1-3-5-7-9-15 pentadekany: Difference between revisions

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[[File:1-3-5-7-9-15_Pentadekany.png|thumb|Circle diagram.]] The simplest possible [[15-odd-limit]] [[pentadekany]]. This creates a scale of 1 35/32 9/8 7/6 5/4 21/16 45/32 35/24 3/2 25/16 5/3 7/4 15/8 2/1, with steps of 35/32 36/35 28/27 15/14 21/20 15/14 28/27 36/35 25/24 16/15 21/20 15/14 16/15. As with hexanies and dekanies, the 15-odd limit is where we start to see combination product sets with duplicated notes. ((5/4 and 15/8 both appear twice here, reducing it to a 13 note scale) This does at least mean there are no intervals smaller than a quartertone and many simple chords available, but there are still more notes than can fit on a standard keyboard, requiring you to either leave one out to map it in a regular fashion or get used to each note being in a different place as you move from one octave to another.

[[File:1-3-5-7-9-15_Pentadekany.png|thumb|Circle diagram.]] The simplest possible [[15-odd-limit]] [[pentadekany]]. This creates a scale of 1 35/32 9/8 7/6 5/4 21/16 45/32 35/24 3/2 25/16 5/3 7/4 15/8 2/1, with steps of 35/32 36/35 28/27 15/14 21/20 15/14 28/27 36/35 25/24 16/15 21/20 15/14 16/15. As with hexanies and dekanies, the 15-odd limit is where we start to see combination product sets with duplicated notes. (5/4 and 15/8 both appear twice here, reducing it to a 13 note scale.) This does at least mean there are no intervals smaller than a quartertone and many simple chords available, but there are still more notes than can fit on a standard keyboard, requiring you to either leave one out to map it in a regular fashion or get used to each note being in a different place as you move from one octave to another.

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	[[File:1-3-5-7-9-15_Pentadekany.png\|thumb\|Circle diagram.]] The simplest possible [[15-odd-limit]] [[pentadekany]]. This creates a scale of 1 35/32 9/8 7/6 5/4 21/16 45/32 35/24 3/2 25/16 5/3 7/4 15/8 2/1, with steps of 35/32 36/35 28/27 15/14 21/20 15/14 28/27 36/35 25/24 16/15 21/20 15/14 16/15. As with hexanies and dekanies, the 15-odd limit is where we start to see combination product sets with duplicated notes. ((5/4 and 15/8 both appear twice here, reducing it to a 13 note scale) This does at least mean there are no intervals smaller than a quartertone and many simple chords available, but there are still more notes than can fit on a standard keyboard, requiring you to either leave one out to map it in a regular fashion or get used to each note being in a different place as you move from one octave to another.		[[File:1-3-5-7-9-15_Pentadekany.png\|thumb\|Circle diagram.]] The simplest possible [[15-odd-limit]] [[pentadekany]]. This creates a scale of 1 35/32 9/8 7/6 5/4 21/16 45/32 35/24 3/2 25/16 5/3 7/4 15/8 2/1, with steps of 35/32 36/35 28/27 15/14 21/20 15/14 28/27 36/35 25/24 16/15 21/20 15/14 16/15. As with hexanies and dekanies, the 15-odd limit is where we start to see combination product sets with duplicated notes. (5/4 and 15/8 both appear twice here, reducing it to a 13 note scale.) This does at least mean there are no intervals smaller than a quartertone and many simple chords available, but there are still more notes than can fit on a standard keyboard, requiring you to either leave one out to map it in a regular fashion or get used to each note being in a different place as you move from one octave to another.

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