Hi, I can't find in your extremely interesting website any reference to MODULATION, that important tool for creating musical structure, at least in the common period. Modulation is closely connected with cromaticism and dominantization.... but no word about applied dominants, for instance. Strange, anyway. Best regards

You are right. There was no specific mention of the word MODULATION in the MusicNovatory site so we have added the term to our term definition list. As pointed out in the definition, the term is often ambiguous because of the range of manifestations and considerations that are implied. In summary, a MODULATION is a travel or shift from one circle to another, not necessarily using chromaticism and/or dominantization.

Looking at your question more closely, lets first consider modulations which produce a change of Key, in other words, which travel to another Key. The imposition of a Key is to be found in its circle, especially the end of the circle (ex: ANTEs and DOMINANT). Traveling to another Key is thus a question of shifting to the end of its circle, using the appropriate Metamorphosis to produce a neat link which respects the Voice-leading. Any chromaticism and dominantization involved would only be with respect to the original Key, not with the new Key where everything is normal, being in its own circle.

On the other hand, the Natural Canons section offers an interesting example of repeated short modulations, each "modulating" into the first beat of a bar, clearly identifying the irregularity of the bars. Yet, the whole passage is clearly in the same Key of C, going around its circle twice.

Many Bridges could very well also be placed in this category of modulating and remaining in the original key. A dominantized ANTE-1 (D⁷) cadencing to G at the end of a Bridge does not impose any change of Key, which also explains why the seventh is often added to the G chord.

Many thanks for your letter and for bringing up this interesting issue. Please tell us if you need more.