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Progression-Scale relationships.


bloodsample

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Good evening ladies & gents.

Haven't posted here in a while, how's everyone? :wave:

 

So I'm writing this piece of software that (ultimately) will be able to output which scales "can" be played over a certain chord progression.

 

Without going into too much detail immediately, I'm just going to ask this simple question, and hopefully more discussion will erupt as a result.

 

In my "jazz improv" thread, Jazzwee mentioned at some point that over a iim7 V7 IM7 progression, one can play a HW-diminished scale with the V as a root, over the V7 chord.

 

I have put off thinking about this too much until recently.

 

Now I ask you this: Why does it work? What's the theory behind it?

 

I'm going to first ask you about this one specific case but hope to turn this thread into a theoretical talk of why certain scales work over certain progressions. Long term goal is to form a database of such progression-scale relationships to use in my software, but for now let's focus on that simple question posed above.

 

So let me start this off by elaborating a bit.

 

Let's take the key of C major.

In this case our ii-V-I will typically be:

Dm7 G7 CM7

 

Now it is claimed that a G HW-diminished scale played over the G7 will work. (I've tried this and to my ears, it "works").

 

Let us dissect a bit...

Take the G HW-dimished scale:

G G# Bb B C# D E F

 

Take the C major scale: (the root key of the ii V I)

C D E F G A B

 

Now take the notes in the three chords:

Dm7: D F A C

G7: G B D F

CM7: C E G B

 

Ok now that we have everything explicitly written out, let's examine this.

 

In our three chords, the union of all the notes of the chords is:

D F A C G B E

 

If we sort this to be in ascending order on the keyboard we get:

C D E F G A B

 

So in fact we get the C major scale. So we're sure that the C major scale will technically work over all three chords of the progression.

 

Now let's go back to our G HW-diminished scale:

G G# Bb B C# D E F

 

Out of these, let's extract the notes common to the C major scale (which incidentally is the union of the notes of all the chords we're considering).

 

The only common notes are:

D E F G B

 

That leaves G#, Bb and C# which seem to have fallen from the sky.

 

So now if we put our thinking caps on we can say that these represent the b9, #9 and #11 (respectively) of the G major scale, or to the #5, dom7 and b9 (respectively) of the C major scale.

 

So now that all this technical data is out on the table. Let me re-ask the question: How does playing the HW-dim scale of the V'th of a ii V I progression over the V make sense? To my ears it makes sense, but why does it make sense theoretically?

 

I'm hoping that with fully understanding this one little fact, I'll be able to "reason" my way to other such things that seem to just "work".

 

Maybe there is no theory involved, maybe some guy just played random notes and decided that to his brain/ears, it just sounds good. What do I know. :)

 

 

...*sigh* I'm exhausted from all this writing, someone else take over please.

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You're overthinking it. It works for the same reason that every other dominant-type scale works, including the mixolydian scale, and that is because it contains the root, third, and seventh of the dominant chord. It all goes back to basic voice-leading. The third and seventh of the V chord resolving to the third and root of the I chord. Just like with the altered scale (or diminished/whole tone), the altered extensions are icing on the cake, so to speak.
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Just look at it as an alternate way to connect the four notes of the dominant chord. The H/W dim. scale contains all of them. Of course, you're supposed to use it on the V7 chord exclusively.

Although the dominant chord is the one which allows the largest number of alternate modes, you could use a few on the other chords too. For example, on the IIm7 chord you can use the dorian b2 mode (2nd mode of melodic minor) instead of the 'regular' dorian mode. Or disguise it as a III an play the phrigian mode. On the Imaj7 chord, the lydian mode is even overused by these days... try the augmented scale, or the ionian b6 ("harmonic major") scale.

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ii7 is an extension of V7 - one can reduce a ii-V to really just V. In a traditional ii-V structure, anything you play over V7 you can play over ii7 because it's eventually leading to V7 anyway.

 

Look at the notes you've highlighted as falling from the sky:

 

b9 of V7 = b5 of ii7. Blues, anyone? Or think of it as a half-diminished (m7b5) chord.

#9 of V7 = b6 of ii7 which is found in the natural minor mode.

#4 of V7 = #7 of ii which can be used as a leading tone, passing tone, or neighbour tone.

 

Also, there's a whole load of theory on the diminished scale alone and the interchangeability of chords that are minor 3rds away. Too tired and too late to get into it now, but suffice it to say you can sub Bb7, Db7, and E7 over G7 (along with their corresponding ii7s) and it'll work. The HW diminished scale generates minor and major triads a minor third apart.

 

David

My Site

Nord Electro 5D, Novation Launchkey 61, Logic Pro X, Mainstage 3, lots of plugins, fingers, pencil, paper.

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Look at the scale again.

 

G the tonic

Ab a note with a string downward tendency to the tonic

 

Bb an interchangeable note with the major third

 

B the third

 

Db the flattened fifth

 

D

 

E The 6, which is very bright

 

F the 7.

 

So you get lots of notes that stand in strong relations to the original chord.

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The idea is that V7 chords can be made to sound more altered as desired and it will fit because dominants are chords full of tension. It is already tense due to the presence of the tritone interval 3/7. So more tension just increases the desire for it to release to the tonic. Something that jazzers take advantage of.

 

What are additional tension notes you can add to a dominant 7 chord?

 

b9, #9, #11(b5), b13. If you use all of this, then you have an ALT. A Half-Whole Diminished would use b9, #9, #11(b5) so it is less altered. Or you can use a Whole Tone scale, which is b5, and b13. So the idea is that different scales used will have various effects on the tension of the chord.

 

Going from more tension to less tension, you have ALT->HW Diminished->Whole Tone->Mixolydian.

 

Now, theory aside, you then try some of these tension notes and you say to yourself, this is familiar. It sounds like it really fits! And you wonder why. It's because some of these notes are the notes of the Tritone Substitute.

 

What is the tritone substitute of a G7? Db right?

 

G7

(G B D F)

 

Db7

Db F Ab Bb (which has the b13, #11(b5), #9 of G7 )

 

Do I have to explain why tritone substitution works? Aside from the fact that the G7 and Db shares the same notes (B and F or 3/7 of G7 and F and B are 3/7 of Db), tritone subs are chromatic movements to the tonic (half step away). So all of those tension notes mentioned above have this tendency to move a half step down to release the tension to the tonic. A little bit of leading tone theory.

 

Some people don't want to think in terms of H-W diminished/ALT/Whole Tone but instead think of the alterations. Either way works and I also visualize it both ways for myself.

Hamburg Steinway O, Crumar Mojo, Nord Electro 4 HP 73, EV ZXA1

 

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Great replies all. Thanks.

 

I gotta hand it to Jazzwee once again, your explanations are to the point and just make sense. Thanks.

 

So is it safe to say that every time we can add certain "colors" (ie 9,11,13 stuff) to a chord successfully we can do the same with a scale? For example someone may play scales that "work" without ever knowing the names of the scales right? He/She would just analyze the chords in question and see which notes are in common and which colors can be added.

 

I know this is not the way people think (or is it?). I'm just trying to gather some hard fast rules so that a computer can figure it out.

 

I'm trying to understand, physically, why certain notes add tension to a scale/chord and why others don't. I guess now it becomes a psychological and neurological question. I guess the answer is subjective to the human being. It's based on what humans agree to sound like "tension" right?

 

I was hoping that by understanding the theory behind it, I would be able to set some rules as to what tension notes are.

 

I think I managed to confuse everyone yet again :) .

 

I guess most of this theory is a combination of evolution and people's general agreement to what will sound "nice".

 

See here's the thing. Given a chord progression I can tell the computer to find common notes in that progression and use those to construct a scale. Now the computer doesn't know that adding a #9 adds "tension" because tension is a feeling only humans can understand. So basically I guess what I want is a set of rules (purely theoretical) to what notes add tension. I say tension here cause that's what Jazzwee said regarding the HW-dim scale on the dominant. But really I want any other rules for any other situation that will somehow link chord progressions to what notes will "work" over them.

 

Sorry for the confusion and thanks for your time.

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Whether it be in chord voicings or soloing, Bloodsample, the rules are still based on 'Tension and Release'.

 

Let's say you're playing a G7 again as in your example. G7 being in the Mixolydian mode of the C scale, you have all the white notes at your disposal. CDEFGAB. Being notes of the scale, all these notes are called diatonic. As soon as you alter the scale, (adding black keys), you add tension.

 

Now you know this already, but this is the other aspect of this that you need to understand. If you choose to play a note out of the scale, that tension you just created will feel like it should be released by wanting to return to a diatonic note. As you know, jazz specifically, is a musical genre that plays with this diatonic sound. Most other music is diatonic at all times.

 

So if you choose a Db, it will want to go up or down a half step to return to something diatonic on the next tone. There is even more satistfaction if you go back a half step to a note in the chord rather than a note not in the chord.

 

Since the whole principle is playing with the listener's emotions by managing the tension and release, you have to have some smarts here. For example V is the tension chord releasing to the I chord. If you add tension to the I chord by adding non-diatonic tones, then you move from Tension --> Tension, not Tension --> Release. This is not characteristic and some listeners will leave you. What jazzers have realized intuitively is that you leave the Release alone and focus on the tension part. We know we can vary the tension.

 

I'll go the other way. If you remove the tritone interval from the V7 chord and turn it into a V7Sus (4th interval no third), you've reduced the tension significantly and you have a fourth chord kind of sound. Jazzers use this too if you have a modal tune where your harmony is staying in place (like the tune 'So What'). But this is why it is called non-functional harmony. The Tension and release feel is 'suspended'.

 

Now inside a bar of 4 quarter note beats, you can also play with tension and release. This is the beauty of jazz because there are multiple layers, even with different instruments. If the chord for the bar is G7, you then have a choice of playing eight 8th notes, for example. It is most relaxing to the listener to play all the 8th notes as diatonic to the chord G7 (G B D F and repetitions thereof -- i.e. arpeggio). But you could choose to play |G Bb B Db D E F Gb |G...

Here you can see that you're alternating diatonic tones (release) to non-diatonic tones (tension). It's all about balance. Notice how in the above example there's more of a tendency to go from diatonic note to non-diatonic. It's alternating. Playing it |G B D F Bb Db Gb| is not characteristic (although it can be done) simply because of the atypical balance of tension and release. This is all a matter of context and what kind of tension and release is desired. It just has to make sense. A mixed up line like |Bb G B Db Gb D F| will not communicate that you're playing a G7 chord while my original example of |G Bb B Db D E F Gb | does. Same notes but different effect.

 

Even inside a diatonic scale there are levels of tensions as well. It isn't just the non-scale notes. For a given chord, the notes of 1,3,5,7 have the least tension. Going to the intervals in between 9,11,13 adds tension too.

 

So levels of tension, from highest to lowest

 

Non-scale tones-->Chord Extensions in scale->Chord tones.

 

Lots of complicated explanations here but in Classical music, these are just referred to as appogiaturas right? A diatonic tone is surrounded by a notes a half step away on either side. This is all following the same principle of brief plays of tension and release.

 

If you get past this, there's more. I recommend getting the book called "Forward Motion" by Hal Galper (online PDF book). It goes through the tension and release as it relates to a bar and explains the tension and release as it relates to downbeats vs. off beats.

Hamburg Steinway O, Crumar Mojo, Nord Electro 4 HP 73, EV ZXA1

 

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bloodsample, are you writing this piece of software for your own use or do you plan on selling it? I ask because you asked a rather simple question.

 

Getting back to a diminished scale used on a dominant 7th chord, a C7 chord already contains an E diminished triad, right? It's not much of a stretch to add a diminished 7th to that triad and come up with a scale based on that chord.

 

I would think it would be more productive for you to get your hands dirty (in real time) as it were instead of punching in a chord and having a scale thrown back to you. Just my thoughts.

No guitarists were harmed during the making of this message.

 

In general, harmonic complexity is inversely proportional to the ratio between chording and non-chording instruments.

 

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Jazzwee: You're a very generous person sharing your knowledge, everything you say inspires me to keep learning, thanks.

 

Dave Horne: The software is just for myself. It's a challenge I gave myself to advance both my music theory and programming knowledge at the same time.

 

I think that questions are only simple if you know the answers to them. I think I have a big problem communicating my questions in to words because my brain gets crowded with questions as I type that by the end I've generated more confusion than actual questions. :)

 

Nonetheless I manage to learn a lot from all of your replies whether you accurately answer my questions or not.

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An additional way to explain why a diminished scale sounds good (over any chord for that matter) is that it is a symmetrical pattern that keeps repeating itself. Our ears like to hear patterns, it catches or "hooks" our ears. We can accept continuos patterns no matter how far outside of the harmony they stretch.

 

SIDE NOTE:

 

The most dissonant harmonic intervals include:

minor second and major seventh

augmented fourth / diminished fifth (tritone)

 

So chords tones, such as the Major 7th in a Major 7th chord and the tritone in a Dominant 7th chord, are not neccessarily less dissonant than the the major 9th, 11th or 13th.

 Find 600 of my jazz piano arrangements and tutorials for educational purposes at patreon.com/HarryLikas Harry was the Technical Editor of Mark Levine's "The Jazz Theory Book" and helped develop "The Jazz Piano Book."

 

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Bloodman

 

I heard you refer to societal factors, "let's agree that such and such is dissonant and such and such is nice, or pleasing or consonant"- right?

 

"I guess the answer is subjective to the human being. It's based on what humans agree to sound like "tension" right?" Bloodsample

 

It may be subjective to you, to me there is a mathematical factor that is, so far, being overlooked.

 

In an elementary book on "Acoustics" you will find that there are ratios involved. An octave is one of the simplest ratios, some call it pure or Perfect even. a 1 to 2 ratio.

 

Example, if the lower pitched tone of an interval is 100 cycles per second , an octave higher is 200 cyles per second. That's science, circa 2007. Grammar school arithmetic.

 

All other intervals or combinations of tones have more complex ratios, except the Unison.

A major seventh interval is a more unwieldy ratio than an octave or a unison, which is btw 1 to 1. A fifth is roughly 2 to 3. So if your A above middle C for instance, is 440, the fifth above is 660 cycles. (I do not want to muddy this explanation up with the Equal Tempered Scale!!) A perfect Fifth above 440 is 660, that's science I believe.

 

Now moving on to chords;

the major triad is thought to be the purest sounding of the traditional triads. It's ratios bear this out.

It resembles the overtone series the closest as well.

And, btw, we measure the purity of the overtone series from the lowest tone not the other way around!!

 

I don't know if this proves my point against subjectivity, but it works for me.

The difference between what the most and the least learned people know is inexpressibly trivial in relation to that which is unknown
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suraci: Hey, I've definitely considered the physical/mathematical aspects. I agree with you 100% that there are resonant frequencies which sound good to us humans, so this is a link between physics (which is human interpretation of nature) and our brain's view of what we think is "nice". Not everything is subjective and conversely not everything can be shown to correspond to physics that have some kind of mathematical relevance.

 

Well I'm not too sure about what I'm saying because I haven't gone through every possible case. But I think we can agree that for every interval that sounds nice to a human there doesn't necessarily have to be a meaningful mathematical relationship between the frequencies. At least as far as I know.

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http://upload.wikimedia.org/wikipedia/en/f/f9/Dissonance-a220-a440-notated.jpg

The spectral analysis shows two sinusoidal tones. The tones remain in unison (220Hz) for the first two seconds of the graph. From the 2nd through the 30th second, the upper tone moves linearly upwards from 220Hz to 440 Hz, while the lower tone remains at 220Hz. For the final two seconds of the graph, the tones remain stable at one octave (220Hz and 440Hz).

 

On this graph, darker colors indicate frequencies that are stronger. The two fundamental tones are indicated by the two darkest lines near the bottom of the graph. Overtones are indicated by the lines and patterns above these two lines.

 

When the frequency ratio between the two tones approaches a simple fraction (3:2, 4:3, 5:4, etc.), the overtone pattern above the two tones at that point converges to a simpler and stronger pattern. Most listeners perceive these as points of greater "purity" or "harmoniousness" in the sound. It is generally considered that these are points of greater consonance, and in general the lower the numbers that are involved in the ratio, the greater the consonance. For instance, a 3:2 interval would be considered more consonant than a 4:3 interval, which itself would be more consonant than a 5:4 interval, and so on.

 

A few of the strongest points of consonance are indicate by arrows and the ratio between the frequencies of the upper tone and the lower tone is indicated.

 

On the graph it can be observed that there is a general correlation between the ratio of the frequencies involved and the number and spacing of the overtones that correspond to those ratios.

 

In between the points where the two tones approach a simple fraction (and thus are generally considered to be relatively consonant), the overtone picture on the graph appears more chaotic and jumbled. Most listeners hear a "roughness" or "disharmony" in the sound at these points. It is generally considered that these are points of greater dissonance.

 

Musical intervals made by the two tones are indicated at the appropriate points. Note that the exact placement of these intervals varies, depending on the tuning system used. In particular, under equal temperament the intervals m3 and m6 lie partway between the two arrows indicated.

 

http://en.wikipedia.org/wiki/Image:Dissonance-a220-a440-notated.jpg

 Find 600 of my jazz piano arrangements and tutorials for educational purposes at patreon.com/HarryLikas Harry was the Technical Editor of Mark Levine's "The Jazz Theory Book" and helped develop "The Jazz Piano Book."

 

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Certainly the purest explanation of why things are consonant and the whole construction of the diatonic scale can be attributed to the overtone series which is actually more complex to understand.

 

Sometimes, we have to just believe our ears when we say chord tones sound most consonant, chord tone extensions less consonant, and non-scale tones are even less consonant, and as jazz+ reminads us, the b9 interval is least consonant.

Hamburg Steinway O, Crumar Mojo, Nord Electro 4 HP 73, EV ZXA1

 

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Music has math in it, but it would miss the point if we said music IS math. Music is music, math is math.

 

A chemist knows better than a cook the chemistry of cooking, yet that isolated fact does not get him a gig in a five star hotel as a chef.

 

We live in a confusing world of too many facts.

 

To play well, associate with stronger players than yourself, or failing that, their recordings.

The difference between what the most and the least learned people know is inexpressibly trivial in relation to that which is unknown
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Originally posted by vicsant:

Wow. Great info!

 

What LH hand voicings can we use over the 2-5-1 progression when using the alt. dominant scale?

If you play a simple voicing on the LH using just the base chord tones, 1-3-5-7 you'll be able to play anything on the right. Think of one of the shell voicings 3/7, 1/7, etc.

 

Or you can play the tritone substitute on the left and that would be fine on the RH as well.

 

I'd avoid tones like 9, 11, 13 on the LH if I'm doing ALT on the RH. b9 intervals don't sound good.

Hamburg Steinway O, Crumar Mojo, Nord Electro 4 HP 73, EV ZXA1

 

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There are simpler ways to approach improvising that are more "ear-centric".

 

This exercise combines horizontal and vertical approaches to improvisation and develops ear training and intuition.

 

The ii-V7-I chord progression in the key of C is Dmi7 - G7- Cmaj7.

 

Step one is to arpeggiate each chord in the right hand. For Dmi7 the notes are "D,F,A,C", or try playing Dmi9 (use "F,A,C,E"). For G7 the notes are "G,B,D,F", or try playing G9 (use "B,D,F,A"). Finally, for C maj7 the notes are "C,E,G,B" or try playing Cmaj9 (use"E,G,B,D"). Isolate each chord for an extended period of time so that you are comfortable with these arpeggios. Always be sure to play with a good time feel and later you can vary the rhythmic content to sustain interest. Try shifting between whole notes, half notes, quarters, eighths, and triplets and use rests liberally.

 

Step two is to play the C major scale over each isolated chord (Dmi7, G7, Cmaj7). Use your ear to determine which notes are "dissonant" over each chord (the note "F" dissonant on C major, the note "C" is dissonant on G7) and try to find resolutions into chord tones. This doesn't quite sound like jazz yet, but we're getting there!

 

Step three is to add one chromatic note to the C major scale at a time while playing each chord, using your ear on the fly to find ways to resolve it. Try leaping to and from the "wrong" note. Try playing the wrong note on the downbeat as well as the upbeat. The point is to improvise melodic lines and being able to improvise numerous resolutions for the "wrong notes" using your ear.

 

For example, try adding the note "Ab" to the C major scale. Play this scale over Dmi7 for a while and see what happens. Use your ear and intuition to find resolutions. Then try this "modified" scale over G7 and Cmaj7 as well.

 

Repeat this process by adding the other chromatic notes to the C major scale one at a time (C#, D#, F#, Bb) creating other "modified" C major scales. Use these modified scales over Dmi7, G7, and Cmaj7. One thing that you will notice is that almost every note in the chromatic scale (except "C"and F#) sounds pretty good on the G7 chord.

 

After you've done this for a while, you should be able to use all 12 notes freely over these chords.

 

Vol.2 "Altered Dominants"

 

Assuming that you've already experimented with the major ii-V7-I chord

progression, seventh arpeggios, and the major scale, you're now ready to

experiment with the ascending melodic minor scale (also called the

"jazz" minor scale and the "real" minor scale) and its usage on dominant

seventh chords. This scale has the same notes as the major scale,

except the third note is flatted.

 

In the context of a major ii-V7-I chord progression in the key of C

(Dmi7-G7-Cmaj), continue using the C major scale on the Dmi7 chord and

the C major chord, but superimpose the Ab ascending melodic minor scale

over the G7 chord (Ab, Bb, B, Db, Eb, F, G). This scale produces all of

the "altered" extensions of G7 (b9, #9, b5, #5). Also experiment

playing Abmi6 and Abmi-maj7 arpeggios over the G7 chord.

 

 

Vol. 3 "Minor Key ii-V7-i"

 

MINOR ii-V7-I

 

The ii-V7-I chord progression in the key of A minor is Bmi7b5 - E7(b9) - Ami.

 

Step one is to arpeggiate each chord. For Bmi7b5 the notes are "B,D,F,A", For E7 the notes are "E,G#,B,D", or try playing E7b9 (use "G#,B,D,F"). Finally, for Ami the notes are "A,C,E,G" or try playing Ami9 (use "C,E,G,B"). Isolate each chord for an extended period of time so that you are comfortable with these arpeggios. Always be sure to play with a good time feel and later you can vary the rhythmic content to sustain interest. Try shifting between whole notes, half notes, quarters, eighths, and triplets and use rests liberally.

 

Step two is to play the A natural minor scale (a.k.a. C major scale) over each isolated chord (Bmi7b5, E7b9, Ami). Use your ear to determine which notes are "dissonant" over each chord and try to find resolutions into chord tones. Note that on the E7 chord, you should add the note G# to the scale. You will find that this added note works well on the A minor chord as well.

 

Step three is to add one chromatic note to the A natural minor scale at a time while playing each chord, using your ear to find ways to resolve it.

 

For example, try adding the note A# to the A natural minor scale. Play this scale over Bmi7b5 for a while and see what happens. Use your ear and intuition to find resolutions. Then try this "modified" scale over E7b9 and Ami as well.

 

Repeat this process by adding the other chromatic notes to the A natural minor scale one at a time creating other "modified" A natural minor scales. Use these modified scales over Bmi7b5, E7b9, and Ami.

 

After you've done this for a while, you should be able to use all 12 notes freely over these chords.

 

These exercises should put you well on your way toward improvising on a professional level.

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Rule Number 1: There Are No Rules.

 

Rule Number 2: Trust Your Own Two Ears, Even If Your Hearing Is Not What It Used To Be.

 

Rule Number 3: The one scale that will always work is the Chromatic Scale, since it always will contain every chord tone.

 

;)

 

 

A little more seriously: if you're writing software, start out by defining a set of "standard scales" (all the modes of major, melodic minor, harmonic minor, whole-tone, and diminished to start), and then for each chord find the subset that contain the chord tones. That will keep you busy for a couple lifetimes :)

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I was going

to add another

comment but find

it a real pain in

the ass to scroll

the screen sideways

to read everything.

 

Can we agree to keep

photos to a smaller size?

No guitarists were harmed during the making of this message.

 

In general, harmonic complexity is inversely proportional to the ratio between chording and non-chording instruments.

 

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Originally posted by stoo schultz:

Rule Number 1: There Are No Rules.

 

Rule Number 2: Trust Your Own Two Ears, Even If Your Hearing Is Not What It Used To Be.

 

Rule Number 3: The one scale that will always work is the Chromatic Scale, since it always will contain every chord tone.

 

:thu: exaxctly right.
♫♫♫ motif XS6, RD700GX
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I once heard it expressed, "Use all 12 notes. Just don't play them all in order and don't play any of them too often".

 

Another cutesy expression: "One wrong note = mistake. Two 'wrong notes" in a row = jazz. Three wrong notes in a row = an arrangement!

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