Kai's House of Odds and Ends

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