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soapfoot

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Feb 10 17 10:34 AM

At the risk of a derail into what should be a whole 'nother thread... "blue" notes are another matter entirely.

"blue" notes aren't "in-between" or 'minor-over major"... they're tunable notes, they just require an entirely different conception of harmony that extends to the seventh partial, whereas Western music only extends to the fifth.

In our Western harmonic system, all twelve pitches of the equal-tempered scale "stand for" just, resonance-based pitches. And all twelve can be arrived at by reckoning only third and fifth partials in various directions. In Indian solfege, "mi", or the third (fifth partial) is known as "ga", and "sol" or the third partial is known as "pa." That will be helpful as we go on...

If I start with "C" as my tonic, the third partial ("pa") is G and the fifth partial ("ga") is E. (that's three of twelve)

The third partial above the third partial (G) is D. (four)
The fifth partial above the third partial (G) is B. (five)
The third partial above the fifth partial is G# (six)
The fifth partial above the fifth partial is A. (seven)
The tonic is the third partial of F --Mathieu would call this "pa below tonic" (eight)
The tonic is the fifth partial of Ab, or "ga below" (which duplicates the G# in equal temperament, but is a slightly different pitch in just tuning; this is the more commonly used of the two. Still eight)
"Pa below" (F) is the fifth partial of Bb, or "pa below pa below" (nine)
"Ga Below" (or Ab) is the fifth partial of Db, this is "pa below ga below" (ten)
"Ga below Pa below" is Db again (but a different Db!), as this is the fifth partial below F. (still ten)
"Ga below Ga below" is Fb (or E natural) again, but a different E natural by a few cents in just tuning (still ten)
"Pa below Pa" is redundant... that's just our "C" tonic (still ten).
But "Ga below Pa" is Eb, our minor third (eleven).

The next few in the sequence are redundant in equal temperament (but are actually distinct pitches in just tuning), so let's skip ahead to the first place we get the twelfth equal-tempered pitch class--

Ga above Pa above Pa, or the fifth partial above the third partial above the third partial above tonic (F# above D above G above C).

Now we've got all of our twelve equal-tempered pitch classes, using only third partials and fifth partials. Western harmony is thusly referred to as a "five limit" system, as we can limit the harmonic series to five partials and still find all the pitches we need.

Now for the blues...

The blues is descended in part from some West African musical traditions that utilize the harmonic series up through the seventh partial, which in C is that slightly out-of-tune (to the Western ear) Bb harmonic.

And these origins are what inform the "blue notes". The blue notes are tunable pitches that are by degrees either in-tune or out-of-tune, sure as a perfect fifth or major third. They're not just random places in-between major and minor. And it's also not random that the I, IV, and V chords are commonly played as dominant seventh chords, and that this isn't well-explained by Western music theory. The lowered seventh is nothing more arcane than an imperfect approximation of the seventh partial which is so integral to the music's tuning and harmonic conception.

The "blue" minor third is the seventh partial below the fifth partial below the tonic. In C, "pa" below is F. And F is the seventh partial of a pitch lying somewhere between Eb and E. The blue minor seventh is, of course, just the seventh partial itself (which Mathieu extrapolates Indian solfege to call, appropriately "blu").

So... not really "bitonal"... a whole other system of harmony.

Now all the reckonings we did above in the five-limit system, imagine doing all of those in the seven-limit system. That is a massive amount of tunable, singable pitches. To try and explain those via our Western system of harmony and solfege is reductive, and doesn't really "work" so well to explain the blues.

Of course, Western hegemony being what it is, the accepted 20th century explanation was that blues was "primitive" music and was somehow naive to our "sophisticated" Western concepts of harmony.

Hardly.

Anything but, really.

brad allen williams

Last Edited By: soapfoot Feb 10 17 10:37 AM. Edited 1 time.

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maarvold

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Posts: 3,143 Member Since:23/01/2011

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Feb 11 17 10:45 AM

soapfoot wrote:
At the risk of a derail into what should be a whole 'nother thread... "blue" notes are another matter entirely.

"blue" notes aren't "in-between" or 'minor-over major"... they're tunable notes, they just require an entirely different conception of harmony that extends to the seventh partial, whereas Western music only extends to the fifth.

In our Western harmonic system, all twelve pitches of the equal-tempered scale "stand for" just, resonance-based pitches. And all twelve can be arrived at by reckoning only third and fifth partials in various directions. In Indian solfege, "mi", or the third (fifth partial) is known as "ga", and "sol" or the third partial is known as "pa." That will be helpful as we go on...

If I start with "C" as my tonic, the third partial ("pa") is G and the fifth partial ("ga") is E. (that's three of twelve)

The third partial above the third partial (G) is D. (four)
The fifth partial above the third partial (G) is B. (five)
The third partial above the fifth partial is G# (six)
The fifth partial above the fifth partial is A. (seven)
The tonic is the third partial of F --Mathieu would call this "pa below tonic" (eight)
The tonic is the fifth partial of Ab, or "ga below" (which duplicates the G# in equal temperament, but is a slightly different pitch in just tuning; this is the more commonly used of the two. Still eight)
"Pa below" (F) is the fifth partial of Bb, or "pa below pa below" (nine)
"Ga Below" (or Ab) is the fifth partial of Db, this is "pa below ga below" (ten)
"Ga below Pa below" is Db again (but a different Db!), as this is the fifth partial below F. (still ten)
"Ga below Ga below" is Fb (or E natural) again, but a different E natural by a few cents in just tuning (still ten)
"Pa below Pa" is redundant... that's just our "C" tonic (still ten).
But "Ga below Pa" is Eb, our minor third (eleven).

The next few in the sequence are redundant in equal temperament (but are actually distinct pitches in just tuning), so let's skip ahead to the first place we get the twelfth equal-tempered pitch class--

Ga above Pa above Pa, or the fifth partial above the third partial above the third partial above tonic (F# above D above G above C).

Now we've got all of our twelve equal-tempered pitch classes, using only third partials and fifth partials. Western harmony is thusly referred to as a "five limit" system, as we can limit the harmonic series to five partials and still find all the pitches we need.

Now for the blues...

The blues is descended in part from some West African musical traditions that utilize the harmonic series up through the seventh partial, which in C is that slightly out-of-tune (to the Western ear) Bb harmonic.

And these origins are what inform the "blue notes". The blue notes are tunable pitches that are by degrees either in-tune or out-of-tune, sure as a perfect fifth or major third. They're not just random places in-between major and minor. And it's also not random that the I, IV, and V chords are commonly played as dominant seventh chords, and that this isn't well-explained by Western music theory. The lowered seventh is nothing more arcane than an imperfect approximation of the seventh partial which is so integral to the music's tuning and harmonic conception.

The "blue" minor third is the seventh partial below the fifth partial below the tonic. In C, "pa" below is F. And F is the seventh partial of a pitch lying somewhere between Eb and E. The blue minor seventh is, of course, just the seventh partial itself (which Mathieu extrapolates Indian solfege to call, appropriately "blu").

So... not really "bitonal"... a whole other system of harmony.

Now all the reckonings we did above in the five-limit system, imagine doing all of those in the seven-limit system. That is a massive amount of tunable, singable pitches. To try and explain those via our Western system of harmony and solfege is reductive, and doesn't really "work" so well to explain the blues.

Of course, Western hegemony being what it is, the accepted 20th century explanation was that blues was "primitive" music and was somehow naive to our "sophisticated" Western concepts of harmony.

Hardly.

Anything but, really.

 
Language, and it's use, are tricky business.  I was actually only referring to bitonal in the Mancini example.  But even that probably is more like two parallel harmonic universes separated by a small fixed amount than being truly bitonal.  

The real, underlying point I was trying to communicate--although this is a different forum--is "Whatever Works" (and whatever doesn't).  And I was attempting to qualify my position by using those examples to show that I am far from afraid of dissonance, as long as it satisfies 'my gut' that it is authentic and 'heard' in its creator's mind's ear.  On the other hand, one person's 'happy accident' during the creative process is only artful to me if it solidly pushes 'the good button', at least upon repeated listening.  It reminds me of the Birth of Reese's Peanut Butter Cups commercial where the chocolate falls into the peanut butter.  Many love those candies; I can understand what people like about the somewhat radical combination of sweet and savory, but I only occasionally want one, and not that much when I do.  

I, honestly, so far only skimmed your explanation (above) about where 'blue notes' come from: it's a far different way of thinking about the blues than I am familiar with and I need to give it a good 10-15 minutes of focussed attention--which I will do later today (hopefully) because I ALWAYS find your 'stuff' interesting and insightful.  But I think it is more likely that Eric Clapton's 'gut' told him where his 3rds should fall, and whether a Major 7 or a minor 7 in the key of the song was appropriate in the "Beano era', although what you wrote might well explain why it works so fabulously well for me.  Thanks for taking the time to spell that all out: it will be read and mulled over.  
morespaceecho wrote:
one of my favorite chords is....i dunno what you'd call it technically...add9b9? but if you're starting on E it's E B F F# low to high. dissonant as hell but it sounds glorious to my ears.

 I'm gonna have to check that out in front of a keyboard--as I 'auralize' the sound of it in my head, I can't fully tell what my 'gut' will tell me about it; I think it has implications of tonic (E B) , V of II (F) and Dominant--5th of V (F#) as I 'play' it in my head.  If you move the top 2 notes up a half step you have a minor 9th chord with a half step in the voicing--something that is pretty often heard in music in this day and age: it's contained in the guitar part in "Officer and a Gentleman" for example, as well as many earlier examples.  

MSE, if you're sitting in front of a piano sometime, using your left hand, with middle C on the bottom, play a C dim 7th (C Eb Gb Bbb--aka A natural) and use your right hand to play the same voicing an octave plus a whole step above it (D F Ab Cbb--aka Bb); I would call this 'a Thad Jones chord'.  I predict you will love the dissonance, although yours might be a bit more 'outside-flavored' and stark and that may be what you like about it.  

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morespaceecho

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Feb 11 17 11:44 AM

maarvold wrote:

MSE, if you're sitting in front of a piano sometime, using your left hand, with middle C on the bottom, play a C dim 7th (C Eb Gb Bbb--aka A natural) and use your right hand to play the same voicing an octave plus a whole step above it (D F Ab Cbb--aka Bb); I would call this 'a Thad Jones chord'.  I predict you will love the dissonance, although yours might be a bit more 'outside-flavored' and stark and that may be what you like about it.  


thanks, i will try it out! that is a super-complicated chord by my standards, i tend to not like dense harmony, "outside and stark" is actually a really great way of describing what i like. 

awhile back i was sitting around trying to think of the most dissonant chord i could play on guitar (good use of time, right?). i came up with two. same fingering. starting on the low E, just alternate 6th fret with open strings, so Bb A G# G F E. then do the same starting from the 4th fret, so G# A F# G D# E. super gnarly! but if you strum them over and over for long enough they start to sound oddly soothing.
 

www.oldcolonymastering.com

morespaceecho.bandcamp.com

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gtoledo3

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Posts: 4,170 Member Since:23/10/2013

#28 [url]

Feb 11 17 12:08 PM

Those dissonant chords are often most effective as shorter transition chords between main chords.

Many times, I will view each note in the chord as an independent voice... that mindset can sometimes seem to lead to interesting chromaticism in one or more of the voices, and can yield some really cool, tense feeling chords, which usually resolve to something a bit more pedestrian.

related: http://tedgreene.com

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maarvold

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Feb 11 17 1:10 PM

seth wrote:
Try A C# E F# B D# - I think of it as a John Williams chord.

 
Probably WAY to inside for mse... just an observation.  And based on what he said, my "Thad" chord is probably massively to dense for his taste.  Re: the John Williams chord--sort of Lydian/non-saccharine.  And I think if you use an exotic woodwind sound and 'dither' the top note between D# and E, it's also something like the flavor of one of the early cues in "Gladiator"--before the battle where they launch the fireballs from catapults.  (Yes--I know "Gladiator" is Hans Zimmer, not JW).  And I might be remembering another film... "Titanic"  or something else.  

Last Edited By: maarvold Feb 11 17 3:23 PM. Edited 3 times.

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soapfoot

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Feb 12 17 9:27 AM

maarvold wrote:
 
I, honestly, so far only skimmed your explanation (above) about where 'blue notes' come from: it's a far different way of thinking about the blues than I am familiar with and I need to give it a good 10-15 minutes of focussed attention--which I will do later today (hopefully) because I ALWAYS find your 'stuff' interesting and insightful.  But I think it is more likely that Eric Clapton's 'gut' told him where his 3rds should fall, and whether a Major 7 or a minor 7 in the key of the song was appropriate in the "Beano era', although what you wrote might well explain why it works so fabulously well for me.  Thanks for taking the time to spell that all out: it will be read and mulled over.  

I think, more likely, his ear told him, as a result of listening to a lot of other musicians whose ear told them that, as a result of working within a tradition or system that has origins somewhere besides Western Europe.

I don't want to allege that use of seventh-partial derived harmony was a conscious choice by anyone, merely that it's part of a different tradition which pushed use of the harmonic series one step deeper than what Western Europe ultimately settled on. Musical theory of any kind exists after-the-fact, to describe sounds that already exist. If there's a musical theory at all, it's because someone said "hey, that sounded cool! I wonder if we can figure out what this cool-sounding thing has in common with that other cool-sounding thing?"

Music theory that doesn't at least intersect with physics is incomplete, in my opinion, since it's these low-prime ratios that define our sense of consonance and dissonance. Unfortuantely, most college music theory courses do not explore the physics at all, and begin with the tempered piano keyboard as a "given" (which it most certainly is not). They begin with abstraction and miss the fundamental basis in the physical sciences.

Once we take time to explore the physics and understand what a consonance is, so many concepts of "music theory" get much clearer and more intuitive. And "the blues" seems much less like a departure, or a misfit, or an aberration... and much more like a logical extension.

brad allen williams

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gtoledo3

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#34 [url]

Feb 12 17 10:12 AM

It seems like the phrase minor seventh implies a minor third is involved somehow, as opposed to the phrase dominant seventh. Is that what was meant - or was minor seventh really meant?

Relatedly, I don't remember a whole lot of "major sevenths" on the Beano record... maybe in one of the licks on "Little Girl".

Last Edited By: gtoledo3 Feb 12 17 10:16 AM. Edited 1 time.

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seth

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Feb 12 17 10:39 AM

A minor seventh is an interval, a dominant seventh is the chord on the fifth scale step. The chord on the fourth step is the subdominant and is a major seventh chord, the chord on the third step is the mediant and is a minor seventh chord. The sixth step is the submediant and is also a minor seventh chord. So the way you posed the question, George, is really just mixing up two naming conventions. A dominant seventh chord contains a minor seventh interval. So the correct comparison would be a mediant seventh chord and a dominant seventh chord, which I haven't heard since college. Just to complete the series, the chord on the second step is the supertonic, also a minor seventh chord, and I don't remember the name on the seventh step, but it's a half-diminished chord.

All of the foregoing and $2.75 will get you on the subway.

Last Edited By: seth Feb 12 17 10:57 AM. Edited 2 times.

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gtoledo3

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#36 [url]

Feb 12 17 10:53 AM

Yes, I thought the discussion was about chords, that's why I was confused. But now, rereading, I see that it had shifted to melodic discussion.

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maarvold

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#37 [url]

Feb 12 17 10:59 AM

gtoledo3 wrote:
It seems like the phrase minor seventh implies a minor third is involved somehow, as opposed to the phrase dominant seventh. Is that what was meant - or was minor seventh really meant?

Relatedly, I don't remember a whole lot of "major sevenths" on the Beano record... maybe in one of the licks on "Little Girl".

 
Only so many hours in the day... I actually considered changing things like Major 7 and minor 7 to a more proper "7th scale degree or lowered 7th degree, which seems more proper still--at least in Berklee terms when I was there.  But I had already devoted many more minutes to that post than my wife or dogs were happy about, so I didn't go back.  I'll try to remember to find you a non-lowered 7 example in "Beano"--I'm quite confident there's one in there.  The solo in "Badge"--although it's out of the era, is the first one that springs to mind... quite likely there's one or more in the long version of "White Room" as well.  

Working backwords, Brad: I believe you are saying what I was trying to communicate: Clapton did the thing he did with his 3rds that is somewhere, pitch-wise, between a 3rd and a lowered 3rd because he heard someone else do it somewhere, decided it worked in a way that he liked and adopted it as a defining aspect of his playing during that era.  Re: tempered vs. untempered intonation, I think one of the reasons I so love working with orchestral instruments is because, when they're really nailing the pitch 'their way', the 5ths and--particularly--the 3rds are beatless, pure and sweet; this is also so completely true on dobro and electric slide guitar and gives them that same wonderful flavor that seems to live pretty well in 'a fretted world'... probably because--with the exception of open strings--'they can put it where they hear it'. 

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seth

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Feb 12 17 11:07 AM

Did you ever ask string players to play in F#? They don't love you for it. If they don't have studio experience you might have to have them try it in Gb, because they will emphatically point out that on their instruments they are not the same key. That's one reason you want session string players if you can get them.

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soapfoot

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Feb 12 17 12:07 PM

maarvold wrote:

gtoledo3 wrote:
It seems like the phrase minor seventh implies a minor third is involved somehow, as opposed to the phrase dominant seventh. Is that what was meant - or was minor seventh really meant?

Relatedly, I don't remember a whole lot of "major sevenths" on the Beano record... maybe in one of the licks on "Little Girl".

 
Only so many hours in the day... I actually considered changing things like Major 7 and minor 7 to a more proper "7th scale degree or lowered 7th degree, which seems more proper still--at least in Berklee terms when I was there.  But I had already devoted many more minutes to that post than my wife or dogs were happy about, so I didn't go back.  I'll try to remember to find you a non-lowered 7 example in "Beano"--I'm quite confident there's one in there.  The solo in "Badge"--although it's out of the era, is the first one that springs to mind... quite likely there's one or more in the long version of "White Room" as well.  

Working backwords, Brad: I believe you are saying what I was trying to communicate: Clapton did the thing he did with his 3rds that is somewhere, pitch-wise, between a 3rd and a lowered 3rd because he heard someone else do it somewhere, decided it worked in a way that he liked and adopted it as a defining aspect of his playing during that era.  Re: tempered vs. untempered intonation, I think one of the reasons I so love working with orchestral instruments is because, when they're really nailing the pitch 'their way', the 5ths and--particularly--the 3rds are beatless, pure and sweet; this is also so completely true on dobro and electric slide guitar and gives them that same wonderful flavor that seems to live pretty well in 'a fretted world'... probably because--with the exception of open strings--'they can put it where they hear it'. 

Yes, precisely.

Equal tempered pitches are, from a physics standpoint "imaginary" things. "Real" pitches are low-prime ratios.

And to say something that SOUNDS new-agey, but is in fact basic, down-in-the-dirt physics: Harmonic consonances are the same as polyrhythms. They're all one thing... one just occurs slowly, and the other occurs fast.

A just-tuned perfect fifth is a 3:2 vibrational ratio. If a drummer is playing 3-against-2 on a snare drum and you speed it up really fast, it becomes a very sweetly-tuned perfect fifth.

A just-tuned major third is a 5:4 relationship. A slightly trickier polyrhythm, and 5:4 is a slightly less perfect consonance.

In Western music, we use these two consonances to arrive at all sorts of things.

A major triad, for example, is just both of them at once: C, the 5:4 E, and the 3:2 G. 

A minor triad is a C, the 3:2 G, and the Eb which is a 5:4 below G. This 5:4 below the 3:2 also happens to be a 6:5 ratio above tonic, making it its own kind of consonace... but the theoretical source is the 5:4 below the 3:2. 

Etc etc etc.

In blues, we don't stop at the 3:2 and 5:4... we also utilize the 7:4. If you have a drummer playing a 7-against-4 and speed it up, it will sound like a slightly detuned (to the western ear) minor seventh interval. Somewhere below an equal-tempered minor seventh. 

Using this, we arrive at all SORTS of new tones.

The "blues scale" we teach middle schoolers includes a lowered fifth degree, and this stands in for the 5:4 below the 7:4. In other words, in the key of C, if we consider that 7:4 Bb and then consider that 7:4 as the fifth partial of a tone a major third below it, we get the 7:6 Gb.

And the "blue" minor third is the 7:4 above the fourth scale degree... which is itself the 3:2 below tonic.

etc etc etc.

Western musicologists misundertand this, as a rule, and tend to treat "blues" as though it were primitive, and treat these "blue notes" as though they are sharp or flat by arbitrary amounts. But they're not... they're tunable pitches based on low-prime ratios, same as anything in western music, and can be tuned just as sweetly if the ear is attuned to it.
 

brad allen williams

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