Here’s what Wikipedia shows on the table for 32 directions. Each 32 direction takes up 11.5 degrees. For 8 directions that would be 45 degrees or 22.5 each side. So southeast clearly does not include south according to this. Whether I can apply the technical definition to HOA, I am not sure.
- East by south EbS Quarto di Levante verso Scirocco 95.625° 101.250° 106.875° 10 East-southeast ESE Levante-Scirocco 106.875° 112.500° 118.125° 11 Southeast by east SEbE Quarto di Scirocco verso Levante 118.125° 123.750° 129.375° 12 Southeast SE Scirocco 129.375° 135.000° 140.625° 13 Southeast by south SEbS Quarto di Scirocco verso Ostro 140.625° 146.250° 151.875° 14 South-southeast SSE Ostro-Scirocco 151.875° 157.500° 163.125° 15 South by east SbE Quarto di Ostro verso Scirocco 163.125° 168.750° 174.375° 16 South S Ostro 174.375° 180.000° 185.625° 17 South by west SbW Quarto di Ostro verso Libeccio 185.625° 191.250° 196.875° 18 South-southwest SSW Ostro-Libeccio 196.875° 202.500° 208.125° 19 Southwest by south SWbS Quarto di Libeccio verso Ostro 208.125° 213.750° 219.375° 20 Southwest SW Libeccio 219.375° 225.000° 230.625° 21 Southwest by west SWbW Quarto di Libeccio verso Ponente 230.625° 236.250° 241.875° 22 West-southwest WSW Ponente-Libeccio 241.875° 247.500° 253.125° 23 West by south WbS Quarto di Ponente verso Libeccio 253.125° 258.750° 264.375°