Abstract: Wound strings for a musical instrument include inharmonicity compensation. A portion of the wound string, preferably at one or both ends thereof, includes a concentric winding. The concentric winding has a length l.sub.comp given by: ##EQU1## where D.sub.s is the outer diameter of portions of the wound string remote from the compensating winding, D.sub.comp is the diameter of the wound string at the compensating winding, d is the diameter of the core wire and l.sub.bare is the length of the bare end of the string.

Abstract: A wound musical string includes a core wire and a wrapped wire covering about the core wire. End turns of the wrapped wire covering are coextensive portions of transition sections of the core wire. The transition sections have equilateral triangular, square or other cross sections such that the cross section exhibits equal principal moments of inertia. Consequently the inharmonicity of the string about two axes will be the same and the string will not produce false beats.

Abstract: Wound strings for a musical instrument include inharmonicity compensation. A portion of the wound string, preferably at one or both ends thereof, includes a concentric winding. The concentric winding has a length l.sub.comp given by: ##EQU1## where D.sub.s is the outer diameter of portions of the wound string remote from the compensating winding, D.sub.comp is the diameter of the wound string at the compensating winding, d is the diameter of the core wire and l.sub.bare is the length of the bare end of the string.

Abstract: A method and apparatus for tuning a musical instrument. Measurements are made of the inharmonicities of three notes (e.g., F3, A4 and C6 in a piano). One of the notes (e.g. A4) is a standard note that is to be tuned to a standard frequency. The measured inharmonicities of these notes determine a slope of a tuning curve and a position to intercept the standard note frequency according to the following: ##EQU1## Y(p,N) is the cents deviation relative to the equally tempered scale of partial p of note N, F is a factor by which the inharmonicity increases per octave taken from the measurement, B(N) is the inharmonicity of note N, and B(STD) is the inharmonicity factor of a standard note (e.g., A4 at 440 Hz).

Abstract: Temperature-compensated solid-state oscillators. A temperature sensitive voltage regulator provides to the oscillator a supply voltage which varies in accordance with a temperature-dependent voltage across a diode junction in the oscillator timing circuit. The oscillator frequency thereby remains substantially constant over a wide range of ambient temperatures and input voltages.

Abstract: A musical tuning aid. The tuning aid generates a digital note signal at the frequency of a selected partial of a note being sounded and combines this note signal and a four-phase digital clock output having a reference frequency to produce four output signals which low-pass filters convert to dc output signals. Each output signal indicates the instantaneous phase difference between the note and a respective one of the clocking signals.Each dc output output signal controls the light from a pair of lamps. Individual lamps in each pair are diametrically opposed on a circle with all the pairs being equiangularly spaced. The lamp pairs reach maximum brightness in sequence, providing the illusion of a rotating light bar. The direction of rotation indicates whether the note being tuned is flat or sharp and the speed of rotation is proportional to the frequency deviation from the reference.

Abstract: A series direct-current voltage regulator. The regulator comprises a field effect transistor as a series regulating element and a reference element comprising a forward-biased PN junction.

Abstract: A phase difference detector and display unit. A digital pulse train at the frequency to be measured is combined with a multiple-phase digital clock output having a reference frequency to produce multiple-phase signals which low-pass filters convert to dc output signals. Each output signal indicates the instantaneous phase difference between the digital pulse train and a respective one of the clocking signals.Each dc output signal controls the light from a pair of lamps. Individual lamps in each pair are diametrically opposed on a circle with all the pairs being spaced around the circumference of the circle. The lamp pairs reach maximum brightness in sequence, providing the illusion of a rotating light bar. The direction of rotation indicates whether the digital pulse train is higher or lower in frequency than the reference while the speed of rotation is proportional to the frequency deviation from the reference.

Abstract: A method for tuning a piano or other instrument. A characteristic stretch is measured using a tuning instrument which compares an internally generated reference signal and the corresponding partial of a note from the instrument and indicates the instantaneous phase difference between the two. A reference note in the instrument (e.g., the 440 Hz "A") is tuned to a standard frequency for the scale. Then, using the characteristic stretch, the deviation from a reference scale frequency for each successive note is determined and each note is tuned to a frequency which is the sum of the reference scale frequency and corresponding deviation for that note. In one particular embodiment, the stretch correction, Y(n,N), in cents is based upon the following:Y(n,N)=B.sub.0 [(n.sup.2 +K.sub.2)2.sup.(N.sup.-N.sbsp.0 )/K.sbsp.1 -1-K.sub.2 ]wherein n equals the number of the partial of the note for which the deviation is being calculated, N is a number assigned to each note in a scale, B.sub.