Theory of Helmholtz-Beat Frequencies

1984 ◽  
Vol 1 (3) ◽  
pp. 308-322 ◽  
Author(s):  
Rudolf A. Rasch

In musical tuning, deviations from the simple frequency ratios of pure consonant intervals are often necessary. These deviations are called temperings. They result in beats in the sounding interval. Rules are developed according to which the beat frequencies can be determined, both exactly and by way of easy integer approximations. Beat frequencies of consonant intervals are most easily expressed as relative beat frequencies, the quotient of the beat frequency and the lower fundamental frequency of the interval. The relative beat frequency is a constant for a certain interval in a certain tuning, whereas the absolute beat frequencies vary with fundamental frequencies. Also described are the relationships between the beat frequencies of the three intervals that make up a consonant triad. Numerical data are given for five model tunings: Pythagorean, equal, Silbermann, meantone, and Salinas.

1979 ◽  
Vol 10 (4) ◽  
pp. 246-248 ◽  
Author(s):  
Peter B. Mueller ◽  
Marla Adams ◽  
Jean Baehr-Rouse ◽  
Debbie Boos

Mean fundamental frequencies of male and female subjects obtained with FLORIDA I and a tape striation counting procedure were compared. The fundamental frequencies obtained with these two methods were similar and it appears that the tape striation counting procedure is a viable, simple, and inexpensive alternative to more costly and complicated procedures and instrumentation.


1997 ◽  
Vol 119 (4) ◽  
pp. 451-456 ◽  
Author(s):  
C. Lay ◽  
O. A. Abu-Yasein ◽  
M. A. Pickett ◽  
J. Madia ◽  
S. K. Sinha

The damping coefficients and ratios of piping system snubber supports were found to vary logarithmically with pipe support nodal displacement. For piping systems with fundamental frequencies in the range of 0.6 to 6.6 Hz, the support damping ratio for snubber supports was found to increase with increasing fundamental frequency. For 3-kip snubbers, damping coefficient and damping ratio decreased logarithmically with nodal displacement, indicating that the 3-kip snubbers studied behaved essentially as coulomb dampers; while for the 10-kip snubbers studied, damping coefficient and damping ratio increased logarithmically with nodal displacement.


Author(s):  
Johan Sundberg

The function of the voice organ is basically the same in classical singing as in speech. However, loud orchestral accompaniment has necessitated the use of the voice in an economical way. As a consequence, the vowel sounds tend to deviate considerably from those in speech. Male voices cluster formant three, four, and five, so that a marked peak is produced in spectrum envelope near 3,000 Hz. This helps them to get heard through a loud orchestral accompaniment. They seem to achieve this effect by widening the lower pharynx, which makes the vowels more centralized than in speech. Singers often sing at fundamental frequencies higher than the normal first formant frequency of the vowel in the lyrics. In such cases they raise the first formant frequency so that it gets somewhat higher than the fundamental frequency. This is achieved by reducing the degree of vocal tract constriction or by widening the lip and jaw openings, constricting the vocal tract in the pharyngeal end and widening it in the mouth. These deviations from speech cause difficulties in vowel identification, particularly at high fundamental frequencies. Actually, vowel identification is almost impossible above 700 Hz (pitch F5). Another great difference between vocal sound produced in speech and the classical singing tradition concerns female voices, which need to reduce the timbral differences between voice registers. Females normally speak in modal or chest register, and the transition to falsetto tends to happen somewhere above 350 Hz. The great timbral differences between these registers are avoided by establishing control over the register function, that is, over the vocal fold vibration characteristics, so that seamless transitions are achieved. In many other respects, there are more or less close similarities between speech and singing. Thus, marking phrase structure, emphasizing important events, and emotional coloring are common principles, which may make vocal artists deviate considerably from the score’s nominal description of fundamental frequency and syllable duration.


2017 ◽  
Vol 9 (7) ◽  
pp. 1441-1445 ◽  
Author(s):  
Yunlong Lu ◽  
Yi Wang ◽  
Taijun Liu ◽  
Bo Yu ◽  
Kai Li

A miniaturized substrate-integrated coaxial line (SICL) bandpass filter with improved upper stopband using asymmetrical spiral stub-loaded resonators is presented in this paper. Owing to the space-filling feature of the spiral structure, the size of the proposed filter is significantly reduced. A theoretical analysis is carried out to examine the resonance property of the proposed resonator. It is found that the frequency ratios of the second and third harmonics to the fundamental frequency can be extended to 2.86 and 4.4. Benefiting from the circuit structure and SICL technology, the designed filter has a small size, wide stopband, low crosstalk, and high-density integration ability. The measured results show that the proposed filter, with dimensions of 0.051λ0 × 0.044λ0, operates at 1.056 GHz and the 20-dB rejection band is extended to 3.94f0.


1992 ◽  
Vol 247 ◽  
Author(s):  
M. Tokumoto ◽  
A. G. Swanson ◽  
J. S. Brooks ◽  
C. C. Agosta ◽  
S. T. Hannahs ◽  
...  

ABSTRACTObservations of Shubnikov-de Haas(SdH) and de Haas-van Alphen(dHvA) oscillations in organic metals (BEDT-TTF)2X, with X=KHg(SCN)4, θ-I3 and β″-AuBr2. are reported. In KHg(SCN)4 salt, in addition to the SdH oscillations with fundamental frequency of 670 T corresponding to about 16% of the first Brillouin zone(FBZ), we observed splitting of each SdH peak which we ascribed to “spin-splitting” We have also found that the ground state of this salt is not a simple metal but has some magnetic character. In θ-l3 salt we have succeeded in an observation of dHvA oscillations for the first time. We observed a “saw-tooth” dHvA oscillation characteristic to a highly two-dimensional and extraordinary clean electronic system. In addition to the fundamental frequency of 4170 T corresponding to 50.4 % of the FBZ and its higher harmonics, we observed an oscillation with lower frequency of 730 T corresponding to about 8.8 % of the FBZ. A new Fermi surface topology for θ-l3 salt is proposed based on the analysis of the dHvA effect. In β″-AuBr2, we observed complex dHvA oscillations, which can be explained in terms of the mixing of two fundamental frequencies of 47 and 268 T, suggesting the presence of very small pockets corresponding to 0.6 and 2.9 % of the FBZ.


2014 ◽  
Vol 709 ◽  
pp. 157-161
Author(s):  
Li Guo Zhang ◽  
Kang Yang ◽  
Wei Ping Zhao ◽  
Song Xiang

Optimization of material properties is performed to maximize the fundamental frequency of the laminated composite panels by means of the genetic algorithm. The global radial basis function collocation method is used to calculate the fundamental frequency of clamped laminated composite panels. In this paper, the objective function of optimization problem is the maximum fundamental frequency; optimization variables are material properties of laminated panels. The results for the optimal material properties and the maximum fundamental frequencies of the 2-layer plates are presented to verify the validity of present method.


1998 ◽  
Vol 87 (2) ◽  
pp. 595-600 ◽  
Author(s):  
S. P. Whiteside

This experiment assessed whether fundamental frequency or formant frequencies have more perceptual salience in the identification of the sex of the speaker from synthesized vowels. Four sets of ten vowels were synthesized by combining fundamental frequencies and formant frequencies with different permutations 50 listeners took part in a listening test. Analysis of the listening test scores suggested that for 36 vowels, the fundamental frequency (F0) was probably the most salient perceptual cue. For the remaining four vowels, however, this was not the case as either the formant frequencies or the onset-offset patterns of the F0 appeared to have some perceptual salience.


2000 ◽  
Author(s):  
George Weiss

Abstract A new formula has been developed in this study, to calculate the fundamental frequency of a multistory building. This formula is derived from Dunkerley’s estimate, complies with the requirements of Uniform Building Code (UBC) and the Building Officials Code Administrators (BOCA) Code, and accounts for multistory building frames of different type and size. A coefficient Γ, function of moments of inertia and lengths of column/girder was introduced in the formula, in order to obtain a relative simple algebraic equation. To verify the validity of the new formula a thorough investigation has been conducted. Fundamental frequencies and periods have been calculated for different building frames using the new formula (Formula 1). A formula for buildings with rigid floors, Formula 2, has been derived from Formula 1. Formula 2 has been used to calculate the fundamental frequency for the same type and size of buildings used in the calculations with Formula 1, considered with rigid floors. In addition, three different empirical formulas have been used to calculate the fundamental period for the same buildings. Two of these formulas are recommended in different versions of the codes. For the same type and size of buildings the fundamental frequencies and periods have been determined by computer. Comparing with the computer values, formulas 1 and 2 give the best results and can be used in preliminary design, in vibration problems or to determine seismic lateral loads for buildings with a maximum height of 160/65 ft. The empirical formulas show large differences and have to be used with caution, only in the limited range imposed by UBC and BOCA.


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