Merciful intonation: Difference between revisions
Cmloegcmluin (talk | contribs) Created page with "'''Merciful Intonation (MI)''' is intonation which stands in contrast to Just Intonation (JI), by using [https://mathworld.wolfram.com/NobleNumber.html nob..." |
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'''Merciful Intonation (MI)''' is intonation which 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]]. | '''Merciful Intonation (MI)''' is intonation which 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 JI intervals is taken. For example, the noble mediant between 5/4 ≈386.3¢ and 9/7 ≈435.1¢ is equal to (5 + 9ɸ):(4 + 7ɸ) ≈422.5¢. | Specifically, the noble (phi-weighted) [[mediant]] between two nearby JI intervals is taken. For example, the noble mediant between 5/4 ≈386.3¢ and 9/7 ≈435.1¢ is equal to (5 + 9ɸ):(4 + 7ɸ) ≈422.5¢. | ||
An MI interval may also be referred to as a "metastable interval", by analogy with [https://en.wikipedia.org/wiki/Metastability the physics concept] whereby opposing gravitational pulls on an object are balanced, insofar as the noble mediant is the interval which is placed at the precise point between the two JI intervals such that it sensed as equally distant from both of them. Such intervals are often near [[harmonic entropy]] maxima. | An MI interval may also be referred to as a "metastable interval", by analogy with [https://en.wikipedia.org/wiki/Metastability the physics concept] whereby opposing gravitational pulls on an object are balanced, insofar as the noble mediant is the interval which is placed at the precise point between the two JI intervals such that it sensed as equally distant from both of them. Such intervals are often near [[harmonic entropy]] maxima. | ||