How do the customized world settings work?

In Minecraft 1.8 (snapshot 14w17a) and later, there is a new Customized world type. It is based on Wedge, but the settings are different. How do they work?

There are four pages of settings. The first is basic settings, next comes ore settings, and the last two pages are advanced settings. Page 3 changes the advanced settings with sliders, and page 4 changes the same settings with textboxes.

Page 1: Basic Settings

• Sea Level changes sea level. It ranges between 1 and 255, and has a default value of 63.
• Caves changes whether or not caves appear. It defaults to Yes.
• Strongholds changes whether or not Strongholds appear. It defaults to Yes.
• Villages changes whether or not villages appear. It defaults to Yes.
• Mineshafts changes whether or not Abandoned Mineshafts appear. It defaults to Yes.
• Temples changes whether or not Desert Temples appear. It defaults to Yes.
• Ravines changes whether or not ravines appear. It defaults to Yes.
• Dungeons changes whether or not dungeons appear. It defaults to Yes.
• Dungeon Count is how many times per chunk a dungeon attempts to be placed (I think). It ranges between 1 and 100, and has a default value of 7.
• Water Lakes changes whether or not ponds appear. It defaults to Yes.
• Water Lake Rarity is how rare ponds are; a higher number equals more rarity. It ranges between 1 and 100, and has a default value of 4.
• Lava Lakes changes whether or not lava lakes appear. It defaults to Yes.
• Lava Lake Rarity is how rare lava lakes are; a higher number equals more rarity. It ranges between 1 and 100, and has a default value of 80.
• Lava Oceans changes whether or not oceans are made of lava. It defaults to No.
• Biome changes what biomes appear. The possible values are All, Ocean, Plains, Desert, Extreme Hills, Forest, Taiga, Swampland, River, FrozenOcean, FrozenRiver, Ice Plains, Ice Mountains, MushroomIsland, MushroomIslandShore, Beach, DesertHills, ForestHills, TaigaHills, Extreme Hills Edge, Jungle, JungleHills, JungleEdge, Deep Ocean, Stone Beach, Cold Beach, Birch Forest, Birch Forest Hills, Roofed Forest, Cold Taiga, Cold Taiga Hills, Mega Taiga, Mega Taiga Hills, Extreme Hills+, Savanna, Savanna Plateau, Mesa, Mesa Plateau F, and Mesa Plateau. It defaults to All
• Biome Size changes the size of biomes. It ranges between 1 and 8, and defaults to 4.
• River Size changes the size of rivers. It ranges between 1 and 5, and defaults to 4.

Page 2: Ore Settings

Each of the eleven sections of this page changes the settings for each type of "ore".

• Spawn Size is the maximum number of blocks in a single vein.
• Spawn Tries is the number of times the world generator attempts to place a vein in a chunk. Each time, it picks a completely random spot. If the spot is a valid location for a vein, it will place the vein. If it is not a valid location, it doesn't place the vein.
• Min Height is the minimum height at which the ore spawns.
• Max Height is the maximum height at which the ore spawns.

Page 3: Advanced settings (sliders)

• Main Noise Scale X stretches the terrain along the x-axis, consequently making the terrain more smooth. Larger values for smoother terrain.
• Main Noise Scale Y stretches the terrain along the y (height) axis. Larger values for smoother, higher and more hilly terrain. Ranges from 1 to 5000, and defaults to 160.
• Main Noise Scale Z stretches the terrain along the z-axis, consequently making the terrain more smooth. Larger values for smoother terrain. Ranges from 1 to 5000, and defaults to 80.
• Depth Noise Scale X changes the abruptness of terrain height along the x axis. It ranges from 1 to 2000, and defaults to 200.
• Depth Noise Scale Z changes the abruptness of terrain height along the z axis. It ranges from 1 to 2000, and defaults to 200.
• Depth Noise Exponent ranges from 0.01 to 20, and defaults to 0.5. Not quite sure what it does.
• Depth Base Size changes the base height of land. It ranges from 1 to 25, and defaults to 8.5. 1 in this value corresponds to 8 blocks, so the default is 8.5 * 8, which is 68.
• Coordinate Scale: Larger values sharpen and create more frequent hills without stretching the biome. It is best used last to tweak the terrain. Ranges from 1 to 6000, and defaults to 684.412.
• Height Scale stretches the base hills vertically before more details are made. It ranges from 1 to 6000, and defaults to 684.412.
• Height Stretch pulls terrain upward, with smaller values causing more extreme stretching. Ranges from 0.01 to 50, and defaults to 12.
• Upper Limit Scale makes terrain more solid/riddled with holes depending on how close the values are to the lower limit scale values. Ranges from 1 to 5000, and defaults to 512.
• Lower Limit Scale makes terrain more solid or riddled with holes depending on how close the values are to the upper limit scale values. Ranges from 1 to 5000, and defaults to 512.
• Biome Depth Weight stretches terrain vertically. All biomes have a number that is added to or subtracted from the Depth Base Size. That number is then multiplied by this field. Ranges from 1 to 20, and defaults to 1.
• Biome Depth Offset offsets the default terrain level by a specified amount proportional to a power of this field. Ranges from 0 to 20, and defaults to 0.
• Biome Scale Weight changes how much a biome's settings alter the terrain. Ranges from 1 to 20, and defaults to 1.
• Biome Scale Offset stretches/squash terrain vertically based on the biomes default height settings. Ranges from 0 to 20, and defaults to 0. Not quite sure what it does.

Page 4: Advanced settings (text boxes)

This page is the same as the previous one, but you can change the values by typing.

Here is a video that demonstrates some of the controls: