Talk:Anhemitonic scale

How do we judge or measure the dissonance of a scale?

How does this statement even make sense?:

In the same way that an anhemitonic scale is less dissonant than a hemitonic scale, an unhemitonic scale is less dissonant than a dihemitonic scale.

It claims, firstly, that "an anhemitonic scale is less dissonant than a hemitonic scale", or in simple English, "a scale that contains no semitones is less dissonant than a scale that does contain one or more semitones", and then proceeds to make a similar claim comparing scales of one and two semitones. In short, it says that the more semitones a scale has, the more dissonant it is. The problem I have with this assertion is that it fails to explain or define its terms: in particular, the dissonance of a scale.

How do we judge or measure the dissonance of a scale? Is it the sum, or some average, of the dissonances of all the dyadic (two-note) intervals it contains? There are measures of the dissonance (or conversely but equivalently, the consonance) of dyads, based usually on some mathematical function of the (perceptual) fundamental frequencies of the two notes. Surely the perception of how dissonant a scale is must be a summary judgment on how dissonant pieces of music in that scale are, and such a judgment will depend on the musical style of those pieces, including the degree of polyphony they use, as well as the dyads it contains. Without constraining these other factors, perhaps unrealistically, it's not obvious that there's any simple measure of scale dissonance.

Or perhaps the theory is comparing scales, based on their maximum potential dissonance, obtained by playing all scale tones simultaneously, as a single chord? If so, again, how do we judge or measure the dissonance of those chords?

We can do better than this article presently does. yoyo (talk) 11:21, 31 October 2015 (UTC)

I agree whole-heartedly. In addition to the acoustically based factors you name, there are also contextual/stylistic aspects to which you allude obliquely. One of the most perplexing of these is the so-called "dissonant fourth" in European polyphonic music from the 15th century onward; another, less well-known example is the relative consonance/dissonance in late-13th-century polyphony of the major second on the one hand versus the major and minor thirds and sixths on the other—dependent in part on the Pythagorean tuning commonly employed at that time. Therefore, the particular tuning used for any given pentatonic scale may provide an acoustic as well as cultural/stylistic basis for making judgments of consonance and dissonance, even if we restrict the investigation to constituent dyads. The claim as currently formulated lacks a source, though it may be that Michael Keith's book cited at the end of the next paragraph is where it originates. If so, then adding a citation for this seemingly foolish claim may be sufficient. Perhaps the context of Keith's discussion supplies the necessary explanation. If not, then we have got a problem: how do we point out the dubiousness of the claim, unless we can find a contravening source to support the criticism?—Jerome Kohl (talk) 23:42, 31 October 2015 (UTC)

Above comments on how to judge dissonance of a scale are based on lack of context. Straightforward: evaluate the scale matrixwise against itself, segregating and counting intervals; apply some preferred notion of what constitutes a dissonant interval to the resulting vector. Hanson and Forte and Ladka all did so. No need to look to individual compositions or style or "play all the notes at once". 72.183.193.44 (talk) 00:11, 20 December 2015 (UTC)

Surely you mean they are based on context, rather than the lack of it. The example of the perfect fourth is a case in point: undisputably a consonance up to the 14th century, and subsequently dissonant or consonant depending entirely on context. Applying this kind of "preferred notion" to an interval vector is problematic, to say the least.—Jerome Kohl (talk) 00:29, 20 December 2015 (UTC)