This idea creates a picture of a progression that is helical, rather than linear. As each day moves forward in time, we can imagine a vector shift that is forward and upward and turns an angle, so that by the time eight days have progressed, a full circle has been turned and the eighth is directly above the first. We have traced out seven days of the week, and then the significant addition of another day takes us to another Sunday, sitting vertically above the previous Sunday which is a pitch of the thread beneath it. So although it has the same name, Sunday, it is a new Sunday and marks simultaneously the end of the last octave and the beginning of the next. This way by following the liturgical weekly cycle traces a holy spiral, upwards to heaven. All we have to do is participate in the liturgical life and we are transported along this path.
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This pattern of seven being resolved finally in eight is present within the structure of each day also. Quoting Psalm 118 in Chapter 16 of his Rule, St Benedict establishes the eight traditional Offices (seven daytime and one night time) and their hours in the Divine Office: ' "Now that the sacred number of seven will be fulfilled by us if we perform the Offices of our service at the time of the Morning Office, of Prime, of Terce, of Sext, of None,of Vespers and of Compline, since it was of these day Hours that he said,"Seven times in the day I have rendered praise to You" (Ps. 118[119]:164). For as to the Night Office the same Prophet says,"In the middle of the night I arose to glorify You" (Ps. 118[119]:62). Let us therefore bring our tribute of praise to our Creator "for the judgments of His justice" at these times: the Morning Office, Prime, Terce,Sext, None,Vespers and Compline; and in the night let us arise to glorify Him.’
It occurs to me that one might think of the prayer of the Church, which is the prayer of Christ himself, ushering the world forward on a path of redemption through sacred time that is a triple helix. The tight daily helix spirals its way on the weekly helix, which in turn sits on a giant helix which rotates once in a year.
Speaking in a sermon for Low Sunday, which is reproduced in the Office of Readings for that day, eight days after Easter, Augustine tells us how the Octave was anticipated in Old Testament:‘This is the octave day of your new birth. Today is fulfilled in you the sign of faith that was prefigured in the Old Testament by the circumcision of the flesh on the eighth day after birth. When the Lord rose from the dead, he put off the mortality of the flesh; his risen body was still the same body, but it was no longer subject to death. By his resurrection he consecrated Sunday, or the Lord’s day. Though the third after his passion, this day is the eighth after the Sabbath, and thus also the first day of the week.’
The psalms, as we can see from the quotes of Benedict above, though placed in the Old Testament anticipate the New also. This should be no surprise. For as was recently pointed out to me, St Thomas Aquinas tells us in his commentary on the psalms that this is a special book that contains all the content of theology: 'The material is universal for while the particular books of the Canon of Scripture contain special materials, this book has the general material of Theology as a whole.' Then in referring to their special place in the liturgy where they are to be sung he says: 'This is what Dionysius [the Areopagite] says in Book 3 of the Celestial Hierarchy,the sacred scripture of the Divine Songs (Psalms) is intended to sing of all sacred and divine workings.'
This points to the psalms as a special source of wisdom, most especially in the context of the liturgy. Given that the purpose of education is to instill wisdom, one wonders why more educational institutions do not have the liturgy of the hours, as well as Mass offered daily (as traditional universities used to). I wrote about this value of psalms and the liturgy in education as a source of wisdom, here.
St Thomas goes on to explain in the same commentary that not only is the content containing all of theology but also the very structure of the book itself conforms to the symbolism of seven and eight: 'The first distinction is that there are one hundred and fifty psalms; this is a mystery, because this number is composed of 70 and 80. By 7, from which 70 is named, the course of this time is signified, which is carried out in seven days; by 8, from which 80 is named, the state of the future life. For the number eight according to the Gloss concerns those who rise from the dead;and it signifies that in this book there is a treatment of those things that pertain to the course of the present life, and to future glory. Again, by seven the old testament is signified. The fathers of the old testament observed that which is seventh: they observed the seventh day, the seventh week, the seventh month, and the seventh year of the seventh decade, which is called the Jubilee. By eight the new testament is signified: we celebrate the eighth day, namely the Lord's Day, on account of the solemnity of the Lord's resurrection; and in this book are contained the mysteries of the old and new testament.’ (The Gloss is the glossa ordinaria, a standard biblical commentary based upon comments of the Fathers, predominantly Jerome, Augustine, Bede and Gregory.)
This 7:8 structure it seems is a ratio that signifies faithful anticipation and then fulfillment, we see it represented in the lenten/pentecostal relationship that Corbon describes and the Old/New Testament convenantal relationship that St Thomas describes.
As, this ratio of 7:8 when incorporated into the proportions of the structure of the book of psalms is appropriate to it and this lends a greater beauty to the book as a whole; due proportion being one of the essential attributes of beauty. We respond to this intuitively as we read it whether we are aware of it or not, and so the structure of it aids our understanding. Just as God offers wisdom through this book in a pattern appropriate to it, so we are made by Him so that we naturally desire to take it in when it is sliced up in this way; and we respond to the beauty of it. Furthermore, when this is presented in its appropriate context, in the liturgy, which itself conforms to these patterns, the power is multiplied many times over.
If we talk of octaves in casual conversation, most people will assume we are talking about music and of course we find that the beautiful patterns of harmony in music correspond to this also. The musical scale is seven notes, and the eighth is higher still, simultaneously the last note of the previous octave and the first of the next. What is extraordinary, I always feel, is the fact of this peculiarly human apprehension of this progression which hears this eighth note as one that is at a higher pitch, yet of the same quality – for example a high and low C (a musical representation of Easter Sunday and Low Sunday perhaps!).
How does this relate to design? Because number can be used to order man’s activity in time and space, potentially all human activity can be made to conform to this liturgical beauty. The symbolism of eight and seven is only one pair of examples that could govern it. So we could use eight sided geometric shapes to indicate this. Within music, harmonious relationships can be described numerically a different way by consideration of the relative lengths of pieces of string (or lengths of pitch pipe) that produce particular notes when plucked (or blown). To describe the interval of an octave you would have one string twice the length of another, so this means that the ratio 1:2 is another way of showing the harmony of an octave. You could have a picture, for example bounded by a rectangle, with one side twice the length of another. As many will know, the other fundamental music harmonies with the octave, the fourth and the fifth produce ratios of 3:4 and 2:3. So a simple design for a church with ratio 1:2:3 for the main structure of it, invokes this liturgical logic and is all the more beautiful for it. There are many more proportions in the tradition beside these, but all point to and are derived from this liturgical principle.
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What might seem at first the ordinary act of chanting a psalm to its simple tone while marking the Hour, is in fact invoking a whole host of intertwining harmonious relationships. We hear only one note at a time; yet it speak to us of something that is dazzling in its beauty and complexity. The wonder of all of this is that God made us all so that we can grasp this effortlessly: each hears monophony and apprehends symphony.
Below: the musical harmonies appear in the design of Attingham House, in Shropshire. The design of the house is simple - a square box with a Palladian/faux Roman portico stuck onto the front. It's beauty is derived from the harmonious proportions in the stories going upwards, indicated by differing window size. They are two, four and six window panes high respectively, corresponding to the propotion 1:2:3. This is based upon the musical harmonies of the octave and perfect fifth respectively. This is not a sacred building, but it demonstrates how any house (it needn't be as large or grand as this) can be a subliminal signpost to the liturgy.