Deneb: Difference between revisions

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=== Add 8 ===

5 generators stacked actually is a very good approximation of [[8/3]], so if you're okay with introducing limited factors of 2, Deneb can be easily extended to the 3.8.5.11 subgroup (or using the technically "canonical" ordering, 8.3.5.11, but using [[8/1]] as an equivalence would be rather impractical). This extension tempers out [[121/120]] and [[2200/2187]] and is related to the octave-repeating [[amity]]/[[hitchcock]] temperament. Interestingly, in the 3.5.8.11 extension, ~[[8/1]] = ~[[55/27]]<sup>2</sup> * ~[[64/33]], with ~55/27 being the aforementioned sharp quasi-octave, and ~64/33 being the undecimal infraoctave. Furthermore, ~55/27 and ~64/33 share the same scale degree in Deneb[11].

5 generators stacked actually is a very good approximation of [[8/3]], so if you're okay with introducing limited factors of 2, Deneb can be easily extended to the 3.8.5.11 subgroup (or using the technically "canonical" ordering, 8.3.5.11, but using [[8/1]] as an equivalence would be rather impractical). This extension tempers out [[121/120]] and [[2200/2187]] and is related to the octave-repeating [[amity]]/[[hitchcock]] temperament. Interestingly, in the 3.8.5.11 extension, ~[[8/1]] = ~[[55/27]]<sup>2</sup> * ~[[64/33]], with ~55/27 being the aforementioned sharp quasi-octave, and ~64/33 being the undecimal infraoctave. Furthermore, ~55/27 and ~64/33 share the same scale degree in Deneb[11].

== Interval chain ==

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 === Add 8 ===
-generators stacked actually is a very good approximation of [[8/3]], so if you're okay with introducing limited factors of 2, Deneb can be easily extended to the 3.8.5.11 subgroup (or using the technically "canonical" ordering, 8.3.5.11, but using [[8/1]] as an equivalence would be rather impractical). This extension tempers out [[121/120]] and [[2200/2187]] and is related to the octave-repeating [[amity]]/[[hitchcock]] temperament. Interestingly, in the 3.5.8.11 extension, ~[[8/1]] = ~[[55/27]]<sup>2</sup> * ~[[64/33]], with ~55/27 being the aforementioned sharp quasi-octave, and ~64/33 being the undecimal infraoctave. Furthermore, ~55/27 and ~64/33 share the same scale degree in Deneb[11].
+generators stacked actually is a very good approximation of [[8/3]], so if you're okay with introducing limited factors of 2, Deneb can be easily extended to the 3.8.5.11 subgroup (or using the technically "canonical" ordering, 8.3.5.11, but using [[8/1]] as an equivalence would be rather impractical). This extension tempers out [[121/120]] and [[2200/2187]] and is related to the octave-repeating [[amity]]/[[hitchcock]] temperament. Interestingly, in the 3.8.5.11 extension, ~[[8/1]] = ~[[55/27]]<sup>2</sup> * ~[[64/33]], with ~55/27 being the aforementioned sharp quasi-octave, and ~64/33 being the undecimal infraoctave. Furthermore, ~55/27 and ~64/33 share the same scale degree in Deneb[11].
 == Interval chain ==

Deneb: Difference between revisions

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