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

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-Color notation can name every regular temperament. The name is based on the comma(s) tempered out. The magnitude is part of the name: [[Schismatic]] is LyT and [[Diaschismic]] is sggT. The degree is too, but only if the comma is not the smallest of the 7 ratios in that '''row segment''' (i.e. of that magnitude and color): [[Mavila]] is Ly1T and [[Father family|Father]] is g2T. The degree is never needed if the comma is ≤ 90¢. The degree is also unneeded if the smaller ratio is a multiple of a simpler comma. For example, the smallest ratio in the central segment of the zozogugu row is 441/440. But since this is (21/20)<sup>2</sup>, tempering it out would simply result in zgT. Thus zzggT refers to tempering out the next largest ratio, 784/675 = 259¢.
+Color notation can name every regular temperament. The name is the same as that of the comma(s) tempered out, but without the degree (unison, 2nd, etc.). The color defines a lattice row and the magnitude (large, small, etc.) defines a '''segment''' of that row. Each segment contains 7 ratios. The comma that is tempered out is assumed to be the smallest in cents of those 7, excluding any ratio that is a multiple of another comma. For example, the smallest ratio in the central segment of the zozogugu row is 441/440. But since this is (21/20)<sup>2</sup>, tempering it out would simply result in zgT. Thus zzggT refers to tempering out the next largest ratio, 784/675 = 259¢.
-[''<u>Idea to consider</u>: the Wesley comma (-13,-2,7) has the awkward name of lasepyo-negative-two. Should there be a word for the 2nd biggest ratio in the segment? The degree doesn't matter much, and is tedious to calculate.'']
+If the comma is the 2nd largest valid ratio in the row segment, the temperament name ends with "2". For example, [[Schismatic]] is LyT and [[Mavila]] is LyT2. Likewise, LyT3 would temper out the 3rd largest ratio. Any comma ≤ 90¢ is guaranteed to be the smallest ratio in its segment.
-Words like large, small, double, etc. are abbreviated to make the names a reasonable length.
+Words like large, small, double, etc. are abbreviated, to make the names a reasonable length.
-* Double = '''bi-''' ("bee"), triple = '''tri-''' ("tree"), quadruple = '''quad-''', quintuple = '''quin-'''
+* Double = '''bi-''' ("bee"), triple = '''tri-''' ("tree"), quadruple = '''quad-''', quintuple = '''quin-''', septuple = '''sep-'''
-* 6-fold = tribi-, 7-fold = '''sep-''', 8-fold = quabi-, 9-fold = tritri-, 10-fold = quinbi-
-* 12-fold = quadtri-, 14-fold = sepbi-, 15-fold = quintri-, 16-fold = quadquad-, etc.
 * Large = '''la-''', small = '''sa-''', double large = lala-, triple small = trisa-, etc.
-Higher primes use their color word, but with the suffix '''-e''' for exponent: 11-fold = '''le-''' ("leh"), 13-fold = '''the-''' (unvoiced "th"). 17 = '''se-''', 19 = '''ne-''', 23 = '''twenty-the-''', etc.
+Some 5-limit examples, sorted by color depth. Many more examples can be found on the [[Comma|Commas]] page.
+# [[Schismatic]] = Layo = LyT, [[Mavila]] = Layo-two = LyT2, [[Superpyth]] = Sayo = syT. [[Meantone]] = Gu = gT, [[Father]] = Gu-two = gT2.
-Even with these abbreviations, temperament names can get quite long. To make them quicker to say, "bee" and "tree" are preferred over "bye" and "try", and quadbi- is shortened to '''quabi-'''. If the comma's ratio has N digits, the temperament name will usually have N, N-1, N+1 or occasionally N+2 syllables.
+# [[Dicot]] = Yoyo = yyT, [[Immunity family|Immunity]] = Sasayoyo = ssyyT.  [[Bug]] = Gugu = ggT, [[Diaschismic]] = Sagugu = sggT, [[Beatles]] = Sasagugu = ssggT.
+# [[Porcupine]] = Triyo = y<sup>3</sup>T. [[Augmented]] = Trigu = g<sup>3</sup>T, [[Laconic family|Laconic]] = Latrigu = Lg<sup>3</sup>T, [[Misty comma|Misty]] = Sasatrigu = ssg<sup>3</sup>T.
+# [[Negri]] = Laquadyo = Ly<sup>4</sup>T, [[Tetracot]] = Saquadyo = sy<sup>4</sup>T, [[Vulture]] = Sasaquadyo = ssy<sup>4</sup>T. [[Diminished]] = Quadgu = g<sup>4</sup>T.
+Multipliers like bi-, tri-, etc. can be combined: 6-fold = tribi-, 8-fold = quadbi-, 9-fold = tritri-, 10-fold = quinbi-, 12-fold = quadtri-, 14-fold = sepbi-, 15-fold = quintri-, 16-fold = quadquad-, etc. Higher primes use their color word, but with the suffix '''-e''' for exponent:
+* 11-fold = '''le-''' ("leh"), 13-fold = '''the-''' (unvoiced "th"). 17 = '''se-''', 19 = '''ne-''', 23 = '''twenty-the-''', 29 = '''twenty-ne-''', etc.
+Even with these abbreviations, temperament names can get quite long. To make them quicker to say, "bee" and "tree" are preferred over "bye" and "try". If the comma's ratio has N digits, the temperament name will usually have N, N-1, N+1 or occasionally N+2 syllables.
 La also means 11-all. The meaning will almost always be clear from context, however "this piece uses la notes" is ambiguous. To clarify, one should say either "large notes" (fifthward notes) or "ila notes" (11-limit notes). Likewise, sa also means 17-all, and "sa notes" should become either "small notes" or "isa notes".
 La is also the La note in solfege, and Sa is the tonic in saregam. The meaning will always be clear from context. Notes are never large or small. In fixed-do countries, the chord ALw (81/64 3rd) is "La lawa".
-Common examples: Porcupine = Triyo, Pajara = Sagugu, Augmented = Trigu, Diminished = Quadgu, Helmholtz = Layo. Many more examples can be found on the [[Comma|Commas]] page.
 There are two obvious ways to name multi-comma temperaments. The odd name minimizes the [[Odd limit|double odd limit]] of the comma set, and the prime name minimizes the number and size of the primes used by each comma. The odd name for 7-limit [[Pajara]] is rryy&rT, and the prime name is sgg&rT. Often the two names are identical, e.g. y<sup>3</sup>&rT. The odd name is often shorter, and usually indicates commas more likely to be pumped. The prime name shows relationships between bicolored rank-2 temperaments better. The question of which name to use is not yet fully resolved.
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 * Multiplier syllables fuse into one multiplier word: tribizogu = (tribi) x (zogu) = z<sup>6</sup>g<sup>6</sup>, not (tri) x (bizogu) = z<sup>6</sup>g<sup>3</sup>.
 * Avoid using the -a- delimiter if possible: z<sup>4</sup>gg = bizozogu, not quadzoagugu
-Therefore if the name starts with a multiplier word, and there's no -a- delimiter, that first multiplier word indicates the GCD and thus the pergen's split(s). e.g. bizozogu = (P8, P5/2, /1). (In the following list, an asterisk marks cases where this isn't possible, and the GCD is hidden.)
+Therefore if the name starts with a multiplier word, and there's no -a- delimiter, that first multiplier word indicates the color GCD and thus the pergen's split(s). e.g. bizozogu = (P8, P5/2, /1). In the following list, an asterisk marks cases where this isn't possible, and the GCD is hidden.
-Gugu is generally preferred over bigu (zogugu not zobigu). But bizo is preferred over zozo sometimes to indicate the GCD, e.g. bizogugu not zozoquadgu. Likewise, tribigu is preferred over trigugu, as is quabigu over quadgugu, and quinbigu over quingugu.
+Gugu is generally preferred over bigu (zogugu not zobigu). But bizo is preferred over zozo sometimes to indicate the GCD, e.g. bizogugu not zozoquadgu. Likewise, tribigu is preferred over trigugu, as is quabigu over quadgugu, etc.
 There follows examples of remote colors, for illustration. These examples don't all correspond to musically useful temperaments!
@@ Line 39: / Line 40: @@
 zzg = zozogu
-g = trigu<br />
+g<sup>3</sup> = trigu<br />
-z+3g = zotrigu (Starling)<br />
+zg<sup>3</sup> = zotrigu (Starling)<br />
-zz+3g = zozotrigu<br />
+zzg<sup>3</sup> = zozotrigu<br />
-z+3g = trizogu<br />
+z<sup>3</sup>g<sup>3</sup> = trizogu<br />
-z+gg = trizoagugu<br />
+z<sup>3</sup>gg = trizoagugu<br />
-z+g = trizoagu
+z<sup>3</sup>g = trizoagu
-g = quadgu<br />
+g<sup>4</sup> = quadgu (Diminished)<br />
-z+4g = zoquadgu<br />
+zg<sup>4</sup> = zoquadgu<br />
-z+4g = bizogugu<br />
+zzg<sup>4</sup> = bizogugu<br />
-z+4g = trizoaquadgu<br />
+z<sup>3</sup>g<sup>4</sup> = trizoaquadgu<br />
-z+4g = quadzogu<br />
+z<sup>4</sup>g<sup>4</sup> = quadzogu<br />
-z+3g = quadzoatrigu<br />
+z<sup>4</sup>g<sup>3</sup> = quadzoatrigu<br />
-z+2g = bizozogu (Breedsmic)<br />
+z<sup>4</sup>gg = bizozogu (Breedsmic)<br />
-z+g = quadzoagu
+z<sup>4</sup>g = quadzoagu
-g = quingu<br />
+g<sup>5</sup> = quingu<br />
-z+5g = zoquingu<br />
+zg<sup>5</sup> = zoquingu<br />
-z+5g = zozoquingu<br />
+zzg<sup>5</sup> = zozoquingu<br />
-z+5g = trizoaquingu<br />
+z<sup>3</sup>g<sup>5</sup> = trizoaquingu<br />
-z+5g = quadzoaquingu<br />
+z<sup>4</sup>g<sup>5</sup> = quadzoaquingu<br />
-z+5g = quinzogu<br />
+z<sup>5</sup>g<sup>5</sup> = quinzogu<br />
-z+4g = quinzoaquadgu<br />
+z<sup>5</sup>g<sup>4</sup> = quinzoaquadgu<br />
-z+3g = quinzoatrigu<br />
+z<sup>5</sup>g<sup>3</sup> = quinzoatrigu<br />
-z+2g = quinzoagugu<br />
+z<sup>5</sup>gg = quinzoagugu<br />
-z+g = quinzoagu
+z<sup>5</sup>g = quinzoagu
-g = tribigu<br />
+g<sup>6</sup> = tribigu<br />
-z+6g = zotribigu<br />
+zg<sup>6</sup> = zotribigu<br />
-z+6g = bizotrigu<br />
+zzg<sup>6</sup> = bizotrigu<br />
-z+6g = trizogugu<br />
+z<sup>3</sup>g<sup>6</sup> = trizogugu<br />
-z+6g = bizozotrigu<br />
+z<sup>4</sup>g<sup>6</sup> = bizozotrigu<br />
-z+6g = quinzoatribigu<br />
+z<sup>5</sup>g<sup>6</sup> = quinzoatribigu<br />
-z+6g = tribizogu<br />
+z<sup>6</sup>g<sup>6</sup> = tribizogu<br />
-z+5g = tribizoaquingu<br />
+z<sup>6</sup>g<sup>5</sup> = tribizoaquingu<br />
-z+4g = tribizoaquadgu*<br />
+z<sup>6</sup>g<sup>4</sup> = tribizoaquadgu*<br />
-z+3g = trizozogu<br />
+z<sup>6</sup>g<sup>3</sup> = trizozogu<br />
-z+2g = tribizoagugu*<br />
+z<sup>6</sup>gg = tribizoagugu*<br />
-z+g = tribizoagu
+z<sup>6</sup>g = tribizoagu
-g = sepgu<br />
+g<sup>7</sup> = sepgu<br />
-z+7g = zosepgu<br />
+zg<sup>7</sup> = zosepgu<br />
-z+7g = zozosepgu<br />
+zzg<sup>7</sup> = zozosepgu<br />
-z+7g = trizoasepgu<br />
+z<sup>3</sup>g<sup>7</sup> = trizoasepgu<br />
-z+7g = quadzoasepgu<br />
+z<sup>4</sup>g<sup>7</sup> = quadzoasepgu<br />
-z+7g = quinzoasepgu<br />
+z<sup>5</sup>g<sup>7</sup> = quinzoasepgu<br />
-z+7g = tribizoasepgu<br />
+z<sup>6</sup>g<sup>7</sup> = tribizoasepgu<br />
-z+7g = sepzogu<br />
+z<sup>7</sup>g<sup>7</sup> = sepzogu<br />
-z+6g = sepzoatribigu<br />
+z<sup>7</sup>g<sup>6</sup> = sepzoatribigu<br />
-z+5g = sepzoaquingu<br />
+z<sup>7</sup>g<sup>5</sup> = sepzoaquingu<br />
-z+4g = sepzoaquadgu<br />
+z<sup>7</sup>g<sup>4</sup> = sepzoaquadgu<br />
-z+3g = sepzoatrigu<br />
+z<sup>7</sup>g<sup>3</sup> = sepzoatrigu<br />
-z+2g = sepzoagugu<br />
+z<sup>7</sup>gg = sepzoagugu<br />
-z+g = sepzoagu
+z<sup>7</sup>g = sepzoagu
-g = quabigu<br />
+g<sup>8</sup> = quabigu<br />
-z+8g = zoquabigu<br />
+zg<sup>8</sup> = zoquabigu<br />
-z+8g = bizoquadgu<br />
+zzg<sup>8</sup> = bizoquadgu<br />
-z+8g = trizoaquabigu<br />
+z<sup>3</sup>g<sup>8</sup> = trizoaquabigu<br />
-z+8g = quadzogugu<br />
+z<sup>4</sup>g<sup>8</sup> = quadzogugu<br />
-z+8g = quinzoaquabigu<br />
+z<sup>5</sup>g<sup>8</sup> = quinzoaquabigu<br />
-z+8g = tribizoaquabigu* <br />
+z<sup>6</sup>g<sup>8</sup> = tribizoaquabigu* <br />
-z+8g = sepzoaquabigu<br />
+z<sup>7</sup>g<sup>8</sup> = sepzoaquabigu<br />
-z+8g = quabizogu<br />
+z<sup>8</sup>g<sup>8</sup> = quabizogu<br />
-z+7g = quabizoasepgu<br />
+z<sup>8</sup>g<sup>7</sup> = quabizoasepgu<br />
-z+6g = quabizoatribigu*<br />
+z<sup>8</sup>g<sup>6</sup> = quabizoatribigu*<br />
-z+5g = quabizoaquingu<br />
+z<sup>8</sup>g<sup>5</sup> = quabizoaquingu<br />
-z+4g = quadzozogu<br />
+z<sup>8</sup>g<sup>4</sup> = quadzozogu<br />
-z+3g = quabizoatrigu<br />
+z<sup>8</sup>g<sup>3</sup> = quabizoatrigu<br />
-z+2g = quabizoagugu*<br />
+z<sup>8</sup>gg = quabizoagugu*<br />
-z+g = quabizoagu
+z<sup>8</sup>g = quabizoagu
-g = tritrigu<br />
+g<sup>9</sup> = tritrigu<br />
-z+9g = zotritrigu<br />
+zg<sup>9</sup> = zotritrigu<br />
-z+9g = zozotritrigu<br />
+zzg<sup>9</sup> = zozotritrigu<br />
-z+9g = trizotrigu<br />
+z<sup>3</sup>g<sup>9</sup> = trizotrigu<br />
-z+9g = quadzoatritrigu<br />
+z<sup>4</sup>g<sup>9</sup> = quadzoatritrigu<br />
-z+9g = quinzoatritrigu<br />
+z<sup>5</sup>g<sup>9</sup> = quinzoatritrigu<br />
-z+9g = trizozotrigu<br />
+z<sup>6</sup>g<sup>9</sup> = trizozotrigu<br />
-z+9g = sepzoatritrigu<br />
+z<sup>7</sup>g<sup>9</sup> = sepzoatritrigu<br />
-z+9g = quabizoatritrigu<br />
+z<sup>8</sup>g<sup>9</sup> = quabizoatritrigu<br />
-z+9g = tritrizogu<br />
+z<sup>9</sup>g<sup>9</sup> = tritrizogu<br />
-z+8g = tritrizoaquabigu<br />
+z<sup>9</sup>g<sup>8</sup> = tritrizoaquabigu<br />
-z+7g = tritrizoasepgu<br />
+z<sup>9</sup>g<sup>7</sup> = tritrizoasepgu<br />
-z+6g = tritrizoatribigu*<br />
+z<sup>9</sup>g<sup>6</sup> = tritrizoatribigu*<br />
-z+5g = tritrizoaquingu<br />
+z<sup>9</sup>g<sup>5</sup> = tritrizoaquingu<br />
-z+4g = tritrizoaquadgu<br />
+z<sup>9</sup>g<sup>4</sup> = tritrizoaquadgu<br />
-z+3g = tritrizoatrigu*<br />
+z<sup>9</sup>g<sup>3</sup> = tritrizoatrigu*<br />
-z+2g = tritrizoagugu<br />
+z<sup>9</sup>gg = tritrizoagugu<br />
-z+g = tritrizoagu
+z<sup>9</sup>g = tritrizoagu
 ''<u>Possible solution to the GCD problem</u>:''
@@ Line 134: / Line 135: @@
 ''bi- + -a- = double-all --> affects the whole name''
-z+4g = tribizoaquadgu* = biatrizoagugu?<br />
+z<sup>6</sup>g<sup>4</sup> = tribizoaquadgu* = biatrizoagugu?<br />
-z+2g = tribizoagugu* = biatrizoagu?<br />
+z<sup>6</sup>gg = tribizoagugu* = biatrizoagu?<br />
-z+8g = tribizoaquabigu* = biatrizoaquadgu?<br />
+z<sup>6</sup>g<sup>8</sup> = tribizoaquabigu* = biatrizoaquadgu?<br />
-z+6g = quabizoatribigu* = biaquadzoatrigu?<br />
+z<sup>8</sup>g<sup>6</sup> = quabizoatribigu* = biaquadzoatrigu?<br />
-z+2g = quabizoagugu* = biaquadzoagu?<br />
+z<sup>8</sup>gg = quabizoagugu* = biaquadzoagu?<br />
-z+6g = tritrizoatribigu* = triatrizoagugu?<br />
+z<sup>9</sup>g<sup>6</sup> = tritrizoatribigu* = triatrizoagugu?<br />
-z+3g = tritrizoatrigu* = triatrizoagu?
+z<sup>9</sup>g<sup>3</sup> = tritrizoatrigu* = triatrizoagu?
 == Tricolored examples ==
 if ilo is not doubled or tripled, it just gets tacked onto the beginning:
-o+z+2g = lozogugu<br />
+ozgg = lozogugu<br />
-o+2z+2g = lobizogu<br />
+ozzgg = lobizogu<br />
-o+2z+g = lozozogu<br />
+ozzg = lozozogu<br />
-o+z+3g = lozotrigu<br />
+ozg<sup>3</sup> = lozotrigu<br />
 etc.
-oo+z+g = lolozogu<br />
+oozg = lolozogu<br />
-oo+z+2g = lolozogugu<br />
+oozgg = lolozogugu<br />
-oo+2z+2g = bilozogu<br />
+oozzzgg = bilozogu<br />
-oo+2z+g = bilozoagu
+oozzg = bilozoagu
-oo+z+3g = lolozotrigu<br />
+oozg<sup>3</sup> = lolozotrigu<br />
-oo+2z+3g = bilozoatrigu<br />
+oozzg<sup>3</sup> = bilozoatrigu<br />
-oo+3z+3g = lolotrizogu<br />
+ooz<sup>3</sup>g<sup>3</sup> = lolotrizogu<br />
-oo+3z+2g = lolotrizoagugu<br />
+ooz<sup>3</sup>gg = lolotrizoagugu<br />
-oo+3z+g = lolotrizoagu
+ooz<sup>3</sup>g = lolotrizoagu
-ooozg = triloazogu<br />
+o<sup>3</sup>zg = triloazogu<br />
-ooozgg = triloazogugu<br />
+o<sup>3</sup>zgg = triloazogugu<br />
-ooozzgg = triloabizogu<br />
+o<sup>3</sup>zzgg = triloabizogu<br />
-ooozzg = triloazozogu
+o<sup>3</sup>zzg = triloazozogu
-ooo+z+3g = triloazotrigu<br />
+o<sup>3</sup>zg<sup>3</sup> = triloazotrigu<br />
-ooo+2z+3g = triloazozotrigu<br />
+o<sup>3</sup>zzg<sup>3</sup> = triloazozotrigu<br />
-ooo+3z+3g = trilozogu<br />
+o<sup>3</sup>z<sup>3</sup>g<sup>3</sup> = trilozogu<br />
-ooo+3z+2g = trilozoagugu<br />
+o<sup>3</sup>z<sup>3</sup>gg = trilozoagugu<br />
-ooo+3z+g = trilozoagu
+o<sup>3</sup>z<sup>3</sup>g = trilozoagu
 == Quadricolored examples ==