Do Half steps in a diatonic scales need to be separated by two whole steps? [duplicate]

Question

I've been reading about what makes a scale diatonic, and so far it seems that any scale that is constructed with a pattern of 5 whole steps and 2 half steps inside an octave could be considered diatonic, with the little added detail of needing half steps to be apart from each other. In the articles or answers I've read so far they use as an example the modes of a major scale.

Ionian - WWHWWWH
Dorian - WHWWWHW
Phrygian - HWWWHWW

And so on...

The thing that is not metioned in what I've read so far is why do half steps need to be separated by at least two whole steps for a scale to be considered diatonic.

Why would a scale with the pattern HWHWWWW not be considered as diatonic and, if it is not diatonic, then what is it?

Answer 1

I've never heard the concept of diatonic explained like that. I understand what your source is trying to say, but it's quite unintuitive when explained like that.

Simply, a Diatonic scale can mean any scale which is a mode of the Major scale.

A mode, in music, is when a scale starts at any degree other than the first. For example, if we stated the Major scale (WWHWWWH) from the fifth degree we would get the pattern WWHWWHW, which is also known as Mixolydian. Therefore Mixolydian is the fifth mode of the Major scale.

The reason why no diatonic scales ever have two half-steps without at least two whole-steps between them is that the pattern doesn't occur anywhere in the Major scale.

---

In order to make things more difficult, there is another definition of diatonic.

Diatonic can also mean any scale that is a mode of the 'prevailing' key.

For example if your band is playing BAlt, you could play in C Ascending Melodic Minor. Because Altered (HWHWWWW)is the seventh mode C Melodic Minor (WHWWWWH).

---

The first two sources support my first definition of diatonic. The second two support my second definition.

1. https://www.soundonsound.com/sound-advice/q-what-does-diatonic-mean
2. http://www.tonalcentre.org/Diatonic.html
3. https://www.britannica.com/art/diatonic
4. https://en.oxforddictionaries.com/definition/us/diatonic

Answer 2

It depends on your definition of the term diatonic. If it only applies to the interval structure available on the non-accidental ("white") keys of a western keyboard, then obviously there will always be two whole steps on one side of a half step, and three on the other side.

But in my experience, the term diatonic is usually also applied to some scale patterns typically found in western music, that diverge slightly from this.
Some examples below, I'll write the size of the steps in amounts of chromatic steps. So 1 for a half step, 2 for a whole step, 3 for an augmented step.

ascending melodic minor: 2 1 2 2 2 2 1 - e.g.: a b c d e f# g# a
Note that this scale produces an augmented triad (two consecutive major thirds) on step III

harmonic minor: 2 1 2 2 1 3 1 - e.g.: a b c d e f g# a
Note that this scale produces a diminished 7th chord (three consecutive minor thirds) on step VII

moll-dur (scale with major 3rd and minor 6th and 7th, combining a major triad on step I with minor triads on steps IV and V) 2 2 1 2 1 2 2 - e.g.: a b c# d e f g a
Typically used when a piece or section of music ends with a minor triad on step IV resolving to a major triad on step I

"flamenco" (also used in various other Latin, Greek, Balkan music, etc.): 1 3 1 2 1 2 2 - e.g.: e f g# a b c d e
Note that this is the same interval structure as harmonic minor, but starting on step V of the harmonic minor scale

If the term diatonic is used to refer to these scale patterns, then you could say that a half step must have at least one whole step or augmented step below and above it for the scale to be diatonic. But using this rule alone you could construct an octatonic scale: 1 2 1 2 1 2 1 2 - e.g.: b c d eb f f# g# a b
I wouldn't refer to this octatonic scale as diatonic, allthough I find that it is typically used in music that is (mostly) diatonic in nature, for example to construct a melody over a diminished 7th chord.

The example that you give: 1 2 1 2 2 2 2 - e.g.: b c d eb f g a b - I wouldn't call that diatonic if it were the base scale of a piece of music, because it doesn't have a pure fourth (5 semitones) or pure fifth (7 semitones) from the root. If I had to give it a western name, I would call it "locrian with a diminished fourth", or an "altered dominant 7 scale".

This scale could be a western approximation of a maqam. I actually came across an Egyptian guy that sang using this scale.

In jazz this scale might be used in a tritone substitution, for example if Db7 - C is substituted for G7b9 - C. Over the Db7 chord you would play 2 2 2 1 2 1 2 (db eb f g ab bb cb dd), relative to a G in the bass this becomes 1 2 1 2 2 2 2.

So for the qualification as diatonic, it also depends whether a scale serves as the base scale for a piece of music, or only as a temporary scale in a progression.

If I had to create an algorithm to generate diatonic scales, or qualify scales as either diatonic or not, I would use the following rules:

• must have a pure fourth (5 semitones) or pure fifth (7 semitones) from the root (most should have both)
• where a fourth is filled in with two steps
• where a fifth is filled in with three steps
• may not have consecutive half steps
• may have a single augmented step (three semitones) with a half step below it and above it

Answer 3

Think of the pattern of months - January, February, March, April and so on to December and back to January, and again to February, and so on. As this is a cyclic pattern, to know which month comes next it doesn't really matter which of these is the "first" month in a year - often in a neutral context we'd say that January is the first month, but when talking about tax (in the UK at least), April is the 'first' month of the tax year, while the first month of the academic year might be considered to be September, and so on. However, the order of the months is the same wherever you start.

I think of the diatonic scale in a similar way - that "The diatonic scale" is the name give to a particular cyclic pattern of whole and half steps that doesn't define a starting point. So you could say that the diatonic scale is WWHWWWHWWHWWWHWWHWWWH... or WHWWHWWWHWWHWWWHWWHWW... or HWWHWWWHWWHWWWHWWHWWW... it doesn't really matter. Those are all illustrations of the same, specific, pattern of whole and half steps.

Of course musical compositions are usually built around a specific home note - requiring us to pick a starting point on the diatonic scale. Picking this starting point is what gives us each of the (modern) modes:

Ionian: W W H W W W H
Dorian: W H W W W H W
Phrygian: H W W W H W W
Lydian: W W W H W W H
Mixolydian: W W H W W H W
Aeolian: W H W W H W W
Locrian: H W W H W W W

...and, to use the word diatonic in a slightly different sense, we could say that each of those is a diatonic scale - in other words, the diatonic scale with a specific starting point selected.

Personally, I don't like to define the diatonic scale in terms of the major scale, as my (woolly) understanding is that historically, the diatonic scale and its modes were the earlier concept; the terms "Major" and "Minor" relate later developments in which the Ionian and variations of the Aeolian mode became particularly fashionable.

Answer 4

Diatonic is one of those words whose definition is a bit murky. In the strictest sense, it fails to include what might usefully be considered diatonic. In the most inclusive sense, it’s meaningless.

The strictest sense is: the major scale and its modes: Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, and Locrian. Natural minor is in. Other minor scales are out.

As for the pattern of whole steps and half steps and all those rules for how far apart they need to be, they are a poor way to approach what diatonic means and they only give you a rote way to identify them. It’s like saying a number is even if its one’s digit is even. No! That’s not what makes it even; it’s just a property that even numbers exhibit (in even bases). It’s the same for diatonic scales. There is a deeper way to understand the term.

So how do we arrive at a strict-sense diatonic scale if we don’t base it on the WWHWWWH pattern, or some shifted version of it? Stacking fifths. Stacking fifths is how all 12 notes are derived. @MattL.'s answer to this question addresses it. I took a physics approach to it here. Octaves and fifths are the most consonant intervals. It turns out that a stack of fifths and a stack of octaves—even stacked to infinity—never lines up exactly. But, if you stack 12 fifths, it’s just over 7 octaves. You can temper them and force them to be equal to 7 octaves. (We generally do, but that is a whole other topic.)

Now if you take the 12 notes you derived and repeatedly halve their frequency (which is the same as repeatedly lowering them by an octave) until they fall into the same octave, you’ll end up with the chromatic scale.

You can also do this fifth-stacking to get just 7 notes. Let’s try, choosing F as the starting note to avoid accidentals:

F C G D A E B

Arrange them into order by pitch and, no matter which letter you start with, the aforementioned pattern of whole steps and half steps emerges. (Make no mistake, though. That pattern is a byproduct of being diatonic, not what makes it diatonic.) As an example, let’s start with A. When we do, we get the Aeolian mode / natural minor scale:

A B C D E F G

And here is where we begin to dilute strict-sense diatonic. We really want that G sharped so we can have an E7 chord and make it easy to get back to Am. Fine. Let’s do that. Now we have harmonic minor. And let’s call it diatonic, too. It’s still rooted in stacking fifths and it has just one small alteration.

Or you could say, “It’s not chromatic, after all!” But if that’s our definition of diatonic, then all sorts of scales enter the picture and we’ve lost the idea of a heptatonic scale based on stacking fifths.