5edo
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=5 tone equal temperament= ==="tempered pentatonic scale"=== First from edos containing interval different form the ones from 12edo. Scales similar to 5edo2 can be found in Indonesian slendros. 5-et can be regarded as either a chord or a scale. Considered as a scale, the fact that it can be heard as a chord is very significant--it's impossible to sound very dissonant in 5-et. However, it has the scale-like feature that there are (barely) enough notes to create melody, in the form of an equal version of pentatonic. Moreover, any pentatonic melody may be imported into 5-et, though some degradation may occur. If 5-edo is regarded as a temperament, which is to say as 5-et, then the most salient fact is that 16/15 is tempered out. This means in 5-et the major third and the fourth, and the minor sixth and the fifth, are not distinguished. This is at the very edge what can sensibly be called temperament, but it does make sense and can be used. Also tempered out is 27/25, leading to beep temperament. This equates 10/9 with 6/5, and is a little more perverse even than father. Because these intervals are so large, this sort of analysis is less significant with 5 than it becomes with larger and more accurate divisions, but it still plays a role. Step: 240.00 c. || step || **c**|| **interval**|| || 1 ||0.000 || **prima** || || 2 || 240.000 || **second, third** 8.826 c from septimal second 8/7 (231.174 c) -4.969 c from diminished third 144/125 (244.969 c) -13.076 c from augmented second 125/108 (253.076 c) -26.871 c from septimal minor third 7/6 (266.871 c)|| || 3|| 480.000|| **fourth** 9.219 c from narow fourth 21/16 -0.686 c from smaler fourth 33/25 -18.045 c from just fourth 4/3 (498.045 c)|| || 4|| 720.000|| **fifth** 18.045 c from just fifth 3/2 (701.955 c) 0.686 c from bigger fifth 50/33 -9.219 c from wide fifth 32/21|| || 5|| 960.000|| **sixth, seventh** 26.871 c from septimal major sixth 12/7 13.076 c from diminished seventh 216/125 4.969 c from augmented sixth 125/72 -8.826 c from septimal seventh 7/4|| || 6|| 1200.000|| **eigth**|| Can be constructed as a chain of five bigger fifths 50/33, which makes three octaves 3,227 c flat. (50/33)^5=7.985099. This comma can be tempered out by narrowing all the fifths by 0,686 c. ==Cycles, Divisions== 5 is prime. No divisions. All cycles are simple. Cycle of fourths: 1-3-5-2-4-1 Cycle of fifths: 1-4-2-5-3-1 ==Harmony== Scale does not have any strong consonance nor dissonance. Interval 240,000 c can serve as major second or minor third. Interval 960,000 c can serve as major sixth or minor seventh. Fourth is about 18 c flat than just fourth, it is rather "dirty"but jednoznačně identifikovatelná. Fifth is about 18 c sharp than just fifth, it is more dissonant than the fourth but still jednoznačně identifikovatelná. Important chords: 1+2+4 1+3+4 1+2+4+5 1+3+4+5 ==Melody== First from edos which can be use for melodies in "standard" way. Relatively large step of 240.00 c can be used as major second for the melody construction. The scale has whole-tone as well as pentatonic character. **Compositions** [[http://home.comcast.net/%7Eteamouse/daybreak-vsc.mp3|Daybreak on Slendro Mountain]] by [[http://home.comcast.net/%7Eteamouse/|Herman Miller]]
Original HTML content:
<html><head><title>5edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="x5 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 -->5 tone equal temperament</h1>
<br />
<!-- ws:start:WikiTextHeadingRule:2:<h3> --><h3 id="toc1"><a name="x5 tone equal temperament--"tempered pentatonic scale""></a><!-- ws:end:WikiTextHeadingRule:2 -->"tempered pentatonic scale"</h3>
<br />
First from edos containing interval different form the ones from 12edo. <br />
<br />
Scales similar to 5edo2 can be found in Indonesian slendros.<br />
<br />
5-et can be regarded as either a chord or a scale. Considered as a scale, the fact that it can be heard as a chord is very significant--it's impossible to sound very dissonant in 5-et. However, it has the scale-like feature that there are (barely) enough notes to create melody, in the form of an equal version of pentatonic. Moreover, any pentatonic melody may be imported into 5-et, though some degradation may occur.<br />
<br />
If 5-edo is regarded as a temperament, which is to say as 5-et, then the most salient fact is that 16/15 is tempered out. This means in 5-et the major third and the fourth, and the minor sixth and the fifth, are not distinguished. This is at the very edge what can sensibly be called temperament, but it does make sense and can be used. Also tempered out is 27/25, leading to beep temperament. This equates 10/9 with 6/5, and is a little more perverse even than father. Because these intervals are so large, this sort of analysis is less significant with 5 than it becomes with larger and more accurate divisions, but it still plays a role.<br />
<br />
Step: 240.00 c.<br />
<br />
<table class="wiki_table">
<tr>
<td>step<br />
</td>
<td><strong>c</strong><br />
</td>
<td><strong>interval</strong><br />
</td>
</tr>
<tr>
<td>1<br />
</td>
<td>0.000<br />
</td>
<td><strong>prima</strong><br />
</td>
</tr>
<tr>
<td>2<br />
</td>
<td>240.000<br />
</td>
<td><strong>second, third</strong><br />
8.826 c from septimal second 8/7 (231.174 c)<br />
-4.969 c from diminished third 144/125 (244.969 c)<br />
-13.076 c from augmented second 125/108 (253.076 c)<br />
-26.871 c from septimal minor third 7/6 (266.871 c)<br />
</td>
</tr>
<tr>
<td>3<br />
</td>
<td>480.000<br />
</td>
<td><strong>fourth</strong><br />
9.219 c from narow fourth 21/16<br />
-0.686 c from smaler fourth 33/25<br />
-18.045 c from just fourth 4/3 (498.045 c)<br />
</td>
</tr>
<tr>
<td>4<br />
</td>
<td>720.000<br />
</td>
<td><strong>fifth</strong><br />
18.045 c from just fifth 3/2 (701.955 c)<br />
0.686 c from bigger fifth 50/33<br />
-9.219 c from wide fifth 32/21<br />
</td>
</tr>
<tr>
<td>5<br />
</td>
<td>960.000<br />
</td>
<td><strong>sixth, seventh</strong><br />
26.871 c from septimal major sixth 12/7<br />
13.076 c from diminished seventh 216/125<br />
4.969 c from augmented sixth 125/72<br />
-8.826 c from septimal seventh 7/4<br />
</td>
</tr>
<tr>
<td>6<br />
</td>
<td>1200.000<br />
</td>
<td><strong>eigth</strong><br />
</td>
</tr>
</table>
<br />
Can be constructed as a chain of five bigger fifths 50/33, which makes three octaves 3,227 c flat. (50/33)^5=7.985099. This comma can be tempered out by narrowing all the fifths by 0,686 c.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="x5 tone equal temperament-Cycles, Divisions"></a><!-- ws:end:WikiTextHeadingRule:4 -->Cycles, Divisions</h2>
5 is prime. No divisions. All cycles are simple.<br />
Cycle of fourths: 1-3-5-2-4-1<br />
Cycle of fifths: 1-4-2-5-3-1<br />
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="x5 tone equal temperament-Harmony"></a><!-- ws:end:WikiTextHeadingRule:6 -->Harmony</h2>
<br />
Scale does not have any strong consonance nor dissonance. Interval 240,000 c can serve as major second or minor third. Interval 960,000 c can serve as major sixth or minor seventh. Fourth is about 18 c flat than just fourth, it is rather "dirty"but jednoznačně identifikovatelná. Fifth is about 18 c sharp than just fifth, it is more dissonant than the fourth but still jednoznačně identifikovatelná. <br />
Important chords:<br />
1+2+4<br />
1+3+4<br />
1+2+4+5<br />
1+3+4+5 <br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:<h2> --><h2 id="toc4"><a name="x5 tone equal temperament-Melody"></a><!-- ws:end:WikiTextHeadingRule:8 -->Melody</h2>
<br />
First from edos which can be use for melodies in "standard" way. Relatively large step of 240.00 c can be used as major second for the melody construction. The scale has whole-tone as well as pentatonic character.<br />
<br />
<br />
<strong>Compositions</strong><br />
<br />
<a class="wiki_link_ext" href="http://home.comcast.net/%7Eteamouse/daybreak-vsc.mp3" rel="nofollow">Daybreak on Slendro Mountain</a> by <a class="wiki_link_ext" href="http://home.comcast.net/%7Eteamouse/" rel="nofollow">Herman Miller</a></body></html>