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Geometric representation of the equal temperament
from Sopplimenti musicali (1588) by Gioseffo Zarlino
Equal temperament (or equal temperament) is the name given to a tuning system that divides an octave into twelve equal semitone steps of 100 cents.
Equal temperament is currently the most common in our culture.
In equal temperament, all equal intervals have the same frequency ratios: Except for their pitch, equal intervals do not differ in anything. That is why this tuning is called „equal temperament“. The advantage of this tuning is the versatility of all chords equally.
In the end, equal temperament is a kind of compromise that tries to reconcile many different needs.
Equal temperament – Reference Frequency 1 Hz – Diapason 430.5(389646) Hz
| Note name | Hz |
|---|---|
| 8.0000000 | |
| 8.4757048 | |
| 8.9796964 | |
| 9.5136569 | |
| 10.0793684 | |
| 10.6787188 | |
| 11.3137085 | |
| 11.9864566 | |
| 12.6992084 | |
| 13.4543426 | |
| 14.2543795 | |
| 15.1019890 | |
| 16.0000000 | |
| 16.9514095 | |
| 17.9593928 | |
| 19.0273138 | |
| 20.1587368 | |
| 21.3574377 | |
| 22.6274170 | |
| 23.9729132 | |
| 25.3984168 | |
| A0 | 26.9086853 |
| A#0/Bb0 | 28.5087590 |
| B0 | 30.2039780 |
| C1 | 32.0000000 |
| C#1/Db1 | 33.9028190 |
| D1 | 35.9187855 |
| D#1/Eb1 | 38.0546277 |
| E1 | 40.3174736 |
| F1 | 42.7148753 |
| F#1/Gb1 | 45.2548340 |
| G1 | 47.9458265 |
| G#1/Ab1 | 50.7968337 |
| A1 | 53.8173706 |
| A#1/Bb1 | 57.0175180 |
| B1 | 60.4079560 |
| C2 | 64.0000000 |
| C#2/Db2 | 67.8056380 |
| D2 | 71.8375711 |
| D#2/Eb2 | 76.1092554 |
| E2 | 80.6349472 |
| F2 | 85.4297507 |
| F#2/Gb2 | 90.5096680 |
| G2 | 95.8916529 |
| G#2/Ab2 | 101.5936673 |
| A2 | 107.6347412 |
| A#2/Bb2 | 114.0350359 |
| B2 | 120.8159120 |
| C3 | 128.0000000 |
| C#3/Db3 | 135.6112761 |
| D3 | 143.6751422 |
| D#3/Eb3 | 152.2185107 |
| E3 | 161.2698944 |
| F3 | 170.8595013 |
| F#3/Gb3 | 181.0193360 |
| G3 | 191.7833058 |
| G#3/Ab3 | 203.1873347 |
| A3 | 215.2694823 |
| A#3/Bb3 | 228.0700718 |
| B3 | 241.6318240 |
| C4 (middle C) | 256.0000000 |
| C#4/Db4 | 271.2225522 |
| D4 | 287.3502844 |
| D#4/Eb4 | 304.4370214 |
| E4 | 322.5397888 |
| F4 | 341.7190027 |
| F#4/Gb4 | 362.0386720 |
| G4 | 383.5666117 |
| G#4/Ab4 | 406.3746693 |
| A4 concert pitch | 430.5389646 |
| A#4/Bb4 | 456.1401437 |
| B4 | 483.2636481 |
| C5 | 512.0000000 |
| C#5/Db5 | 542.4451043 |
| D5 | 574.7005687 |
| D#5/Eb5 | 608.8740429 |
| E5 | 645.0795775 |
| F5 | 683.4380053 |
| F#5/Gb5 | 724.0773439 |
| G5 | 767.1332234 |
| G#5/Ab5 | 812.7493386 |
| A5 | 861.0779292 |
| A#5/Bb5 | 912.2802874 |
| B5 | 966.5272962 |
| C6 | 1024.0000000 |
| C#6/Db6 | 1084.8902086 |
| D6 | 1149.4011375 |
| D#6/Eb6 | 1217.7480858 |
| E6 | 1290.1591551 |
| F6 | 1366.8760107 |
| F#6/Gb6 | 1448.1546879 |
| G6 | 1534.2664467 |
| G#6/Ab6 | 1625.4986772 |
| A6 | 1722.1558584 |
| A#6/Bb6 | 1824.5605748 |
| B6 | 1933.0545924 |
| C7 | 2048.0000000 |
| C#7/Db7 | 2169.7804172 |
| D7 | 2298.8022749 |
| D#7/Eb7 | 2435.4961715 |
| E7 | 2580.3183102 |
| F7 | 2733.7520213 |
| F#7/Gb7 | 2896.3093757 |
| G7 | 3068.5328934 |
| G#7/Ab7 | 3250.9973544 |
| A7 | 3444.3117169 |
| A#7/Bb7 | 3649.1211495 |
| B7 | 3866.1091847 |
| C8 | 4096.0000000 |
| C#8/Db8 | 4339.5608345 |
| D8 | 4597.6045499 |
| D#8/Eb8 | 4870.9923431 |
| E8 | 5160.6366204 |
| F8 | 5467.5040427 |
| F#8/Gb8 | 5792.6187515 |
| G8 | 6137.0657869 |
| G#8/Ab8 | 6501.9947089 |
| A8 | 6888.6234338 |
| A#8/Bb8 | 7298.2422990 |
| B8 | 7732.2183695 |
| C9 | 8192.0000000 |
| C#9/Db9 | 8679.1216690 |
| D9 | 9195.2090998 |
| D#9/Eb9 | 9741.9846861 |
| E9 | 10321.2732407 |
| F9 | 10935.0080854 |
| F#9/Gb9 | 11585.2375030 |
| G9 | 12274.1315738 |
Equal temperament – Reference Frequency 27 Hz – Diapason 432 Hz
| Note name | Hz |
|---|---|
| 8.0271480 | |
| 8.5044671 | |
| 9.0101690 | |
| 9.5459415 | |
| 10.1135728 | |
| 10.7149571 | |
| 11.3521016 | |
| 12.0271327 | |
| 12.7423032 | |
| 13.5000000 | |
| 14.3027518 | |
| 15.1532377 | |
| 16.0542961 | |
| 17.0089342 | |
| 18.0203380 | |
| 19.0918831 | |
| 20.2271455 | |
| 21.4299142 | |
| 22.7042032 | |
| 24.0542654 | |
| 25.4846064 | |
| A0 | 27.0000000 |
| A#0/Bb0 | 28.6055035 |
| B0 | 30.3064753 |
| C1 | 32.1085921 |
| C#1/Db1 | 34.0178683 |
| D1 | 36.0406761 |
| D#1/Eb1 | 38.1837662 |
| E1 | 40.4542911 |
| F1 | 42.8598284 |
| F#1/Gb1 | 45.4084064 |
| G1 | 48.1085308 |
| G#1/Ab1 | 50.9692129 |
| A1 | 54.0000000 |
| A#1/Bb1 | 57.2110071 |
| B1 | 60.6129506 |
| C2 | 64.2171842 |
| C#2/Db2 | 68.0357367 |
| D2 | 72.0813521 |
| D#2/Eb2 | 76.3675324 |
| E2 | 80.9085822 |
| F2 | 85.7196568 |
| F#2/Gb2 | 90.8168128 |
| G2 | 96.2170616 |
| G#2/Ab2 | 101.9384258 |
| A2 | 108.0000000 |
| A#2/Bb2 | 114.4220142 |
| B2 | 121.2259012 |
| C3 | 128.4343684 |
| C#3/Db3 | 136.0714734 |
| D3 | 144.1627043 |
| D#3/Eb3 | 152.7350647 |
| E3 | 161.8171643 |
| F3 | 171.4393136 |
| F#3/Gb3 | 181.6336257 |
| G3 | 192.4341231 |
| G#3/Ab3 | 203.8768515 |
| A3 | 216.0000000 |
| A#3/Bb3 | 228.8440284 |
| B3 | 242.4518024 |
| C4 (middle C) | 256.8687368 |
| C#4/Db4 | 272.1429468 |
| D4 | 288.3254085 |
| D#4/Eb4 | 305.4701295 |
| E4 | 323.6343286 |
| F4 | 342.8786272 |
| F#4/Gb4 | 363.2672514 |
| G4 | 384.8682462 |
| G#4/Ab4 | 407.7537031 |
| A4 concert pitch | 432.0000000 |
| A#4/Bb4 | 457.6880568 |
| B4 | 484.9036049 |
| C5 | 513.7374737 |
| C#5/Db5 | 544.2858936 |
| D5 | 576.6508170 |
| D#5/Eb5 | 610.9402589 |
| E5 | 647.2686572 |
| F5 | 685.7572545 |
| F#5/Gb5 | 726.5345028 |
| G5 | 769.7364925 |
| G#5/Ab5 | 815.5074062 |
| A5 | 864.0000000 |
| A#5/Bb5 | 915.3761135 |
| B5 | 969.8072097 |
| C6 | 1027.4749474 |
| C#6/Db6 | 1088.5717871 |
| D6 | 1153.3016340 |
| D#6/Eb6 | 1221.8805179 |
| E6 | 1294.5373144 |
| F6 | 1371.5145089 |
| F#6/Gb6 | 1453.0690056 |
| G6 | 1539.4729849 |
| G#6/Ab6 | 1631.0148123 |
| A6 | 1728.0000000 |
| A#6/Bb6 | 1830.7522271 |
| B6 | 1939.6144195 |
| C7 | 2054.9498947 |
| C#7/Db7 | 2177.1435742 |
| D7 | 2306.6032680 |
| D#7/Eb7 | 2443.7610358 |
| E7 | 2589.0746288 |
| F7 | 2743.0290178 |
| F#7/Gb7 | 2906.1380111 |
| G7 | 3078.9459699 |
| G#7/Ab7 | 3262.0296246 |
| A7 | 3456.0000000 |
| A#7/Bb7 | 3661.5044541 |
| B7 | 3879.2288390 |
| C8 | 4109.8997894 |
| C#8/Db8 | 4354.2871484 |
| D8 | 4613.2065360 |
| D#8/Eb8 | 4887.5220716 |
| E8 | 5178.1492577 |
| F8 | 5486.0580356 |
| F#8/Gb8 | 5812.2760222 |
| G8 | 6157.8919398 |
| G#8/Ab8 | 6524.0592493 |
| A8 | 6912.0000000 |
| A#8/Bb8 | 7323.0089082 |
| B8 | 7758.4576779 |
| C9 | 8219.7995789 |
| C#9/Db9 | 8708.5742969 |
| D9 | 9226.4130720 |
| D#9/Eb9 | 9775.0441431 |
| E9 | 10356.2985154 |
| F9 | 10972.1160712 |
| F#9/Gb9 | 11624.5520445 |
| G9 | 12315.7838796 |
Equal Temperament – Reference Frequency 55 Hz – Diapason 440 Hz
| Note name | Hz |
|---|---|
| 8.1757989 | |
| 8.6619572 | |
| 9.1770240 | |
| 9.7227182 | |
| 10.3008612 | |
| 10.9133822 | |
| 11.5623257 | |
| 12.2498574 | |
| 12.9782718 | |
| 13.7500000 | |
| 14.5676175 | |
| 15.4338532 | |
| 16.3515978 | |
| 17.3239144 | |
| 18.3540480 | |
| 19.4454365 | |
| 20.6017223 | |
| 21.8267645 | |
| 23.1246514 | |
| 24.4997147 | |
| 25.9565436 | |
| A0 | 27.5000000 |
| A#0/Bb0 | 29.1352351 |
| B0 | 30.8677063 |
| C1 | 32.7031957 |
| C#1/Db1 | 34.6478289 |
| D1 | 36.7080960 |
| D#1/Eb1 | 38.8908730 |
| E1 | 41.2034446 |
| F1 | 43.6535289 |
| F#1/Gb1 | 46.2493028 |
| G1 | 48.9994295 |
| G#1/Ab1 | 51.9130872 |
| A1 | 55.0000000 |
| A#1/Bb1 | 58.2704702 |
| B1 | 61.7354127 |
| C2 | 65.4063913 |
| C#2/Db2 | 69.2956577 |
| D2 | 73.4161920 |
| D#2/Eb2 | 77.7817459 |
| E2 | 82.4068892 |
| F2 | 87.3070579 |
| F#2/Gb2 | 92.4986057 |
| G2 | 97.9988590 |
| G#2/Ab2 | 103.8261744 |
| A2 | 110.0000000 |
| A#2/Bb2 | 116.5409404 |
| B2 | 123.4708253 |
| C3 | 130.8127827 |
| C#3/Db3 | 138.5913155 |
| D3 | 146.8323840 |
| D#3/Eb3 | 155.5634919 |
| E3 | 164.8137785 |
| F3 | 174.6141157 |
| F#3/Gb3 | 184.9972114 |
| G3 | 195.9977180 |
| G#3/Ab3 | 207.6523488 |
| A3 | 220.0000000 |
| A#3/Bb3 | 233.0818808 |
| B3 | 246.9416506 |
| C4 (middle C) | 261.6255653 |
| C#4/Db4 | 277.1826310 |
| D4 | 293.6647679 |
| D#4/Eb4 | 311.1269837 |
| E4 | 329.6275569 |
| F4 | 349.2282314 |
| F#4/Gb4 | 369.9944227 |
| G4 | 391.9954360 |
| G#4/Ab4 | 415.3046976 |
| A4 concert pitch | 440.0000000 |
| A#4/Bb4 | 466.1637615 |
| B4 | 493.8833013 |
| C5 | 523.2511306 |
| C#5/Db5 | 554.3652620 |
| D5 | 587.3295358 |
| D#5/Eb5 | 622.2539674 |
| E5 | 659.2551138 |
| F5 | 698.4564629 |
| F#5/Gb5 | 739.9888454 |
| G5 | 783.9908720 |
| G#5/Ab5 | 830.6093952 |
| A5 | 880.0000000 |
| A#5/Bb5 | 932.3275230 |
| B5 | 987.7666025 |
| C6 | 1046.5022612 |
| C#6/Db6 | 1108.7305239 |
| D6 | 1174.6590717 |
| D#6/Eb6 | 1244.5079349 |
| E6 | 1318.5102277 |
| F6 | 1396.9129257 |
| F#6/Gb6 | 1479.9776908 |
| G6 | 1567.9817439 |
| G#6/Ab6 | 1661.2187903 |
| A6 | 1760.0000000 |
| A#6/Bb6 | 1864.6550461 |
| B6 | 1975.5332050 |
| C7 | 2093.0045224 |
| C#7/Db7 | 2217.4610478 |
| D7 | 2349.3181433 |
| D#7/Eb7 | 2489.0158698 |
| E7 | 2637.0204553 |
| F7 | 2793.8258515 |
| F#7/Gb7 | 2959.9553817 |
| G7 | 3135.9634879 |
| G#7/Ab7 | 3322.4375806 |
| A7 | 3520.0000000 |
| A#7/Bb7 | 3729.3100921 |
| B7 | 3951.0664100 |
| C8 | 4186.0090448 |
| C#8/Db8 | 4434.9220956 |
| D8 | 4698.6362867 |
| D#8/Eb8 | 4978.0317396 |
| E8 | 5274.0409106 |
| F8 | 5587.6517029 |
| F#8/Gb8 | 5919.9107634 |
| G8 | 6271.9269757 |
| G#8/Ab8 | 6644.8751613 |
| A8 | 7040.0000000 |
| A#8/Bb8 | 7458.6201843 |
| B8 | 7902.1328201 |
| C9 | 8372.0180896 |
| C#9/Db9 | 8869.8441913 |
| D9 | 9397.2725734 |
| D#9/Eb9 | 9956.0634791 |
| E9 | 10548.0818212 |
| F9 | 11175.3034059 |
| F#9/Gb9 | 11839.8215268 |
| G9 | 12543.8539514 |
Scala data
! equal.scl
!
Equal temperament with 12 degrees / octave
12
!
100.0
200.0
300.0
400.0
500.0
600.0
700.0
800.0
900.0
1000.0
1100.0
2/1
About Scala scale file (.scl) format