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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