Equal Temperament

Geometric representation of the equal temperament

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 nameHz
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
A026.9086853
A#0/Bb028.5087590
B030.2039780
C132.0000000
C#1/Db133.9028190
D135.9187855
D#1/Eb138.0546277
E140.3174736
F142.7148753
F#1/Gb145.2548340
G147.9458265
G#1/Ab150.7968337
A153.8173706
A#1/Bb157.0175180
B160.4079560
C264.0000000
C#2/Db267.8056380
D271.8375711
D#2/Eb276.1092554
E280.6349472
F285.4297507
F#2/Gb290.5096680
G295.8916529
G#2/Ab2101.5936673
A2107.6347412
A#2/Bb2114.0350359
B2120.8159120
C3128.0000000
C#3/Db3135.6112761
D3143.6751422
D#3/Eb3152.2185107
E3161.2698944
F3170.8595013
F#3/Gb3181.0193360
G3191.7833058
G#3/Ab3203.1873347
A3215.2694823
A#3/Bb3228.0700718
B3241.6318240
C4 (middle C)256.0000000
C#4/Db4271.2225522
D4287.3502844
D#4/Eb4304.4370214
E4322.5397888
F4341.7190027
F#4/Gb4362.0386720
G4383.5666117
G#4/Ab4406.3746693
A4 concert pitch430.5389646
A#4/Bb4456.1401437
B4483.2636481
C5512.0000000
C#5/Db5542.4451043
D5574.7005687
D#5/Eb5608.8740429
E5645.0795775
F5683.4380053
F#5/Gb5724.0773439
G5767.1332234
G#5/Ab5812.7493386
A5861.0779292
A#5/Bb5912.2802874
B5966.5272962
C61024.0000000
C#6/Db61084.8902086
D61149.4011375
D#6/Eb61217.7480858
E61290.1591551
F61366.8760107
F#6/Gb61448.1546879
G61534.2664467
G#6/Ab61625.4986772
A61722.1558584
A#6/Bb61824.5605748
B61933.0545924
C72048.0000000
C#7/Db72169.7804172
D72298.8022749
D#7/Eb72435.4961715
E72580.3183102
F72733.7520213
F#7/Gb72896.3093757
G73068.5328934
G#7/Ab73250.9973544
A73444.3117169
A#7/Bb73649.1211495
B73866.1091847
C84096.0000000
C#8/Db84339.5608345
D84597.6045499
D#8/Eb84870.9923431
E85160.6366204
F85467.5040427
F#8/Gb85792.6187515
G86137.0657869
G#8/Ab86501.9947089
A86888.6234338
A#8/Bb87298.2422990
B87732.2183695
C98192.0000000
C#9/Db98679.1216690
D99195.2090998
D#9/Eb99741.9846861
E910321.2732407
F910935.0080854
F#9/Gb911585.2375030
G912274.1315738

Equal temperament – Reference Frequency 27 Hz – Diapason 432 Hz

Note nameHz
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
A027.0000000
A#0/Bb028.6055035
B030.3064753
C132.1085921
C#1/Db134.0178683
D136.0406761
D#1/Eb138.1837662
E140.4542911
F142.8598284
F#1/Gb145.4084064
G148.1085308
G#1/Ab150.9692129
A154.0000000
A#1/Bb157.2110071
B160.6129506
C264.2171842
C#2/Db268.0357367
D272.0813521
D#2/Eb276.3675324
E280.9085822
F285.7196568
F#2/Gb290.8168128
G296.2170616
G#2/Ab2101.9384258
A2108.0000000
A#2/Bb2114.4220142
B2121.2259012
C3128.4343684
C#3/Db3136.0714734
D3144.1627043
D#3/Eb3152.7350647
E3161.8171643
F3171.4393136
F#3/Gb3181.6336257
G3192.4341231
G#3/Ab3203.8768515
A3216.0000000
A#3/Bb3228.8440284
B3242.4518024
C4 (middle C)256.8687368
C#4/Db4272.1429468
D4288.3254085
D#4/Eb4305.4701295
E4323.6343286
F4342.8786272
F#4/Gb4363.2672514
G4384.8682462
G#4/Ab4407.7537031
A4 concert pitch432.0000000
A#4/Bb4457.6880568
B4484.9036049
C5513.7374737
C#5/Db5544.2858936
D5576.6508170
D#5/Eb5610.9402589
E5647.2686572
F5685.7572545
F#5/Gb5726.5345028
G5769.7364925
G#5/Ab5815.5074062
A5864.0000000
A#5/Bb5915.3761135
B5969.8072097
C61027.4749474
C#6/Db61088.5717871
D61153.3016340
D#6/Eb61221.8805179
E61294.5373144
F61371.5145089
F#6/Gb61453.0690056
G61539.4729849
G#6/Ab61631.0148123
A61728.0000000
A#6/Bb61830.7522271
B61939.6144195
C72054.9498947
C#7/Db72177.1435742
D72306.6032680
D#7/Eb72443.7610358
E72589.0746288
F72743.0290178
F#7/Gb72906.1380111
G73078.9459699
G#7/Ab73262.0296246
A73456.0000000
A#7/Bb73661.5044541
B73879.2288390
C84109.8997894
C#8/Db84354.2871484
D84613.2065360
D#8/Eb84887.5220716
E85178.1492577
F85486.0580356
F#8/Gb85812.2760222
G86157.8919398
G#8/Ab86524.0592493
A86912.0000000
A#8/Bb87323.0089082
B87758.4576779
C98219.7995789
C#9/Db98708.5742969
D99226.4130720
D#9/Eb99775.0441431
E910356.2985154
F910972.1160712
F#9/Gb911624.5520445
G912315.7838796

Equal Temperament – Reference Frequency 55 Hz – Diapason 440 Hz

Note nameHz
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
A027.5000000
A#0/Bb029.1352351
B030.8677063
C132.7031957
C#1/Db134.6478289
D136.7080960
D#1/Eb138.8908730
E141.2034446
F143.6535289
F#1/Gb146.2493028
G148.9994295
G#1/Ab151.9130872
A155.0000000
A#1/Bb158.2704702
B161.7354127
C265.4063913
C#2/Db269.2956577
D273.4161920
D#2/Eb277.7817459
E282.4068892
F287.3070579
F#2/Gb292.4986057
G297.9988590
G#2/Ab2103.8261744
A2110.0000000
A#2/Bb2116.5409404
B2123.4708253
C3130.8127827
C#3/Db3138.5913155
D3146.8323840
D#3/Eb3155.5634919
E3164.8137785
F3174.6141157
F#3/Gb3184.9972114
G3195.9977180
G#3/Ab3207.6523488
A3220.0000000
A#3/Bb3233.0818808
B3246.9416506
C4 (middle C)261.6255653
C#4/Db4277.1826310
D4293.6647679
D#4/Eb4311.1269837
E4329.6275569
F4349.2282314
F#4/Gb4369.9944227
G4391.9954360
G#4/Ab4415.3046976
A4 concert pitch440.0000000
A#4/Bb4466.1637615
B4493.8833013
C5523.2511306
C#5/Db5554.3652620
D5587.3295358
D#5/Eb5622.2539674
E5659.2551138
F5698.4564629
F#5/Gb5739.9888454
G5783.9908720
G#5/Ab5830.6093952
A5880.0000000
A#5/Bb5932.3275230
B5987.7666025
C61046.5022612
C#6/Db61108.7305239
D61174.6590717
D#6/Eb61244.5079349
E61318.5102277
F61396.9129257
F#6/Gb61479.9776908
G61567.9817439
G#6/Ab61661.2187903
A61760.0000000
A#6/Bb61864.6550461
B61975.5332050
C72093.0045224
C#7/Db72217.4610478
D72349.3181433
D#7/Eb72489.0158698
E72637.0204553
F72793.8258515
F#7/Gb72959.9553817
G73135.9634879
G#7/Ab73322.4375806
A73520.0000000
A#7/Bb73729.3100921
B73951.0664100
C84186.0090448
C#8/Db84434.9220956
D84698.6362867
D#8/Eb84978.0317396
E85274.0409106
F85587.6517029
F#8/Gb85919.9107634
G86271.9269757
G#8/Ab86644.8751613
A87040.0000000
A#8/Bb87458.6201843
B87902.1328201
C98372.0180896
C#9/Db98869.8441913
D99397.2725734
D#9/Eb99956.0634791
E910548.0818212
F911175.3034059
F#9/Gb911839.8215268
G912543.8539514

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