19edo: Difference between revisions

: This revision was by author [[User:igliashon|igliashon]] and made on <tt>2011-07-19 16:51:10 UTC</tt>.<br>

: The original revision id was <tt>241994673</tt>.<br>

The most salient characteristic of 19-et is that, having an almost just minor third and perfect fifths and major thirds about seven cents narrow, it serves as a good tuning for [[Meantone#|meantone]] temperament. It is also a suitable for [[Regular Temperaments#magic|magic]] temperament, because five of its major thirds are equivalent to one of its //twelfths.// For both of these there are more optimal tunings: the fifth of 19-et is flatter than the usual for meantone, and a more accurate approximation is [[31edo|31 equal temperament]]. Similarly, the generating interval of magic temperament is a major third, and again 19-et's is flatter; [[41edo|41 equal temperament]] more closely matches it.

However, for all of these 19-et has the practical advantage of requiring fewer pitches, which makes physical realizations of it easier to build. (Many 19-et instruments have been built.) 19-et is in fact the second equal temperament, after 12-et which is able to deal with [[Harmonic Limit|5-limit]] music in a tolerable manner, and is the fifth (after 12) [[The Riemann Zeta Function and Tuning#Zeta EDO lists|zeta integral edo]]. It is less successful with [[7-limit]] (but still better than 12-et), as it eliminates the distinction between a septimal minor third ([[7_6|7/6]]), and a septimal whole tone ([[8_7|8/7]]). 19-EDO also has the advantage of being excellent for negri, godzilla, sensi, and triton, and fairly decent for kleismic temperaments. Negri is of particular note for being a very simple 7-limit temperament, and its MOS scales in 19-EDO offer the greatest abundance of otonal tetrads.  

The most salient characteristic of 19-et is that, having an almost just minor third and perfect fifths and major thirds about seven cents narrow, it serves as a good tuning for [[Meantone#|meantone]] temperament. It is also a suitable for &lt;a class="wiki_link" href="/Regular%20Temperaments#magic"&gt;magic&lt;/a&gt; temperament, because five of its major thirds are equivalent to one of its &lt;em&gt;twelfths.&lt;/em&gt; For both of these there are more optimal tunings: the fifth of 19-et is flatter than the usual for meantone, and a more accurate approximation is &lt;a class="wiki_link" href="/31edo"&gt;31 equal temperament&lt;/a&gt;. Similarly, the generating interval of magic temperament is a major third, and again 19-et's is flatter; &lt;a class="wiki_link" href="/41edo"&gt;41 equal temperament&lt;/a&gt; more closely matches it.&lt;br /&gt;

However, for all of these 19-et has the practical advantage of requiring fewer pitches, which makes physical realizations of it easier to build. (Many 19-et instruments have been built.) 19-et is in fact the second equal temperament, after 12-et which is able to deal with &lt;a class="wiki_link" href="/Harmonic%20Limit"&gt;5-limit&lt;/a&gt; music in a tolerable manner, and is the fifth (after 12) &lt;a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta EDO lists"&gt;zeta integral edo&lt;/a&gt;. It is less successful with &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt; (but still better than 12-et), as it eliminates the distinction between a septimal minor third (&lt;a class="wiki_link" href="/7_6"&gt;7/6&lt;/a&gt;), and a septimal whole tone (&lt;a class="wiki_link" href="/8_7"&gt;8/7&lt;/a&gt;). 19-EDO also has the advantage of being excellent for negri, godzilla, sensi, and triton, and fairly decent for kleismic temperaments. Negri is of particular note for being a very simple 7-limit temperament, and its MOS scales in 19-EDO offer the greatest abundance of otonal tetrads. &lt;br /&gt;