3.5 subgroup: Difference between revisions

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The 3.5 subgroup is a [[retraction]] of the [[5-limit]], obtained by removing prime 2. Its simplest [[expansion]] is the [[3.5.7 subgroup]], which adds prime [[7/1|7]].

If used with tritave-equivalence, it is an infinite chain of stacking the classical major sixth [[5/3]] with tritave-reduction, analogous to how [[Pythagorean tuning]] (also known as the 2.3 subgroup or 3-limit) involves stacking [[2/1]] with octave-reduction. It can be regarded as an application of the [[Pythagorean tuning]] principle (the stacking the smallest prime larger than the equave) to tritave-equivalence. The 3.5 subgroup is related to tritave-equivalent [[rank-2 ~~temperaments~~]] generated by ~[[5/3]], such as [[Arcturus]] and [[Delta Centauri]]. The famous rank 2 Bohlen-Pierce/sensamagic temperament, however, is generated by [[7/3]].

If used with [[3/1|tritave]]-equivalence, it is an infinite chain of stacking the classical major sixth [[5/3]] with tritave-reduction, analogous to how [[Pythagorean tuning]] (also known as the 2.3 subgroup or 3-limit) involves stacking [[2/1]] with octave-reduction. It can be regarded as an application of the [[Pythagorean tuning]] principle (the stacking the smallest prime larger than the equave) to tritave-equivalence. The 3.5 subgroup is related to tritave-equivalent [[rank-2 temperament]]s generated by ~[[5/3]], such as 3.5.7 [[Arcturus]] and 3.5.11 [[Delta Centauri]]. The famous rank 2 Bohlen-Pierce/sensamagic temperament, however, is generated by [[7/3]].

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	The 3.5 subgroup is a [[retraction]] of the [[5-limit]], obtained by removing prime 2. Its simplest [[expansion]] is the [[3.5.7 subgroup]], which adds prime [[7/1\|7]].		The 3.5 subgroup is a [[retraction]] of the [[5-limit]], obtained by removing prime 2. Its simplest [[expansion]] is the [[3.5.7 subgroup]], which adds prime [[7/1\|7]].

	If used with tritave-equivalence, it is an infinite chain of stacking the classical major sixth [[5/3]] with tritave-reduction, analogous to how [[Pythagorean tuning]] (also known as the 2.3 subgroup or 3-limit) involves stacking [[2/1]] with octave-reduction. It can be regarded as an application of the [[Pythagorean tuning]] principle (the stacking the smallest prime larger than the equave) to tritave-equivalence. The 3.5 subgroup is related to tritave-equivalent [[rank-2 ~~temperaments~~]] generated by ~[[5/3]], such as [[Arcturus]] and [[Delta Centauri]]. The famous rank 2 Bohlen-Pierce/sensamagic temperament, however, is generated by [[7/3]].		If used with [[3/1\|tritave]]-equivalence, it is an infinite chain of stacking the classical major sixth [[5/3]] with tritave-reduction, analogous to how [[Pythagorean tuning]] (also known as the 2.3 subgroup or 3-limit) involves stacking [[2/1]] with octave-reduction. It can be regarded as an application of the [[Pythagorean tuning]] principle (the stacking the smallest prime larger than the equave) to tritave-equivalence. The 3.5 subgroup is related to tritave-equivalent [[rank-2 temperament]]s generated by ~[[5/3]], such as 3.5.7 [[Arcturus]] and 3.5.11 [[Delta Centauri]]. The famous rank 2 Bohlen-Pierce/sensamagic temperament, however, is generated by [[7/3]].