7th-octave temperaments: Difference between revisions
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7th octave temperament | {{Technical data page}} | ||
{{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. | |||
Temperaments discussed elsewhere include: | Temperaments discussed elsewhere include: | ||
* ''[[Septant]]'' → [[Schismatic family #Septant|Schismatic family]] | |||
* ''[[Brahmagupta]]'' → [[Ragismic microtemperaments #Brahmagupta|Ragismic microtemperaments]] | |||
* ''[[Absurdity]]'' → [[Porwell temperaments #Absurdity|Porwell temperaments]] | |||
== Nitrogen == | |||
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 | |||
[[Comma list]]: 3955078125/3954653486, {{monzo| 47 -7 -7 -7 }} | |||
{{Mapping|legend=1| 7 10 17 20 | 0 22 -15 -7 }} | |||
: mapping generators: ~1157625/1048576, ~1029/1024 | |||
[[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 }} | |||
{{Optimal ET sequence|legend=1| 140, 847, 987, 1127, 1267, 1407, 1547, 2954 }} | |||
[[Badness]] (Sintel): 1.50 | |||
{{Navbox fractional-octave}} | |||
[[Category:7edo]] | [[Category:7edo]] | ||
Latest revision as of 11:47, 8 June 2026
- 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:
- Septant → Schismatic family
- Brahmagupta → Ragismic microtemperaments
- Absurdity → Porwell temperaments
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
- 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