Is old Fur Elise mistuned today?


Fur Elise is one of the most famous masterpiece of one of the greatest composers of the world Ludwig Van Beethoven. This finest piece was first published in 1867, 40 years after death of Beethoven in 1827. There are some controversies. But the most accepted finding is that, this bagatelle piece was written in 27th April, 1810 in the key note of A Minor set in 3/8 time signature. The musical notes are standardized now and all musical instruments including pianos are tuned on a standard pitch set where the note A is with 440 Hrtz. At the time of Beethoven the pitch of piano notes were not in standard pitches like today.


Pitch Standard

Standard pitch of the note A, often known as A440 or just A4 in short, was first suggested as 440 Hrtz in 1936 by the American Standards Association. Later International Organization for Standardization (ISO) accepted the note A as 440 Hrtz in 1955 and ISO reaffirmed this in 1975 by naming this as ISO 16. Before this, the standard pitches of musical notes were based on French Standard, which was given in 1860s where A was set as 435 Hrtz. Earlier this note was also set in 432 Hrtz and other pitches with some little deviations. And, of course, at times the manufacturers used to make instruments according to their own standard pitches of notes. In Indian music industry, even up to recent past, musical instruments used to be tuned manually. The master tuner’s extra-ordinary sense of pitch of sound was the most dependable source of tuning the various musical instruments. Once a note is set into a certain pitch, say for example, A is set on 440 Hrtz, other notes come along with comparative pitches according to the mathematical calculations. Comparative pitch calculations were traditionally based on Pythagorean ratios. Table-1 shows the Musical Notes with the frequencies calculated with Pythagorean ratios.


Table-1: Pitch of Musical Notes in Traditional System

Today, notes are pitched with a same ratio. Each next note is of 1.059463094 times of higher pitch of the immediate previous note. This is actually twelfth root of two [2^(1/12)] times higher pitch. In my next article I will write about more details of the calculations of pitch. From the Table-1, we see the pitch of note C is 264 Hrtz when the pitch of A is 440 Hrtz. In the current practice of same ratio table we have the pitch of note C is 261.626 Hrtz taking the pitch of note A is 440 Hrtz. Pitch of other notes like B, C, D, E, F and G will also be changed accordingly if we consider the different calculation methods from traditional to current. What would happen with the A Minor based Fur Elise what we had been listening for a long time? Can’t we recognize the difference between two C’s with 264 Hrtz and 261.626 Hrtz, or two G’s with 396 Hrtz and 392 Hrtz?


The answer regarding the Fur Elise question is not straight and easy. Though the answer to the second question is ‘yes, we can.’ If we listen to two sounds with pitches 396 Hrtz and 392 Hrtz one after another, we can easily identify them different. There are twelve different musical notes in one octave. According to Indian music system, there can be twenty two different notes possible in one octave that can be used as musical notes. Sounds with other frequencies can not be used as musical notes. So the comparative pitches of notes according to their different positions in the octave make a harmony that creates the feeling of a musical piece. Thus, when the Fur Elise starts with the structure A–B–A–C–A, we can feel the music whatever the exact pitch of each note we listen. We actually take the sounds with comparative pitches.


This is a layman answer. There are other important questions since the comparative positions of notes are not same as of now what were before in the time of Beethoven. I will write another article  to put some more light on this matter.

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