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

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#The prime limit of each comma must be higher than the one before.

#The color name must indicate strong vs. weak extensions, if possible.

#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 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. ~~Likewise~~, ~~Liese~~ is ~~Gu & Trizogu~~ (81/80 & 1029/1000), ~~not~~ Gu & Trizo-aquadgu ~~(81/80 & 686/675),~~ because ~~the latter would imply~~ a strong extension of Gu, whereas Liese is a weak extension.

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.

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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''z6g4 = tribizo-aquadgu* = biatrizo-agugu? ''

''z6gg = tribizo-agugu* = biatrizo-agu? ''

''z6g8 = tribizo-aquadbigu* = biatrizo-aquadgu?

''z6g8 = tribizo-aquadbigu* = biatrizo-aquadgu? ''

z8g6 = quadbizo-atribigu* = biaquadzo-atrigu?

z8gg = quadbizo-agugu* = biaquadzo-agu?

z9g6 = tritrizo-atribigu* = triatrizo-agugu?

z9g3 = tritrizo-atrigu* = triatrizo-agu?''

z9g3 = tritrizo-atrigu* = triatrizo-agu?

=== Tricolored examples ===

@@ Line 47: / Line 47: @@
 #The prime limit of each comma must be higher than the one before.
 #The color name must indicate strong vs. weak extensions, if possible.
+#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 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. Likewise, Liese is Gu & Trizogu (81/80 & 1029/1000), not Gu & Trizo-aquadgu (81/80 & 686/675), because the latter would imply a strong extension of Gu, whereas Liese is a weak extension.
+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.
+.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 213: / Line 216: @@
 ''z<sup>6</sup>g<sup>4</sup> = tribizo-aquadgu* = biatrizo-agugu?<br />''
 ''z<sup>6</sup>gg = tribizo-agugu* = biatrizo-agu?<br />''
-''z<sup>6</sup>g<sup>8</sup> = tribizo-aquadbigu* = biatrizo-aquadgu?<br />
+''z<sup>6</sup>g<sup>8</sup> = tribizo-aquadbigu* = biatrizo-aquadgu?<br />''
 z<sup>8</sup>g<sup>6</sup> = quadbizo-atribigu* = biaquadzo-atrigu?<br />
 z<sup>8</sup>gg = quadbizo-agugu* = biaquadzo-agu?<br />
 z<sup>9</sup>g<sup>6</sup> = tritrizo-atribigu* = triatrizo-agugu?<br />
-z<sup>9</sup>g<sup>3</sup> = tritrizo-atrigu* = triatrizo-agu?''
+z<sup>9</sup>g<sup>3</sup> = tritrizo-atrigu* = triatrizo-agu?
 === Tricolored examples ===