Tetracot family: Difference between revisions

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{{Technical data page}}

The parent of the '''tetracot family''' is [[tetracot]], the 5-limit temperament [[tempering out]] [[20000/19683]] = {{monzo| 5 -9 4 }}, the minimal diesis or tetracot comma. The dual of this comma is the wedgie {{multival| 4 9 5 }}, which tells us [[~]][[10/9]] is a generator, and that four of them give [[~]][[3/2]]. In fact, (10/9)4 = 20000/19683 × 3/2. We also have (10/9)9 = (20000/19683)2 × 5/2. From this it is evident we should flatten the generator a bit, and [[34edo]] does this and makes for a recommendable tuning. Another possibility is to use (5/2)1/9 for a generator. The 13-note [[mos]] gives enough space for eight triads, with the 20-note mos supplying many more.

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			{{Technical data page}}<br><br>
	The parent of the '''tetracot family''' is [[tetracot]], the 5-limit temperament [[tempering out]] [[20000/19683]] = {{monzo\| 5 -9 4 }}, the minimal diesis or tetracot comma. The dual of this comma is the wedgie {{multival\| 4 9 5 }}, which tells us [[~]][[10/9]] is a generator, and that four of them give [[~]][[3/2]]. In fact, (10/9)<sup>4</sup> = 20000/19683 × 3/2. We also have (10/9)<sup>9</sup> = (20000/19683)<sup>2</sup> × 5/2. From this it is evident we should flatten the generator a bit, and [[34edo]] does this and makes for a recommendable tuning. Another possibility is to use (5/2)<sup>1/9</sup> for a generator. The 13-note [[mos]] gives enough space for eight triads, with the 20-note mos supplying many more.		The parent of the '''tetracot family''' is [[tetracot]], the 5-limit temperament [[tempering out]] [[20000/19683]] = {{monzo\| 5 -9 4 }}, the minimal diesis or tetracot comma. The dual of this comma is the wedgie {{multival\| 4 9 5 }}, which tells us [[~]][[10/9]] is a generator, and that four of them give [[~]][[3/2]]. In fact, (10/9)<sup>4</sup> = 20000/19683 × 3/2. We also have (10/9)<sup>9</sup> = (20000/19683)<sup>2</sup> × 5/2. From this it is evident we should flatten the generator a bit, and [[34edo]] does this and makes for a recommendable tuning. Another possibility is to use (5/2)<sup>1/9</sup> for a generator. The 13-note [[mos]] gives enough space for eight triads, with the 20-note mos supplying many more.