A geometrical approach to find the preferred intonation of chords

Previous work suggested that convexity in the Euler lattice can be interpreted in terms of consonance [1]. In this paper, a second hypothesis is presented that states that compactness in the Euler lattice is an indication of consonance. The convexity and compactness of chords is used as the basis of a model for the preferred intonation of chords in isolation (without a musical context). It is investigated if, and to which degree convexity and compactness are in agreement with the preferred intonation of chords in isolation. As measure of consonance to compare the model to, Euler’s Gradus function is used. It is stressed however, that in the context of this paper, Euler’s consonance model is able to represent a general consonance model rather than only the Gradus function itself. First, the diatonic chords are observed, after which the compactness, convexity and consonance according to Euler, is calculated for all chords in general containing 2, 3 and 4 notes within a bounded note name space, such that the relation between these three measures can be obtained. The principle of compactness turns out to be a strong indicative of consonance for chords, having the preference over other consonance models that it is simple and intuitive to use

Integrating Convexity and Compactness into the ISSM: Melodic Analysis of Music

This paper reports on a short project that aimed to integrate two mathematical measures, convexity and compactness, into the ISSM, a model for music analysis. The measures convexity and compactness have been successfully used before in music informatics research. It turned out that the combination of these two tools has not been as successful as initially hoped for, and therefore the project has been aborted. We report here on the methods and give a rationale for not pursuing this project any further

A 490 GHz planar circuit balanced Nb-Al2_\mathbf{2}O3_{\mathbf{3}}-Nb quasiparticle mixer for radio astronomy: Application to quantitative local oscillator noise determination

This article presents a heterodyne experiment which uses a 380-520 GHz planar circuit balanced Nb-$\mathrm{Al_2O_3}$-Nb superconductor-insulator-superconductor (SIS) quasiparticle mixer with 4-8 GHz instantaneous intermediate frequency (IF) bandwidth to quantitatively determine local oscillator (LO) noise. A balanced mixer is a unique tool to separate noise at the mixer's LO port from other noise sources. This is not possible in single-ended mixers. The antisymmetric IV characteristic of a SIS mixer further helps to simplify the measurements. The double-sideband receiver sensitivity of the balanced mixer is 2-4 times the quantum noise limit $h\nu/k_B$ over the measured frequencies with a maximum LO noise rejection of 15 dB. This work presents independent measurements with three different LO sources that produce the reference frequency but also an amount of near-carrier noise power which is quantified in the experiment as a function of the LO and IF frequency in terms of an equivalent noise temperature $T_{LO}$. In a second experiment we use only one of two SIS mixers of the balanced mixer chip, in order to verify the influence of near-carrier LO noise power on a single-ended heterodyne mixer measurement. We find an IF frequency dependence of near-carrier LO noise power. The frequency-resolved IF noise temperature slope is flat or slightly negative for the single-ended mixer. This is in contrast to the IF slope of the balanced mixer itself which is positive due to the expected IF roll-off of the mixer. This indicates a higher noise level closer to the LO's carrier frequency. Our findings imply that near-carrier LO noise has the largest impact on the sensitivity of a receiver system which uses mixers with a low IF band, for example superconducting hot-electron bolometer (HEB) mixers.Comment: 13 pages, 8 figures, 2 tables, see manuscript for complete abstrac

A low noise 410-495 heterodyne two tuner mixer, using submicron Nb/Al2O3/Nb tunneljunctions

A 410-495 GHz heterodyne receiver, with an array of two Nb/Al2O3/Nb tunneljunctions as mixing element is described. The noise temperature of this receiver is below 230 K (DSB) over the whole frequency range, and has lowest values of 160 K in the 435-460 GHz range. The calculated DSB mixergain over the whole frequency range varies from -11.9 plus or minus 0.6 dB to -12.6 plus or minus 0.6 dB and the mixer noise is 90 plus or minus 30 K

Comparison of measured and predicted performance of a SIS waveguide mixer at 345 GHz

The measured gain and noise of a SIS waveguide mixer at 345 GHz have been compared with theoretical values, calculated from the quantum mixer theory using a three port model. As a mixing element, we use a series array of two Nb-Al2O3-Nb SIS junctions. The area of each junction is 0.8 sq microns and the normal state resistance is 52 omega. The embedding impedance of the mixer has been determined from the pumped DC-IV curves of the junction and is compared to results from scale model measurements (105 x). Good agreement was obtained. The measured mixer gain, however, is a factor of 0.45 plus or minus 0.5 lower than the theoretical predicted gain. The measured mixer noise temperature is a factor of 4-5 higher than the calculated one. These discrepancies are independent on pump power and are valid for a broad range of tuning conditions

Observation of Andreev Reflection Enhanced Shot Noise

We have experimentally investigated the quasiparticle shot noise in NbN/MgO/NbN superconductor - insulator - superconductor tunnel junctions. The observed shot noise is significantly larger than theoretically expected. We attribute this to the occurrence of multiple Andreev reflection processes in pinholes present in the MgO barrier. This mechanism causes the current to flow in large charge quanta (Andreev clusters), with a voltage dependent average value of m = 1+ 2 Delta/eV times the electron charge. Because of this charge enhancement effect, the shot noise is increased by the factor m.Comment: 4 pages, 5 figures include

Atomic Carbon in M82: Physical conditions derived from simultaneous observations of the [CI] fine structure submillimeter wave transitions

We report the first extragalactic detection of the neutral carbon [CI] 3P2-3P1 fine structure line at 809 GHz. The line was observed towards M82 simultaneously with the 3P1-3P0 line at 492 GHz, providing a precise measurement of the J=2-1/J=1-0 integrated line ratio of 0.96 (on a [K km s^-1] -scale). This ratio constrains the [CI] emitting gas to have a temperature of at least 50 K and a density of at least 10^4 cm^-3. Already at this minimum temperature and density, the beam averaged CI-column density is large, 2.1 10^18 cm^-2, confirming the high CI/CO abundance ratio of approximately 0.5 estimated earlier from the 492 GHz line alone. We argue that the [CI] emission from M82 most likely arises in clouds of linear size around a few pc with a density of about 10^4 cm^-3 or slightly higher and temperatures of 50 K up to about 100 K.Comment: 4 pages, 2 figures, ApJL in press, postscript also available at ftp://apollo.ph1.uni-koeln.de/pub/stutzki/m82_pap.ps.gz e-mail-contact:[email protected]

QRiH: Towards a fitting system for humanities research evaluation .

Merit, Expertise and Measuremen

Herschel observations of EXtra-Ordinary Sources: The Terahertz spectrum of Orion KL seen at high spectral resolution

We present the first high spectral resolution observations of Orion KL in the frequency ranges 1573.4 - 1702.8 GHz (band 6b) and 1788.4 - 1906.8 GHz (band 7b) obtained using the HIFI instrument on board the Herschel Space Observatory. We characterize the main emission lines found in the spectrum, which primarily arise from a range of components associated with Orion KL including the hot core, but also see widespread emission from components associated with molecular outflows traced by H2O, SO2, and OH. We find that the density of observed emission lines is significantly diminished in these bands compared to lower frequency Herschel/HIFI bands.Comment: Accepted for publication in the Herschel HIFI special issue of Astronomy and Astrophysics Letters, 5 pages, 3 figure