Minor Perfect 5th Interval? (Music Theory from Hell)

[MartinJ]

I'm reading a chapter by Rich Appleman in The Bass Player Book (Karl Coryat, ed.), and one thing has me stumped. The books is absolutely fantastic, by the way, and I'm really enjoying it a great deal!

 

Here's what I do understand:

When the higher note in a major interval is flatted by 1/2 step, the interval becomes a minor interval. If this minor interval is further reduced by a 1/2 step, it becomes a diminished interval.

 

So here's what I do not understand:

When the higher note in a perfect interval is flatted by 1/2 step, the interval becomes a diminished interval.

 

The examples provided are:

perfect 5th = Bb to F

dim. 5th = Bb to Fb (I know that this is the enharmonic for E, but I guess that they wanted to emphasize that the 5th is flatted.)

 

Why isn't it:

perfect 5th = Bb to F

min. 5th = Bb to Fb (or E)

dim. 5th = Bb to Eb

 

 

I've reviewed this material for a couple of days, and I've searched through the archives, but I'm still missing something here.

 

Thanks!

[Max Valentino]

well, I think you may be making this harder on yourself due to confusing your semantics......

 

Intervals are the measured distance between two notes. Most commonly this is the measured distance between the root note (tonic) and another scale tone. They are either Major, minor, perfect, diminished or augmented intervals.

The stacking and coresponding of these intervals gives us the construction of chords/scales.

 

Perfect intervals are the tonic, fourth and fifth intervals of the scale.

There are maj and minor 2nds (a minor 32nd is sometimes refered to as a dim 2), 3rds, 6ths and 7ths.

There are augmented fourths and fifths.

There are diminshed fifths and sevenths.

 

Stacking a root note with a major third above it, and and a perfect fifth gives us a Major chord.

Stacking a root with a minor third above and a perect fifth is a minor chord.

A root with a minor third and a diminshed fifth is a Diminished chord.

A root with a major third and a augmented fifth is an augmented chord.

 

A diminished fifth is a measured distance of 6 half steps from the tonic tone. This is also the measured distance of an augmented fourth...just to add to confusion.

the name chosen is dependent upon the chord/scales being used.

 

A perfect fifth is a distance of 7 half steps from the tonic

 

An augmented fifth is a distance of 8 half steps. This interval is also known as a minor 6th.

 

A major 6th, also known as a diminished 7th is 9 half steps from the tonic.

 

A minor 7th is 10 half steps......

 

A perfect fourth is 5 half steps.

 

Chart of Intervals:

 

Unison: 0 half steps

Minor 2nd: 1 half step

Major 2nd: 2 half steps

Minor 3rd: 3 half steps

Major 3rd: 4 half steps

Perfect 4th: 5 half steps

Aug 4th/Dim 5th 6 half steps

Perfect 5th 7 half steps

Aug 5th/min 6th 8 half steps

maj 6/Dim 7 9 half steps

minor 7th 10 half steps

Major 7th 11 half steps

Octave 12 half steps

 

FYI: the tone of Fb does occur in the key signature of Cb, and the tones of E#, and B# occur in the key of C#, with E# also apearing in the key of F#. Cb occurs in the key of Gb. These are all known as "enharmonic keys", and while these notes may seem "mis-spelled" they occur as to allow for the neccessary number of sharps/flats to appear in each key signature (C3 having 7 sharps, F# having 6 sharps, Gb having 6 flats and Cb having 7 flats). Very little music is written in these keys due to the confusing key sigs..tho I have noticed more and more tunes popping up in these keys somewhat due to the proliferation of "de-tuning" gtrs down to C#'s and such.

 

For what it is worth...the note Cb is the same as B, yet the key for Cb is Cb,Db, Eb,Fb, Gb, Ab, Bb.

The key sig for B is B, C#,D#,E,F#,G#,A#...notice a similarity?

 

Max

[MartinJ]

Originally posted by Max Valentino:

...

Intervals are the measured distance between two notes. Most commonly this is the measured distance between the root note (tonic) and another scale tone. They are either Major, minor, perfect, diminished or augmented intervals.

...

There are augmented fourths and fifths.

...

A diminished fifth is a measured distance of 6 half steps from the tonic tone. This is also the measured distance of an augmented fourth...just to add to confusion.

the name chosen is dependent upon the chord/scales being used.

 

A perfect fifth is a distance of 7 half steps from the tonic

 

An augmented fifth is a distance of 8 half steps. This interval is also known as a minor 6th.

 

Max

Hi Max,

 

Thanks for ALL the information!

 

I know that a perfect 5th is 7 half steps above the tonic, so I would assume that a minor 5th would be 6 half steps and a diminished 5th would be 5 half steps up. This is the pattern for the other intervals, if I am understanding correctly. That is, flat the upper note = minor, double flat the upper note = diminished, right?

 

However, we call the 6 half step interval a diminished 5th, even though it's only 1 half step less than the perfect 5th (so it looks like a minor 5th to me).

 

Is this simply a nomenclature quirk? Is there no name for a minor 5th, so it is called a diminished 5th for some weird reason?

 

Thanks!

[jeremy c]

It's just a terminology.

 

4ths, 5ths and octaves are considered "perfect" intervals so there is no major or minor version. They can be augmented or diminished by a half step. There is no such thing as a minor 5th or minor octave.

 

On the other hand, 2nds, 3rds, 6ths and 7ths have both major and minor versions. The minor version is a half-step lower than the major version. An augmented 2nd, 3rd, 6th or 7th is one half step higher than the major version. A diminished 2nd, 3rd, 6th or 7th is one half step lower than the minor version.

 

In the list of intervals below, the ones in parenthesis are theoretically possible, but I can't say I've ever seen them.

 

(C Dbb diminished second)

C Db minor second

C D major second

(C D# augmented second)

(C Ebb diminished third)

C Eb minor third

C E major third

(C E# augmented third)

C Fb diminished fourth

C F perfect fourth

C F# augmented fourth

C Gb diminished fifth

C G perfect fifth

C G# augmented fifth

(C Abb diminished sixth)

C Ab minor sixth

C A major sixth

(C A# augmented sixth)

C Bbb diminished seventh (this is where we get the chord name from)

C Bb minor seventh

C B major seventh

(C B# augmented seventh)

(C Cb diminished octave)

C C octave

(C C# augmented octave)

(C Cbb diminished ninth)

C Db minor ninth

C D major ninth

C D# augmented ninth

[MartinJ]

Originally posted by jeremyc:

It's just a terminology.

 

4ths, 5ths and octaves are considered "perfect" intervals so there is no major or minor version. They can be augmented or diminished by a half step. There is no such thing as a minor 5th or minor octave.

Hi Jeremy,

 

Thanks, as always, for the great information. ( If I'm ever able to swing it, I ought to get to Berkeley and pay you for a BUNCH of lessons based on your help here!)

 

Do you know why the word diminished is used instead of minor when refering to the 5th interval that's been reduced by 1/2 step? Is it a historical thing? (It doesn't seem to fit into my - very limited - understanding of theory thus far.)

 

Thanks!

[AlChuck]

The words are different because calling an lowered fifth a "minor," for example, would imply there was such a thing as a major fifth. Using the word "diminished" keeps the distinction clear.

 

Also, I'm not sure this statement in your first post was addressed:

 

Here's what I do understand:

When the higher note in a major interval is flatted by 1/2 step, the interval becomes a minor interval. If this minor interval is further reduced by a 1/2 step, it becomes a diminished interval.

So, at the risk of being repetitive, I'll say this --

 

Reducing a minor interval by another half-step does not make a diminished interval.

 

Let's consider a major third in the key of C: C to E.

 

Flat the E, you get a minor third: C to Eb.

 

Lower the third again, you get a major second: C to D.

 

Not a diminished third. There is no such beast.

[Mike Dawson]

Hi Jeremy,

Thanks, as always, for the great information. ( If I'm ever able to swing it, I ought to get to Berkeley and pay you for a BUNCH of lessons based on your help here!)

or you could go to Berklee and pay them a REDICULOUS BUNCH of money to learn about theory

[davebrownbass]

Here is an idea about that. There is a fundamental difference in the Perfect intervals (which can ONLY be diminished or Augmented) and the Major/minor intervals (which can ONLY be Major or minor, except the seventh scale step.) The primary reason is the relative consonance/dissonance of the interval. P4 and P5 are very consonant with the root. The intervals 2,3,6,7 have varying degrees of dissonance with the root. No matter how an interval might be spelled, the determining factor is how it functions.

 

Perfect intervals are called perfect because of the high degree of consonance with the root. A root note has a perfect fifth and octave embedded in the harmonic series. There is a perfect fourth as well (but not the fourth above the root. The distance from the Perfect Fifth to the octave is a Perfect Fourth)

 

So, when the Perfect Fifth is altered, the word diminished or Augmented is used. There is no diminished P4 (well, theoretically there is, but it doesn't FUNCTION as a diminished fourth) There is no diminished or Augmented P8 (Again, technically you could spell an octave so it would look diminished or Augmented; again, it doesn't function that way. A diminished Octave more correctly functions as a major seventh.

 

Additionally, there are no augmented intervals in common usage except the fifth. Again, you could spell the Major third c-E# and it would technically be an Augmented third, but it's function would be as a Suspension, and in common usage it would be written as C-F

 

Finally, there are no diminished intervals on 2,3 and 6. There is a diminished seventh, which functions in a diminshed chord in a unique way.

 

Major and minor intervals are correctly applied to 2,3,6,7 because their quality in relation to the tonal center implies either a major or minor variant scale.

 

To sum up. Perfect intervals on 4 and 5, when altered, either diminish or Augment the basic chord. Major/Minor intervals on 2,3,6,7 do something fundamentally different. There is only one minor interval that, when lowered, can be called diminished...the seventh.

 

Anyway, that's what I think.

[jeremy c]

Dave, there is one you missed. We regularly use an augmented ninth. I suppose it is related to an augmented second which we never use.

 

The chord C7 with an augmented ninth

is usually written

C7#9

(although I have seen C7aug9 and C7+9)

 

It's a good old "Taxman" chord, C E G Bb D#.

 

In terms of sound, this chord has both a major third and a minor third, but in terms of spelling it has a major third and an augmented ninth.

[davebrownbass]

You're right as usual, Jeremy.

 

I was sticking to the first octave...I felt like color extensions would be grad school for the initial poster.

 

In fact, what would you call the common #11? Never though about that before, but I'd think it would have to be thought about as Augmented...in the same sense as the diminished seventh.

 

To readers who make it this far: in normal jazz parlance, I often hear terms like #9 or b5 more frequently than their technical equivalents "Augmented" and "diminished"

[music-man]

MartinJ - I'd encourage you to dump the self-effacing signature line, since you've now surpassed in your understanding of enharmonics and intervals the collective knowledge of three "musicians" (who are paid to play) I rehearsed with last night.

 

I'll piggy-back on DBB's consonance/dissonance distinction with a cloddish description of something I seem to remember from my music history classes (first year music school is clouded by a self-induced haze, I'll admit).

 

The odd terminology of "perfect" vs. Major/minor can be traced back to the sacred origins of Western Music, which was "built" on the perfect intervals (1, 4, 5, 8). The "imperfect" intervals (2, 3, 6, and 7) were avoided, as they were thought to be tainted by having unholy impurities (insert Dr. Strangelove out-take) ...

 

Eventually, as with all things "pure," the impure invaded and made things a lot more interesting. (Although the cadences and harmonic orientation of Western music are still founded on the roots established in early sacred music).

 

Anyway, I thought it amusing that the subject line of this post was "Music Theory from Hell" because I seem to remember that a tritone (diminished 5th or augmented 4th) was thought of as the "Devil's interval." (And I think Black Sabbath must have known that too ).

 

Now ... someone who's a lot closer (physically, temporally, or even just intellectually) to a Norton's Anthology should correct my admittedly simplistic rendering of six centuries of music.

[MartinJ]

Max, Jeremy, Al, Dave, & Music-Man -

 

Thanks, as always, for the comprehensive, understandable, and downright interesting information! I have been printing these pages so that I can keep them close at hand while I spend my summer trying to understand music theory (and even learn to play my bass in some fashion).

 

The downside is that I do not understand this chapter as well as I had delusionally imagined, but, what the hell, all this learning is good fun.

 

Thanks again,

Martin

[MartinJ]

Originally posted by music-man:

Anyway, I thought it amusing that the subject line of this post was "Music Theory from Hell" because I seem to remember that a tritone (diminished 5th or augmented 4th) was thought of as the "Devil's interval." (And I think Black Sabbath must have known that too ).

 

Cool that you mentioned the tritone. According to Rich Appleman:

 

"A late-medieval nickname for the tritone was diabolus in musica, bacause it was considered a dangerous and awkward interval. (I've even heard that the three tines of the devil's pitchfork signify the three whole-steps in a tritone.)"

[jeremy c]

Dave, of course you are right too.

 

The diminished fifth, augmented ninth and augmented eleventh are much more likely to be called b5, #9 and #11. That's how I would always write them to avoid confusion.

 

The same way I would write b6 instead of minor sixth, or b7 instead of minor seventh.

 

The only time I use the name augmented is for the 5th, even then sometimes I will say #5 instead.

 

And I would say b5 instead of diminished 5th.

 

I'll of course use the word diminished when describing a diminished seventh chord which of course has a diminished seventh interval in it (as well as a minor third and a diminished fifth).

 

I hate the name "half-diminished seventh" although I use it because everyone understands what it means. It's the chord with a minor third, diminished 5th and minor seventh. The logical name for this chord is "minor seven flat five".

[Jode]

A simple point of order: the "rules" as we know them are a product of musical evolution. As my high school theory teacher used to say, "It's not like a couple of Italian monks got drunk one night three hundred years ago and just wrote the book." The catch-all term for why we do things the way we do is convention.

[SolSol]

As far as the "why are perfect intervals called perfect?" debate goes, I believe the answer lies in the nature of the 4th and 5th. The tonic and the note a perfect 5th away from it have a very close frequency relationship...they are, in fact, almost the same pitch. But, more importantly, the 5th (and 4th) are the only intervals that when inversed stay in the same major key. So, in C, if you go up a 5th you get a G and down a 5th you get an F, which is a 4th above C. F is a diatonic note in C major.

 

On the other hand, if you go up a major third in C you get an E, but if you go down a major 3rd you get a G#...not a diatonic note.

 

There's your answer I believe!