Your web site has a section on Harmony where you speak of "4 strong modes." I was a little confused by this - in my music classes I learned about modes like "Dorian," "Phrygian," etc. How do these modes relate to what you are talking about?

A mode is a tonal system with a specific center or "chord of rest." A strong mode is one in which the chord of rest, or "tonic" is approached via a strong, or "dominant," type chord. (A dominant chord has a tri-tone between its median and its motrix). You may want to visit Harmony-Basic Materials and The Four Strong Modes to review these concepts. Two of the four strong modes occur naturally in a diatonic system. They are: the fundamental flattening (descending) major mode (the one everybody is used to), and its inverse, the sharpening (ascending) minor. The other two strong modes are produced by a process of dominantization. They are: the chromatic flattening (descending) minor (again, the one most Western ears are used to), and its inverse the chromatic sharpening (ascending) major.

As for the other modes you refer to, they have had different meanings and usages at different times in history. To the Ancient Greeks they meant one thing; to the church musicians of the Middle Ages they meant another; and, today those terms are usually used to mean something somewhat different still. The most logical and practical way of understanding those modes from today's standpoint is that they are simply what we would call the "weak modes." That is, they have a chord of rest that is not approached via a dominant chord. The chord of rest is made to sound as such by devices such as static harmony, a repeating drone note, or very carefully constructed chord patterns that do not use a dominant/tonic progression.

Is it possible to consider the diatonic major mode as basic material and the other 3 strong modes as transformations?

It certainly makes sense to consider the two chromatic modes as transformations, since they are created via the process of dominantization. The diatonic minor comes into being simultaneously with the diatonic major as its symmetrical counterpart, and hence might best be thought of as "basic material."

On the other hand, one might argue that diatonicism is itself a transformation applied to the basic material of free harmony, and, in a sense, subsequent dominantization is the "un-doing" of diatonicism. So, you see, you have raised an interesting philosophical question. We promised to give it some more thought, and we have.

Harmony/Basic Materials/Four Strong Modes/Preface - The Bach fugue in Ebm
Yes, yes, yes, the new version of the Ebm fugue is it! I prefer the melodic quality of the individual voices as well as the total sound. And the most important, it's such an elegant proof of the reality of the window, by avoiding the troubled waters of Bbm (which Bach navigates flawlessly by managing to adhere to the principle of KISS). I assume that your final remark ("It will probably meet with greater resistance and provoke more controversy") refers to the probability that it would not have occurred to the old man to go to Abm so soon in the fugue, but I would suggest either that you remove it or explain it by referring to Bach's habits in fugue composition. In any case, congratulations!

We are happy to see that you agree with our suggestion of having the second entry on the fugue in Abm rather than in Bbm, which is the traditional choice when the Diatonic Major and the Chromatic Minor are considered as parallel modes. The advantages seem to be both harmonic and melodic.

As far as the "controversy" is concerned, we are not totally convinced that "Bach navigates flawlessly" to Bbm because he does it completely diatonically which does not seem in the style of the chromatic mode. There is room for far more discussion here.

There are countless tunes in the diatonic major and in the chromatic minor mode. Could you please name some examples of tunes written in the diatonic minor and in the chromatic major mode?

The diatonic minor and chromatic major modes have been stumbled upon by various composers throughout the centuries, yet they have not, to our knowledge, been recognized theoretically as self-sufficient, free-standing tonalities. Therefore, most of the examples we have found consist of antecedent phrases in the ascending (sharpening) minor which have consequent phrases in the familiar descending (flattening) major. Such examples can be found in the music of Couperin, Ravel, and Fauré, as well as in the theme to "Flashdance," for a more modern example. Rameau gives a clear example of an ascending cadence in minor in his Treatise on Harmony of 1722. The only popular tune that we know of that remains completely in the ascending minor is "The Volga Boatmen." The chromatic major mode occurs even less frequently, yet as a cadence, the ascending minor 6th to a major chord pops up quite often in jazz and popular music, as well as in other periods of the last three to four hundred years, where it has traditionally been analyzed as a half-diminished ii to I progression. This all goes to show that there are many possibilities inherent in the musical language which have not yet been fully explored and utilized. Hopefully the ideas presented here on this site will inspire some to take the plunge!

I was wondering if you guys could possibly include brief sections on the mixolydian and dorian modes on your website. (The mixolydian seems to be just as popular as diatonic major in today's music, probably because it has a little more of an edge to it.) There seems to be an order of feeling between these 4 modes, in this order :
     diatonic major
     mixolydian
     dorian
     diatonic minor
Happiest on top, saddest on bottom. I'm sure there is a way to explain this theoretically somehow :).

     At some point we may add a section on what we call the "weak modes" (as opposed to the Four Strong Modes discussed on the site). In the meantime, a very interesting way to explore modes while at the same time experiencing the effect of Chrominicism is to do the following experiment :
     We are going to approach modes by observing the six chord frames that exist within the diatonic window (there are seven if you count the diminished "buckle" chord, but we will leave that one out for now because it does not make a good chord of rest due to its diminished frame). Each mode will be created by taking a particular frame position within the window and making it sound like the point of reference or point of repose. In other words, making it sound like "home." This can be achieved through repetition of the home chord, or with a drone note, or via restricted, carefully constructed chord progressions that do not fall into the gravitational pull of one of the Strong Modes.
     We will arbitrarily select the frame of A-E, and we will move it through each of the six possible positions that it might occupy within the diatonic window. If you have a keyboard, you can play an A-E-A (octave with 5th in the middle) drone in the left hand while improvising with the right. If you have a guitar, you can keep an A drone going on the A string while improvising up and down the D string (a little bit of palm muffling gives a nice effect).
          1. We will start by placing the A-E frame at the topmost position in the window. This will give us the sound of A phrygian, with the key signature of one flat corresponding to Fmaj/Dmin. Keep the drone going while improvising in A phrygian, being sure to center around A as the home note. Notice the quality or feeling of this mode. Relating this to chrominicism, you will notice that relative to the frame all the other notes are flatter in the window.
          2. Now we move the A-E frame down a notch, into the diatonic system of all naturals. Keep the drone going, but now you will have a B natural instead of Bb in your improvised lines. You will be in A aeolian, or natural minor. You will notice that this system contains only one note sharper than the frame, and all the rest flatter. How does this affect the quality or feeling?
          3. Now move the frame down another notch to A dorian. An F# will appear at the top of the window as the F-natural disappears out the bottom. Continue your drones and improvisations as before. Notice that there are two notes sharper than the frame, and three notes flatter.
          4.Next move the frame down a notch to A mixolydian, into the diatonic system of two sharps. At this point we have crossed into territory where there are, relative to the frame, more sharper notes (three - B,F#,C#) than flatter notes (two - D,G). Not only that, but the third or median of the home chord is now major (two whole steps above the root) instead of minor (one-and-a-half steps above the root). Listen for the effect.
          5. Next we put the A-E frame in "Ionian" position, one more notch down and in the center of the major nucleus. By now you should be getting the hang of this process. Note the key signature, necessary changes in your improvised lines, and the relationship in chrominicism that the frame notes have to the rest of the notes in the window.
          6. Lastly, we put the frame at the very bottom of the window, into the diatonic system of four sharps, or A lydian. Note the relationships in chrominicism and the effect on the quality or feeling.
     What you are calling happy and sad, some might call bright and dark, or light and heavy. The words are not so important, but it does appear that you have placed the four modes you mentioned in the exact order one would predict if looking at modes from the perspective of frames and relative chrominicism ! You just left out the two modes at the extremes of the window. Nice work ! Now that you have done the suggested experiment, I'm sure you can now come up with "a way to explain this theoretically somehow :)".