Duplexes or aliquot scales; In 1872 Theodore Steinway patented a system to control different components of string vibrations by tuning their secondary parts in octave relationships with the sounding lengths. Similar systems developed by Blüthner (1872), as well as Taskin (1788), and Collard (1821) used more distinctly ringing undamped vibrations to modify tone.
Since the 1980s, digital pianos have been available, which use digital sampling technology to reproduce the sound of each piano note. The best digital pianos are sophisticated, with features including working pedals, weighted keys, multiple voices, and MIDI interfaces. However, with current technology, it remains difficult to duplicate a crucial aspect of acoustic pianos, namely that when the damper pedal (see below) is depressed, the strings not struck vibrate sympathetically when other strings are struck as well as the unique instrument-specific mathematical non-linearity of partials on any given unison. Since this sympathetic vibration is considered central to a beautiful piano tone, in many experts' estimation digital pianos still do not compete with the best acoustic pianos in tone quality. Progress is being made in this area by including physical models of sympathetic vibration in the synthesis software.
The square piano had horizontal strings arranged diagonally across the rectangular case above the hammers and with the keyboard set in the long side, it is variously attributed to Silbermann and Frederici and was improved by Petzold and Babcock. Built in quantity through the 1890s (in the United States), Steinway's celebrated iron framed over strung squares were more than two and a half times the size of Zumpe's wood framed instruments that were successful a century before, their overwhelming popularity was due to inexpensive construction and price, with performance and sonority frequently restricted by simple actions and closely spaced strings.
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