Alright, I spent some time examine the rhodes sound with MATLAB ®. I used the FFT on a single key, copied a sample with the length of 1 second and transformed it into a spectrum... but I dont want to bore you with all the technical details.
the main question when stretched tuning is concerned is if the rhodes' tines suffer from inharmonicity of the partials. inharmonicity is when the higher harmonics are not integer multiples of the fundamental frequency.
I wrote a little script that finds all the peaks in the spectrum (=harmonics) of a rhodes' tine and its frequencies. and this is the result:
for example:
F1 (second key on my Mark II 73)
explanation
n# = number of harmonics, 1 = fundamental frequency
mag(dB) = magnitude in dB of the harmonics (measured)
freq (HZ) = frequency of the harmonic (measured)
var equal temp = variance of the measured harmonic to the next note of the equal temperament in cents (1 cent is a 1/100th of a semitone in equal temperament)
note = next note of the equal temperament
var ham = variance of the measured harmonic to the natural harmonic in cents
Result:
I tuned the F1 3 cents too high (which is pretty good as you all know the game of moving the tuning spring up and down the tine)
all other harmonics are not integer multiples of the fundamental frequency
for all other tines from E1 to H1 it can be said that the harmonics differ from real integer multiples of the fundamental frequency.
the range of variance is from 3 cents to 10, some single harmonics even have a variance of 100 cents (which is a semitone), but as only one single harmonic per tine is that way off it could be a bad tine !?!).
From C2 on the variance of measured to natural harmonics becomes smaller and is neglectable from C3 to C4. I didnt examine the higher octaves yet.
As I am not able to do the same thing on a acoustic piano someone else has to see if the harmonicity of a piano is bigger than the result above in order to judge whether stretch tuning in neccessary (/an option) or not. I hope this is in some way helpfull for answering the question about stretch tuning.
kind regards
Mark II
the main question when stretched tuning is concerned is if the rhodes' tines suffer from inharmonicity of the partials. inharmonicity is when the higher harmonics are not integer multiples of the fundamental frequency.
I wrote a little script that finds all the peaks in the spectrum (=harmonics) of a rhodes' tine and its frequencies. and this is the result:
for example:
F1 (second key on my Mark II 73)
Code Select
'n#' 'mag(dB)' ' freq (Hz) ' 'var equal temp' 'note' 'var harm'
[ 1] [-10.4876] [ 43.7393] [ 3.3961] 'F1 ' [ 3.3961]
[ 2] [ 0] [ 87.4786] [ 3.3981] 'F2 ' [ 3.3981]
[ 3] [ -2.7309] [ 131.8909] [ 14.2065] 'C3 ' [ 12.2065]
[ 4] [ -3.6319] [ 175.6302] [ 10.0459] 'F3 ' [ 10.0459]
[ 5] [ -1.5443] [ 219.3695] [ -4.9686] 'A3 ' [ 9.0314]
[ 6] [-12.9016] [ 263.1088] [ 9.7845] 'C4 ' [ 7.7845]
[ 7] [ -3.5731] [ 306.8481] [ -23.9745] 'D#4' [ 7.0255]
[ 8] [-22.6191] [ 351.2604] [ 10.0459] 'F4 ' [ 10.0459]
[ 9] [ -6.7262] [ 394.9997] [ 13.2195] 'G4 ' [ 9.2195]
[10] [-13.0943] [ 438.7390] [ -4.9686] 'A4 ' [ 9.0314]
[11] [-11.6204] [ 482.4783] [ -40.4462] 'B4 ' [ 8.5538]
[12] [-12.0037] [ 526.2177] [ 9.7878] 'C5 ' [ 7.7878]
[13] [-20.6433] [ 569.9570] [ 48.0202] 'C#5' [ 7.0202]
[14] [-13.0879] [ 614.3692] [ -22.0772] 'D#5' [ 8.9228]
[15] [-33.1867] [ 657.4356] [ -4.7844] 'E5 ' [ 7.2156]
[16] [-15.4013] [ 701.8478] [ 8.3869] 'F5 ' [ 8.3869]explanation
n# = number of harmonics, 1 = fundamental frequency
mag(dB) = magnitude in dB of the harmonics (measured)
freq (HZ) = frequency of the harmonic (measured)
var equal temp = variance of the measured harmonic to the next note of the equal temperament in cents (1 cent is a 1/100th of a semitone in equal temperament)
note = next note of the equal temperament
var ham = variance of the measured harmonic to the natural harmonic in cents
Result:
I tuned the F1 3 cents too high (which is pretty good as you all know the game of moving the tuning spring up and down the tine)
all other harmonics are not integer multiples of the fundamental frequency
for all other tines from E1 to H1 it can be said that the harmonics differ from real integer multiples of the fundamental frequency.
the range of variance is from 3 cents to 10, some single harmonics even have a variance of 100 cents (which is a semitone), but as only one single harmonic per tine is that way off it could be a bad tine !?!).
From C2 on the variance of measured to natural harmonics becomes smaller and is neglectable from C3 to C4. I didnt examine the higher octaves yet.
As I am not able to do the same thing on a acoustic piano someone else has to see if the harmonicity of a piano is bigger than the result above in order to judge whether stretch tuning in neccessary (/an option) or not. I hope this is in some way helpfull for answering the question about stretch tuning.
kind regards
Mark II
