relative minor to G major?)

Otherwise:

E to E, it is as it is, understandable.
E to F#, so one whole note = major second, understandable.
E to G, 3 semitones from E = minor 3rd, understandable.
E to A and E to B = perfect fourth and fifth, understandable.
E to C, 8 semitones = minor 6th, understandable.
E to D, 10 semitones = minor 7th, understandable.
E to E, octave, understandable.



E to F being a minor second, again, bit confused about minor 2nds, this book doesn't explain this in a way I can really understand.
E to G#, two whole notes, understandable. Or from E to Ab within E minor, I just about understand that.
E to A#, augmented 4th, I get that if we're looking at the notes from E to it's octave E as notes from within G major (even though they are the same as E minor). And I understand from E to Bb as a diminished 5th if looking at the notes as note from E minor.
E to C# as a major 6th I understand if going from E as it's own E major scale. And I understand from E to Bb if going from as as it's own E minor scale.
And E to D# as a major 7th if going from E as it's own E major scale.

And having picked your post apart, I think I've wracked my brain cause I still can't really tell what is and isn't diatonic or chromatic. I just understand why the intervals are major, minor, diminished or augmented.

[Musique, I cross-posted with you. I'll answer your questions in your post immediately preceding mine, but it may not be till this evening since I'm in training today. I'm sorry to confuse you! I was trying to be a model of clarity, but clearly failed!]

Some definitions of diatonic include all the notes in both the major and minor versions of a scale. JPDelmore hints at this by listing the three C minor scales as well as C major.

By this definition, in the key of C (major or minor) all intervals between any two of the notes C, D, Eb, E, F, G, Ab, Bb, B are diatonic. So for the intervals built on C:

C to C, perfect unison, diatonic
C to Db, minor second, chromatic
C to D, major second, diatonic
C to Eb, minor third, diatonic
C to E, major third, diatonic
C to F, perfect fourth, diatonic
C to Gb, diminished fifth, chromatic
C to G, perfect fifth, diatonic
C to Ab, minor sixth, diatonic
C to A, major sixth, diatonic
C to Bb, minor seventh, diatonic
C to B, major seventh, diatonic
C to C, perfect octave, diatonic

If the more restrictive definition of diatonic is used, where only the notes of the scale are used, and not its major/minor versions, then the following would be chromatic in the key of C major: C to Eb, C to Ab, C to Bb.

I can't remember which definition the Piano Handbook uses.

At any rate, it seems the point of the exercise is:
1. knowing the notes of the scale
2. being able to name intervals
3. being able to tell when the two notes of an interval are both in a given scale, or not.

Okay, so natural minor, basically it contains all the notes of Eb major. The harmonic is the one where you sharpen the 7th by a semitone, and melodic minors I've seen a bit about. So far, so good.



C to C, unison (unison being a word for the same note? as in C1 to C1?)
C,C#, same deal except you sharpen the C augmenting it, or you diminish the D. Isn't a minor 2nd? and in what case is this used?
C to D, major second, I get it.
etc..etc...

So in short, there are no chromatic notes within any normal major or minor scale? As an interval can only be chromatic if it's augmented or diminished? And if that's right, why the bloody heck is this book asking me to find all the chromatic intervals for G, D and F (major and minor)?

Or maybe it's just asking me to find the notes which can be augmented or diminished? I don't know, this book is confusing at times... But is the bolded paragraph above this right?

Thanks for the reply.

I applaud you for the attempt, it's that kind of informative reply I'm looking for. The confusion is on my part!

Anyway, so simply put, anything that is augmented or diminished (which will usually cause a semitone gap between itself and the preceding or proceeding note) is a chromatic interval? But anything strictly within the notes of the scale, be it major or minor, despite whole tones and semitones is diatonic, right?



Okay, assuming the top half of this reply is right, I think I get it.

Thanks for all the help so far guys, I really appreciate it.

Hi, Musique, I'm back! (On a break from my training.)

I'll come back to your specific questions later, but I want to try explaining intervals and chromatic/diatonic in a slightly different way. I think the Piano Handbook has made things unclear with how they bring scales into it.

To name an interval, you only need to know the two notes involved. You don't need to know what key you're in. For example:

C to D, major second
D to G, perfect fourth
G to B, major third
B to C, minor second

You can check all of the above by counting half-steps.

Practice taking any two notes and naming the interval. For example, C to E, F# to G#, A to D, D to Bb.

To identify an interval as diatonic or chromatic, you just need to know what scale you're working in. An interval is diatonic if both notes are in the scale. An interval is chromatic if at least one note is not in the scale.

For example, in the key of C major, the four intervals I named above (C to D, D to G, G to B, B to C) are all diatonic in the key of C major, because all the notes involved (C, D, G, B) are in the scale of C major.

Practice with the other four intervals I named (C to E, F# to G#, A to D, D to Bb). Which of these are diatonic in the key of C major? Which are chromatic?

If we were in the key of E major, then the four intervals I named above are all chromatic in the key of E major, because each has at least one note that is not in the scale of E major (D and B are in the scale, C and G are out of the scale).

Practice with the other four intervals I named (C to E, F# to G#, A to D, D to Bb). Which of these are diatonic in the key of E major? Which are chromatic?

The Piano Handbook seems to be starting from the bottom note of the scale for its exercises. But this is sort of a red herring, because an interval can start anywhere and you can still name the interval, and also identify diatonic/chromatic.

There are 7 notes (8 counting octave) in a major scale. From Any one of the notes to any other is a diatonic interval. Any two white keys form a diatonic interval in the key of C major and A natural minor.

Any note, interval, or chord that requires an accidental not in the key sig is not diatonic to the key.

Hi Musique, this will be a very repetitive post applying this principle from my previous post:

To name an interval, you only have to know the notes in the interval. You don't have to know the scale.

Sorry it's so long. Sometimes face to face would be much better, where there could be an easier back and forth of ideas.



Naming intervals doesn't depend on the scale. You just count half steps. Two half-steps from G to A, that makes it a major second. One half-step from B to C, that makes it a minor second.

To name an interval, it doesn't matter if you're in the key of G, or B, or C, or D, or F# minor, or anything. You just count the half-steps. Perhaps the Piano Handbook has been focussing on intervals counting up from the keynote of a scale, but intervals can appear anywhere; they don't have to start from the bottom of a scale.


Yes, it's common to call a minor second a semitone (British) or half-step (American). Different names for the same interval.

Incidentally, it's also common to call a major second a tone (British) or a whole step (American).



To name intervals, it doesn't matter what key you're in. The number of half-steps is always the same. There are 11 half-steps from G to F#, so that's a major seventh, whether you're in the key of G, the key of D, the key of E minor, or any other key. There are 6 half-steps from C to F#, so that's an augmented fourth, whether you're in the key of C and using the F# as a chromatic note (outside of the C scale), or whether you're in the key of G and using the F# as a diatonic note (inside the G scale).


I'm not quite sure what you're saying. If either note, or both notes, are out of the scale, then it's a chromatic interval. For example, in the key of C, the following are all chromatic intervals: C to F#, Eb to A, Db to Bb.



I misread the Piano Handbook exercise which was just asking you to start at the keynote of the scale. E.g. in the key of G major, name intervals starting from G.

I was illustrating that you can start on any note in the scale, form intervals using the notes of that scale, and name the intervals. So, in the key of G. Pick a random note. Say, E. Form all the intervals from E using the notes of the G scale: E to E, E to F#, E to G, etc. Name those intervals counting half-steps. To name the intervals, it doesn't matter what scale we think we're in, the names are always the same.

For this example, it's coincidence that E minor has the same notes as G major. I could have made a similar example starting, say on A, and looking at the eight intervals A to A, A to B, A to C, A to D, ..., A to F#, A to G, A to A.



Exactly!


A minor second is two notes that are one half-step apart. Or in British terminology, two notes that are one semitone apart. Sometimes people say minor second. Sometimes they say half-step.


Again, identifying an interval just depends on counting half-steps, it doesn't matter what key you're in.

The following may go beyond what the Piano Handbook has covered yet:

Actually, there's a little bit more than counting half-steps. Technically, you also look at how many letters it takes to get from one note to the other (ignoring sharps and flats). E to G# takes 3 letters: E, F, G. So it's a type of third. 4 half-steps from E to G#, so it's a major third.

E to Ab takes four letters: E, F, G, A. So it's a type of fourth. 4 half-steps from E to Ab, so it's a diminished fourth.

This reveals that just as notes can have multiple names (e.g. G#, Ab), intervals also can have multiple names (major third, diminished fourth). But if this is confusing for now, just ignore it.



Again, all of these interval names are the same regardless of which key we're in. You don't have to start an interval from the keynote of a scale.


Major, minor, diminished, augmented is a big step! This post has been all about the names of intervals, and very little about diatonic or chromatic. (I see that StudioJoe has given a nice simple definition of diatonic. I wish I could write so concisely!)

Agreed, Joe,

That is true of all the natural church modes, and I believe that is the purest way to look at it. However, there is an equally large school of theoreticians who consider the melodic and harmonic minors as diatonic scales. In that school of thought, raised 6ths and 7ths are considered diatonic in the context of minor tonalities.

Ed

I'm not sure I agree with the bolded statement.

Given a scale, all the notes in the scale are called diatonic. All the notes not in the scale are called chromatic.

So, as StudioJoe points out, in the key of C major, the white keys are diatonic. The black keys are chromatic.

In the key of G major, the notes G, A, B, C, D, E, and F# are diatonic. The other five notes -- G#, A#, C#, D#, and F -- are chromatic.

You can use notes out of a major scale to form any major or minor interval, and also to form an augmented fourth and diminished fifth. For example, using notes from the C major scale, E to G is a minor second. C to D is a major second. E to G is a minor third. F to A is a major third. F to B is an augmented fourth. This is the same size as the interval from B up to F, which is technically called a diminished fifth. D to A is a perfect fifth. And so on. Notice that I am using any pairs of notes out of the scale, not just starting from the keynote.

These intervals are all called diatonic intervals in the key of C major, because they use notes from the C major scale.

You can form many of the same intervals using chromatic notes. For example, using at least one note that is chromatic to the C major scale, you can form G to Ab, minor second. E to F#, major second. C# to E, minor third. F# to A#, major third. And so on. These intervals are all called chromatic intervals in the key of C major, because they include at least one note that is not in the C major scale.

I think the Piano Handbook is asking you this: Pick a scale. Start from the keynote. (You could start from any note, but they're making it simple by saying just start from the keynote.) Form all 12 intervals that can be formed on that keynote (e.g. C to C, C to Db, C to D, C to Eb, C to E, etc. up to C to B, C to C) Then (1) Name each interval. And (2) Say which intervals are diatonic (only use notes from the scale) and which are chromatic (use a note out of the scale).

Now that I've written the Encyclopedia Britannica, I hope some part of that is helpful! Please let me know if it's not, and I'll try to see if I can say it better. Others are winning the prize for saying things elegantly and concisely though, which I am not.

Sorry guys, the basics of intervals I get. I just felt like the book was trying to put all this in context to specific scales. Either way, there's plenty of information here to go on with, but I must ask one more thing. A minor second, I understand the interval, one semitone, but in which case would a second interval in a scale be a semitone? I think that's what I was trying to ask before.

Thanks for all the replies though!

I scale degrees: 3 to 4 and 7 to 8 (for major scale)

Any two adjacent notes in any scale will be a semitone.

Hi Muzica,

In the context of starting from the keynote of a scale, there's a nice pretty pattern for the intervals.

The diatonic intervals starting from the keynote of a scale are all major or perfect intervals. For example, in C major: C to C, perfect unison; C to D, major second; C to E, major third; C to F perfect fourth; etc.

The chromatic intervals starting from the keynote of a scale fill in the minor intervals, and add a diminished interval:
C to Db minor second
C to Eb, minor third
C to Gb, diminished fifth
C to Ab, minor sixth
C to Bb, minor seventh

C to Gb can also be called C to F#, in which case it is called an augmented fourth.

You can identify this same pattern of intervals starting from the keynote of any scale.

Okay, slowly digesting this. I feel like I already know what I'm being told, but the way it's being explained is suggesting that perhaps there's more to it than I thought, and so I'm questioning whether I knew it at all!

But I'll keep re-reading parts and trying to take it in, and I'll be back with more questions if I get stuck.

Thanks for the replies guys, I really appreciate it!

Boy was I wrong, Thanks for the great discussion everyone. There is a lot to this stuff. Just when I thought I knew what I was doing, I had it all wrong.