Kai's House of Odds and Ends
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author kai.lugheidh and made on 2018-01-17 04:49:17 UTC.
- The original revision id was 624971673.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
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 [[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.) The octave above the Eb[7] reference pitch is as follows: ||= ||= **<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: ||= 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: || <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 || || ||
Original HTML content:
<html><head><title>Kai's House of Odds and Ends</title></head><body>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!<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="La Monte Young's tuning from The Well-Tuned Piano, in Rational Comma Notation (and brand spankin' new KAIGI SIGNATURES!)"></a><!-- ws:end:WikiTextHeadingRule:0 -->La Monte Young's tuning from <em>The Well-Tuned Piano,</em> in Rational Comma Notation (and brand spankin' new KAIGI SIGNATURES!)</h1>
<br />
With Concert Pitch (1/1) being C4@256Hz, Eb4[7] = 7/6 = (298+2/3)Hz serves nicely as the tonic in <a class="wiki_link" href="http://xenharmonic.wikispaces.com/Rational%20Comma%20Notation%20%28RCN%29">Rational Comma Notation (RCN). </a>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.)<br />
<br />
The octave above the Eb[7] reference pitch is as follows:<br />
<table class="wiki_table">
<tr>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><strong><span style="background-color: #000000; color: #ffffff;">"Eb"</span></strong><br />
</td>
<td style="text-align: center;"><strong>"E"</strong><br />
</td>
<td style="text-align: center;"><strong>"F"</strong><br />
</td>
<td style="text-align: center;"><strong><span style="background-color: #000000; color: #ffffff;">"F#"</span></strong><br />
</td>
<td style="text-align: center;"><strong>"G"</strong><br />
</td>
<td style="text-align: center;"><strong><span style="background-color: #000000; color: #ffffff;">"G#"</span></strong><br />
</td>
<td style="text-align: center;"><strong>"A"</strong><br />
</td>
<td style="text-align: center;"><strong><span style="background-color: #000000; color: #ffffff;">"Bb"</span></strong><br />
</td>
<td style="text-align: center;"><strong>"B"</strong><br />
</td>
<td style="text-align: center;"><strong>"C"</strong><br />
</td>
<td style="text-align: center;"><strong><span style="background-color: #000000; color: #ffffff;">"C#"</span></strong><br />
</td>
<td style="text-align: center;"><strong>"D"</strong><br />
</td>
<td style="text-align: center;"><strong><span style="background-color: #000000; color: #ffffff;">"Eb"</span></strong><br />
</td>
</tr>
<tr>
<td style="text-align: center;"><strong>RATIO</strong><br />
</td>
<td style="text-align: center;">1/1<br />
</td>
<td style="text-align: center;">567/512<br />
</td>
<td style="text-align: center;">9/8<br />
</td>
<td style="text-align: center;">147/128<br />
</td>
<td style="text-align: center;">21/16<br />
</td>
<td style="text-align: center;">1323/1024<br />
</td>
<td style="text-align: center;">189/128<br />
</td>
<td style="text-align: center;">3/2<br />
</td>
<td style="text-align: center;">49/32<br />
</td>
<td style="text-align: center;">7/4<br />
</td>
<td style="text-align: center;">441/256<br />
</td>
<td style="text-align: center;">63/32<br />
</td>
<td style="text-align: center;">2/1<br />
</td>
</tr>
<tr>
<td style="text-align: center;"><strong>CENTS</strong><br />
</td>
<td style="text-align: center;">0.000000<br />
</td>
<td style="text-align: center;">176.645910<br />
</td>
<td style="text-align: center;">203.910002<br />
</td>
<td style="text-align: center;">239.606814<br />
</td>
<td style="text-align: center;">470.780907<br />
</td>
<td style="text-align: center;">443.516816<br />
</td>
<td style="text-align: center;">674.690909<br />
</td>
<td style="text-align: center;">701.955001<br />
</td>
<td style="text-align: center;">737.651813<br />
</td>
<td style="text-align: center;">968.825906<br />
</td>
<td style="text-align: center;">941.561815<br />
</td>
<td style="text-align: center;">1172.735908<br />
</td>
<td style="text-align: center;">1200.000000<br />
</td>
</tr>
<tr>
<td style="text-align: center;"><strong>KAIGI SIGNATURE</strong><br />
</td>
<td style="text-align: center;">–<br />
</td>
<td style="text-align: center;">◻4<span style="color: #00edff;">▲</span><br />
</td>
<td style="text-align: center;">◻2<br />
</td>
<td style="text-align: center;">◻<span style="color: #00edff;">▲</span>2<br />
</td>
<td style="text-align: center;">◻<span style="color: #00edff;">▲</span><br />
</td>
<td style="text-align: center;">◻3<span style="color: #00edff;">▲</span>2<br />
</td>
<td style="text-align: center;">◻3<span style="color: #00edff;">▲</span><br />
</td>
<td style="text-align: center;">◻<br />
</td>
<td style="text-align: center;"><span style="color: #00edff;">▲</span>2<br />
</td>
<td style="text-align: center;"><span style="color: #00edff;">▲</span><br />
</td>
<td style="text-align: center;">◻2<span style="color: #00edff;">▲</span>2<br />
</td>
<td style="text-align: center;">◻2<span style="color: #00edff;">▲</span><br />
</td>
<td style="text-align: center;">–<br />
</td>
</tr>
<tr>
<td style="text-align: center;"><strong>ABS. PITCH (RCN)</strong><br />
</td>
<td style="text-align: center;">Eb4[7]<br />
</td>
<td style="text-align: center;">F4[49]<br />
</td>
<td style="text-align: center;">F4[7]<br />
</td>
<td style="text-align: center;">Gb4[343]<br />
</td>
<td style="text-align: center;">Ab4[49]<br />
</td>
<td style="text-align: center;">Ab4[343]<br />
</td>
<td style="text-align: center;">Bb4[49]<br />
</td>
<td style="text-align: center;">Bb4[7]<br />
</td>
<td style="text-align: center;">Cb4[343]<br />
</td>
<td style="text-align: center;">Db4[49]<br />
</td>
<td style="text-align: center;">Db4[343]<br />
</td>
<td style="text-align: center;">Eb5[49]<br />
</td>
<td style="text-align: center;">Eb5[7]<br />
</td>
</tr>
<tr>
<td style="text-align: center;"><strong>FREQUENCY (Hz)</strong><br />
</td>
<td style="text-align: center;">298+2/3<br />
</td>
<td style="text-align: center;">330+3/4<br />
</td>
<td style="text-align: center;">336<br />
</td>
<td style="text-align: center;">343<br />
</td>
<td style="text-align: center;">392<br />
</td>
<td style="text-align: center;">385+7/8<br />
</td>
<td style="text-align: center;">441<br />
</td>
<td style="text-align: center;">448<br />
</td>
<td style="text-align: center;">457+1/3<br />
</td>
<td style="text-align: center;">522+2/3<br />
</td>
<td style="text-align: center;">514+1/2<br />
</td>
<td style="text-align: center;">588<br />
</td>
<td style="text-align: center;">597+1/3<br />
</td>
</tr>
</table>
The pitch classes of this tuning as a lattice in RCN:<br />
<table class="wiki_table">
<tr>
<td style="text-align: center;">Cb[343]<br />
</td>
<td style="text-align: center;">Gb[343]<br />
</td>
<td style="text-align: center;">Db[343]<br />
</td>
<td style="text-align: center;">Ab[343]<br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
<tr>
<td style="text-align: center;">Db[49]<br />
</td>
<td style="text-align: center;">Ab[49]<br />
</td>
<td style="text-align: center;">Eb[49]<br />
</td>
<td style="text-align: center;">Bb[49]<br />
</td>
<td style="text-align: center;">F[49]<br />
</td>
</tr>
<tr>
<td style="text-align: center;">Eb[7]<br />
</td>
<td style="text-align: center;">Bb[7]<br />
</td>
<td style="text-align: center;">F[7]<br />
</td>
<td style="text-align: center;"><br />
</td>
<td style="text-align: center;"><br />
</td>
</tr>
</table>
The same lattice in tonic-agnostic Kaigi Signatures, which makes the logic of the system clear:<br />
<table class="wiki_table">
<tr>
<td><span style="color: #00edff;">▲</span>2<br />
</td>
<td>◻<span style="color: #00edff;">▲</span>2<br />
</td>
<td>◻2<span style="color: #00edff;">▲</span>2<br />
</td>
<td>◻3<span style="color: #00edff;">▲</span>2<br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><span style="color: #00edff;">▲</span><br />
</td>
<td>◻<span style="color: #00edff;">▲</span><br />
</td>
<td>◻2<span style="color: #00edff;">▲</span><br />
</td>
<td>◻3<span style="color: #00edff;">▲</span><br />
</td>
<td>◻4<span style="color: #00edff;">▲</span><br />
</td>
</tr>
<tr>
<td>–<br />
</td>
<td>◻<br />
</td>
<td>◻2<br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
</table>
</body></html>