Kite's color notation: Difference between revisions
→Chord Progressions, Keys, Scales and Modulations: edited to allow II, III, VI and VII chords to omit the root color and default to wa. added an explanation of IIIy vs LwIIIy. |
→Color Names for Higher Primes: added the degrees for harmonics 64-127. added the supercalifragalistic mnemonic. other minor rewrites. |
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'''So''' = 17-over, '''su''' = 17-under, and '''sa''' = 17-all, abbreviated as '''17o''', '''17u''' and '''17a'''. '''Iso''' is an alternate form of so, to distinguish it from the solfege syllable So. 17/12 = 17o5 = iso So. '''Isa''' is an alternate form of sa, to distinguish it from sa for small, and from the Indian saregam syllable Sa. | '''So''' = 17-over, '''su''' = 17-under, and '''sa''' = 17-all, abbreviated as '''17o''', '''17u''' and '''17a'''. '''Iso''' is an alternate form of so, to distinguish it from the solfege syllable So. 17/12 = 17o5 = iso So. '''Isa''' is an alternate form of sa, to distinguish it from sa for small, and from the Indian saregam syllable Sa. | ||
'''Ino''' = 19-over, '''nu''' = 19-under, and '''na''' = 19-all, abbreviated as '''19o''', '''19u''' and '''19a'''. Ino because "no 3rd" could mean either 19/16 or thirdless. '''Inu''' is an alternate form of nu, to distinguish "the nu chord" from "the new chord" | '''Ino''' = 19-over, '''nu''' = 19-under, and '''na''' = 19-all, abbreviated as '''19o''', '''19u''' and '''19a'''. Ino because "no 3rd" could mean either 19/16 or thirdless. '''Inu''' is an alternate form of nu, to distinguish "the nu chord" from "the new chord". | ||
The prefix i- is only used when confusion is possible. Thus 19/15 = nogu 4th, not inogu 4th, and 2.3.5.17.19 is yasana not yasaina. | The prefix i- is only used when confusion is possible. Thus 19/15 = nogu 4th, not inogu 4th, and 2.3.5.17.19 (implied by 12edo) is yasana not yasaina. | ||
'''Twetho''' = 23-over, '''twethu''' = 23-under, and '''twetha''' = 23-all, abbreviated as '''23o''', '''23u''' and '''23a'''. 2.3.5.7.23 = yaza23a = yazatwetha. 23/16 = 23o5 = twetho 5th, and 23/22 = 23o1u2 = twetholu 2nd. 529/512 = 23oo2 = bitwetho 2nd (not twethotho, because that means 23-over 13-over). | '''Twetho''' = 23-over, '''twethu''' = 23-under, and '''twetha''' = 23-all, abbreviated as '''23o''', '''23u''' and '''23a'''. 2.3.5.7.23 = yaza23a = yazatwetha. 23/16 = 23o5 = twetho 5th, and 23/22 = 23o1u2 = twetholu 2nd. 529/512 = 23oo2 = bitwetho 2nd (not twethotho, because that means 23-over 13-over). | ||
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{| class="wikitable" | {| class="wikitable" | ||
!prime | !prime | ||
| | |5 | ||
| | |7 | ||
| | |11 | ||
| | |13 | ||
| | |17 | ||
| | |19 | ||
| | |23 | ||
| | | 29 | ||
| | |31 | ||
| | |37 | ||
| | |41 | ||
| | |43 | ||
| | |47 | ||
| | |53 | ||
| | |59 | ||
| | | 61 | ||
| | |67 | ||
|- | |||
!P/2<sup>n</sup> | |||
|y3 | |||
|z7 | |||
|1o4 | |||
|3o6 | |||
|17o2 | |||
|19o3 | |||
|23o5 | |||
|29o7 | |||
|31o7 | |||
|37o3 | |||
|41o3 | |||
|43o4 | |||
|47o5 | |||
|53o6 | |||
|59o7 | |||
|61o7 | |||
|67o2 | |||
|- | |- | ||
!word | !word | ||
| | |ya | ||
| | |za | ||
|(i) | |(i)la | ||
| | |tha | ||
|(i) | |(i)sa | ||
|(i) | |(i)na | ||
| | |twetha | ||
| | |twena | ||
| | | thiwa | ||
| | |thisa | ||
| | |fowa | ||
| | |fotha | ||
| | |fosa | ||
| | |fitha | ||
| | |fina | ||
| | |siwa | ||
| | |sisa | ||
|} | |} | ||
Unfortunately seventy can't become se- because that already means 17-exponent (see [[#Exponents]] below). Setho means 13<sup>17</sup>-over, so it can't mean 73-over. So starting at 71, one might use the longer form: 71o is seventy-wo, 73o is seventy-tho, etc. Or one might use these terms: | Mnemonic (sung to the tune of "Supercalifragilisticexpialidocious"): | ||
''Yaza latha sana twetha twena thiwa thisa / Fowa fotha fosa fitha fina siwa sisa'' | |||
Unfortunately seventy can't become se- because that already means 17-exponent (see [[#Exponents]] below). Setho means 13<sup>17</sup>-over, so it can't mean 73-over. So starting at 71, one might use the longer form: 71o is seventy-wo, 73o is seventy-tho, etc. 103o is hundred-tho and 113o is one-ten-tho. Or one might use these terms: | |||
{| class="wikitable" | {| class="wikitable" | ||
!prime | !prime | ||
| | |71 | ||
| | |73 | ||
| | |79 | ||
| | |83 | ||
| | |89 | ||
| | |97 | ||
| | |101 | ||
| | | 103 | ||
| | |107 | ||
| | |109 | ||
| | |113 | ||
| | |127 | ||
|- | |||
!P/2<sup>n</sup> | |||
|71o2 | |||
|73o2 | |||
|79o3 | |||
|83o4 | |||
|89o4 | |||
|97o5 | |||
|101o6 | |||
|103o6 | |||
|107o6 | |||
|109o6 | |||
|113o7 | |||
|127o8 | |||
|- | |- | ||
! word | ! word | ||
| | |fitwewa | ||
| | | fitwetha | ||
| | |fitwena | ||
| | |fithitha | ||
| | |fithina | ||
| | |fifosa | ||
| | |fifiwa | ||
| | |fifitha | ||
| | |fifisa | ||
| | |fifina | ||
| | |fisitha | ||
| | |sisisa | ||
|} | |} | ||
For any prime P, the degree of the ratio P/1 is chosen to minimize negative intervals. It is determined by its 8ve-reduced cents, and how it relates to 12edo: | Note that 23/16 = 628¢ is a 5th, not a 4th. Furthermore 31/16 = 1145¢ is a 7th not an 8ve, and 37/32 = 251¢ is a 3rd not a 2nd. For any prime P, the degree of the ratio P/1 is chosen to minimize negative intervals. It is determined by its 8ve-reduced cents, and how it relates to 12edo: | ||
{| class="wikitable" | {| class="wikitable" | ||
!unison | !unison | ||
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|1150-1200¢ | |1150-1200¢ | ||
|} | |} | ||
This makes the "pseudo-edomapping" <7 11 16 20 24 26 29 30 32 34 37...]. An alternative method would use the actual 7edo [[edomapping]], but that requires using every other 14edostep as boundaries, harder to remember and much less convenient than the 24edo boundaries used here. Since negative intervals will arise no matter what, convenience is prioritized. For the first 26 primes, the 24edo-based degrees correspond to [[Val#Shorthand_notation|7klmrs-edo]]. | |||
==Exponents== | ==Exponents== | ||