As seen above, any of these thirds can be held as common tones from a major or minor triad, but the fact that there are two minor thirds allows for some ambiguity in possible destination keys. A dominant seventh chord is composed of three stacked thirds: a major third, and two minor thirds. (They are also contained in the G minor scale.)Īs to whether this is a "coincidence," I'm not sure what the definition is for a "coincidence." These destination tonic notes all occur in particular scales because of the rules you set up.
It's true that all of these destination tonic notes are contained in the B-flat major scale. Overall, these allow modulations to F, G, A, B-flat, D, and E-flat. If so, Tim has a large part of it, which I'll repeat here: Okay, so the criteria seem to be two common tones on a major or minor triad from the C major scale, held in common the with dominant seventh of the new key. In order to use B7 I want to place a chord before it which isĮither a minor or a major triad from c major scale, that will containĪt least two tones in common with B7. I'll try to answer based on this comment from OP to Tim's attempt at an answer: I understand the question might be formulated in a confusing way, so am open to edits. Question: Is it a 1) coincidence (overfit) 2) a bug in my calculation 3) a worthy observation worth a further meditation?įurther observation: If instead of resolving to a new tonic we do a deceptive resolution to the 6th scale degree (relative key), then the possible destination keys are those contained in G major scale. I find it very interesting that the keys that I can modulate to in a way defined earlier, ALL of them are contained in a different major scale. If we choose only those modulating chords then it seems like the "destination" keys are those contained in the scale of B-flat major. Motivation of this definition is that I want a dominant seventh to be well-connected and supported by a consonant chord.
In this case I define the word "easily" in the following way - There should be at least one CONSONANT chord in C major in which at least TWO of its tones are contained in the modulating dominant seventh. I decided to research where I can "easily" modulate from C major using dominant seventh chord (modulating to a major key we are).
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