Jump to content

INTERVALS explained - The Magical Unicorn World of Music Theory!


Recommended Posts

  • Members

Sorry for the tease, but there are no Unicorns here (it's actually just a feral cat in a unicorn costume), but there is a "smidgen" of magic none the less!
 

00 My Little Pony.jpg

 

Anyway, here's my comparatively lifeless, colorless, not quite so cute introduction...


MUSIC THEORY basically exists to explain how various sounds work together - but not just any old sounds - a "structurally consistent set of sounds" as it relates to music... and it all begins with something we affectionately call a “Pitch”.

When it comes to music, a “Pitch” can be simply defined as “a single, definable, recognizable and reasonably pleasing sound” - such as a string being plucked on a guitar.

While a single Pitch can be, ummm... “nice”, us humans have developed an insatiable appetite for listening to more than one Pitch - and that’s where “Intervals” come into play...

An “Interval” can be basically defined as “The sound created when two pitches are played and the 'distance' between them”.

When two Pitches are played one after another, that interval is considered to be “Melodic”.

“Scales” are melodic.

When two Pitches are played together at the SAME time, that interval is considered to be “Harmonic”.

“Chords” are harmonic *(when the notes are are allowed to ring out simultaneously).

~~


Most of the music we are familiar with in the 21st Century, such as Rock, Classical, Country, Disco, Jazz and, yes, even Hip Hop, aligns itself to what is universally referred to as "Western Music".

While Western Music has been described as a "Major / minor system" (I even mention the importance of "Major 3rds" and "minor 3rds" several times below), in this discussion our focus is most notably based on the concept of a 12-note “Chromatic Scale”.

If you play all the black and white keys on the piano consecutively, you are playing “Chromatically”

 

1 PIANO - Chromatic Generic.jpg




Similarly, if you start at the bottom of the low E-string on a guitar and play every note from the nut to the the 12-fret you are ALSO playing “Chromatically”

Assuming you started with the “low E” note on the fattest string on a typical guitar and played each note up to the "12th-fret E" note, you would be playing the “E Chromatic Scale”.

 

2 GUITAR - E Chromatic Scale.JPG





*So if you've ever wondered about the significance of the 12th fret on the guitar... well... now you know!


~~


Going back to the piano... the single WHITE key that’s to the left of the TWO BLACK keys is called “C”

 

3 PIANO ''C''.jpg




If you were to play that key, along with the next 12 consecutive keys, you would be playing the “C Chromatic Scale”:

 

4 PIANO - C Chromatic.jpg




Here are the twelve notes of the “C Chromatic Scale” *(the “C” notes are only counted once):

C
C#/D♭
D
D#/E♭
E
F
F#/G♭
G
G#/A♭
A
A#/B♭
B
C

 

5 PIANO - C Chrom Notes.jpg




As you can see, the notes on the black keys have two names. Anytime a sound or a note has two or more names in Music it is said to be “Enharmonic”.



~~



Going from “C” to “C#/D♭” is measured as an interval of a “Half-Step” or “Half-Tone” or “Semi-Tone”, depending on things we won’t get into right now.



Two “Half-Steps” equals a “Whole-Step” and two “Half-Tones” or two “Semi-Tones” equals a “Whole-Tone”.

For the time being we’re just going to stick with the term “Half-Step”.



So, as I mentioned a moment ago, “C” to “C#/D♭” is a “Half-Step”... but it has also been given a certain Interval Name. Actually it has more than one interval name, therefore it’s considered to be “Enharmonic”.

But, before I give you all those names I’d like to point out that going from “C” to “C” (if you’re playing the exact same pitch twice) also has a name: It’s called a “Unison”.




*A quick side note regarding the “Unison”:

On a traditional piano it is virtually impossible to play two of the exact same pitch at the same time (Harmonically) but on the guitar (and other stringed instruments) you can easily play the same pitch on two or more strings at the same time.

But even if you play the same pitch back to back (Melodically) it’s still called a Unison.

Anyway, just to be all-inclusive, if you happen to have two pianos sitting side-by-side next to each other, you could then happily play a Unison Harmonically on them... so there ya go...



~~


If a note is shown to have a single letter name and nothing else, it is considered to be "Natural". For instance a "G" note by itself is a "G Natural" ("G♮" or just a "G"). But if you go UP a "half-step" it would be called a "G#" (G Sharp), and conversely, if it went DOWN a "half-step" it would be called a "G♭" (G Flat). BUT, if you go UP a "half-step" from "G♭" or DOWN a "half-step" from G#", then you would be back at "G Natural".

To make things even more complicated, a "G#" can also be called "A♭", and a "G♭" can also be called an "F#" (their "Enharmonic Equivalents"). The reasons have to do with what key you're in and other functions that we won't worry about now.

*Note: There are also "Double Sharps" and "Double Flats", but we'll just stick the regular ones right now as well.

The "Natural", "Sharp" and "Flat" are identified by symbols called "Accidentals". In music, the word "Accidental" has two meanings, but in our case it just refers to the symbols that are added to notes to identify them:
 

6 # b Natural signs.jpg



*Notice how a "Natural" sort of looks like a "Sharp" with most of its tips cut off...

*Also note that a "Natural" sign is only used when needed, such as when they would normally be "Sharp" or "Flat" in a piece of music.


~~~


Anyway, going back to Intervals... If you play from one “C” to another “C” twelve keys away on the piano, that is called the “Octave”:

 

7 PIANO - C Octave.jpg




If you play JUST the eight WHITE KEYS from “C” to “C” within the range of those twelve keys, you’d be playing the “C Major Scale” (what makes it a Major Scale will be further explained later on)... and the notes of the C Major Scale are:

C
D
E
F
G
A
B
C

In Music Theory numbers are often assigned to each consecutive note in a certain key:

C-1
D-2
E-3
F-4
G-5
A-6
B-7
C-1

These are called “Arabic Numerals”, for those who are fond of that term, but I just refer to them as “Numbers” myself.

These numbers represent what is often referred to as "Scale Degrees":

In the “Key of C” the note “C” would be “1”, the note “D” would be “2” and so on...

In Music Theory “Scale Degree” numbers are also shown as “Roman Numerals”:

C - I
D - II
E - III
F - IV
G - V
A - VI
B - VII
C - I

If you've ever read or heard the phrase; "Play I-IV-V-I in the Key of C Major" that typically means "Play a C Major chord, then an F Major chord, then a G Major chord, then back to a C Major chord"...

Also notice how the first note and the last note are both either “1” or “I”.

So, in the “Key of C”, the note “C” is essentially considered to be the same, no matter where it’s played - just at a higher or lower pitch. The beginning and the end. The Alpha and the Omega... the relevancy of which is just so mindbogglingly profound that I would run the risk of literally breaking your brain trying to explain it!

That’s exactly why in the “Key of C” the pitch “C” also has very VERY special name, and is called the “Tonic”.

In the Key of D the Tonic is “D”.
In the Key of G♭ the Tonic is “G♭”.
In the Key of Bm the Tonic is “B”.
In the Key of C#m the Tonic is “C#”.

“Tonic” means “Tonal Center”.

No matter which key you are playing in, EVERYTHING revolves around the “Tonic”!



~~



So, as to how the Tonic relates to “Interval Names”, we’ve already learned about the “Unison” and the “Octave”:

"Low C" to "Low C" (same C) “Unison”
C to D
C to E
C to F
C to G
C to A
C to B
"Low C" to "High C" “Octave”


In between these two extremes the rest of the notes are mostly labeled by their “Scale Degree”. *(They too have other fancy names, but nothing we have to get into right now).

Using the notes of the “C Major Scale” you can easily see that “D” is some sort of “2nd” and “E” is some sort of “3rd”, etc:

C
D-2
E-3
F-4
G-5
A-6
B-7
C
 

12 PIANO Intervals.jpg





But if you look at ALL of the notes between the Unison and the Octave you’ll see that there’s a lot more than seven notes:

C
C#/D♭
D
D#/E♭
E
F
F#/G♭
G
G#/A♭
A
A#/B♭
B
C
 

13 PIANO 12 half steps.jpg





So, how does one go about labeling the intervals between the Unison and Octave when there are twelve notes involved?

Well, that’s where the “Half-Steps” come into play...

Before I go any further, it would be my pleasure to introduce the five “Qualities of Intervals":

Perfect
Major
minor
Augmented
diminished


Notice how the “Perfect”, “Major” and “Augmented” intervals start with “Upper Case” letters, while “minor” and “diminished” intervals have “lower case” letters.



These are listed in order of what degree the Interval is “Consonant” or “Dissonant”.

“Perfect” is the most “Consonant” (stable), while “diminished” is the most “Dissonant” (unstable).

But don’t confuse “Dissonance” with “Discordance”, since Discordance is noise.

By “Stable” we mean “Rest”. The more Consonant something is, the more “satisfying” the “state of rest” it’s in.

The more “Dissonant” something is, the more it wants to go somewhere else.



*Special Note: As you will see in a bit, not all “diminished” or “Augmented” Intervals are “Dissonant”, which we’ll address shortly.



~~~



So, getting back to the “Half-Step” discussion, here is the amazing “Half-Step List” *(you can just skim through these right now since they'll be whittled down quite a bit soon😞


(0) Zero Half-Steps = “Unison”.

(1) One Half-Step = “Augmented Unison” or “minor 2nd”

(2) Two Half-Steps = “Major 2nd” (or "diminished 3rd")

(3) Three Half-Steps = “Augmented 2nd” or “minor 3rd”

(4) Four Half-Steps = “Major 3rd” (or “diminished 4th”)

(5) Five Half-Steps = “Augmented 3rd” or “Perfect 4th”

(6) Six Half-Steps = “Augmented 4th” or “diminished 5th”

(7) Seven Half-Steps = “Perfect 5th” (or "diminished 6th")

(8) Eight Half-Steps = “Augmented 5th” or “minor 6th”

(9) Nine Half-Steps = “Major 6th” or "diminished 7th"

(10) Ten Half-Steps = “Augmented 6th” or “minor 7th”

(11) Eleven Half-Steps = “Major 7th" (or "diminished Octave")

(12) Twelve Half-Steps = “Augmented 7th” or “Perfect Octave”



A couple clarifications before we continue...

Any Perfect or Major interval that goes UP in pitch a half-step becomes “Augmented”.

Any Perfect or minor interval that goes DOWN in pitch a half-step becomes “diminished”.

Any Major interval that goes DOWN in pitch a half-step becomes “minor”.

Any minor interval that goes UP in pitch a half-step becomes “Major”.



~~



There are some glaring contradictions with how those intervals were labeled though...

For one thing, why would a “Perfect” interval be anything but perfect?

Well, the short answer is that they are almost always Perfect, with VERY few exceptions.

Similarly, a “Major 3rd” or “minor 3rd” are rarely, if ever, considered to be anything other than Major or minor, since they are crucial in defining the Key, Chord or Scale which they are a part of.


(continued)...



`

Link to comment
Share on other sites

  • Members

INTERVALS Explained - PART 2


Let’s go over each "questionable interval label” one by one and see what makes sense...


*Note: As a preface to the following comments below, I'd just like to mention that some of the labels attached to the various Interval types listed earlier are either purely "academic" (works in theory but doesn't really help anyone create actual music) or were made in relation to tuning systems, musical structures and other factors from the "olden days" that don't readily apply as well today, and, barring some obscure theoretical context (that conveniently explains certain rarely used applications), most of my observations are just meant to point out why I wouldn't put too much effort into justifying them myself.

Others may not totally agree with some of my views though, but I wouldn't say it's a "right or wrong" thing, but more like a "theoretical debate" thing...

**EDIT: As predicted, there are already several comments made addressing my personal views below - so (to avoid repeating the same things over and over) for those of you who are knowledgeable about Music Theory that disagree with my assertions, please scroll past these lessons and read the commentary following it before adding the same redundant points. Thanks!



Anyway, my personal perspective as it applies to "old rules" in "modern times":

(1) Augmented Unison / minor 2nd

The "Unison" is pure and angelic compared to the "finger nails on the chalkboard" minor 2nd, so intertwining those two labels seems counter-intuitive at the very least.

There may be some convincing argument for an “Augmented Unison” somewhere, but, as far as I’m concerned, a Unison is a Unison and ain’t no Augmented nothing!

(3) Augmented 2nd / minor 3rd

Harmonically speaking, I'm not particularly enamored with calling something an "Augmented 2nd", since, for reasons difficult to explain right now, an "Augmented 2nd" is more likely to be (for instance) a "#9th" in a Major chord, (the interval of a "9th" will be discussed in a bit). So the short answer is that an "Augmented 2nd" doesn't really exist in a minor chord (due to the already present "minor 3rd") and is most likely to be a "9th" in a Major chord.

Where melody is concerned, an "Augmented 2nd" in a scale may occur as an odd "one and a half step leap" from the expected "whole-step" movement normally anticipated by a listener and, due to that impact, certainly has relevancy when describing it's peculiar sound at times.

But Harmonically speaking, since the "minor 3rd" is such a crucial part of what defines Western Music (along with the "Major 3rd"), I don't find myself drawn to calling something an Augmented 2nd in that context unless absolutely necessary... as further explained in the next paragraph...

(4) Major 3rd /diminished 4th

There are apparently reasons to use the description "diminished 4th" in a scale, but these are almost always "theoretical" reasons and, while they make sense in certain situations (like a "Melodic Leap" similar to what was described in the "Augmented 2nd" section), the choice of a "diminished 4th" on a whole is only useful for staying within certain theoretical boundaries rather than sonically making any real musical sense.

While there are no doubt nit-picky theoretical reasons for wanting to call something a "diminished 4th" in Harmony, the fact that the Major 3rd (along with the minor 3rd) is so critical to the tonality of all Western Music, that leads me to relegate the "diminished 4th" to being more like an easily avoidable "foot-note" rather than something worth any serious consideration here in the 21st century.

I'd even go out on a limb and state that a Major 3rd is JUST AS important as a Perfect 5th (if not more so at times). And, by that logic, since the Perfect 4th would technically be next in line to those two, labeling something as a "diminished 4th" is so far removed from all of them that it really ends up being a non-factor to me...

(5) Augmented 3rd / Perfect 4th

Calling a Perfect 4th something other than a Perfect 4th requires some fancy explaining in my book. In that same sense, putting something that's not "Perfect" into that category is also much too ambiguous to be worth arguing about as well.

(6) Augmented 4th / diminished 5th

I get why you'd want a raised Perfect 4th to be called "Augmented", but your ears will tell you that it's diminished. By the way, the six half-steps that makes up the Augmented 4th / diminished 5th is also called a "Tritone".

Plus, add the fact that a lot of chords call it a "♭5" (flatted 5th or just "flat 5"), and this interval suddenly has four "Enharmonically Equivalent" names!

(7) Perfect 5th / diminished 6th

Really?

The Perfect 5th is not a "diminished anything" and, like the ambiguous "Augmented 3rd / Perfect 4th", this discussion can only move forward if some obscure archaic analogy is needed to be made, which ain't very often... 'nough said...

(9) Major 6th / diminished 7th

There is actually a case for having a “diminished 7th” and that mostly has to do with how it’s used as part of a “diminished 7th chord”.

(10) Augmented 6th / minor 7th

Just like the Unison / Octave / both Major & minor 3rds and both Perfect 4th & 5th, the "minor 7th" has become such an integral part of Western Music that calling it an "Augmented 6th" requires special consideration as well, but is not beyond the realm of possibilities... theoretically speaking.


(12) Augmented 7th / Octave

In my world an Octave is an Octave is an Octave... Period. End of story.


~~


So here's my "Revised Interval Half-Step" list that applies to 99.999% of what most of us will need to remember:

(0) Zero Half-Steps = “Unison”.

(1) One Half-Step = “minor 2nd”

(2) Two Half-Steps = “Major 2nd”

(3) Three Half-Steps = “minor 3rd” 
(Augmented 2nd Melodically)

(4) Four Half-Steps = “Major 3rd”

(5) Five Half-Steps = “Perfect 4th”

(6) Six Half-Steps = “Augmented 4th” or “diminished 5th” (Tritone)

(7) Seven Half-Steps = “Perfect 5th”.

(8) Eight Half-Steps = “Augmented 5th” or “minor 6th”

(9) Nine Half-Steps = “Major 6th” or “diminished 7th”

(10) Ten Half-Steps = “minor 7th”

(11) Eleven Half-Steps = “Major 7th"

(12) Twelve Half-Steps = "Octave”



You don’t necessarily have to memorize all the half-steps right now... but it certainly doesn’t hurt!


~~


Before we move on I'd like to point out that these intervals can be preceded by single letters notating the Interval's quality, such as "P4" for "Perfect 4th" and "m3" for "minor 3rd".

This follows the same Upper and lower case lettering guidelines as listed before (“Perfect”, “Major” and “Augmented” intervals start with “Upper Case” letters, while “minor” and “diminished” intervals have “lower case” letters), although "Augmented" intervals can be preceded by a "#" sign (sharp) and "diminished" intervals can be preceded by a "♭" sign (flat).

If you look at my previous examples you might get the impression that all intervals start at the first note of a scale, but that is FAR from the truth!

Sure you CAN start at the first note of a scale, like, if you're starting with "C" and go to "D", that would be a "Major 2nd" (counting the half-steps will verify this):


C-(1)
D-(M2) "Major 2nd"
E
F
G
A
B
C


If you start with "C" and go to "E", that is called a "Major 3rd":

C-(1)
D
E-(M3) "Major 3rd"
F
G
A
B
C

And, if you start with "C" and go to "G", that is called a "Perfect 5th":

C-(1)
D
E
F
G-(P5) "Perfect 5th"
A
B
C


BUT! You can also start on "D" and go to "E", which is ALSO a "Major 2nd":

C
D-(1)
E-(M2) "Major 2nd"
F
G
A
B
C

Similarly, going from "F" to "A" is also a "Major 3rd":

C
D
E
F-(1)
G
A-(M3) "Major 3rd"
B
C

And, once more, going from "E" to "B" is yet another "Perfect 5th":

C
D
E-(1)
F
G
A
B-(P5) "Perfect 5th"
C


We can also extend this scale into the next Octave and add more Intervals in similar ways. The following is a "minor 3rd":

C
D
E
F
G
A
B-(1)
C
D-(m3) "minor 3rd"
E
F
G
A
B
C


This one is a "diminished 5th":

C
D
E
F
G
A
B-(1)
C
D
E
F-(♭5) "diminished 5th"
G
A
B
C


And, finally, a "Major 7th" followed by a "minor 7th":


C
D
E
F-(1)
G
A
B
C
D
E-(M7) "Major 7th"
F
G
A
B
C



C
D
E
F
G-(1)
A
B
C
D
E
F-(m7) "minor 7th"
G
A
B
C


So, as you can see, an Interval is an Interval is an Interval, no matter where it starts!


Let's "modify" a scale to produce an "Augmented 5th" Interval (which does not naturally occur in a Major Scale). Note how the accidental "#" ("sharp") is added to the "G" note to create an "Augmented 5th":

C-(1)
D
E
F
G#-(#5) "Augmented 5th"
A
B
C


Here's another "Augmented 5th":


C
D-(1)
E
F
G
A#-(#5) "Augmented 5th"
B
C


And one more "Augmented 5th":

C
D
E
F-(1)
G
A
B
C#-(#5) "Augmented 5th


Plus, let's not forget the "diminished 5th" (aka "Flatted 5th"):

C-(1)
D
E
F
G♭-(♭5) "diminished 5th" / "Flatted 5th"
A
B
C

And:


C
D
E-(1)
F
G
A
B♭-(♭5) "diminished 5th" / "Flatted 5th"
C

Oh, yeah, of course there is the ubiquitous "minor 3rd":

C-(1)
D
E♭-(♭3) "minor 3rd"
F
G
A
B
C


C
D
E
F-(1)
G
A♭-(♭3) "minor 3rd"
B
C



~~


Intervals can also be "Inverted"...

Starting with "F" and going UP to "C" there's a "Perfect 5th":

C
D
E
F-(1)
G
A
B
C-(P5) "Perfect 5th"


But, starting with "F" and going DOWN to "C" it becomes a "Perfect 4th":

C-(P4) "Perfect 4th"
D
E
F-(1)
G
A
B
C
 

11 PIANO Inversions.jpg





A similar (but somewhat different) thing happens with all the intervals...


The "minor 2nd" becomes a "Major 7th":

C
D
E
F
G
A
B-(1)
C-(m2)


C-(M7)
D
E
F
G
A
B-(1)
C


The "Major 2nd" becomes a "minor 7th":

C-(M2)
D-(1)
E
F
G
A
B
C


C
D-(1)
E
F
G
A
B
C-(m7)


The "Major 3rd" becomes a "minor 6th":

C-(M3)
D
E-(1)
F
G
A
B
C


C
D
E-(1)
F
G
A
B
C-(m6)


The "minor 3rd" becomes a "Major 6th":

C
D-(m3)
E
F-(1)
G
A
B
C


C
D
E
F-(1)
G
A
B
C
D-(M6)


Going even farther beyond the Octave we get "9ths", 11ths" and 13ths:

C-(1)
D
E
F
G
A
B
C
D-(9th)
E
F
G
A
B
C



C-(1)
D
E
F
G
A
B
C
D
E
F-(11th)
G
A
B
C



C-(1)
D
E
F
G
A
B
C
D
E
F
G
A-(13th)
B
C



A "9th" has the same notes as a "2nd":


C-(1)
D
E
F
G
A
B
C
D-(9th)
E
F
G
A
B
C


C-(1)
D-(2nd)
E
F
G
A
B
C



An "11th" has the same notes as a "4th"

C-(1)
D
E
F
G
A
B
C
D
E
F-(11th)
G
A
B
C


C-(1)
D
E
F-(4th)
G
A
B
C


A "13th" has the same notes as a "6th"

C-(1)
D
E
F
G
A
B
C
D
E
F
G
A-(13th)
B
C



C-(1)
D
E
F
G
A-(6th)
B
C


Of course you can add sharps and flats to get ♭9ths and #11ths, etc.


Just a quick note about "9ths", "11ths" and "13ths" (and how they relate to "2nds", "4ths" and "6ths"). It's not just that they are an Octave higher than their lower counterparts, but chords that they are built on usually include other notes that change their overall character significantly. I'll address that better when I get to the parts that describe chords...



~~



So far we have been taking about music as if it is built entirely out of intervals...

...well... essentially it is!

BUT!

Of course there is more to it than that...


(continued)...



`

Link to comment
Share on other sites

  • Members

SCALES!


In its simplest form, a "Scale" is a series of "Pitches" arranged with a certain set of "Intervals" between each note. The Pitches that make up the notes in a scale defines that scale.

Before I go any further I really need to throw out another important term: "Diatonic".

"Diatonic" refers to the notes that are part of a specific Key, the scale that defines that Key, as well as the chords made from those same notes (to be discussed more in the next post)...

Scales are also called "Modes" and the terms are often used interchangeably, but just be aware that the scales or modes used in "Modal Music" are different than what is used for "Tonal Music". We are just interested in "Tonal Music" right now.

I'm not going to go too far into defining Scales in this discussion, except to outline what is often referred to as the "Major Scale", which I believe most people would agree is THEE MOST IMPORTANT scale in Western Music.

Going back to the piano keyboard, if you play all the WHITE keys from one "C" to the next "C" higher up, you are playing a "C Major Scale". In fact, the piano is the perfect platform for explaining almost everything in what we call "Western Music Theory".

If you play the notes of the C Major scale you should recognize the ever-so popular "Do-Re-Mi" scale often taught to school children (and sweetly sung by Julie Andrews in "The Sound of Music")...
 

9 Julie Andrews.JPG

 

10 PIANO - C Major Scale.jpg




So, what exactly makes this a "Major Scale"? Well, it's the "HALF-STEPS" of course!

Actually it's a combination of "Whole-Steps" and "Half-Steps" (remember, two "Half-Step" equals a "Whole-Step"). In a nutshell:


"C" to "D" is a Whole-Step.
"D" to "E" is a Whole-Step.
"E" to "F" is a Half-Step.
"F" to "G" is a Whole-Step.
"G" to "A" is a Whole-Step.
"A" to "B" is a Whole-Step.
"B" to "C" is a Half-Step.


W = Whole-Step
H = Half-Step

So the order is: W-W-H-W-W-W-H
 

11b PIANO - C Major Scale.jpg




If you start with ANY note on the piano and play the "Whole-Steps" and "Half-Steps" in that order (W-W-H-W-W-W-H), you will be playing a "Major Scale". Here are a few more examples:

Key of E Major:

"E" to "F#" is a Whole-Step.
"F#" to "G#" is a Whole-Step.
"G#" to "A" is a Half-Step.
"A" to "B" is a Whole-Step.
"B" to "C#" is a Whole-Step.
"C#" to "D#" is a Whole-Step.
"D#" to "E" is a Half-Step.
 

11 PIANO - E Major Scale.jpg




Key of D♭ Major:

"D♭" to "E♭" is a Whole-Step.
"E♭" to "F" is a Whole-Step.
"F" to "G♭" is a Half-Step.
"G♭" to "A♭" is a Whole-Step.
"A♭" to "B♭" is a Whole-Step.
"B♭" to "C" is a Whole-Step.
"C" to "D♭" is a Half-Step.
 

12 PIANO - Db Major Scale.JPG



Coincidentally there's this crazy thing called "The Circle of Fifths" that shows the amazing connections between all these notes and how they relate to each other:
 

Circle 5ths with staffs.png




As an added bonus here are the Whole/Half Steps for creating a minor scale:

W-H-W-W-H-W-W
 

13 PIANO - A minor Scale.JPG



`

Link to comment
Share on other sites

  • Members

TRIADS & CHORDS!


Chords are often built from the notes of a specific scale.

Basic "triads" are normally built from "every other note" in a scale *(a "Triad" is a chord made up of only three unique pitches).

A "Chord" is made up of three or more unique pitches - so a "triad" is also considered to be a "chord", but not all "chords" are necessarily "triads".


The reason "Triads" are so important is because they represent the basic building blocks of "Harmony" as it relates to what we call "Western Music".


For instance, (to refresh your memory) here are the notes for the Key of C Major:

C
D
E
F
G
A
B
C

Let's attach numbers to represent what is often referred to as "scale degrees":

C-1
D-2
E-3
F-4
G-5
A-6
B-7
C-1

If you are starting with "C" and go to "D", that is called a "2nd":

C-1
D-2
E
F
G
A
B
C

If you are starting with "C" and go to "E", that is called a "3rd":

C-1
D-2
E-3
F
G
A
B
C

BUT, you can start from any point in the scale and if you start with "E" and go to "G", that is ALSO called a "3rd":

C
D
E-1
F-2
G-3
A
B
C


====================

Let's take a small detour and revisit that term I mentioned in the "Scales" post: "Diatonic".

Once again, if I were to play the notes of the C Major Scale they would be:

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

So if I just played the note "F", you could say I played a note that was "Diatonic to the Key of C Major".

But if I were to play the note "F#", you would say that I just played a note that was "NOT Diatonic to the Key of C Major".

Anytime a note is introduced that is not part of a certain key, that note would be considered an "Alteration".

The reason I'm discussing it now is because the "Triads" and "Chords" in this post are mostly built using notes that are "diatonic" to a certain Major scale, but I didn't want to give the impression that all chords necessarily made this way (and how boring would THAT be?)...


====================


Triads are typically built using "3rds", starting with the "root". The term "Root" should not be confused with "Tonic" though... a "Tonic" relates to the "Tonal Center" and is the "Key Note" of the "Scale" that defines a specific "Key". A "Root" is the base note in a "Chord" which defines that chord. (*I added a brief note about the difference further below)...


The "root" is the often called the "first note" of a chord, so if we're building a chord off the first note in the Key of C, that root would be "C":

C < root
D
E
F
G
A
B
C

The notes C, E & G makes up the C Major triad:

"C" is the "root"
"E" is the "3rd"
"G" is the "5th"

C < root
D
E < 3rd
F
G < 5th
A
B
C

As you can see, we are using "every other note" here...

The "root" is the base note of a "triad". Going up a "3rd" takes you to the next note, which is the chord's actual "3rd". Going up another "3rd" gets you the chord's actual "5th".

In addition, there are "Major 3rds" and "minor 3rds"...

~

A "Major 3rd" is "4 half-steps" (starting from "C" then counting up chromatically: C-C#-D-D#-E). A "minor 3rd" is "3 half-steps" (starting from "C" then counting up chromatically: C-C#-D-D#) *Note: "C#" is the same pitch as "D♭" and "D#" is the same pitch as "E♭", so we could have just as easily counted up like this: C-D♭-D-E♭... thus...

Going from "C" to "E" is a "Major 3rd"
Going from "C" to "E♭" is a "minor 3rd"

Going from "E" to "G" is a "minor 3rd"
Going from "E" to "G#" is a "Major 3rd"

So, if you count the half-steps between C, E & G (which is a Major triad) it should make sense that a "Major Triad" is built by having a "Major 3rd" with a "minor 3rd" stacked on top of it:

C-E = Major 3rd
E-G = minor 3rd

C-E-G = C Major Triad
 

16a PIANO Major.jpg




BUT WAIT! You can start from ANY note in the scale... so, taking the same approach, you can start with "D" and do the same thing:

C
D < root
E
F < 3rd
G
A < 5th
B
C

The notes D, F & A makes up the "D minor" or "Dm" triad.

In this case, if you count the "half-steps" you'll find that a "minor Triad" is built by having a "minor 3rd" with a "Major 3rd" stacked on top of it:

D-F = minor 3rd
F-A = Major 3rd

D-F-A = Dm Triad
 

16b PIANO minor.jpg




*Real quick... Notice how the Dm triad is built off the notes of the C Major scale, but, while "D" is the "Root" of the "Dm triad", "C" is still the "Tonic" of both that "Scale" and that "Key":

C - "Tonic"
D < root
E
F < 3rd
G
A < 5th
B
C - "Tonic"

And that's one reason why the notes of a "Dm triad" sound good when played in the Key of C Major...

*(Note that a Dm triad can be made from the notes of other keys and scales as well)!

~~~

While not diatonic to any Major key, you'll find that an "Augmented Triad" is built by having a "Major 3rd" with a "Major 3rd" stacked on top of it:
 

16a PIANO Augmented.jpg




Notice how an Augmented chord can also be abbreviated "C+".

~~

So, "most" triads built this way from any given Major scale are either "Major" or "minor", but in every Major Key there is also one "diminished Triad"...

In the Key of C Major that would be the "B diminished triad", which is built on the seventh degree of that scale (*the following scale has been expanded to better illustrate this):

C
D
E
F
G
A
B < root
C
D < 3rd
E
F < 5th
G
A
B
C

The notes B, D & F make up the "B diminished" or "B°" triad.

Note how a diminished chord or triad is written with the "°" following it, like A°, B°, C°, C#°, Db°... etc.

In this case, if you count the "half-steps" you'll find that a "diminished Triad" is built by having a "minor 3rd" with another "minor 3rd" stacked on top of it:

B-D = minor 3rd
D-F = minor 3rd

B-D-F = B° Triad

 

16c PIANO diminished.jpg




*As mentioned in a previous post, there is a common situation where an interval of a “diminished 7th” is used, and that would be as a part of a “diminished 7th chord” - which is what happens when you stack one more "minor 3rd" on top of a "diminished Triad":

B-D = minor 3rd
D-F = minor 3rd
F-A♭ = minor 3rd

B-D-F-A♭ = B°7 Chord
 

16d PIANO diminished 7th.jpg





But, let's say you raise that A♭ up one half-step and make it an "A Natural" (A♮):

B-D = minor 3rd
D-F = minor 3rd
F-A = Major 3rd

As you can see we stacked a "Major 3rd" on top of our "diminished Triad", making something that is often referred to as a "Half-diminished" chord, and written with a "ø" symbol:

B-D-F-A = Bø7 Chord

*I personally dislike the term "Half-diminished" because it is still FULLY diminished! Therefore I much prefer the following:

The so-call "Half-diminished chord" is also commonly referred to as a Bm7♭5 chord as well ("B minor 7th / flatted 5th"),

B-D-F-A = Bm7♭5

 

16e PIANO diminished m7th.jpg




At least Bm7♭5 makes a lot more sense than "Half-diminished" in my book. Of course some will argue that "Half-diminished" is easier to say, and is well established,... blaa...blaa... blaa...


*More importantly though:

Notice how I'm now referring to these examples as "Chords". Remember that the definition of a chord is "three or more unique pitches"? When you start adding 7ths, then they have definitely become chords!



Anyway, the main point is that you can build 7th chords, 9th chords, etc, in a similar fashion...

~~

Sooo... up until very recently we had been using only three notes at a time, but now it's quite obvious that you can keep on stacking 3rds and get more chords:

C < root
D
E < 3rd
F
G < 5th
A
B < 7th
C
D < 9th
E
F < 11th
G
A < 13th
B
C

If you played all these notes together that would be considered to be some sort of "13th chord", but the reality is that you will rarely play a chord this way in an actual piece of music.

For one thing, some of these notes will clash with other notes...


For instance, in the Key of C Major the "11th" and the "4th" are both "F":

C < root
D
E
F < 4th
G
A
B
C
D
E
F < 11th
G
A
B
C

If you also played a "Major 3rd" (E) it would clash with the (F), since they are only a "half-step" away from each other and the sound would be very "dissonant" (of course if you want dissonance then it's okay):

C < root
D
E < 3rd
F < 4th/11th
G
A
B
C

Plus, since there are so many notes (which can be fairly difficult to play) oftentimes other notes are omitted, such as the "5th" or the even the "root"! It really depends on the piece being played and the 13th chord's relationship with the other chords coming before and after it. So a typical "C13" chord might only have these notes:

C
D
E < 3rd
F
G
A
B < 7th
C
D < 9th
E
F
G
A < 13th
B
C


~~~


Now, if we go back to something I mentioned awhile ago, the interval of a "13th" and the "6th" are the same notes (A):

C < root
D
E
F
G
A < 6th
B
C
D
E
F
G
A < 13th
B
C


So, why is the chord called a "13th" and not a "6th"?

Well, that also has to do with how the chord is to be used, but in a nutshell, a "C6 Chord" would mostly just have the "6th" added to the "C Triad"...

C < root
D
E < 3rd
F
G < 5th
A < 6th
B
C
D
E
F
G
A
B
C

...while a "C13 Chord" usually (but not always) has the 7th and 9th as well, which is what makes it sound unique (notice how the "A" is no longer considered to be a "6th" anymore - although the "A" would ideally be as far from closely adjacent notes as possible in most cases):


C < root
D
E < 3rd
F
G < 5th
A < 13th
B < 7th
C
D < 9th
E
F
G
A < 13th
B
C

~~

One last thing I'd like to mention is that, like intervals, chords can also be inverted.

For instance, lets take a C Major chord with the notes C-E-G, but instead of C being at the bottom (the "Bass") we can have the "E" or the "G" at the bottom:
 

17a PIANO Major Root Pos.JPG

 

17b PIANO Major 1st inversion.JPG

 

17c PIANO Major 2nd inversion.JPG




A couple of things to point out are:

1) The "Bass" note is the note with the lowest pitch.
2) The Bass note defines the two Inverted chords - the order of the other notes does not change what it's called.
3) When the Root is in the Bass, the chord is said to be in "Root Position"
4) When the 3rd is in the Bass, the chord is said to be in "First Inversion"
5) When the 5th is in the Bass, the chord is said to be in "Second Inversion"


Also notice how the intervals between the notes change, I mean, they're all the same notes, right? But each arrangement has a slightly different character depending in how the notes are ordered... hmmm... interesting...

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Anyway, I think that is quite enough information to chew on for the time being don't you think?

Now that you know the basics of Western Harmonic Music it should be a lot easier to connect both the sounds and the language in Music Theory and hopefully it will help you to proceed with a greater understanding and confidence going forward...

GOOD LUCK!





 

`

Edited by axemanvr
Link to comment
Share on other sites

  • 1 year later...
  • Members
On 5/3/2022 at 6:47 PM, axemanvr said:

Sorry for the tease, but there are no Unicorns here (it's actually just a feral cat in a unicorn costume), but there is a "smidgen" of magic none the less!
 

00 My Little Pony.jpg

 

Anyway, here's my comparatively lifeless, colorless, not quite so cute introduction...


MUSIC THEORY basically exists to explain how various sounds work together - but not just any old sounds - a "structurally consistent set of sounds" as it relates to music... and it all begins with something we affectionately call a “Pitch”.

When it comes to music, a “Pitch” can be simply defined as “a single, definable, recognizable and reasonably pleasing sound” - such as a string being plucked on a guitar.

While a single Pitch can be, ummm... “nice”, us humans have developed an insatiable appetite for listening to more than one Pitch - and that’s where “Intervals” come into play...

An “Interval” can be basically defined as “The sound created when two pitches are played and the 'distance' between them”.

When two Pitches are played one after another, that interval is considered to be “Melodic”.

“Scales” are melodic.

When two Pitches are played together at the SAME time, that interval is considered to be “Harmonic”.

“Chords” are harmonic *(when the notes are are allowed to ring out simultaneously).

~~


Most of the music we are familiar with in the 21st Century, such as Rock, Classical, Country, Disco, Jazz and, yes, even Hip Hop, aligns itself to what is universally referred to as "Western Music".

While Western Music has been described as a "Major / minor system" (I even mention the importance of "Major 3rds" and "minor 3rds" several times below), in this discussion our focus is most notably based on the concept of a 12-note “Chromatic Scale”.

If you play all the black and white keys on the piano consecutively, you are playing “Chromatically”

 

1 PIANO - Chromatic Generic.jpg




Similarly, if you start at the bottom of the low E-string on a guitar and play every note from the nut to the the 12-fret you are ALSO playing “Chromatically”

Assuming you started with the “low E” note on the fattest string on a typical guitar and played each note up to the "12th-fret E" note, you would be playing the “E Chromatic Scale”.

 

2 GUITAR - E Chromatic Scale.JPG





*So if you've ever wondered about the significance of the 12th fret on the guitar... well... now you know!


~~


Going back to the piano... the single WHITE key that’s to the left of the TWO BLACK keys is called “C”

 

3 PIANO ''C''.jpg




If you were to play that key, along with the next 12 consecutive keys, you would be playing the “C Chromatic Scale”:

 

4 PIANO - C Chromatic.jpg




Here are the twelve notes of the “C Chromatic Scale” *(the “C” notes are only counted once):

C
C#/D♭
D
D#/E♭
E
F
F#/G♭
G
G#/A♭
A
A#/B♭
B
C

 

5 PIANO - C Chrom Notes.jpg




As you can see, the notes on the black keys have two names. Anytime a sound or a note has two or more names in Music it is said to be “Enharmonic”.



~~



Going from “C” to “C#/D♭” is measured as an interval of a “Half-Step” or “Half-Tone” or “Semi-Tone”, depending on things we won’t get into right now.



Two “Half-Steps” equals a “Whole-Step” and two “Half-Tones” or two “Semi-Tones” equals a “Whole-Tone”.

For the time being we’re just going to stick with the term “Half-Step”.



So, as I mentioned a moment ago, “C” to “C#/D♭” is a “Half-Step”... but it has also been given a certain Interval Name. Actually it has more than one interval name, therefore it’s considered to be “Enharmonic”.

But, before I give you all those names I’d like to point out that going from “C” to “C” (if you’re playing the exact same pitch twice) also has a name: It’s called a “Unison”.




*A quick side note regarding the “Unison”:

On a traditional piano it is virtually impossible to play two of the exact same pitch at the same time (Harmonically) but on the guitar (and other stringed instruments) you can easily play the same pitch on two or more strings at the same time.

But even if you play the same pitch back to back (Melodically) it’s still called a Unison.

Anyway, just to be all-inclusive, if you happen to have two pianos sitting side-by-side next to each other, you could then happily play a Unison Harmonically on them... so there ya go...



~~


If a note is shown to have a single letter name and nothing else, it is considered to be "Natural". For instance a "G" note by itself is a "G Natural" ("G♮" or just a "G"). But if you go UP a "half-step" it would be called a "G#" (G Sharp), and conversely, if it went DOWN a "half-step" it would be called a "G♭" (G Flat). BUT, if you go UP a "half-step" from "G♭" or DOWN a "half-step" from G#", then you would be back at "G Natural".

To make things even more complicated, a "G#" can also be called "A♭", and a "G♭" can also be called an "F#" (their "Enharmonic Equivalents"). The reasons have to do with what key you're in and other functions that we won't worry about now.

*Note: There are also "Double Sharps" and "Double Flats", but we'll just stick the regular ones right now as well.

While I was studying all this theory in college, on the website https://edusson.com/powerpoint-presentation-writing-service good authors help create presentations for my assignments. They take a lot of time, so the guys from Edusson helped me a lot. Still, my main priority is music.

The "Natural", "Sharp" and "Flat" are identified by symbols called "Accidentals". In music, the word "Accidental" has two meanings, but in our case it just refers to the symbols that are added to notes to identify them:

6 # b Natural signs.jpg



*Notice how a "Natural" sort of looks like a "Sharp" with most of its tips cut off...

*Also note that a "Natural" sign is only used when needed, such as when they would normally be "Sharp" or "Flat" in a piece of music.


~~~


Anyway, going back to Intervals... If you play from one “C” to another “C” twelve keys away on the piano, that is called the “Octave”:

 

7 PIANO - C Octave.jpg




If you play JUST the eight WHITE KEYS from “C” to “C” within the range of those twelve keys, you’d be playing the “C Major Scale” (what makes it a Major Scale will be further explained later on)... and the notes of the C Major Scale are:

C
D
E
F
G
A
B
C

In Music Theory numbers are often assigned to each consecutive note in a certain key:

C-1
D-2
E-3
F-4
G-5
A-6
B-7
C-1

These are called “Arabic Numerals”, for those who are fond of that term, but I just refer to them as “Numbers” myself.

These numbers represent what is often referred to as "Scale Degrees":

In the “Key of C” the note “C” would be “1”, the note “D” would be “2” and so on...

In Music Theory “Scale Degree” numbers are also shown as “Roman Numerals”:

C - I
D - II
E - III
F - IV
G - V
A - VI
B - VII
C - I

If you've ever read or heard the phrase; "Play I-IV-V-I in the Key of C Major" that typically means "Play a C Major chord, then an F Major chord, then a G Major chord, then back to a C Major chord"...

Also notice how the first note and the last note are both either “1” or “I”.

So, in the “Key of C”, the note “C” is essentially considered to be the same, no matter where it’s played - just at a higher or lower pitch. The beginning and the end. The Alpha and the Omega... the relevancy of which is just so mindbogglingly profound that I would run the risk of literally breaking your brain trying to explain it!

That’s exactly why in the “Key of C” the pitch “C” also has very VERY special name, and is called the “Tonic”.

In the Key of D the Tonic is “D”.
In the Key of G♭ the Tonic is “G♭”.
In the Key of Bm the Tonic is “B”.
In the Key of C#m the Tonic is “C#”.

“Tonic” means “Tonal Center”.

No matter which key you are playing in, EVERYTHING revolves around the “Tonic”!



~~



So, as to how the Tonic relates to “Interval Names”, we’ve already learned about the “Unison” and the “Octave”:

"Low C" to "Low C" (same C) “Unison”
C to D
C to E
C to F
C to G
C to A
C to B
"Low C" to "High C" “Octave”


In between these two extremes the rest of the notes are mostly labeled by their “Scale Degree”. *(They too have other fancy names, but nothing we have to get into right now).

Using the notes of the “C Major Scale” you can easily see that “D” is some sort of “2nd” and “E” is some sort of “3rd”, etc:

C
D-2
E-3
F-4
G-5
A-6
B-7
C
 

12 PIANO Intervals.jpg





But if you look at ALL of the notes between the Unison and the Octave you’ll see that there’s a lot more than seven notes:

C
C#/D♭
D
D#/E♭
E
F
F#/G♭
G
G#/A♭
A
A#/B♭
B
C
 

13 PIANO 12 half steps.jpg





So, how does one go about labeling the intervals between the Unison and Octave when there are twelve notes involved?

Well, that’s where the “Half-Steps” come into play...

Before I go any further, it would be my pleasure to introduce the five “Qualities of Intervals":

Perfect
Major
minor
Augmented
diminished


Notice how the “Perfect”, “Major” and “Augmented” intervals start with “Upper Case” letters, while “minor” and “diminished” intervals have “lower case” letters.



These are listed in order of what degree the Interval is “Consonant” or “Dissonant”.

“Perfect” is the most “Consonant” (stable), while “diminished” is the most “Dissonant” (unstable).

But don’t confuse “Dissonance” with “Discordance”, since Discordance is noise.

By “Stable” we mean “Rest”. The more Consonant something is, the more “satisfying” the “state of rest” it’s in.

The more “Dissonant” something is, the more it wants to go somewhere else.



*Special Note: As you will see in a bit, not all “diminished” or “Augmented” Intervals are “Dissonant”, which we’ll address shortly.



~~~



So, getting back to the “Half-Step” discussion, here is the amazing “Half-Step List” *(you can just skim through these right now since they'll be whittled down quite a bit soon😞


(0) Zero Half-Steps = “Unison”.

(1) One Half-Step = “Augmented Unison” or “minor 2nd”

(2) Two Half-Steps = “Major 2nd” (or "diminished 3rd")

(3) Three Half-Steps = “Augmented 2nd” or “minor 3rd”

(4) Four Half-Steps = “Major 3rd” (or “diminished 4th”)

(5) Five Half-Steps = “Augmented 3rd” or “Perfect 4th”

(6) Six Half-Steps = “Augmented 4th” or “diminished 5th”

(7) Seven Half-Steps = “Perfect 5th” (or "diminished 6th")

(8) Eight Half-Steps = “Augmented 5th” or “minor 6th”

(9) Nine Half-Steps = “Major 6th” or "diminished 7th"

(10) Ten Half-Steps = “Augmented 6th” or “minor 7th”

(11) Eleven Half-Steps = “Major 7th" (or "diminished Octave")

(12) Twelve Half-Steps = “Augmented 7th” or “Perfect Octave”



A couple clarifications before we continue...

Any Perfect or Major interval that goes UP in pitch a half-step becomes “Augmented”.

Any Perfect or minor interval that goes DOWN in pitch a half-step becomes “diminished”.

Any Major interval that goes DOWN in pitch a half-step becomes “minor”.

Any minor interval that goes UP in pitch a half-step becomes “Major”.



~~



There are some glaring contradictions with how those intervals were labeled though...

For one thing, why would a “Perfect” interval be anything but perfect?

Well, the short answer is that they are almost always Perfect, with VERY few exceptions.

Similarly, a “Major 3rd” or “minor 3rd” are rarely, if ever, considered to be anything other than Major or minor, since they are crucial in defining the Key, Chord or Scale which they are a part of.


(continued)...



`

Thanks, it was interesting to read!

Edited by ervinhall
Link to comment
Share on other sites

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.
Note: Your post will require moderator approval before it will be visible.

Guest
Reply to this topic...

×   Pasted as rich text.   Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.   Display as a link instead

×   Your previous content has been restored.   Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

×
×
  • Create New...