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

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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 [[/cdn-cgi/l/email-protection|[email protected]]], 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:
Line 103: Line 103:
{| class="wikitable"
{| class="wikitable"
|-
|-
| 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:
Line 143: Line 143:
| |  
| |  
|}
|}
[[Category:Impression]]
[[Category:Impression]]

Revision as of 20:36, 23 April 2023

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
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