#1
Got stuck somewhere in my music theory book:

Major and Minor Intervals
When you describe intervals by degree, you still have to deal with those pitches
that fall above or below the basic notes—the sharps and flats, or the black keys
on a keyboard.
When measuring by degrees, you see that the second, third, sixth, and seventh
notes can be easily flattened
. When you flatten one of these notes, you create
what is called a minor interval
. The natural state of these intervals (in a major
scale) is called a major interval.
Here’s what these four intervals look like, with C as the root, in both major and
minor forms.
Major and minor intervals, starting on C.
Perfect Intervals
Certain intervals don’t have separate major or minor states (although they can
still be flattened or sharpened). These intervals—fourths, fifths, and octaves—
exist in one form only, called a perfect interval. You can’t lower these intervals to
make them minor or raise them to make them major; there’s no such thing as a
minor fifth or a major octave. The intervals, because of their acoustical properties,
are perfect as-is.



Why only the second, third, sixth, and seventh intervals can be easily falttened? As far as i know ANY note can be falttened. Even a B can be considered as C flat. And what is minor interval? I know what a minor chord is on a guitar, what is a minor scale - but minor interval??

And i would be happy to be a little more informed about those "perfect intervals" beyond the 3:2 and 4:3 math behind.
#3
The only Perfect intervals are unison (same note), Perfect Octave (12 semitones), Perfect Fourth (5 semitones) and Perfect Fifth (7 semitones). They are called perfect intervals because these are the main intervals used for Gregorian chants, and the church deemed them perfect. You can flatten ANY interval, but only flattened major intervals will become minor intervals.

http://magicbooktheory.com/intervals.php
http://www.musictheory.net/exercises/interval
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#4
There's really two ways to go about answering this.

1.)

Intervals come in two basic flavors, perfect and imperfect. Perfect intervals are insanely consonant, ranging from sounding exactly the same to not quite the same, but so damn close that you could call them the same. These include unisons, octaves, 4ths, and 5ths.

Imperfect intervals are, as they're name suggests, anything but perfect. They range from fairly consonant to downright dissonant. These include 2nds, 3rds, 6ths, 7ths, & the tritone. Because they are not perfect, no one note can describe them entirely, therefore, they have two notes to describe them, a major and a minor.

Like you have suggested any interval can be sharpened or flattened. When you flatten an interval it becomes diminished and when you sharpen an interval it becomes augmented.

Diminished <-flatten- Perfect -sharpen-> Augmented

Because imperfect intervals have two notes to describe them instead of one they have an extra step in this chain.

Diminsihed <-flatten- Minor <-sharpen/flatten-> Major -sharpen-> Augmented

So if you flatten a major interval you get a minor instead of a diminished(which in this case would require a double flat). Likewise if you sharpen a minor you get a major(double sharp for an augmented).

If you want more information on this subject then refer back to colon/hyphen/D's long post which kind of renders mine moot in hindsight, but whatever.

2.)

You may have noticed that answer 1 only explains how to define intervals and manipulate them, but it doesn't at all answer the question, "Why is it done this way?"

The answer to this is very long and complicated and is a matter that I have been studying on for about the past 8 months and am still grinding through. It involves a combination of not only musical, but world history, physic, mathmatics, and psychoacoustics.

Needless to say, it's a very deep subject with a lot of histroy behind it and to fully understand it you have to dive into it headfirst. If you're not willing to do this then just accept option 1 as "this is the way it's done" and move on, because it's really all just superficial knowledge anyway.

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#5
Quote by Standarduser
Got stuck somewhere in my music theory book:

Major and Minor Intervals
When you describe intervals by degree, you still have to deal with those pitches
that fall above or below the basic notes—the sharps and flats, or the black keys
on a keyboard.
When measuring by degrees, you see that the second, third, sixth, and seventh
notes can be easily flattened
. When you flatten one of these notes, you create
what is called a minor interval
. The natural state of these intervals (in a major
scale) is called a major interval.
Here’s what these four intervals look like, with C as the root, in both major and
minor forms.
Major and minor intervals, starting on C.
Perfect Intervals
Certain intervals don’t have separate major or minor states (although they can
still be flattened or sharpened). These intervals—fourths, fifths, and octaves—
exist in one form only, called a perfect interval. You can’t lower these intervals to
make them minor or raise them to make them major; there’s no such thing as a
minor fifth or a major octave. The intervals, because of their acoustical properties,
are perfect as-is.



Why only the second, third, sixth, and seventh intervals can be easily falttened? As far as i know ANY note can be falttened. Even a B can be considered as C flat.


This is correct. This is poor wording on their part - they mean that the note can be flattened to a black key on the piano.

And what is minor interval? I know what a minor chord is on a guitar, what is a minor scale - but minor interval??


You'll get to the minor scale later. Notice how B to C is a "second" and C to D is also a second. But notice how one of those intervals is larger than the other. If an interval is referred to as major, then the smaller version of it is referred to as minor.

And i would be happy to be a little more informed about those "perfect intervals" beyond the 3:2 and 4:3 math behind.


Honestly, the explanations won't help. Just remember that 4ths, 5ths, and octaves are considered perfect. It'll all come together. One of the frustrating aspects of learning theory is that some of the naming conventions don't make a ton of sense, being more historical in nature. A little rote memorization (and it's really not much) will get you through.
#6
^ is it just me or is that post completely blank?

TS, any note can be flattened. If you flatten the fourth, you get the diminished fourth, which is the same as the major third. If you flatten the fifth, you get the diminished fifth, which is the tritone, which sounds weird mane.
#7
Why only the second, third, sixth, and seventh intervals can be easily falttened? As far as i know ANY note can be falttened. Even a B can be considered as C flat.


This is correct. This is poor wording on their part - they mean that the note can be flattened to a black key on the piano.


You'll get to the minor scale later. Notice how B to C is a "second" and C to D is also a second. But notice how one of those intervals is larger than the other. If an interval is referred to as major, then the smaller version of it is referred to as minor.


Honestly, the explanations won't help. Just remember that 4ths, 5ths, and octaves are considered perfect. It'll all come together. One of the frustrating aspects of learning theory is that some of the naming conventions don't make a ton of sense, being more historical in nature. A little rote memorization (and it's really not much) will get you through.


i salvaged what i could, just a coding issue with the quote tags but unless HSJ edits his post i can't tell most of what he quoted
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#8
A perfect interval is one that inverts to a perfect interval.

For example a Perfect Fifth would be A up to E
If we invert that (so that E is the lower note) then E up to A is a Perfect Fourth.

Octaves and Unisons are also perfect.

A Major and minor interval will invert to a minor or Major interval respectively.

Thus a Major interval will invert to a minor interval. A minor interval will invert to a Major interval. For example C up to A is a Major sixth. If we invert that then A up to C is a minor third. (Thus they are not perfect.)

So what does it mean to invert an interval?? Well first I will show you how to name an interval which is what you're looking at then I'll explain how to invert an interval and the above will make more sense.

Here's a more in depth look at naming intervals...

Naming Intervals

There are two parts to naming an interval: Quality and Quantity
(The Quantity is the number value we use in naming an interval. The Quality is the type of interval i.e. major minor perfect augmented diminised etc.

To find the quantity of an interval you count the letters;
To find it's quality you count the semitones.
To get the whole name you have to count both. (at least until you know it simply and easily off the top of your head)

It pays to know the intervals of the major scale since that is where intervals get their name. So what we do is take our major scale and give each note a number starting with C as 1.
C D E F G A B C
1 2 3 4 5 6 7 8


So we have...
Some kind of C to some kind of D is some kind of 2nd.
Some kind of C to some kind of E is some kind of 3rd.
Some kind of C to some kind of F is some kind of 4th.
Some kind of C to some kind of G is some kind of 5th.
Some kind of C to some kind of A is some kind of 6th.
Some kind of C to some kind of B is some kind of 7th.
C to C is an 8th or an OCTave. (or it could be a unison)

We can carry past the octave if we want.
Some kind of C to some kind of D is some kind of 2nd or some kind of 9th
Some kind of C to some kind of E is some kind of 3rd or some kind of 10th
Some kind of C to some kind of F is some kind of 4th or some kind of 11th etc etc
you get the idea.

As you can see all we need to do to find out the kind of interval between any two notes is to start and count the first interval letter as 1 then count each letter up till we get to the right one. So to use an example G to D# we count letters G=1 A=2 B=3 C=4 D=5. Haha so we know some kind of G to some kind of D is some kind of 5th. But what kind of 5th is it exactly?? What is the quality of that particular 5th interval?

This is where our major scale comes back into play. There are two kinds of intervals found in the major scale - Major Intervals and Perfect Intervals. We'll come to why they are called what they are in a minute but first I'll just tell you which are which.
The perfect intervals are the Unison (1st or root), the 4th, the 5th, and the Octave (8th). The Major Intervals are the 2nd 3rd 6th and 7th.

As we said all the intervals in the major scale are either major or perfect. So we can apply these qualities to our major scale.
C=1 = Unison (perfect but usually just called unison)
D=2 = Major Second
E=3 = Major Third
F=4 = Perfect Fourth
G=5 = Perfect Fifth
A=6 = Major Sixth
B=7 = Major Seventh
C=8 = Octave (Perfect but usually just called Octave)

Now because these distances are derived from the major scale and the step pattern in the major scale is always the same we can see that the distances in terms of intervals are always the same. A Major Second will always be one whole tone. A Major Third will always be two tones. A Perfect Fourth will always be two and a half tones. etc etc.

So what happens when the interval we are dealing with is outside the major scale?? Well the first thing to do is determine what size the interval is. Is it a fourth or a fifth etc. You do this by counting letters. If we look at the previous example G to D# we see G A B C D, is some kind of fifth. Now we want to know it's quality.

We know the fifth in our major scale is perfect and that it is a distance of seven semitones. Thus a perfect fifth is always seven semitones up from the first note. If we count the steps from G to D# we get 8 semitones. So it's not a perfect fifth, but we know it's some kind of fifth so what is it?

When a Major or Perfect Interval is raised one semitone it becomes Augmented. Augmented? What the **** is that? It's simply when a Major or Perfect interval is raised one semitone. (So our G to D# is an augmented fifth because it's one semitone bigger than a perfect fifth.)
Similarly...
When a Major interval is lowered by a semitone it becomes Minor.
When a Minor or Perfect Interval is lowered by a semitone it becomes Diminished.

These relationships also works in reverse
So when a Minor interval is raised by a semitone it becomes Major.

Here's a little chart
[CENTER] [size="4"] _____________________
 |      Augmented      |
 ↑|---------------------|↑
 |  Major   |          |
↕|----------|  Perfect |
 |  Minor   |          |
 ↓|---------------------|↓
 |[U]     Diminished      [/U]|[/SIZE]

If you follow the arrows you should be able to see how it works.  
On the left you have your Major and minor intervals.
On the right are your Perfect Intervals
Here's a summary:
A major interval raised one semitone is an augmented interval.  
A major interval lowered one semitone becomes a minor interval.
A minor interval raised one semitone becomes a major interval.
A minor interval lowered one semitone becomes a diminished interval.

A Perfect interval raised one semitone becomes an augmented interval.
A Perfect interval lowered one semitone becomes a diminished interval[/CENTER]


So we can then work out and name any interval by referencing our knowledge of the major scale.

Interval Inversions

To invert an interval we take the lower note and raise it one octave, OR we take the higher note and lower it one octave. The net effect of this is to use the same pitch classes (same notes) but "inverting" them so that the note that was the lower note is now the higher note and the note that was the higher note is now the lower note.

For example here we have a perfect fifth between C and G. We invert in this case by taking the C and moving it up an octave and the resulting interval is a perfect fourth.


A perfect interval will always invert to another perfect interval.

However a Major interval will always invert to a minor interval.

Take the example from the beginning of the post.
If we have a Major sixth C between C and A then C will be the lower note. If we invert this interval then A will be the lower note and the distance between the two will now be some kind of third and a distance of three semitones which is a minor third.

There are two things to remember to make interval inversions easy
1.) The way quality (Major, minor, augmented etc) of the interval changes when inverted :
Perfect inverts to Perfect
Major inverts to minor (and vice versa)
Augmented inverts to Diminished (and vice versa)

2. The intervals always add to nine.
For example:
A perfect fifth inverts to a perfect fourth (five plus four is nine)
A major sixth inverts to a minor third (six plus three is nine)
etc

Regardless of the historical reasons or hypothetical conjectures as to how we could name intervals this is the rational that I used to understand why some intervals are called perfect while others were major and or minor.
Si
#9
I found it easier looking at this

1 #/b 2 #/b 3 4 #/b 5 #/b 6 #/b 7 1

All 12 notes accounted for in the chromatic scale. The major scale is the whole numbers, sticks out like sore thumb.
Last edited by metalmetalhead at Oct 11, 2012,
#10
Quote by Hail
i salvaged what i could, just a coding issue with the quote tags but unless HSJ edits his post i can't tell most of what he quoted

You were right he was missing an 'end quote' tag which for some reason made his whole post disappear. I edited it for him with my magic mod powers.
Si
#12
Mini rant:

As an aside, I really hate the terminology that this uses because I think it's better to say "Lowered by a half step" than "flattened". I think its a sloppy approach. I do not permit any of my students to use that term when giving me an answer.

It's too easy for the uninformed to equate "flattened" with "add a flat symbol".

Best,

Sean
Last edited by Sean0913 at Oct 11, 2012,
#13
No need to avoid the word, teach them what it means and be done with it.

Otherwise you run the risk of perpetuating the problem in your students because they will come to equate flatten with add a flat symbol rather than lower by a semitone. After all that would be the only context they will have heard the term used and language is learned through context.

It's not that hard and I am sure your students are bright enough to understand and you are clever enough to explain it in a way that they do understand.

Having said that I don't think I used the term flattened in the above post. But that's just one post - i do use it though.

e.g.
"Dude you need to flatten that note."
"Which one?"
"The D# should be a D"
"Oh yeah that sounds better."
Si
#14
Quote by Sean0913
I think it's better to say "Lowered by a half step" than "flattened". I think its a sloppy approach.


Yeah, but isn't flattening a note the same thing as lowering it by a half-step or semitone?
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#16
Quote by mdc
Depends if it's a diatonic or chromatic semitone.


Really? How so?
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#17
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#18
Quote by Sleepy__Head
Really? How so?

In terms of sound, yeah, it's the same. Notation wise, it's more a matter of what you prefer, really.

Take C-Bb - Flatten the Bb, to make it... Bbb.

Or lower it by a semitone.

Diatonic or chromatic semitone? A or Bbb respectively.

It's not just the note that's affected, it's the interval as well.
#19
Quote by mdc
In terms of sound, yeah, it's the same. Notation wise, it's more a matter of what you prefer, really.

Take C-Bb - Flatten the Bb, to make it... Bbb.

Or lower it by a semitone.

Diatonic or chromatic semitone? A or Bbb respectively.

It's not just the note that's affected, it's the interval as well.

Ah yes. I was coming at the question more from the angle of: Put a flat sign in front of the note. But yes you're right: Depending on how you want to treat the lowered note you might want to use an accidental or not (treat the note diatonically or chromatically).

Still not entirely convinced it makes much difference if you call that flattening a note as opposed to lowering it by a semitone, but I take your point.
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#20
If F is the note then is it E if we "lower that F by a semitone"? Is a lowered F an E?

We were talking in a specific context in this thread and that context was in regard to intervals. Within that context then no it is not the same thing flattening and F becomes Fb and if we lower an F a semitone then it becomes Fb - not E which would be a different interval - diatonic or chromatic.

Is "flattening a semitone" the same as "lowering a note a semitone" and is that the same as "playing a the note one semitone below".

It all comes down to a useless argument about semantics which is resolved only when we take into consideration the context.
Si
#21
whats the definition of lowered?

1. Below another in rank, position, or authority.
2. Physically situated below a similar or comparable thing: a lower shelf.
3. Lower Geology & Archaeology Relating to or being an earlier or older division of the period named.
4. Biology Less advanced in organization or evolutionary development.
5. Denoting the larger and usually more representative house of a bicameral legislature.
1. To let, bring, or move down to a lower level.
2. To reduce in value, degree, or quality.
3. To weaken; undermine: lower one's energy.
4. To reduce in standing or respect.
1. To move down: Her hand lowered.
2. To become less; diminish: The temperature has lowered gradually this month.

now flatten?
1. (sometimes foll by out) to make or become flat or flatter

3. (Music, other) (tr) Music to lower the pitch of (a note) by one chromatic semitone Usual US word flat

they are the same thing. doesn't matter what you call them. the definition for both of them are to similar.

to lower a note is to flatten a note to flatten a note is to lower a note. you cant TEACH anyone other wise or else it wouldn't be true.

Either way you use both of those words to describe one another. more so lowered describes the function of flattening a note

the Note was flattened from where it once was. diatonic formula only allows each note name to be used once. But that doesn't mean ya gotta I didn't learn that first. I doubt anyone learned about proper context before they learned any theory.

so flattening a note F stays F but flattened = Fb. so you don't end up with a Eb, E instead its going to be a Eb, Fb keeping true to diatonic.
#22
All valid points, but you have to make sure they understand the difference between "lowering" and simply equating it to, "add a b symbol" Because that's a common error in thinking. Another one equally perplexing is how many people confuse an "Xb" with "Xminor", and get those juxtaposed.

Best,

Sean