32/27: Difference between revisions
→See also: +5th complement |
Hotcrystal0 (talk | contribs) Mention alteraugment |
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{{Infobox Interval | {{Infobox Interval | ||
| Name = Pythagorean minor third | | Name = Pythagorean minor third | ||
| Color name = w3, wa 3rd | | Color name = w3, wa 3rd | ||
| Line 9: | Line 5: | ||
}} | }} | ||
The '''Pythagorean minor third''' of '''32/27''' is the interval between [[9/8]] and [[4/3]] which arises naturally in [[3-limit]] just intonation. | The '''Pythagorean minor third''' of '''32/27''' is the interval between [[9/8]] and [[4/3]] which arises naturally in [[3-limit]] [[just intonation]]. Compared to the more typical [[6/5]]- with which it is conflated in [[meantone]]- this interval is more dissonant, with a [[harmonic entropy]] level roughly on par with that of 9/8. | ||
It is 352/351 sharp of [[13/11]], and tempering 352/351 out equates it with 13/11 and leads to [[minthmic chords]]. | |||
== Temperaments == | |||
32/27 is treated as a comma in edos 3 & 6, where the best approximation of a perfect 5th is the 800 cent interval that wraps around to the octave again after only three iterations, producing [[alteraugment]]. Temperaments it can be interpreted as if used as a generator include [[Kleismic_family#Kleiboh|Kleiboh]] or [[Gariberttet]]. | |||
== Approximation == | |||
{{Interval edo approximation|32/27}} | |||
== See also == | == See also == | ||
* [[ | * [[27/16]] – its [[octave complement]] | ||
* [[ | * [[81/64]] – its [[fifth complement]] | ||
* [[ | * [[9/8]] – its [[fourth complement]] | ||
* [[Gallery of just intervals]] | |||
* [[Pythagorean tuning]] | |||
[[Category:Third]] | [[Category:Third]] | ||
[[Category:Minor third]] | [[Category:Minor third]] | ||