Fully tempered duplex scale

摘要

Disclosed herein are exemplary embodiments of methods, systems, and apparatus for improving pianos and like musical instruments. For example, in certain embodiments, the improvements are in the structures of the piano (or like musical instruments) that affect the vibratory relationships between the struck string and other segments of said string. The improvements affect how these vibratory relationships of the string segments interact with the bridge, soundboard, the plate of a piano, the string rests, and/or the string terminations. For example, in embodiments of the disclosed technology, the vibratory relationships of the string segments involve transient transverse (T) and longitudinal (L) frequencies as well as sustained transverse, longitudinal, and horizontal (H) modes carried by said string segments and their support structures. Embodiments of the disclosed technology also affect how these relationships are defined across the compass of the standard piano keyboard.

主权项

1. A stringed instrument, comprising:
a plurality of string sets, each string set comprising one or more strings having a speaking length portion tuned to a respective frequency, the string sets together forming a graduated musical scale that ascends from a lower frequency to a higher frequency, the strings of each respective string set being divided between at least a duplex length portion and the speaking length portion, a ratio between a length of string in the speaking length portion and a length of string in the duplex length portion defining a duplex ratio, the string sets being further arranged into at least a first grouping of two or more of the string sets and a second grouping of two or more of the string sets, wherein the duplex ratios of the string sets in the first grouping are consecutively graduated from one another and are all within a first duplex ratio range having no harmonic duplex ratios, wherein the duplex ratios of the strings in the second grouping are consecutively graduated from one another and are all within a second duplex ratio range having no harmonic duplex ratios, the second duplex ratio range being separated from the first duplex ratio range by at least one harmonic duplex ratio, wherein the strings in the first grouping are tuned to higher frequencies than the strings in the second grouping, and wherein the strings of each respective string set further include a hitching length portion, the hitching length portion for a respective string being equal or substantially equal in length to the speaking length portion for the respective string.