|
|
| (7 intermediate revisions by 3 users not shown) |
| Line 1: |
Line 1: |
| {{Fractional-octave navigation|8}} | | {{Technical data page}} |
| Discussed elsewhere are:
| | {{Infobox fractional-octave|8}} |
| * ''Octant'', → [[Schismatic family#Octant|Schismatic family]]
| | An 8th-octave temperament can be described by temperament merging of edos whose greatest common divisor is 8. |
| * ''Octoid'', → [[Ragismic microtemperaments#Octoid|Ragismic microtemperaments]]
| |
| == Octatonic ==
| |
| [[12/11]] is very close to 1 step of 8edo, and hence this temperament tempers out the octatonic comma, the difference between a stack of 8 12/11's and the octave. The octatonic temperament makes a [[consistent circle]].
| |
|
| |
|
| Subgroup: 2.3.11
| | Temperaments discussed elsewhere include: |
| | | * ''[[Octant]]'' → [[Schismatic family #Octant|Schismatic family]] |
| Comma list: {{monzo|15 8 0 0 -8}}
| | * ''[[Octonion]]'' → [[Diminished family #Octonion|Diminished family]] |
| | | * ''[[Twilight]]'' → [[Undim family #Twilight|Undim family]] |
| {{Mapping|legend=1|8 0 15|0 1 1}}
| | * [[Octoid]] → [[Ragismic microtemperaments #Octoid|Ragismic microtemperaments]] |
| | | * ''[[Octatonic (temperament)|Octatonic]]'' → [[No-fives subgroup temperaments #Octatonic|No-fives subgroup temperaments]] |
| : mapping generators: ~12/11 = 1\8, ~3
| |
| | |
| [[Support]]ing [[ET]]s: {{EDOs|16, 24, 32, 48, 56, 80, 72, 120, 128, 152}}, ... | |
| | |
| == Octium ==
| |
| Octium temperament is named after an "extended provisional" name for oxygen, the 8th element. The term [[oxygen]] itself is already the name of an exotemperament. It reaches [[24/23]] in one generator and [[19/16]] in two.
| |
| | |
| Subgroup: 2.3.19.23.29.31
| |
| | |
| Comma list: 94221/94208, 419957/419904, 219501/219488, 7997934975003/7996960669696
| |
| | |
| {{Mapping|legend=2| 8 2 35 25 47 2 | 0 21 -2 22 -16 74 }}
| |
| | |
| : mapping generators: ~10051/9216 = 1\8, ~24/23 = 76.284
| |
| | |
| [[Optimal tuning]] ([[CTE]]): ~24/23 = 76.284 | |
| | |
| [[Support]]ing [[ET]]s: {{EDOs|472, 1400, 1872, 3272, 5144}} | |
| | |
| == Octoid (5-limit) ==
| |
| ''For the 7-limit temperament, see [[Ragismic microtemperaments#Octoid]].''
| |
| | |
| Subgroup: 2.3.5
| |
| | |
| Comma list: 59604644775390625/59296646043258912
| |
| | |
| {{Mapping|legend=2| 8 1 3 | 0 3 4 }}
| |
| | |
| [[Optimal tuning]] ([[CWE]]): ~2125764/1953125 = 1\8, ~4374/3125 = 584.025 | |
| | |
| [[Support]]ing [[ET]]s: {{EDOs|8, 152, 224, 72, 376, 80, 600, 528, 296, 64c, 232, 88bc, 824, 680}}
| |
|
| |
|
| {{Navbox fractional-octave}} | | {{Navbox fractional-octave}} |
- 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.
An 8th-octave temperament can be described by temperament merging of edos whose greatest common divisor is 8.
Temperaments discussed elsewhere include: