25edo: Difference between revisions

Line 1:

<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:~~Osmiorisbendi~~|~~Osmiorisbendi~~]] and made on <tt>2011-03-~~13 16~~:08~~:18~~ UTC</tt>.

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-04-02 17:52:08 UTC</tt>.

: The original revision id was <tt>~~210043894~~</tt>.

: The original revision id was <tt>216499096</tt>.

: The revision comment was: <tt></tt>

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Line 10:

25EDO divides the octave in 25 equal steps of exact size 48 cents each. It is a good way to tune the Blackwood temperament, which takes the very sharp fifths of [[5EDO]] as a given, tempers out 28/27 and 49/48, and attempts to optimize the tunings for 5 and 7.

25EDO has fifths 18 cents sharp, but its major thirds are excellent and its 7/4 is acceptable. It therefore makes sense to use it as a [2, 5, 7] [[Just intonation subgroups|subgroup]] tuning. Looking just at 2, 5, and 7, it equates five 8/7s with the octave, and so tempers out (8/7)^5 / 2 = 16807/16384. It also equates a 128/125 diesis and two septimal tritones of 7/5 with the octave, and hence tempers out 3136/3125. If we want to temper out both of these and also have decent fifths, the obvious solution is [[50EDO]].

25EDO has fifths 18 cents sharp, but its major thirds are excellent and its 7/4 is acceptable. It therefore makes sense to use it as a 2.5.7 [[Just intonation subgroups|subgroup]] tuning. Looking just at 2, 5, and 7, it equates five 8/7s with the octave, and so tempers out (8/7)^5 / 2 = 16807/16384. It also equates a 128/125 diesis and two septimal tritones of 7/5 with the octave, and hence tempers out 3136/3125. If we want to temper out both of these and also have decent fifths, the obvious solution is [[50EDO]].

If 5/4 and 7/4 aren't good enough, it also does 17/16 and 19/16, just like 12EDO.

If 5/4 and 7/4 aren't good enough, it also does 17/16 and 19/16, just like 12EDO. In fact, on the subgroup 2.9.5.7.33.39.17.19 it provides the same tuning and tempers out the same commas as 50et, which makes for wide range of harmony.

Some example of a keyboard in 25-EDO

Line 51:

25EDO divides the octave in 25 equal steps of exact size 48 cents each. It is a good way to tune the Blackwood temperament, which takes the very sharp fifths of <a class="wiki_link" href="/5EDO">5EDO</a> as a given, tempers out 28/27 and 49/48, and attempts to optimize the tunings for 5 and 7.

25EDO has fifths 18 cents sharp, but its major thirds are excellent and its 7/4 is acceptable. It therefore makes sense to use it as a [2, 5, 7] <a class="wiki_link" href="/Just%20intonation%20subgroups">subgroup</a> tuning. Looking just at 2, 5, and 7, it equates five 8/7s with the octave, and so tempers out (8/7)^5 / 2 = 16807/16384. It also equates a 128/125 diesis and two septimal tritones of 7/5 with the octave, and hence tempers out 3136/3125. If we want to temper out both of these and also have decent fifths, the obvious solution is <a class="wiki_link" href="/50EDO">50EDO</a>.

25EDO has fifths 18 cents sharp, but its major thirds are excellent and its 7/4 is acceptable. It therefore makes sense to use it as a 2.5.7 <a class="wiki_link" href="/Just%20intonation%20subgroups">subgroup</a> tuning. Looking just at 2, 5, and 7, it equates five 8/7s with the octave, and so tempers out (8/7)^5 / 2 = 16807/16384. It also equates a 128/125 diesis and two septimal tritones of 7/5 with the octave, and hence tempers out 3136/3125. If we want to temper out both of these and also have decent fifths, the obvious solution is <a class="wiki_link" href="/50EDO">50EDO</a>.

If 5/4 and 7/4 aren't good enough, it also does 17/16 and 19/16, just like 12EDO.

If 5/4 and 7/4 aren't good enough, it also does 17/16 and 19/16, just like 12EDO. In fact, on the subgroup 2.9.5.7.33.39.17.19 it provides the same tuning and tempers out the same commas as 50et, which makes for wide range of harmony.

Some example of a keyboard in 25-EDO

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2011-03-13 16:08:18 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-04-02 17:52:08 UTC</tt>.<br>
-: The original revision id was <tt>210043894</tt>.<br>
+: The original revision id was <tt>216499096</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>
@@ Line 10: / Line 10: @@
 EDO divides the octave in 25 equal steps of exact size 48 cents each. It is a good way to tune the Blackwood temperament, which takes the very sharp fifths of [[5EDO]] as a given, tempers out 28/27 and 49/48, and attempts to optimize the tunings for 5 and 7.
-EDO has fifths 18 cents sharp, but its major thirds are excellent and its 7/4 is acceptable. It therefore makes sense to use it as a [2, 5, 7] [[Just intonation subgroups|subgroup]] tuning. Looking just at 2, 5, and 7, it equates five 8/7s with the octave, and so tempers out (8/7)^5 / 2 = 16807/16384. It also equates a 128/125 diesis and two septimal tritones of 7/5 with the octave, and hence tempers out 3136/3125. If we want to temper out both of these and also have decent fifths, the obvious solution is [[50EDO]].
+EDO has fifths 18 cents sharp, but its major thirds are excellent and its 7/4 is acceptable. It therefore makes sense to use it as a 2.5.7 [[Just intonation subgroups|subgroup]] tuning. Looking just at 2, 5, and 7, it equates five 8/7s with the octave, and so tempers out (8/7)^5 / 2 = 16807/16384. It also equates a 128/125 diesis and two septimal tritones of 7/5 with the octave, and hence tempers out 3136/3125. If we want to temper out both of these and also have decent fifths, the obvious solution is [[50EDO]].
-If 5/4 and 7/4 aren't good enough, it also does 17/16 and 19/16, just like 12EDO.
+If 5/4 and 7/4 aren't good enough, it also does 17/16 and 19/16, just like 12EDO. In fact, on the subgroup 2.9.5.7.33.39.17.19 it provides the same tuning and tempers out the same commas as 50et, which makes for wide range of harmony.
 Some example of a keyboard in 25-EDO
@@ Line 51: / Line 51: @@
 EDO divides the octave in 25 equal steps of exact size 48 cents each. It is a good way to tune the Blackwood temperament, which takes the very sharp fifths of &lt;a class="wiki_link" href="/5EDO"&gt;5EDO&lt;/a&gt; as a given, tempers out 28/27 and 49/48, and attempts to optimize the tunings for 5 and 7.&lt;br /&gt;
 &lt;br /&gt;
-EDO has fifths 18 cents sharp, but its major thirds are excellent and its 7/4 is acceptable. It therefore makes sense to use it as a [2, 5, 7] &lt;a class="wiki_link" href="/Just%20intonation%20subgroups"&gt;subgroup&lt;/a&gt; tuning. Looking just at 2, 5, and 7, it equates five 8/7s with the octave, and so tempers out (8/7)^5 / 2 = 16807/16384. It also equates a 128/125 diesis and two septimal tritones of 7/5 with the octave, and hence tempers out 3136/3125. If we want to temper out both of these and also have decent fifths, the obvious solution is &lt;a class="wiki_link" href="/50EDO"&gt;50EDO&lt;/a&gt;.&lt;br /&gt;
+EDO has fifths 18 cents sharp, but its major thirds are excellent and its 7/4 is acceptable. It therefore makes sense to use it as a 2.5.7 &lt;a class="wiki_link" href="/Just%20intonation%20subgroups"&gt;subgroup&lt;/a&gt; tuning. Looking just at 2, 5, and 7, it equates five 8/7s with the octave, and so tempers out (8/7)^5 / 2 = 16807/16384. It also equates a 128/125 diesis and two septimal tritones of 7/5 with the octave, and hence tempers out 3136/3125. If we want to temper out both of these and also have decent fifths, the obvious solution is &lt;a class="wiki_link" href="/50EDO"&gt;50EDO&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
-If 5/4 and 7/4 aren't good enough, it also does 17/16 and 19/16, just like 12EDO.&lt;br /&gt;
+If 5/4 and 7/4 aren't good enough, it also does 17/16 and 19/16, just like 12EDO. In fact, on the subgroup 2.9.5.7.33.39.17.19 it provides the same tuning and tempers out the same commas as 50et, which makes for wide range of harmony.&lt;br /&gt;
 &lt;br /&gt;
 Some example of a keyboard in 25-EDO&lt;br /&gt;