Examples of tunings, showing the value of major 3rd intervals
in cents. A pure (just) 3rd is 386 cents; an equal tempered 3rd is 400 cents; a Pythagorean
3rd is 408 cents: this is considered to be as wide as the ear will tolerate for sustained chords.
Tuning | C-E | G-B | D-F# | A-C# | E-G# | B-Eb |
F#-Bb | C#-F | G#-C | Eb-G | Bb-D | F-A |
Just Scale | 386 | 386 | 386 | 427 | 427 | 427
| 406 | 386 | 386 | 386 | 408 | 386 | |
1/4c. Mean Tone | 386 | 386 | 386 | 386 | 386 | 427
| 427 | 427 | 427 | 386 | 386 | 386 |
1/5c. Mean Tone | 391 | 391 | 391 | 391 | 391 | 419
| 419 | 419 | 419 | 391 | 391 | 391 |
4/25c. Mean Tone | 394 | 394 | 394 | 394 | 394 | 412
| 412 | 412 | 412 | 394 | 394 | 394 |
Wm. Hawkes Mod. M.T. | 391 | 391 | 391 | 391 | 395 | 415
| 419 | 419 | 414 | 395 | 391 | 391 |
J.P. Rameau's Mod. M.T. | 386 | 386 | 391 | 397 | 402 | 413
| 420 | 417 | 411 | 400 | 388 | 386 |
D'Alembert's Mod. M.T. | 386 | 387 | 388 | 389 | 390 | 399
| 406 | 415 | 424 | 414 | 405 | 395 |
18c. English | 386 | 390 | 393 | 397 | 400 | 403
| 407 | 410 | 414 | 407 | 400 | 393 |
Werckmeister III | 390 | 396 | 396 | 402 | 402 | 402
| 408 | 408 | 408 | 402 | 396 | 390 |
Kirnberger II | 386 | 386 | 386 | 395 | 406 | 406
| 406 | 408 | 408 | 408 | 408 | 397 |
Kirnberger III | 386 | 392 | 397 | 400 | 406 | 406
| 406 | 408 | 408 | 402 | 397 | 392 |
Bach (Kellner) | 389 | 394 | 394 | 398 | 403 | 403
| 408 | 408 | 408 | 403 | 398 | 394 |
Young I | 392 | 394 | 396 | 400 | 404 | 406
| 408 | 406 | 404 | 400 | 396 | 394 |
Young II | 392 | 392 | 392 | 396 | 400 | 404
| 408 | 408 | 408 | 404 | 400 | 396 |
N. Taylor | 388 | 393 | 396 | 401 | 406 | 406
| 408 | 406 | 406 | 401 | 396 | 393 |
Vallotti | 392 | 392 | 396 | 400 | 404 | 408
| 408 | 408 | 404 | 400 | 396 | 392 |
Equal Temp. | 400 | 400 | 400 | 400 | 400 | 400
| 400 | 400 | 400 | 400 | 400 | 400 |
Pythagorean (Van Zwolle) | 408 | 408 | 384 | 384 | 384 | 384
| 408 | 408 | 408 | 408 | 408 | 408 |
The following table shows the values of minor 3rds in different tunings,
with the intervals given in cents. 316 cents is a pure (just) minor 3rd; a 1/4 comma mean tone
3rd is 310 cents, and an equal tempered 3rd is 300 cents.
Tuning | C-Eb | G-Bb | D-F | A-C | E-G | B-D |
F#-A | C#-E | G#-B | Eb-F# | Bb-C# | F-G# |
Just Scale | 316 | 294 | 294 | 316 | 316 | 316
| 294 | 275 | 275 | 275 | 316 | 316 | |
1/4c. Mean Tone | 310 | 310 | 310 | 310 | 310 | 310
| 310 | 310 | 310 | 269 | 269 | 269 |
1/5c. Mean Tone | 307 | 307 | 307 | 307 | 307 | 307
| 307 | 307 | 307 | 279 | 279 | 279 |
4/25c. Mean Tone | 304 | 304 | 304 | 304 | 304 | 304
| 304 | 304 | 304 | 286 | 286 | 286 |
Wm. Hawkes Mod. M.T. | 303 | 307 | 307 | 307 | 307 | 307
| 307 | 307 | 303 | 283 | 279 | 283 |
J.P. Rameau's Mod. M.T. | 296 | 308 | 310 | 310 | 310 | 310
| 305 | 299 | 294 | 289 | 281 | 285 |
D'Alembert's Mod. M.T. | 282 | 292 | 301 | 310 | 310 | 309
| 308 | 307 | 307 | 299 | 291 | 282 |
18c. English | 290 | 297 | 303 | 310 | 310 | 307
| 303 | 300 | 300 | 297 | 293 | 290 |
Werckmeister III | 294 | 300 | 306 | 312 | 306 | 300
| 300 | 300 | 300 | 294 | 294 | 294 |
Kirnberger II | 294 | 294 | 294 | 305 | 316 | 316
| 305 | 296 | 296 | 296 | 294 | 294 |
Kirnberger III | 294 | 300 | 305 | 310 | 310 | 305
| 300 | 296 | 296 | 296 | 294 | 294 |
Bach (Kellner) | 294 | 299 | 304 | 308 | 308 | 304
| 304 | 299 | 299 | 294 | 294 | 294 |
Young I | 298 | 302 | 304 | 306 | 308 | 304
| 302 | 306 | 296 | 294 | 294 | 296 |
Young II | 294 | 298 | 302 | 306 | 306 | 306
| 306 | 302 | 298 | 294 | 294 | 294 |
N. Taylor | 296 | 301 | 304 | 309 | 309 | 304
| 301 | 306 | 296 | 294 | 294 | 296 |
Vallotti | 298 | 302 | 306 | 306 | 306 | 306
| 302 | 298 | 294 | 294 | 294 | 294 |
Equal Temp. | 300 | 300 | 300 | 300 | 300 | 300
| 300 | 300 | 300 | 300 | 300 | 300 |
Pythagorean(Van Zwolle) | 294 | 294 | 294 | 294 | 294 | 294
| 318 | 318 | 318 | 294 | 294 | 294 |
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