A Slower Rate of Decay of the Stuart Fundamental Frequency.
Introduction:
A more stable harmonic balance was audibly present in the sound of the Stuart piano, when the decay rate of its fundamental frequency was found to be slower than Steinway’s after .5s. Sustained sound qualities were found to be enhanced in the Stuart sound at the same time period as the slower fundamental frequency decay.
Sustained sound in piano tone, is closely related to that rate (dB/s) at which it decays, because a vibrating coupled steel piano string is in a constant state of decay, restoring back to it’s rest position after the forced disturbance of the hammer strike. Therefore the size, or amplitude of the composite sound is constantly reducing, becoming quieter. When the rate of the reduction in amplitude is steady and slow, it can be referred to as sustain.
The sustain portion of the sound, is the steady state to which the sound decays after a time determined by the decay parameters.242
A period during which the loudness varies little, called the sustain243
The fundamental frequency is the composite note’s primary pure tone, which vibrates periodically at a frequency rate by which the note is named, and by which multiple frequencies of superimposed upper partial frequencies vibrate. The fundamental is therefore the vibrational frequency that combines the upper partials into their composite group, and in that sense is a primary ‘driver’ of the composite tonal and decay characteristics of the sound.
In the following pages, the transient qualities of the Stuart fundamental frequency has been found to affect the nature of the sound of the upper partials and visa versa, in qualities which were not present in the Steinway fundamental frequency and partial tones.
Notes about Fundamental + Upper Partial Frequencies.
The partial tones are separated by multiples of the frequency of the fundamental frequency. 261.63Hz is the fundamental frequency of middle C or C4. The 2nd partial of C4will therefore be vibrate at double the 261.63Hz frequency, which is an octave above at 523.2 Hz. The next partial frequency will vibrate at 3x the 261.63Hz fundamental frequency, at 784.8Hz, which sounds the 12th interval above the fundamental. Each frequency harmonically lines up with the harmonic series, so for the first 7 partials, nearly three octave of pitch range is covered, within one sound.
The spectrograms in the following pages illustrate the amplitudes of the fundamental and upper partials at their graphically spaced frequencies, measured in decibels dB on the ‘y’ axis. The combined dB of the partials make up the volume of the composite dB level of the note, the composite note volume, or
242 2Sethares,30.
243 5Wolfe, “Pyshclips.” (Retrieved 10 April 2015).
