BASS

BASS AND REGISTER

The CRITICAL BAND¹, or ERB (Equivalent Rectangular Bandwidth), indicates the zone of greatest dissonance around a note. The critical band grows non-linearly as we move toward the upper part of the musical register, where the highest-pitched notes with the highest frequencies are found. In the low register the critical band covers many semitones, while moving toward the high register only a few semitones near the note are critical and more dissonant. For example, C1 (32.7 Hz) has a critical band of 28.2 Hz, approximately 11 semitones, meaning that within this range of 11 semitones one must be careful about adding other notes. Middle C4 (261.6 Hz) has an ERB of 52.9 Hz but covers only 3.3 semitones. In the low register, the distance between notes must be much greater to be perceived as a clear separation and to avoid sounding dissonant. An ascending minor third from C1 sounds dissonant; from C4 it is more than tolerated. Or again: a fifth above C2 (7 semitones) is beyond the band, stable. A minor third above C2 (3 semitones) is still inside the band.This explains why harmonic tradition prefers close intervals in the middle and high registers.

NOTE	FREQ (Hz)	ERB (Hz)	ERB (st)
C1	32.7	28.2	11.4
C2	65.4	31.8	7
C3	130.8	38.8	4.6
C4	261.60	52.9	3.3

RHYTHM

Several studies show that when two sound streams overlap, the brain detects timing deviations more accurately in the low channel, and motor synchronization is dominated by the lowest voice². Low frequencies generate more precise neural spike patterns in the temporal domain.

PITCH DEFINITION

The low register aids the perception of rhythm but slows the perception of pitch. A note at 40 Hz completes one cycle every 25 ms: the auditory system needs at least 2–3 cycles to stabilize the perception of which note is sounding, approximately 50–75 ms before the pitch is defined. The bass arrives first as a rhythmic impulse, and only afterward as a recognizable pitch. The perceived attack and the perceived note are not simultaneous; in practice there is a window of harmonic ambiguity on the order of 50–100 ms with each new note in the low register. This latency is the reason why melodically dense bass lines sound confused, and why the bass "breathes" better on longer durations.

HARMONIC SERIES

The lowest note of a chord also generates its harmonic series, which often extends into the middle and high register and will orient the perception of everything we add to it in orchestration. The partials of a low note extend upward and overlap with the partials of the upper voices. Dissonance also depends on the interaction between the bass partials and those of the other instruments, increasing the risk of generating beats and dissonances across a very wide range.

NOTES

1. See article DISSONANZA:BANDA CRITICA

2. Hove, Marie, Bruce, Trainor – *"Superior time perception for lower musical pitch explains why bass-ranged instruments lay down musical rhythms"*, PNAS 111 (2014)