Bohpier/Chords: Difference between revisions
Wikispaces>keenanpepper **Imported revision 290308191 - Original comment: ** |
Wikispaces>keenanpepper **Imported revision 290308213 - 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:keenanpepper|keenanpepper]] and made on <tt>2012-01-08 00:18: | : This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2012-01-08 00:18:34 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>290308213</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 10: | Line 10: | ||
Bohpier has MOS of size 8, 9, 17, 25, 33, 41 and 49, and it may be seen that even the eight-note MOS comes equipped with some triads and tetrads. It should also be noted that the generator chain of 7-limit bohpier is the [[Bohlen-Pierce]] scale, and the same is true of 11-limit bohpier if we do not regard 11/4 as a forbidden interval because the denominator is an even number. Hence, every chord listed below has a voicing which makes it a chord of Bohlen-Pierce, showing Bohlen-Pierce contains many essentially tempered chords. The listed transversals my be converted to Bohlen-Pierce transversals by adjusting up an octave past 9/5~20/11, so that 7/6 becomes 7/3, 14/11 becomes 28/11, 11/8 becomes 11/4, 3/2 becomes 3, 18/11 becomes 36/11, 5/4 becomes 5, 7/4 becomes 7, and 9/8 becomes 9. It should also be noted that 13-limit bohpier, and hence 13-limit Bohlen-Pierce, has many more 13-limit essentially tempered chords. | Bohpier has MOS of size 8, 9, 17, 25, 33, 41 and 49, and it may be seen that even the eight-note MOS comes equipped with some triads and tetrads. It should also be noted that the generator chain of 7-limit bohpier is the [[Bohlen-Pierce]] scale, and the same is true of 11-limit bohpier if we do not regard 11/4 as a forbidden interval because the denominator is an even number. Hence, every chord listed below has a voicing which makes it a chord of Bohlen-Pierce, showing Bohlen-Pierce contains many essentially tempered chords. The listed transversals my be converted to Bohlen-Pierce transversals by adjusting up an octave past 9/5~20/11, so that 7/6 becomes 7/3, 14/11 becomes 28/11, 11/8 becomes 11/4, 3/2 becomes 3, 18/11 becomes 36/11, 5/4 becomes 5, 7/4 becomes 7, and 9/8 becomes 9. It should also be noted that 13-limit bohpier, and hence 13-limit Bohlen-Pierce, has many more 13-limit essentially tempered chords. | ||
In strictly traditional Bohlen-Pierce theory, only ratios with odd numbers are considered, such as produce coincident partials on instruments with only odd harmonics (e.g. an ideal clarinet). The essentially tempered chords of this 3.5.7 system are much more limited - besides the JI chords (otonal, utonal, and ambitonal), only the sensamagic chords exist in strict Bohlen-Pierce. | In strictly traditional Bohlen-Pierce theory, only ratios with odd numbers are considered, such as produce coincident partials on instruments with only odd harmonics (e.g. an ideal clarinet). The essentially tempered chords of this 3.5.7 system are much more limited - besides the JI chords (otonal, utonal, and ambitonal), only the [[sensamagic chords]] exist in strict Bohlen-Pierce. | ||
=Triads= | =Triads= | ||
| Line 183: | Line 183: | ||
Bohpier has MOS of size 8, 9, 17, 25, 33, 41 and 49, and it may be seen that even the eight-note MOS comes equipped with some triads and tetrads. It should also be noted that the generator chain of 7-limit bohpier is the <a class="wiki_link" href="/Bohlen-Pierce">Bohlen-Pierce</a> scale, and the same is true of 11-limit bohpier if we do not regard 11/4 as a forbidden interval because the denominator is an even number. Hence, every chord listed below has a voicing which makes it a chord of Bohlen-Pierce, showing Bohlen-Pierce contains many essentially tempered chords. The listed transversals my be converted to Bohlen-Pierce transversals by adjusting up an octave past 9/5~20/11, so that 7/6 becomes 7/3, 14/11 becomes 28/11, 11/8 becomes 11/4, 3/2 becomes 3, 18/11 becomes 36/11, 5/4 becomes 5, 7/4 becomes 7, and 9/8 becomes 9. It should also be noted that 13-limit bohpier, and hence 13-limit Bohlen-Pierce, has many more 13-limit essentially tempered chords.<br /> | Bohpier has MOS of size 8, 9, 17, 25, 33, 41 and 49, and it may be seen that even the eight-note MOS comes equipped with some triads and tetrads. It should also be noted that the generator chain of 7-limit bohpier is the <a class="wiki_link" href="/Bohlen-Pierce">Bohlen-Pierce</a> scale, and the same is true of 11-limit bohpier if we do not regard 11/4 as a forbidden interval because the denominator is an even number. Hence, every chord listed below has a voicing which makes it a chord of Bohlen-Pierce, showing Bohlen-Pierce contains many essentially tempered chords. The listed transversals my be converted to Bohlen-Pierce transversals by adjusting up an octave past 9/5~20/11, so that 7/6 becomes 7/3, 14/11 becomes 28/11, 11/8 becomes 11/4, 3/2 becomes 3, 18/11 becomes 36/11, 5/4 becomes 5, 7/4 becomes 7, and 9/8 becomes 9. It should also be noted that 13-limit bohpier, and hence 13-limit Bohlen-Pierce, has many more 13-limit essentially tempered chords.<br /> | ||
<br /> | <br /> | ||
In strictly traditional Bohlen-Pierce theory, only ratios with odd numbers are considered, such as produce coincident partials on instruments with only odd harmonics (e.g. an ideal clarinet). The essentially tempered chords of this 3.5.7 system are much more limited - besides the JI chords (otonal, utonal, and ambitonal), only the sensamagic chords exist in strict Bohlen-Pierce.<br /> | In strictly traditional Bohlen-Pierce theory, only ratios with odd numbers are considered, such as produce coincident partials on instruments with only odd harmonics (e.g. an ideal clarinet). The essentially tempered chords of this 3.5.7 system are much more limited - besides the JI chords (otonal, utonal, and ambitonal), only the <a class="wiki_link" href="/sensamagic%20chords">sensamagic chords</a> exist in strict Bohlen-Pierce.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Triads"></a><!-- ws:end:WikiTextHeadingRule:0 -->Triads</h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Triads"></a><!-- ws:end:WikiTextHeadingRule:0 -->Triads</h1> | ||