Patrick, the montanas which bloom early in the spring, with a delicious vanilla fragrance are incredibly profuse bloomers. The blossoms are followed by a dense covering of disease free leaves which last well into fall. A montana will easily surround your upstairs windows and much of the walls surrounding.
This is Montana Rubens Pink Perfection
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Patrick, there are several clematis that are fragrant or at least that can be. Clematis by and large typically don't have strong overpowering fragrances except for maybe clematis terniflora or sweet autumn clematis and some of the montanas. Betty Corning is also one that has a definite fragrance but it is more subtle than terniflora. I brought a few blossoms of Betty Corning in this spring and could definitely smell the fragrance within the room in which the bouquet was placed. Hakuree is another one with a fragrance but it is even more subtle but very jasminey up close. Aromatica is another one that is purportedly fragrant and is described as smelling like hawthorne. Mine wasn't noticeably fragrant last year but perhaps it is like my terniflora which wasn't fragrant at all until after it had been in the ground for four years. As Roserobin pointed out, some of the montanas are fragrant. Fragrant Spring, Elizabeth, Mayleen, Rubens, Grandiflora, and Pink Perfection are a few of the montanas that are noted to be fragrant. In my garden, a heracleifolia called Blue Mood is fragrant upclose and reminds me of hyacinth blossoms. Another one that is fragrant but again only up close is Olgae. Mine is slightly sweet scented. I am sure there are others that will be mentioned by those that have them.

One thing to note is that not all clematis are fragrant to everyone. I am unsure if it is due to each person's own individuality when it comes to perceiving odors or if there are some cultivars that depending on whom you purchase them from are either fragrant or not. I have previously mentioned my Hakuree and Olgae as being fragrant while others who have them have said they cannot detect any fragrance. Another point that needs to be made is that the fragrances tend to be more pronounced in the early morning and late evening and when the air is still and the humidity high. Not sure if this serves some biological purpose or not but often plants are fragrant at certain times of the day to attract specific pollinators that are active at those specific times of the day.

None of our clematis have more than a very slight fragrance. I have to stick my right in the bloom and sniff to detect any. If the roses are blooming... I don't even try to smell the clematis.

You spoke of encircling a window with scented bloom. That means either a Montana, if your zone will tolerate overwintering them, or else the pruning group 3 varieties mentioned above. Both Triternata Rubromarginata and Betty Corning can grow to enormous size also, which means attention must be paid early to their supporting structues. Also, think about painting the stucco house in the futur too!

Betty Corning is fairly pale in my view, might not stand out against your white walls. She certainly is gorgeous though. TxR is gorgeous too, the flowers being very small and looking good combined with another clematis.

Both of the above vines would take 3-4 years to reach the size you are speaking of. When searching CotW, do pay attention to ultimate sizes.

Here is a photo of TxR with Hagley's Hybrid growing in Michigan:
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And here is Betty in Canada:
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I want to thank those who responded. Your suggestions have been very helpful and the images are to die for. Based upon your comments I'm definately getting BETTY CORNING and RUBROMARGINATA.

C. ororata might be hard to place, which makes it a doubtful choice. SdCT has flowers that are too large for my taste. I confess that I'm not fond of the large flowered clematis. I much prefer cultivars with smaller flowers that cover the vines during the first bloom period.

Roserobin's pink montana images are ravishing but this type of clematis has a couple of issues that are a concern. First, they only bloom once in the spring. I like plants that repeat bloom or at least have an extended period of bloom. Second, it might not be winter hardy in zone 6.

Image of Rubromarginata by deusex at the Hortiplex database

Here is a link that might be useful: RUBROMARGINATA at the International Clematis Society

Another fragrant clematis is C. tubulosa WYEVALE (also C. heracleifolia 'Davidiana'). This true blue clematis is said to have flowers that look and smell like hyacinths. Wyevale is supposed to be an improvement over the species, coming into bloom earlier (mid summer) and continuing through autumn until stopped by winter cold. Strangly, it isn't a vine but rather a small herbaceous shrub to about 3' high. I think this clematis will be an excellent companion plant for my roses, especially where a fragrant blue accent is needed.

Recommended for zones 5-9.

Here is a link that might be useful: C. heracleifolia at the International Clematis Society