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Kite's color notation: Difference between revisions

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→Color Names for Higher Primes: added twetho for 23o, etc.
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'''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 key" from "the new key". 12edo implies yasana = 2.3.5.17.19.  
'''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 key" from "the new key". 12edo implies yasana = 2.3.5.17.19.  


'''Twenty-tho''' = 23-over, '''twenty-thu''' = 23-under, '''twenty-tha''' =23-all, abbreviated as '''23o''', '''23u''' and '''23a'''. 2.3.5.7.23 = yaza23a = yaza-twenty-tha. 23/16 = 23o5 = twenty-tho 5th, and 23/22 = 23o1u2 = twenty-tholu 2nd. 529/512 = bi-twenty-tho 2nd.  
'''Twetho''' = 23-over, '''twethu''' = 23-under, '''twentha''' =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 = bitwetho 2nd (not twethotho, because that means a ratio that's both 23-over and 13-over).  


Similarly, '''twenty-no/-nu/-na''' = 29o/29u/29a, '''thirty-wo/-wu/-wa''' = 31o/31u/31a, '''thirty-so/-su/-sa''' = 37o/37u/37a, etc.   
Similarly, '''tweno/-nu/-na''' = 29o/29u/29a, '''thiwo/-wu/-wa''' = 31o/31u/31a, '''thiso/-su/-sa''' = 37o/37u/37a, etc.   
 
{| class="wikitable"
The prefix i- is only used when confusion is possible. Thus 19/15 = nogu 4th, not inogu 4th, and 29o = twenty-no, not twenty-ino.     
|11
|13o
|17o
|19o
|23o
|29o
|31o
|37o
|41o
|43o
|47o
|53o
|59o
|61o
|67o
|-
|(i)lo
|tho
|(i)so
|(i)no
|twetho
|tweno
|thiwo
|thiso
|fowo
|fotho
|foso
|fitho
|fino
|siwo
|siso
|}
Unfortunately seventy- can't be abbreviated as se- because that already means 17-exponent. Setho means 13^17, so it can't mean 73-over. So starting at 71, the longer form is used: 71o is seventy-wo, 73o is seventy-tho, etc.     


While a double-yo ratio such as 25/24 is yoyo, a double-twenty-tho ratio is not twenty-thotho, because that means a ratio that's both 23-over and 13-over. Twenty-tho doubled is bi-twenty-tho.     
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.     


For any prime P, the degree of the ratio P/1 is determined by its 8ve-reduced cents, and how it relates to 12edo: 0-50¢ = 1sn, 50-250¢ = 2nd, 250-450¢ = 3rd, 450-600¢ = 4th, 600-750¢ = 5th, 750-950¢ = 6th, 950-1150¢ = 7th, and 1150-1200¢ = 8ve. Thus 23/16 = 628¢ is a 5th, 31/16 = 1145¢ is a 7th, and 37/32 = 251¢ is a 3rd. This makes the "pseudo-edomapping" <7 11 16 20 24 26 29 30 32 34 34 37...]. (An alternative method is to use the 7edo [[edomapping]], but that requires using every other 14edostep as boundaries, harder to remember and much less convenient than the 24edo boundaries used here.)
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: 0-50¢ = 1sn, 50-250¢ = 2nd, 250-450¢ = 3rd, 450-600¢ = 4th, 600-750¢ = 5th, 750-950¢ = 6th, 950-1150¢ = 7th, and 1150-1200¢ = 8ve. Thus 23/16 = 628¢ is a 5th, 31/16 = 1145¢ is a 7th, and 37/32 = 251¢ is a 3rd. This makes the "pseudo-edomapping" <7 11 16 20 24 26 29 30 32 34 34 37...]. (An alternative method is to use the 7edo [[edomapping]], but that requires using every other 14edostep as boundaries, harder to remember and much less convenient than the 24edo boundaries used here.)


== Converting a Ratio to/from a Color Name ==
== Converting a Ratio to/from a Color Name ==
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Every wa comma implies an edo, and a temperament with such a comma uses that edo in its name. Thus Catler is 12-edo plus za. An exception is made for 5-edo and 7-edo: Blackwood is Sawa + ya and Whitewood is Lawa + ya.           
Every wa comma implies an edo, and a temperament with such a comma uses that edo in its name. Thus Catler is 12-edo plus za. An exception is made for 5-edo and 7-edo: Blackwood is Sawa + ya and Whitewood is Lawa + ya.           


The color name of a rank-2 temperament can be used to name MOS and MODMOS scales, as in Triyo[8]. Individual modes can be named as 2nd Triyo[8], 3rd Triyo[7] b7, etc. This notation is discussed here: [[Naming Rank-2 Scales using Mode Numbers]].           
The color name of a rank-2 temperament can be used to name MOS and MODMOS scales, as in Triyo[8]. Individual modes can be named as 2nd Triyo[8], 3rd Triyo[7] b7, etc. See [[Naming Rank-2 Scales using Mode Numbers]].           


Temperament names are further explained here: [[Color notation/Temperament Names]].         
Temperament names are further explained at [[Color notation/Temperament Names]].         


== Ups and Downs, Lifts and Drops, Plain and Mid ==
== Ups and Downs, Lifts and Drops, Plain and Mid ==
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== Glossary / Crash Course ==
== Glossary / Crash Course ==
Over = prime in the numerator, under = prime in the denominator. All = over, under or neither: wa = 3-limit, ya = 2.3.5, yaza = 2.3.5.7.  
Over = prime in the numerator, under = prime in the denominator. All = over, under or neither: wa = 3-limit, ya = 2.3.5, yaza = 2.3.5.7. Exponent = prime in the monzo: triyo = yo-cubed = 125-over.  
{| class="wikitable" style="text-align:center"
{| class="wikitable" style="text-align:center"
|+
|+
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! colspan="2" |-u ("oo") for under
! colspan="2" |-u ("oo") for under
! colspan="2" |-a ("ah") for all
! colspan="2" |-a ("ah") for all
!multiplier
! colspan="2" |-e ("eh") for exponent
|-
|-
|2
|2
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| —
| —
|bi
|bi
|squared
|-
|-
|3
|3
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| —
| —
|tri
|tri
|cubed
|-
|-
|5
|5
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| —
| —
|quin
|quin
|^5
|-
|-
|7
|7
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| —
| —
|sep
|sep
|^7
|-
|-
|11
|11
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|1a
|1a
|le
|le
|^11
|-
|-
|13
|13
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|3a
|3a
|the
|the
|^13
|-
|-
|17
|17
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|17a
|17a
|se
|se
|^17
|-
|-
|19
|19
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|19a
|19a
|ne
|ne
|^19
|-
|-
|23
|23
|twenty-tho
|twetho
|23o
|23o
|twenty-thu
|twethu
|23u
|23u
|twenty-tha
|twetha
|23a
|23a
|twenty-the
|twethe
|^23
|}
|}
29o = twenty-no, 31o = thirty-wo, 37o = thirty-so, etc. In the multiplier words for primes 11 and above, -e ("eh") stands for exponent.
29o = tweno, 31o = thiwo, 37o = thiso, 41o = fowo, 43o = fotho, 47o = foso, 53o = fitho, 59o = fino, 61o = siwo, 67o = sino.  
{| class="wikitable"
{| class="wikitable"
|+
|+
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|-
|-
| colspan="2" |quad
| colspan="2" |quad
|quadruple, multiplier of 4
|quadruple, exponent of 4
|Diminished temperament = 648/625 = Quadgu = g<sup>4</sup>T
|Diminished temperament = 648/625 = Quadgu = g<sup>4</sup>T
|-
|-
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|-
|-
| colspan="2" | -a-
| colspan="2" | -a-
|delimits a multiplier such as bi-, tri-, etc.
|delimits an exponent such as bi-, tri-, etc.
|Trizogu = z<sup>3</sup>g<sup>3</sup> = 1029/1000, Trizo-agu = z<sup>3</sup>g = 343/320
|Trizogu = z<sup>3</sup>g<sup>3</sup> = 1029/1000, Trizo-agu = z<sup>3</sup>g = 343/320
|-
|-
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