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| | {{Technical data page}} |
| | {{Infobox fractional-octave|10}} |
| [[10edo]] is notable for having close approximations of [[15/14]] to one step, and [[13/8]] to 7 steps. 10th-octave temperaments naturally occur between any equal divisions of the octave whose greatest common divisor is 10. | | [[10edo]] is notable for having close approximations of [[15/14]] to one step, and [[13/8]] to 7 steps. 10th-octave temperaments naturally occur between any equal divisions of the octave whose greatest common divisor is 10. |
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| Temperaments discussed elsewhere include: [[Breedsmic temperaments #Decoid|decoid]], [[Ragismic microtemperaments #Deca|deca]], [[Pental family #Decal|decal]], [[Metric microtemperaments #Decimetra|decimetra]], [[Stearnsmic clan #Decistearn|decistearn]], and [[Vishnuzmic family #Decavish|decavish]]. | | Temperaments discussed elsewhere include: [[Quintosec family #Decoid|decoid]], [[Ragismic microtemperaments #Deca|deca]], [[Quintile family #Decile|decile]], [[Metric microtemperaments #Decimetra|decimetra]], [[Stearnsmic clan #Decistearn|decistearn]], [[Vishnuzmic family #Decavish|decavish]], and [[Kalismic temperaments #Linus|linus]]. |
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| == Linus (rank-3) == | | == Neon == |
| Tempering out the '''linus comma''', 578509309952 / 576650390625 = {{monzo|11 -10 -10 10}} leads a number of regular temperaments, some of which are listed above. Linus rank three temperament can be described as the 130 & 190 & 270 temperament, which tempers out 9801/9800 and 391314/390625 in the 11-limit; 1001/1000, 4225/4224, and 4459/4455 in the 13-limit. The 1/10-octave period interval represents 15/14, three of which represents 16/13, and five of which represents both 99/70 and 140/99.
| | Neon tempers out {{monzo| 21 60 -50 }} in the 5-limit, equating [[3125/2916]] with one step of 10edo. Neon extensions discussed elsewhere include [[deca]], [[calcium]], and [[zinc]]. |
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| Subgroup: 2.3.5.7 | | [[Subgroup]]: 2.3.5 |
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| Comma list: 578509309952/576650390625
| | [[Comma list]]: {{monzo| 21 60 -50 }} |
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| Mapping: [{{val|10 0 0 -11}}, {{val|0 1 0 1}}, {{val|0 0 1 1}}]
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| : mapping generators: ~15/14 = 1\10, ~3/2 = 702.095, ~5/4 = 386.574
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| {{Optimal ET sequence|legend=1| 10, 40, 50, 80, 130, 140, 190, 270, 1270, 1400, 1540, 1670, 1810, 1940 }}
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| === 11-limit ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 9801/9800, 391314/390625 | |
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| Mapping: [{{val|10 0 0 -11 4}}, {{val|0 1 0 1 -1}}, {{val|0 0 1 1 2}}]
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| : mapping generators: ~15/14 = 1\10, ~3/2 = 702.034, ~5/4 = 386.648
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| {{Optimal ET sequence|legend=1| 10e, 50, 80, 130, 190, 270, 860, 940, 1130, 1400, 1670 }}
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| === 13-limit ===
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 1001/1000, 4225/4224, 4459/4455
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| Mapping: [{{val|10 0 0 -11 4 37}}, {{val|0 1 0 1 -1 0}}, {{val|0 0 1 1 2 0}}]
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| : mapping generators: ~15/14 = 1\10, ~3/2 = 701.931, ~5/4 = 386.473 | |
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| {{Optimal ET sequence|legend=1| 10e, 50, 80, 130, 190, 270, 590, 730, 860, 1130 }}
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| == Neon ==
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| Neon tempers out the {{Monzo|21 60 -50}} comma in the 5-limit. Neon extensions discussed elsewhere include [[deca]], [[calcium]], and [[zinc]].
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| Subgroup: 2.3.5
| | {{Mapping|legend=1| 10 4 9 | 0 5 6 }} |
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| Comma list: {{Monzo|21 60 -50}}
| | : Mapping generators: ~3125/2916, {{monzo| 10 29 -24 }} |
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| {{Mapping|10 4 9|0 5 6|legend=1}} | | [[Optimal tuning]] ([[CTE]]): ~3125/2916 = 1\10, {{monzo| 10 29 -24 }} = 284.3888 |
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| : mapping generators: ~3125/2916 = 1\10, 70277506421640192/59604644775390625 = 284.389
| | {{Optimal ET sequence|legend=1| 80, 190, 270, 460, 730, 1730, 2460, 3190, 5650 }} |
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| Optimal tuning (CTE): ~70277506421640192/59604644775390625 = 284.389
| | [[Badness]]: 0.206596 |
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| [[Support]]ing [[ET]]s: {{EDOs|80, 190, 270, 460, 730, 1000, 1190, 1270, 1460, 2460}}
| | {{Navbox fractional-octave}} |
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| [[Category:10edo]] | | [[Category:10edo]] |
| [[Category:Temperament collections]]
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