#1
So I got to this part in my theory book which I recently bought where we're talking about intervals etc.

Like if we reduce a major interval we get a minor one. If continued, we get a diminished one. But there was a song example. The song is in the key of G (If one sharp (#F) means it's G major). So there's this descending from B-A-G-F-E-D->. The books claims there are major and minor 2nds here. I agree with the major 2nds but I can't understand why it says there are minor 2nds.. I don't see any flats so how is it possible to have a minor 2nd?

Does it have something to do with the interval between G and F? In this case, as we are descending the interval is G-#F so is that the minor 2nd? Is G-F a major 2nd but the sharpened F brings them"closer together" as if it was lowered by a half-step to get a minor 2nd?

Could you explain what's going on. Even if I just explained it like it is.. I just don't understand why..
#2
G to F# is a m2 (aka half step) intervallic movement.

Major 2 is a whole step.

...modes and scales are still useless.


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#3
the interval between e and f is only a half step, or minor second. when descending you'd see something like g-f#-f-e.

there's nothing between e and f or b and c.
#4
Also since this next point will be inevitably discussed:

To flatten something means to lower it one half step. Not to put a flat sign in front of it. Same principle holds true for sharps.
"There are two styles of music. Good music and bad music." -Duke Ellington

"If you really think about it, the guitar is a pointless instrument." - Robert Fripp
#5
Quote by Jet Penguin
To flatten something means to lower it one half step. Not to put a flat sign in front of it. Same principle holds true for sharps.


Pretty much this. An A minor scale for an easy example has the notes A B C D E F G. No sharps or flats here, but it still contains a minor third, a minor sixth and a minor seventh.
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#6
The note names are based on the major scale. We have one major scale that has no sharps or flats and it's C major. But to make something sound like the major scale, you need to have both whole and half steps. The major scale always has a half step between the 3rd and 4th, and 7th and 8th (same as 1st) notes. C major has no sharps so let's find the 3rd, 4th, 7th and 8th notes of the scale. They are E, F, B and C. Because there is a half step between the 3rd and 4th, and 7th and 8th notes, and the 3rd, 4th, 7th and 8th notes of C major (the key with no sharps and flats) are E, F, B and C, this means there's a half step between E-F and B-C. I feel like I have explained the same thing for you before.
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#8
Quote by Billie_J

Does it have something to do with the interval between G and F? In this case, as we are descending the interval is G-#F so is that the minor 2nd? Is G-F a major 2nd but the sharpened F brings them"closer together" as if it was lowered by a half-step to get a minor 2nd?


smaller intervals = closer together. It doesn't matter if the interval is measured above or below the root note, the only thing interval measures is distance.
#9
Bille-J

These articles, lessons may help you.

http://www.ultimate-guitar.com/columns/music_theory/drastically_cut_learning_time_with_intervals.html

http://www.ultimate-guitar.com/lessons/the_basics/drastically_reduce_learning_time_with_intervals_part_2.html

Intervals are first and foremost sounds, regardless of how they get notated. It's always two pitches some number of semitones apart (see 2nd link above)... that distance determines the sound quality of the interval.

Two pitches a semitone apart form a minor 2nd. Two pitches a tone apart form a major 2nd.

Strictly speaking, the letter names involved dictate the correct choice of interval name.

Unison: same letter name.
Some sort of second: adjacent letter names (e.g A,B ... B,C etc)
Some sort of third ... two letter names away (e.g. A,C ... B,D etc).
Some sort of fourth ... three letter names away (e.g A,D ... B,E etc.)

Then sharps or flats are added to create the correct interval.

So, for a minor second: A,Bb ... A#,B ... Bb,Cb and so on.
For a major second: A,B ... A#,B#, Ab,Bb and so.

Personally, I care very little for this aspect (the correct pitch letter choices) ... I just care about the sound ... and for that you don't need to know any pitch names, just how to mechanically create the interval on-instrument. Loads of people will disagree with this approach ...but I promise, in mid-solo (unless you're sight reading) you're very vert unlikely to be thinking of every note name as you play it, especially at fast tempos.

cheers, Jerry
Last edited by jerrykramskoy at Jul 17, 2015,
#10
Quote by jerrykramskoy

Strictly speaking, the letter names involved dictate the correct choice of interval name.
True. You count the letters first, the semitones second.
Hence the difference between (eg) an augmented 4th and diminished 5th.
Quote by jerrykramskoy

Personally, I care very little for this aspect (the correct pitch letter choices) ... I just care about the sound ... and for that you don't need to know any pitch names, just how to mechanically create the interval on-instrument. Loads of people will disagree with this approach ...but I promise, in mid-solo (unless you're sight reading) you're very vert unlikely to be thinking of every note name as you play it, especially at fast tempos.

cheers, Jerry
Knowing the correct note names, the right enharmonics (and therefore the right interval name) is about understanding the theory.
I agree that one doesn't think about all that when playing - it's all about the sound in the end, and knowing how to find those sounds - but I still think it helps to get the theory right.
As mentioned elsewhere, it's not just about being able to talk (or write) sensibly about music with other musicians (or teaching properly), it's about the rational organisation of concepts in one's own head.
Naturally, all that is best forgotten (relegated to subconscious anyway) when one is playing.
#11
This book is seriously like math books. The examples are "2+2" and then the questions "Determine X given that the elephant eats mango and Y is 5".

In the example it's explained clearly but then when the book showed me examples of songs it got hard. In this song there are 4 flats (idk the key) and in this one part there's a descending from F to E (the E has that natural sign). It claims it's a minor 2nd. Again, nothing makes sense in what the book has explained. The book tells me to count the intervals on the staff. If we count those, it's a 2nd, major second.

I know BC and EF are only half a step away from each other but on the staff they aren't. You can count 2nds between them.

If there was no natural sign it would be F-bE of which enharmonic equivalent is F- #D. Here we have one whole step. Yet on the staff that's a 2nd. On the Staff F-E should be a major 2nd. If it's F-bE then shouldn't it be an augmented 2nd because the E " falls down" half a step away.

I'm confused about the staff and how it goes on the guitar. I can't understand this because this book gives easy explanations and then hard examples of songs with no explanations.
#12
No, no, no, no. The 12-tone system was made with half-steps between E and F, as well as B and C. There is no 12-tone note between these two intervals, on the piano (as makes sense for staff music), on the guitar (fret 0/open and fret 1 on one string is 1 half-step by construction), or on any other 12-tone instrument.

Separate intervals (2nd, 3rd, 4th) from tones/steps. Intervals are determined by note names and the tonal distance; steps are the tonal distance alone.

Example: For the two notes you wrote, you could also write E#-Eb (which is a double-augmented unison). This interval is based on the note names. However, they are a whole step, a tone apart.
#13
For a second I thought I had understood it, then I started looking at other example songs and no, I couldn't get the intervals. A song in the key of G. A descending from G to B is a minor 6th.. How come... I really have no idea anymore how to approach them. Counting on the staff gives 6, where does the minor come? If I start counting in mind like how many HS and WS there are, I'll most likely fail doing it.
#15
Think about a C major chord. It goes C E G.
C to D is a major second. D to E is a major second. C to E is a major third.

Now think of a D minor chord. D F A.
D to E is a major second. E to F is a minor second. D to F is a minor third.

The staff represents each letter, not each interval. This is just how it works.
#16
Quote by Billie_J
For a second I thought I had understood it, then I started looking at other example songs and no, I couldn't get the intervals. A song in the key of G. A descending from G to B is a minor 6th.. How come... I really have no idea anymore how to approach them. Counting on the staff gives 6, where does the minor come? If I start counting in mind like how many HS and WS there are, I'll most likely fail doing it.
"Minor" and "major" just mean "smaller" and "larger", out of two choices. That applies to 2nds, 3rds, 6ths and 7ths.

2nds measure 1 or 2 semitones
3rds measure 3 or 4 semitones
6ths measure 8 or 9 semitones
7ths measure 10 or 11 semitones

G to B downwards = B to G upwards. That's 6 letters (BCDEFG), and 8 semitones, so it's a minor 6th.

A possibly useful tip is that a major interval inverted becomes a minor one, and vice versa, and the numbers add up to 9 (not 8 because one letter is counted twice).
So G-B (upwards) is a major 3rd, and inverted (B-G) is a minor 6th.

It's often said that you need to refer intervals to the major scale of the root, but that's not necessary if you know the formula of the natural notes ABCDEFG.
(B to G is a minor 6th whatever scale you find the notes in.)

"Major" and "minor" scales and chords derive their names from their intervals (not vice versa) - the 3rd in particular.
A "major" scale or chord is one that has a major (larger) 3rd.
A "minor" scale or chord is one that has a minor (smaller) 3rd.

The major scale happens to have major 2, 6 and 7 too, but the minor scale has a major 2, and variable 6 and 7. Only the 3rd is always minor.

Major and minor triads both have a perfect 5th, and the interval between 3rd and 5th can be ignored. (Chord intervals and extensions are always defined from the root.) The 3rd is all that differentiates them.
If the 5th is altered then that becomes a more significant interval, and the chord is named after that - either "augmented" (with raised 5th) or "diminished" with lowered 5th.
Last edited by jongtr at Jul 17, 2015,
#17
Quote by Billie_J
For a second I thought I had understood it, then I started looking at other example songs and no, I couldn't get the intervals. A song in the key of G. A descending from G to B is a minor 6th.. How come... I really have no idea anymore how to approach them. Counting on the staff gives 6, where does the minor come? If I start counting in mind like how many HS and WS there are, I'll most likely fail doing it.

Just count half steps. Each interval has a set number of semitones.
1 semitone - minor second
2 semitones - major second
3 semitones - minor third
4 semitones - major third
5 semitones - perfect fourths
6 semitones - augmented fourth/diminished fifth
7 semitones - perfect fifth
8 semitones - minor sixth
9 semitones - major sixth
10 semitones - minor seventh
11 semitones - major seventh
12 semitones - octave

There are two half steps between each letter name except between B and C and E and F which only have a half step between them.
#18
Might be worth adding that you can have augmented 2nds, 5ths and 6ths, and diminished 4ths and 7ths.
The A harmonic minor scale contains:
an augmented 2nd (2 notes, 3 semitones, 1 larger than major) - F-G#
a diminished 4th (4 notes 4 semitones, 1 smaller than perfect) - G#-C
an augmented 5th (5 notes, 8 semitones) - C-G#
a diminished 7th (7 notes, 9 semitones, 1 smaller than minor) - G#-F.

The last one gives its name to the vii chord in a minor key, eg G#dim7 (G# B D F) in A minor.

The augmented 6th (6 notes 10 semitones) is exclusive to classical theory, due to strict voice-leading (resolves outwards to an octave). In jazz (etc) it tends to get called a minor 7th, because that's what it sounds like. (In jazz, augmented 6th chords get treated like dom7s.)
Last edited by jongtr at Jul 17, 2015,
#19
You can have augmented and diminished anything. C-A# is strictly augmented sixth, one half-step larger than a major sixth, and cannot be interpreted as a minor seventh without enharmonic respelling.
#20
Major and minor seconds look the same on staff. Notation is also based on the major scale, just like note names are. Major and minor intervals look no different on staff. When reading sheet music, just pay attention to the note names. That's what sheet music tells - the note names.
Quote by AlanHB
Just remember that there are no boring scales, just boring players.

Gear

Bach Stradivarius 37G
Charvel So Cal
Fender Dimension Bass
Hartke HyDrive 210c
Ibanez BL70
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Tokai TB48
Yamaha FG720S-12
Yamaha P115
#21
Quote by Billie_J
For a second I thought I had understood it, then I started looking at other example songs and no, I couldn't get the intervals. A song in the key of G. A descending from G to B is a minor 6th.. How come... I really have no idea anymore how to approach them. Counting on the staff gives 6, where does the minor come? If I start counting in mind like how many HS and WS there are, I'll most likely fail doing it.


In Western music, convention breaks the range of an octave into 12 semitones.

Now think of a 24-fret guitar, and let's arbitrarily choose the 3rd string (G). Just using that string, we can play from open G to an octave above that (at the 12 th fret), and the 2nd octave of the open G at the 24th fret.

Now let's choose an arbitrary pitch, e.g. B (4th fret, and its octave at the 4+12=16th fret).

If we measure from the G at the 12th fret to the B at the 16th fret, the B is 4 semitones higher. (aka maj 3rd)

Exactly the same way, measuring from the open string G to the B at the 4th fret, we also get an interval of 4 semitones.

But, if we measure from the G at the 12th fret to this lower B at the 4th fret, the interval is 12-4=8 semitones. (aka min 6th).

All that's happening is we take the original interval (G UP to B), the maj 3rd, and then flip the upper pitch (B) down an octave giving us the resulting distance of 8 semitones from the original G DOWN to the B in the lower octave.

On guitar, if you know your octave shapes, the above is dead easy ... just apply the shape to B to drop it down to that lower octave.

But of course, from the view point of that lower octave, the G (open string) to the B (4th fret), is still 4 semitones, a maj 3rd.

We can also flip the lower pitch of an interval UP an octave.

E.g. with open G -> B at 4th fret, we have an interval of 4 semitones (maj 3)
Flip the B up to the next octave (12th fret), and we now have a distance of 8 semitones between these two pitches (from 4th fret to 12th fret) (min 6).

Think about how a chord is labelled (if shown with interval names) ... consider a major triad, E. Convention labels the intervals relative to the nearest lower root.

So ... suggest you read this from bottom to top.

0 <---- next root
0 <---- 5th above the nearest lower root (on 4th string). [It's also a 4th (5 semitones) below next root. This is never shown on diagram]
1 <---- maj 3rd above nearest lower root. [It's also a m6 (8 semitones) below the next root. This is never shown on diagram]
2 <---- next root
2 <---- this is a 5th (7 semitones) above the E on the 6th string. [It's also a 4th (5 semitones) below next root. This is never shown on diagram]
0 <--- lowest root

(I'll ignore chord extensions, where intervals larger than an octave are named ...)

That E major triad voicing is shown in chord diagrams, where intervals are used, as

1
5
3
1
5
1

Just remember the interval name, in isolation, denotes the distance in semitones between two pitches. Then, describing a melody, we can talk about successive intervals (up a maj3, now down a maj3, down a m6, up an octave ...), and notate these on the stave.

But when we're discussing a chord or showing it in a diagram, or when we discuss how a given pitch relates to a key centre (e.g. in a scale recipe), then we mostly measure the interval to that pitch from the nearest lower key centre pitch.

Once you get familiar with the sound the various intervals make against the key centre, you can consciously choose to use a given interval, and which octave you want to place it in ... but you'd be thinking "I'm going to land on a b7 at the end of this lick" for example.

cheers, Jerry
Last edited by jerrykramskoy at Jul 18, 2015,
#22
Could you just give me something to solve here so you can judge whether I'm doing it correctly. Just give me a song on staff or something and I'll try to determine the intervals.
#23
Quote by Billie_J
Could you just give me something to solve here so you can judge whether I'm doing it correctly. Just give me a song on staff or something and I'll try to determine the intervals.


Ok.

Here's a simple melody to play on one string. I've just given the frets.

0 5 5 7 9 9 7 9 10 4 7 5

First, measure the semitones between each pair of notes. To start you off, 0 -> 5 is up 5 semitones; 5 -> 5 is 0 semitones (unison). 10 -> 4 is down 6 semitones

Then name the above intervals.

Next, measure the interval from each pitch in the melody to the pitch at the 5th fret (which is the tonal centre of this melody). This is far more useful than knowing the individual intervals from pitch to pitch along the melody.

Finally, to assess the family of intervals in this melody, relative to the tonal centre pitch at the 5th fret, raise any pitches below that tonal centre pitch by an octave (e.g. 0 goes to 0+12), and then measure the resulting interval to the tonal centre pitch.

Now write down the intervals you've just found in ascending order, to reveal the scale (most of it) used for this melody.

Realise that if the melody was all shifted up by say 6 frets, nothing of your analysis above changes.

Have a go, and I or someone else will see how you got on.

cheers, Jerry
Last edited by jerrykramskoy at Jul 18, 2015,
#24
0-5= 5st, 5-5=0st, 5-7=2st, 7-9=2st, 9-9=0st, 9-7=2st, 7-9=2st, 9-10=1st, 10-4=6st, 7-5=2st
--------------------------------------
0-5= Perfect fourth, 5-5= (I can't remember the name for "1st intervals"), 5-7= Major 2nd, 7-9= Major 2nd, 9-9= Same as 5-5, 9-7= Major 2nd, 7-9= Major 2nd, 9-10= Minor 2nd, 10-4= Augmented fourth, 7-5= Major 2nd
--------------------------------------
0-5=Perfect fourth, 5-5= Same as previous 9-9 and 5-5, 7-5= Major 2nd, 9-5= Major 3rd, 10-5= Perfect fourth, 4-5= Minor 2nd
--------------------------------------
At this part, there's only two below 5th fret which is 4 and 0. 0+12= 12 that is 12-5= 7st= Perfect fifth

4+12=16, 16-5= 11st= Major Seventh
-------------------------------------

Minor 2nd->Major 2nd->(Major 3rd)->Perfect 4th->Augmented 4th->(Perfect 5th)->(Major 7th)
#25
Quote by Billie_J
0-5= 5st, 5-5=0st, 5-7=2st, 7-9=2st, 9-9=0st, 9-7=2st, 7-9=2st, 9-10=1st, 10-4=6st, 7-5=2st
--------------------------------------
0-5= Perfect fourth, 5-5= (I can't remember the name for "1st intervals"), 5-7= Major 2nd, 7-9= Major 2nd, 9-9= Same as 5-5, 9-7= Major 2nd, 7-9= Major 2nd, 9-10= Minor 2nd, 10-4= Augmented fourth, 7-5= Major 2nd
--------------------------------------
0-5=Perfect fourth, 5-5= Same as previous 9-9 and 5-5, 7-5= Major 2nd, 9-5= Major 3rd, 10-5= Perfect fourth, 4-5= Minor 2nd
--------------------------------------
At this part, there's only two below 5th fret which is 4 and 0. 0+12= 12 that is 12-5= 7st= Perfect fifth

4+12=16, 16-5= 11st= Major Seventh
-------------------------------------

Minor 2nd->Major 2nd->(Major 3rd)->Perfect 4th->Augmented 4th->(Perfect 5th)->(Major 7th)


Hi Billie_J.

All good!! Well done.

Just a bit of tidying up need doing. Two intervals need removing from the final list ...

1/ the minor 2nd (that's gone once you moved fret 4 up to fret 16, where it became a maj7 against the 5th fret)

2/ Aug 4th ... that too resulted from the interval involving the 4th fret (from fret 10 down to 4 originally).

I've emphasised the ones that need to be removed.

Minor 2nd->Major 2nd->(Major 3rd)->Perfect 4th->Augmented 4th->(Perfect 5th)->(Major 7th)

BTW: you may have wondered whether to name the 6 semitone interval as "Aug 4th" or "Dim 5th" ...

Because I didn't give you any note names, either is just as good. But with note names, then you'd know which ... just count the number of different letters (in the names) involved from the one to the other.

But, as you're successfully getting into this, at this stage, I think it's less to worry about by just observing the semitones involved as you've done ... because this exact same analysis would result if we'd shifted that melody to anywhere else on the guitar ... why? Because music is mostly about relations (relative distances ... semitones), between each pitch involved, and between each pitch and the chosen tonal centre. Whereas, if I gave you note names, of course the same intervals are still there. but if I ask you to start that identical melody from a different pitch, you'd see a huge difference in the names (and possibly b's and #'s) involved ... that can easily obscure the very simple fact that we've started the same melody from a different pitch.

A lot of teachers will strongly disagree here ... that you should know every name from day one. At some point, yes, it's needed, but I suggest keeping it simple for awhile.

And the above translates directly into your hand movements on guitar. Playing the above melody would require the exact same hand movements relative to the chosen tonal centre, no matter where you choose that (unless of course you run out of pitches on a string !!).

A chord is similar ... a bunch of pitches at various semitones from each other, and at various semitones from a designated pitch (the chord root).

When you slide around a chord shape, the exact same principle is going on ... so long as you don't change the shape, the relationship stays the same, the chord type stays the same, the chord sound stays essentially the same (just higher or lower).

The only reason we get "non-movable" chords is simply because trying to shift the entire shape (including any pitches that are originally at fret zero, the open string) becomes physically impossible unless you have inhumanly long fingers. So, if you only moved some of the pitches, but not the open string ones, then you've broken the original relationships ... semitone distances have changed.


Back to your exercise...

Last thing then is to mention the pitch at the 5th fret, the tonal centre of the melody, in the final list

Two coincident pitches form an interval of "unison" ... the one you couldn't remember the name of.

So, we get, ordered from the nearest to the tonal centre, to the furthest away, the following:

unison, major 2nd, major 3rd, perf 4th, perf 5th, maj 7th.

Now, next task for you ... instead of using the written names, like "perfect 5th" etc., replace the above list by interval symbols (such as "1" for unison, "2" for maj 2nd ...). When you see it written out like this, does it ring any bells for what scale type is has approximately the same intervals? Hint ... there's one interval missing that wasn't used in the melody ... but if present, we'd have the entire set of intervals in a hugely employed scale?

cheers, Jerry
Last edited by jerrykramskoy at Jul 18, 2015,