Formula for harmonized triads of the minor scale

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Mark Featherstone
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Formula for harmonized triads of the minor scale

Postby Mark Featherstone » Sun Aug 30, 2015 2:14 pm

Two apologies: One if this is not the right subforum for this question. Two, my question must be awfully basic.
I was recently inspired on another thread to go back to my languishing music theory education. I thought I was doing OK, having got through harmonizing the major scale. But then I hit harmonizing the minor scale and there is something I just can't figure out. The formula for harmonized triads of the minor scale looks like this (below). The author appears to mean a natural minor scale.
Formula for harmonized triads of minor scale.JPG

My no doubt simple question is where on earth do those flats come from? The book I'm reading states, "This of course is due to their corresponding scale steps". But for me, there is no "of course". There is nothing consistent about the scale steps that I can see that would explain the flatted III, VI and VII. Any help would be much appreciated.

Thanks,
Mark
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Jack Dawkins
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Re: Formula for harmonized triads of the minor scale

Postby Jack Dawkins » 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.

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

Postby Mark Featherstone » Sun Aug 30, 2015 3:35 pm

Jack Dawkins wrote: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.

Wow! Thanks so much, Jack! You're quite right. The author was taking the relative minor of C Major, therefore A minor. But he made no mention whatsoever that he was now referencing A Major to account for the flats. Thanks again!
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wchymeus
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Re: Formula for harmonized triads of the minor scale

Postby wchymeus » Sun Aug 30, 2015 6:46 pm

Understood the logic, but is it really common to use a flat sign to get a natural note? like bF#=F is really weird thinking.
What's the motivation to compare to the relative major this way?
Sorry to ask this naive question...
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Jack Dawkins
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Re: Formula for harmonized triads of the minor scale

Postby Jack Dawkins » Sun Aug 30, 2015 7:17 pm

Well, it seems to be quite common to describe modes by reference to the major scale, possibly reflecting a view that they are derived from it. While I don't believe that they are, I suppose this system could be justified on the basis that the major scale is a pretty familiar point of reference, and that it makes it easy to remember the structure of the modes by the order in which the degrees of the scale are flattened (not unlike the way you might remember key signatures by the order in which sharps and flats are added). Also it is scale-independent, so you can use it in the abstract without worrying about whether going down a notch in any given scale will actually take you to a flat. My personal view (which may well change as I learn more) is that it is better to define your scale and use the Roman numerals without prefixes to refer to the degrees of that scale, but even then there can be uses for the b notation - for example, an augmented sixth chord is conventionally described as being built on the bVI.

mainterm
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Re: Formula for harmonized triads of the minor scale

Postby mainterm » Thu Oct 08, 2015 11:15 pm

Mark Featherstone wrote:The book I'm reading states...


May I ask what book you are reading?

I just read through this short set of posts and feel like I'm taking crazy pills. I mean if you flat the 3rd, 6th and 7th scale degrees of the major scale, you get a natural minor scale. It is also true that if you build triads on the pitches in said natural minor scale you will get minor on 1, diminished on 2, major 3, etc...

So if you want to say... show an example of a major scale such as C major with triads built on each scale degree and then show what happens when you make it C natural minor, then you get these flats and the other adjustments to the interval structure of the triads. I would suppose without further context, that is where the flats are coming from.

Some theory texts/theorists define the minor scale as a modification to (or even degradation of) the major scale, (e.g. a minor scale is a major scale with some flats, e.g. the 3rd scale degree and often the 6th and less frequently the 7th)

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

Postby Mark Featherstone » Fri Oct 09, 2015 2:23 pm

mainterm wrote:
Mark Featherstone wrote:The book I'm reading states...


May I ask what book you are reading?


This is "Music Theory" by Tom Kolb in the Hal Leonard Guitar Method series. I've seen another author use the same notation since posting. I thought it was Walter Piston in Harmony, but in fact I don't see it on a couple of flips through the chapter on the minor mode and its triads. You're right in that Kolb is simply expressing the triads of the minor mode as flats of the major, e.g C minor vs C major. (Something I understand now, thanks to those who responded.)
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markworthi
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Re: Formula for harmonized triads of the minor scale

Postby markworthi » Fri Oct 09, 2015 3:04 pm

Hi Mark,

I, too, was confused, at first, by this way of describing the harmonization of the minor scale. The problem becomes worse-- and the mental gymnastics more complex-- when you begin to harmonize other minor scales. For instance, the melodic minor scale has a flat third (relative to the major scale), while the 6th and 7th are the same as in the major scale. But some writers will tell us to think of the melodic minor scale by comparing it to the natural minor scale (that is, as a natural minor with a raised 6th and 7th). So writers are not all consistent with each other in how they teach this stuff; and sometimes they are not explicit enough about which relative scale they are using.

Compounding this is that when we try to visualize the method of lowering or raising the mediant, submediant and leading tones by half tones using a mental notation that includes flats or sharps, it's very easy to get confused about what is truly a sharp or flat note and what is simply a convenience that makes sense relative to some other scale.

It has taken a while, but eventually I have overcome this type of confusion. I am sure you will, too! Best of luck,

Mark

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Re: Formula for harmonized triads of the minor scale

Postby Mark Featherstone » Sat Oct 10, 2015 7:31 am

markworthi wrote:Hi Mark,

I, too, was confused, at first, by this way of describing the harmonization of the minor scale. The problem becomes worse-- and the mental gymnastics more complex-- when you begin to harmonize other minor scales. For instance, the melodic minor scale has a flat third (relative to the major scale), while the 6th and 7th are the same as in the major scale. But some writers will tell us to think of the melodic minor scale by comparing it to the natural minor scale (that is, as a natural minor with a raised 6th and 7th). So writers are not all consistent with each other in how they teach this stuff; and sometimes they are not explicit enough about which relative scale they are using.

Compounding this is that when we try to visualize the method of lowering or raising the mediant, submediant and leading tones by half tones using a mental notation that includes flats or sharps, it's very easy to get confused about what is truly a sharp or flat note and what is simply a convenience that makes sense relative to some other scale.

It has taken a while, but eventually I have overcome this type of confusion. I am sure you will, too! Best of luck,

Mark

Well summarized, Mark. Thank you. Yeah, I'll keep at it. A while ago I decided that the mental energy I put into Sudoku puzzles could be better directed to something useful. I guess this is one those. :)
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guitareleven
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Re: Formula for harmonized triads of the minor scale

Postby guitareleven » Mon Oct 12, 2015 10:53 pm

wchymeus wrote:Understood the logic, but is it really common to use a flat sign to get a natural note? like bF#=F is really weird thinking.
What's the motivation to compare to the relative major this way? ....


I, too, resist this this usage. It can be useful as a mental tool to think this way, I suppose- as "Jack Dawkins" says in his post above, it is simply a comparison to what position those scale degrees would be in, in the parallel (NOT the "relative") major scale. But as such, it is only a mental "tool" to think this way, and it needs to be understood that it is a tool with limited application that leads to a lot of confusion when misused. Saliently, it does not mean that some action has been performed upon those notes to put them in their minor scale position. The minor scale simply is what it is; the "flat" observation is a comparison only, and, it is a comparison to a model that has been adopted arbitrarily because, also as Jack points out, it is familiar.

The confusion arises from the use of the chromaticism (i.e., the flat) simultaneously in two different senses, one suggesting that something has been done, the other reflecting an absolute state. You've already alluded to this in your query as to the rationality of the "bF#" construction, i.e., calling a note that is natural, a flat. It can get worse; consider the minor keys of G#, D# and A#. In the natural minor scale manifestation by which the key signatures are determined, and in the descending melodic minor, the seventh degrees in all of these, and the sixth degree in A# minor, are sharps. Yet the "comparative model" tool suggests that they are to be understood as flats. What are they, sharp flats, or flat sharps?

This sort of confusion-by-comparison can be a pervasive one, and I have found it hard to get students free of it when they have internalized it as an axiom. For instance, it crops up in their understanding of triads. They persist in thinking of a minor triad as one in which the third has "been lowered", or so too the fifth in a diminished triad, which affects their comprehension that these triads simply occur, without any alteration, in any diatonic system.

If a comparison has to be made, I find it much more useful, and resulting in less confusion, to describe and have students keep in mind where parallel majors and minors are the same, instead of where they are different. This would be in the positions of the first, second, fourth, and fifth degrees of the scales. These are the Tonal degrees, and can be considered to be fixed in position most of the time. They stand there like pillars (this over-arching construction, BTW, is not merely another arbitrariness removed to a higher level, it can be justified as a cultural development in response to the actual physics of sound). There are some exceptions, for instance, usages in which the second degree appears at a half-step above the tonic, which are not so common and used in circumscribed situations, and also those in which the fourth degree is a half step below the dominant, which actually is quite frequent, but has a connotation of disrupting the tonality. For most purposes, these four degrees can be taken as points of stability, the structural posts which are the foundation of an undisrupted tonality.

The other degrees, the third, sixth and seventh, are the Modal degrees. These are the changeable ones, they are transitional, or they are melodic inflections that have coloristic effect in the expression of the tonality. Between major and minor, each of these degrees can be in either of two positions, to serve purposes that are local to where they occur in a composition. If one understanding of a scale, then, is to serve not as a construction for linear expression but simply as a lexicon of notes that may most freely be used in association with each other in suggestion of a tonality centered on any one note as a key tonic, then, the result, as seen in actual use in the common-practice era of music on which our theory is based, which practice includes the freedom to move back and forth between parallel major and minor, is more like a ten-note scale, or, all but a chromatic scale, but with two notes left out. This would be, the first degree, the second degree, two alternate third degrees, the fourth and fifth degrees, and two alternates each of the sixth and seventh degrees, before attaining to the octave. This can be conceived of as a stable set out of which are taken either the major or the minor as required, with out one being forced into view as a deformation of the other.

mainterm
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Re: Formula for harmonized triads of the minor scale

Postby mainterm » Wed Oct 21, 2015 5:32 am

Jack: any further thoughts?


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