MusicNovatory/Introduction/Reference/Comments and Questions/Harmony/Preface/Chords and Scales

I can't find anything on your site concerning scales. Have they suddenly disappeared from music altogether?

Not at all. Start by looking at the section called CHROMINICISM and come back to us.

Both the classical roman numeral harmonic analysis and the more advanced and interesting Schenkerian analysis use the concept of scale degree, a melodic construct based in the ionian mode (or the aeolian mode) over the tonic. Strange : we are using traditionally a melodical concept pretending to grasp the harmony of the music. Your ordinance by fifths seems more logical but in that case to label, for instance, the sub (counter) dominant with IV (or iv) is nonsense. How about the "traditional" (mainly jazz) concepts of chord-scale reationships (I mean ionian, lydian, locrian,....stuff) ??? I find your MusicNovatory revolutionary, great, wonderful, clever. The rest of theory, harmony,... treatises become obsolete and dull !

Thanks for your compliments. It's always pleasant to know that more people appreciate what we are doing. MusicNovatory uses symbols or terms like IV (or iv) only to give traditionally trained readers something to relate to. We agree with you that these terms are quite incoherent. You must understand that this applies to a huge number of terms (including for intervals) and to better make sense and communicate, MusicNovatory rather uses the terms "TONIC, DOMINANT, COUNTER", with "ANTE-1, ANTE-2, ANTE-3", and the inevitable "BUCKLE" chord, each one with its specific place in the diatonic Window. Scale degrees are used here because readers may still need to refer to them. Of course, revising terminology is not a simple issue as it implies agreeing about the new terms and definitions. MusicNovatory works to limit the changes to a minimum, but we still need adequate vocabulary to better communicate and understand. There does not seem to be much point in using scales of any kind as a theoretical tool. In a melody, scales are merely arpeggios "filled-in" with passing tones. The arpeggio is a spread-out version of the chord that we are on and the passing notes are borrowed from the neighboring chords. Our advice about scales would be : "you'll see that you can easily live without them".

...Sorry, one last question. you say that the major scale inverted is the minor scale, but isn't it actually the phrygian?

No reason to apologize, we love questions! Another astute observation. First of all, we don't think we said that the major scale inverted is the minor scale. We think we said that the fundamental diatonic (descending) major mode inverted is the diatonic (ascending) minor mode, and what we mean by mode is revealed more clearly by looking at the diatonic window with the notes disposed in the series of fifths. Inversion involves rotating the entire system around the central note of the window (in Cmaj/Amin this would be the note D). Look what happens to the Tonic triad when you do this inversion - the frame inverts, so the root of the major tonic becomes the fifth of the minor tonic. Therefore, any melodic structure (such as a scale) that begins on C (root of the tonic chord) in major will, when inverted into diatonic minor, begin on E (fifth of the Am tonic chord). So, getting back to your question, yes, in a way a C major scale inverted (around the note D) does give you a phrygian scale, but not a C phrygian or A phrygian, but E phrygian. But of course, it makes no sense to call it E phrygian, because E is not the tonal center, i.e., it is not the root of the tonic chord; A is. So this is an A natural minor scale. All this goes to reinforce the concept that scales are not fundamental, they are results of something deeper: the series of perfect fifths, generated from the simplest productive ratio.

I have a question about the chromatic minor mode. What scale does it use? does it change for each chord in the mode?

     You may not realize it, but this is really quite a loaded question! First of all, let us begin by saying that Music Novatory theory does not recognize the scale as being a fundamental musical building block. You may find that a scale passage is best understood as an embellished tetrad. If you look at any swing progression, you will notice that it defines a set of seven notes (there are four notes in each tetrad with one note being the common tone). On either chord of the swing, a scale passage can be generated by embellishing the four chord tones of the tetrad with non-chordal passing tones borrowed from the other chord of the swing.
     Let's apply this to your question about the chromatic minor mode. In C chromatic minor, for example, we have a Dominant/Tonic swing of G7/Cm6. This swing delineates the seven notes C D Eb F G A B C, or put in a different disposition G A B C D Eb F G. If you are on a G7 chord, the G B D F are chord tones, while the remaining three notes are non-chordal passing tones borrowed from the Cm6. If you are on a Cm6 chord, the C Eb G A are chord tones, while the remaining three notes are non-chordal passing tones borrowed from the G7.
     Now, what happens when you move to the Counter/Tonic swing? Now we are dealing with Fm6/Cm7. This swing delineates the seven notes F G Ab Bb C D Eb F, or put in a different disposition C D Eb F G Ab Bb C. If you are on an Fm6 chord, the F Ab C D are chord tones, while the remaining three notes are non-chordal passing tones borrowed from the Cm7. If you are on a Cm7 chord, the C Eb G Bb are chord tones, while the remaining three notes are non-chordal passing tones borrowed from the Fm6.
     So, to answer your question "Does it change for each chord in the mode?" - It might be more accurate to say that it changes for each swing.
     Incidentally, it may be interesting to compare the so-called "scales" (embellished tetrads) generated above with how they would traditionally be analyzed according to academic theory. In the Dominant/Tonic example, the C D Eb F G A B C would be called a "melodic minor" scale. The only problem there (besides giving the impression that the scale is a fundamental building block) is that the melodic minor is usually taught as having the raised 6th and 7th ascending and the diatonic 6th and 7th descending. In actual fact and usage, it has nothing to do with ascending and descending, but rather with what swing progression you are on. The G A B C D Eb F G "scale" does not have a name in academic theory that we know of - it would most likely be analyzed as C melodic minor - although we have heard of Jazz players calling this "melodic major." (Don't forget, the G7/Cm6 swing also exists in G chromatic major as well as C chromatic minor!)
     In the Counter/Tonic example, the F G Ab Bb C D Eb F and C D Eb F G Ab Bb C would both be seen simply as C "natural minor." Jazzers would tend to call the F G Ab Bb C D Eb F "dorian."
     It should also be noted that in the chromatic modes, on a Dominant/Tonic swing, the choice of embellishment of the common tone will differ depending on if the embellishing non-chordal tone is being used as a passing tone or as an embroidery ("neighbor tone"). For example, on the G7 chord in the G7/Cm6 swing, when passing from the common tone G to the median B (as in a straight scale passage), the non-chordal tone A would be used. However, when embroidering the G with an upper neighbor, the Ab would be used. Likewise, on the Cm6 when passing from the common tone G to the median Eb, the non-chordal tone F would be used. However, when embroidering the G with a lower neighbor, the F# would be used.

I've been doing some ear-training with intervals lately, and it seems to me like major 3rds and perfect fifths both have the top note sounding like an extension of the bottom note, and vice versa for min6 and p4. aug4/dim5 are completely ambiguous, seconds are ambiguous, and min3/maj6 are ambiguous. It's the maj 3rds (min6) and perfect 5ths (p4) alone that have this unique quality.
     Then I thought about major and minor chords. In a major chord, the third and fifth both sound like extensions of the root note. It is a very stable sound.
     In a minor chord, the 5th sounds like an extension of the 3rd, while the 5th points to the root. It is more unstable/uncertain as to what note gets precedence.
     I just came up with this idea so there is more that can come from it (or refuted). Why do diminished 7th chords sound completely ambiguous? Because there are no maj3/p5 anywhere in the chord and each note stands alone. Why does a major chord sound so direct? Because everything points back to the root. So the answer lies in analyzing the individual components (intervals) of the chord and hearing what is connected or underlying.
     As far as scales go, I am not convinced that scales are not individual entities. There is no denying that each scale has its own flavor and unique sound, and I will continue to use them freely and generally be aware of 'what scale i'm in' while playing music. The blues scale and the harmonic minor are 2 of my favs, and I'm not ready to throw them out based on theory alone. They exist.

Your observations are divided in two different parameters : (a) chords, where the sounds are heard simultaneously, which we call the vertical parameter of The Structure of Pitch, and (b) scales, where the sounds are heard successively, which we call the horizontal parameter of The Structure of Pitch. We will examine these individually, because we firmly believe that the vertical parameter is more fundamental (because it is more demanding, as you accurately observed) and the horizontal parameter derives from the vertical chords, more specifically in the Orbit Lines of the Voice-leading.
     (a) In Generating Basic Materials, it was clearly established that the perfect fifth and the major third were the two, actually the only two, generating intervals, and that the perfect fourth was "change" from the octave, and the minor third was "change" from the perfect fifth. The major second was established as the basic interval of diatonic scales and the minor second as the two secondary intervals where we pass from one Window to the next as we take each second note. The major Triad has a 4-5-6 frequency ratio and the minor Triad has a 10-12-15 frequency ratio, certainly more complex and less stable. Diminished Seventh chords are not fundamental chords (merely sonorities) that have been produced by three different forms of Transformations. Your listening and our thinking seem to fit quite well.
     (b) Jumping to the conclusion that scales are undivided entities might be a little rash and I see that you express yourself with care. However, you are perfectly correct when you say that scales exist - they DO - do not throw them out - no theory asks you to, including ours. We are presently composing "more musical" scales for practitioners of the "Uniform Keyboard" (the Paul Janko model) which is presently produced in Japan. We will keep you posted on this as soon as we can lay our hands on one.