1-5-7-9-11-15 pentadekany: Difference between revisions

Line 1:

[[File:1-5-7-9-11-15_Pentadekany.png|thumb|Circle diagram.]] [[File:1-5-7-9-11-15_Pentadekany_(rotated).png|thumb|Circle diagram (rotated).]] A [[15-odd-limit]] [[pentadekany]]. This creates a scale of 1 33/32 11/10 9/8 99/80 21/16 11/8 7/5 3/2 63/40 27/16 7/4 9/5 15/8 77/40 2/1, with steps of 33/32 16/15 45/44 11/10 35/33 22/21 56/55 15/14 21/20 15/14 28/27 36/35 25/24 77/75 80/77 2/1. With 5 perfect fifths, plus several more imperfect ones that still fall into the diatonic range, such as the [[225/224]] flat one above 15/8 and and the [[100/99]] sharp one above 99/80, this is quite strong both melodically and harmonically, with the only melodically dubious step between 11/7 & 7/5. While it does have a perfect fifth above the root, the most stable mode is probably the one above the 3/2, as that has both 5-limit major & minor chords above it.

[[File:1-5-7-9-11-15_Pentadekany.png|thumb|Circle diagram.]] [[File:1-5-7-9-11-15_Pentadekany_(rotated).png|thumb|Circle diagram (rotated).]] A [[15-odd-limit]] [[pentadekany]]. This creates a scale of 1 33/32 11/10 9/8 99/80 21/16 11/8 7/5 3/2 63/40 27/16 7/4 9/5 15/8 77/40 2/1, with steps of 33/32 16/15 45/44 11/10 35/33 22/21 56/55 15/14 21/20 15/14 28/27 36/35 25/24 77/75 80/77 2/1. With 5 perfect fifths, plus several more imperfect ones that still fall into the diatonic range, such as the [[225/224]] flat one above 15/8 and and the [[100/99]] sharp one above 99/80, this is quite strong both melodically and harmonically, with the only melodically dubious step between 11/8 & 7/5. While it does have a perfect fifth above the root, the most stable mode is probably the one above the 3/2, as that has both 5-limit major & minor chords above it.

<pre>

Revision as of 11:56, 5 March 2026 view source Yourmusic Productions (talk \| contribs) autopatrolled, emailconfirmed 2,037 edits Create Page.		Latest revision as of 17:58, 17 July 2026 view source Yourmusic Productions (talk \| contribs) autopatrolled, emailconfirmed 2,037 edits m Fix math error.
Line 1:		Line 1:
	[[File:1-5-7-9-11-15_Pentadekany.png\|thumb\|Circle diagram.]] [[File:1-5-7-9-11-15_Pentadekany_(rotated).png\|thumb\|Circle diagram (rotated).]] A [[15-odd-limit]] [[pentadekany]]. This creates a scale of 1 33/32 11/10 9/8 99/80 21/16 11/8 7/5 3/2 63/40 27/16 7/4 9/5 15/8 77/40 2/1, with steps of 33/32 16/15 45/44 11/10 35/33 22/21 56/55 15/14 21/20 15/14 28/27 36/35 25/24 77/75 80/77 2/1. With 5 perfect fifths, plus several more imperfect ones that still fall into the diatonic range, such as the [[225/224]] flat one above 15/8 and and the [[100/99]] sharp one above 99/80, this is quite strong both melodically and harmonically, with the only melodically dubious step between 11/7 & 7/5. While it does have a perfect fifth above the root, the most stable mode is probably the one above the 3/2, as that has both 5-limit major & minor chords above it.		[[File:1-5-7-9-11-15_Pentadekany.png\|thumb\|Circle diagram.]] [[File:1-5-7-9-11-15_Pentadekany_(rotated).png\|thumb\|Circle diagram (rotated).]] A [[15-odd-limit]] [[pentadekany]]. This creates a scale of 1 33/32 11/10 9/8 99/80 21/16 11/8 7/5 3/2 63/40 27/16 7/4 9/5 15/8 77/40 2/1, with steps of 33/32 16/15 45/44 11/10 35/33 22/21 56/55 15/14 21/20 15/14 28/27 36/35 25/24 77/75 80/77 2/1. With 5 perfect fifths, plus several more imperfect ones that still fall into the diatonic range, such as the [[225/224]] flat one above 15/8 and and the [[100/99]] sharp one above 99/80, this is quite strong both melodically and harmonically, with the only melodically dubious step between 11/8 & 7/5. While it does have a perfect fifth above the root, the most stable mode is probably the one above the 3/2, as that has both 5-limit major & minor chords above it.

	<pre>		<pre>