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New musical moods using mathematics-based tunings


Traditionally, Western music divides the octave into 12 logarithmically equal parts. This 12-tone scale exploits one fact about how we humans appreciate music; pleasant or ‘consonant’ sounds are mathematically simple. For 2 or more different pitches being played at the same time, when the ratio of their frequencies uses simple low numbers, we hear a pure and blissful harmonious sound. For example 3/2 (a musical “perfect fifth”) sounds consonant whereas 13/8 (a musical “thirteenth harmonic”), a more complex pitch sounds worse.

The 12-tone scale approximates many simple ratios, which has helped make the scale a common and universal kind of harmony. But what happens if we make music without using this scale? A crowd of note-splitting musicians came together to find out exactly that…

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Astronomers Discover an Unusual Cosmic Lens

Astronomers have discovered the first known case of a distant galaxy being magnified by a quasar acting as a gravitational lens.

Quasars, which are extraordinary luminous objects in the distant universe, are thought to be powered by supermassive black holes in the cores of galaxies. A single quasar could be a thousand times brighter than an entire galaxy, which makes studies of their host galaxies exceedingly difficult. Using gravitational lensing astronomers now can measure the masses of these quasar host galaxies and overcome this difficulty.

According to Einstein’s general theory of relativity, if a large mass (such as a big galaxy or a cluster of galaxies) is placed along the line of sight to a distant galaxy, the part of the light that comes from the galaxy will split. Because of this, an observer on Earth will see two or more close images of the now-magnified background galaxy.

To find the cosmic lens, the astronomers searched a large database of quasar spectra obtained by the Sloan Digital Sky Survey (SDSS) to select candidates for “reverse” quasar-galaxy gravitational lensing. Follow-up observations with the Keck Observatory’s 10-meter telescope of the quasar SDSS J0013+1523, located about 1.6 billion light years away, confirmed that it was indeed magnifying a distant galaxy about 7.5 billion light years away.

Quasars are valuable probes of galaxy formation and evolution. Discoveries of more such systems will help understand better the relationship between quasars and the galaxies which contain them, and their coevolution.

Image: the quasar SDSS J0013+1523 (blue), bracketed by the lensed images of the background galaxy (red), obtained with the W. M. Keck Observatory’s 10-m telescope and Adaptive Optics + illustration of the gravitational lensing.

Source: Caltech | See also: EPFL YouTube video.

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