In Declare, Tim Powers focuses on "powers and principalities" as written about in the Scripture, that hold sway over a nation; his idea of a nation being more the pre-modern notion of a people group, a nationality, rather than a political state.
The Apostle Paul refers to "the prince of the power of the air" in Ephesians 2 which is at work among us to make us into children of wrath. And again in Eph. 6, Paul writes, "For we do not wrestle against flesh and blood, but against the rulers, against the authorities, against the cosmic powers over this present darkness, against the spiritual forces of evil in the heavenly places." (v.6-12) We also read from 1 Peter 3:21-22, "Baptism, which corresponds to this (meaning the Ark) now saves you, not as a removal of dirt from the body, but as an appeal to God for a good conscience, through the resurrection of Jesus Christ, who has gone into heaven and is at the right hand of God, with angels, authorities, and powers having been subjected to him".
I would suggest that these verses are key to what Powers was thinking, and then developed, along the lines of the angels in Declare, and the ultimate protection against them - baptism. Those angels, while awfully and awesomely powerful, were restricted to a specific geographic location. Also, of the 3 primary characters: Andrew Hale, Kim Philby, and Elena Ceniza-Bendiga, only Hale and Ceniza-Bendia are baptized, and it is quite obvious early in the book that baptism (or not) is extremely significant.
But, to the angels and frequencies. Powers uses the concept of frequency as a display of the power of the evil angels. When God created the heavens and the earth, He spoke and all things came into being. I don't know the Hebrew words and meaning for "He spoke", but I would guess that it denotes some idea of great power. All things that exist were shaped by the power of His word, and indeed hold together by that same power. Scientists tells us that matter has frequency, and that various types of matter have various frequencies - whether the sun, a rock, butterfly or brain-wave. I speculate that before the Fall, before sin corrupted man and creation, those frequencies 'rang true'. For man was created in God's image, perfectly, and God pronounced all of creation 'good'. However, with the corruption of sin in creation, all things - including frequencies, men, and rebellious angels, became less than what they would have been. I can understand why Powers would focus so much on these evil angels and the overwhelming effect of their frequencies. Yet those same angels were not all-powerful, but were subject to higher authority, even suffering death.
As I consider and muse upon these things, the principle of Eastern medicine come to mind - that the body's health is related to its energy. If the energy is flowing properly, health is optimal; if not, health is less than optimal. This energy (frequency) moves along meridians in the body with several primary contact points. Eastern medicine seeks to open up congested meridians and points to let the body's energy flow, thus bringing healing. Western medicine and thought has been wary of this philosophy of healing, perhaps because Eastern thought and Western thought are theologically incompatible.
But, I suggest that we have something to learn from Eastern medicine when it comes to health and healing and the ideas surrounding energy and meridians. Dogs have been trained to detect cancer in a human before tests can diagnose it. They have also been trained to detect a seizure before it occurs, and it's widely accepted that animals and birds can 'forecast' tumultuous natural events such as earthquakes, storms, or tsunamies. How do they do these things? They are much more sensitive to frequency than we are. (Remember the ol' dog whistle?) And, of course, sea creatures communicate by frequency - we call it sonar.
So, why wouldn't it be plausible that the falleness of our flesh would produce fallen frequencies, and thus cause illness, poor health, and eventually, death? And why wouldn't it be plausible that if we could improve the frequencies of the body, we could improve our health? It's a thought, and something worth considering. I've recently begun reading And the Trees Clap Their Hands - Faith, Perception, and the New Physics by Virginia Stem Owens. It will be interesting to see what she writes about the physics of creation.
Tim Powers writes a great, almost overwhelming story, again, in Declare, and among the many things to consider in this novel was the idea of frequency and it's effect upon creation, whether man, angel, or matter. Powers takes a hard look at the falleness of creation and the overriding redemption that Grace brings, no matter what you've been through.