The following is intended to help you understand the basics of Lady Gouldian finch genetics for body color.
All gouldians produce and deposit yellow pigment and eumelanin (a blue structural color) in their feathers. When the yellow pigment and eumelanin combine, it produces the green body color. (Yellow + Blue = Green) Concentrations of eumelanin produce the blue and black colored feathers, whereas, concentrations of yellow pigment produce the yellow on the belly, red on the head, etc. Gouldians that produce/deposit the yellow pigment and eumelanin normally are called "Normal" goulds.
In addition to this, there exists a gene that we shall call the "pastel" gene since that is what it was originally named. This pastel gene prevents a gouldian from producing/depositing eumelanin. When the bird cannot produce/deposit eumelanin -- the blue structural color -- what you see is the yellow pigment that is still being produced/deposited in the feathers. (Green - blue = yellow) The pastel gene is a co-dominant sex-linked gene. This means the pastel gene is located on the chromosome that determines the sex of the offspring. If a male gouldian has one pastel gene, he can produce female offspring that have the pastel gene (Yellow hens) as well as female offspring that do not have the gene (Normal hens). If a male gouldian has inherited two pastel genes, he can only produce female offspring that also have the pastel gene. If a female gouldian has the pastel gene (a Yellow hen), she will pass that gene to all of her male offspring. If a female gouldian does not have the pastel gene (a Normal hen), she does not have the gene to pass to her male offspring.
If a male gouldian has inherited one "pastel" gene, he is called a "dilute", a "SF Pastel", or a "SF Yellow." For this discussion, we shall use the term "SF Yellow." In a male gouldian, one "pastel" gene is only able to partially suppress the production and deposition of eumelanin. So, a SF Yellow male gouldian with a purple breast has a visually light green body color and the black bib and ring around the face mask are blue in color. A SF Yellow male with a white or lilac breast is visually yellow in body color and the bib and ring around the face mask are a lighter blue in color. This is due to how the breast gene influences the one "pastel" gene in male gouldians that have inherited only one pastel gene. Also, a SF Yellow male that has inherited a black head color will have a visually lighter black head color -- like charcoal. This is because the one "pastel" gene is partially suppressing the production/deposition of eumelanin in the head.
If a male gouldian has inherited two "pastel" genes, he is called a "Yellow", a "DF Pastel", or a "DF Yellow." For this discussion, we shall use the term "DF Yellow." The two "pastel" genes fully prevent the bird from producing and depositing eumelanin in the feathers, so the bird has a yellow body color and the bib and ring around the face mask are white in color. It does not matter if a DF Yellow has a purple, white, or lilac breast, he will always be visually yellow in color. However, a DF Yellow that has inherited a black head color, will have a visually white or off-white head color. This is because the bird is unable to produce/deposit the eumelanin in the head feathers to create the black color.
Note: if a female gouldian has inherited one "pastel" gene, she is called a "Yellow." Since hens only have one gene that dictates body color, the one "pastel" gene is able to fully suppress the production and deposition of eumelanin, so the hen is visually yellow in body color. And, like a DF Yellow male, a Yellow hen can have any breast color and still be visually yellow in body color. Furthermore, a Yellow hen with a black head, will have a visually white or off-white head color like a DF Yellow male.
When genes are mutated, they don't function properly. This is the basis of the blue body mutation. Unlike the inheritance of a specific gene (or set of genes) that creates the yellow body, the blue body mutation is caused by a mutation of both of the alleles on the genes that are responsible for producing and depositing yellow pigment in the feathers. When both of these alleles are mutated, the gouldian cannot produce/deposit yellow pigmentation, and what you see is the eumelanin that is still being produced/deposited in the feathers. (Green - yellow = blue) The mutation of the alleles that creates the blue body is a autosomal recessive trait. This means that both male and female gouldians can pass the mutated allele(s) to either sex of their offspring.
If a gouldian has inherited one mutated allele, it is said to be "split to blue." The one mutated allele is not able to suppress the production/deposition of yellow pigmentation, so there is no visual change to the bird's color (in either sex). If a gouldian has inherited two mutated alleles, it is called a "blue" body mutation. Both mutated alleles are able to fully suppress the production/deposition of yellow pigment, which changes the bird's body color. For example, if a "normal" gouldian inherits one mutated allele, the one allele is not able to suppress the production/deposition of yellow pigment, so the bird's body color remains "normal" (green). However, if a "normal" gouldian inherits two mutated alleles, those alleles prevent the birds from producing/depositing yellow pigment in the feathers, which results in a bird that visually has a blue body.
Combining the "pastel" gene with the blue body mutation ......
"Dilute-blue"/"SF Pastel-blue"/"SF Yellow-blue" -- If a male gouldian has one "pastel" gene and one mutated allele for the blue body, he is called a "dilute split to blue" (dilute-blue), a "SF Pastel split to blue" (SF Pastel-blue), or a "SF Yellow split to blue" (SF Yellow-blue). The one "pastel" gene partially suppresses the production/deposition of eumelanin and the one mutated allele partially suppresses the production/deposition of yellow pigment. So, a "dilute-blue"/"SF Pastel-blue"/"SF Yellow-blue" with a purple breast has a visually light green body color and a blue bib and ring around the face mask. A "dilute-blue"/"SF Pastel-blue"/"SF Yellow-blue" with a white or lilac breast is visually yellow in body color and the bib and ring around the face mask are a lighter blue in color. The one mutated allele has no effect on the visual color of the bird.
"Yellow-blue"/"DF Pastel-blue"/"DF Yellow-blue" -- If a male gouldian has two "pastel" genes and one mutated allele, he is called a "Yellow split to blue" (Yellow-blue), a "DF Pastel split to blue" (DF Pastel-blue), or a "DF Yellow-blue" (DF Yellow-blue). The two pastel genes fully prevent the bird from producing and depositing eumelanin in the feathers and the one mutated allele partially suppresses the production/deposition of yellow pigment. So, a "Yellow-blue"/"DF Pastel-blue"/"DF Yellow-blue" has a yellow body color regardless of breast color and the bib and ring around the face mask are white in color. Again, the one mutated allele has no effect on the visual color of the bird.
"Pastel"/"Blue SF Pastel"/"Blue SF Yellow" -- If a male gouldian has one "pastel" gene and two mutated alleles, he is called a "Pastel" or "Blue SF Yellow" in the US and a "Blue SF Pastel" in other parts of the world. The one "pastel" gene partially suppresses the production/deposition of eumelanin and the two mutated alleles fully suppress the production/deposition of yellow pigment. So, a "Pastel"/"Blue SF Pastel"/"Blue SF Yellow" with a purple breast has a visually light blue body color (like faded or stone washed denin) and a blue bib and ring around the face mask.
A "Pastel"/"Blue SF Pastel"/"Blue SF Yellow" with a white or lilac breast is visually white in body color and the bib and ring around the face mask are a lighter blue in color. This is due to how the breast gene influences the one "pastel" gene. These male gouldians are sometimes referred to as "silvers" since they have a white body color. However, there is still some debate as to whether or not a "Pastel"/"Blue SF Pastel"/"Blue SF Yellow" with a white or lilac breast should be referred to as a "silver."
"Silver"/"Blue DF Pastel"/"Blue DF Yellow" -- If a male gouldian has two "pastel" genes and two mutated alleles, he is called a "Silver" or a "Blue DF Yellow" in the US and a "Blue DF Pastel" in other parts of the world. The two "pastel" genes fully suppress the production/deposition of eumelanin and the two mutated alleles fully suppress the production/deposition of yellow pigment. As a result, no color is produced and deposited in the feathers, so the "Silver"/"Blue DF Pastel"/"Blue DF Yellow" has a white body and the bib and ring around the face mask are white -- regardless of breast color.
Note: if a "Yellow"/"SF Pastel" gouldian hen has one mutated allele, she is called a "Yellow split to blue" (Yellow-blue) or a "SF Pastel split to blue" (SF Pastel-blue). Since hens only have one gene that dictates body color, the one "pastel" gene fully suppresses the production/deposition of eumelanin, so the hen is visually yellow in body color. As with male gouldians, the one mutated allele has no effect on the visual color of the hen. And, like a DF Yellow male, a Yellow hen can have any breast color and still be visually yellow in body color.
If a Yellow gouldian hen has two mutated alleles, she is called a "Silver" or a "Blue SF Pastel." The one "pastel" gene fully suppresses the production/deposition of eumelanin and the two mutated alleles fully suppress the production/deposition of yellow pigmentation. As a result, no color is produced and deposited in the feathers, so the "Silver"/"Blue SF Pastel" hen has a white body -- regardless of breast color.