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| 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]] |
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| == Jamesbond ==
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| 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]]" (a kind of mathematical object representing the temperament) starts with {{multival| 0 0 7 … }} (in fact, it is {{multival| 0 0 7 0 11 16 }})
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| [[Subgroup]]: 2.3.5.7
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| [[Comma list]]: 25/24, 81/80
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| {{Mapping|legend=1| 7 11 16 0 | 0 0 0 1 }}
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| : mapping generators: ~10/9, ~7
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| [[Optimal tuning]]s:
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| * [[WE]]: ~10/9 = 172.790{{c}}, ~7/4 = 949.343{{c}}
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| : [[error map]]: {{val| +9.533 -1.261 -21.668 -0.418 }}
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| * [[CWE]]: ~10/9 = 171.429{{c}}, ~7/4 = 948.499{{c}}
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| : error map: {{val| -0.000 -16.241 -43.457 -20.327 }}
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| {{Optimal ET sequence|legend=1| 7(d), 14c }}
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| [[Badness]] (Sintel): 1.06
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| === 11-limit ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 25/24, 33/32, 45/44
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| Mapping: {{mapping| 7 11 16 0 24 | 0 0 0 1 0 }}
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| Optimal tunings:
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| * WE: ~10/9 = 172.830{{c}}, ~7/4 = 948.784{{c}}
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| * CWE: ~10/9 = 171.429{{c}}, ~7/4 = 946.554{{c}}
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| {{Optimal ET sequence|legend=1| 7(d), 14c }}
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| Badness (Sintel): 0.778
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| ==== 13-limit ====
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 25/24, 27/26, 33/32, 40/39
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| Mapping: {{mapping| 7 11 16 0 24 26 | 0 0 0 1 0 0 }}
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| Optimal tunings:
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| * WE: ~10/9 = 172.390{{c}}, ~7/4 = 954.559{{c}}
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| * CWE: ~10/9 = 171.429{{c}}, ~7/4 = 952.367{{c}}
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| {{Optimal ET sequence|legend=1| 7(d), 14c }}
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| Badness (Sintel): 0.951
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| ==== Austinpowers ====
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| Subgroup: 2.3.5.7.11.13
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| Comma list: 25/24, 33/32, 45/44, 65/63
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| Mapping: {{mapping| 7 11 16 0 24 6 | 0 0 0 1 0 1 }}
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| Optimal tunings:
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| * WE: ~10/9 = 172.873{{c}}, ~7/4 = 960.581{{c}}
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| * CWE: ~10/9 = 171.429{{c}}, ~7/4 = 958.793{{c}}
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| {{Optimal ET sequence|legend=1| 7(df), 14cf }}
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| Badness (Sintel): 0.933
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| == Akjaysmic (rank-3) ==
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| {{See also| Akjaysma }}
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| [[Subgroup]]: 2.3.5.7
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| [[Comma list]]: {{monzo| 47 -7 -7 -7 }}
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| {{Mapping|legend=1| 7 0 0 47 | 0 1 0 -1 | 0 0 1 -1 }}
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| : mapping generators: ~1157625/1048576, ~3, ~5
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| [[Optimal tuning]]s:
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| * [[WE]]: ~1157625/1048576 = 171.427811{{c}}, ~3/2 = 701.962313{{c}}, ~5/4 = 386.328628{{c}}
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| : [[error map]]: {{val| -0.0053 +0.0020 +0.0043 +0.0062 }}
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| * [[CWE]]: ~1157625/1048576 = 171.428571{{c}}, ~3/2 = 701.964859{{c}}, ~5/4 = 386.330310{{c}}
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| : error map: {{val| 0.0000 +0.0099 +0.0166 +0.0218 }}
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| {{Optimal ET sequence|legend=1| 56, 63, 77, 84, 140, 217, 224, 301, 441, 966, 1106, 1407, 1547, 1848, 2513, 2954, 6349, 9303, 11151, 14105, 17500, 20454 }}
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| [[Badness]] (Sintel): 2.22
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| === 11-limit ===
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| Subgroup: 2.3.5.7.11
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| Comma list: 184549376/184528125, 199297406/199290375
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| Mapping: {{mapping| 7 0 0 47 -168 | 0 1 0 -1 10 | 0 0 1 -1 5 }}
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| : mapping generators: ~29160/26411, ~3, ~5
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| Optimal tunings:
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| * WE: ~29160/26411 = 171.427802{{c}}, ~3/2 = 701.964561{{c}}, ~5/4 = 386.329837{{c}}
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| * CWE: ~29160/26411 = 171.428571{{c}}, ~3/2 = 701.967291{{c}}, ~5/4 = 386.331624{{c}}
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| {{Optimal ET sequence|legend=0| 301, 441, 665e, 742, 1106, 1547, 1848, 3395, 4501, 5243, 6349, 17941, 24290, 30639, 45185cde, 63126bcde, 69475bccdde, 75824bccddee }}
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| Badness (Sintel): 1.32
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| == Nitrogen == | | == Nitrogen == |
- 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.
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.
Temperaments discussed elsewhere include:
Nitrogen
Nitrogen may be described as the 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
Comma list: 3955078125/3954653486, [47 -7 -7 -7⟩
Mapping: [⟨7 10 17 20], ⟨0 22 -15 -7]]
- mapping generators: ~1157625/1048576, ~1029/1024
Optimal tunings:
- WE: ~1157625/1048576 = 171.4278 ¢, ~1029/1024 = 8.5308 ¢
- error map: ⟨-0.005 +0.001 -0.002 +0.015]
- CWE: ~1157625/1048576 = 171.4286 ¢, ~1029/1024 = 8.5308 ¢
- error map: ⟨0.000 +0.008 +0.010 +0.030]
Optimal ET sequence: 140, 847, 987, 1127, 1267, 1407, 1547, 2954
Badness (Sintel): 1.50