Metallic MOS: Difference between revisions

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</math>

In some materials, the weighted mediant between two ratios using <math>φ</math> as the weight is referred to as the value "phi-way" between these two ratios. This analogy with the word "halfway" is misleading, because while the value halfway between two ratios splits the length into two segments which each are half of the total length, with the weighted mediant, the value splits the length into two segments neither of which is <math>φ</math> of the total length. In fact, that would not be possible, because while half is less than one, <math>φ</math> is greater than one, and part of a length can never be greater than the whole length. An alternative phrasing could be: the value <math>φ</math>-weighted from <math>\frac{a_1}{a_2}</math> to <math>\frac{b_1}{b_2}</math>~~. Besides~~ eschewing the misleading association with "halfway", another advantage of this nomenclature is its ability to specify, via the from/to, which direction the mediant is weighted.

In some materials, the weighted mediant between two ratios using <math>φ</math> as the weight is referred to as the value "phi-way" between these two ratios. This analogy with the word "halfway" is misleading, because while the value halfway between two ratios splits the length into two segments which each are half of the total length, with the weighted mediant, the value splits the length into two segments neither of which is <math>φ</math> of the total length. In fact, that would not be possible, because while half is less than one, <math>φ</math> is greater than one, and part of a length can never be greater than the whole length. An alternative phrasing could be: the value <math>φ</math>-weighted from <math>\frac{a_1}{a_2}</math> to <math>\frac{b_1}{b_2}</math>; besides eschewing the misleading association with "halfway", another advantage of this nomenclature is its ability to specify, via the from/to, which direction the mediant is weighted. Another potential name for this construct is the "phidiant" (or "<math>φ</math>-diant") from <math>\frac{a_1}{a_2}</math> to <math>\frac{b_1}{b_2}</math>, which is especially nice if you a person who pronounces <math>φ</math> like /fiː/ (the same as "fee").

=== As a bizarro average ===

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 </math>
-In some materials, the weighted mediant between two ratios using <span><math>φ</math></span> as the weight is referred to as the value "phi-way" between these two ratios. This analogy with the word "halfway" is misleading, because while the value halfway between two ratios splits the length into two segments which each are half of the total length, with the weighted mediant, the value splits the length into two segments neither of which is <span><math>φ</math></span> of the total length. In fact, that would not be possible, because while half is less than one, <span><math>φ</math></span> is greater than one, and part of a length can never be greater than the whole length. An alternative phrasing could be: the value <span><math>φ</math></span>-weighted from <span><math>\frac{a_1}{a_2}</math></span> to <span><math>\frac{b_1}{b_2}</math></span>. Besides eschewing the misleading association with "halfway", another advantage of this nomenclature is its ability to specify, via the from/to, which direction the mediant is weighted.
+In some materials, the weighted mediant between two ratios using <span><math>φ</math></span> as the weight is referred to as the value "phi-way" between these two ratios. This analogy with the word "halfway" is misleading, because while the value halfway between two ratios splits the length into two segments which each are half of the total length, with the weighted mediant, the value splits the length into two segments neither of which is <span><math>φ</math></span> of the total length. In fact, that would not be possible, because while half is less than one, <span><math>φ</math></span> is greater than one, and part of a length can never be greater than the whole length. An alternative phrasing could be: the value <span><math>φ</math></span>-weighted from <span><math>\frac{a_1}{a_2}</math></span> to <span><math>\frac{b_1}{b_2}</math></span>; besides eschewing the misleading association with "halfway", another advantage of this nomenclature is its ability to specify, via the from/to, which direction the mediant is weighted. Another potential name for this construct is the "phidiant" (or "<span><math>φ</math></span>-diant") from <span><math>\frac{a_1}{a_2}</math></span> to <span><math>\frac{b_1}{b_2}</math></span>, which is especially nice if you a person who pronounces <span><math>φ</math></span> like /fiː/ (the same as "fee").
 === As a bizarro average ===