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EDIT

I edited my question title to better reflect what I am asking.

I am specifically asking about pedagogical sources that present these three forms of minor scales, like this...

enter image description here

My Piston Harmony textbook (1st ed.) presents such a diagram. My Kostka Tonal Harmony (2nd ed.) does not and explains that in reality there is only one minor scale where the ^6 & ^7 are variable.

So, I'm not looking for an origin to minor key harmony - I already know that from figured bass and the rule of the octave - and I'm not arguing the question of one versus three minor scales - better sources like Kostka explain clearly there is one minor scale.

I want to know - to whatever extent is possible - the origin of the three minor scales concept. Surely this idea came earlier that Walter Piston.

I think of this sort of like the origin of roman numeral analysis which I have seen attributed to Georg Volger and Gottfried Weber. which supplanted the earlier figured bass system for analysis and teaching. One system supplants another and obscures the methods and teaching of the past.


2nd EDIT

I thought I should add notes about two historic examples that seem to be melodic minor, but are neither named that in the sources nor presented as one of three different minor scales.

The earliest example I know of is Fenaroli's rule of the octave in Regole musicali per i principianti di cembalo.

enter image description here

From the English translation I have seen, Fenaroli didn't apply a special name to this minor scale and he did not distinguish three different minor scales. It is simply the harmonization rule for the minor mode. Note that the middle bass clef is the actual bass, the lower bass clef gives the theoretical root of each chord.

The next oldest example I know is Clementi's Art of Playing on the Piano Forte.

enter image description here

As in the case with Fenaroli, Clementi presents only one minor scale and it isn't given a special name.

The rest of the book goes on to present the scales for daily practice drills in all keys. After than over 100 pages of short performance pieces. Most of those pieces are in major keys. But of those that are in minor keys when the upper tetra chord of a minor scale is played descending in a figure subdividing the beat the raised ^6 & ^7 are frequently employed.

It seems clear from these examples and those I gave earlier from Bach and Mozart that the treatment of the descending upper tetrachord of the minor scale depends greatly on whether the tones are functioning as essential harmony tones or figurative decoration.

While this particular point is interesting it doesn't answer my question.

I've looked at Bach, Mozart, Clementi, and Fenaroli (@KimFierens shared an example from Rameau which on the whole is the same as Fenaroli) but I don't yet have a historic source for the three types of minor scales concept older than Walter Piston.

My original post follows...


The standard textbook description of the melodic minor scale is the natural minor scale descending and natural minor with raised ^6 and ^7 tone when ascending.

That textbook definition doesn't seem to hold water.

This example to the contrary from Bach's D minor invention is one I easily remember...

enter image description here

enter image description here

...where the circled descending passages maintain the raised ^6 and ^7 tones clearly because they are essential for the dominant harmony.

It's interesting that immediately after m. 43 the original figure is stated again and the scale descent in m. 45 uses the lowered ^6, but this time, despite the harmony being dominant, the chord is specifically a vii°7 and so the lowered Bb is essential to form the diminished 7th chord.

In both cases the inflection of the minor scales seems to be dictated by the harmony not the scale direction.

Other examples can be cited in the two-part inventions. In fact all the minor key ones show descending 'melodic' minor, sometimes in the opening subject material, except when there simply isn't a descending scale passage using ^6 & ^7 (like the A minor invention.) Also, Mozart's Nannerl Notebook shows similar examples. Of course both of these are important historic pedagogical sources. Trying to explain away these as cherry-picked aberrations is a weak argument.

Given the importance of harmony to dictate how the minor scale is inflected it seem especially unfortunate that textbooks use the labels harmonic and melodic minor in a way that doesn't jibe with how the music works.

Equally annoying to me is the explanation that the raised ^6 in melodic minor is used to 'fill the gap'of the augmented second in the harmonic minor. Plenty of examples show that the augmented second was not objectionable in common practice style.

So when and how did this three versions of the minor scale and raised for ascending, lowered for descending concept develop?

It seems clear there is one minor scale and ^6 and ^7 vary depending on the harmony or a preference for a particular tonal color.

If someone could provide actual pedagogical examples from around Bach's to Mozart's time of how the minor scale/harmony was taught, I would be especially appreciative.

  • Not a direct answer, but if this sort of thing interests you (and French doesn't scare you), you might want to read Fétis's essay "Esquisse de l'histoire de l'harmonie", which is on archive.org. (I see there's an English translation, but it's out of print.) What I do remember from my partimento studies, come to think of it, is that the Neapolitan masters of the early 18th century seemed to consider the harmonic minor the "true" minor, and the other minor scales chromatic "licenses". Which would make sense, given the old contrapuntal practice to often raise the 7th degree in the Aeolian mode. – Kim Fierens Nov 30 '18 at 22:55
  • "doesn't seem to hold water": the fact that someone did something that wasn't exactly a harmonic minor scale doesn't imply that the description of the harmonic minor scale is wrong. Maybe Bach was just doing something else (as the answer implies, the concept of "harmonic minor scale" was not so neatly defined at the time). Augmented seconds are not necessarily objectionable, but they are indeed treated with care. – phoog Dec 1 '18 at 0:00
  • @Phoog my example from Bach isn't harmonic minor, but the so-called melodic minor. But, I think you are suggesting I am cherry picking an example. I'm not. I added a note to my post to that point. I just want to know the origin of the three minor scale concept. – Michael Curtis Dec 3 '18 at 14:49
  • I didn't mean to suggest that you're cherry picking (and "harmonic" rather than "melodic" was a moment of confusion). I just meant to point out that any composer's using material inconsistent with a theoretical construct could either mean that the theoretical construct is questionable or that it doesn't apply to the music in question. As an example, consider "the Picardy third is a major third in the final chord of a minor-mode piece, but the final chord in this minor-mode piece has no third." Does that mean the definition of Picardy third is wrong? No; it just means it doesn't apply here. – phoog Dec 3 '18 at 17:13
  • Since the three forms of minor scale were codified after Bach's time (but I do not know when, otherwise I'd post an answer), one would have to ask the inventor of the scheme how (or whether) it is applicable to the examples you cite. – phoog Dec 3 '18 at 17:17
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From Jean-Philipe Rameau's 1722 Treatise on Harmony (the Dover edition, p. 158):

As for the minor mode, it differs from the major only in that the its third and sixth should be minor, although there are various problems with regard to the sixth, which we shall explain in the following book.

p. 264

The octave of the note Re [i.e., D] is usually taken as the model for all minor keys. [Table with the following notes: Re, Do#, Sib, La, Sol, Fa, Mi, Re, which Rameau calls Octave, Leading tone, Sixth note, Dominant-tonic, Fourth note, Mediant, Second note, Tonic.] The only difference between the ascending minor key and the major is that the third is minor on the one hand and major on the other. Descending, however, we must add a flat to the note Si [the submediant] and remove the sharp from the leading note Do.

In summary, Rameau essentially distinguished between the minor mode (our harmonic minor) and the descending and ascending melodic scales, albeit in a not very clearly formulated way.

Furthermore, from Fedele Fenaroli's partimento collection, from about 1770:

The 1 is just. The 2 is major. The 3 is variable [according to the mode]. The 4 is perfect. The 5 is just. The 6 should correspond to the third. And the 7 is always major, being the support of the keynote.

and

Observe that when the minor scale ascends, one makes the 6 major, and in descending one makes the 7 minor. This is all done to avoid the augmented second that occurs between the 6 and 7, the reason being that one recoils from the harshness of the sound caused by a [step larger than a whole tone].

So, also Fenaroli seems to think that the harmonic minor defines the minor mode, whereas he appears to be more specific than Rameau in insisting that the descending and ascending melodic scales apply to scalar motion. Fenaroli probably would have explained your Bach examples as (incomplete) chromatic ascents or descents, to which he devotes a few paragraphs, such as

If the partimento is in the minor mode, it can also descend by semitone [from 1] down to 5 inclusively. And this motion can accept various accompaniments.

and

If the partimento will be in the minor mode, the ascent by semitone will start on 5, and it can proceed by semitone until 8, inclusive.

As a personal opinion, I believe that Fenaroli's way of thinking about the minor mode and scales (i.e., not giving the scales any name, and chalking up any deviations as chromaticisms) is to be preferred to our current misleading and muddled terminology.

  • 1
    I'm glad you gave the part about Rameau and Dorian as the sort of basic minor form. I didn't know he stated it that way. That of course matches up with the Dorian key signature for minor keys practiced during that time. I already know about the figured bass and rule of the octave history. I'm really looking for the origin of the three minor scales concept. – Michael Curtis Dec 3 '18 at 16:15
  • 1
    It's interesting that the rule of the octave and it's use of inverted sixth chords on ^6 & ^7 is so simple and makes fundamental harmonic progressions clear. If we reduce the minor harmony to a sort of quasi-scale of only chord roots we get ^1, ^2, ^4, ^5, and ↑^7. Now contrast that with the concept of 3 minor scales which are sometimes presented as tones for chord roots. That leads to chords in minor like +III or vi° and other chords that aren't basic, fundamental common practice harmony. – Michael Curtis Dec 3 '18 at 16:46
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    I agree the current system (as some teach it) makes a terrible muddle of harmony and melody in minor keys. – Michael Curtis Dec 3 '18 at 16:49
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From a jazz theory perspective, I have always thought of the derivation and naming convention for natural minor, harmonic and melodic minor as having to do with the insertion of the dominant chord in minor to create stronger resolution to the tonic harmonically - a "true V" chord if you will.

The natural minor is simply the scale that comes "naturally" out of its relationship to relative major without alterations - there is no "true V" in harmony built on the 5th step (in above that would A- which has no pull or gravity to D-, it feels decidedly "modal"). The harmonic minor comes about from a "harmonic" consideration - that is an alteration of the natural minor scale to include the leading tone creating A7 dominant harmony. The melodic minor for "melodic" considerations - the ascension of the melody to the root.

Although it would seem the feeling of minor is more enforced with Bb - a signal of minor key in addition to the minor 3rd that distinguishes it from major, it feels awkward to undo the B to Bb in the melody descent in above example given the zone of the melody. You can test it by singing thru it. You are more inclined to keep the B as it was ringing in your ear just previously. That is not the case with bar 45 where C#-Bb-A in bar 45. This is clearly a harmonic signal of implied A dominant to D minor. The Bb has melodic gravity down to the A dominant moving to D minor which is also reinforced by the bass moving to the D minor root. In bar 43 the harmony if over the 3rd of D, F.

The so-called descending form of melodic minor (essentially reversing harmonic minor to natural minor) is and as noted in the Bach example not consistently enforced, especially when it creates an awkwardness from the individual voices (as in bar 43 in above). I remember when taking Classical theory classes in college the professor scoffed somewhat at the so-called descending form of melodic minor with numerous contradictory examples in the musical literature.

Generally speaking, there is a feeling of the quality of minor (as mentioned in the Rameau treatise above) that emphasizes the key characteristics that distinguish it from major - the 3rd and the 6th. The melodic minor in a sense breaks one pillar of minor feeling by having the B natural, making it essentially a major scale with a minor 3rd. But from a melodic perspective it makes more sense to literally ascend to the root as it does with typical passages in major. The Bb would indeed be awkward in this case because it has gravity to A not upward.

Bach's music is inherently harmonically oriented but it is also contrapuntal individual voices so it is the just union of these to aspects that sometimes leads to some "rule breaking".

In the end scale theory, names, etc are a bit stodgy. I would agree with Kim Fierens comment that minor scales terminology is muddled. I have no idea if the way I think of the 3 scale name derivation has any basis in actual fact. I just found it helped me answer the question when students asked me the difference between them :)

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