15/14: Difference between revisions
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"7-limit" |
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'''15/14''' is a [[superparticular]] ratio with a numerator which is the fifth [[triangular number]]. It may be found as the interval between many [[7-limit]] ratios, including: | '''15/14''' is a [[superparticular]] ratio with a numerator which is the fifth [[triangular number]]. It may be found as the interval between many [[7-limit]] ratios, including: | ||
* [[16/15]] and [[8/7]] | * [[16/15]] and [[8/7]] | ||
* [[7/6]] and [[5/4]] | * [[7/6]] and [[5/4]] | ||
* [[6/5]] and [[9/7]] | * [[6/5]] and [[9/7]] | ||
* [[4/3]] and [[10/7]] | * [[4/3]] and [[10/7]] | ||
* [[7/5]] and [[3/2]] | * [[7/5]] and [[3/2]] | ||
* [[14/9]] and [[5/3]] | * [[14/9]] and [[5/3]] | ||
* [[8/5]] and [[12/7]] | * [[8/5]] and [[12/7]] | ||
* [[7/4]] and [[15/8]] | |||
It also arises in higher limits as: | |||
* [[14/13]] and [[15/13]] | |||
* [[14/11]] and [[15/11]] | |||
* [[22/15]] and [[11/7]] | |||
* [[26/15]] and [[13/7]] | * [[26/15]] and [[13/7]] | ||
In combination with [[19/17]] it forms a good approximation of [[golden meantone]]. The untempered combination of five 19/17 and two 15/14 leads to an interval that is sharp to an octave by the [[mercurial comma]]: <code>((19/17)^5 * (15/14)^2 = (2/1) / (mercurial comma))</code> | In combination with [[19/17]] it forms a good approximation of [[golden meantone]]. The untempered combination of five 19/17 and two 15/14 leads to an interval that is sharp to an octave by the [[mercurial comma]]: <code>((19/17)^5 * (15/14)^2 = (2/1) / (mercurial comma))</code> | ||