giorgioesse

hi, I'm making some additive synthesis (triangle and sawthoot) with 10 cycle~ objects...

can somebody explain me why I have to shift every oscillator's phase by 0.25 to get the correct waveforms in this example?

"defrect" : [ 25.0, 69.0, 640.0, 506.0 ],

"patching_rect" : [ 157.0, 16.0, 50.0, 20.0 ],

"patching_rect" : [ 255.0, 10.0, 100.0, 40.0 ],

"outlettype" : [ "preset", "int", "preset", "int" ],

"data" : [ 5, "obj-25", "flonum", "float", 192.0, 5, "obj-53", "flonum", "float", 1.0, 5, "obj-57", "flonum", "float", 384.0, 5, "obj-56", "flonum", "float", 0.0, 5, "obj-65", "flonum", "float", 576.0, 5, "obj-64", "flonum", "float", -0.11, 5, "obj-61", "flonum", "float", 768.0, 5, "obj-60", "flonum", "float", 0.0, 5, "obj-81", "flonum", "float", 960.0, 5, "obj-80", "flonum", "float", 0.04, 5, "obj-77", "flonum", "float", 1152.0, 5, "obj-76", "flonum", "float", 0.0, 5, "obj-73", "flonum", "float", 1344.0, 5, "obj-72", "flonum", "float", -0.02, 5, "obj-69", "flonum", "float", 1536.0, 5, "obj-68", "flonum", "float", 0.0, 5, "obj-89", "flonum", "float", 1728.0, 5, "obj-88", "flonum", "float", 0.012, 5, "obj-85", "flonum", "float", 1920.0, 5, "obj-84", "flonum", "float", 0.0, 6, "obj-91", "gain~", "list", 116, 10.0, 5, "obj-95", "flonum", "float", 192.0, 5, "obj-107", "number", "int", 7, 5, "obj-108", "number", "int", 98, 5, "obj-2", "flonum", "float", 0.25 ]

"data" : [ 5, "obj-25", "flonum", "float", 193.0, 5, "obj-53", "flonum", "float", 1.0, 5, "obj-57", "flonum", "float", 386.0, 5, "obj-56", "flonum", "float", 0.5, 5, "obj-65", "flonum", "float", 579.0, 5, "obj-64", "flonum", "float", 0.25, 5, "obj-61", "flonum", "float", 772.0, 5, "obj-60", "flonum", "float", 0.125, 5, "obj-81", "flonum", "float", 965.0, 5, "obj-80", "flonum", "float", 0.063, 5, "obj-77", "flonum", "float", 1158.0, 5, "obj-76", "flonum", "float", 0.031, 5, "obj-73", "flonum", "float", 1351.0, 5, "obj-72", "flonum", "float", 0.015, 5, "obj-69", "flonum", "float", 1544.0, 5, "obj-68", "flonum", "float", 0.007, 5, "obj-89", "flonum", "float", 1737.0, 5, "obj-88", "flonum", "float", 0.003, 5, "obj-85", "flonum", "float", 1930.0, 5, "obj-84", "flonum", "float", 0.001, 6, "obj-91", "gain~", "list", 116, 10.0, 5, "obj-95", "flonum", "float", 193.0, 5, "obj-107", "number", "int", 7, 5, "obj-108", "number", "int", 98, 5, "obj-2", "flonum", "float", 0.25 ]

"patching_rect" : [ 469.0, 309.0, 50.0, 20.0 ],

"patching_rect" : [ 412.0, 309.0, 50.0, 20.0 ],

"patching_rect" : [ 574.0, 82.0, 32.5, 20.0 ],

"patching_rect" : [ 518.0, 80.0, 32.5, 20.0 ],

"patching_rect" : [ 461.0, 80.0, 32.5, 20.0 ],

"patching_rect" : [ 405.0, 81.0, 32.5, 20.0 ],

"patching_rect" : [ 347.0, 81.0, 32.5, 20.0 ],

"patching_rect" : [ 286.0, 85.0, 32.5, 20.0 ],

"patching_rect" : [ 228.0, 85.0, 32.5, 20.0 ],

"patching_rect" : [ 171.0, 86.0, 32.5, 20.0 ],

"patching_rect" : [ 113.0, 86.0, 32.5, 20.0 ],

"patching_rect" : [ 56.0, 22.0, 50.0, 20.0 ],

"patching_rect" : [ 388.0, 343.0, 130.0, 130.0 ],

"patching_rect" : [ 281.0, 414.0, 45.0, 45.0 ],

"patching_rect" : [ 281.0, 325.0, 39.0, 63.0 ],

"patching_rect" : [ 562.0, 229.0, 32.5, 20.0 ],

"patching_rect" : [ 576.0, 196.0, 50.0, 20.0 ],

"patching_rect" : [ 577.0, 132.0, 50.0, 20.0 ],

"patching_rect" : [ 577.0, 159.0, 45.0, 20.0 ],

"patching_rect" : [ 503.0, 228.0, 32.5, 20.0 ],

"patching_rect" : [ 517.0, 195.0, 50.0, 20.0 ],

"patching_rect" : [ 518.0, 131.0, 50.0, 20.0 ],

"patching_rect" : [ 518.0, 158.0, 45.0, 20.0 ],

"patching_rect" : [ 444.0, 227.0, 32.5, 20.0 ],

"patching_rect" : [ 458.0, 194.0, 50.0, 20.0 ],

"patching_rect" : [ 459.0, 130.0, 50.0, 20.0 ],

"patching_rect" : [ 459.0, 157.0, 45.0, 20.0 ],

"patching_rect" : [ 385.0, 226.0, 32.5, 20.0 ],

"patching_rect" : [ 399.0, 193.0, 50.0, 20.0 ],

"patching_rect" : [ 400.0, 129.0, 50.0, 20.0 ],

"patching_rect" : [ 400.0, 156.0, 45.0, 20.0 ],

"patching_rect" : [ 328.0, 226.0, 32.5, 20.0 ],

"patching_rect" : [ 342.0, 193.0, 50.0, 20.0 ],

"patching_rect" : [ 343.0, 129.0, 50.0, 20.0 ],

"patching_rect" : [ 343.0, 156.0, 45.0, 20.0 ],

"patching_rect" : [ 269.0, 225.0, 32.5, 20.0 ],

"patching_rect" : [ 283.0, 192.0, 50.0, 20.0 ],

"patching_rect" : [ 284.0, 128.0, 50.0, 20.0 ],

"patching_rect" : [ 284.0, 155.0, 45.0, 20.0 ],

"patching_rect" : [ 213.0, 224.0, 32.5, 20.0 ],

"patching_rect" : [ 227.0, 191.0, 50.0, 20.0 ],

"patching_rect" : [ 228.0, 127.0, 50.0, 20.0 ],

"patching_rect" : [ 228.0, 154.0, 45.0, 20.0 ],

"patching_rect" : [ 154.0, 223.0, 32.5, 20.0 ],

"patching_rect" : [ 168.0, 190.0, 50.0, 20.0 ],

"patching_rect" : [ 169.0, 126.0, 50.0, 20.0 ],

"patching_rect" : [ 169.0, 153.0, 45.0, 20.0 ],

"patching_rect" : [ 97.0, 223.0, 32.5, 20.0 ],

"patching_rect" : [ 111.0, 190.0, 50.0, 20.0 ],

"patching_rect" : [ 112.0, 126.0, 50.0, 20.0 ],

"patching_rect" : [ 112.0, 153.0, 45.0, 20.0 ],

"patching_rect" : [ 38.0, 222.0, 32.5, 20.0 ],

"patching_rect" : [ 52.0, 189.0, 50.0, 20.0 ],

"patching_rect" : [ 53.0, 125.0, 50.0, 20.0 ],

"patching_rect" : [ 53.0, 152.0, 45.0, 20.0 ],

"midpoints" : [ 290.5, 400.0, 341.0, 400.0, 341.0, 324.0, 397.5, 324.0 ]

"midpoints" : [ 527.5, 184.0, 512.5, 184.0 ]

"midpoints" : [ 586.5, 185.0, 571.5, 185.0 ]

hi, I'm making some additive synthesis (triangle and sawthoot) with 10 cycle~ objects...
can somebody explain me why I have to shift every oscillator's phase by 0.25 to get the correct waveforms in this example?

{
    "patcher" :     {
        "fileversion" : 1,
        "rect" : [ 25.0, 69.0, 640.0, 506.0 ],
        "bglocked" : 0,
        "defrect" : [ 25.0, 69.0, 640.0, 506.0 ],
        "openrect" : [ 0.0, 0.0, 0.0, 0.0 ],
        "openinpresentation" : 0,
        "default_fontsize" : 12.0,
        "default_fontface" : 0,
        "default_fontname" : "Arial",
        "gridonopen" : 0,
        "gridsize" : [ 15.0, 15.0 ],
        "gridsnaponopen" : 0,
        "toolbarvisible" : 1,
        "boxanimatetime" : 200,
        "imprint" : 0,
        "boxes" : [             {
                "box" :                 {
                    "maxclass" : "flonum",
                    "patching_rect" : [ 157.0, 16.0, 50.0, 20.0 ],
                    "id" : "obj-2",
                    "fontname" : "Arial",
                    "numinlets" : 1,
                    "numoutlets" : 2,
                    "fontsize" : 12.0,
                    "outlettype" : [ "float", "bang" ]
                }

            }
,             {
                "box" :                 {
                    "maxclass" : "preset",
                    "patching_rect" : [ 255.0, 10.0, 100.0, 40.0 ],
                    "id" : "obj-109",
                    "numinlets" : 1,
                    "numoutlets" : 4,
                    "outlettype" : [ "preset", "int", "preset", "int" ],
                    "preset_data" : [                         {
                            "number" : 1,
                            "data" : [ 5, "obj-25", "flonum", "float", 192.0, 5, "obj-53", "flonum", "float", 1.0, 5, "obj-57", "flonum", "float", 384.0, 5, "obj-56", "flonum", "float", 0.0, 5, "obj-65", "flonum", "float", 576.0, 5, "obj-64", "flonum", "float", -0.11, 5, "obj-61", "flonum", "float", 768.0, 5, "obj-60", "flonum", "float", 0.0, 5, "obj-81", "flonum", "float", 960.0, 5, "obj-80", "flonum", "float", 0.04, 5, "obj-77", "flonum", "float", 1152.0, 5, "obj-76", "flonum", "float", 0.0, 5, "obj-73", "flonum", "float", 1344.0, 5, "obj-72", "flonum", "float", -0.02, 5, "obj-69", "flonum", "float", 1536.0, 5, "obj-68", "flonum", "float", 0.0, 5, "obj-89", "flonum", "float", 1728.0, 5, "obj-88", "flonum", "float", 0.012, 5, "obj-85", "flonum", "float", 1920.0, 5, "obj-84", "flonum", "float", 0.0, 6, "obj-91", "gain~", "list", 116, 10.0, 5, "obj-95", "flonum", "float", 192.0, 5, "obj-107", "number", "int", 7, 5, "obj-108", "number", "int", 98, 5, "obj-2", "flonum", "float", 0.25 ]
                        }
,                         {
                            "number" : 2,
                            "data" : [ 5, "obj-25", "flonum", "float", 193.0, 5, "obj-53", "flonum", "float", 1.0, 5, "obj-57", "flonum", "float", 386.0, 5, "obj-56", "flonum", "float", 0.5, 5, "obj-65", "flonum", "float", 579.0, 5, "obj-64", "flonum", "float", 0.25, 5, "obj-61", "flonum", "float", 772.0, 5, "obj-60", "flonum", "float", 0.125, 5, "obj-81", "flonum", "float", 965.0, 5, "obj-80", "flonum", "float", 0.063, 5, "obj-77", "flonum", "float", 1158.0, 5, "obj-76", "flonum", "float", 0.031, 5, "obj-73", "flonum", "float", 1351.0, 5, "obj-72", "flonum", "float", 0.015, 5, "obj-69", "flonum", "float", 1544.0, 5, "obj-68", "flonum", "float", 0.007, 5, "obj-89", "flonum", "float", 1737.0, 5, "obj-88", "flonum", "float", 0.003, 5, "obj-85", "flonum", "float", 1930.0, 5, "obj-84", "flonum", "float", 0.001, 6, "obj-91", "gain~", "list", 116, 10.0, 5, "obj-95", "flonum", "float", 193.0, 5, "obj-107", "number", "int", 7, 5, "obj-108", "number", "int", 98, 5, "obj-2", "flonum", "float", 0.25 ]
                        }
 ]
                }

            }
,             {
                "box" :                 {
                    "maxclass" : "number",
                    "patching_rect" : [ 469.0, 309.0, 50.0, 20.0 ],
                    "id" : "obj-108",
                    "fontname" : "Arial",
                    "numinlets" : 1,
                    "numoutlets" : 2,
                    "fontsize" : 12.0,
                    "outlettype" : [ "int", "bang" ]
                }

            }
,             {
                "box" :                 {
                    "maxclass" : "number",
                    "patching_rect" : [ 412.0, 309.0, 50.0, 20.0 ],
                    "id" : "obj-107",
                    "fontname" : "Arial",
                    "numinlets" : 1,
                    "numoutlets" : 2,
                    "fontsize" : 12.0,
                    "outlettype" : [ "int", "bang" ]
                }

            }
,             {
                "box" :                 {
                    "maxclass" : "newobj",
                    "text" : "* 10",
                    "patching_rect" : [ 574.0, 82.0, 32.5, 20.0 ],
                    "id" : "obj-105",
                    "fontname" : "Arial",
                    "numinlets" : 2,
                    "numoutlets" : 1,
                    "fontsize" : 12.0,
                    "outlettype" : [ "int" ]
                }

            }
,             {
                "box" :                 {
                    "maxclass" : "newobj",
                    "text" : "* 9",
                    "patching_rect" : [ 518.0, 80.0, 32.5, 20.0 ],
                    "id" : "obj-101",
                    "fontname" : "Arial",
                    "numinlets" : 2,
                    "numoutlets" : 1,
                    "fontsize" : 12.0,
                    "outlettype" : [ "int" ]
                }

            }
,             {
                "box" :                 {
                    "maxclass" : "newobj",
                    "text" : "* 8",
                    "patching_rect" : [ 461.0, 80.0, 32.5, 20.0 ],
                    "id" : "obj-102",
                    "fontname" : "Arial",
                    "numinlets" : 2,
                    "numoutlets" : 1,
                    "fontsize" : 12.0,
                    "outlettype" : [ "int" ]
                }

            }
,             {
                "box" :                 {
                    "maxclass" : "newobj",
                    "text" : "* 7",
                    "patching_rect" : [ 405.0, 81.0, 32.5, 20.0 ],
                    "id" : "obj-103",
                    "fontname" : "Arial",
                    "numinlets" : 2,
                    "numoutlets" : 1,
                    "fontsize" : 12.0,
                    "outlettype" : [ "int" ]
                }

            }
,             {
                "box" :                 {
                    "maxclass" : "newobj",
                    "text" : "* 6",
                    "patching_rect" : [ 347.0, 81.0, 32.5, 20.0 ],
                    "id" : "obj-104",
                    "fontname" : "Arial",
                    "numinlets" : 2,
                    "numoutlets" : 1,
                    "fontsize" : 12.0,
                    "outlettype" : [ "int" ]
                }

            }
,             {
                "box" :                 {
                    "maxclass" : "newobj",
                    "text" : "* 5",
                    "patching_rect" : [ 286.0, 85.0, 32.5, 20.0 ],
                    "id" : "obj-99",
                    "fontname" : "Arial",
                    "numinlets" : 2,
                    "numoutlets" : 1,
                    "fontsize" : 12.0,
                    "outlettype" : [ "int" ]
                }

            }
,             {
                "box" :                 {
                    "maxclass" : "newobj",
                    "text" : "* 4",
                    "patching_rect" : [ 228.0, 85.0, 32.5, 20.0 ],
                    "id" : "obj-100",
                    "fontname" : "Arial",
                    "numinlets" : 2,
                    "numoutlets" : 1,
                    "fontsize" : 12.0,
                    "outlettype" : [ "int" ]
                }

            }
,             {
                "box" :                 {
                    "maxclass" : "newobj",
                    "text" : "* 3",
                    "patching_rect" : [ 171.0, 86.0, 32.5, 20.0 ],
                    "id" : "obj-98",
                    "fontname" : "Arial",
                    "numinlets" : 2,
                    "numoutlets" : 1,
                    "fontsize" : 12.0,
                    "outlettype" : [ "int" ]
                }

            }
,             {
                "box" :                 {
                    "maxclass" : "newobj",
                    "text" : "* 2",
                    "patching_rect" : [ 113.0, 86.0, 32.5, 20.0 ],
                    "id" : "obj-97",
                    "fontname" : "Arial",
                    "numinlets" : 2,
                    "numoutlets" : 1,
                    "fontsize" : 12.0,
                    "outlettype" : [ "int" ]
                }

            }
,             {
                "box" :                 {
                    "maxclass" : "flonum",
                    "patching_rect" : [ 56.0, 22.0, 50.0, 20.0 ],
                    "id" : "obj-95",
                    "fontname" : "Arial",
                    "numinlets" : 1,
                    "numoutlets" : 2,
                    "fontsize" : 12.0,
                    "outlettype" : [ "float", "bang" ]
                }

            }
,             {
                "box" :                 {
                    "maxclass" : "scope~",
                    "patching_rect" : [ 388.0, 343.0, 130.0, 130.0 ],
                    "id" : "obj-93",
                    "numinlets" : 2,
                    "bufsize" : 98,
                    "numoutlets" : 0,
                    "calccount" : 7
                }

            }
,             {
                "box" :                 {
                    "maxclass" : "ezdac~",
                    "patching_rect" : [ 281.0, 414.0, 45.0, 45.0 ],
                    "id" : "obj-92",
                    "numinlets" : 2,
                    "numoutlets" : 0
                }

            }
,             {
                "box" :                 {
                    "maxclass" : "gain~",
                    "patching_rect" : [ 281.0, 325.0, 39.0, 63.0 ],
                    "id" : "obj-91",
                    "numinlets" : 2,
                    "numoutlets" : 2,
                    "outlettype" : [ "signal", "int" ]
                }

            }
,             {
                "box" :                 {
                    "maxclass" : "newobj",
                    "text" : "*~",
                    "patching_rect" : [ 562.0, 229.0, 32.5, 20.0 ],
                    "id" : "obj-83",
                    "fontname" : "Arial",
                    "numinlets" : 2,
                    "numoutlets" : 1,
                    "fontsize" : 12.0,
                    "outlettype" : [ "signal" ]
                }

            }
,             {
                "box" :                 {
                    "maxclass" : "flonum",
                    "patching_rect" : [ 576.0, 196.0, 50.0, 20.0 ],
                    "id" : "obj-84",
                    "fontname" : "Arial",
                    "numinlets" : 1,
                    "numoutlets" : 2,
                    "fontsize" : 12.0,
                    "outlettype" : [ "float", "bang" ]
                }

            }
,             {
                "box" :                 {
                    "maxclass" : "flonum",
                    "patching_rect" : [ 577.0, 132.0, 50.0, 20.0 ],
                    "id" : "obj-85",
                    "fontname" : "Arial",
                    "numinlets" : 1,
                    "numoutlets" : 2,
                    "fontsize" : 12.0,
                    "outlettype" : [ "float", "bang" ]
                }

            }
,             {
                "box" :                 {
                    "maxclass" : "newobj",
                    "text" : "cycle~",
                    "patching_rect" : [ 577.0, 159.0, 45.0, 20.0 ],
                    "id" : "obj-86",
                    "fontname" : "Arial",
                    "numinlets" : 2,
                    "numoutlets" : 1,
                    "fontsize" : 12.0,
                    "outlettype" : [ "signal" ]
                }

            }
,             {
                "box" :                 {
                    "maxclass" : "newobj",
                    "text" : "*~",
                    "patching_rect" : [ 503.0, 228.0, 32.5, 20.0 ],
                    "id" : "obj-87",
                    "fontname" : "Arial",
                    "numinlets" : 2,
                    "numoutlets" : 1,
                    "fontsize" : 12.0,
                    "outlettype" : [ "signal" ]
                }

            }
,             {
                "box" :                 {
                    "maxclass" : "flonum",
                    "patching_rect" : [ 517.0, 195.0, 50.0, 20.0 ],
                    "id" : "obj-88",
                    "fontname" : "Arial",
                    "numinlets" : 1,
                    "numoutlets" : 2,
                    "fontsize" : 12.0,
                    "outlettype" : [ "float", "bang" ]
                }

            }
,             {
                "box" :                 {
                    "maxclass" : "flonum",
                    "patching_rect" : [ 518.0, 131.0, 50.0, 20.0 ],
                    "id" : "obj-89",
                    "fontname" : "Arial",
                    "numinlets" : 1,
                    "numoutlets" : 2,
                    "fontsize" : 12.0,
                    "outlettype" : [ "float", "bang" ]
                }

            }
,             {
                "box" :                 {
                    "maxclass" : "newobj",
                    "text" : "cycle~",
                    "patching_rect" : [ 518.0, 158.0, 45.0, 20.0 ],
                    "id" : "obj-90",
                    "fontname" : "Arial",
                    "numinlets" : 2,
                    "numoutlets" : 1,
                    "fontsize" : 12.0,
                    "outlettype" : [ "signal" ]
                }

            }
,             {
                "box" :                 {
                    "maxclass" : "newobj",
                    "text" : "*~",
                    "patching_rect" : [ 444.0, 227.0, 32.5, 20.0 ],
                    "id" : "obj-67",
                    "fontname" : "Arial",
                    "numinlets" : 2,
                    "numoutlets" : 1,
                    "fontsize" : 12.0,
                    "outlettype" : [ "signal" ]
                }

            }
,             {
                "box" :                 {
                    "maxclass" : "flonum",
                    "patching_rect" : [ 458.0, 194.0, 50.0, 20.0 ],
                    "id" : "obj-68",
                    "fontname" : "Arial",
                    "numinlets" : 1,
                    "numoutlets" : 2,
                    "fontsize" : 12.0,
                    "outlettype" : [ "float", "bang" ]
                }

            }
,             {
                "box" :                 {
                    "maxclass" : "flonum",
                    "patching_rect" : [ 459.0, 130.0, 50.0, 20.0 ],
                    "id" : "obj-69",
                    "fontname" : "Arial",
                    "numinlets" : 1,
                    "numoutlets" : 2,
                    "fontsize" : 12.0,
                    "outlettype" : [ "float", "bang" ]
                }

            }
,             {
                "box" :                 {
                    "maxclass" : "newobj",
                    "text" : "cycle~",
                    "patching_rect" : [ 459.0, 157.0, 45.0, 20.0 ],
                    "id" : "obj-70",
                    "fontname" : "Arial",
                    "numinlets" : 2,
                    "numoutlets" : 1,
                    "fontsize" : 12.0,
                    "outlettype" : [ "signal" ]
                }

            }
,             {
                "box" :                 {
                    "maxclass" : "newobj",
                    "text" : "*~",
                    "patching_rect" : [ 385.0, 226.0, 32.5, 20.0 ],
                    "id" : "obj-71",
                    "fontname" : "Arial",
                    "numinlets" : 2,
                    "numoutlets" : 1,
                    "fontsize" : 12.0,
                    "outlettype" : [ "signal" ]
                }

            }
,             {
                "box" :                 {
                    "maxclass" : "flonum",
                    "patching_rect" : [ 399.0, 193.0, 50.0, 20.0 ],
                    "id" : "obj-72",
                    "fontname" : "Arial",
                    "numinlets" : 1,
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additive-synthesis-puzzle

also, why changing decimals in the master frequency, changes waveform????

some waveshapes are made by summing cosines, and some are made by summing sines. Note: the waveforms will sound the same if you use either, but may not look like the traditional shape.

I don't know much about audio, but I assume it's because a function of sin() has it's extremes at 0.25, 0.75, 1.25 etc, and all the peaks need to be aligned, not the zeroes for them to add up correctly?

Also, would you please use the 'copy compressed' option from the file menu to post patches here?

@ oli larkin yes I know, as a matter of fact you can see negative values also in partial amplification... the problem was that I don't understand why ALL cycles~ need a 0.25 shift plus their own phase... I think that Bas van der Graaff is right.

@Bas van der Graaff sorry for the copy compressed thing, the forum has changed layout and it's kind of new for me..

@ oli larkin yes I know, as a matter of fact you can see negative values also in partial amplification... the problem was that I don't understand why ALL cycles~ need a 0.25 shift plus their own phase... I think that Bas van der Graaff is right. 

@Bas van der Graaff sorry for the copy compressed thing, the forum has changed layout and it's kind of new for me..


well, check where cycle starts to play and you will see. :)

The cycle~ object is an interpolating oscillator ... 

Its default waveform is one cycle of a *cosine* wave.

The cycle~ object is an interpolating oscillator ... 
Its default waveform is one cycle of a *cosine* wave.


Hmmm, so my idea makes no sense then. Anyone with a better explanation?

ok, so running a cycle~ with phase 0-1 produces a cosine.

adding 0.25 to the phase sort of fixes the way the waveshapes lookg, because at least you make the component cycles~ start at amplitude 0. they do go into the negative part of the sine waveform first, so to get it completely right you need to offset the phases such that they start at phase 0.75.

additive synthesis puzzle