Kite's color notation: Difference between revisions
| (5 intermediate revisions by the same user not shown) | |||
| Line 467: | Line 467: | ||
We've seen bi- for double and tri- for triple. Quadruple and quintuple are abbreviated '''quad-''' and '''quin-''', as in quadyo or quingu. Colorspeak syllables usually end in one of the five basic vowels. Quad and quin are both exceptions, so quad may optionally be spoken as "kwah", and quin as "kwee". | We've seen bi- for double and tri- for triple. Quadruple and quintuple are abbreviated '''quad-''' and '''quin-''', as in quadyo or quingu. Colorspeak syllables usually end in one of the five basic vowels. Quad and quin are both exceptions, so quad may optionally be spoken as "kwah", and quin as "kwee". | ||
Except for quad, all exponent syllables are prime numbers. Septuple is '''sep-'''. | Except for quad, all exponent syllables are prime numbers. Septuple is '''sep-'''. For extreme cases above 7, all exponent syllables are the root color word plus -e for exponent. Eleven-fold is '''le-''' = "e'''<u>l</u>'''even '''<u>e</u>'''xponent", pronounced as in "<u>le</u>ns". Thirteen-fold is '''the-''' as in "<u>the</u>saurus". Note that sep- means seven-fold and '''se-''' means seven<u>teen</u>-fold. | ||
Exponents can be combined: sextuple = tribi-, 8-fold = quadbi-, 9-fold = tritri-, 10-fold = quinbi-, 12-fold = quadtri-, 14-fold = sepbi-, 15-fold = quintri-, 16-fold = quadquad-, etc. The component syllables are simply the number's prime factors in descending order, except that quad replaces bibi and comes before tri. | Exponents can be combined: sextuple = tribi-, 8-fold = quadbi-, 9-fold = tritri-, 10-fold = quinbi-, 12-fold = quadtri-, 14-fold = sepbi-, 15-fold = quintri-, 16-fold = quadquad-, etc. The component syllables are simply the number's prime factors in descending order, except that quad replaces bibi and comes before tri. | ||
| Line 578: | Line 578: | ||
=== Po and qu === | === Po and qu === | ||
'''Po''' and '''qu''' ("coo") (short forms '''p''' and '''q''') are two optional inflections that indicate raising/lowering by a pythagorean comma. (Mnemonics: p stands for pythagorean, and q is the mirror image of p.) Why would one want to | '''Po''' and '''qu''' ("coo") (short forms '''p''' and '''q''') are two optional inflections that indicate raising/lowering by a pythagorean comma. (Mnemonics: p stands for pythagorean, and q is the mirror image of p. The pythagorean comma is fifthward, hence 3-over, hence "-o".) Why would one want to raise by this comma? Because by first subtracting that comma and then adding it on again, one can rename a note as another note. This is similar to [[Sagittal notation |Sagittal]] notation (see [http://tallkite.com/misc_files/Sagittal-JI-Translated-To-Colors.png Sagittal-JI-Translated-To-Colors.png]). | ||
For example, F# minus a pythagorean comma is Gb. And Gb plus a pythagorean comma is po Gb. Thus an alternate name for F# is po Gb. <u>Adding po raises the degree by one</u>. The new note name is always a 12edo equivalent of the old note name. Adding qu lowers the degree: {{nowrap|Gb {{=}} qu F#}}. If one is resolving from 31oGb to G, one can rename 31oGb as 31oqF# = thiwoqu F sharp. | For example, F# minus a pythagorean comma is Gb. And Gb plus a pythagorean comma is po Gb. Thus an alternate name for F# is po Gb. <u>Adding po raises the degree by one</u>. The new note name is always a 12edo equivalent of the old note name. Adding qu lowers the degree: {{nowrap|Gb {{=}} qu F#}}. If one is resolving from 31oGb to G, one can rename 31oGb as 31oqF# = thiwoqu F sharp. | ||
| Line 590: | Line 590: | ||
Another reason is to avoid an awkward unison trill. [[File:Notation example 5a.png|992x992px]] | Another reason is to avoid an awkward unison trill. [[File:Notation example 5a.png|992x992px]] | ||
== | == Comma names and temperament names == | ||
{{Main | Color notation/Temperament names}} | {{Main | Color notation/Temperament names}} | ||
Temperaments are named after the comma(s) they temper out. Commas are named using an alternate format that replaces the degree (unison, 2nd, etc.) with the suffix "-ma" (mnemonics: com'''ma''', or -is'''ma''' as in schisma and kleisma). The degree isn't needed because the comma is | Temperaments are named after the comma(s) they temper out. Commas are named using an alternate format that replaces the degree (unison, 2nd, etc.) with the suffix "-ma" (mnemonics: com'''ma''', or -is'''ma''' as in schisma and kleisma). The degree isn't needed because the comma is assumed to be the smallest interval in cents of that color and magnitude. For example, the guma is the smallest of the 7 central gu intervals, which is [[81/80]]. Tempering out the guma creates [[Meantone]] or Guti or gT, where "-ti" and "T" stand for temperament. [[2048/2025]] is the saguguma, abbreviated sggM, and [[Srutal]] is Saguguti or sggT. [[Porcupine]] is Triyoti or 3yT. Example usage of -ti and -ma: triyoti inflates the guma. | ||
The logic for M and T being upper case is that in color notation abbreviations, nouns are always capitalized and adjectives are generally not. | The logic for M and T being upper case is that in color notation abbreviations, nouns are always capitalized and adjectives are generally not. Color notation nouns: M and T, note names A B C D E F G, roman numerals I II III IV V VI VII, and degrees 1 2 3 etc. (L for large is an exception to this rule, because otherwise Ly7 would be ly7, which looks like a y7 chord on the tonic.) | ||
Some commas over 90¢ (but not all) are the ''2nd'' smallest interval in cents of that color and magnitude. These use the -bi- syllable. For example, [[Schismic]] is Layoti or LyT, but [[Mavila]] is Layobiti or LybT, where "-bi-" and "-b-" indicate it's the 2nd largest layo interval. Likewise 135/128 is named layobima or LybM. | |||
Multi-comma temperaments have multiple commas in their name. [[Meantone family#Septimal meantone | Septimal Meantone]] is | Most wa commas use yet another alternate format, e.g. [[Mercator's comma]] is 53wama or 53wM. The only exceptions are lawama (LwM = A1), sawama (swM = m2) and lalawama (LLwM = pythagorean comma). | ||
Multi-comma temperaments have multiple commas in their name. [[Meantone family#Septimal meantone | Septimal Meantone]] is gu & ruyoyoti or g&ryyT, and [[Meantone family#Dominant | Dominant Meantone]] is gu & ruguti or g&rgT. Untempered primes are included with a plus sign. The 2.3.5.7 prime subgroup with 81/80 tempered out is Guti + za = gT+z, and [[Blackwood]] is Sawati + ya = swT+y. | |||
MOS and MODMOS scales can be named as e.g. Triyoti[8]. Individual modes can be named as 2nd Triyoti[8], 3rd Triyoti[7] b7, etc. See [[Genchain mode numbering]]. | MOS and MODMOS scales can be named as e.g. Triyoti[8]. Individual modes can be named as 2nd Triyoti[8], 3rd Triyoti[7] b7, etc. See [[Genchain mode numbering]]. | ||
| Line 752: | Line 754: | ||
| colspan="2" | -a- | | colspan="2" | -a- | ||
| delimits an exponent such as bi-, tri-, etc. | | delimits an exponent such as bi-, tri-, etc. | ||
| | | trizoguma = 3zgM = 1029/1000, but trizo-aguma = 3zagM = 343/320 | ||
|- | |- | ||
| co- | | co- | ||
| Line 787: | Line 789: | ||
| T | | T | ||
| the temperament that tempers out that comma | | the temperament that tempers out that comma | ||
| guma = 81/80, | | guma = 81/80, guti = meantone | ||
|- | |- | ||
| -bi | | -bi | ||
| style="text-align: center;" | b | | style="text-align: center;" | b | ||
| as a suffix, 2nd smallest comma in the row segment | | as a suffix, 2nd smallest comma in the row segment | ||
| | | guti = gT is Meantone, but gubiti = gbT is [[Father]] (16/15 vanishes) | ||
|- | |- | ||
| | | -wama | ||
| | | wM | ||
| alternate interval format, only used for 3-limit commas | | alternate interval format, only used for 3-limit commas | ||
| [[Mercator's comma]] = | | [[Mercator's comma]] = 53wama = 53wM | ||
|- | |- | ||
| colspan="2" | nowa | | colspan="2" | nowa | ||
| remove 3 (wa) from the prime subgroup, i.e. no-threes | | remove 3 (wa) from the prime subgroup, i.e. no-threes | ||
| 2.5.7 = yaza nowa, 2.5.7 & 50/49 = | | 2.5.7 = yaza nowa, 2.5.7 & 50/49 = biruyoti nowa | ||
|- | |- | ||
| colspan="2" | noca | | colspan="2" | noca | ||
| remove 2 (clear) from the prime subgroup, i.e. non-8ve | | remove 2 (clear) from the prime subgroup, i.e. non-8ve | ||
| 3.5.7 = yaza noca, 3.5.7 & 245/243 = | | 3.5.7 = yaza noca, 3.5.7 & 245/243 = zozoyoti noca | ||
|- | |- | ||
| colspan="2" | nowaca | | colspan="2" | nowaca | ||
| Line 814: | Line 816: | ||
| style="text-align: center;" | + | | style="text-align: center;" | + | ||
| add an untempered prime to the temperament | | add an untempered prime to the temperament | ||
| Blackwood = 2.3.5 with 256/243 tempered out = | | Blackwood = 2.3.5 with 256/243 tempered out = sawati + ya = swT+y | ||
|- | |- | ||
| and | | and | ||
| style="text-align: center;" | & | | style="text-align: center;" | & | ||
| joins commas that are tempered out | | joins commas that are tempered out | ||
| 7-limit Porcupine = 2.3.5.7 with 250/243 & 64/63 = | | 7-limit Porcupine = 2.3.5.7 with 250/243 & 64/63 = triyo & ruti = 3y&rT | ||
|- | |- | ||
| -ward | | -ward | ||
| Line 837: | Line 839: | ||
* "bi" means both "doubled" as in biruyo and "2nd smallest" as in Layobi. The meaning is always clear from context. | * "bi" means both "doubled" as in biruyo and "2nd smallest" as in Layobi. The meaning is always clear from context. | ||
* "b" means both the short form of -bi and the flat sign. The meaning is always clear from context. | * "b" means both the short form of -bi and the flat sign. The meaning is always clear from context. | ||
* "M" means both "comma" and "major", as in CM7. The meaning is always clear from context. | |||
Temperaments use "virtual colors" represented with arrows ^ v and perhaps slashes / \ | Temperaments use "virtual colors" represented with arrows ^ v and perhaps slashes / \ | ||