NanoMuse Blog by Randy Chance

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Guitar Chords March 24, 2011

Some Chords

Some Chords

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Note Durations December 15, 2009

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Note Durations

Note Durations

 

More on Note Durations

More on Note Durations

More on Note Durations

 

Sixteenth Notes

Durations

Durations of Notes

 

Music Theory Part Two (Scroll down for Part One!) September 17, 2009

An Outline of Music Theory, Part 2 * * *

Here are the names of all the modes, based on each scale step.

    Ionian – the standard major scale, based on the first scale step
    Dorian – based on the second scale step
    Phrygian – (pronounced “Frigian,”) based on the third scale step
    Lydian – based on the fourth scale step
    Mixolydian – based on the fifth scale step
    Aeolian – based on the sixth scale step
    Locrian – based on the seventh scale step

If these names seem really weird, it’s because they’re named after ancient Greek city states.  (To the ancient Greeks, names like “Jimi Hendricks” and Curt Cobaine” would probably seem just as strange).

At this point you’re probably itching to surf the web further, if nothing else, just to find out if I’ve spelled Curt Cobaine’s name properly – but try to stay with me – we’re starting to get to the good part.

If you super-impose the modal concept in any key signature, you get the same thing in that key.  In other words, in D major [Ionian] one step up in that key would give us E Dorian, F# Phyrygian, G Lydian, etc.

* * *

Something that may be of help here.  Each time you go up five scale steps, you create a key that needs a new sharp [or a new flat if you go down five scale steps.  Both sharps and flats are referred to as “Accidentals”.  An accidental is either a sharp or flat – in other words, a note that is not natural.].   I call this new accidental that appears in each new key
signature, the “Hot Note”.  In the Myxolydian mode, the “Hot Note” is the seventh.  That’s the note that is flatted from the major scale five steps below it.  Another five steps up gives us the Dorian mode, which continues with the flatted seventh, but adds the flatted third.  Therefore, in the Dorian mode, the Hot Note is the third.  Here’s a list of all of them:

Hot Notes

Ionian – There is no Hot Note, this is the standard major scale, based on the first scale step
Mixolydian – the Hot Note is the seventh [it’s flatted]
Dorian -the Hot Note is the third [it’s flatted]
Aeolian – the Hot Note is the sixth [it’s flatted]
Phrygian – the Hot Note is the second [it’s flatted]
Locrian – the Hot Note is the fifth [it’s flatted] When I started to learn all the diatonic modes, I found that I had enormous tools at my disposal to increase my compositional abilities.

* * *

Harmony

The Hot Notes helped me in my understanding of harmony in the same way it helped me with melody.  Here’s how.

What is harmony?  It’s notes being played at the same time.  When you think you the modes when you’re constructing chords, think of each mode as a FAMILY of chords.

First we have the Ionian, or major family of chords:

    Major Triad
    Major Seventh
    Major Ninth
    Major Eleventh
    Major Thirteenth

If this stuff looks scary, don’t worry.  We’ll cover it in a minute and it doesn’t take long before it starts to look pretty simple.  It all fits together very logically, or at least as logically as anything else in music [nineteenth century slaves work songs, or the spelling of Curt Cobaine’s name,  for instance].

The basic building blocks of harmony are the minor third and the major third.

A minor third is a whole step and a half step put together.

If we go up a whole step from a C note, we get to a to a D note.  If we add another half step to that we get to D# or Eb.

So it is a minor third from C to Eb.

A major third is two whole steps put together.

If we go up a whole step from C, we get to D, then another whole step brings us to E.

The third scale step in a major [diatonic] scale is always a major third above the root note.

If we go up a whole step, and then a half step from E, we get to G.  This is an interval of a minor third.

In the key of C major,  E is the third scale step, or “Third” and G is the fifth scale step, or “Fifth.

A major triad chord consists of three notes: the root, or first scale step, the third scale step [a major third above the root] and the fifth scale step [a minor third above].

Consider this our starting point for harmony: the major triad.  All that other “Ninth” and Eleventh” stuff is just continuing to add more scale steps on top of the triad:

A Seventh chord adds the seventh scale step to the triad.
A Ninth chord adds the ninth scale step to the triad and the seventh.
An Eleventh chord adds the eleventh scale step to the seventh and the ninth.
A Thirteenth chord adds the thirteenth scale step to the seventh, ninth and eleventh.

What do we mean by ninth scale step, etc.?  We just keep counting scale steps up from the root.

This may make it easier for you [it sure did for me]:

The ninth is the same thing as the second [an octave – eight notes, plus one more].

The eleventh is the same thing as the fourth [an octave plus four more notes brings us to the eleventh].

The thirteenth is the same as the sixth [octave plus eight more notes equals the thirteenth].

Maybe this helps:

Our C diatonic scale stretched across two octaves again, with scale steps in the top row:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

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

1 1 1/2 1 1 1 1/2 1 1 1/2 1 1 1 1/2

Scale step number 8 is the octave. Nine is the same as two, eleven is the same as four, thirteen is the same as six. Of course, ten is the same as three, twelve is the same as five, and fourteen is the same as seven, but we’ve already used the three, five and seven. This brings us to an interesting conclusion:

We’ve used up all the diatonic scale steps!

So, when we extend the major triad with:

Major Triad Major Seventh Major Ninth Major Eleventh Major Thirteenth

The only way we can make more chords is to begin to ALTER chord tones. More about that later.

So this is what we mean by a family of chords.

* * *

But what happens if we go to another mode? Let’s try Myxolidian.

Remember that Myxolydian is based on the fifth scale step of the diatonic scale, and the Hot Note is the seventh [it’s flatted].

The major triad remains the same (no seventh is involved yet).

The seventh is flatted.

In the ninth chord, we still get the major triad, the flatted seventh, and then we add the ninth.

The rest of the chords are filled out in the same way. The only thing we’ve changed is the seventh, which is flatted.

This family of chords, based on the Myxolydian scale, are called, “Dominant” chords.

Major Triad Dominant Seventh Dominant Ninth Dominant Eleventh Dominant Thirteenth

All these chords have a major triad, a flatted seventh, and are in the Myxolydian, or Dominant family of chords. If you are playing in a major key, they would most likely be the chords you would play if you were going to form chords on the fifth scale step of the scale. Of course, that would be a big cliche, but just think of it that way to begin with. The more familiar you get, the more you can take chances. For now, just associate the family of chords with the scale step. This will help sort out the confusion. Whatever scale step you’re on, remember the previous notes that have been changed, and then think of the Hot Note.

Any chord in the family can be substituted for any other. That is also a cliche, and it’s like the scales themselves: It’s just something you can use to untangle the confusion. The more familiar you are with these tools, the more you can make informed, tasteful decisions of your own.

(Remember: “Fusion” is the little word inside the bigger word, “CONfusion”.) (?)

* * *

Let’s look at Dorian. Remember, in Dorian, we continue the flatted seventh and add a flatted third. The third is the Hot Note. This means that, in the triad, the third is going to be flatted, and the triad chord is going to be considered minor.

Minor Triad Minor Seventh Minor Ninth Minor Eleventh Minor Thirteenth

All these chords have a minor third, a flatted seventh, and are in the Dorian family of chord, and are usually called “Minor Seventh” chords (duh).

* * *

If we go up another fifth (another five scale steps), we get to A, which in C major is Aeolian. The hot note here is the flatted sixth. Aeolian is also called the Natural Minor. It is the relative minor from the Major (in this case, C major). The relative minor will always have the same number of flats or sharps, in other words, the same key signature, as the relativ major. The relative minor is always the sixth scale step in the diatonic major key (or, for convenience, you can think of it as a minor third below the root of the major scale – from C to B to A is a minor third).

The Aeolian family of chords is formed on a minor triad, because the third is minor, or flatted. As we extend, or add to, the triad, here’s what we get:

Minor Triad Minor Seventh, sharp five Minor Ninth, sharp five Minor Eleventh, sharp five

Traditionally, the Thirteenth chord is not included as a valid extension because the sharp five is going to conflict with the added Thirteenth note. In the key of C, it would be an G# next to an A natural – a half step that is considered to add too much disonance. Again, this doesn’t mean you can’t use it, I’m just teaching you the traditional way musicians look at things. You can depart from this all you want, if you want. It’s really the variations that make things interesting. This is true if you’re listening to Bach, Debussey or Lou Reed.

You may also ask, “Why isn’t it just called a flat sixth instead of a sharp five? After all, that’s what it is!” If anyone has a solid answer to this, e-mail me and let me know. All I can say is, it’s an alteration that is superimposed on top of the diatonic formula to begin with, so it’s considered that the sixth is already used up as the thirteenth in the usuall array of extensions (that doesn’t really hold water with me, because, since we’re in the Aeolian mode to begin with, it is diatonic, and the sixth has every right being flatted. Also, since it’s built into the scale, it should really be thought of as appearing before any extensions like eleventh and thirteenth (if that were not true, it should be thought of as a sharp twelvth!). So it might have to fit into the catagory of, “That’s just how you play the blues, boy!”.

More shall be revealed.

* * *

Going up another fifth, we get the Phrygian family of chords, which continues with the previous flatted tones and now add the “flatted ninth” as the Hot Note.

Why isn’t it called the “flatted second”? Well, the reason (maybe a bit flimsy) is that we’ve gone up nine scale steps to get to it (bacause we’ve already created the major triad in the first octave). Anyway, the octave being what it is, the ninth and second are essentially the same note, so it’s not that important (again, it falls into the “that’s how the blues are played . . . etc”).

So we have, as a family of chords –

Minor Triad Minor Seventh,flat nine Minor Eleventh, flat nine Minor Thirteenth, flat nine

The “Minor Ninth, Flat Ninth” is eliminated here for the same reason the thirteenth is eliminated in the Aeolian family of chords: It gets in the way of the Hot Note.

* * *

Another fifth up and we get to Locrian. Now we’ve gotten to the point where everything is flatted except the fourth. The Hot Note, the flatted fifth, gives us a “minor seventh, flat five” tonality which is very close to a diminished chord.

Here are the full family names:

Diminish Triad Minor Seventh,flat five Minor Eleventh, flat five Minor Thirteenth, flat five

* * *

Using the diatonic formula, we’ve just about filled up our quota of hot notes. We are as far away from a major scale as we can get (every note flattened except the fourth). The only way we can get more disonant than this is to alter the scale structure completely: take it out of the diatonic realm. That will be the subject of another tutorial.

The only other scale step left to construct harmony and scales on is the fourth step. The best way to deal with this is to think of it NOT as a fourth up but as a fifth down from the Ionian (major) tonic. In this way, we have a major scale, but in order to maintain the Diatonic formula, we need to make the fourth note SHARP. In the key of F (a fourth up, or a fifth down from C), this would be:

F G A B C D E F

We are then maintaining the C diatonic (major) scale, by sharping the fourth note in the F scale (it would normally be a Bb).

In the key of C, this would be:

C D E F# G A B C

The chord structures built on this mode are the same as the chords built on the Major scale, until you get to chords containing the added tenth step (same as a fourth, an octave higher). So, basically, you have:

Major Triad Major Seventh Major Ninth Major Sharp Eleventh Major Thirteenth Sharp Eleventh

So the hot note in the Lydian mode is the fourth scale step.

* * *

Getting back to the diminished triad, why do we call this triad diminished? Because the five and the third are both flatted. This creates a diminished chord: A minor third interval on top of another minor third interval.

When a major interval is flatted TWICE from it’s natural pitch, it is called “diminish”. In other words, if C to E is a major third, C to Eb is a minor third, then C to D (technically called, E double flat – Ebb) is a diminished third.

You might ask, “Why not just call it D, or a major third?” The answer is, “We do! – in Practice, remember – we’re discussing THEORY here!”

By the way, a triad built on two MAJOR thirds is called an augmented triad, because it consists of a root, major third and augmented fifth (when an interval is raised a half step from it’s natural pitch, it’s said to be “augmented”).

Types of Triads:

Major Triad – Major Third interval, Minor Third interval (for instance, C E G) Minor Triad – Minor Third interval, Major Third interval(for instance, C Eb G) Diminished Triad – Minor Third interval, Minor Third interval (for instance, C Eb Gb) Augmented Triad – Major Third interval, Major Third interval (for instance, C E G#)

I also may mention here that when a perfect interval is flatted ONCE, it’s called diminished. So, from C to G is a perfect fifth; from C to Gb is a diminished fifth.

Time for this –

Major intervals:

Second Third Sixth Seventh

Perfect intervals:

Unison (two notes, same pitch) Fourth Fifth Octave (two notes, same pitch, an octave apart)

Major intervals flatted once:

Minor Second Minor Third Minor Sixth Minor Seventh

Major intervals flatted TWICE:

Diminished Second Diminished Third Diminished Sixth Diminished Seventh

Perfect intervals flatted ONCE:

Diminished Unison Diminished Fourth Diminished Fifth Diminished Octave

Now, you may ask, “Why does a major interval have to be flatted twice to be diminished, and a perfect interval flatted only once?” The first answer to that is, when you have a perfect interval, there is no such thing as minor, it just goes straight to dimished. When you have a major interval, you flat it once and it becomes minor, you flat it again and it becomes diminished.

Then you may ask, “Why is that?”

Well, it goes back to the Middle Ages, when the Roman Catholic Church owned (that’s right, OWNED) music. They considered that certain intervals were perfect and certain were not. Same with time signatures. 3/4 time was considered perfect time, because it had to do with the Holy Trinity, that’s why 4/4 was called “common time” etc. . . .

Hey, we don’t have to get THAT theoretical !

Anyway, ANY interval (whether it’s major or perfect) is called “Augmented” when it is raised up one half step):

Up 1/2 step from Perfect to Augmented Unison

Up 1/2 step from Major to Augmented Second

Up 1/2 step from Major to Augmented Third

Up 1/2 step from Perfect to Augmented Fourth

Up 1/2 step from Perfect to Augmented Fifth

Up 1/2 step from Major to Augmented Sixth

Up 1/2 step from Major to Augmented Seventh

Up 1/2 step from Perfect to Augmented Octave

At least that rule’s fairly painless (isn’t “copy and paste” great?).

* * *

Now, back to our family of chords and Hot Notes:

Just to review, when we are dealing with chords, it’s just like dealing with scales. Each mode reproduces the flatted notes of the previous mode (one fifth, or five scale steps below it) and adds a Hot Note of it’s own. Using the key of C as an example, we have:

C – root – diatonic major Ionian mode no Hot Note

Up one fifth (five scale steps)

G – root – diatonic Myxolydian mode – the Hot Note is the seventh (flatted)

Up one fifth (five scale steps) from G we get

D – root – diatonic Dorian mode – the Hot Note is the third (flatted) – previous flat still flatted.

Up one fifth (five scale steps) from D we get

A – root – diatonic Aolian mode – the Hot Note is the sixth (flatted) – previous flats still flatted.

Up one fifth (five scale steps) from A we get

E – root – diatonic Phrygian mode – the Hot Note is the second (flatted) – previous flats still flatted.

Up one fifth (five scale steps) from E we get

B – root – diatonic Locrian mode – the Hot Note is the fifth (flatted) – previous flats still flatted.

And starting on the F, (one fifth below C), the Hote Note is the fourth (sharped) otherwise, it’s a major scale.

I hope some of this stuff helps in your understanding of music. Remember: It’s what you do with it – a brick is nothing brilliant in itself, it’s how the builders structure the bricks that creates a great building.

e-mail me if you want. I’ll do my best to get back to you.

Jam On!!

 

Music Theory Part One September 16, 2009

An Outline of Music Theory

A musician can really only go in a combination of four directions. Like an explorer who gets to choose between North, South, East or West, a musician can make choices within four contexts:

1) Improvisation
2) Written notation
3) Roots – Previous Influences
4) Music Theory

Most music exists in combinations of these four elements. Even the most “preconceived” orchestral music is usually open to at least some interpretation, if not improvisation. Even the loosest, most improvised jazz generally has some basic structure to it. Even the earthiest blues singer has some sense of music structure or theory to hang his laments on. Even the most abstract serialist has some kind of previous emotional/musical influences that may be affecting his musical choices.

George Gershwin incorporated elements of blues and jazz into his very schooled orchestral pieces; John Lennon incorporated elements of classical music theory on top of a blues foundation; Miles Davis developed a very improvisational jazz, which nevertheless had strong structures; even the coldest serialist sequences evoke memories of musical idioms.

Of course there are exceptions to all these rules and examples. They are given here as a kind of model with which to approach musical structure.

So many musicians (including myself, for a long time) spend most of their time sitting with our guitars or keyboards or whatever, listening to a record, and pulling riffs, licks, chords progressions, and other ideas off of it. Then we string these ideas together when we’re jamming in the hopes that we will homogenize them into a personal sense of style. This is a good thing. There is nothing that can take the place of being informed of one’s roots, and creating music that presents those roots in a meaningful fashion. Because if music isn’t connected to emotion, then it’s just a bunch of notes. We’d be better off practicing typing than jamming. Emotion is always connected to memory. This is why roots music is so powerful and so popular.

But what happens when a musician (like myself) who is oriented this way wants to progress further? How do you get beyond your roots and riffs into some new, unexplored territory?

When I reached a point in my life when I wanted to get beyond rock, blues and folk in order to bring other musical realms back to my music and make use of them (to increase the number of tools at my disposal), I started studying jazz. And I found out very quickly that jazz guitar teachers don’t really teach much theory. (This came as a big surprise, because I’d always thought of jazz as being pretty cerebral). They mostly just want to give you a song to learn and then when you come back again next week, you work on that song and they give you another song.

For me there were two problems with this. This first problem was that this process never seemed to answer any of my questions about why jazz is the way it is. (Why is that called a sharp five when it seems like it would be must easier to call it a flat six? How can you have a major third and a minor third in the same chord? Why does this chord have both sharps and flats in it? Etc.). The second problem was that I wasn’t that crazy about most of the songs I was learning. I’d just wanted to get into jazz to learn more, not cause I really loved the idea of sitting around playing, “Misty”, etc. (not as much fun as “Roll Over Beethoven” – at least for me).

The thing that amazed me was that when I asked jazz teachers these questions, they fell back on their roots, too. It was that way simply because that’s the way jazz is played. If you ask a blues musician why there are twelve bars in a twelve bar blues progression, he’ll just say, “That’s the way you play the Blues, boy!” (Here’s why: when the slaves
were working out in the fields, the “leader” would call out a line, everyone would repeat that line, and then the leader would call out a response to that line. That’s how blues got it’s A A B structure – 4 bars for each section. If nineteenth century slaves had a reason for what they did, certainly Duke Ellington should have a reason too!?(.

Anyway –

I wanted to see what it was like to compose music based on the building blocks of music – from the ground up. I was tired of figuring out this or that blues, reggae or rockabilly riff. I still loved that music, but I wanted to go someplace new.

So here’s some stuff that I came up with. It’s been a big help to me. Maybe it’ll be of help to you, too.

* * *

Basic Building Blocks:

The smallest building block that we usually use in Western music is the half step. The half step is simply the interval between any two keys of the piano (including the black keys), or any two frets on the guitar. The half step is also called “semi-tone”.

Two halves make a whole, and two half steps make a whole step. Half steps and whole steps are what we use to create modes and scales in music composition. More about modes and scales later. The diatonic formula, at the cornerstone of the western musical tradition, states that an octave is made of seven steps. What is an octave? This is a phenomena of sound that dictates that if a note is vibrated exactly twice as fast as another note, it repeats the same pitch, only higher. We are all used to octaves, and seldom consider what a peculiar arrangement this is.

Nevertheless, assuming the diatonic scale to be the primary configuration of the basic building blocks of music (half steps – or semitones, and whole steps – or wholetones), we will proceed to illustrate how modes are arranged.

These building blocks are just that – building blocks. What one person does with them may be entirely different from what another person does. This information is presented purely to give a musician tools to work with. What you do with these tools is entirely up to you.

In any event, the seven steps of the diatonic scale are arranged as follows:

whole step whole step half step whole step whole step whole step half step.

or,

two whole steps and a half step, three whole steps and a half step

In this form, the diatonic formula creates the Major scale.

If you look at a piano keyboard, this configuration accounts for why there is no black key between the B and the C, and also no black key between the E and the F. Counting up from C, one whole step (two half steps) brings you to D, another whole step to E, then one half step (to retain the diatonic formula) to F (notice, no black key). One whole step from F to G, (two half steps, including the black key again), one whole step from G to A, one whole step from A to B, and a half step (completing the diatonic formula) from B to C (again, no black key).

C (whole step) D (whole step) E (half step) F (whole step) G (whole step) A (whole step) B (half step) C

Here’s another way to look at it:

C D E F G A B C
1 1 ½ 1 1 1 ½
.
Think of the diatonic scale, for the time being, as home ground.

In keeping this formula intact, we can map out every key signature.

* * *

Let’s look at the G major (diatonic) scale.

If we retain the diatonic formula in the key of G:

two whole steps and a half step three whole steps and a half step

we realize that in order to maintain this formula beginning with G, the F has to be sharped. The sixth to seventh scale step in a diatonic scale has to be a whole step, and the seventh to eight is a half step. This cannot happen if the F remains natural.

So, a G diatonic, or major, scale is :

G A B C D E F# G
1 1 ½ 1 1 1 ½
.
* * *

Let’s look at what happens if we start on a D note.

If we maintain the diatonic formula, here’s what we get:

D E F# G A B C# D
1 1 ½ 1 1 1 ½
.
You will note that in order to make a D major scale we have to make both the F and the C sharp.

* * *

Let’s look at one more scale, the A scale.

If we use the diatonic formula moving upward from the A note, we get:

A B C# D E F# G# A
1 1 ½ 1 1 1 ½
.
If you look carefully, a pattern begins to emerge here. With each new note we picked, we kept the previous sharps and picked up one new one. The C scale had no sharps. The G scale had one sharp and it was F#. The D scale had two sharps, keeping the F# and adding a C#. The A scale kept both the F# and the C# and added a G#.

So, each major scale has a specific number of sharps (or flats – we’ll get to those in a minute).

But how did I know which notes to pick that would give us an increasing number of sharps?

Here’s the key:

G is five scale steps up from C.
D is five scale steps up from G.
A is five scale steps up from D.

So, every time we move up five scale steps, we have to add another sharp to keep the diatonic formula: two whole step, half step, three whole steps, half step.

This is the phenomenon known as the Circle of Fifths.

Here’s the complete formula:

C no sharps
up five scale steps
G one sharp
up five scale steps
D two sharps
up five scale steps
A three sharps
up five scale steps
E four sharps
up five scale steps
B five sharps
up five scale steps
F# six sharps
up five scale steps
C# seven sharps

You will notice that when we get to C#, every single note is exactly one half step above C. We have succeeded in raising the entire scale up one. You will notice also that seven sharps is the highest number of sharps we can get in a scale that involves seven scale steps (!). The only thing we can do from here on is to start using double sharps – but that’s for
another lesson.

So, the key of C has no sharps, the key of C# has ALL sharps.

* * *

I said I would talk about flats. If we go down five scale steps from C, here’s what happens:

F G A Bb C D E F
1 1 ½ 1 1 1 ½
.
So now we have one flat – Bb.

Down another five scale steps and we get:

Bb C D E F G A Bb
1 1 ½ 1 1 1 ½
.
So it’s the same thing with flats if we go down five scale steps each time. This is also part of the Circle of Fifths:

C no flats
down five scale steps
F one flat
down five scale steps
Bb two flats
down five scale steps
Eb three flats
down five scale steps
Ab four flats
down five scale steps
Db five flats
down five scale steps
Gb six flats
down five scale steps
Cb seven flats.

Once again, after seven flats, the maximum possible for a seven step scale, we get to Cb, a point exactly one half step below C, where we started, and each scale step is one half step below it’s counterpart in the key of C.

* * *

Modes

There’s a lot of superstition concerning modes. I mean there are a lot of times when someone will say, “That’s very modal.” And it might be hard to understand what he or she is saying. Of course there’s always the possibility that they’re not sure either, but, anyway, a mode is a very simple thing, and an understanding of modes can really increase one’s array of musical tools.

A mode is just a scale formed on the diatonic formula, but starting at a different point in the formula.

Let’s take our diatonic model and spread it out twice identically over two octaves:

1 1 ½ 1 1 1 ½ One Octave 1 1 ½ 1 1 1 ½ Two Octaves

Two octaves of C scales, end to end, superimposed over the diatonic formula, would look like this:

C D E F G A B C D E F G A B C
1 1 ½ 1 1 1 ½ 1 1 ½ 1 1 1 ½
.
Now, let’s start a scale on the second scale step of C and, maintaining the diatonic scheme, end an octave above where we started:

D E F G A B C D
1 ½ 1 1 1 ½ 1
.
This scale, based on the second scale step, is called the Dorian mode.