Kite's color notation/Temperament names: Difference between revisions

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#The color name must indicate the best downward extension.

#Double odd limit must be minimized.

The first rule completely determines the first comma, except for the edo problem (see below).

The first rule completely determines the first comma, except for the edo problem (see issues below).

The name of a comma indicates the amount of splitting in the pergen: Zozo splits something in half, Triyo something into 3 parts, Ruyoyo ~~splits~~ nothing, etc. ~~More importantly~~, ~~the name~~ can ~~differentiate between strong extensions and weak extensions~~. ~~Gugu~~ = ~~27/25, and Zozo = 49/48, and each one is~~ (P8~~, P4~~/2~~). Combining both commas~~, ~~Gugu & Zozo is a bad name, because it looks like a weak extension of Gugu (and of Zozo~~) ~~when it is actually strong. Instead we call it Gugu & Zogu~~. The ~~Zogu~~ comma is 21/20, so this name also has the advantage of using a lower odd-limit comma. However, often the effect of implying the right kind of extension is to raise the odd limit. For example, Pajara is Sagugu & Ru (2048/2025 & 64/63), not Sagugu & Biruyo, even though the ~~Biruyo comma 50/49 is a lower odd limit~~.

The color name of a comma indicates the amount of splitting in the pergen: Zozo splits something in half, Triyo something into 3 parts, Ru and Ruyoyo split nothing, etc. Some double-splits are false doubles, which means a quad- comma can make an 8-fold split, e.g. Laquadlo = (P8/2, M2/4). The comma splits the 8ve "by accident".

2.3.7 Liese is called Latriru, after its comma |-9 11 0 -3>. Its pergen is (P8, P11/4). The best downward extension of Latriru, also called Liese, has commas 81/80, 686/675 (z3gg) and 1029/1000 (z3g3), all lower odd limit than the Latrilu comma. Gu & Trizo-aquadgu isn't a good name because it implies a strong extension of Gu, whereas Liese is a weak extension. Gu & Trizogu isn't a good name because it doesn't indicate that it's the best downward extension of Latriru.Thus yaza Liese is called Gu & Latriru.

More importantly, the name can differentiate between strong extensions and weak extensions. Gugu = 27/25, and Zozo = 49/48, and each one is (P8, P4/2). Combining both commas, Gugu & Zozo is a bad name, because it looks like a weak extension of Gugu (and of Zozo) when it is actually strong. Instead we call it Gugu & Zogu. The Zogu comma is 21/20, so this name also has the advantage of using a lower odd-limit comma. However, often the effect of implying the right kind of extension is to raise the odd limit. For example, Pajara is Sagugu & Ru (2048/2025 & 64/63), not Sagugu & Biruyo, even though the Biruyo comma 50/49 is a lower odd limit.

2.3.7 Liese is called Latriru, after its comma |-9 11 0 -3>. Its pergen is (P8, P11/4). The best downward extension of Latriru, also called Liese, has commas 81/80, 686/675 (z3gg) and 1029/1000 (z3g3), all lower odd limit than the Latrilu comma. Gu & Trizo-aquadgu isn't a good name because it implies a strong extension of Gu, whereas Liese is a weak extension. Gu & Trizogu isn't a good name because it doesn't indicate that it's the best downward extension of Latriru. Thus yaza Liese is called Gu & Latriru.

=== Inheriting temperament names ===

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=== Issues ===

DEFINITION OF BADNESS:

The definition should take into account both error and complexity. There are two main definitions, logflat badness and cangwu badness. The latter has a weighting parameter to be determined. So the definition will inevitably be somewhat arbitrary. The best extension will also not be obvious from merely examining the commas, but will require lengthy computations. This removes one of the main advantages of color names, that the comma set, and hence the mapping, the pergen, etc., can be derived from the name.

The best metric for naming purposes is one that tends to give the same inheritances that have already been agreed on. This hasn't been determined yet.

QUARTER-SPLIT PROBLEM:

@@ Line 49: / Line 49: @@
 #The color name must indicate the best downward extension.
 #Double odd limit must be minimized.
-The first rule completely determines the first comma, except for the edo problem (see below).
+The first rule completely determines the first comma, except for the edo problem (see issues below).
-The name of a comma indicates the amount of splitting in the pergen: Zozo splits something in half, Triyo something into 3 parts, Ruyoyo splits nothing, etc. More importantly, the name can differentiate between strong extensions and weak extensions. Gugu = 27/25, and Zozo = 49/48, and each one is (P8, P4/2). Combining both commas, Gugu & Zozo is a bad name, because it looks like a weak extension of Gugu (and of Zozo) when it is actually strong. Instead we call it Gugu & Zogu. The Zogu comma is 21/20, so this name also has the advantage of using a lower odd-limit comma. However, often the effect of implying the right kind of extension is to raise the odd limit. For example, Pajara is Sagugu & Ru (2048/2025 & 64/63), not Sagugu & Biruyo, even though the Biruyo comma 50/49 is a lower odd limit.
+The color name of a comma indicates the amount of splitting in the pergen: Zozo splits something in half, Triyo something into 3 parts, Ru and Ruyoyo split nothing, etc. Some double-splits are false doubles, which means a quad- comma can make an 8-fold split, e.g. Laquadlo = (P8/2, M2/4). The comma splits the 8ve "by accident".
-.3.7 Liese is called Latriru, after its comma |-9 11 0 -3>. Its pergen is (P8, P11/4). The best downward extension of Latriru, also called Liese, has commas 81/80, 686/675 (z<sup>3</sup>gg) and 1029/1000 (z<sup>3</sup>g<sup>3</sup>), all lower odd limit than the Latrilu comma.  Gu & Trizo-aquadgu isn't a good name because it implies a strong extension of Gu, whereas Liese is a weak extension. Gu & Trizogu isn't a good name because it doesn't indicate that it's the best downward extension of Latriru.Thus yaza Liese is called Gu & Latriru.
+More importantly, the name can differentiate between strong extensions and weak extensions. Gugu = 27/25, and Zozo = 49/48, and each one is (P8, P4/2). Combining both commas, Gugu & Zozo is a bad name, because it looks like a weak extension of Gugu (and of Zozo) when it is actually strong. Instead we call it Gugu & Zogu. The Zogu comma is 21/20, so this name also has the advantage of using a lower odd-limit comma. However, often the effect of implying the right kind of extension is to raise the odd limit. For example, Pajara is Sagugu & Ru (2048/2025 & 64/63), not Sagugu & Biruyo, even though the Biruyo comma 50/49 is a lower odd limit.
+.3.7 Liese is called Latriru, after its comma |-9 11 0 -3>. Its pergen is (P8, P11/4). The best downward extension of Latriru, also called Liese, has commas 81/80, 686/675 (z<sup>3</sup>gg) and 1029/1000 (z<sup>3</sup>g<sup>3</sup>), all lower odd limit than the Latrilu comma.  Gu & Trizo-aquadgu isn't a good name because it implies a strong extension of Gu, whereas Liese is a weak extension. Gu & Trizogu isn't a good name because it doesn't indicate that it's the best downward extension of Latriru. Thus yaza Liese is called Gu & Latriru.
 === Inheriting temperament names ===
@@ Line 67: / Line 69: @@
 === Issues ===
+DEFINITION OF BADNESS:
+The definition should take into account both error and complexity. There are two main definitions, logflat badness and cangwu badness. The latter has a weighting parameter to be determined. So the definition will inevitably be somewhat arbitrary. The best extension will also not be obvious from merely examining the commas, but will require lengthy computations. This removes one of the main advantages of color names, that the comma set, and hence the mapping, the pergen, etc., can be derived from the name.
+The best metric for naming purposes is one that tends to give the same inheritances that have already been agreed on. This hasn't been determined yet.
 QUARTER-SPLIT PROBLEM: