8th-octave temperaments: Difference between revisions

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An 8th-octave temperament can be described by temperament merging of edos whose greatest common divisor is 8.
An 8th-octave temperament can be described by temperament merging of edos whose greatest common divisor is 8.


Discussed elsewhere are:
Temperaments discussed elsewhere include:
* ''Octant'', → [[Schismatic family#Octant|Schismatic family]]
* ''[[Octant]]'' → [[Schismatic family #Octant|Schismatic family]]
* ''Octoid'', → [[Ragismic microtemperaments#Octoid|Ragismic microtemperaments]]
* ''[[Octonion]]'' → [[Diminished family #Octonion|Diminished family]]
 
* ''[[Twilight]]'' → [[Undim family #Twilight|Undim family]]
== Octatonic ==
* [[Octoid]] → [[Ragismic microtemperaments #Octoid|Ragismic microtemperaments]]
[[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]].
* ''[[Octatonic (temperament)|Octatonic]]'' → [[No-fives subgroup temperaments #Octatonic|No-fives subgroup temperaments]]
 
Subgroup: 2.3.11
 
Comma list: {{monzo|15 8 0 0 -8}}
 
{{Mapping|legend=1|8 0 15|0 1 1}}
 
: 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}}

Latest revision as of 07:04, 5 July 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.

← 7th-octave • 8th-octave • 9th-octave →

An 8th-octave temperament can be described by temperament merging of edos whose greatest common divisor is 8.

Temperaments discussed elsewhere include:

View • Talk • EditFractional-octave temperaments 
← 3rd • 4th • 5th • 6th • 7th • 8th-octave • 9th • 10th • 11th • 12th • 13th →
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