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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: [[Miscellaneous 5-limit temperaments #Neon|neon]]/[[Ragismic microtemperaments #Deca|deca]], [[Quintosec family #Decoid|decoid]], [[Quintile family #Decile|decile]], [[Metric microtemperaments #Decimetra|decimetra]], [[Stearnsmic clan #Decistearn|decistearn]], [[Vishnu family #Decavish|decavish]], and [[Kalismic temperaments #Linus|linus]]. |
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| == Linus (rank-3) ==
| | {{Navbox fractional-octave}} |
| 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.
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| Subgroup: 2.3.5.7
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| Comma list: 578509309952/576650390625
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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
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| Comma list: {{Monzo|21 60 -50}}
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| {{Mapping|10 4 9|0 5 6|legend=1}}
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| : mapping generators: ~3125/2916 = 1\10, 70277506421640192/59604644775390625 = 284.389
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| Optimal tuning (CTE): ~70277506421640192/59604644775390625 = 284.389
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| [[Support]]ing [[ET]]s: {{EDOs|80, 190, 270, 460, 730, 1000, 1190, 1270, 1460, 2460}}
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| [[Category:10edo]] | | [[Category:10edo]] |
| [[Category:Temperament collections]]
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- This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.
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.
Temperaments discussed elsewhere include: neon/deca, decoid, decile, decimetra, decistearn, decavish, and linus.