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| {{Fractional-octave navigation|15}} | | {{Fractional-octave navigation|15}} |
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| == Pentadecal ==
| | == Quindecic == |
| The ''pentadecal'' temperament tempers out the 15-5/3-comma (Quintriyo, pentadecatonic minor thirds comma), {{monzo|-11 -15 15}}. This temperament can be described as 15&60 temperament; in the 7-limit, it tempers out the [[cloudy comma]], 16807/16384, and the [[875/864|keema]], 875/864.
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| Subgroup: 2.3.5
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| [[Comma]]: 30517578125/29386561536
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| [[Mapping]]: [{{Val| 15 0 11 }}, {{Val| 0 1 1 }}]
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| [[POTE generator]]: ~3/2 = 702.652
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| {{Optimal ET sequence|legend=1| 15, 45, 60, 75, 135, 210c, 345cc }}
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| [[Badness]]: 0.692042
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| === 7-limit ===
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| [[Subgroup]]: 2.3.5.7
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| [[Comma list]]: 875/864, 16807/16384
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| {{Mapping|legend=1| 15 0 11 42 | 0 1 1 0 }}
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| : mapping generators: ~21/20, ~3
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| [[Optimal tuning]] ([[POTE]]): ~21/20 = 1\15, ~3/2 = 700.223 (~126/125 = 19.777)
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| {{Optimal ET sequence|legend=1| 15, 45, 60 }}
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| [[Badness]]: 0.114833
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| === 11-limit ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 100/99, 385/384, 1372/1331
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| Mapping: {{mapping| 15 0 11 42 52 | 0 1 1 0 0 }}
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| : mapping generators: ~21/20, ~3
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| Optimal tuning (POTE): ~21/20 = 1\15, ~3/2 = 702.733 (~56/55 = 17.267)
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| {{Optimal ET sequence|legend=1| 15, 45, 60, 75de, 135de }}
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| Badness: 0.077420
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| ==== 13-limit ====
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 100/99, 105/104, 144/143, 1372/1331
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| Mapping: {{mapping| 15 0 11 42 52 8 | 0 1 1 0 0 2 }}
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| : mapping generators: ~21/20, ~3
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| Optimal tuning (POTE): ~21/20 = 1\15, ~3/2 = 701.715 (~91/90 = 18.285)
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| {{Optimal ET sequence|legend=1| 15, 45f, 60, 135de, 195cddee }}
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| Badness: 0.051740
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| === Quindecal ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 121/120, 441/440, 875/864
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| Mapping: {{mapping| 15 0 11 42 28 | 0 1 1 0 1 }}
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| : mapping generators: ~21/20, ~3
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| Optimal tuning (POTE): ~21/20 = 1\15, ~3/2 = 700.318 (~126/125 = 19.682)
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| {{Optimal ET sequence|legend=1| 15, 45e, 60e }}
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| Badness: 0.044405
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| ==== 13-limit ====
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 121/120, 196/195, 352/351, 875/864
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| Mapping: {{mapping| 15 0 11 42 28 103 | 0 1 1 0 1 -2 }}
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| : mapping generators: ~21/20, ~3
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| Optimal tuning (POTE): ~21/20 = 1\15, ~3/2 = 701.647 (~65/64 = 18.353)
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| {{Optimal ET sequence|legend=1| 15f, 45e, 60e }}
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| Badness: 0.055361
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| === Quindecic ===
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| Quindecic preserves the [[11-limit]] structure of [[15edo]], with an independent generator for [[13/1|harmonic 13]]. | | Quindecic preserves the [[11-limit]] structure of [[15edo]], with an independent generator for [[13/1|harmonic 13]]. |
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