Merciful intonation: Difference between revisions
Cmloegcmluin (talk | contribs) add footnote per Dave's request and spruce up the math expressions |
Dave Keenan (talk | contribs) Introduced the idea that MI is a kind of anti-JI, thanks to Mike Battaglia |
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'''Merciful Intonation (MI)''' is intonation | '''Merciful Intonation (MI)''' is a kind of '''anti-just intonation (anti-JI)'''. Merciful intonation stands in contrast to [[Just Intonation|Just Intonation (JI)]] by using [https://mathworld.wolfram.com/NobleNumber.html noble number] frequency ratios as a way of maximally avoiding coinciding harmonics. It was first systematically described by [[Margo Schulter]] and [[Dave Keenan]]. | ||
Specifically, the noble (phi-weighted) [[mediant]] between two nearby<ref>For the phi-weighted mediant to give a noble number, it is necessary that the two ratios <span><math>\frac{n_1}{d_1}</math></span> and <span><math>\frac{n_2}{d_2}</math></span> satisfy the equation <span><math>|n_{1}d_{2}-d_{1}n_{2}| = 1</math></span>. | Specifically, the noble (phi-weighted) [[mediant]] between two nearby<ref>For the phi-weighted mediant to give a noble number, it is necessary that the two ratios <span><math>\frac{n_1}{d_1}</math></span> and <span><math>\frac{n_2}{d_2}</math></span> satisfy the equation <span><math>|n_{1}d_{2}-d_{1}n_{2}| = 1</math></span>. | ||