Talk:William Sethares

"C to Shining C"
Is it accurate to say that "C to Shining C" has no key? It appears to me to have an unambiguous tonic, and although the widths of the various intervals arranged around that tonic vary as the tuning bends, the relationships among those intervals remain constant (i.e., the shape of the syntonic tonnetz does not change). This suggests to me that it DOES have a key, i.e., Do-mode of the diatonic scale, with Do having the pitch G.

Why is this not correct?

Certainly the piece has an unambiguous C (Do) tonic, but it lacks other features of a musical key. From the Key (music) page, we read that "...the establishment of key is brought about via functional harmony, a sequence of chords leading to one or more cadences." In the "C to Shining C", there really is no proper functional harmony, as there are really no "chord changes". The sounds that appear to be chord changes are really timbre changes -- from a Do chord in one tuning with one timbre to the "same" Do chord in another tuning with a corresponding timbre. Pseudo-Octave (talk) 04:14, 4 January 2010 (UTC)

Removed "Pythagoras observed that the physical length of objects is proportional to their pitches"
I do not think that Pythagoras could have made this observation, as he would not have known the "pitches" in the sense of frequencies. The statement as it stood relates to our modern understanding of the basis of what Pythagoras probably/possibly observed.FrankSier (talk) 00:31, 23 January 2011 (UTC)

Early consonance
The following paragraph needs rewriting:
 * Among the earliest musical traditions, musical consonance was thought to arise in a quasi-mystical manner from ratios of small whole numbers. (For instance, Pythagoras made observations relating to this, and the ancient Chinese Guqin contains a dotted scale representing the harmonic series.) The source of these ratios, in the pattern of vibrations known as the harmonic series, was exposed by Joseph Sauveur the early 18th century and even more clearly by Helmholtz in the 1860s.

Consonance was not "thought to arise from ratios of small numbers", in was defined as being the same thing as these ratios. One cannot assume that the physical world was understood in former times as it is now (nor that our modern understanding is the "true" one). The Pythagoricians/Platonicians of Ancient Greece considered that the physical world was ruled by simple ratios, which could be called "harmonious" or "consonant". They counted 9:8 (i.e. 3:2 x 3:2 x 1:2) among these "consonant" ratios, which evidences that what they called "consonance" was not at all what we understand by it (9:8 is a musical ratio of the whole tone).

The source of the simple ratios is certainly not in "the pattern of vibrations known as the harmonic series". The harmonic series is and was a mathematical series ever before its application to music -- it merely is the series of whole numbers, 1 2 3 4 5 etc. What Sauveur evidenced merely is that complex musical sounds "contain" partial sounds of frequencies matching the series of whole numbers. That the series of these frequencies was called "harmonic" merely reflects their being mathematically harmonic. This is a property of sounds with a constant frequency, which have often been dubbed "musical" sounds as opposed to "noises" ("non musical sounds"). The property itself was demonstrated as non trivial by Joseph Fourier in the early 19th century.

What Helmholtz demonstrated is how, in the particular case of sounds with constant frequency, the "consonance" (in the physio-acoustic sense of the word, which is different from that of the Ancient Greeks) is a consequence of their having harmonic partials. Sethares' theory (which I do not particularly know) appears to concern sounds with inharmonic partials -- i.e. most of the "real" sounds. The inharmonicity of the partials indeed is one way (among others) to consider timbre.

Hucbald.SaintAmand (talk) 14:34, 18 September 2013 (UTC)

Pythagoras
I appreciate your interest in this article. Please feel free to edit the offending passage to reflect what you believe to be a more accurate treatment of Pythagoras' view (which I may counter-edit, and you may then edit, and so on). Together, we'll make a better article. :-)

Jim Plamondon —Preceding undated comment added 02:01, 19 September 2013 (UTC)