Metallic MOS: Difference between revisions

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=== Beyond golden cases ===
=== Beyond golden cases ===


The silver generator, as it did for its <span><math>L{:}s</math></span> sequence, alternates in quality between its two > 1 isotopes for its intervals. For half of its scales,
The silver generator, as it did for its <span><math>L{:}s</math></span> sequence, alternates in quality between its two <span><math>>1</math></span> isotopes for its intervals. For half of its scales,


<math> L{:}s = (2L+s):L = (5L+2s):(2L+s) = (12L+5s):(5L+2s) = (29L+12s):(12L+5s) = = δ_s
<math>
δ_s =
\begin{align}
\begin{cases}
L&:s \\
2L+s&:L \\
5L+2s&:2L+s \\
12L+5s&:5L+2s \\
29L+12s&:12L+5s \\
\\
\end{cases}
\end{align}
</math>
</math>


and the other half,  
and the other half,  


<math>\qquad L{:}s = (L+2s):(L+s) = (3L+4s):(2L+3s) = (7L+10s):(5L+7s) = (17L+24s):(12L+17s) = = δ_s - 1
<math>
δ_s - 1 =
\begin{align}
\begin{cases}
L&:s \\
L+2s&:L+s \\
3L+4s&:2L+3s \\
7L+10s&:5L+7s \\
17L+24s&:12L+17s \\
\\
\end{cases}
\end{align}
</math>
</math>


Bronze’s scales cycle through three different interval patterns related to its respective > 1 isotopes.  
Bronze’s scales cycle through three different interval patterns related to its respective <span><math>>1</math></span> isotopes.  


This pattern continues for other metallic means. As another entry to our family of sequence terms (along with scale sequence and <span><math>L{:}s</math></span> sequence) we shall use the term ''interval pattern sequence'', and for the periodic part at the end, the ''interval pattern cycle''.
This pattern continues for other metallic means. As another entry to our family of sequence terms (along with scale sequence and <span><math>L{:}s</math></span> sequence) we shall use the term ''interval pattern sequence'', and for the periodic part at the end, the ''interval pattern cycle''.