31edo solfege: 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:<br>

: This revision was by author [[User:~~phylingual~~|~~phylingual~~]] and made on <tt>~~2012~~-06-~~10 16~~:14:38 UTC</tt>.<br>

: This revision was by author [[User:circular|circular]] and made on <tt>2015-04-29 15:09:44 UTC</tt>.<br>

: The original revision id was <tt>~~344234942~~</tt>.<br>

: The original revision id was <tt>549194276</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>

<h4>Original Wikitext content:</h4>

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">[[Andrew Heathwaite]] proposes the following solfege system for singing the intervals of [[31edo]]. Note that this is a subset of the syllables used for singing [[41edo]].

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">===Quarter tone system===

While [[31edo]] is a system with fifth of tones, the quarter tone notations is handy and allow to name all the notes in a logical way. Because one tone is 5 degrees, between C and D (do and re) for example, we have the following notes:

|| **Degree** || **Letter** || **Name** || **English full name** ||

|| 0 || C || do || C ||

|| 1 || C+ || do+ || C half-sharp ||

|| 2 || C# || do# || C sharp ||

|| 3 || Db || re b || D flat ||

|| 4 || Dd || re d || D half-flat ||

|| 5 || D || re || D ||

Otherwise we can use double sharp and double flat:

|| **Degree** || **Letter** || **Name** || **English full name** ||

|| 0 || C || do || C ||

|| 1 || Dbb || do bb || D double flat ||

|| 2 || C# || do# || C sharp ||

|| 3 || Db || re b || D flat ||

|| 4 || Cx || re x || C double sharp ||

|| 5 || D || re || D ||

While using double sharp and double flat seem a bit confusing because it then alternates between C and D, it makes sense from a musical point of view. Indeed as far as harmonics and chords are concerned, using double sharp and double flat allow to have a way of writing chord that is consistent with traditional solfege.

Indeed, if we consider the subminor chord, and write it with D# for the second note and A# for the seventh harmonic, we get the following chords:

* C / D# / G / A#

* C# / Dx / G# / Ax

* Db / E / Ab / B

* D / E# / A / B#

So, as in 12-ET, we have the equation C# = Db and E# = F, in 31-ET, we have C# ≠ Db and E# ≠ F but we have:

* Cx = Dd

* C+ = Dbb

* E# = Fd

* E+ = Fb

* Ex = F+

* Ed = Fbb

It is not necessary to learn all by heart. Simply that there are 5 degrees in a tone, and 3 degrees in a diatonic semitone. So going from one note name to another name is always an odd difference of degrees. If the change is even, it can be written as sharp and flat.

An exception to using flat and sharp is the rast scale, where there is Ed and Bd, which are defined as such and not derived from other intervals.

===Andrew Heathwaite system===

[[Andrew Heathwaite]] proposes the following solfege system for singing the intervals of [[31edo]]. Note that this is a subset of the syllables used for singing [[41edo]].

|| degrees of 31edo || syllable ||

Line 85:

Line 126:

**da** => **su**</pre></div>

<h4>Original HTML content:</h4>

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>31edo solfege</title></head><body><a class="wiki_link" href="/Andrew%20Heathwaite">Andrew Heathwaite</a> proposes the following solfege system for singing the intervals of <a class="wiki_link" href="/31edo">31edo</a>. Note that this is a subset of the syllables used for singing <a class="wiki_link" href="/41edo">41edo</a>.<br />

<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>31edo solfege</title></head><body><h3 id="toc0"><a name="x--Quarter tone system"></a>Quarter tone system</h3>

<br />

While <a class="wiki_link" href="/31edo">31edo</a> is a system with fifth of tones, the quarter tone notations is handy and allow to name all the notes in a logical way. Because one tone is 5 degrees, between C and D (do and re) for example, we have the following notes:<br />

<tr>

<td><strong>Degree</strong><br />

</td>

<td><strong>Letter</strong><br />

</td>

</td>

<td><strong>English full name</strong><br />

</td>

</tr>

<tr>

</td>

</td>

</td>

</td>

</tr>

<tr>

</td>

</td>

</td>

<td>C half-sharp<br />

</td>

</tr>

<tr>

</td>

</td>

</td>

<td>C sharp<br />

</td>

</tr>

<tr>

</td>

</td>

</td>

</td>

</tr>

<tr>

</td>

</td>

</td>

</td>

</tr>

<tr>

</td>

</td>

</td>

</td>

</tr>

</table>

Otherwise we can use double sharp and double flat:<br />

<tr>

<td><strong>Degree</strong><br />

</td>

<td><strong>Letter</strong><br />

</td>

</td>

<td><strong>English full name</strong><br />

</td>

</tr>

<tr>

</td>

</td>

</td>

</td>

</tr>

<tr>

</td>

</td>

</td>

<td>D double flat<br />

</td>

</tr>

<tr>

</td>

</td>

</td>

<td>C sharp<br />

</td>

</tr>

<tr>

</td>

</td>

</td>

</td>

</tr>

<tr>

</td>

</td>

</td>

<td>C double sharp<br />

</td>

</tr>

<tr>

</td>

</td>

</td>

</td>

</tr>

</table>

While using double sharp and double flat seem a bit confusing because it then alternates between C and D, it makes sense from a musical point of view. Indeed as far as harmonics and chords are concerned, using double sharp and double flat allow to have a way of writing chord that is consistent with traditional solfege.<br />

<br />

Indeed, if we consider the subminor chord, and write it with D# for the second note and A# for the seventh harmonic, we get the following chords:<br />

So, as in 12-ET, we have the equation C# <h1 id="toc1"><a name="Db and E#"></a> Db and E# </h1>

F, in 31-ET, we have C# ≠ Db and E# ≠ F but we have:<br />

It is not necessary to learn all by heart. Simply that there are 5 degrees in a tone, and 3 degrees in a diatonic semitone. So going from one note name to another name is always an odd difference of degrees. If the change is even, it can be written as sharp and flat.<br />

<br />

An exception to using flat and sharp is the rast scale, where there is Ed and Bd, which are defined as such and not derived from other intervals.<br />

<br />

<h3 id="toc2"><a name="Db and E#--Andrew Heathwaite system"></a>Andrew Heathwaite system</h3>

<br />

<a class="wiki_link" href="/Andrew%20Heathwaite">Andrew Heathwaite</a> proposes the following solfege system for singing the intervals of <a class="wiki_link" href="/31edo">31edo</a>. Note that this is a subset of the syllables used for singing <a class="wiki_link" href="/41edo">41edo</a>.<br />

<br />

Line 293:

Line 502:

See also: <a class="wiki_link" href="/17edo%20Solfege">17edo Solfege</a>, <a class="wiki_link" href="/22edo%20Solfege">22edo Solfege</a>, <a class="wiki_link" href="/29edo%20Solfege">29edo Solfege</a><br />

<br />

<h1 id="~~toc0~~"><a name="Comments"></a>Comments</h1>

<h1 id="toc3"><a name="Comments"></a>Comments</h1>

For intervals that appear in the diatonic scale, the traditional solfege names are grandfathered in. While this makes it easier to learn the new syllables as extensions of the old ones -- if you are trained with the old ones to begin with -- it also makes for many irregularities.<br />

<br />

@@ 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:phylingual|phylingual]] and made on <tt>2012-06-10 16:14:38 UTC</tt>.<br>
+: This revision was by author [[User:circular|circular]] and made on <tt>2015-04-29 15:09:44 UTC</tt>.<br>
-: The original revision id was <tt>344234942</tt>.<br>
+: The original revision id was <tt>549194276</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>
 <h4>Original Wikitext content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">[[Andrew Heathwaite]] proposes the following solfege system for singing the intervals of [[31edo]]. Note that this is a subset of the syllables used for singing [[41edo]].
+<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">===Quarter tone system===
+While [[31edo]] is a system with fifth of tones, the quarter tone notations is handy and allow to name all the notes in a logical way. Because one tone is 5 degrees, between C and D (do and re) for example, we have the following notes:
+|| **Degree** || **Letter** || **Name** || **English full name** ||
+|| 0 || C || do || C ||
+|| 1 || C+ || do+ || C half-sharp ||
+|| 2 || C# || do# || C sharp ||
+|| 3 || Db || re b || D flat ||
+|| 4 || Dd || re d || D half-flat ||
+|| 5 || D || re || D ||
+Otherwise we can use double sharp and double flat:
+|| **Degree** || **Letter** || **Name** || **English full name** ||
+|| 0 || C || do || C ||
+|| 1 || Dbb || do bb || D double flat ||
+|| 2 || C# || do# || C sharp ||
+|| 3 || Db || re b || D flat ||
+|| 4 || Cx || re x || C double sharp ||
+|| 5 || D || re || D ||
+While using double sharp and double flat seem a bit confusing because it then alternates between C and D, it makes sense from a musical point of view. Indeed as far as harmonics and chords are concerned, using double sharp and double flat allow to have a way of writing chord that is consistent with traditional solfege.
+Indeed, if we consider the subminor chord, and write it with D# for the second note and A# for the seventh harmonic, we get the following chords:
+* C / D# / G / A#
+* C# / Dx / G# / Ax
+* Db / E / Ab / B
+* D / E# / A / B#
+So, as in 12-ET, we have the equation C# = Db and E# = F, in 31-ET, we have C# ≠ Db and E# ≠ F but we have:
+* Cx = Dd
+* C+ = Dbb
+* E# = Fd
+* E+ = Fb
+* Ex = F+
+* Ed = Fbb
+It is not necessary to learn all by heart. Simply that there are 5 degrees in a tone, and 3 degrees in a diatonic semitone. So going from one note name to another name is always an odd difference of degrees. If the change is even, it can be written as sharp and flat.
+An exception to using flat and sharp is the rast scale, where there is Ed and Bd, which are defined as such and not derived from other intervals.
+===Andrew Heathwaite system===
+[[Andrew Heathwaite]] proposes the following solfege system for singing the intervals of [[31edo]]. Note that this is a subset of the syllables used for singing [[41edo]].
 || degrees of 31edo || syllable ||
@@ Line 85: / Line 126: @@
 **da** =&gt; **su**</pre></div>
 <h4>Original HTML content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;31edo solfege&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;a class="wiki_link" href="/Andrew%20Heathwaite"&gt;Andrew Heathwaite&lt;/a&gt; proposes the following solfege system for singing the intervals of &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt;. Note that this is a subset of the syllables used for singing &lt;a class="wiki_link" href="/41edo"&gt;41edo&lt;/a&gt;.&lt;br /&gt;
+<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;31edo solfege&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc0"&gt;&lt;a name="x--Quarter tone system"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Quarter tone system&lt;/h3&gt;
+ &lt;br /&gt;
+While &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt; is a system with fifth of tones, the quarter tone notations is handy and allow to name all the notes in a logical way. Because one tone is 5 degrees, between C and D (do and re) for example, we have the following notes:&lt;br /&gt;
+&lt;table class="wiki_table"&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;strong&gt;Degree&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;Letter&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;Name&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;English full name&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;0&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;C&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;do&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;C&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;C+&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;do+&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;C half-sharp&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;C#&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;do#&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;C sharp&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Db&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;re b&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;D flat&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Dd&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;re d&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;D half-flat&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;D&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;re&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;D&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+&lt;/table&gt;
+Otherwise we can use double sharp and double flat:&lt;br /&gt;
+&lt;table class="wiki_table"&gt;
+    &lt;tr&gt;
+        &lt;td&gt;&lt;strong&gt;Degree&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;Letter&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;Name&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;&lt;strong&gt;English full name&lt;/strong&gt;&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;0&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;C&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;do&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;C&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;1&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Dbb&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;do bb&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;D double flat&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;2&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;C#&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;do#&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;C sharp&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;3&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Db&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;re b&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;D flat&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;4&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;Cx&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;re x&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;C double sharp&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+    &lt;tr&gt;
+        &lt;td&gt;5&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;D&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;re&lt;br /&gt;
+&lt;/td&gt;
+        &lt;td&gt;D&lt;br /&gt;
+&lt;/td&gt;
+    &lt;/tr&gt;
+&lt;/table&gt;
+While using double sharp and double flat seem a bit confusing because it then alternates between C and D, it makes sense from a musical point of view. Indeed as far as harmonics and chords are concerned, using double sharp and double flat allow to have a way of writing chord that is consistent with traditional solfege.&lt;br /&gt;
+&lt;br /&gt;
+Indeed, if we consider the subminor chord, and write it with D# for the second note and A# for the seventh harmonic, we get the following chords:&lt;br /&gt;
+&lt;ul&gt;&lt;li&gt;C / D# / G / A#&lt;/li&gt;&lt;li&gt;C# / Dx / G# / Ax&lt;/li&gt;&lt;li&gt;Db / E / Ab / B&lt;/li&gt;&lt;li&gt;D / E# / A / B#&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
+So, as in 12-ET, we have the equation C#  &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Db and E#"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt; Db and E# &lt;/h1&gt;
+ F, in 31-ET, we have C# ≠ Db and E# ≠ F but we have:&lt;br /&gt;
+&lt;ul&gt;&lt;li&gt;Cx = Dd&lt;/li&gt;&lt;li&gt;C+ = Dbb&lt;/li&gt;&lt;li&gt;E# = Fd&lt;/li&gt;&lt;li&gt;E+ = Fb&lt;/li&gt;&lt;li&gt;Ex = F+&lt;/li&gt;&lt;li&gt;Ed = Fbb&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
+It is not necessary to learn all by heart. Simply that there are 5 degrees in a tone, and 3 degrees in a diatonic semitone. So going from one note name to another name is always an odd difference of degrees. If the change is even, it can be written as sharp and flat.&lt;br /&gt;
+&lt;br /&gt;
+An exception to using flat and sharp is the rast scale, where there is Ed and Bd, which are defined as such and not derived from other intervals.&lt;br /&gt;
+&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="Db and E#--Andrew Heathwaite system"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Andrew Heathwaite system&lt;/h3&gt;
+ &lt;br /&gt;
+&lt;a class="wiki_link" href="/Andrew%20Heathwaite"&gt;Andrew Heathwaite&lt;/a&gt; proposes the following solfege system for singing the intervals of &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt;. Note that this is a subset of the syllables used for singing &lt;a class="wiki_link" href="/41edo"&gt;41edo&lt;/a&gt;.&lt;br /&gt;
 &lt;br /&gt;
@@ Line 293: / Line 502: @@
 See also: &lt;a class="wiki_link" href="/17edo%20Solfege"&gt;17edo Solfege&lt;/a&gt;, &lt;a class="wiki_link" href="/22edo%20Solfege"&gt;22edo Solfege&lt;/a&gt;, &lt;a class="wiki_link" href="/29edo%20Solfege"&gt;29edo Solfege&lt;/a&gt;&lt;br /&gt;
 &lt;br /&gt;
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   For intervals that appear in the diatonic scale, the traditional solfege names are grandfathered in. While this makes it easier to learn the new syllables as extensions of the old ones -- if you are trained with the old ones to begin with -- it also makes for many irregularities.&lt;br /&gt;
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