3-5-11-15 by 21/11 bihexany: Difference between revisions

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[[File:3-5-11-15_by_21-11_Bihexany.png|thumb|Circle diagram.]] An [[11-limit]] [[bihexany]]. This creates a scale of 1 21/20 11/10 105/88 5/4 21/16 11/8 63/44 3/2 7/4 11/6 21/11 2/1, with steps of 21/20 22/21 525/484 22/21 21/20 22/21 126/121 22/21 7/6 22/21 126/121 22/21. Since half the steps in the base hexany have 11 as the numerator, this cancels out those factors to produce a string of simple ratios that fit neatly in the gaps between the smallest steps, producing long strings of approximately 80 cent semitones that are highly effective melodically, separated by a couple of larger gaps. It does only have four perfect fifths though, and these are all clustered in one quarter of the scale, making this a heavily modal scale that is excellent melodically but not able to modulate to produce chord sequences in the way that ones based on chains of fifths are.

[[File:3-5-11-15_by_21-11_Bihexany.png|thumb|Circle diagram.]] An [[11-limit]] [[bihexany]]. This creates a scale of 1 21/20 11/10 105/88 5/4 21/16 11/8 63/44 3/2 7/4 11/6 21/11 2/1, with steps of 21/20 22/21 525/484 22/21 21/20 22/21 126/121 22/21 7/6 22/21 126/121 22/21. Since half the steps in the [[3-5-11-15_hexany|base hexany]] have 11 as the numerator, this cancels out those factors to produce a string of simple ratios that fit neatly in the gaps between the smallest steps, producing long strings of approximately 80 cent semitones that are highly effective melodically, separated by a couple of larger gaps. It does only have four perfect fifths though, and these are all clustered in one quarter of the scale, making this a heavily modal scale that is excellent melodically but not able to modulate to produce chord sequences in the way that ones based on chains of fifths are.

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	[[File:3-5-11-15_by_21-11_Bihexany.png\|thumb\|Circle diagram.]] An [[11-limit]] [[bihexany]]. This creates a scale of 1 21/20 11/10 105/88 5/4 21/16 11/8 63/44 3/2 7/4 11/6 21/11 2/1, with steps of 21/20 22/21 525/484 22/21 21/20 22/21 126/121 22/21 7/6 22/21 126/121 22/21. Since half the steps in the base hexany have 11 as the numerator, this cancels out those factors to produce a string of simple ratios that fit neatly in the gaps between the smallest steps, producing long strings of approximately 80 cent semitones that are highly effective melodically, separated by a couple of larger gaps. It does only have four perfect fifths though, and these are all clustered in one quarter of the scale, making this a heavily modal scale that is excellent melodically but not able to modulate to produce chord sequences in the way that ones based on chains of fifths are.		[[File:3-5-11-15_by_21-11_Bihexany.png\|thumb\|Circle diagram.]] An [[11-limit]] [[bihexany]]. This creates a scale of 1 21/20 11/10 105/88 5/4 21/16 11/8 63/44 3/2 7/4 11/6 21/11 2/1, with steps of 21/20 22/21 525/484 22/21 21/20 22/21 126/121 22/21 7/6 22/21 126/121 22/21. Since half the steps in the [[3-5-11-15_hexany\|base hexany]] have 11 as the numerator, this cancels out those factors to produce a string of simple ratios that fit neatly in the gaps between the smallest steps, producing long strings of approximately 80 cent semitones that are highly effective melodically, separated by a couple of larger gaps. It does only have four perfect fifths though, and these are all clustered in one quarter of the scale, making this a heavily modal scale that is excellent melodically but not able to modulate to produce chord sequences in the way that ones based on chains of fifths are.

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