|
|
| (18 intermediate revisions by 9 users not shown) |
| Line 1: |
Line 1: |
| {{Fractional-octave navigation|7}} | | {{Technical data page}} |
| a 7th-octave temperament can be described by temperament merging of edos whose greatest common divisor is 7. The most notable 7th-octave family is the [[whitewood family]] – tempering out [[2187/2048]] and associating 4\7 to [[3/2]].
| | {{Infobox fractional-octave|7}} |
| | A 7th-octave temperament can be described by temperament merging of edos whose greatest common divisor is 7. The most notable 7th-octave family is the [[whitewood family]] – tempering out [[2187/2048]] and associating 4\7 to [[3/2]]. |
|
| |
|
| A comma that frequently appears in 7th-octave temps is [[akjaysma]], which sets [[105/64]] to be equal to 5\7. | | A comma that frequently appears in 7th-octave temps is [[akjaysma]], which sets [[105/64]] to be equal to 5\7. |
|
| |
|
| Temperaments discussed elsewhere include: | | Temperaments discussed elsewhere include: |
| * ''Septant →'' [[Schismatic family #Septant|Schismatic family]] | | * ''[[Septant]]'' → [[Schismatic family #Septant|Schismatic family]] |
| * ''Brahmagupta →'' [[Ragismic microtemperaments #Brahmagupta|Ragismic microtemperaments]] | | * ''[[Brahmagupta]]'' → [[Ragismic microtemperaments #Brahmagupta|Ragismic microtemperaments]] |
| * ''Absurdity'' ''→'' [[Syntonic-chromatic equivalence continuum #Absurdity|Syntonic chromatic equivalence continuum]] | | * ''[[Absurdity]]'' → [[Porwell temperaments #Absurdity|Porwell temperaments]] |
|
| |
|
| == Jamesbond == | | == Nitrogen == |
| This temperament uses exactly the same 5-limit as 7et, but the harmonic 7 is mapped to an independent generator. It is so named because its [[wedgie]] starts with {{multival| 0 0 7 … }}.
| | Nitrogen may be described as the {{nowrap| 140 & 1407 }} temperament in the 7-limit. It was named after the 7th element for having a 7th-octave period and also because 140 and 1407 only contain numbers 7 and 14, atomic number and atomic weight of nitrogen respectively. On top of this connection to the number 7, it also reaches the 7th harmonic 7 generators down. |
|
| |
|
| [[Subgroup]]: 2.3.5.7 | | [[Subgroup]]: 2.3.5.7 |
|
| |
|
| [[Comma list]]: 25/24, 81/80 | | [[Comma list]]: 3955078125/3954653486, {{monzo| 47 -7 -7 -7 }} |
| | |
| {{Mapping|legend=1| 7 11 16 0 | 0 0 0 1 }}
| |
| | |
| {{Multival|legend=1| 0 0 7 0 11 16 }}
| |
| | |
| [[Optimal tuning]] ([[POTE]]): ~10/9 = 1\7, ~7/4 = 941.861
| |
| | |
| {{Optimal ET sequence|legend=1| 7, 14c }}
| |
| | |
| [[Badness]]: 0.041714
| |
| | |
| === 11-limit ===
| |
| Subgroup: 2.3.5.7.11
| |
| | |
| Comma list: 25/24, 33/32, 45/44
| |
| | |
| Mapping: {{mapping| 7 11 16 0 24 | 0 0 0 1 0 }}
| |
| | |
| Optimal tuning (POTE): ~10/9 = 1\7, ~7/4 = 941.090
| |
| | |
| {{Optimal ET sequence|legend=1| 7, 14c }}
| |
| | |
| Badness: 0.023524
| |
| | |
| ==== 13-limit ====
| |
| Subgroup: 2.3.5.7.11.13
| |
| | |
| Comma list: 25/24, 27/26, 33/32, 40/39
| |
| | |
| Mapping: {{mapping| 7 11 16 0 24 26 | 0 0 0 1 0 0 }}
| |
| | |
| Optimal tuning (POTE): ~10/9 = 1\7, ~7/4 = 949.236
| |
| | |
| {{Optimal ET sequence|legend=1| 7, 14c }}
| |
| | |
| Badness: 0.023003
| |
| | |
| ==== Septimal ====
| |
| Subgroup: 2.3.5.7.11.13
| |
| | |
| Comma list: 25/24, 33/32, 45/44, 65/63
| |
| | |
| Mapping: {{mapping| 7 11 16 0 24 6 | 0 0 0 1 0 1 }}
| |
| | |
| Optimal tuning (POTE): ~10/9 = 1\7, ~7/4 = 952.555
| |
| | |
| {{Optimal ET sequence|legend=1| 7, 14cf }}
| |
| | |
| Badness: 0.022569
| |
| | |
| == Akjaysmic (rank-3) ==
| |
| {{Main| Akjaysma }}
| |
| Subgroup: 2.3.5.7
| |
| | |
| [[Comma list]]: {{monzo| 47 -7 -7 -7 }}
| |
| | |
| [[Mapping]]: [{{val| 7 0 0 47 }}, {{val| 0 1 0 -1 }}, {{val| 0 0 1 -1 }}]
| |
| | |
| Mapping generators: ~1157625/1048576, ~3, ~5
| |
| | |
| [[POTE generator]]s: ~3/2 = 701.965, ~5/4 = 386.330
| |
| | |
| {{Optimal ET sequence|legend=1| 140, 224, 301, 441, 665, 742, 966, 1106, 1407, 1547, 1848, 2289, 2513, 2954, 3395, 4802 }}
| |
| | |
| === 11-limit ===
| |
| | |
| Subgroup: 2.3.5.7.11
| |
| | |
| Comma list: 184549376/184528125, 199297406/199290375
| |
| | |
| Mapping: [{{val| 7 0 0 47 -168 }}, {{val| 0 1 0 -1 10 }}, {{val| 0 0 1 -1 5 }}]
| |
| | |
| Mapping generators: ~29160/26411, ~3, ~5
| |
| | |
| POTE generators: ~3/2 = 701.968, ~5/4 = 386.332
| |
| | |
| {{Optimal ET sequence|legend=1| 301, 364, 441, 742, 805, 1043, 1106, 1407, 1547, 1848, 2289, 2653, 2954, 3395, 4501, 5243, 6349, 8197 }}
| |
| | |
| == Nitrogen ==
| |
| Described as 140 & 1407 temperament in the 7-limit, named after the 7th element for being period-7 and also because 140 and 1407 only contain numbers 7 and 14, atomic number and atomic weight of nitrogen respectively. On top of this connection to the number 7, it also reaches 7th harmonic 7 generators down.
| |
| | |
| Subgroup: 2.3.5.7
| |
|
| |
|
| Comma list: 3955078125/3954653486, 140737488355328/140710042265625
| | {{Mapping|legend=1| 7 10 17 20 | 0 22 -15 -7 }} |
| | : mapping generators: ~1157625/1048576, ~1029/1024 |
|
| |
|
| Mapping: [{{val|7 10 17 20}}, {{val|0 22 -15 -7}}]
| | [[Optimal tuning]]s: |
| | * [[WE]]: ~1157625/1048576 = 171.4278{{c}}, ~1029/1024 = 8.5308{{c}} |
| | : [[error map]]: {{val| -0.005 +0.001 -0.002 +0.015 }} |
| | * [[CWE]]: ~1157625/1048576 = 171.4286{{c}}, ~1029/1024 = 8.5308{{c}} |
| | : error map: {{val| 0.000 +0.008 +0.010 +0.030 }} |
|
| |
|
| Mapping generators: ~1157625/1048576, ~1029/1024
| | {{Optimal ET sequence|legend=1| 140, 847, 987, 1127, 1267, 1407, 1547, 2954 }} |
|
| |
|
| Optimal tuning (CTE): ~1157625/1048576 = 1\7, ~1029/1024 = 8.531
| | [[Badness]] (Sintel): 1.50 |
|
| |
|
| {{Optimal ET sequence|legend=1|140, 1407, 1547}}, ... | | {{Navbox fractional-octave}} |
|
| |
|
| [[Category:7edo]] | | [[Category:7edo]] |
| [[Category:Temperament collections]]
| |