One division of the Saptamsha spans 30 degrees divided by seven, which is 4 degrees 17 minutes and about 9 seconds of arc, eighty four divisions in the zodiac. The ascendant crosses that arc in roughly seventeen minutes.
Seven is the first divisor in the scheme that does not go evenly into thirty, and the consequence is practical rather than theoretical. Every saptamsha boundary after the first falls on a fraction of a minute of arc, so two programs that round the division width differently, or that carry a different number of decimal places in the planetary longitude, can place a planet sitting near a boundary in different divisions. When a D-7 reading turns on a planet within a few minutes of arc of a cusp, the honest report is that the placement is uncertain rather than that it is one thing or the other.
The counting rule is settled: in an odd sign the seven divisions are counted from that sign onward, and in an even sign from the seventh sign from it.
The Saptamsha is the chart that turns the shadvarga of six into the saptavarga of seven, and it carries through into the dashavarga and the shodashavarga as well, so it is one of the more heavily weighted divisions despite its awkward arithmetic. Its subject is children and the prospect of them.