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Ragismic microtemperaments: Difference between revisions

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[[Wedgie]]: <<18 27 18 1 -22 -34||
[[Wedgie]]: <<18 27 18 1 -22 -34||
Mapping generators: ~27/25, ~5/3


[[POTE Tuning|POTE generators]]: ~36/35 = 49.0205; ~10/9 = 182.354; ~6/5 = 315.687; ~49/40 = 350.980
[[POTE Tuning|POTE generators]]: ~36/35 = 49.0205; ~10/9 = 182.354; ~6/5 = 315.687; ~49/40 = 350.980
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Tuning ranges:  
Tuning ranges:  
* valid range: [13.333, 22.222] (90bcd, 54c)
* valid range: [13.333, 22.222] (1\90 to 1\54)
* nice range: [17.304, 17.985]
* nice range: [17.304, 17.985]
* strict range:  [17.304, 17.985]
* strict range:  [17.304, 17.985]
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Tuning ranges:  
Tuning ranges:  
* valid range: [16.667, 22.222] (72 to 54cf)
* valid range: [16.667, 22.222] (1\72 to 1\54)
* nice range: [17.304, 18.309]
* nice range: [17.304, 18.309]
* strict range: [17.304, 18.309]
* strict range: [17.304, 18.309]
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Tuning ranges:  
Tuning ranges:  
* valid range: [48.485, 50.000] (99ef to 72)
* valid range: [48.485, 50.000] (4\99 to 3\72)
* nice range: [48.825, 52.592]
* nice range: [48.825, 52.592]
* strict range: [48.825, 50.000]
* strict range: [48.825, 50.000]
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Tuning ranges:  
Tuning ranges:  
* valid range: [48.485, 50.000] (99ef to 72)
* valid range: [48.485, 50.000] (4\99 to 3\72)
* nice range: [46.363, 52.592]
* nice range: [46.363, 52.592]
* strict range: [48.485, 50.000]
* strict range: [48.485, 50.000]
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Enneadecal temperament tempers out the enneadeca, |-14 -19 19>, and as a consequence has a period of 1/19 octave. This is because the enneadeca is the amount by which nineteen just minor thirds fall short of an octave. If to this we add 4375/4374 we get the 7-limit temperament we are considering here, but note should be taken of the fact that it makes for a reasonable 5-limit microtemperament also, where the generator can be 25/24, 27/25, 10/9, 5/4 or 3/2. To this we may add possible 7-limit generators such as 225/224, 15/14 or 9/7. Since enneadecal tempers out 703125/702464, the amount by which 81/80 falls short of three stacked 225/224, we can equate the 225/224 generator with (81/80)^(1/3). This is the interval needed to adjust the 1/3 comma meantone flat fifths and major thirds of [[19edo]] up to just ones. [[171edo]] is a good tuning for either the 5 or 7 limits, and [[494edo]] shows how to extend the temperament to the 11 or 13 limit, where it is accurate but very complex. Fans of near-perfect fifths may want to use [[665edo]] for a tuning.
Enneadecal temperament tempers out the enneadeca, |-14 -19 19>, and as a consequence has a period of 1/19 octave. This is because the enneadeca is the amount by which nineteen just minor thirds fall short of an octave. If to this we add 4375/4374 we get the 7-limit temperament we are considering here, but note should be taken of the fact that it makes for a reasonable 5-limit microtemperament also, where the generator can be 25/24, 27/25, 10/9, 5/4 or 3/2. To this we may add possible 7-limit generators such as 225/224, 15/14 or 9/7. Since enneadecal tempers out 703125/702464, the amount by which 81/80 falls short of three stacked 225/224, we can equate the 225/224 generator with (81/80)^(1/3). This is the interval needed to adjust the 1/3 comma meantone flat fifths and major thirds of [[19edo]] up to just ones. [[171edo]] is a good tuning for either the 5 or 7 limits, and [[494edo]] shows how to extend the temperament to the 11 or 13 limit, where it is accurate but very complex. Fans of near-perfect fifths may want to use [[665edo]] for a tuning.


Commas: 4375/4374, 703125/702464
[[Comma list]]: 4375/4374, 703125/702464


POTE generator: ~3/2 = 701.880
[[Mapping]]: [<19 0 14 -37|, <0 1 1 3|]


Map: [<19 0 14 -37|, <0 1 1 3|]
[[Wedgie]]: <<19 19 57 -14 37 79||


Generators: 28/27, 3
Mapping generators: ~28/27, ~3


EDOs: 19, 152, 171, 665, 836, 1007, 2185
[[POTE tuning|POTE generator]]: ~3/2 = 701.880


Badness: 0.0110
[[EDO|Vals]]: {{Val list| 19, 152, 171, 665, 836, 1007, 2185 }}


==Hemienneadecal==
[[Badness]]: 0.010954
Commas: 3025/3024, 4375/4374, 234375/234256
 
== Hemienneadecal ==
Comma list: 3025/3024, 4375/4374, 234375/234256
 
Mapping: [<38 0 28 -74 11|, <0 1 1 3 2|]


POTE generator: ~3/2 = 701.881
POTE generator: ~3/2 = 701.881


Map: [<38 0 28 -74 11|, <0 1 1 3 2|]
Vals: {{Val list| 152, 342, 494, 836, 1178, 2014 }}


EDOs: 152, 342, 494, 836, 1178, 2014
Badness: 0.009985


Badness: 0.00999
=== 13-limit ===
Comma list: 3025/3024, 4096/4095, 4375/4374, 31250/31213


===13-limit===
Mapping: [<38 0 28 -74 11 502|, <0 1 1 3 2 -6|]
Commas: 3025/3024, 4096/4095, 4375/4374, 31250/31213


POTE generator: ~3/2 = 701.986
POTE generator: ~3/2 = 701.986


Map: [<38 0 28 -74 11 502|, <0 1 1 3 2 -6|]
Vals: {{Val list| 152, 342, 494, 836 }}
 
EDOs: 152, 342, 494, 836


Badness: 0.0304
Badness: 0.030391


=Deca=
= Deca =
Commas: 4375/4374, 165288374272/164794921875
Commas: 4375/4374, 165288374272/164794921875


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