Diatonic Intervals

You're right in your thinking, perhaps just getting lost in your application.

The major scale is TTSTTTS, so a major 6th is 9 semitones (TTSTT).
Your example is confusing because you don't mention the key that you're in - this is crucial. So, let's take the key of C:

C - D - E - F - G - A - B - C

The sixth is A - let's count the semitones:

C-C#-D-D#-E-F-F#-G-G#-A - 9 semitones, so C- A is a major interval and, as we've already counted, it's a 6th, so a major 6th.

So let's look at your example applied to C.

A major 3rd is 4 semitones and a minor 3rd, 3 semitones.

C-C#-D-D#-E  gives us 4 semitones, therefore a major interval and counting C, D, E a third, ergo a major 3rd.

D-D#-E-F  is only 3 semitones, which is a minor interval. Counting D, E, F also gives us a third interval, so giving us a minor 3rd.

For more info :

Greybeard's Pages - Intervals

Greybeard,

When you say "semitone", I assume you are referring to a half step?

yeah semi-tone means half-step, tone means full step.

in any major key, the diatonic invervals from the root are...

Root - A -
Major Second = B
Major Third = C#
Perfect Fourth = D
Perfect Fifth = E
Major Sixth = F#
Major Seventh = G#
Octave = A

These are the 'correct' interval names for the distances of tones and semi-tones.

Major Second = 2 semitones
Major Third = 4 Semitones
Perfect Fourth = 5 semitones
Perfect Fifth = 7 semitones
Major Sixth = 9 semitones
Major seventh = 11 semitones
Octave = 12 semitones.

These are all in relationship to the root.

A - B = major second
A - G# = major seventh

etc etc.

(im adding this because this helped me understand intervals a lot better, i dont know why)

Minor Third = 3 semitones
Major Third = 4 semitones

a major or minor chord has
to have a perfect 5th between the root and the fifth. (7 semitones)

so as you can see if we do 4+3, we get 7, 3+4, we get 7 so its a combination of a major and minor third

Any chord with a minor third (3 semitones) between the root note, and the second note of the chord, will be minor, and then there MUST be a major third after that (to add up to 7)
and the other way around for a major chord.

Hope it helped.

- Alex.

I see a bit of confusion here...

The word 'diatonic' means two-tones.  When we talk about diatonic intervals, they need to have two different letter names.  The opposite would be chromatic intervals, which can share a letter name.  The difference can be most easily seen in second intervals: C to Db is a minor second, C to C# is an augmented unison.  The first is a diatonic interval, the second is a chromatic interval (because they share the same letter name).

If you try to identify intervals by counting the semitones, you may end up with the wrong identification.  For example, the space from A to Db is four semitones, but the interval A to Db is NOT a major third! (It's a diminished 4th).

The next part of confusion is the need to know what key you're in -- you don't.  You should assume you're in the key of the lower note.  In the key of F, you may see an interval from Bb to D... to identify this interval, assume you are in Bb.  Worrying about the key would mean an interval, like D to F, would have different names in different keys, and it doesn't.

There are three steps to properly identifying a diatonic interval:

1. Determine the scale to be used
2. Determine the distance between the notes
3. Identify the interval quality

Here's how it works on your D to F interval...

1. The scale to be used is the major scale of the lower note, regardless of the key we're in, so you use a D major scale:

D-E-F#-G-A-B-C#-D

2. Starting from the root of that scale, count the distance to the upper note:

D-E-F#

three diatonic names, so the interval D to F will be some type of third

3. Determine the quality.  There are five possibilities:

A. If the upper note is part of the lower note's major scale, the interval will be perfect if it's a fourth, fifth, or octave, and major if it's anything else.

B. If the upper note is one semitone lower than it 'should' be to fit the major scale, it's diminished if it's a fourth, fifth, or octave, and minor if it's anything else

C. If the lower note is one full tone lower than it 'should' be to fit the major scale, its a doubly-diminished interval if it's a fourth, fifth, or octave, and a diminished interval if it's anything else

D. If the upper note is one semitone higher than it 'should' be, it's an augmented interval, regardless of the distance

E. If the upper note is one full tone higher than it 'should' be, it's a doubly-diminished interval, regardless of the distance.

Thank you Noteboat! You definitely shed some light on the subject.

Does the "quality rules" apply to all diatonic intervals? For instance . . .

D-E is a major second
D-Eb is a minor second
D-G is a perfect fourth
D-Gb is a diminished fourth

Do I have the general flow here?

My only question would be what would a D-G# be? Augmented?

Thanks for your help noteboat. You too Alex.

You've got the flow of it perfectly!

And yes, the 'quality' rule applies to all intervals.

By the way, it doesn't matter what key you're in, all intervals are based on a major scale -- so in A minor, you figure the intervals based on the A major scale... so you end up with A-C = minor 3rd, etc.

Tom

And yes, D-G# is an augmented fourth :)

Argh, was trying to do a grid of what NoteBoat said so it was easier to read, failed miserably though, lol.

alex,

it's here:

http://people.freenet.de/greybeard/Interval_1.htm

8)

oh god thats confusing.

I cant make sense of most of it lol.

wait i get it

you should fill in the other parts like..

first of all the can you make the C - note, on the same line in the boxes, it looks confusing with a list of four notes, thats what confused me before.

C - Gb.. you have marked as a Augmented 4th or Diminished fifth..

i thought

G - Gb = Diminished Fifth
C - F# = Augmented Fourth.

Besides that one, i think the side with single notes is very confusing, and it should be one line and should have a line going across.

It looks like you have 2 notes and 2 names for the same thing.

for example the "8 Semitones" away.

looks like G# and Ab fall into the same category, and theyre marked Augmented fifth and Minor 6th.

To me now i can understand what it means but to someone who doesnt know that it could be very confusing.

i mean like a barline should be seperating G# and Ab, because it looks like that same thing.

Also the table i was thinking of was more like 'how to work it out' based on NoteBoat's post.

I think that diagram would be very good on your page.

Like

"If the upper note is in the lower notes scale, the interval is perfect if its a fourth or a fifth"

but easier to understand.

Im not complaining about your chart lol, nothing like that, just looking around for improvements and things that can make it better, after getting used to what it all stood for, it makes sense.

- Alex.

Just a little correction along with my $0.02…

It's easy to get confused regarding the Greek prefixes, “di” and “dia.”  Di, means “two”, but dia means “through” or “across.”  Tonos, of course means “tone” or “accent.”  So, the etymology of the word, diatonic, would be better translated as “through tone.”  We think of the concept of diatonic basically the same as the ancient Greeks.  Nicomachus tells us:

“For the diatonic [genus], about which we spoke earlier, progresses in this way; semitone, then a whole tone, then a whole tone – three intervals within four numbers, that is to say, within four notes.  For this reason, it is called ‘diatonic,' from the fact that it is the only one of the rest of the genera that progresses ‘by tones.'” [The Manual of Harmonics, Nichomachus the Pythagorean (2nd century)]

With this explanation of the diatonic genus, Nichomachus also differentiates between the chromatic and enharmonic [quarter step] genera.  Now, whether Nicomachus' exact definition is the same as other Greek philosophers or not, we can certainly understand the idea of diatonic.  So, given the scale construction (a different issue entirely), we can discern whether a note or interval is diatonic or not.  A term like “diatonic scale” means a scale constructed in the specific order of semitones and whole tones that originated with the Greeks (Pythagoras, traditionally), which is where our musical scales come from.  This intervallic order makes up what we call the major, minor and modal scales.  We can take a diatonic scale like C major – CDEFGAB – and know that all of the notes and intervals the use only those notes in the scale are diatonic.  Any note or interval outside of the scale is considered non-diatonic (e.g. C-F# is a non-diatonic interval to C major; Db is a non-diatonic note in C major).  This, of course, means that even though a note or interval may be non-diatonic to one scale, it may diatonic to another (e.g. C-F# is a diatonic interval to G major).  Simply put, diatonic means adherence to the major/minor/modal scale.        

Sorry bro, but that has to be one of THE scariest attempts to explain diantonic scales that I have ever seen! A Harvard graduate I am not. I cannot speak for the rest of the crew.

I feel like throwing on a toga and reading poetry all day!

Don't apologize; just let me know what you don't understand:-)

Diatonic means "in the scale".

Non-diatonic means "not in the scale".