The Jacobins: Difference between revisions
→Sextilimeans: maybe FloraC misread the mapping? subgroup is no-threes, it's 2.5.7.11.13 and it is the 5th harmonic that is reached 482 generators down. |
m Clarify that the mappings are subgroup-val mappings, so that I won't make the same mistake again |
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[[Comma list]]: 6656/6655, {{monzo| -119 -46 15 47 }} | [[Comma list]]: 6656/6655, {{monzo| -119 -46 15 47 }} | ||
[[ | [[Sval]] [[mapping]]: [{{val| 1 74 3 74 }}, {{val| 0 -156 1 -153 }}] | ||
[[Optimal tuning]] ([[CTE]]): ~11/8 = 551.370 | [[Optimal tuning]] ([[CTE]]): ~11/8 = 551.370 | ||
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Named so because it is described as the 1789 & 3125 temperament due to 3125 providing the optimal patent val for the jacobin comma, 3125 is 5 to the 5th power, and Estates General were called by Louis XVI on 5th May 1789 (05/05). Defined starting with the 2.5.11.13.19 subgroup, upwards to the 2.5.11.13.19.23.29.31 subgroup. | Named so because it is described as the 1789 & 3125 temperament due to 3125 providing the optimal patent val for the jacobin comma, 3125 is 5 to the 5th power, and Estates General were called by Louis XVI on 5th May 1789 (05/05). Defined starting with the 2.5.11.13.19 subgroup, upwards to the 2.5.11.13.19.23.29.31 subgroup. | ||
Subgroup: 2.5.11.13.19 | [[Subgroup]]: 2.5.11.13.19 | ||
Comma list: 6656/6655, 40960000000/40943078891, {{monzo| -133 50 -7 18 -6 }} | [[Comma list]]: 6656/6655, 40960000000/40943078891, {{monzo| -133 50 -7 18 -6 }} | ||
[[Sval]] [[mapping]]: [{{val| 1 118 -107 -212 450 }}, {{val| 0 -266 254 496 -1025 }}] | |||
Optimal tuning (CTE): ~2588443885831192576/1914932769775390625 = 521.856 | [[Optimal tuning]] ([[CTE]]): ~2588443885831192576/1914932769775390625 = 521.856 | ||
=== 2.5.11.13.19.23 subgroup === | === 2.5.11.13.19.23 subgroup === | ||
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Comma list: 6656/6655, 62500/62491, 190676992/190653125, {{Monzo|-92 23 -2 14 -10 8}} | Comma list: 6656/6655, 62500/62491, 190676992/190653125, {{Monzo|-92 23 -2 14 -10 8}} | ||
Sval mapping: [{{val| 1 118 -107 -212 450 579}}, {{val| 0 -266 254 496 -1025 -1321}}] | |||
Optimal tuning (CTE): ~2592407900127232/1918105439453125 = 521.856 | Optimal tuning (CTE): ~2592407900127232/1918105439453125 = 521.856 | ||
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Comma list: 6656/6655, 62500/62491, 190676992/190653125, 7592198144/7591796875, 897740062375/897648164864 | Comma list: 6656/6655, 62500/62491, 190676992/190653125, 7592198144/7591796875, 897740062375/897648164864 | ||
Sval mapping: [{{val| 1 118 -107 -212 450 579 251}}, {{val| 0 -266 254 496 -1025 -1321 -566}}] | |||
Optimal tuning (CTE): ~184000/136097 = 521.856 | Optimal tuning (CTE): ~184000/136097 = 521.856 | ||
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Comma list: 6656/6655, 62500/62491, 9425/9424, 190676992/190653125, 507528125/507510784, 519411073024/519363934375 | Comma list: 6656/6655, 62500/62491, 9425/9424, 190676992/190653125, 507528125/507510784, 519411073024/519363934375 | ||
Sval mapping: [{{val| 1 118 -107 -212 450 579 251 -179}}, {{val| 0 -266 254 496 -1025 -1321 -566 423}}] | |||
Optimal tuning (CTE): ~80275/59392 = 521.856 | Optimal tuning (CTE): ~80275/59392 = 521.856 | ||
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Sextilimeans is like sextilififths, but the fourth that is divided into 6 in sextilififths is tuned to a meantone fourth in the optimal tuning, or about 1/4.26-commma meantone. It should be noted, however, that this meantone fourth is not ~4/3 despite that the name may suggest so. In fact, the 3rd harmonic is not mapped in this temperament at all. It is described as the 229 & 1789 temperament. | Sextilimeans is like sextilififths, but the fourth that is divided into 6 in sextilififths is tuned to a meantone fourth in the optimal tuning, or about 1/4.26-commma meantone. It should be noted, however, that this meantone fourth is not ~4/3 despite that the name may suggest so. In fact, the 3rd harmonic is not mapped in this temperament at all. It is described as the 229 & 1789 temperament. | ||
Subgroup: 2.5.7.11.13 | [[Subgroup]]: 2.5.7.11.13 | ||
Comma list: 6656/6655, 8122034375/8120172544, {{monzo|-12 -29 36 -2 -4}} | [[Comma list]]: 6656/6655, 8122034375/8120172544, {{monzo|-12 -29 36 -2 -4}} | ||
[[Sval]] [[mapping]]: [{{val|1 36 23 -24 -45}}, {{val|0 -482 -289 393 697}}] | |||
Optimal tuning (CTE): ~16807/16000 = 83.846 | [[Optimal tuning]] ([[CTE]]): ~16807/16000 = 83.846 | ||
Vals: {{EDOs|229, 1789}}, ... | Vals: {{EDOs|229, 1789}}, ... | ||
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Described as the 1789 & 2814 temperament, and named because 2814 divided in two is 1407, and Bastille storming happened on 14 July 1789. Unfortunately the 1407 & 1789 temperament in the patent val does not temper out the jacobin comma, so it is not included here. | Described as the 1789 & 2814 temperament, and named because 2814 divided in two is 1407, and Bastille storming happened on 14 July 1789. Unfortunately the 1407 & 1789 temperament in the patent val does not temper out the jacobin comma, so it is not included here. | ||
Subgroup: 2.5.7.11.13 | [[Subgroup]]: 2.5.7.11.13 | ||
Comma list: 6656/6655, {{monzo|43 -18 0 5 -5}}, {{monzo|6 -30 -3 8 12}} | [[Comma list]]: 6656/6655, {{monzo|43 -18 0 5 -5}}, {{monzo|6 -30 -3 8 12}} | ||
[[Sval]] [[mapping]]: [{{Val|1 26 -938 -51 -136}}, {{Val|0 -30 1192 69 177}}] | |||
Optimal tuning (CTE): ~91750400/53094899 = 947.121 | [[Optimal tuning]] ([[CTE]]): ~91750400/53094899 = 947.121 | ||
Vals: 1789, 2814, ... | Vals: 1789, 2814, ... | ||