Harmonium Tuning

The chart below shows the network of frequency relationships among all pitches between the two harmoniums in my just intonation ensemble. (Note that not every pitch is present in each instrument.) Each line’s length and angle indicate its relationship to the pitch it branches off from. For example, all pitches with a 3/2 relationship to its “parent” are indicated by a short vertical line (see the one labeled “3” near the bottom). Some ratios approximate other meaningful relationships. For example, 19/16 (the 19th partial) is very close to 2431/2048 (the 11th partial over the 13th partial over the 17th partial!!). That relationship is expressed with the gray dotted arc that connects 19 with 2431. The approximated ratio is shown in blue.

To keep the chart readable, many meaningful relationships are not expressed explicitly but are still easy to infer. For example, the approximation of 609 is not only a 3/2 above 203/128 but is also (very nearly) 7/4 above 87/64.

Below are tuning charts for each harmonium, the larger instrument in the four left columns, the smaller instrument in the four right columns. The “Cents Off” column assumes A=440.

NoteBass HzMale HzCents OffPartialNoteBass HzMale HzCents OffPartial
C365.4065130.81301
C#367.4504531134.900906-46.72733
D373.0713242146.142648-8.144143
D#378.6921953157.38439120.14477
E381.758125163.51625-13.6865
F385.8460313171.692063-29.21921F388.9119609177.82392231.53287
F#389.9339375179.867875-48.68211F#394.0218438188.04368828.27423
G398.10975196.21951.9553G395.5548086191.109617-43.727187
G#3101.17568202.351359-44.77299G#3103.730621207.461242-1.597203
A3109.606986219.213973-6.2429A3108.201769216.403537-28.538847
A#3114.461375228.92275-31.1747A#3118.549281237.09856329.57729
B3123.659164247.3183282.636121B3121.615211243.230422-26.219119
C4129.280035258.56007-20.408253C4130.813261.62601
C#4141.032766282.06553130.22969C#4134.900906269.801813-46.72733
D4142.629604285.259208-50.2792233D4144.481937288.963873-27.941131
D#4152.785496305.570992-31.2299D#4157.384391314.76878120.14477
E4163.51625327.0325-13.6865E4163.51625327.0325-13.6865
F4177.823922355.64784431.53287F4171.692063343.384125-29.21921
F#4188.043688376.08737528.27423F#4185.999734371.9994699.35491
G4192.642582385.285164-29.895377G4196.2195392.4391.9553
G#4207.461242414.922484-1.597203G#4202.351359404.702719-44.77299
A4216.403537432.807074-28.538847A4219.213973438.427945-6.2429
A#4237.098563474.19712529.57729A#4228.92275457.8455-31.1747
B4247.318328494.6366562.636121B4247.318328494.6366562.636121
C5261.626523.25201C5261.626523.25201
C#5269.801813539.603625-46.72733C#5277.977625555.955254.95517
D5292.285297584.570594-8.144143D5285.259208570.518416-50.2792233
D#5314.768781629.53756320.14477D#5310.680875621.36175-2.48719
E5327.0325654.065-13.6865E5327.0325654.065-13.6865
F5343.384125686.76825-29.21921F5355.647844711.29568831.53287
F#5359.73575719.4715-48.68211F#5376.087375752.1747528.27423
G5392.439784.8781.9553G5382.219234764.438469-43.727187
G#5404.702719809.405438-44.77299G#5414.922484829.844969-1.597203
A5438.427945876.855891-6.2429A5432.807074865.614148-28.538847
A#5457.8455915.691-31.1747A#5474.197125948.3942529.57729
B5494.636656989.2733132.636121B5486.460844972.921688-26.219119
C6517.1201411034.24028-20.408253C6523.2521046.50401
C#6564.1310631128.2621330.22969
D6570.5184161141.03683-50.2792233
D#6611.1419841222.28397-31.2299
E6654.0651308.13-13.6865
F6711.2956881422.5913831.53287

1 thought on “Harmonium Tuning”

  1. Pingback: Harmoniums: Keyboard Layouts – Neil Thornock

Leave a Comment

Your email address will not be published. Required fields are marked *

css.php