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=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 [[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:


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


{| class="wikitable"
{| class="wikitable center-all"
|-
|-
| style="text-align:center;" | Cb[343]
| Cb[343]
| style="text-align:center;" | Gb[343]
| Gb[343]
| style="text-align:center;" | Db[343]
| Db[343]
| style="text-align:center;" | Ab[343]
| Ab[343]
| style="text-align:center;" |  
|  
|-
|-
| style="text-align:center;" | Db[49]
| Db[49]
| style="text-align:center;" | Ab[49]
| Ab[49]
| style="text-align:center;" | Eb[49]
| Eb[49]
| style="text-align:center;" | Bb[49]
| Bb[49]
| style="text-align:center;" | F[49]
| F[49]
|-
|-
| style="text-align:center;" | Eb[7]
| Eb[7]
| style="text-align:center;" | Bb[7]
| Bb[7]
| style="text-align:center;" | F[7]
| F[7]
| style="text-align:center;" |  
|  
| style="text-align:center;" |  
|  
|}
|}
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:
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| |  
| |  
|}
|}
[[Category:Impression]]
{{todo|link|move to userspace}}
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