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Just intonation is any musical tuning in which the frequencies of notes are related by whole number ratios. This table shows one possible scheme of implementing just intonation frequencies.
Just tuning frequencies of all notes in each key based on A = 440 Hz when in the key of C. The just intonation scale ratios of 24:27:30:32:36:40:45 are used and each key note has the same frequency in the scales with +/- 1 sharp or flat.
Note that the 6th note in a key changes frequency by a ratio of 81/80 when it becomes the 2nd of the key with one more sharp or one less flat. All other notes retain the same frequency. In C all frequencies are an exact number of Hertz.
In just intonation incidentals tuning must be worked out on a case by case basis. Often the minor third and minor seventh take the ratios 28 and 42 when the tonic is taken as 24, so that in C the tuning for Eb and Bb would be 308 Hz and 462 Hz. These frequencies allow dominant seventh chords with frequency ratios of 4:5:6:7.
For frequencies in other octaves repeatedly double or halve the tabulated figures.
There is a difference between Gb and F# which amounts to a ratio of <math>{3^{12}}/{2^{19}}<math> = 1.0136433 as discovered by Pythagoras.
| Key \ Note
| C
| Db
| D
| Eb
| E
| F
| Gb
| G
| Ab
| A
| Bb
| B
|
| Gb (6b)
|
| 278.123
|
| 309.026
|
| 347.654
| 370.831
|
| 417.185
|
| 463.539
| 494.442
|
| Db (5b)
| 260.741
| 278.123
|
| 312.889
|
| 347.654
| 370.831
|
| 417.185
|
| 463.539
|
|
| Ab (4b)
| 260.741
| 278.123
|
| 312.889
|
| 347.654
|
| 391.111
| 417.185
|
| 469.333
|
| Eb (3b)
| 260.741
|
| 293.333
| 312.889
|
| 352
|
| 391.111
| 417.185
|
| 469.333
|
|
| Bb (2b)
| 264
|
| 293.333
| 312.889
|
| 352
|
| 391.111
|
| 440
| 469.333
|
|
| F (1b)
| 264
|
| 293.333
|
| 330
| 352
|
| 396
|
| 440
| 469.333
|
|
| C (0)
| 264
|
| 297
|
| 330
| 352
|
| 396
|
| 440
|
| 495
|
| G (1#)
| 264
|
| 297
|
| 330
|
| 371.25
| 396
|
| 445.5
|
| 495
|
| D (2#)
|
| 278.438
| 297
|
| 334.125
|
| 371.25
| 396
|
| 445.5
|
| 495
|
| A (3#)
|
| 278.438
| 297
|
| 334.125
|
| 371.25
|
| 417.656
| 445.5
|
| 501.188
|
| E (4#)
|
| 278.438
|
| 313.242
| 334.125
|
| 375.891
|
| 417.656
| 445.5
|
| 501.188
|
| B (5#)
|
| 281.918
|
| 313.242
| 334.125
|
| 375.891
|
| 417.656
|
| 469.863
| 501.188
|
| F# (6#)
|
| 281.918
|
| 313.242
|
| 352.397
| 375.891
|
| 422.877
|
| 469.863
| 501.188
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| Key / Note
| C
| C#
| D
| D#
| E
| F
| F#
| G
| G#
| A
| A#
| B
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| Equitempered
| 261.626
| 277.183
| 293.665
| 311.127
| 329.628
| 349.228
| 369.994
| 391.995
| 415.305
| 440.000
| 466.164
| 493.883
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External links
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Example Usage of tuning |
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csareb: tuning out for a while now to begin a pair of socks promised long ago to a friend. Will watch Christmas Carol. Now, where are those needles? |
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adash66: RT @DIRECTV: NFL Sunday Ticket channel listings have been corrected. If a game is not available to you there, please try tuning to your ... |
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Sheri1009: NFL sun Ticket channel listings have bn corrected. If a game is not available 2 U thr, please try tuning 2 yr local channel. (via @DIRECTV) |
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