Logarithmic approximants: Difference between revisions
Wikispaces>MartinGough **Imported revision 563715177 - Original comment: ** |
Wikispaces>MartinGough **Imported revision 563715357 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User:MartinGough|MartinGough]] and made on <tt>2015-10-24 06: | : This revision was by author [[User:MartinGough|MartinGough]] and made on <tt>2015-10-24 06:13:51 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>563715357</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
| Line 383: | Line 383: | ||
\qquad \frac{q[10/7]}{q[7/5]}= \frac{ \tfrac{3} {2\sqrt{70}} } { \tfrac{2} {2\sqrt{35}} } = \tfrac{3}{2\sqrt{2}}. | \qquad \frac{q[10/7]}{q[7/5]}= \frac{ \tfrac{3} {2\sqrt{70}} } { \tfrac{2} {2\sqrt{35}} } = \tfrac{3}{2\sqrt{2}}. | ||
[[math]] | [[math]] | ||
This means that in | This means that in argent temperament the augmented fourth is very close to 10/7 and the diminished fifth is very close to 7/5. The discrepancy in each case is just 0.175 cents. | ||
Another way to express the first of these relationships is | Another way to express the first of these relationships is | ||
[[math]] | [[math]] | ||
\qquad 3 (\tfrac{1}{2\sqrt{6}} – \tfrac{1}{4\sqrt{3}}) ≈ \tfrac{3}{2\sqrt{70}}, | \qquad 3 (\tfrac{1}{2\sqrt{6}} – \tfrac{1}{4\sqrt{3}}) ≈ \tfrac{3}{2\sqrt{70}}, | ||
[[math]] | [[math]] | ||
| Line 1,076: | Line 1,075: | ||
\qquad \frac{q[10/7]}{q[7/5]}= \frac{ \tfrac{3} {2\sqrt{70}} } { \tfrac{2} {2\sqrt{35}} } = \tfrac{3}{2\sqrt{2}}.&lt;br/&gt;[[math]] | \qquad \frac{q[10/7]}{q[7/5]}= \frac{ \tfrac{3} {2\sqrt{70}} } { \tfrac{2} {2\sqrt{35}} } = \tfrac{3}{2\sqrt{2}}.&lt;br/&gt;[[math]] | ||
--><script type="math/tex">\qquad \frac{q[10/7]}{q[7/5]}= \frac{ \tfrac{3} {2\sqrt{70}} } { \tfrac{2} {2\sqrt{35}} } = \tfrac{3}{2\sqrt{2}}.</script><!-- ws:end:WikiTextMathRule:40 --><br /> | --><script type="math/tex">\qquad \frac{q[10/7]}{q[7/5]}= \frac{ \tfrac{3} {2\sqrt{70}} } { \tfrac{2} {2\sqrt{35}} } = \tfrac{3}{2\sqrt{2}}.</script><!-- ws:end:WikiTextMathRule:40 --><br /> | ||
This means that in | This means that in argent temperament the augmented fourth is very close to 10/7 and the diminished fifth is very close to 7/5. The discrepancy in each case is just 0.175 cents.<br /> | ||
Another way to express the first of these relationships is<br /> | Another way to express the first of these relationships is<br /> | ||
<!-- ws:start:WikiTextMathRule:41: | <!-- ws:start:WikiTextMathRule:41: | ||