#1
Hi guys, just finding something really confusing about intervals. I understand the concept of intervals from the root note (I think), but my confusion starts when trying to categorize intervals not starting from the root note. Say I play the 4th and the 5th in the minor pentatonic scale. In my mental library of intervals, what would that be categorized as? Is it the same as the interval from the root note to a major second since both have 2 semitones between them?
#2
Within the scale, they are always the perfect fourth and the perfect fifth. The interval between them is a whole tone (or two semitones), which may also be called a major second. The individual notes, however, will always be called the fourth and the fifth.

So you can say you move up a major second from the fourth to the fifth, but you wouldn't call the fifth the major second of the fourth or anything to that effect.
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#4
Quote by Tandaman23
So the sound should reflect the major second interval?

If you just play those two notes, then yes. If you're playing over chords, the more important factor is how those notes relate to the chord and the key.
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#5
Hmm okay that makes much more sense. So when I play through the minor pentatonic in the first position, the intervals on the A, D, and G strings are the same sound played from left to right, and the intervals on the E and B strings are the same? The point then for hearing a scale and understanding the "Words" of guitar language would be to memorize the combinations of each respective interval, and apply them across the scale? Then what is the point of root notes in scales besides identifying the key signature? Say the 2nd root note in the first position of the minor pentatonic for example. Why would I need to know that root note?
#6
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#7
Quote by Tandaman23
Hmm okay that makes much more sense. So when I play through the minor pentatonic in the first position, the intervals on the A, D, and G strings are the same sound played from left to right, and the intervals on the E and B strings are the same? The point then for hearing a scale and understanding the "Words" of guitar language would be to memorize the combinations of each respective interval, and apply them across the scale? Then what is the point of root notes in scales besides identifying the key signature? Say the 2nd root note in the first position of the minor pentatonic for example. Why would I need to know that root note?

The same distance between two notes is the same interval. So a 2 fret jump is always a major second and a 3 fret jump is always a minor third.

Why should you know what the root note is? Because the root always sounds like the root. You need to have some kind of a reference point. Even though the distance between E-G and B-D is the same (minor third), going from E to G sounds pretty different from going to B to D (if we are in the same key all the time). That's because we are talking about different scale degrees. And scale degrees is the way I would memorize the sound of a scale. That means, you are using the root of the scale as your reference point.

The minor third scale degree always sounds like the minor third scale degree. And at least to me that's a lot more easier to memorize than having to memorize the interval between G and every other note. It doesn't really make sense outside of context. At least for a "normal" person the key is what defines how everything sounds like and what kind of functions the different notes have.

You can also use chords as your reference point and think about how the note is related to the chord. For example in the key of Em the G is the minor third of the key but if we are playing an Am chord, the G is the minor seventh of that chord.


So, I wouldn't just memorize how different intervals sound like out of context. That's not that useful. Context is what matters because it changes the sound of notes. Learn how the different scale degrees sound like. Pentatonic scale is a good starting point because it only has five different notes in it. Learn how the root note sounds like. The learn how the minor third sounds like. Then learn how the perfect 4th and 5th and minor 7th sounds like. Then you know how every note in the pentatonic scale sounds like and you can apply that same knowledge to every key. The 7th note in every pentatonic scale sounds the same.
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Last edited by MaggaraMarine at Feb 12, 2016,
#8
Quote by Tandaman23
Hi guys, just finding something really confusing about intervals. I understand the concept of intervals from the root note (I think), but my confusion starts when trying to categorize intervals not starting from the root note. Say I play the 4th and the 5th in the minor pentatonic scale. In my mental library of intervals, what would that be categorized as? Is it the same as the interval from the root note to a major second since both have 2 semitones between them?


You can take any 2 notes and compare the interval between them. It's a relative not an absolute comparison.

When you say root note, then you are talking in absolutes. It's the root of something, and that something is the musical key of the song or progression.

Another way of looking at it is this: you can take a pentatonic scale shape on the fretboard. In one key it's a minor pentatonic, in another key it's a major pentatonic.
#9
Quote by Tandaman23
Hi guys, just finding something really confusing about intervals. I understand the concept of intervals from the root note (I think), but my confusion starts when trying to categorize intervals not starting from the root note. Say I play the 4th and the 5th in the minor pentatonic scale. In my mental library of intervals, what would that be categorized as? Is it the same as the interval from the root note to a major second since both have 2 semitones between them?


Hi Tandaman, check out https://www.ultimate-guitar.com/lessons/the_basics/drastically_reduce_learning_time_with_intervals_part_2.html.
#10
An interval is the musical distance between two notes or pitches.

A scale is a step pattern. So in a way it is a specifically ordered set of intervals. The tonic of the scale tells us the starting point from which the specific set of intervals is applied.

You can certainly think of a scale as a pattern of ordered intervals (e.g. major pentatonic = major second - major second - minor third - major second - minor third)

However, a scale on it's own is somewhat abstract. It is a representation of a collection of notes in ascending or descending order. Where scales start to have real meaning is (of course) in music.

In music these notes are used in ways that form relationships with each other and specifically those relationships gravitate around a tonal centre or tonic. And so the relationship between the tonic note and each note of the scale is important and should not be overlooked.

Hence we have the step pattern (which you could measure in intervals but are normally measured in tones and semitones) and we have the scale degrees.

The dominant (fifth scale degree) of a major scale is more than just a major second above the fourth scale degree and a major second below the sixth scale degree. It is a perfect fifth above the tonic (first scale degree).

This relationship is one of the most fundamental relationships in music, ignoring it in favour of looking only at the distance between the fifth and it's neighbouring scale degrees will do you a grave disservice in any attempt to make sense of music.
Si
#11
Tandaman, this may help further.

An interval ALWAYS involves precisely 2 pitches, some number of semitones apart. That distance determines the sound of the interval. We can represent that using a pair of numbers, e.g. (0, 3) ... to describe a pattern for how to locate actual pitches:

The pattern says "locate one member of the interval at a distance of zero semitones from (COINCIDENT WITH) some chosen pitch, and locate the other at 3 semitones higher.

E.g.suppose you choose the open 6th string to create this interval from. This gets you the open string pitch (your choice), and the 3rd fret (3 semitones above your choice). The actual pitches involved are E and G.

Now suppose you choose the 1st fret. Therefore the interval made by the pattern (0,3) involves the pitches at the 1st fret and the 4th fret (3 semitones higher than our chosen pitch): so the actual pitches as F and Ab.

Musicians established naming conventions a long long time back, and they called this interval (0,3) a MINOR 3rd (b3). There are a few names. You mentioned a maj 2nd ... the name for the interval (0,2). An octave is the name for the interval (0,12).

This is easy, right?

Next, let's look at the pattern for selecting intervals that make up a minor 7th chord. The individual intervals involved are (0,3), (0,7), and (0,10). For convenience, we can write down the pattern for the chord as (0,3,7,10) ... implying that once we choose a pitch to apply this pattern to, then the members of the chord are found at 0,3,7 and 10 semitones from that choice. The actual chord shape on guitar (Assuming you use more than one string) usually involves some octaves of some of these resulting pitches ... but that doesn't change the fundamental sound of the chord.

If we apply this to open E say, we get the pitches E, G, B and D at the open string, and frets 3, 7 and 10.. A chord voicing on the guitar would use some combination of these pitches in different octaves

When this is heard, the pitch chosen to coincide (0) with (E above) is the one that is most prominent to the ear, and we tend tend to hear the intervals made from that pitch (which we call the ROOT) to the other selected pitches ... so, while there are other intervals present (for example between G and B (4 semitones), B and D (3 semitones), these don't stand out, so we don't have any real use for recognising their existence.

We can continue this discussion to scales.

E.g. the major scale has the individual intervals (0,2), (0,4), (0,5), (0,7), (0,9) and (0,11). Again, its less verbose to write this is (0,2,4,5,7,9) as we did for the chord above. The term "Major scale" is shorhand for this pattern. But musicians don't discuss patterns for chords and scales using semitones (which is a real shame, as an awful lot of confusion could be avoided), and instead used "interval names" ... with this naming covention you'll see the major scale written out as (1,2,3,4,5,6,7) ... but let's forget that for now.

Different scales have different interval patterns, which gives each scale its own characteristic flavour. If a writer wants to use that flavour, again, the pattern is applied to the writer's choice of starting pitch from which all the other pitches are determined by using the interval pattern. Now, the writer / player's skill is employing these resulting pitches in such a way as to make the starting pitch the most prominent over a period of time (a verse, a bridge, a whole song) ... if done correctly, this prominence is achieved. So, just like the root of the chord, the other pitches are often heard as intervals formed with the scale root, over time. As above with a chord , other intervals are formed during use of the scale notes, but again, they are less noticeable, so we don't worry about these too much.

Coming to your question now, the minor pentatonic pattern, in semitones, is (0,3,5,7,10) ... quite similar to the minor 7th chord pattern above. (using correct interval names, this is (1,b3,4,5,b7). As above, yes, there are various intervals found there, but we only really care about the intervals involving the choice of pitch for the scale start note (the TONIC, the TONAL CENTRE, the KEY NOTE ... take your pick) and any of the other scale notes.

So ... yes, there is an interval formed by the 4th and 5th of the minor pentatonic, that interval is 2 semitones (aka a major 2nd). BUT, it really isn't anything to worry about.

We analyse from the chord root, or from a scale root. This then raises the obvious question ,,, what about when we use chords built from the scale pitches? Which pitch wins in prominence. The answer to that depends on context ... if the chords are whizzing by, then the scale root, the TONAL CENTRE, wins ... at least it's much easier to think and hear like this, in this situation. The improvisation can build around the triad found at the tonal centre (but dressed up with passing notes, chromaticism maybe). When the chords are slow moving ... the chord root will become prominent during that time. The improvisation could then focus on that chord's members, but still using the other scale notes.

Hope this has helped.
Last edited by jerrykramskoy at Feb 13, 2016,
#12
I haven't read all of the replies, so apologies if I'm repeating people.

But basically, an interval consists of two notes. It doesn't matter what key you're in, what scale you're using, what song your playing etc, the first note of those two notes, is considered the root note in terms of that particular interval. So you calculate the interval from the root note.

Eg.
You're playing in the key of G Major, and play an E followed by a A.. That is a perfect fourth, because E is your root note (I) and A is your fourth note (IV). The fact that you're in G major doesn't affect the interval between these two notes.

An excellent tool for learning intervals, one that I cannot recommend strongly enough, is the EarBeater app on iPhone. If you have an iPhone I'd definitely say get this app if you're wanting to master intervals.

Hope this helps!
Last edited by Dom Hawthorn at Feb 13, 2016,
#13
Wow I really can't overstate how impressive and helpful the replies in this thread have been. I think gap in my understanding has been more than adequately bridged. Thanks everyone!
#14
^Cool

Quote by Dom Hawthorn

Eg.
You're playing in the key of G Major, and play an E followed by a A.. That is a perfect fourth, because E is your root note (I) and A is your fourth note (IV).
Are you ascending from E to A or descending A to E? It changes the interval.

e.g. E up to A is a perfect fourth. E down to A is a perfect fifth.

The term root note refers usually to a chord or scale.

Roman numerals I and IV refer to scale degrees not intervals. So if the root note is E then A is a IV regardless of whether it is above or below the E. If it is above the interval is a perfect fourth and it is the IV against the E root. If it is below the E then it is an interval of a perfect fifth but it is still a IV against the root E (which is still I).

This will probably confuse more than help but the intervals and scale degrees are not the same thing. Intervals are purely a measure of difference between two pitches regardless of scale degree or which of the two notes is the "root note".
Si
#15
Quote by 20Tigers
^Cool

Are you ascending from E to A or descending A to E? It changes the interval.

e.g. E up to A is a perfect fourth. E down to A is a perfect fifth.

The term root note refers usually to a chord or scale.

Roman numerals I and IV refer to scale degrees not intervals. So if the root note is E then A is a IV regardless of whether it is above or below the E. If it is above the interval is a perfect fourth and it is the IV against the E root. If it is below the E then it is an interval of a perfect fifth but it is still a IV against the root E (which is still I).

This will probably confuse more than help but the intervals and scale degrees are not the same thing. Intervals are purely a measure of difference between two pitches regardless of scale degree or which of the two notes is the "root note".


I was implying that you were playing an E ascending to an A, I should've had made that clear though of course. You're right, descending form an E to an A would be a perfect fifth.

The term root note still applies in terms of intervals, the first note of any intervals is considered the root of that interval.

And yes, I know that the roman numerals refer to scale degrees, but some people find it easier to think of first, second, third etc in terms of roman numerals, so thought I'd just include the roman numerals in brackets. I don't do this personally, but have come across many people who do. But yeah, I can see how people may get confused, fair play for pointing that out!
#16
Quote by Dom Hawthorn


The term root note still applies in terms of intervals, the first note of any intervals is considered the root of that interval.


Dom, if you mean lower pitch by "first", then this is not true. The interval root depends on the interval type E.g. the root of a perfect fifth is the lower pitch, but the root of a perfect fourth is the upper pitch. There's also a hierarchy of interval strengths, when combined in a chord, that help determine which pitch is the chord root.
#17
Quote by jerrykramskoy
Dom, if you mean lower pitch by "first", then this is not true. The interval root depends on the interval type E.g. the root of a perfect fifth is the lower pitch, but the root of a perfect fourth is the upper pitch. There's also a hierarchy of interval strengths, when combined in a chord, that help determine which pitch is the chord root.


No, I do not mean lower pitch by 'first'. I think things are getting confused due to different ways of looking at things. I apologise as I should've made my original reply a lot clearer.

By root, I was referring to the first note of any ascending or descending interval. I refer to it as the root so that, without a sound clip or visual aid, it's easy to explain which note you're starting from. Eg, if D is your root, a minor fifth descending would be G. If C is your root, a minor seventh ascending would be Bb.

But, when looking at intervals harmonically, the idea of calling one note the root can become confusing, due to the idea of determining the root by finding its nearest approximation in the harmonic series. It basically works out that the bottom note of all odd diatonically numbered intervals is the root, and the top note of all even diatonically numbered intervals is the root.

The idea of calling the first note of an ascending/descending interval the root is just the way I learnt and was taught. I never really found it confusing but can see how it may cause confusion in relation to other things.
Last edited by Dom Hawthorn at Feb 14, 2016,
#18
there's duality all over music. In this case for intervals, think about it as chromatic and diatonic. Just like the circle of 4ths/5ths, you can always go up a perfect 4th starting from the root note (keeping the same chord quality) and end up who knows where (up to you). you can also go up 4ths diatonically, meaning always staying in the scale and changing the quality of the chord as needed to reach back "home" if that makes any sense.

And that's for chords, for single notes is easier, just requires practice.
#19
Quote by jerrykramskoy
Dom, if you mean lower pitch by "first", then this is not true. The interval root depends on the interval type E.g. the root of a perfect fifth is the lower pitch, but the root of a perfect fourth is the upper pitch. There's also a hierarchy of interval strengths, when combined in a chord, that help determine which pitch is the chord root.
Well, there's two kinds of "root".
You're talking about the natural or acoustic root of the interval.
But if that was the only root, then there'd be no such thing as a perfect 4th! It would be an inverted 5th every time.

There is the nominal root, which is always the lower note in any interval, regardless of what the acoustic root might be.

Even when we talk about a descending interval (as in melodic intervals), the measure is still from the lower note. Eg, E down to A is a 5th because A-E is a 5th.

With some intervals the acoustic root is not in the interval itself. Eg, the acoustic root of an A-C minor 3rd is F, because A and C are both overtones of F, but neither one is an overtone of the other. (Unless you go very high in the harmonic series of A, where there is a practically negligible C.)
But of course we can choose either A or C as the nominal root - of the minor 3rd or major 6th accordingly.
#20
Intervals are measures of absolute distance between two notes. No relevance is given to which note (if any) of the two are the root or tonic.

Technically "root" is to chord as "tonic" is to scale. Without a chord there is no root without a scale there is no tonic.

An interval is discrete. Root and tonic simply do not apply.

I can understand the colloquial usage of the term "root" as simply meaning a starting point. and of course this idea is reinforced as we all (myself included) tend to misapply the term root when talking of scales etc.

Running with this then when we consider an interval then either of the two notes could be considered the root depending on where you start your measurement.

However, this stuff about acoustic/natural vs nominal roots of intervals and that the interval root being determined by the type of interval is getting a little too loose with the term root.

There certainly are some valid points in regard to a hierarchy of interval relationships and considering the harmonic series to explain why we hear certain notes as more fundamental etc. But when it comes to debating which note in an interval is the "real" root of the interval then the answer is none of them.
Si
#21
Quote by 20Tigers
Intervals are measures of absolute distance between two notes. No relevance is given to which note (if any) of the two are the root or tonic.

Technically "root" is to chord as "tonic" is to scale. Without a chord there is no root without a scale there is no tonic.

An interval is discrete. Root and tonic simply do not apply.

I can understand the colloquial usage of the term "root" as simply meaning a starting point. and of course this idea is reinforced as we all (myself included) tend to misapply the term root when talking of scales etc.

Running with this then when we consider an interval then either of the two notes could be considered the root depending on where you start your measurement.

However, this stuff about acoustic/natural vs nominal roots of intervals and that the interval root being determined by the type of interval is getting a little too loose with the term root.

There certainly are some valid points in regard to a hierarchy of interval relationships and considering the harmonic series to explain why we hear certain notes as more fundamental etc. But when it comes to debating which note in an interval is the "real" root of the interval then the answer is none of them.
Fair enough, but this is a semantic issue. I appreciate terminological exactitude as much as you do, so what term would you suggest for the two kinds of "roots" I was describing?
I.e., the note we measure from, and the note (if any) of which both notes are overtones? (I accept the latter concept is debatable anyway.)
#22
Technically 'root' only applies to chords or to intervals in the sense Jerry was talking about: the root of a 3rd, 5th or 7th is the lower note, but 2nds, 4ths and 6ths are understood as inversions and so their root is the upper note (the concept is called interval roots and is kind of stupid). That said, if you talked about the lower note of an interval as it's root virtually everyone would know what you're talking about so it's probably fine.

p.s. I don't really know what this thread is about I'm just replying to the last couple of posts.
#23
Inversions are particularly important to Bassist.
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#24
Quote by jongtr
Well, there's two kinds of "root".
You're talking about the natural or acoustic root of the interval.
But if that was the only root, then there'd be no such thing as a perfect 4th! It would be an inverted 5th every time.

There is the nominal root, which is always the lower note in any interval, regardless of what the acoustic root might be.

Even when we talk about a descending interval (as in melodic intervals), the measure is still from the lower note. Eg, E down to A is a 5th because A-E is a 5th.

With some intervals the acoustic root is not in the interval itself. Eg, the acoustic root of an A-C minor 3rd is F, because A and C are both overtones of F, but neither one is an overtone of the other. (Unless you go very high in the harmonic series of A, where there is a practically negligible C.)
But of course we can choose either A or C as the nominal root - of the minor 3rd or major 6th accordingly.



Yes, I'm talking about which pitch of an interval is more prominent to the ear, not thinking about inversions. E.g

e.g
x x
x 5
4 4
4 4
5 5
5 5

The first chord has 2 stacked perfect fourths (and others with weaker roots), and the overall root of the chord is the top of the lowest fourth (D) as a result.

The second chord includes a pefrect fifth (from bass A to treble E) ... that is the strongest interval ... the lower pitch of this interval (A) is the interval root, and as its the mosty prominent interval acoustically, A is the root of the chord

A lot of people don't really look at this stuff, but can be very useful determing a chord root for a handful of pitches in an unknown shape.

Clearly, the surroundig context (what others are playing, especially bass), affect the overal sonic result. Especially when the other guys are playing melodically (a bass line with several differnt pitches) ... but for static stuff ... the results are clear.

Another example ... I've pointed out strongest intervals present, both involving the D on the G string.:

5 (5th)
8 (4th)
7
x
x
x

D is the root. If someone played a low C, then the 5th from that C to the G would win, and become the chord root.
Last edited by jerrykramskoy at Feb 18, 2016,
#25
Quote by jazz_rock_feel
Technically 'root' only applies to chords or to intervals in the sense Jerry was talking about: the root of a 3rd, 5th or 7th is the lower note, but 2nds, 4ths and 6ths are understood as inversions and so their root is the upper note (the concept is called interval roots and is kind of stupid). That said, if you talked about the lower note of an interval as it's root virtually everyone would know what you're talking about so it's probably fine.

p.s. I don't really know what this thread is about I'm just replying to the last couple of posts.

I had a look into this and yeah there are some sources that assign roots to intervals based on the harmonic series. I'm not overly keen on the idea. I prefer to think of an interval as a discrete distance between two notes. In practice intervals are always found in context and form relationships with other intervals. When that happens is when you really start to get an idea of a "root" and a "tonic".

For example you could say the "root" of a perfect fourth interval is the upper note. But what if that perfect fourth is found between a root and fourth in a sus4 chord? The fourth interval doesn't change the root - it's still the lower note.

But I get how you might want to classify and describe the various strengths and relationships between notes in various stand alone intervals...but really once you add context chords have roots not intervals, or maybe now I'm just being stubborn
Si
#26
Quote by 20Tigers
I had a look into this and yeah there are some sources that assign roots to intervals based on the harmonic series. I'm not overly keen on the idea. I prefer to think of an interval as a discrete distance between two notes. In practice intervals are always found in context and form relationships with other intervals. When that happens is when you really start to get an idea of a "root" and a "tonic".

For example you could say the "root" of a perfect fourth interval is the upper note. But what if that perfect fourth is found between a root and fourth in a sus4 chord? The fourth interval doesn't change the root - it's still the lower note.

But I get how you might want to classify and describe the various strengths and relationships between notes in various stand alone intervals...but really once you add context chords have roots not intervals, or maybe now I'm just being stubborn



See my previous answer ... as you say, each different interval type has a "strength" in terms of its sonic prominence, when it appears in a bunch of intervals (a chord).

There are a very few cases where this doesn't lead to an overall chord root ... e.g. stack two fourths, there's no clear winner to the ear. But if you have a mix of different interval types, and there is one or more perfect 5ths in that mix ... the lower note of the lowest p5th is the chord root. If there are no 5ths, but 4ths and other types, the top note of the lowest 4th wins. I'm going to submit a short lesson on this to UG. For some reason, the concept gets little attention.
#27
Yeah I saw your post but still don't buy it. But maybe that's just cause I'm not in the market.

What I was trying to get at was this:

Any two notes the same distance apart always form the same interval regardless of the context within which you find it, but either of the two notes that form that interval could be the root depending on context.

While in isolation you can ascribe one of the two notes of an interval as being more "fundamental" according to the harmonic series, when in music an interval does not appear in isolation and in fact has a number of other horizontal and vertical intervals all affecting each other at the same time.

The combination of all these intervals (the context) will determine which note sounds like the root of the interval.

It's a context dependent thing. If you have a bunch of notes acting together you have a chord. The root of the chord is dependent on the wider context and a number of things play into which note sounds like the root.

Any interval can have either note acting as the root. For example in a Csus4 chord the C up to F is a perfect fourth but the C is the root...where the C is doubled you will find an interval of a perfect fifth from the F up to the C but the C is still the root.

In an F chord where the F is doubled then the C up to F is a perfect fourth but F is the root while the F up to C is a perfect fifth and the F is the root.

In a CMaj11 chord you will also find an F and a C and the C is the root.

Quote by jerrykramskoy
...if you have a mix of different interval types, and there is one or more perfect 5ths in that mix ... the lower note of the lowest p5th is the chord root. If there are no 5ths, but 4ths and other types, the top note of the lowest 4th wins. I'm going to submit a short lesson on this to UG. For some reason, the concept gets little attention.

There's a reason it gets little attention...it's not always true. It's kind of a sometimes rule of thumb that doesn't apply with enough consistency.

Example:
Shell voicings...
In a shell voicing of a Maj7 chord you drop the fifth. This gives you a R 3 7. The distance between the third and seventh is a perfect fifth but neither of those two intervals are the root of the chord. The fifth is present in the root filling out the harmonic series.

Before you argue that one of the other instruments will play the fifth, this is not necessary. It may be the relationship of the chords before and after that establish the C as the root of that chord.

I'm also not arguing that the perfect fifth does NOT contribute to the hierarchy of notes within a chord. It clearly does. I'm saying it doesn't always and either of the two notes in a perfect fifth could be the root note depending on all the other relationships (vertical and horizontal) within which that interval is found.

I don't buy into interval roots.
Si
#28
Quote by 20Tigers
Yeah I saw your post but still don't buy it. But maybe that's just cause I'm not in the market.

What I was trying to get at was this:

Any two notes the same distance apart always form the same interval regardless of the context within which you find it, but either of the two notes that form that interval could be the root depending on context.

While in isolation you can ascribe one of the two notes of an interval as being more "fundamental" according to the harmonic series, when in music an interval does not appear in isolation and in fact has a number of other horizontal and vertical intervals all affecting each other at the same time.

The combination of all these intervals (the context) will determine which note sounds like the root of the interval.
I'd put it slightly differently.
Each interval has its own root (in the sense of "more fundamental according to the harmonic series"), but context determines the overall root of the harmony - which of the interval roots wins out.
Eg, in a Csus4 chord (C-F-G) the C root wins out overall because of the strength of the C-G 5th. But F is still the root (acoustically) of the C-F interval - which is what causes the ambiguous "unresolved" sound of the chord.
Quote by 20Tigers

It's a context dependent thing. If you have a bunch of notes acting together you have a chord. The root of the chord is dependent on the wider context and a number of things play into which note sounds like the root.
Right.
Quote by 20Tigers

Any interval can have either note acting as the root. For example in a Csus4 chord the C up to F is a perfect fourth but the C is the root...where the C is doubled you will find an interval of a perfect fifth from the F up to the C but the C is still the root.
Of the chord, yes, but not of the C-F (or F-C) interval.
Quote by 20Tigers

In an F chord where the F is doubled then the C up to F is a perfect fourth but F is the root while the F up to C is a perfect fifth and the F is the root.
Yep.
Quote by 20Tigers

In a CMaj11 chord you will also find an F and a C and the C is the root.
If you ever find a Cmaj11 chord.... (I've never seen one.))
Quote by 20Tigers

Example:
Shell voicings...
In a shell voicing of a Maj7 chord you drop the fifth. This gives you a R 3 7. The distance between the third and seventh is a perfect fifth but neither of those two intervals are the root of the chord. The fifth is present in the root filling out the harmonic series.
Interesting example!
The acoustic root of the 3-7 interval is clearly the 3.
And the nominal root of chord ("1") is not supported by its own 5th.
However, the 3rd is a strong overtone of the root, and the 7th is a weaker one, while the root is not an overtone of either the 3rd or 7th. That's what makes the root win out as acoustic root overall.
Quote by 20Tigers

Before you argue that one of the other instruments will play the fifth, this is not necessary. It may be the relationship of the chords before and after that establish the C as the root of that chord.
That too, but it's not essential, IMO.
Quote by 20Tigers

I don't buy into interval roots.
I don't follow.
Not even when the interval is in isolation? If you take a C-G 5th, are you saying either of those could be the root (acoustically)?
Obviously I can invert it to G-C and nominate G as root, and call it a 4th. But acoustically C is still the root (because of the harmonic series relationship), albeit a little weaker.
If I then add a D, voicing the chord G-C-D or G-D-C- then that supports G as root - countering the effect of C, because G is lower in the chord.
But if I voice the chord as two stacked 5ths - C-G-D - then C is clearly the root, not G.

Voiced as a stack of 4ths, OTOH, D-G-C, it's a lot more ambiguous, because of the inversion of both 5ths - I think G still wins out because the D-G inverted 5th is lower then the G-C inverted 5th - but not by much.
The root is certainly not D, in acoustic terms, although I can still call it "D7sus4" if I want (and if the context either side supports D as root).
Last edited by jongtr at Feb 21, 2016,
#29
Quote by 20Tigers
Any two notes the same distance apart always form the same interval regardless of the context within which you find it, but either of the two notes that form that interval could be the root depending on context.


Aurally, but not functionally. +6, #9, etc. But I do agree interval is strictly a measure of distance while function depends on the context.
#30
Quote by 20Tigers
Yeah I saw your post but still don't buy it. But maybe that's just cause I'm not in the market.


Any interval can have either note acting as the root. For example in a Csus4 chord the C up to F is a perfect fourth but the C is the root...where the C is doubled you will find an interval of a perfect fifth from the F up to the C but the C is still the root.

In an F chord where the F is doubled then the C up to F is a perfect fourth but F is the root while the F up to C is a perfect fifth and the F is the root.

...

Example:
Shell voicings...
In a shell voicing of a Maj7 chord you drop the fifth. This gives you a R 3 7. The distance between the third and seventh is a perfect fifth but neither of those two intervals are the root of the chord. The fifth is present in the root filling out the harmonic series.

...

I don't buy into interval roots.


Hey 20Tigers... just seen your reply. Entirely your call, if you don't buy it.

Csus4. r 4 5. The root of the chord is C because of the r-5. In the r 4. the F is the root of that interval.

If you remove the 5 of Cmaj7, you don't have a maj7 chord anymore. If you play the C E B with equal force, the E stands out. Obviously. if you whack the C, it makes itself more prominent initially, and as the energy diminishes, the E takes over. The root of that chord as it stands is the E. Put back in the G, all changes.

I've never yet heard a chord (across whatever instruments) that has at least one p5th in it, where the lower note of the p5th doesn't sound like the chord root (or where there are multiple p5ths, the lower note of the lowest.

Have to be careful naming chords.

Try these 2 chords, let me know which note you hear as the root in each:

8 8
8 5
5 5
7 7

There are a very few examples where the interval root falls down, but not in tertian harmony.
Last edited by jerrykramskoy at Feb 21, 2016,
#31
Quote by jerrykramskoy

If you remove the 5 of Cmaj7, you don't have a maj7 chord anymore. If you play the C E B with equal force, the E stands out. Obviously. if you whack the C, it makes itself more prominent initially, and as the energy diminishes, the E takes over. The root of that chord as it stands is the E. Put back in the G, all changes.
I agree with your basic view, but I disagree here.
To me, C does sound like the root of a C-E-B chord.
I offered an explanation in my earlier post, to do with frequency relationships.
It's admittedly a close thing (more so if the C is voiced higher ) but aurally the chord seems to make more sense (to my ears) with C as root than E.
C is certainly the root of the C-E interval. And B is a distant overtone of C (even though it has a much stronger relationship to E).
So both E and B can be heard to relate back down to C, as the natural acoustic root of all 3 notes. B is part of E, but E is in turn part of C.
C is not part of the harmonic series of E or B, so can't "belong" to E or B in the same way as they "belong" to C.
Quote by jerrykramskoy

I've never yet heard a chord (across whatever instruments) that has at least one p5th in it, where the lower note of the p5th doesn't sound like the chord root (or where there are multiple p5ths, the lower note of the lowest.
I agree in general, and certainly about multiple 5ths.
But other interval relationships do have an impact, and in cases like C-E-B they can override the power of the 5th.
Quote by jerrykramskoy

Have to be careful naming chords.

Try these 2 chords, let me know which note you hear as the root in each:

8 8
8 5
5 5
7 7
I'll play. (Assuming top 4 strings, yes?)
C for the first, A for the second.
The first is more ambiguous though. I'd say 60/40 for C, while the second is 90/10 for A.

How about this one?
5
5
5
5



and what's your take on this?
5
5
4
4
Last edited by jongtr at Feb 22, 2016,
#32
Quote by cdgraves
Aurally, but not functionally. +6, #9, etc. But I do agree interval is strictly a measure of distance while function depends on the context.
I think there's three things.
Two kinds of "root" for an interval.
I.e., yes in the first instance, an interval is simply a measure of distance, from lower note to upper note.
But either one of the notes - or maybe neither - might be perceived as an aural (acoustic) root.

In the case of a perfect 4th, the measure is uncontroversial. 4 notes inclusive bottom to top, spanning 5 half-steps. The lower note is the "1st" by definition. The "nominal root" in the sense that that's the note we decide to count from, after which we name the interval.
But the acoustic root is the top note. In isolation, therefore, it sounds like an inverted 5th.

The third element is context, which provides other interval relationships which may alter both the actual measure (ie what we call the top note relative to the context), and the aural perception of the interval.

So the top note will sound like a 4th, if the context determines that the lower note is the overall acoustic root of the context (eg the chord).
IOW, the more we strengthen the claim of the lower note to be the acoustic root (usually by adding the 5th of the lower note), the more the upper note sounds like a dissonance.
The perfect 4th in isolation, however, is a strong consonance - because we perceive the upper note as the root.

Then again, we can take a G-C 4th and place it in an Am7 chord. That changes things all over again, because we now define each note in relation to the A root.
However, how we hear it might still be ambiguous. Is it C6 or Am7? What effect does including or omitting the E have? What effect do different voicings of the chord have?

IOW, just as with intervals, the nominal root of a chord may not be identical with the acoustic root. It just depends on why we are naming it.
#33
Quote by jongtr
I think there's three things.
Two kinds of "root" for an interval.
I.e., yes in the first instance, an interval is simply a measure of distance, from lower note to upper note.
But either one of the notes - or maybe neither - might be perceived as an aural (acoustic) root.

In the case of a perfect 4th, the measure is uncontroversial. 4 notes inclusive bottom to top, spanning 5 half-steps. The lower note is the "1st" by definition. The "nominal root" in the sense that that's the note we decide to count from, after which we name the interval.
But the acoustic root is the top note. In isolation, therefore, it sounds like an inverted 5th.

The third element is context, which provides other interval relationships which may alter both the actual measure (ie what we call the top note relative to the context), and the aural perception of the interval.

So the top note will sound like a 4th, if the context determines that the lower note is the overall acoustic root of the context (eg the chord).
IOW, the more we strengthen the claim of the lower note to be the acoustic root (usually by adding the 5th of the lower note), the more the upper note sounds like a dissonance.
The perfect 4th in isolation, however, is a strong consonance - because we perceive the upper note as the root.

Then again, we can take a G-C 4th and place it in an Am7 chord. That changes things all over again, because we now define each note in relation to the A root.
However, how we hear it might still be ambiguous. Is it C6 or Am7? What effect does including or omitting the E have? What effect do different voicings of the chord have?

IOW, just as with intervals, the nominal root of a chord may not be identical with the acoustic root. It just depends on why we are naming it.


I don't agree with this. The root determination comes first (based on the various intervals present in the chord), and as a result, the naming of the chord around the root arises.

I certainly agree that certain chord voicings / tone omissions will change the chord root. In your example, omit the E, and the strongest root is the C, so C6.

Re- the Cmaj7 without the G, we did an experiment on this (a poll) on Tom Hess a while back, and the consensus came back with the E as root (I think it was around 70% of folk heard it that way). But don't forget that hearing is down to cognitive perception ... and apparently the ear itself physically induces pitches that don't exist in the original sound (due to differences in sound pressure across the ear drum) ... and also very much depends on frequency range as to bass response etc (Fletcher-munson)
#35
Quote by jerrykramskoy
I don't agree with this. The root determination comes first (based on the various intervals present in the chord), and as a result, the naming of the chord around the root arises.
I'm not sure I follow that sentence, but if it means what I think it does, I have no disagreement.

What I meant by my last sentence in the above post was that there are occasional chords whose acoustic root is ambiguous, and we might name them either way depending on context.
And even where the sound of a chord might point one way, we might name it another for contextual reasons. Eg, a chord built A-C-G-C might be named Am7 for good contextual reasons, even though C is stronger acoustically.

Likewise, C-E-B is going to be named Cmaj7, and not "E5b6" or something equally bizarre.
Quote by jerrykramskoy

Re- the Cmaj7 without the G, we did an experiment on this (a poll) on Tom Hess a while back, and the consensus came back with the E as root (I think it was around 70% of folk heard it that way).
That is interesting!
I don't suppose you included various different voicings or registers for the chord, to see if that made a difference?

My own perception of it is certainly ambiguous. C is not a "obvious" root to my ears, and definitely fights it out with E. It may well be that my musical experience, my "theoretical prejudice" if you like, comes down in favour of C.
Quote by jerrykramskoy

But don't forget that hearing is down to cognitive perception ... and apparently the ear itself physically induces pitches that don't exist in the original sound (due to differences in sound pressure across the ear drum) ... and also very much depends on frequency range as to bass response etc (Fletcher-munson)
Sure.
There is the physical perception of the frequencies, via the mechanics of the ear, and there is a mental interpretation of them (into what we call "sound") - and then a cultural interpretation on top of that, into a musical entity, a "chord" of some kind.
The responses of non-musicians, as well as musicians from different cultures, would be equally interesting.
#36
Re the CMaj7...as above about different voicings and was it a stand alone chord or was it in context preceded by other chords? Put a G7 before it and do the poll again.
Si
#37
Quote by 20Tigers
Re the CMaj7...as above about different voicings and was it a stand alone chord or was it in context preceded by other chords? Put a G7 before it and do the poll again.


Hi 20Tigers.
That was just the chord stand-alone.

It's fascinating how the brain both retains sounds, and anticipates future sounds.

I'm sure if G7 preceded, then C would win. I hear C as root, probably because that G is lingering in my head?

So, yes, it's not black and white once there are surrounding progressions, melody ... but the interval analysis of standalone chord is very useful ... if nothing else if points out an unintended interpretation of that chord, which needs tending to (either change the voicing) or provide surrounding context to influence, as you correctly point out.

Obviously we rarely deal in isolation, but this kind of knowledge does help.
#38
Naming chord roots out of context is pretty academic. In reality C E B is going to be Cm7 most of the time and E6 some of the time and potentially something else depending on its context. Without context though any chord is just a collection of notes and it doesn't really matter what its root is. In this case the root is ambiguous with no other information given (although I tend to hear the root as C).
#39
Quote by jazz_rock_feel
Naming chord roots out of context is pretty academic. In reality C E B is going to be Cm7 most of the time and E6 some of the time and potentially something else depending on its context. Without context though any chord is just a collection of notes and it doesn't really matter what its root is. In this case the root is ambiguous with no other information given (although I tend to hear the root as C).


Agreed. (I assume Cm7 is a typo?)