Is the answer to this question simply that both of these concepts aid in understanding which chords and intervals are consonant or is one of these discoveries actually better than the other?
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It may be that they are one in the same. Combinations of notes from lower in the harmonic series are more consonant and mathematically have simpler ratios.– nuggetheadSep 16 at 12:54
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Seems to me that culture, genre, taste, and context are way more important in terms of consonance and dissonance than either ratios or the harmonic series.– Todd WilcoxSep 16 at 13:00
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@nuggethead But doesn’t the major third technically appear much earlier than an actual fourth? If we start with C let’s say 64hz as the fundamental, we get 2.C 3.G 4.C 5.E and we don’t get an F until the 11th overtone. I don’t have the answer for why, but I think octaves are irrelevant. My personal explanation for it is, if we count in between overtones to say that the fourth comes earlier, that’s not in relationship to the fundamental (basically the tonic), but the relationship between those two overtones.– LeciferSep 16 at 13:40
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@ToddWilcox Interesting! It’s still hard for me to fathom that anyone could ever find chords such as C, C#, D (0, 1, 2) as consonant or say that Trichord sounds good. I’ve gone through the trouble of learning about set classes and the 12 unique trichords and personally it seems very easy to tell that I don’t like the ones that are further from having only “consonant” tones. Even diminished trichords sound kind of bad to me and have to be used carefully. The closest to me are sus chords or the “minor 7th shells”, but even then I can understand why they wouldn’t be the center of composing.– LeciferSep 16 at 13:46
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@ToddWilcox Also, can you look at my reply above to nuggethead. Do you have any additional verification to how the major 3rd comes before the perfect fourth in the harmonic series. Does what I said about it make sense or am I far off?– LeciferSep 16 at 13:49
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1 Answer
As the "rules" for handling dissonance seem (to me) to be a bit convoluted, I think it's easier just to use a table of intervals. Historically, intervals were classed into three broad types.
Perfect perfect consonances (no major or minor form): unison, octave, fifth, fourth*
Imperfect consonances (major and minor): thirds, sixths
Dissonances: (major or minor) seconds, sevenths, all augmented or diminished intervals, *perfect fourth against the bass note but not against upper notes
For counterpoint (especially between bass and melody in popular styles) this seems about detailed enough. There have been lots of attempts to classify dissonance and consonance through auditory measurements; none seem to agree exactly with musical practice.
Ludmila Ulehla's book, "Contemporary Harmony" lists various chords as to their dissonance intensity; she also discusses how this has changed.
