Xenharmonic Wiki

Kai's House of Odds and Ends: Difference between revisions

VisualWikitext
Wikispaces>kai.lugheidh
**Imported revision 624971083 - Original comment: **
 
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
18,215 edits
m Todo
 
(5 intermediate revisions by 4 users not shown)
Line 1: Line 1:
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
Hai, I'm Kai! This is a place for musings, messings, and novelties of mine that I'm not sure deserve their own page, or that I'm having trouble fitting into an existing page, but that I think will be of interest to my fellow xen-heads anyways!
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:kai.lugheidh|kai.lugheidh]] and made on <tt>2018-01-17 04:29:47 UTC</tt>.<br>
: The original revision id was <tt>624971083</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">Hai, I'm Kai! This is a place for musings, messings, and novelties of mine that I'm not sure deserve their own page, or that I'm having trouble fitting into an existing page, but that I think will be of interest to my fellow xen-heads anyways!


=La Monte Young's tuning from //The Well-Tuned Piano,// in Rational Comma Notation (and brand spankin' new KAIGI SIGNATURES!)=  
=La Monte Young's tuning from ''The Well-Tuned Piano,'' in Rational Comma Notation (and brand spankin' new KAIGI SIGNATURES!)=


With Concert Pitch (1/1) being C4@256Hz, Eb4[7] = 7/6 = (298+2/3)Hz serves nicely as the tonic. Originally, Young tuned his "A", 189/128, to 440Hz, giving Eb of (297+187/189)Hz. These two pitches are less than 0.7Hz apart, a difference that can be essentially ignored, unless you're playing along to a recording with the same reference pitch, or feel like giving an officially sanctioned performance of the WTP (yeah right.)
With Concert Pitch (1/1) being C4 = 256Hz, Eb4[7] = 7/6 = (298+2/3)Hz serves nicely as the tonic in [[rational comma notation]] (RCN). Originally, Young tuned his "A", 189/128, to 440Hz, giving Eb of (297+187/189)Hz. These two pitches are less than 0.7Hz apart, a difference that can be essentially ignored, unless you're playing along to a recording with the same reference pitch, or feel like giving an officially sanctioned performance of the WTP (yeah right.)


The octave above the Eb[7] reference pitch is as follows:
The octave above the Eb[7] reference pitch is as follows:
||  || "Eb" || "E" || "F" || "F#" || "G" || "G#" || "A" || "Bb" || "B" || "C" || "C#" || "D" ||
|| RATIO || 1/1 || 567/512 || 9/8 || 147/128 || 21/16 || 1323/1024 || 189/128 || 3/2 || 49/32 || 7/4 || 441/256 || 63/32 ||
|| CENTS || 0.000000 || 176.645910 || 203.910002 || 239.606814 || 470.780907 || 443.516816 || 674.690909 || 701.955001 || 737.651813 || 968.825906 || 941.561815 || 1172.735908 ||
|| KAIGI SIG. || – || ◻4▲ || ◻2 || ◻▲2 || ◻▲ || ◻3▲2 ||  ◻3▲ || ◻ || ▲2 || ▲ || ◻2▲2 || ◻2▲ ||
|| ABS. PITCH (RCN) || Eb4[7] || F4[49] ||  ||  ||  ||  ||  ||  ||  ||  ||  ||  ||
|| FREQUENCY || 298+2/3 ||  ||  ||  ||  ||  ||  ||  ||  ||  ||  ||  ||


{| class="wikitable center-all"
|-
|
| '''<span style="background-color: #000000; color: #ffffff;">"Eb"</span>'''
| '''"E"'''
| '''"F"'''
| '''<span style="background-color: #000000; color: #ffffff;">"F#"</span>'''
| '''"G"'''
| '''<span style="background-color: #000000; color: #ffffff;">"G#"</span>'''
| '''"A"'''
| '''<span style="background-color: #000000; color: #ffffff;">"Bb"</span>'''
| '''"B"'''
| '''"C"'''
| '''<span style="background-color: #000000; color: #ffffff;">"C#"</span>'''
| '''"D"'''
| '''<span style="background-color: #000000; color: #ffffff;">"Eb"</span>'''
|-
| '''RATIO'''
| 1/1
| 567/512
| 9/8
| 147/128
| 21/16
| 1323/1024
| 189/128
| 3/2
| 49/32
| 7/4
| 441/256
| 63/32
| 2/1
|-
| '''CENTS'''
| 0.000000
| 176.645910
| 203.910002
| 239.606814
| 470.780907
| 443.516816
| 674.690909
| 701.955001
| 737.651813
| 968.825906
| 941.561815
| 1172.735908
| 1200.000000
|-
| '''KAIGI SIGNATURE'''
| –
| ◻4<span style="color: #00edff;">▲</span>
| ◻2
| ◻<span style="color: #00edff;">▲</span>2
| ◻<span style="color: #00edff;">▲</span>
| ◻3<span style="color: #00edff;">▲</span>2
| ◻3<span style="color: #00edff;">▲</span>
| ◻
| <span style="color: #00edff;">▲</span>2
| <span style="color: #00edff;">▲</span>
| ◻2<span style="color: #00edff;">▲</span>2
| ◻2<span style="color: #00edff;">▲</span>
| –
|-
| '''ABS. PITCH (RCN)'''
| Eb4[7]
| F4[49]
| F4[7]
| Gb4[343]
| Ab4[49]
| Ab4[343]
| Bb4[49]
| Bb4[7]
| Cb4[343]
| Db4[49]
| Db4[343]
| Eb5[49]
| Eb5[7]
|-
| '''FREQUENCY (Hz)'''
| 298+2/3
| 330+3/4
| 336
| 343
| 392
| 385+7/8
| 441
| 448
| 457+1/3
| 522+2/3
| 514+1/2
| 588
| 597+1/3
|}
The pitch classes of this tuning as a lattice in RCN:


</pre></div>
{| class="wikitable center-all"
<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;Kai's House of Odds and Ends&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Hai, I'm Kai! This is a place for musings, messings, and novelties of mine that I'm not sure deserve their own page, or that I'm having trouble fitting into an existing page, but that I think will be of interest to my fellow xen-heads anyways!&lt;br /&gt;
| Cb[343]
&lt;br /&gt;
| Gb[343]
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="La Monte Young's tuning from The Well-Tuned Piano, in Rational Comma Notation (and brand spankin' new KAIGI SIGNATURES!)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;La Monte Young's tuning from &lt;em&gt;The Well-Tuned Piano,&lt;/em&gt; in Rational Comma Notation (and brand spankin' new KAIGI SIGNATURES!)&lt;/h1&gt;
| Db[343]
&lt;br /&gt;
| Ab[343]
With Concert Pitch (1/1) being C4@256Hz, Eb4[7] = 7/6 = (298+2/3)Hz serves nicely as the tonic. Originally, Young tuned his &amp;quot;A&amp;quot;, 189/128, to 440Hz, giving Eb of (297+187/189)Hz. These two pitches are less than 0.7Hz apart, a difference that can be essentially ignored, unless you're playing along to a recording with the same reference pitch, or feel like giving an officially sanctioned performance of the WTP (yeah right.)&lt;br /&gt;
|
&lt;br /&gt;
|-
The octave above the Eb[7] reference pitch is as follows:&lt;br /&gt;
| Db[49]
| Ab[49]
| Eb[49]
| Bb[49]
| F[49]
|-
| Eb[7]
| Bb[7]
| F[7]
|
|
|}
The same lattice in tonic-agnostic Kaigi Signatures, which makes the logic of the system clear:


{| class="wikitable"
|-
| | <span style="color: #00edff;">▲</span>2
| | ◻<span style="color: #00edff;">▲</span>2
| | ◻2<span style="color: #00edff;">▲</span>2
| | ◻3<span style="color: #00edff;">▲</span>2
| |
|-
| | <span style="color: #00edff;">▲</span>
| | ◻<span style="color: #00edff;">▲</span>
| | ◻2<span style="color: #00edff;">▲</span>
| | ◻3<span style="color: #00edff;">▲</span>
| | ◻4<span style="color: #00edff;">▲</span>
|-
| | –
| | ◻
| | ◻2
| |
| |
|}


&lt;table class="wiki_table"&gt;
[[Category:Impression]]
    &lt;tr&gt;
{{todo|link|move to userspace}}
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&amp;quot;Eb&amp;quot;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&amp;quot;E&amp;quot;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&amp;quot;F&amp;quot;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&amp;quot;F#&amp;quot;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&amp;quot;G&amp;quot;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&amp;quot;G#&amp;quot;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&amp;quot;A&amp;quot;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&amp;quot;Bb&amp;quot;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&amp;quot;B&amp;quot;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&amp;quot;C&amp;quot;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&amp;quot;C#&amp;quot;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&amp;quot;D&amp;quot;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;RATIO&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;567/512&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;147/128&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;21/16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1323/1024&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;189/128&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;49/32&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;441/256&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;63/32&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;CENTS&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0.000000&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;176.645910&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;203.910002&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;239.606814&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;470.780907&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;443.516816&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;674.690909&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;701.955001&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;737.651813&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;968.825906&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;941.561815&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1172.735908&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;KAIGI SIG.&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;–&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;◻4▲&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;◻2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;◻▲2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;◻▲&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;◻3▲2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;◻3▲&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;◻&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;▲2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;▲&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;◻2▲2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;◻2▲&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;ABS. PITCH (RCN)&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Eb4[7]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;F4[49]&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;FREQUENCY&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;298+2/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;/body&gt;&lt;/html&gt;</pre></div>
Retrieved from "https://en.xen.wiki/w/Kai%27s_House_of_Odds_and_Ends"