One of the things which I will never be, is a Musician. However, I think I have some skills in Math and Technology. This allows me to play with open-source software such as the “Linux Multimedia Studio”, and also, to try testing a subwoofer which I bought back in 2019. However, my lack of skill in the field actually caused me to underrate the performance of the subwoofer considerably. Why? Let me explain.
I once had an acquaintance, who was a Musician, and who told me, that the musical scale had intentionally been detuned, or retuned, in a specific way. I had already heard that the note ‘A below Middle C’ was meant since olden times, to refer to a frequency of 440Hz. Yet, according to this Musician, in more recent times, that same note had been retuned to 441Hz. My own personal guess as to why would be, to force at least one note on the Chromatic Scale to have a rational relationship with the sample-rate of Audio CDs, which was 44.1kHz.
According to Western music several centuries ago, the Diatonic Scale had been invented, so that its notes had frequencies with rational relationships. But it was missing the so-called ‘black keys’. What the Chromatic Scale, which was invented later, did, was to detune the existing Diatonic notes, so that all the key-positions, including the black keys, became a sort of logarithm of frequency. According to modern realities, the exact relationships between two adjacent Chromatic notes, is the same over an entire octave, so that each octave again, represents an exact doubling or halving of frequencies. According to that, a maximum of one note, ‘A’, could have a rational frequency in Hertz, and all the other frequencies, in Hertz, end up being irrational.
But, that same note can have slightly greater clarity when sampled, if one sine-wave occupied exactly 100 samples. Thus, my presumed reason for retuning A-below-Middle-C to 441Hz. Theoretically, a sine-wave can be sampled, with an irrational frequency, in relationship to the sample rate. But, when that is done, the clarity with which it gets played back depends strongly on the quality of ‘the low-pass filter’, which is also known as the quality of ‘the interpolation’.
(Edit 10/28/2020, 8h20: )
Actually, playing back a frequency of 440Hz at that sample rate, differs from the rational situation by 1Hz. Because it’s factually untrue, that the period of time taken into account by the low-pass filter, would be as long as 1 second, what should result is non-participation by the low-pass filter, but possibly audibly, for people who have very fine hearing, some sort of ‘beating’ or ‘interference effect’, with its own frequency of 1Hz.
To make things worse, what the listener will seem to hear is, one frequency at 441Hz anyway, even though the scale might be tuned to place that note at 440Hz, but with that one note being modulated in some non-specific way.
(End of Edit 10/28/2020, 8h20. )
(Edit 10/28/2020, 19h00: )
In addition to that, a third frequency will physically be present, at ~439Hz, to account of this modulation. This would be similar to the concept of ‘amplitude modulation’.
(End of Edit 10/28/2020, 19h00. )
So, here is the mistake I made. I did not know that the note ‘C’ always begins a new octave. Thus, I was able to play the ‘A’ note which is below ‘Middle C’, as well as the ‘A’ note which is below ‘C1′. But, even when playing with this software, I had failed to notice that the numbering of ‘Middle C’ was ‘C5′, not, ‘
C4‘. But, ‘A below Middle C’ was still ‘A4′.
Therefore, naively, I played ‘A below C1′. But I thought that I was sending a frequency of 55.125Hz to my newly purchased subwoofer, when in fact, I was sending it a frequency of 27.5625Hz. The subwoofer reproduced the lower of the two frequencies with excellence, causing my walls to shake, and, making it impossible for me to discern that it was in fact an ‘A’. But a person with musically trained ears would have noticed, that the musical tone of ‘A below C2′ is easy to discern, while this musical tone of ‘A below C1′ is almost impossible to discern.
So, the subwoofer performs much better, than I gave it credit for doing.