Formula for harmonized triads of the minor scale

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VasquezBob
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Re: Formula for harmonized triads of the minor scale

Post by VasquezBob » Thu Sep 05, 2019 11:18 pm

Jack Dawkins wrote:
Sun Aug 30, 2015 2:25 pm
It's because the degrees are stated with respect to the major scale, and those are the flats that result - so if we are in A natural minor, the sixth degree is F, but the sixth degree of A major would be F#, so this degree has been marked with a flat.
You got me there! I'm going to have to noodle this one, as I don't know why you've linked 'A natural minor' to 'A major'. I guess that I don't know why the '...degrees are stated with respect to the major scale...' I love this stuff. :casque:

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Mark Featherstone
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Re: Formula for harmonized triads of the minor scale

Post by Mark Featherstone » Fri Sep 06, 2019 5:35 pm

VasquezBob wrote:
Thu Sep 05, 2019 11:08 pm
By 'pentagram', I'm just referring to the staff; those 5 beautiful parallel lines. What has frustrated me (as I learn music) is that many musical concepts can easily be explained on the staff. Too often, authors resort to 'personally-designed graphics, e.g., matrices, kinked lines and, especially, non-sensical jingles, such as, 'all cows eat grass' as well as tons of words. The circle of fifths is also confusing, unless one just wants to memorize one #, then, 2 #s, then, 3#s, etc. One simple illustration on the staff of how the upper tetrachord is the lower tetrachord of the next scale, etc., explained it all for me. Further, I didn't need to learn about the circle of fourths (which is nonsense) and the spiral of fifths, etc. Okay, okay, I'm done. :desole:
Oh, I see. Hmm, it's great that you can pick all that up by simple inspection of the staff, but it wouldn't have been sufficient for me. What about the staff would tell me that the F must sharped in G major? It doesn't leap out at me, that's for sure. I would have to first know the M-m-m-M-M-m-dim pattern, and then apply that to a harmonized scale beginning with G as its tonic, and calculate where to apply the needed accidental(s).
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Tonit
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Re: Formula for harmonized triads of the minor scale

Post by Tonit » Fri Sep 06, 2019 10:03 pm

Hi,
It is a mistake.

If the author meant in classical way, they should have been:

i - iio - III - iv - v - VI - VII

If the author meant in Jazz/Pop way, they should have been:

Im - IIo - bIII - IVm - Vm - bVI - bVII

If you mixed these up, you would end up something like the author's.

There is a reason behind the difference between jazz/pop way and classical way.

The classical way of chord indication has been done this way, because there are only two modes, that is to say, major and minor. So if the first chord is " i " chord, it automatically decides the interval between the tonic and other scale degrees, so that you do not have to specify whether they are major, minor, or perfect interval. The upper/lower cases indicate the third intervals (lower = minor 3rd, upper = major 3rd).

In the mean time, Jazz/Pop mixes up at least 6 of 7 modes sharing the same tonic (i.e. C major, C Dor, C Phr, C Lyd, C Mixo, and C minor in case of C key (whether major or minor), which means, the chords from these 6 modes are quite often used in a key. For example, when you are in the key of C, you can use both Dbmaj7 (which is indicated as "bIImaj7") from C Phrygian mode, as well as Dm7 (which is indicated as "IIm7") in the same key of C major.

To verify this, you can watch "Girl from Ipanema" with its leadsheet.

https://www.youtube.com/watch?v=MNJKILmi6NM


As you see, it is in the key of F (major).
Look at the 5th measure on the second line. It is Gm7 which is IIm7 of the key.
Then look at the 11th measure after the 2nd ending. It is Gbmaj7 which is bIImaj7 of the key.

There has been a wide-spread confusion that, it is transposed from F to another key, but in jazz terms it is not transposed.

To back this up, there is no new key signature through the tune. And as you know, the leadsheet is taken from the "Real Book" that has long been the standard for jazz players.

So what is the Gbmaj7 chord then?
It is considered to be a chord from F phrygian mode, and thus called a phrygian "modal interchange" chord which is one of the "subdominant minor" chords.

So hopefully you see why jazz/pop way of chord analysis symbols employ bs and #s with all upper cases.

Cheers,

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Mark Featherstone
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Re: Formula for harmonized triads of the minor scale

Post by Mark Featherstone » Sat Sep 07, 2019 6:11 am

Tonit wrote:
Fri Sep 06, 2019 10:03 pm
Hi,
It is a mistake.
That's very interesting regarding the use of other modes in jazz and pop. Thanks.

If you read some of the early responses to my original post, you'll see that it is not a mistake to flat those triads, but rather a confusing (and common) practice of relating the harmonized minor scale to the parallel major scale.
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Mark Clifton-Gaultier
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Re: Formula for harmonized triads of the minor scale

Post by Mark Clifton-Gaultier » Sat Sep 07, 2019 7:41 am

The word pentagram is not a synonym for staff. Whilst the Greek etymological roots may (to a non musician) appear to give a perfectly reasonable description it is in fact incorrect and insufficient - a musical staff does not merely consist of five lines.

The musician's lexicon is already replete with countless terms requiring a certain level of understanding not only of multiple languages but of multiple definitions related to changes associated with time, colloquial use, localised culture, misappropriation through translation etc., etc.

The pointless and apparently random introduction of unrelated terminology is particularly unhelpful within a discussion particpated in by those seeking clarity.

Tonit
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Re: Formula for harmonized triads of the minor scale

Post by Tonit » Sat Sep 07, 2019 9:22 am

Mark Featherstone wrote:
Sat Sep 07, 2019 6:11 am
Tonit wrote:
Fri Sep 06, 2019 10:03 pm
Hi,
It is a mistake.
That's very interesting regarding the use of other modes in jazz and pop. Thanks.

If you read some of the early responses to my original post, you'll see that it is not a mistake to flat those triads, but rather a confusing (and common) practice of relating the harmonized minor scale to the parallel major scale.
OK, that's fine if you (all) are not up for any exam.

I have heard "pentagram" every now and then, supposedly the term excludes various neums and tablatures (or do we call the regular six course a "hexagram"?).

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Mark Clifton-Gaultier
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Re: Formula for harmonized triads of the minor scale

Post by Mark Clifton-Gaultier » Sat Sep 07, 2019 10:32 am

Tonit wrote:I have heard "pentagram" every now and then ...
As have I. Hearing something however does not make it correct.

VasquezBob
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Re: Formula for harmonized triads of the minor scale

Post by VasquezBob » Mon Sep 09, 2019 2:52 am

Jack Dawkins wrote:
Sun Aug 30, 2015 2:25 pm
It's because the degrees are stated with respect to the major scale, and those are the flats that result - so if we are in A natural minor, the sixth degree is F, but the sixth degree of A major would be F#, so this degree has been marked with a flat.
I've reviewed this thread a couple of times and the approach seems quite confusing. I just harmonized the three A-minor scales and didn't need a flat. Further, if a flat was required, then, the F# only needed a 'natural sign' to get back to 'F'. Now, I must admit that I'm learning, too, but, I don't understand why "the degrees are stated with respect to the major scale..." I assumed that this thread is about diatonic scales. The sixth degree of A-natural-minor is F and why it is compared to the F# of the A-Major scale is beyond my noodle. I guess that I don't know why "the degrees are stated with respect to the major scale"; I assume, you are referring to A-Major which is a bit of a remote scale to A-natural-minor. Is there a name to the system of analysis that is being used here?

Tonit
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Re: Formula for harmonized triads of the minor scale

Post by Tonit » Tue Sep 10, 2019 3:19 am

Mark Clifton-Gaultier wrote:
Sat Sep 07, 2019 10:32 am
Tonit wrote:I have heard "pentagram" every now and then ...
As have I. Hearing something however does not make it correct.
Right. Pentagram is most often five pointed star, and Hexagram is David's.

musikai
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Re: Formula for harmonized triads of the minor scale

Post by musikai » Tue Sep 10, 2019 11:26 am

VasquezBob wrote:
Mon Sep 09, 2019 2:52 am
Jack Dawkins wrote:
Sun Aug 30, 2015 2:25 pm
It's because the degrees are stated with respect to the major scale, and those are the flats that result - so if we are in A natural minor, the sixth degree is F, but the sixth degree of A major would be F#, so this degree has been marked with a flat.
I've reviewed this thread a couple of times and the approach seems quite confusing. I just harmonized the three A-minor scales and didn't need a flat. Further, if a flat was required, then, the F# only needed a 'natural sign' to get back to 'F'. Now, I must admit that I'm learning, too, but, I don't understand why "the degrees are stated with respect to the major scale..." I assumed that this thread is about diatonic scales. The sixth degree of A-natural-minor is F and why it is compared to the F# of the A-Major scale is beyond my noodle. I guess that I don't know why "the degrees are stated with respect to the major scale"; I assume, you are referring to A-Major which is a bit of a remote scale to A-natural-minor. Is there a name to the system of analysis that is being used here?
The problem is that the formular is stated with respect to the C-Major scale, then this is made into a c-minor scale and only there the b appear like in the formular.
i-ii°-bIII-iv-v-bVI-bVII

I think the formular just shouldn't mix things up, but should better be based directly on a minor scale:
i-ii°-III-iv-v-VI-VII
Major-Minor Scale_0001.png
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Tonit
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Re: Formula for harmonized triads of the minor scale

Post by Tonit » Tue Sep 10, 2019 1:45 pm

musikai wrote:
Tue Sep 10, 2019 11:26 am
VasquezBob wrote:
Mon Sep 09, 2019 2:52 am
Jack Dawkins wrote:
Sun Aug 30, 2015 2:25 pm
It's because the degrees are stated with respect to the major scale, and those are the flats that result - so if we are in A natural minor, the sixth degree is F, but the sixth degree of A major would be F#, so this degree has been marked with a flat.
I've reviewed this thread a couple of times and the approach seems quite confusing. I just harmonized the three A-minor scales and didn't need a flat. Further, if a flat was required, then, the F# only needed a 'natural sign' to get back to 'F'. Now, I must admit that I'm learning, too, but, I don't understand why "the degrees are stated with respect to the major scale..." I assumed that this thread is about diatonic scales. The sixth degree of A-natural-minor is F and why it is compared to the F# of the A-Major scale is beyond my noodle. I guess that I don't know why "the degrees are stated with respect to the major scale"; I assume, you are referring to A-Major which is a bit of a remote scale to A-natural-minor. Is there a name to the system of analysis that is being used here?
The problem is that the formular is stated with respect to the C-Major scale, then this is made into a c-minor scale and only there the b appear like in the formular.
i-ii°-bIII-iv-v-bVI-bVII

I think the formular just shouldn't mix things up, but should better be based directly on a minor scale:
i-ii°-III-iv-v-VI-VII
Major-Minor Scale_0001.png
This is it.

Tonit
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Re: Formula for harmonized triads of the minor scale

Post by Tonit » Tue Sep 10, 2019 1:46 pm

musikai wrote:
Tue Sep 10, 2019 11:26 am
VasquezBob wrote:
Mon Sep 09, 2019 2:52 am
Jack Dawkins wrote:
Sun Aug 30, 2015 2:25 pm
It's because the degrees are stated with respect to the major scale, and those are the flats that result - so if we are in A natural minor, the sixth degree is F, but the sixth degree of A major would be F#, so this degree has been marked with a flat.
I've reviewed this thread a couple of times and the approach seems quite confusing. I just harmonized the three A-minor scales and didn't need a flat. Further, if a flat was required, then, the F# only needed a 'natural sign' to get back to 'F'. Now, I must admit that I'm learning, too, but, I don't understand why "the degrees are stated with respect to the major scale..." I assumed that this thread is about diatonic scales. The sixth degree of A-natural-minor is F and why it is compared to the F# of the A-Major scale is beyond my noodle. I guess that I don't know why "the degrees are stated with respect to the major scale"; I assume, you are referring to A-Major which is a bit of a remote scale to A-natural-minor. Is there a name to the system of analysis that is being used here?
The problem is that the formular is stated with respect to the C-Major scale, then this is made into a c-minor scale and only there the b appear like in the formular.
i-ii°-bIII-iv-v-bVI-bVII

I think the formular just shouldn't mix things up, but should better be based directly on a minor scale:
i-ii°-III-iv-v-VI-VII
Image
This is it.

VasquezBob
Posts: 198
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Re: Formula for harmonized triads of the minor scale

Post by VasquezBob » Tue Sep 10, 2019 11:32 pm

musikai wrote:
Tue Sep 10, 2019 11:26 am
VasquezBob wrote:
Mon Sep 09, 2019 2:52 am
Jack Dawkins wrote:
Sun Aug 30, 2015 2:25 pm
It's because the degrees are stated with respect to the major scale, and those are the flats that result - so if we are in A natural minor, the sixth degree is F, but the sixth degree of A major would be F#, so this degree has been marked with a flat.
I've reviewed this thread a couple of times and the approach seems quite confusing. I just harmonized the three A-minor scales and didn't need a flat. Further, if a flat was required, then, the F# only needed a 'natural sign' to get back to 'F'. Now, I must admit that I'm learning, too, but, I don't understand why "the degrees are stated with respect to the major scale..." I assumed that this thread is about diatonic scales. The sixth degree of A-natural-minor is F and why it is compared to the F# of the A-Major scale is beyond my noodle. I guess that I don't know why "the degrees are stated with respect to the major scale"; I assume, you are referring to A-Major which is a bit of a remote scale to A-natural-minor. Is there a name to the system of analysis that is being used here?
The problem is that the formular is stated with respect to the C-Major scale, then this is made into a c-minor scale and only there the b appear like in the formular.
i-ii°-bIII-iv-v-bVI-bVII

I think the formular just shouldn't mix things up, but should better be based directly on a minor scale:
i-ii°-III-iv-v-VI-VII
Major-Minor Scale_0001.png
Thank you for the response and explanation. I still don't know why any minor scale should be based on a major scale that has the same tonic, namely, "C" in the case above. Minor scales are extensions of related major scales and they carry the same accidentals (where appropriate); added accidentals being included for harmonic and melodic minor scales, q.v. That's why I thought that the approach might be for a different type of scales. Anyway, thanks again.

Tonit
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Re: Formula for harmonized triads of the minor scale

Post by Tonit » Wed Sep 11, 2019 12:22 am

VasquezBob wrote:
Tue Sep 10, 2019 11:32 pm
musikai wrote:
Tue Sep 10, 2019 11:26 am
VasquezBob wrote:
Mon Sep 09, 2019 2:52 am


I've reviewed this thread a couple of times and the approach seems quite confusing. I just harmonized the three A-minor scales and didn't need a flat. Further, if a flat was required, then, the F# only needed a 'natural sign' to get back to 'F'. Now, I must admit that I'm learning, too, but, I don't understand why "the degrees are stated with respect to the major scale..." I assumed that this thread is about diatonic scales. The sixth degree of A-natural-minor is F and why it is compared to the F# of the A-Major scale is beyond my noodle. I guess that I don't know why "the degrees are stated with respect to the major scale"; I assume, you are referring to A-Major which is a bit of a remote scale to A-natural-minor. Is there a name to the system of analysis that is being used here?
The problem is that the formular is stated with respect to the C-Major scale, then this is made into a c-minor scale and only there the b appear like in the formular.
i-ii°-bIII-iv-v-bVI-bVII

I think the formular just shouldn't mix things up, but should better be based directly on a minor scale:
i-ii°-III-iv-v-VI-VII
Major-Minor Scale_0001.png
Thank you for the response and explanation. I still don't know why any minor scale should be based on a major scale that has the same tonic, namely, "C" in the case above. Minor scales are extensions of related major scales and they carry the same accidentals (where appropriate); added accidentals being included for harmonic and melodic minor scales, q.v. That's why I thought that the approach might be for a different type of scales. Anyway, thanks again.
That in fact is a good question.

If you construe that A (natural) minor scale is an extension of C major scale, that would help your understanding of the respective scale degrees in A minor scale. Our key signatures are taking advantage of this way of understanding, in a sense.

However, the concept of "key" in music refers only to the tonal center, while major/minor difference refers to "modes", i.e. major/minor modes in classical (ADD: and of course we say "major key" and "minor key", while these are not mistakes at all, the matter of fact is, those remarks only refer to the "mode" centered by the key in more strict technicality), and seven or more in jazz. So the modes are discussed with one single tonal center, instead of relativity of the various modes under one key sgnature. And the set benchmark is the major scale (or mode). Why? There are several reasons, of which I explain two most important ones below.

One thing that might help your understanding of the foregoing is; If you see and compare C major and C melodic minor scales, there is in fact only one note differentiating the two: major 3rd and minor 3rd.

In fact, there are several ways to explain why the major key has been set as the standard, including the one I selected for the most concise details I can give. You can explore further into this matter, but roughly, the conclusion is, the major scale is best facilitated for both melody and harmony.

If you have the 5th circle at hand and go around 5th down from B seven times, it will give you B, E, A, D, G, C, and F, which are all the constituents of C major scale. And this is how those notes are gravitated acoustically, ending up with F instead of C, because the motion of perfect 5th down is considered to be the strongest gravity in terms of the acoustics, as you see the 2nd overtone is the 5th of the acoustic root.

[ADD] This means that, if two notes, B and E for example, are played simultaneously or in a series, our ears will follow the law of acoustics and tend to assume, E may be more likely to be the root, because E is fifth down from B. (The gravity works regardless of any inversion or compound of the perfect 5th, so that the gravity kicks in as long as they are B and E.) So if a tune consists of B, E, A, D, G, C, and F and nothing else, being played in any order, our ears would try to follow this acoustic "gravity". As you see, we get down 5th from B to E, E to A...and likewise to F, and then find F cannot go any further down 5th, because there is no Bb included in the constituents. Then, F should be the very bottom (i.e. acoustic root of the group of 7 notes).

So if you follow the acoustic gravity, the key should be set to F, if the seven notes (B, E, A, D, G, C, and F) are played in a composition. This might be a complicated concept, but you will see what it means over a little longer duration of time thinking about it.

But that's not the case as we all know. It is referred instead to as C major with C as the "key".

This is because of the harmonic reason, being, the famous "tritone" between B and F resolving to C and E. Therefore, they found that, if the set of seven notes (B, E, A, D, G, C, and F) are presented, it is better to set C as the "key" for harmonic functionality purpose.

You can explore more about these things in some web resources.

I would also recommend to explore about "Tetracord", which can be considered to see why major mode is preferred to minor mode.

Anyways, thus C major key has been set as the standard, and all the other modes are compared to the C major scale. So for example, C natural minor is represented with 1, 2, b3, 4, 5, b6, and b7, while C Lydian is represented with 1, 2, 3, #4, 5, 6, and 7 and so on and so forth.

I hope this helps you.

VasquezBob
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Re: Formula for harmonized triads of the minor scale

Post by VasquezBob » Wed Sep 11, 2019 9:12 pm

Tonit wrote:
Wed Sep 11, 2019 12:22 am
VasquezBob wrote:
Tue Sep 10, 2019 11:32 pm
musikai wrote:
Tue Sep 10, 2019 11:26 am


The problem is that the formular is stated with respect to the C-Major scale, then this is made into a c-minor scale and only there the b appear like in the formular.
i-ii°-bIII-iv-v-bVI-bVII

I think the formular just shouldn't mix things up, but should better be based directly on a minor scale:
i-ii°-III-iv-v-VI-VII
Major-Minor Scale_0001.png
Thank you for the response and explanation. I still don't know why any minor scale should be based on a major scale that has the same tonic, namely, "C" in the case above. Minor scales are extensions of related major scales and they carry the same accidentals (where appropriate); added accidentals being included for harmonic and melodic minor scales, q.v. That's why I thought that the approach might be for a different type of scales. Anyway, thanks again.
That in fact is a good question.

There appears to be more than one path to get at the answer. To address the question of where do all the flats (b's) come from, one just needs to go from "C minor" to its relative major which is "E" but, which E? The E major on the sharp side or the flat side of the signature chart? Well, if E is the tonic and F is the supertonic, then, E must be flat; if we are to apply the whole tone, whole tone, half tone to the upper and lower tetrachords. Now, one can either look-up Eb major or write it out and one will find that "E, A, and B" are flat and that's from where all the flats descend (pardon the play on words). Just an aside: sometimes it's easier to "see" the answer when one applies the musical alphabet rather than using Roman numerals, q.v., but, to each his/her own.

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