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

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older edit
VisualWikitext
Wikispaces>kai.lugheidh
**Imported revision 624971673 - Original comment: **
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
18,215 edits
m Todo
 
(4 intermediate revisions by 3 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 04:49:17 UTC</tt>.<br>
: The original revision id was <tt>624971673</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 in [[xenharmonic/Rational Comma Notation (RCN)|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.)
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:
||=  ||= **&lt;span style="background-color: #000000; color: #ffffff;"&gt;"Eb"&lt;/span&gt;** ||= **"E"** ||= **"F"** ||= **&lt;span style="background-color: #000000; color: #ffffff;"&gt;"F#"&lt;/span&gt;** ||= **"G"** ||= **&lt;span style="background-color: #000000; color: #ffffff;"&gt;"G#"&lt;/span&gt;** ||= **"A"** ||= **&lt;span style="background-color: #000000; color: #ffffff;"&gt;"Bb"&lt;/span&gt;** ||= **"B"** ||= **"C"** ||= **&lt;span style="background-color: #000000; color: #ffffff;"&gt;"C#"&lt;/span&gt;** ||= **"D"** ||= **&lt;span style="background-color: #000000; color: #ffffff;"&gt;"Eb"&lt;/span&gt;** ||
 
||= **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 ||
{| class="wikitable center-all"
||= **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&lt;span style="color: #00edff;"&gt;▲&lt;/span&gt; ||= ◻2 ||= ◻&lt;span style="color: #00edff;"&gt;▲&lt;/span&gt;2 ||= ◻&lt;span style="color: #00edff;"&gt;▲&lt;/span&gt; ||= ◻3&lt;span style="color: #00edff;"&gt;▲&lt;/span&gt;2 ||= ◻3&lt;span style="color: #00edff;"&gt;▲&lt;/span&gt; ||= ◻ ||= &lt;span style="color: #00edff;"&gt;▲&lt;/span&gt;2 ||= &lt;span style="color: #00edff;"&gt;▲&lt;/span&gt; ||= ◻2&lt;span style="color: #00edff;"&gt;▲&lt;/span&gt;2 ||= ◻2&lt;span style="color: #00edff;"&gt;▲&lt;/span&gt; ||= – ||
|  
||= **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] ||
| '''<span style="background-color: #000000; color: #ffffff;">"Eb"</span>'''
||= **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 ||
| '''"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:
The pitch classes of this tuning as a lattice in RCN:
||= Cb[343] ||= Gb[343] ||= Db[343] ||= Ab[343] ||=  ||
 
||= Db[49] ||= Ab[49] ||= Eb[49] ||= Bb[49] ||= F[49] ||
{| class="wikitable center-all"
||= Eb[7] ||= Bb[7] ||= F[7] ||=  ||=  ||
|-
| Cb[343]
| Gb[343]
| Db[343]
| Ab[343]
|  
|-
| 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:
The same lattice in tonic-agnostic Kaigi Signatures, which makes the logic of the system clear:
|| &lt;span style="color: #00edff;"&gt;▲&lt;/span&gt;2 || ◻&lt;span style="color: #00edff;"&gt;▲&lt;/span&gt;2 || ◻2&lt;span style="color: #00edff;"&gt;▲&lt;/span&gt;2 || ◻3&lt;span style="color: #00edff;"&gt;▲&lt;/span&gt;2 ||  ||
|| &lt;span style="color: #00edff;"&gt;▲&lt;/span&gt; || ◻&lt;span style="color: #00edff;"&gt;▲&lt;/span&gt; || ◻2&lt;span style="color: #00edff;"&gt;▲&lt;/span&gt; || ◻3&lt;span style="color: #00edff;"&gt;▲&lt;/span&gt; || ◻4&lt;span style="color: #00edff;"&gt;▲&lt;/span&gt; ||
|| – || ◻ || ◻2 ||  ||  ||</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;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;
&lt;br /&gt;
&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;
&lt;br /&gt;
With Concert Pitch (1/1) being C4@256Hz, Eb4[7] = 7/6 = (298+2/3)Hz serves nicely as the tonic in &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Rational%20Comma%20Notation%20%28RCN%29"&gt;Rational Comma Notation (RCN). &lt;/a&gt;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;
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;strong&gt;&lt;span style="background-color: #000000; color: #ffffff;"&gt;&amp;quot;Eb&amp;quot;&lt;/span&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;strong&gt;&amp;quot;E&amp;quot;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;strong&gt;&amp;quot;F&amp;quot;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;strong&gt;&lt;span style="background-color: #000000; color: #ffffff;"&gt;&amp;quot;F#&amp;quot;&lt;/span&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;strong&gt;&amp;quot;G&amp;quot;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;strong&gt;&lt;span style="background-color: #000000; color: #ffffff;"&gt;&amp;quot;G#&amp;quot;&lt;/span&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;strong&gt;&amp;quot;A&amp;quot;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;strong&gt;&lt;span style="background-color: #000000; color: #ffffff;"&gt;&amp;quot;Bb&amp;quot;&lt;/span&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;strong&gt;&amp;quot;B&amp;quot;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;strong&gt;&amp;quot;C&amp;quot;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;strong&gt;&lt;span style="background-color: #000000; color: #ffffff;"&gt;&amp;quot;C#&amp;quot;&lt;/span&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;strong&gt;&amp;quot;D&amp;quot;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;strong&gt;&lt;span style="background-color: #000000; color: #ffffff;"&gt;&amp;quot;Eb&amp;quot;&lt;/span&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;strong&gt;RATIO&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1/1&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;567/512&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;9/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;147/128&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;21/16&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1323/1024&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;189/128&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;49/32&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;7/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;441/256&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;63/32&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;2/1&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;strong&gt;CENTS&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;0.000000&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;176.645910&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;203.910002&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;239.606814&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;470.780907&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;443.516816&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;674.690909&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;701.955001&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;737.651813&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;968.825906&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;941.561815&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1172.735908&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;1200.000000&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;strong&gt;KAIGI SIGNATURE&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;–&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;◻4&lt;span style="color: #00edff;"&gt;▲&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;◻2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;◻&lt;span style="color: #00edff;"&gt;▲&lt;/span&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;◻&lt;span style="color: #00edff;"&gt;▲&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;◻3&lt;span style="color: #00edff;"&gt;▲&lt;/span&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;◻3&lt;span style="color: #00edff;"&gt;▲&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;◻&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;span style="color: #00edff;"&gt;▲&lt;/span&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;span style="color: #00edff;"&gt;▲&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;◻2&lt;span style="color: #00edff;"&gt;▲&lt;/span&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;◻2&lt;span style="color: #00edff;"&gt;▲&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;–&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;strong&gt;ABS. PITCH (RCN)&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Eb4[7]&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;F4[49]&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;F4[7]&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Gb4[343]&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Ab4[49]&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Ab4[343]&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Bb4[49]&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Bb4[7]&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Cb4[343]&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Db4[49]&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Db4[343]&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Eb5[49]&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Eb5[7]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;&lt;strong&gt;FREQUENCY (Hz)&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;298+2/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;330+3/4&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;336&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;343&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;392&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;385+7/8&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;441&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;448&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;457+1/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;522+2/3&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;514+1/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;588&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;597+1/3&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
The pitch classes of this tuning as a lattice in RCN:&lt;br /&gt;
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;Cb[343]&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Gb[343]&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Db[343]&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Ab[343]&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;Db[49]&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Ab[49]&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Eb[49]&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Bb[49]&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;F[49]&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td style="text-align: center;"&gt;Eb[7]&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;Bb[7]&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;F[7]&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td style="text-align: center;"&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
The same lattice in tonic-agnostic Kaigi Signatures, which makes the logic of the system clear:&lt;br /&gt;


&lt;table class="wiki_table"&gt;
{| class="wikitable"
    &lt;tr&gt;
|-
        &lt;td&gt;&lt;span style="color: #00edff;"&gt;▲&lt;/span&gt;2&lt;br /&gt;
| | <span style="color: #00edff;">▲</span>2
&lt;/td&gt;
| | ◻<span style="color: #00edff;">▲</span>2
        &lt;td&gt;◻&lt;span style="color: #00edff;"&gt;▲&lt;/span&gt;2&lt;br /&gt;
| | ◻2<span style="color: #00edff;">▲</span>2
&lt;/td&gt;
| | ◻3<span style="color: #00edff;">▲</span>2
        &lt;td&gt;◻2&lt;span style="color: #00edff;"&gt;▲&lt;/span&gt;2&lt;br /&gt;
| |
&lt;/td&gt;
|-
        &lt;td&gt;◻3&lt;span style="color: #00edff;"&gt;▲&lt;/span&gt;2&lt;br /&gt;
| | <span style="color: #00edff;">▲</span>
&lt;/td&gt;
| | ◻<span style="color: #00edff;">▲</span>
        &lt;td&gt;&lt;br /&gt;
| | ◻2<span style="color: #00edff;">▲</span>
&lt;/td&gt;
| | ◻3<span style="color: #00edff;">▲</span>
    &lt;/tr&gt;
| | ◻4<span style="color: #00edff;">▲</span>
    &lt;tr&gt;
|-
        &lt;td&gt;&lt;span style="color: #00edff;"&gt;▲&lt;/span&gt;&lt;br /&gt;
| | –
&lt;/td&gt;
| | ◻
        &lt;td&gt;◻&lt;span style="color: #00edff;"&gt;▲&lt;/span&gt;&lt;br /&gt;
| | ◻2
&lt;/td&gt;
| |
        &lt;td&gt;◻2&lt;span style="color: #00edff;"&gt;▲&lt;/span&gt;&lt;br /&gt;
| |
&lt;/td&gt;
|}
        &lt;td&gt;◻3&lt;span style="color: #00edff;"&gt;▲&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;◻4&lt;span style="color: #00edff;"&gt;▲&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;–&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;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;


&lt;/body&gt;&lt;/html&gt;</pre></div>
[[Category:Impression]]
{{todo|link|move to userspace}}

Latest revision as of 06:24, 20 October 2024

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!)

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:

"Eb" "E" "F" "F#" "G" "G#" "A" "Bb" "B" "C" "C#" "D" "Eb"
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▲ ◻2 ◻▲2 ◻▲ ◻3▲2 ◻3▲ ◻ ▲2 ▲ ◻2▲2 ◻2▲ –
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:

Cb[343] Gb[343] Db[343] Ab[343]
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:

▲2 ◻▲2 ◻2▲2 ◻3▲2
▲ ◻▲ ◻2▲ ◻3▲ ◻4▲
– ◻ ◻2
Retrieved from "https://en.xen.wiki/index.php?title=Kai%27s_House_of_Odds_and_Ends&oldid=161325"