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Question about Intervals

K

Kamael83

Dec 7, 2011
140
2
Cork City, Ireland
#1
Hi all!
For me there are 3 basic types of learning stuff:
1. Practice
2. Memorization
3. Understanding (explaining something to myself on logical level)

While I understand that a lot of theory (not only musical) have to be simple memorized, I`m always trying to UNDERSTAND as much as possible. It makes life easier when memory fails :)))

Bassybill recommended pdf about music theory here on TB. I started reading it and on first few pages I came across this:

"The name of an interval depends on the number of notes it contains, including the end notes; for
example, the interval C - F contains 4 notes (C, D, E, F), and will be called a “fourth”.
The type of an interval depends on the number of H's and W's that it contains. An interval can be
"minor" (m), "major" (M) or “perfect” (P); in addition, intervals can be “augmented” (aug or # or
+) (raised by an H) or “diminished” (dim or b) (lowered by an H). When nothing is specified, the
interval is considered to be major or perfect."

First of all I would like to say that this is the first time someone explained where intervals are getting their name from! I read few books (music theory for dummies, bass for dummies, few pdfs and some stuff on websites). Everywhere authors say something like this without any explanation:
Here is interval, know it by heart: major 3rd - 4 half steps.

Sure you can just memorize it....but it`s easier (at least for me to know that "3rd" stands for 3 note "gap".

Now to the point:
Author of that pdf says:

"the type of an interval depends on the number of H's and W's that it contains."

My question is: in what way type of interval depends on the number of hal and whole steps???
I mean is there a rule for this?
For instance (this is out of my head) : when you have odd number of whole steps and 1 half step interval becomes minor.
 
#2
rather than memorize a bunch of H's and W's,
I just compare all intervals to their natural position in a major scale.

For example: a major third is the distance form the Root to the 3rd of a major scale.
A minor 3rd is 1/2 step below a major 3rd.

this rule applies to all 7 intervals in a major scale.
(but 4ths and 5ths are never called "minor" or "Major",
they are "Perfect" in their natural position scale
or "diminished" when flattened, "augmented" when raised
 
#3
You first have to learn all the notes between an octave.

In this way you can determine the type of intervals.
If you say there are 8 notes in the octave,you then have

1st,2nd,3rd,4th,5th,6th,7th and 8th
The intervals will always be the same,regardless what the first note is.
As for the quality of the intervals,you will find that

2nd is major, a whole step above of 1st,with two other options : flat 2nd,sharp 2nd (minor and augmented respectively)

3rd can be minor (one and a half step above 1st) or major (2 whole steps above 1st)

4th is called perfect when is 2 whole and 1/2 step above 1st,can be sharp or flat (augmented or diminished respectively)

5th is 3 whole and 1/2 steps above first, can be sharp or flat (augmented or diminished)

6th can be minor (4 whole steps above first) or major (4 whole and 1/2 steps above 1st)

7th can be minor (5 whole steps above 1st) or major (5 whole and 1/2 step above first)

8th is 6 whole steps above 1st,and is the same note.

When you said ""when you have odd number of whole steps and 1 half step interval becomes minor"",is INCORRECT.
By the examples above,major 7th is an odd number of whole steps + 1/2 step,and is MAJOR.
There are no rules in this respect.

Now,is simpler if you learn the intervals in context,within a scale.
At first,you should learn a scale and locate its notes,using a major scale as an example,you can start by setting intervals by strings :
1st and 2nd in one string,then
3rd,4th and 5th in the next string,then
6th,7th and 8th in the next string.
In this way,you start to relate intervals with finger position,and understand their options (minor,major,augmented,diminished,when applies).

All this will also help you to understand how a scale can be played finger wise : an example,you want to play a major scale with a raised 6th,you locate this note,and play the scale replacing the natural 6th with the new note.
This will alter the "usual" way you play the scale,and sometimes present a small challenge that will contribute to develop your technique.
 
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#4
mambo4 said:
rather than memorize a bunch of H's and W's,
I just compare all intervals to their natural position in a major scale.

For example: a major third is the distance form the Root to the 3rd of a major scale.
A minor 3rd is 1/2 step below a major 3rd.

this rule applies to all 7 intervals in a major scale.
(but 4ths and 5ths are never called "minor" or "Major",
they are "Perfect" in their natural position scale
or "diminished" when flattened, "augmented" when raised
Click to expand...



bingo. If you want some good reading material, get this.
 
As an Amazon Associate, TalkBass may receive commissions from qualifying purchases made via links on this site.
#5
ACalbass said:
You first have to learn all the notes between an octave.

In this way you can determine the type of intervals.
If you say there are 8 notes in the octave,you then have

1st,2nd,3rd,4th,5th,6th,7th and 8th
The intervals will always be the same,regardless what the first note is.
As for the quality of the intervals,you will find that

2nd is always a whole step above of 1st,with two other options : flat 2nd,sharp 2nd (diminished and augmented respectively)

3rd can be minor (one and a half step above 1st) or major (2 whole steps above 1st)

4th is called perfect when is 2 whole and 1/2 step above 1st,can be sharp or flat (augmented or diminished respectively)

5th is 3 whole and 1/2 steps above first, can be sharp or flat (augmented or diminished)

6th can be minor (4 whole steps above first) or major (4 whole and 1/2 steps above 1st)

7th can be minor (5 whole steps above 1st) or major (5 whole and 1/2 step above first)

8th is 6 whole steps above 1st,and is the same note.

When you said ""when you have odd number of whole steps and 1 half step interval becomes minor"",is INCORRECT.
By the examples above,major 7th is an odd number of whole steps + 1/2 step,and is MAJOR.
There are no rules in this respect.

Now,is simpler if you learn the intervals in context,within a scale.
At first,you should learn a scale and locate its notes,using a major scale as an example,you can start by setting intervals by strings :
1st and 2nd in one string,then
3rd,4th and 5th in the next string,then
6th,7th and 8th in the next string.
In this way,you start to relate intervals with finger position,and understand their options (minor,major,augmented,diminished).
Click to expand...

This post is confusing. A flat 2nd is a minor 2nd (one semitone up from root), a diminished second is the enharmonic equivalent to the root. A sharp 2nd is augmented.

I read some more but got confused. My advice to the OP is compare the interval to the natural major scale. As listed in the post above.
 
#6
I know my....idea was incorrect...just wanted to give an example of formula I would like to get :)))

I see there is none and I will just have to find most suitable way to memorize / understand this.

Thanks for quick answers!
It`s good to know I can always count on TB even with most noobish questions :)
 
#7
mambo4 said:
rather than memorize a bunch of H's and W's,
I just compare all intervals to their natural position in a major scale.

For example: a major third is the distance form the Root to the 3rd of a major scale.
A minor 3rd is 1/2 step below a major 3rd.

this rule applies to all 7 intervals in a major scale.
(but 4ths and 5ths are never called "minor" or "Major",
they are "Perfect" in their natural position scale
or "diminished" when flattened, "augmented" when raised
Click to expand...

I'll elaborate a little more on this:

First find out an interval's generic name (which is its number), so Root, 2nd, 3rd, 4th, 5th, 6th, 7th, or Octave.

Then find out its specific name (diminished, minor, Major, Augmented, or Perfect).

2nds, 3rds, 6ths, and 7ths, can be only specified as diminished, minor, Major, or Augmented. If it fits in as it would in the natural Major scale then it is Major. If it's one semitone lower, it's minor. If it's two semitones lower then the Major, then it is diminished, and if it's one semitone higher than the Major, it's Augmented.

Roots, 4ths, 5ths, and Octaves can only be specified as diminished, Perfect, or Augmented. A Perfect is how it fits in with the major scale. One semitone lower and it's diminished. One higher and it's augmented. If you have any further questions, don't hesitate to ask.
 
#8
A long time ago I was reading an interview with Robert Fripp (or maybe it was Al Dimeola?) in some guitar magazine. When asked what advice he had for young musicians, he said, "learn your intervals. They are the basis of chords, scales, arpeggios etc." That made a lot of sense to me as a linear progression to learn things in. But the thing is, I spent nearly 15 years learning the intervals. There may only be 12 intervals, but gosh it takes a long time to play them in all their combinations, and to really hear them as well.
The other best advice I ever heard was "the difference between the wrong note and the right note is almost always a semitone."
 
#9
Matthew_84 said:
This post is confusing. A flat 2nd is a minor 2nd (one semitone up from root), a diminished second is the enharmonic equivalent to the root. A sharp 2nd is augmented.

I read some more but got confused. My advice to the OP is compare the interval to the natural major scale. As listed in the post above.
Click to expand...

Ooops,let me correct it.
But we are all in the same page anyway,there is no confusion.
All posts are correct (except that minor 2nd)
 
#10
How about this formula for minor intervals? it`s a bit shaky but i`m working on it at the moment:

Major interval minus 1 half step:
eg. 3maj : C-E 3min C-Eb

It seems to work for all of them: (diatonic scale only)
For instance:
I know that 7M has 7 note gap.
lets start from C: C D E F G A B

So 7M will be distance between C and B, now if I will flatten B I will get C - Bb and this will be 7m.

While thinking about it I went to Wikipedia and it actually gives some kind of formula:
I use bold letters for important stuff :

Major/minor



As shown in the table, a diatonic scale defines seven intervals for each interval number, each starting from a different note (seven unisons, seven seconds, etc.). The intervals formed by the notes of a diatonic scale are called diatonic. Except for unisons and octaves, the diatonic intervals with a given interval number always occur in two sizes, which differ by one semitone. For example, six of the fifths span seven semitones. The other one spans six semitones. Four of the thirds span three semitones, the others four. If one of the two versions is a perfect interval, the other is called either diminished (i.e. narrowed by one semitone) or augmented (i.e. widened by one semitone). Otherwise, the larger version is called major, the smaller one minor. For instance, since a 7-semitone fifth is a perfect interval (P5), the 6-semitone fifth is called "diminished fifth" (d5). Conversely, since neither kind of third is perfect, the larger one is called "major third" (M3), the smaller one "minor third" (m3).
Within a diatonic scale, unisons and octaves are always qualified as perfect, fourths as either perfect or augmented, fifths as perfect or diminished, and all the other intervals (seconds, thirds, sixths, sevenths) as major or minor.

It`s quite twisted but it actually works when I`m thinking about it :))
 
#11
Kamael83 said:
How about this formula for minor intervals? it`s a bit shaky but i`m working on it at the moment:

Major interval minus 1 half step:
eg. 3maj : C-E 3min C-Eb

It seems to work for all of them: (diatonic scale only)
For instance:
I know that 7M has 7 note gap.
lets start from C: C D E F G A B

So 7M will be distance between C and B, now if I will flatten B I will get C - Bb and this will be 7m.
Click to expand...

You are correct with all of this ^.

Kamael83 said:
While thinking about it I went to Wikipedia and it actually gives some kind of formula:
I use bold letters for important stuff :

Major/minor



As shown in the table, a diatonic scale defines seven intervals for each interval number, each starting from a different note (seven unisons, seven seconds, etc.). The intervals formed by the notes of a diatonic scale are called diatonic. Except for unisons and octaves, the diatonic intervals with a given interval number always occur in two sizes, which differ by one semitone. For example, six of the fifths span seven semitones. The other one spans six semitones. Four of the thirds span three semitones, the others four. If one of the two versions is a perfect interval, the other is called either diminished (i.e. narrowed by one semitone) or augmented (i.e. widened by one semitone). Otherwise, the larger version is called major, the smaller one minor. For instance, since a 7-semitone fifth is a perfect interval (P5), the 6-semitone fifth is called "diminished fifth" (d5). Conversely, since neither kind of third is perfect, the larger one is called "major third" (M3), the smaller one "minor third" (m3).
Within a diatonic scale, unisons and octaves are always qualified as perfect, fourths as either perfect or augmented, fifths as perfect or diminished, and all the other intervals (seconds, thirds, sixths, sevenths) as major or minor.

It's quite twisted but it actually works when I`m thinking about it :))
Click to expand...

I tried reading that several times and disagree with some of it, personally.

Except for unisons and octaves, the diatonic intervals with a given interval number always occur in two sizes, which differ by one semitone

That simply doesn't make sense to me. It may to others, I've had a long day... If by two sizes, they mean the size of the generic name of the interval, and the size of the specific name of the interval, then okay, but that's an odd way to word it.

EDIT TO ADD: I re-read some of the paragraph again, and I think by two sizes it means minor and Major. Now I get it a bit... When using the 7 common modes (Ionian, Dorian, Phrygian, lydian, mixolydian, Aeolian, or Locrian) and playing them diatonically (using only notes from the scale), you will not run into any diminished or Augmented 2nds, 3rds, 6ths, or 7ths. But there are many other scales that don't fit into these seven diatonic modes... It gets very complicated, and don't start to figure this stuff out yet, but my point is that I now understand what wikipedia is trying to tell you by two sizes, but it's not technically correct. 2nds, 3rds, 6ths, 7ths can be diminished and Augmented as well.

If one of the two versions is a perfect interval, the other is called either diminished (i.e. narrowed by one semitone) or augmented (i.e. widened by one semitone). Otherwise, the larger version is called major, the smaller one minor.

This doesn't, to me, clarify that only unisons (roots), 4ths, 5ths, and Octaves can only be diminished, Perfect, or Augmented. And the second sentence seems to neglect that 2nds, 3rds, 6ths, and 7ths, while they're usually minor and Major, they can still be diminished or Augmented.

And the whole discussion about "six of the fifths" span seven semitones is correct. But it takes some decent modal knowledge to understand this, which to me, is something that should be learned after naming basic intervals. And discussing this in a conversation about naming intervals would only add to some serious confusion.
 
#12
A lot of this stuff can get seriously over-complicated. and trying to get too much in too soon can seriously confuse people who are just starting out.

I learned all this stuff on the piano before I played bass, and that really helped because it gave your fingers numbers. "1" was the thumb (right hand). So to play the first five notes of the C scale, you went 1 (thumb), 2 (index finger), 3 (middle), 4 (ring), 5 (pinky). C-D-E-F-G. Moving on from that, it's easy to pick up what 4th, 5th et cetera mean and really get an intuitive grasp of scale degrees (or position of the notes in a scale). The idea of the interval between those notes naturally follows just after.

Take things one step at a time and break learning down into small, manageable chunks. All the stuff about diminished seconds and enharmonic equivalences can come later.
 
#13
bassybill said:
A lot of this stuff can get seriously over-complicated. and trying to get too much in too soon can seriously confuse people who are just starting out.

Take things one step at a time and break learning down into small, manageable chunks. All the stuff about diminished seconds and enharmonic equivalences can come later.
Click to expand...

Agree :) This episode was sponsored by Interval numbers :))
Now ìm trying to understand whole major / minor, dim/aug thing...
As far as I understand it so far: minors are smaller by semitone from majors and I`m happy with that knowledge for now :P

whole dim / aug and perfect thing seems more complicated
Perfect 4 raised by 1 semitone becomes augmented...
Perfect 5 lowered by 1 semitone becomes diminished...

Seems more complicated...
If you would want to follow logic here....
there should be augmented 5th and diminished 4th as well..but there isn`t haha :) at least not in diatonic interval table on wikipedia :P

Thanks all again...
Thanks to TB i`m tiny step closer to understanding music theory :)
 
#15
mambo4 said:
rather than memorize a bunch of H's and W's,
I just compare all intervals to their natural position in a major scale.

For example: a major third is the distance form the Root to the 3rd of a major scale.
A minor 3rd is 1/2 step below a major 3rd.

this rule applies to all 7 intervals in a major scale.
(but 4ths and 5ths are never called "minor" or "Major",
they are "Perfect" in their natural position scale
or "diminished" when flattened, "augmented" when raised
Click to expand...

yes... this. Why do people make music theory so difficult?
 
#17
Calaverasgrande said:
I am confused by this statement. All the musicians I know say minor 5th all day long for that well known interval. I say diminished 5th and I get blank stares.
Then I play the triad and they say "Oh!"
Click to expand...

They are wrong. Terminology is important.
Octaves are always perfect, as there is only one kind. 2nds, 3rds, 6ths and 7ths have two flavors: minor and major. 4ths and 5ths have three flavors: perfect, diminished, and augmented.

Western music is based on the major scale, everything is named in relation to the corresponding interval in the major scale, starting on the root.
 
#19
bassybill said:
A lot of this stuff can get seriously over-complicated. and trying to get too much in too soon can seriously confuse people who are just starting out.

I learned all this stuff on the piano before I played bass, and that really helped because it gave your fingers numbers. "1" was the thumb (right hand). So to play the first five notes of the C scale, you went 1 (thumb), 2 (index finger), 3 (middle), 4 (ring), 5 (pinky). C-D-E-F-G. Moving on from that, it's easy to pick up what 4th, 5th et cetera mean and really get an intuitive grasp of scale degrees (or position of the notes in a scale). The idea of the interval between those notes naturally follows just after.

Take things one step at a time and break learning down into small, manageable chunks. All the stuff about diminished seconds and enharmonic equivalences can come later.
Click to expand...

So, this PDF you originally recommended. . . .care to offer it up again?
 

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