# Theoretically common scales



## tpl2000 (Apr 2, 2014)

Greetings!

I have known the major/minor, blues minor, pentatonic, and harmonic minor scales for the last few years, and... Not too much else. I recently learned Her Ghost in the Fog, by Cradle of Filth (by ear, hooray for progress!) and realized that they go over one particular scale, which seems to be half-whole-half-whole-half-whole,with the steps used. 

So I ask of you: what other scales are typically used in common music, these days? (Excluding thrash bands, like Slayer. It sounds cool once or twice, but they're a genre I'm well past)


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## Mr. Big Noodles (Apr 2, 2014)

Vegetarian Major has been picking up steam since the 80's.


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## tpl2000 (Apr 2, 2014)

Mr. Big Noodles said:


> Vegetarian Major has been picking up steam since the 80's.



Thank goodness they haven't moved to Vegetarian Minor yet...


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## Mr. Big Noodles (Apr 2, 2014)

Tell me about it. 

These scales are used in 90% of Western music:

Major (1 2 3 4 5 6 7)
Natural minor (1 2 &#9837;3 4 5 &#9837;6 &#9837;7)
Harmonic minor (1 2 &#9837;3 4 5 &#9837;6 7)
Melodic minor (1 2 &#9837;3 4 5 6 7)

The pentatonic scales are subsets of those:

Major pentatonic (1 2 3 5 6)
Minor pentatonic (1 &#9837;3 4 5 &#9837;7)

Blue notes are added per stylistic preference and can really include any chromatic inflection.

You'll encounter these scales occasionally:

Mixolydian (1 2 3 4 5 6 &#9837;7)
Dorian (1 2 &#9837;3 4 5 6 &#9837;7)
Phrygian (1 &#9837;2 &#9837;3 4 5 &#9837;6 &#9837;7)
Lydian (1 2 3 #4 5 6 7)

These are some important symmetrical scales:

Whole tone (1 2 3 #4 #5 &#9837;7)
Octatonic (1 &#9837;2 &#9837;3 3 #4 5 6 &#9837;7)

There are innumerable other pitch collections out there. You are better off learning the how and why rather than all of the what. Do the lessons on this website: musictheory.net

This cute little PDF is not perfect, but it is a good read: http://tobyrush.com/theorypages/pdf/complete.pdf


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## tpl2000 (Apr 2, 2014)

Actually, I have a question about that as well... Why are the additional scales you mentioned (Mixolydian through Lydian) considered extra scales, when they're really just major/natural minor based on different roots, with the same notes in the key? I've been wondering this over the years, it doesn't make too much sense. (Not to mentioned, it would be much easier to say "Bb major, but the root is actually the 3rd in the key")


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## JohnIce (Apr 2, 2014)

tpl2000 said:


> Actually, I have a question about that as well... Why are the additional scales you mentioned (Mixolydian through Lydian) considered extra scales, when they're really just major/natural minor based on different roots, with the same notes in the key? I've been wondering this over the years, it doesn't make too much sense. (Not to mentioned, it would be much easier to say "Bb major, but the root is actually the 3rd in the key")



Well, A minor is just a C major scale starting on A. I very much disagree that saying "Bb major but the root is actually the 3d in the key" is easier  that's like saying "Grass is the fourth colour from Red" or something


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## stevexc (Apr 2, 2014)

tpl2000 said:


> when they're really just major/natural minor based on different roots, with the same notes in the key?



They're not all "just major/natural minor". They do all have either a major or minor tonality, but they're all different scales with different relationships.

"Bb major but the root is actually the 3rd" is confusing and inaccurate compared to "D Phrygian" - this gets the actual root across, as well as the tonality. If you wanted to say "D Minor, flat 2nd" you'd be closer, though.

For the same reason you wouldn't say "C major, but start the root from the 6th!" because A minor makes a lot more sense.


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## celticelk (Apr 2, 2014)

tpl2000 said:


> Actually, I have a question about that as well... Why are the additional scales you mentioned (Mixolydian through Lydian) considered extra scales, when they're really just major/natural minor based on different roots, with the same notes in the key? I've been wondering this over the years, it doesn't make too much sense. (Not to mentioned, it would be much easier to say "Bb major, but the root is actually the 3rd in the key")



IMO, you gain nothing in terms of application by viewing the "modal" scales as "versions" of a parent major scale. You're better off thinking of that relationship as coincidental - D Dorian happens to contain the same pitches as C Ionian and G Mixolydian.


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## Mr. Big Noodles (Apr 2, 2014)

Basically what everybody has said.



tpl2000 said:


> Actually, I have a question about that as well... Why are the additional scales you mentioned (Mixolydian through Lydian) considered extra scales, when they're really just major/natural minor based on different roots, with the same notes in the key? I've been wondering this over the years, it doesn't make too much sense. (Not to mentioned, it would be much easier to say "Bb major, but the root is actually the 3rd in the key")



You're operating under a common misconception here. It doesn't help that many musicians (especially those on the internet) perpetuate misinformation, mostly because they themselves are trying to figure out this whole music thing, and all the little shortcuts and mistakes they make pile up, making for a shaky foundation. Case in point, your use of the word "root". Chords have roots. Scales and keys _do not_ have roots. Scales and keys have a tonic. This is relevant because chords are built from the major and minor scales, and chord progressions are built from those chords. All of those chords want to go to the tonic, so we must have delineation. 







Above: the major and minor scale harmonized. Notice that the minor scale borrows a couple of chords from the major scale. This allows a more tonal presentation of the minor mode. Here is the flowchart for diatonic chord progressions in the major mode:






Swap out those numerals for the equivalent in the minor mode, and you get the diatonic progressions in minor.

Don't worry about "modes" or whatever. Read that PDF I linked, do the lessons and exercises on that site I showed you, and let that stew in your brain for three months. You'll be a much better musician than when you started.


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## viesczy (Apr 2, 2014)

Just something to toss in, for the longest time now I have been LOVING me the bebop scales bot the dominant and melodic minor - adding either the passing tone btwn the 5 & 6 or 6 & 7. 

Yes they tend to "work" best over dom 7ths or maj 6ths chords, but when played with conviction and resolving any tension, they "work" other places as well. If I 'lose' my melodic thought... I just use them both. 

Back to the convo at hand.

Derek


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## ncfiala (Apr 3, 2014)

I'd say that all one really needs are major, natural minor, harmonic minor, melodic minor, major pentatonic, minor pentatonic, whole-tone, half-whole diminished, and whole-half diminished. This may seem like a lot but there are lots of modal and subset relationships amongst these and the last three are symmetric. It may also seem a little arbitrary but if you study diatonic set theory you will see that these scales have interesting properties that distinguish them from all or almost all other scales. For instance, the major scale is essentially the only heptatonic scale with all of the following properties: it has the deep scale property, the maximal evenness property, the cardinality equals variety property, the structure implies multiplicity property, Myhill's property, and it is generated and well-formed.


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## tedtan (Apr 3, 2014)

tpl2000 said:


> one particular scale, which seems to be half-whole-half-whole-half-whole



That would be the half step/whole step diminished scale (there is also a whole step/half step diminished scale). Beyond that tidbit, everyone else beat me to the party.


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## Mr. Big Noodles (Apr 3, 2014)

ncfiala said:


> It may also seem a little arbitrary but if you study diatonic set theory you will see that these scales have interesting properties that distinguish them from all or almost all other scales. For instance, the major scale is essentially the only heptatonic scale with all of the following properties: it has the deep scale property, the maximal evenness property, the cardinality equals variety property, the structure implies multiplicity property, Myhill's property, and it is generated and well-formed.



Would you mind elaborating?


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## ncfiala (Apr 3, 2014)

Mr. Big Noodles said:


> Would you mind elaborating?


 
I'd rather not. I don't have the patience to make the elaborate posts that you do SW, or I guess it's MBN now. The book Foundations of Diatonic Theory by Johnson is a really basic book on diatonic set theory if you're interested in this stuff.


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## JustMac (Apr 3, 2014)

JohnIce said:


> "Grass is the fourth colour from Red" or something


 And the blue is the b5th colour from the (grass)root!


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## redstone (Apr 3, 2014)

If I'd list the most interesting scales to understand in my opinion, it would be the seven holy circles of thirds : major, melodic minor, harmonic minor, harmonic major, whole tone, diminished and augmented scales. People might use other scales for melodic purpose, but our sense of harmony is deeply triadic, those little circles of 3rds rule our emotions..


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## Mr. Big Noodles (Apr 3, 2014)

ncfiala said:


> I'd rather not. I don't have the patience to make the elaborate posts that you do SW, or I guess it's MBN now.



Thank you. You've been very informative.



> The book Foundations of Diatonic Theory by Johnson is a really basic book on diatonic set theory if you're interested in this stuff.



I'm not, but I'll look into it.

A review on the book: http://trace.tennessee.edu/cgi/viewcontent.cgi?article=1064&context=gamut

From what I read in the preview on Amazon, it looks like an interesting concept. I'd be interested to see where this kind of thinking goes. Apparently, Milton Babbitt had some involvement, and I like Milton Babbitt. ncfiala, did you take a class on this stuff or maybe read up on it on your own?



redstone said:


> If I'd list the most interesting scales to understand in my opinion, it would be the seven holy circles of thirds : major, melodic minor, harmonic minor, harmonic major, whole tone, diminished and augmented scales. People might use other scales for melodic purpose, but our sense of harmony is deeply triadic, those little circles of 3rds rule our emotions..



redstone, what are these "circles of thirds"?


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## redstone (Apr 3, 2014)

Pretty much like the chromatic scale is a circle of 5ths or 4ths, those 7 scales are circles of 3rds, literally. The 3 symmetric scales consist in two symmetric circles instead of one, but the result is the same, triads everywhere


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## AugmentedFourth (Apr 4, 2014)

redstone said:


> Pretty much like the chromatic scale is a circle of 5ths or 4ths, those 7 scales are circles of 3rds, literally. The 3 symmetric scales consist in two symmetric circles instead of one, but the result is the same, triads everywhere



So... correct me if I'm wrong, but by this do you mean

Diminished scales = 2 rings of minor thirds (a.k.a. dim7 chords) offset by 1 or 2 semitones

Whole tone scale = 2 rings of major thirds (a.k.a. augmented chords) offset by 2 semitones

Symmetric half-augmented scale (not sure what to call it, e.g. C Db E F G# A) = 2 rings of major thirds (a.k.a. augmented chords) offset by 1 semitone?


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## redstone (Apr 4, 2014)

Yup


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## ElRay (Apr 7, 2014)

tpl2000 said:


> Thank goodness they haven't moved to Vegetarian Minor yet...



Ditto here. I keep hearing talk about "Whole Grain" begin better. I'm not sure what to do with no half-grains, or chromatic-grains. I think Vegetarian Whole-Grain Minor might be the death of me.

Ray


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## celticelk (Apr 7, 2014)

redstone said:


> Pretty much like the chromatic scale is a circle of 5ths or 4ths, those 7 scales are circles of 3rds, literally. The 3 symmetric scales consist in two symmetric circles instead of one, but the result is the same, triads everywhere



I'm uncomfortable with that terminology, for two reasons:

1. The circles of 4ths and 5ths use the same interval throughout. If you're talking about the diatonic scales as "circles of 3rds," you're actually varying the interval between major and minor thirds in a way that is not obvious unless you already know what scale you're deriving.

2. The circles of 4ths and 5ths pass through all twelve chromatic pitches before returning to their starting point. Neither a "pure" circle of thirds (the augmented or diminished-7th chords) nor your "diatonic circle of thirds" have that property.


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## redstone (Apr 7, 2014)

It's just a way to "explain" why only those ones are completely triadic, thus so favored in western harmony.

Thirds are either major or minor, so they're circles of thirds, but I understand your discomfort. However, maybe the real issue is that calling those two intervals "third" doesn't make any (known) mathematical sense to begin with. What kind of geometrical properties are we looking for anyways ? What's the purpose of rationalizing music ?


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## Mr. Big Noodles (Apr 7, 2014)

redstone said:


> It's just a way to "explain" why only those ones are completely triadic, thus so favored in western harmony.



I still don't really understand what your circle of thirds is. As celticelk pointed out, you would need to know what you're looking for in order to find it with that system. The maximal evenness exercises in that diatonic set theory book seem like they would better address what you're getting at. How would you express the diatonic scale with circles of thirds? You would need at least three triadic circles, or one triadic circle and one tetradic circle, and that abstraction would be totally arbitrary. Unless I am misunderstanding you. A diagram would help.



> Thirds are either major or minor, so they're circles of thirds, but I understand your discomfort.



Because a cycle purely of minor thirds repeats after the fourth entry, and a cycle purely of major thirds repeats after only the third entry, and yet our tuning system has twelve notes that are completely accounted for when using a cycle of perfect fifths or minor seconds? The only way I see this working is if your cycle alternates between major and minor thirds.

A C E G B D F# A C# E G# B D# F# A# C# F A&#9837;C E&#9837;G B&#9837;D F

And as you can see, it's not the cleanest solution. For every entry, there is a duplicate. Hey, watch what happens if you take out every other note. 

A E B F# C# A&#9837; E&#9837; B&#9837; F C G D

Woo! Circle of fifths!



> However, maybe the real issue is that calling those two intervals "third" doesn't make any (known) mathematical sense to begin with.



It makes plenty of musical sense, though. Our musical culture is founded on the diatonic scale. The third note of said scale is the third note of said scale, also known as te third. Similar harmonic intervallic structures built from other degrees of said scale strongly resemble the initial third, hence the naming of the interval. 



> What kind of geometrical properties are we looking for anyways ?



Ask Pythagorus.

Music theory is usually descriptive: we see a structure, then put a name to it.



> What's the purpose of rationalizing music ?



Humans like to rationalize. We also like to defy rationale. Ours is a paradoxical existence. There is an Apollonian/Dionysian dichotomy at play. Both sides have their ups and downs, and to say that one should be favored over the other is kind of silly. Try getting into a discussion over which direction you put the toilet paper on the dispenser sometime and see how ridiculous people get over such an insignificant opinion. I think it makes perfect sense to codify music, because it makes it easy to communicate ideas, learn, and experiment. As a composer and arranger, it definitely helps to slap a bunch of notes on a page for the sole purpose of filling out a harmony and knowing that they will sound pretty good. And I don't think you can keep people from analyzing and theorizing. If you destroyed the body of music literature that we have created and erased the memories of all who knew it, we would write it all again. I have had conversations with people who perform my music on structures within the music that don't have established names. We have to discuss these things for rehearsal purposes. Ultimately, having a technical language makes things easier.


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## redstone (Apr 7, 2014)

Mr. Big Noodles said:


> I still don't really understand what your circle of thirds is.
> 
> How would you express the diatonic scale with circles of thirds? You would need at least three triadic circles, or one triadic circle and one tetradic circle, and that abstraction would be totally arbitrary. Unless I am misunderstanding you. A diagram would help.



C E G B D F A (C)



Mr. Big Noodles said:


> Because a cycle purely of minor thirds repeats after the fourth entry, and a cycle purely of major thirds repeats after only the third entry, and yet our tuning system has twelve notes that are completely accounted for when using a cycle of perfect fifths or minor seconds? The only way I see this working is if your cycle alternates between major and minor thirds.
> 
> A C E G B D F# A C# E G# B D# F# A# C# F A&#9837;C E&#9837;G B&#9837;D F



I never intended to describe the chromatic structure with such circles of thirds, wouldn't make any sense indeed, they just highlight how our attraction for triads "commonized" such scales in the harmonic context of western music : out of necessity. It helps people to realize why most exotic/eastern/unidentified scales are marginalized even though they might be melodically attractive.



Mr. Big Noodles said:


> It makes plenty of musical sense, though. Our musical culture is founded on the diatonic scale. The third note of said scale is the third note of said scale, also known as te third. Similar harmonic intervallic structures built from other degrees of said scale strongly resemble the initial third, hence the naming of the interval.



Indeed, that's my point, I'm not using those circles to draw some rose windows. Being geometrically logic, symmetric, is irrelevant.. 





Mr. Big Noodles said:


> Ask Pythagorus.
> 
> Music theory is usually descriptive: we see a structure, then put a name to it.



Also my point  (we already discussed about that, if you remember)



Mr. Big Noodles said:


> Humans like to rationalize. We also like to defy rationale. Ours is a paradoxical existence. There is an Apollonian/Dionysian dichotomy at play. Both sides have their ups and downs, and to say that one should be favored over the other is kind of silly. Try getting into a discussion over which direction you put the toilet paper on the dispenser sometime and see how ridiculous people get over such an insignificant opinion. I think it makes perfect sense to codify music, because it makes it easy to communicate ideas, learn, and experiment. As a composer and arranger, it definitely helps to slap a bunch of notes on a page for the sole purpose of filling out a harmony and knowing that they will sound pretty good. And I don't think you can keep people from analyzing and theorizing. If you destroyed the body of music literature that we have created and erased the memories of all who knew it, we would write it all again. I have had conversations with people who perform my music on structures within the music that don't have established names. We have to discuss these things for rehearsal purposes. Ultimately, having a technical language makes things easier.



tl;dr

just kidding, I don't have the time to write a proper answer, it was a rhetorical question by the way


--


To summarize, some scales became common because, that's my theory, our growing need for a diversity of enjoyable chord progressions pushed us to select scales with the largest triadic content, thus scales consisting in circles of thirds, which is in my opinion a useful way to describe them in this context. Those are my "theoretically common scales".


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## lelandbowman3 (Apr 21, 2014)

I feel really bad because I don't understand the numbers/letters when someone posts a "linear" scale. Like the scale:1 2 3 4 5 etc


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## AugmentedFourth (Apr 21, 2014)

redstone said:


> C E G B D F A (C)
> 
> .....
> 
> To summarize, some scales became common because, that's my theory, our growing need for a diversity of enjoyable chord progressions pushed us to select scales with the largest triadic content, thus scales consisting in circles of thirds, which is in my opinion a useful way to describe them in this context. Those are my "theoretically common scales".



OK, so yes. You can describe the major scale (and thus all of its modes) using a cycle of thirds, but what kind of third you use when you move up a third is completely arbitrary and without context.

In your example of



redstone said:


> C E G B D F A (C)



You start at a "root," in this case C, and go up by these thirds:

M3
m3
M3
m3
m3
M3
(m3)



How does that seemingly 'random' sequence of thirds constitute the scale upon which western music is practically _based upon_?

I think that cycles of thirds explanations for symmetrical scales like whole tone and H-W diminished makes perfect sense. But you can't extend the same concept to explain why other scales like the major scale are common. For that I might recommend the diatonic set theory text.

Let's take a similarly arbitrary cycle of thirds like you did to construct your major scale and follow essentially the same rules:

*Only major and minor thirds, no diminished or augmented ones
*No overlapping (can't hit the same note at a higher octave, this rule can probably be removed to create even more bizarre scales)
*Must arrive @ the tonic


```
C -> E -> G# -> B -> D# -> F# -> A -> (C)
  M3   M3    m3   M3    m3    m3   m3

C D# E F# G# A B (C)
```

In 'major scale notation':

1 #2 3 #4 #5 6 7

What is this scale? I don't even think it has a name as far as I'm concerned, that's how not common it is.

Anyways... to answer lelandbowman3's question,

When people notate things like that they usually refer to the notation I called 'major scale notation' above. Basically 1 refers to the root note. Then the 2, 3, 4, etc. refer to the second, third, fourth, etc. tones of the scale. They are written with respect to the major scale. so by default we have

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

But then we can notate things like, for example, natural minor:

1 2 b3 4 5 b6 b7
C D Eb F G Ab Bb

So, really, I lied about '5' being the 5th tone. A '5' just means a note a fifth away from the root and 'b5' is a diminished fifth from the tonic, etc.

The 'blues' scale:

1 b3 4 b5 5 b7
C Eb F Gb G Bb

Lydian:

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

H-W Diminished:

1 b2 b3 b4 b5 5 6 b7
C Db Eb Fb Gb G A Bb


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## lelandbowman3 (Apr 22, 2014)

Gotcha. OK that makes since now
Do they have set notes, or can they be transitioned into any scale?


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## AugmentedFourth (Apr 22, 2014)

lelandbowman3 said:


> Gotcha. OK that makes since now
> Do they have set notes, or can they be transitioned into any scale?



No. The root may be any note you like. I just used examples starting on C because that's pretty much the default note we start on since C major is all of the white (no sharp/flats) keys on a piano. With the examples starting on C you can get an idea of what the notation sounds like when turned into actual scale form.


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## JustMac (Apr 22, 2014)

I don't mean to derail the strictly-theoretical interval/scale discussion, but I also don't want to start a new thread because it is really limited in scope, but I was wondering, does the music by the band SikTh employ any real "scales" besides chromatic? I'm sure it isn't atonal because it is still 'structured', but when I'm learning their stuff I'm constantly amazed at how they make it sound nice . Hope one of you guys listen to them so you can demistify the mystery of their sound


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## AugmentedFourth (Apr 22, 2014)

JustMac said:


> I don't mean to derail the strictly-theoretical interval/scale discussion, but I also don't want to start a new thread because it is really limited in scope, but I was wondering, does the music by the band SikTh employ any real "scales" besides chromatic? I'm sure it isn't atonal because it is still 'structured', but when I'm learning their stuff I'm constantly amazed at how they make it sound nice . Hope one of you guys listen to them so you can demistify the mystery of their sound



Maybe with (a) more specific example(s) people may be able to help out. Personally I'm not the greatest transcriber so I may be of limited help.


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## JustMac (Apr 22, 2014)

I think this is a good example. I *think* it floats around some kind of diminished sound but I find it extremely hard to rationally analyse. I hate it because I love whatever they're doing, but I can't understand it on a technical level (even by learning to play most of it).


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## ncfiala (Apr 23, 2014)

JustMac said:


> I'm sure it isn't atonal because it is still 'structured'


 
Atonal does not mean unstructured. Lots of atonal music is much more rigidly structured than most tonal music.


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## Gmaj9 (Apr 23, 2014)

JustMac said:


> I don't mean to derail the strictly-theoretical interval/scale discussion, but I also don't want to start a new thread because it is really limited in scope, but I was wondering, does the music by the band SikTh employ any real "scales" besides chromatic? I'm sure it isn't atonal because it is still 'structured', but when I'm learning their stuff I'm constantly amazed at how they make it sound nice . Hope one of you guys listen to them so you can demistify the mystery of their sound



Their music is structured, just not as harmoniously continuous as most other music. That being said, as a huge fan of Sikth, they do jump around between just playing dissonance and consonance. For example: The intro from Part of the Friction (for the best of my hearing) seems to based on Bb mixolydian (or some major mode based off Eb major) with the amazing melodic section towards the end of the song is based on C minor (the relative minor of Eb.) with few Non-chord tones and non-scale tones in between.

Other songs have far more obvious continuity of a tonal center. "Where Do We Fall" is quite entirely based off C # major/a# minor (I'm picking up some d# Dorian licks in the song and some strong G #Mixolydian, but because of their erratic/playful playing style, it's hard to say the song is based on one continuous scale, rather--it's based on one "father" scale and the song is played on different modes derived off of it.)

"In This Light" is one that mostly just on C # minor, with little bounces between its' modes. So I would say, out of the ones I examined, it's the most "continuous" harmonically.

As for songs like Bland Street Bloom: the intro, verse and chorus and chorus seem based on g # minor, with A LOT of clashing dissonant notes in between. It's important to note, that just because a song sounds distorted/dissonant, it doesn't mean there isn't a larger underlying scale.

So, from above, I conclude that Sikth mostly plays in key, however, they switch from various modes in between while also introducing a lot of non-chord tones and non-scale tons for the hell of it.


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## JustMac (Apr 24, 2014)

That's really interesting, they're the only metal band that really foray into this kind of stuff, I assume it's the same story with the song How May I Help You? too  Thanks + rep!


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## Mr. Big Noodles (Apr 25, 2014)

JustMac said:


> I don't mean to derail the strictly-theoretical interval/scale discussion, but I also don't want to start a new thread because it is really limited in scope, but I was wondering, does the music by the band SikTh employ any real "scales" besides chromatic? I'm sure it isn't atonal because it is still 'structured', but when I'm learning their stuff I'm constantly amazed at how they make it sound nice . Hope one of you guys listen to them so you can demistify the mystery of their sound





JustMac said:


> I think this is a good example. I *think* it floats around some kind of diminished sound but I find it extremely hard to rationally analyse. I hate it because I love whatever they're doing, but I can't understand it on a technical level (even by learning to play most of it).



Don't think scales. I had a quick listen. There is some very standard functional tonality in there, a few metalisms (going back and forth between E&#9837;5 and E&#9837;° at 0:30; the thrash bands in the 80's and 90's did this all the time), as well as a lot of techniques from the world of "extended tonality". Traditional tonality (developed in the years 1600-1900) is a tertian language. All of our chords are built by stacking thirds on top of each other, and are linked by tonal relationships that resolve one tertian structure into another. That's how it was for several hundred years. Extended tonality opens up the harmonic palette to other modes of intervallic organization, and therefore more modes of expression. Here are some techniques of extended tonality:



Diatonic planing - Taking a single chord voicing and spamming it around the key without regard to functional diatonic relationships. Completely parallel voice leading. Example: C/E Dm/F Em/G Dm/F C/E
Chromatic planing - Taking a single intervallic structure and spamming it around without regard to key. Parallel voice leading again. Example: Em9 Bm9 B&#9837;m9 Am9 Gm9
Quartal harmony - Chords built from the interval of the perfect fourth. In jazz, quartal harmony is considered to be a voicing strategy for otherwise tertian structures, so having a chord built of fourths does not always put a piece into extended tonality territory.
Secundal harmony - Chords built from major and minor seconds. May be diatonic or chromatic. Sometimes referred to as "clusters".
Chord of mixed intervals - What it sounds like. Works as long as it is not just a voicing of a tertian chord. Example: B C F# A# has elements of secundal (A# B C), tertian (F# A#), and quintal (B F#) harmony, as well as nice tritone in the middle (C F#).
Non-tertian organization in general - Leaving it open. Extended tonality is about opening yourself up to new ideas and expanding upon the old framework. If there is something I have left out here, this should cover it.
Bimodality - Two simultaneous modes happening right on top of each other, or possibly in rapid alteration (though you really need a case for it to call it bimodal). Example: a phrase played by guitar 1 in C major while guitar 2 plays another phrase in C minor at the exact same time. Cross relations (two rhythmically simultaneous or near notes of the same functional class but different qualities) will occur, such as E and E&#9837;, A and A&#9837;, B and B&#9837;...
Bitonality - Two simultaneous tonal centers happening right on top of each other. For example, C major and F# major. The modal information (major) is not as important as the tonal information (C and F#), and the melodic construction is actually more important than functional pitches. The aim is not to convince the listener that there are in fact two simultaneous keys, but rather to juxtapose two melodies that relate to different pitches. *Both bimodality and bitonality rely on counterpoint. It's a melodic thing first and a harmonic thing second.*
Use of non-traditional modes (traditional is major/minor, and the ecclesiastic modes depending on how they are used).
Use of tertian harmony in new and different ways. You need to make a good case for it if you want to lump it in with extended tonality.
Freely chromatic interval organization - In traditional tonality, chromaticism is usually functional. That is to say in the progression Fm F#°7 G7, F#°7 has a specific set of expectations. The tritone F# C is inextricably tied to the G7 that follows it. In extended tonality, one might take that same tritone interval and free it from any harmonic context other than its own. This is hard to articulate verbally, I think it becomes clear when one familiarizes oneself with the repertoire.
Claude Debussy - Pour le piano, No.2, "Sarabande"


0:00 - The piece begins with diatonic planing in the right hand. Each melody note is harmonized with a fifth and an octave above.

0:47 - Chromatic planing. The chords are F#7 E7 D7 E7 F#7 G#7, etc. Notice that this passage sounds like a whole tone sonority. The whole tone scale, a non-traditional mode, is D E F# G# A# C, and those chords would all fit seamlessly into that pitch collection if it weren't for the perfect fifth in each chord. However, we still register it as a whole tone sort of thing.

1:31 - A little tonal ambiguity there. This phrase sounds like it is reinforcing E major right up until that modal cadence in C# minor at the end.

1:45 - Quartal harmony.

2:28 - Diatonic planing.

3:58 - Planing in the left hand.

4:28 - Quartal harmony

Bartók, who is the go-to composer for polytonality and polymodality, does bitonality in two ways: melody + accompaniment, or melody + melody.

Béla Bartók - Mikrokosmos, No.70, "Melody against double notes"







This is melody + accompaniment. Note that each hand has a different key signature. The right hand has the melody first, and is in the key of F#. Doesn't matter whether it's F# major, minor, or whatever. Actually, the melody is modally ambiguous: we get neither a third, sixth, nor seventh, which are the scale degrees we usually use to figure out modality. The left hand has the accompaniment first, and it is in D. Once again, no third, sixth, or seventh, so we're in a modal no-man's land.

It is kind of interesting that Bartók conceived of "amodal" music here. You don't hear that too often, if at all; in the twentieth century, everybody grabbed on to all sorts of modes and wanted to make modally complex music, cram as many notes as you can into that octave, invent new tuning systems to cram even more notes. Thirds of all sorts everywhere. Then here's Béla, using scales that only have four notes and no third. It sounds like, I don't know, a shell.

Anyway, at measure 10 the hands switch roles: the left hand takes the melody, the right hand does accompaniment. You might not catch this unless you know what to look for, but the melody here is the inversion of the melody at the beginning. At measure 17, both hands are playing melody, and at 21 they're both playing accompaniment. We finally get the third for each tonality in measure 23, and the downbeat of 24 has both of the tonic fifths coming together to make a composite sonority that is a tertian chord: D&#8710;. Note, however, that the composer is thinking of this as two interlocking perfect fifths, and not a series of thirds stacks on top of one another. It's a weird thing to say, but it's a quintal harmony while also being a tertian harmony.

Béla Bartók - Mikrokosmos, No.105, "Playsong"


*Sorry, couldn't find a video of just 105. Skip to 9:10 to get to the correct piece.*






And here is melody + melody. Once again, each hand has a different key signature. And once again, the pitch material is amodal - that same 1 2 4 5 scale. B comes into both hands later, screwing up that exclusivity, but B has a purpose. Left hand is in the key of C#, right hand is in the key of D. Minor second relationship, right? Bartók is using a technique called "imitation" in the first system: a melody sounds, and the same melody is echoed in another voice (and, in this case, at a different pitch level).

In the second system (più allegro), he pulls out another technique called "mirror inversion," which is making a countermelody that does the exact same thing that the reference melody is doing, but going the opposite direction (contrary motion).

The third system breaks away from the inversion, then the fourth system utilizes "similar motion," which is almost parallel motion, but the voices are not always moving at the same interval. I think Bartók does this because he is a.) trying to avoid the third of each respective mode, and b.) because he is projecting the pitches from that octave B pedal tone that encases the two melodic voices. That is to say that the lowest pitch in the right hand is D, which is a major sixth _below_ B, and the highest pitch in the left hand is G#, which is a major sixth _above_ B. Additionally, D is the right hand's tonic and G# is the left hand's dominant. Or maybe it's not. The pitch collections are symmetrical: D-E is a major second, A-G is a major second; D-G is a perfect fourth, A-E is a perfect fourth. Theoretically, the material in the first measure could have easily been its own retrograde inversion. If that's the case, try this on for size: left hand's tonic is really G#, right hand is still D. Plot those on either side of B, they're both a minor third away from B. The tritone (outlined here by G#-D and bisected by B) has significance for Bartók because it divides the octave in half. It would be exciting if there was an F somewhere in this piece, because then we would have a neatly quartered octave, but the lack of that pitch suggests to me that this piece is less about dividing the octave up into four symmetric pitch centers and more about building tonal regions at symmetric intervals by using B as a pitch axis. So the tonic is... B? This is crazy shit, I know. I swear that this could be how he was thinking - if you delve too deep into some of his more complex music, the things you find are downright scary.

The last measure is another one of those conglomerate quintal sonorities masquerading as a tertian chord: C#m7.

I was going pull a bit out from the fifth string quartet, but I've done enough fawning over someone who is clearly a better composer than I could ever be.  Still, you should check it out if you have half an hour of your day to dedicate to enriching your musicality.

Béla Bartók - String Quartet No.5


^ This is a mediocre performance. If you want to hear real shredding, buy the Emerson Quartet's double album of all six of the quartets and blast that shit while you're in the drive-thru at Burger King, or I guess Quick if you're in France.

Now that we have some new tonal vocabulary, let's go back to SikTh. The very first thing we hear in the tune is a chugga chugga E. We get a riff that very quickly outlines an arpeggiated B&#9837;ø7 resolving to A. An unusual chord progression, but it has precedent in the world of traditional tonality. The B&#9837;ø7 is actually an augmented sixth (SikTh?) chord, though you won't find it described no matter how good of a Google sleuth you are, because augmented sixth chords that have a half-diminshed seventh sonority are super rare. If you do the Google, you'll likely end up looking at the lame normal augmented sixth chords. Basically, +6 resolution is about approaching an octave chromatically from either direction. G# > A, B&#9837; > A. The rest of the "chord" comes about by filling in what's between B&#9837; and G#. Since that interval is enharmonically equivalent to the minor seventh, that can be quite a few chords. Here is our chord (and resolution) in four parts:






First is resolving to a minor tonic. Second is resolving to a major tonic (My bad, that should be "I" rather than "i"). Neither of those are spelled "correctly" if you go by the chord symbol (B&#9837;ø7 is B&#9837; D&#9837; F&#9837; A&#9837, but this is the correct notation since augmented sixth chords are used solely for voice leading purposes rather than as standalone sonorities. Therefore, we can use whatever enharmonic spelling suits us. The third measure shows the inversion of the augmented sixth interval, which is a diminished third, and how that resolves to a unison.

Here is an incredibly famous example of the same relationship, though not quite kosher with the resolutions:



And look, they went ahead and highlighted it for us too. How thoughtful. Respell that with F as the root, and you get F C&#9837; E&#9837; A&#9837;, which you can reorder as F A&#9837; C&#9837; E&#9837;, or Fø7. The chord in the next measure is E7, with a big fat chromatic passing tone on the downbeat. Unfortunately, the rhetoric surrounding this passage is steeped in bullshit, mostly perpetuated by people who don't know enough about music to comment productively, despite their good intentions, but you can read more on the Tristan Chord at this website if you wish. The disclaimer at the top of the page tells you the important part.



> The connection between the augmented-sixth chord known as the "German Sixth," and Wagner's famous "Tristan Chord," is one of creatively alternative resolution. It is not so much that either the German Sixth or the Tristan Chord is a new harmonic entity; it is that in either case we have a familiar harmonic entity used in a creatively alternative manner.


I'm willing to bet that the guys from SikTh have no idea that they're dabbling in altered augmented sixth chords, probably have never sat through a Wagner opera, and only did it because it "sounded good". Okay, that covers the first two seconds. 

At 0:03, they're doing something harmonized at the interval of a minor second. I'm too lazy to figure out exactly what, but the technique is unmistakeable. Refer back to our extended tonality resources and you have three techniques that cover this: secundal harmony, chromatic planing, and possibly bitonality. At 0:51, it sounds to me like a chromatic line harmonized at the tritone. 1:09 might be a common tone diminished chord sort of deal; something like C and C° going back and forth. 1:32, dem tritones. After the 2:00 mark, it gets a bit more diatonic. Natural minor. 2:28 is a nice groove in 7, performed as 2+2+3. Basically, go crazy: pick some chords you think sound nice, write some angular riffs and make them even more angular by harmonizing them at the tritone and the minor second, use common tone diminished chords, change key often, and groove every now and then.

By the way, doing some research led me to this: Mike Dolbear DRUMS | Interview with Dan Foord of Sikth



> *Mike: How did it all start?*
> Dan: I got into drumming at an early age always taping and winding my parents up and started lessons at about 12, I studied with a local teacher a guy named Peter Hearn for about 4 years who used to teach me lots of Latin rhythms. Even back then I was listening to metal bands. I then went to Music College where I did a B Tec national diploma in popular music.
> 
> 
> ...


Finally! Here's a rock musician telling you kids to learn to read. Go and do iiiiiiiittttt!!!!


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## Konfyouzd (Apr 25, 2014)

ncfiala said:


> I'd say that all one really needs are major, natural minor, harmonic minor, melodic minor, major pentatonic, minor pentatonic, whole-tone, half-whole diminished, and whole-half diminished. This may seem like a lot but there are lots of modal and subset relationships amongst these and the last three are symmetric. It may also seem a little arbitrary but if you study diatonic set theory you will see that these scales have interesting properties that distinguish them from all or almost all other scales. For instance, the major scale is essentially the only heptatonic scale with all of the following properties: it has the deep scale property, the maximal evenness property, the cardinality equals variety property, the structure implies multiplicity property, Myhill's property, and it is generated and well-formed.



Yea these all seem to be linked together like puzzle pieces and they're actually fairly easy to find if you focus on small pieces of a scale or chord at a time. Looking at a whole position at once can make them overwhelming to find at first.


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## JustMac (Apr 25, 2014)

That's more info than I could even wish for MrBigNoodles,I really appreciate it. What you said about harmonising with min 2nds and tritones etc., does the harmonised part keep in line with what it's harmonising (as in, keep the same collection of pitches) or is it like a chromatic movement?

For example, if I was playing a Cdim with the notes C, Eb, Gb, A , and wanted to harmonise with the tritone, would I play the same type of chord for it (ie, Gbdim)? , or would I use the same notes I was using for Cdim but rearrange them to fit? Sorry if it sounds dumb, I'm not too up to speed on this stuff! 

I loved the videos by the way, the String Quartet No.5 was fantastic, will watch in full later.


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## Mr. Big Noodles (Apr 25, 2014)

JustMac said:


> That's more info than I could even wish for MrBigNoodles,I really appreciate it. What you said about harmonising with min 2nds and tritones etc., does the harmonised part keep in line with what it's harmonising (as in, keep the same collection of pitches) or is it like a chromatic movement?



It's going to be chromatic. For instance, a C major melody would be jammed up against the exact same thing in C# major, or F# major. Or whatever. Let's do that really quick. Try harmonizing a melody at different chromatic intervals.






[sc]https://soundcloud.com/menuridae/mary-had-a-bitonal-lamb[/sc]

I think I think the best intervals are the "dissonant" ones. The perfect fourth and perfect fifth are kind of lame, though I think they would sound better with a more chromatic line, or if we had this harmonized in three parts (one in the key of C, one in the key of F, and one in the key of B&#9837;, for example). The minor third isn't working out very well here, but I think it would sound better if the melody was minor. The major third, in contrast, sounds very good. I like the major second more than the minor second, but the major seventh (inversion of the minor second) sounds better than the minor second.

You probably want something more metal than Mary Had A Little Lamb, though. I wrote a quick riff that is closer to the style in question. It's all triadic, and the relationships between each chord is nothing too systematic. I was focusing on keeping the top line moving. You can see though that I pull some common tone diminished chords (C and C°, D&#9837;+ and B&#9837;° [shares D&#9837;]) and a doubly chromatic mediant relationship (Am and F#). Then the harmonization is a mechanical process after that.






[sc]https://soundcloud.com/menuridae/roast-mutton[/sc]



> For example, if I was playing a Cdim with the notes C, Eb, Gb, A , and wanted to harmonise with the tritone, would I play the same type of chord for it (ie, Gbdim)? , or would I use the same notes I was using for Cdim but rearrange them to fit? Sorry if it sounds dumb, I'm not too up to speed on this stuff!



Yes, although with diminished seventh chords, transposing at the tritone just gets you the same chord.

C°7 = C E&#9837; G&#9837; B&#9837;&#9837;
G&#9837;°7 = G&#9837; B&#9837;&#9837; D&#9837;&#9837; F&#9837;&#9837;

F&#9837;&#9837; is enharmonically equivalent to E&#9837;, and D&#9837;&#9837; is enharmonically equivalent to C.

A better example might be Cm and F#m.

C E&#9837; G
F# A C#

There are no repeated pitch classes there, so it sounds more "out".



> I loved the videos by the way, the String Quartet No.5 was fantastic, will watch in full later.



Good to hear. It's a fantastic piece.


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## Konfyouzd (Apr 25, 2014)

Holy crap... Did SchecterWhore's name change?


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## Mr. Big Noodles (Apr 25, 2014)

Yes.


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## Konfyouzd (Apr 25, 2014)

I saw that someone liked one of my posts and I thought... Hmm... That looks like SchecterWhore's avatar, but... Who the hell...?


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## ElRay (Apr 28, 2014)

Mr. Big Noodles said:


> ... I've done enough fawning over someone who is clearly a better composer than I could ever be. Still, you should check it out if you have half an hour of your day to dedicate to enriching your musicality.



I'll take-over the fawning for a bit.

Bartok is big over here. For what ever reason, his stuff has just clicked. My oldest (piano/flute) Does a phenomenal version of "Hungarian Folks Song" and loves the Bartok pieces in her Suzuki program.

I also managed to find a old 1977 printing of book of Bartok pianos pieces (mostly from For Children & Piano Method) arranged for solo guitar and just bought the Mel Bay book of 23 piano pieces arranged for two guitars. It will be a very Bella Summer for the girls and I. I want to see about re-arranging some of the two guitar pieces for flute and guitar.

Check-out "The Daily Beethoven"s  YouTube Channel and Blog. He's got MIDI versions of a lot of Bartok and other non-traditional Classical works arranged for guitar. The sound's not the greatest because it's MIDI, but you can get a good feel for the pieces. Scherzo and a number of the Mikrokosomos pieces are definitely in the queue to add to the repertoire.

Ray


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## redstone (May 1, 2014)

AugmentedFourth said:


> OK, so yes. You can describe the major scale (and thus all of its modes) using a cycle of thirds, but what kind of third you use when you move up a third is completely arbitrary and without context.



The context is to get a max. variety of triad progressions, so the 3rd sequences aren't random and pretty limited.



AugmentedFourth said:


> In 'major scale notation':
> 
> 1 #2 3 #4 #5 6 7
> 
> What is this scale? I don't even think it has a name as far as I'm concerned, that's how not common it is.



Harmonic major, 1 2 3 4 5 b6 7

Some popular chord progressions are based on that scale (4- 5 1 anyone ?), often unintentionally since for cultural reasons people ignore its existence and make few melodic use of it. Think about John Carter's 1M7 4m6, Lord of the rings' implicit 4-M7 3mb6 .. Invisible yet ubiquitous.


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## Mr. Big Noodles (May 1, 2014)

redstone said:


> Harmonic major, 1 2 3 4 5 b6 7
> 
> Some popular chord progressions are based on that scale (4- 5 1 anyone ?), often unintentionally since for cultural reasons people ignore its existence and make few melodic use of it. Think about John Carter's 1M7 4m6, Lord of the rings' implicit 4-M7 3mb6 .. Invisible yet ubiquitous.



Ah, you had me confused there. In film music, you will often see "1M1", "3M5", and the like in the title of the cue.







The notation breaks down thus:

[Reel #] ["Music"] [Music # on reel]

"1M1" is the first cue on the first reel. "1M2" would be the second cue on the first reel. The first cue on the second reel would be "2M1", the fourth cue on the seventh reel is "7M4", and so on.

So yeah, use Roman numerals if you're going to talk about chords. Especially if you're talking about chords in a film cue. Another thing:



> 4-M7 3mb6


Be consistent with your own notation. I assume that 4- is iv, as in F A&#9837; C, and 3m is iii, as in E G B. Normally, one commits to either the "F-" or "Fm" notation, and wouldn't mix chord suffixes in a single context.

I won't touch the "harmonic major" thing right now. Show us some examples, please.

Back to this circle of thirds thing now...



> The context is to get a max. variety of triad progressions, so the 3rd sequences aren't random and pretty limited.


I still don't see the connection between your statements and your concept. Actually, you haven't given us your concept, just a description of it. Since I have nothing from you to tell me otherwise, I'll have to cobble together what it sounds like to me:



Start with a scale. ex: C D E F G A B
Order the scale in thirds. ex: C E G B D F A (Or do you do it the other way around? A F D B G E C)
Make diatonic triads out of that sequence, maybe? You haven't described this or any other step.
...? (What do you do next?)
Profit! (What is the point?)
At some point in there, you make triads and somehow form a progression. Supposedly, this progression uses mediant root movements which are "not random" (How would any other mediant progression be random? By determining that the roots are moving by third, ANY third, we are defining a non-random sequence.), nor is it "pretty limited" (despite the fact that you are deliberately limiting the progression to a specific intervallic root movement while using a specific and limited pitch palette). Is this correct?


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## AugmentedFourth (May 2, 2014)

redstone said:


> The context is to get a max. variety of triad progressions, so the 3rd sequences aren't random and pretty limited.



That still doesn't explain why major/minor scales crop up so damn much.
Let's compare the major scale (and by extension its modes, not that that's relevant) to the scale I "synthesized" previously (which you call a mode of the harmonic major scale, an apparently synthetic scale itself now that I researched it.)


```
Major scale in triads:

I ii iii IV V vi vii°

# of maj. triads: 3
min: 3
aug: 0
dim: 1

My mode (not sure what to call it) of the harmonic major scale in triads:

I+5 ii° III iv° V vi VII

maj: 3
min: 1
aug: 1
dim: 2
```

So under my interpretation of "variety of triad progressions," harmonic major seems to spread the love just a bit more even than major. And it just gets worse if you use 7th chords.



redstone said:


> Harmonic major, 1 2 3 4 5 b6 7
> 
> Some popular chord progressions are based on that scale (4- 5 1 anyone ?), often unintentionally since for cultural reasons people ignore its existence and make few melodic use of it. Think about John Carter's 1M7 4m6, Lord of the rings' implicit 4-M7 3mb6 .. Invisible yet ubiquitous.



I think that the generally accepted interpretation of those kind of things such as I iv V is just modal mixture. The only thing they are really doing is mixing a major scale with its parallel minor, and the examples you cite _just happen to only borrow [and use] the flattened 6th._


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