Spawned by a previous question/answer. It seems that consonance/dissonance in intervals and harmonies have varied over time. So how would a decision be made to change one interval from one to the other, given that the sound will be the same for both? Maybe changing tastes, but who decides?

And, how come d4, sounding exactly as M3, and d7, sounding exactly like M6, are both considered dissonant, but their 'twins' are both consonant?

All this, in 12tet-land. I well appreciate that in other intonations and temperaments, the 'twins' will vary enough for them to have different pitches along with their different names, thus making them sound consonant or dissonant. Or is that just it? On 12tet piano, even d4 and d7 can be consonant intervals?

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    Oof. Tricky. Seeing as how "consonant" and "dissonant" are just fancy words for "I like it" or "I don't," this is almost a question about "How do broad music-cultures evolve their consensus on subjective matters?" Oct 18 '21 at 14:06
  • As for the d4 vs M3 question, I'm thinking the answer has to look beyond intervals to chords and tonal context. I mean, in monophic Gregorian plainchant, why write it as a d4 in the first place instead of M3? The only reason for different enharmonic spellings is to imply that something has mutated from something else. An m3 is just a thing, but an A2 is another thing that has been "blown out of proportion." An M3 is a thing, but a d4 is another thing that has been contorted into new constraints. All of them imply that something's happening in the bigger picture. Oct 18 '21 at 14:11
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    You're onto something with the intonation: A just tritone at 7/5 can sound consonant; a 12TET tritone at 2^(1/2), not so much.
    – Theodore
    Oct 18 '21 at 14:16
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    @AndyBonner That's not it especially since a lot of musicians favorite chords tend to be more dissonant in nature. It's stable vs unstable, but it does have cultural bearings which are hard to quantify.
    – Dom
    Oct 18 '21 at 14:25
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    Again it has cultural bearing. The stable vs unstable is the textbook methods of those terms fitting well with how we use them in functional harmony i.e. a V7 dissonances resolve to the consonance of I. The unstable moves to the stable.
    – Dom
    Oct 18 '21 at 14:55

I think the meanings of consonance and dissonance are more historical than acoustical. I would describe that "consonance" means "doesn't imply change" and "dissonance" means "implies a change"; the "imply" depends on the musical context.

There are a couple of obvious examples. A perfect fourth is acoustically consonant but it can act dissonant if used against the bass in a 64 chord. This seems to be a stylistic effect. One article (I don't remember which; it was probably something on the Romanesca with reference to schemata.), pointed out that the use of 64 chords was somewhat conventional. It could be used as a passing chord (consonant), in an arpeggiated chord (consonant), between a subdominant-type chord and a dominant (cadential, dissonant), and a few other places. One of these other places was in a descending bass line like the Romanesca, One may see I, V6, vi, iii, IV (Pachelbel) or even I, V6, vi, I64, IV (without an example); in the last case, the I64 acts like a typical IV6, I64, IV with a descending bass.

Another contextual example is the use of a I7-IV7-V7 in blues. The I7 and IV are not "secondary dominants"; the only dominant flavor comes from the 5-1 bass movement at the close. However if one writes a Passamezzo Moderno style piece, I-IV-V7 will sound dissonant.

I am sure there are other examples, especially since I didn't mention rhythm or melodic movement as a source of movement vs non-movement (rest sounds too final).


d7, sounding exactly like M6, are both considered dissonant, but their 'twins' are both consonant?

I think it is the combination of the placement within the scale and the alteration of tones from diatonic. By diatonic I mean the diatonic gamut ABCDEFG and its transpositions. There is no diatonic d7. If we consider the commonly used example of leading tone ^7 and flat ♭^6, it's nine half steps, but it also involves an altered tone, either the lowered sixth degree in major, or the raised seventh degree in minor.

The alteration is the important point. A d7 is enharmonically equivalent to M6, but the fact that a tone must be altered from diatonic is heard, the ear recognizes the deviation from diatonic... and it matters.

The general rule is any interval altered to a diminished or augmented interval is considered dissonant, because of the alteration, regardless whether that resulting interval is enharmonically equivalent to another consonant interval.

So, for example, in C minor, B and A♭ are a d7, 9 half steps, and dissonant, but while E♭ to C is a M6, and also 9 half steps, it is a consonance. The difference is the chromatic alteration.

To put it another way: the only diatonic sixth below A♭ in C minor is on C♮, a minor sixth m6. The M6 below would be a C♭, at which point the tonic is altered and things would just become crazy. If you come at it from below, and try to make a M6 above the lower tone, it's starting with an altered seventh degree B♮ up to a G, in this case a G#, which is a second alteration, this time on the dominant.

That's a lot of mucking around with those particular scale degrees. Either the enharmonic spelling to force sixths start to suggest a likely change of tonal center, or we accept that altering intervals to anything that becomes diminished or augmented creates dissonance.

Why? Well, my answer would be the "weirdness" of the chromatic alterations. That may seem arbitrary, but remember, there is no absolute measure or definition of dissonance. The acoustical definition is about simple ratios, but the destabilizing aspect of chromatic changes to the diatonic gamut are also a stylistic factor. Chromatically altered, non-diatonic "weirdness" is dissonance... because the harmonic style says so. This gets to the other part of your question.

So how would a decision be made to change one interval from one [consonant] to the other [dissonant]

The perfect fourth already provides a historic example. Some styles treat it as a dissonance (which I think makes little sense to modern ears like mine), other styles treat it as a consonance. In the style that treats it as a dissonance it gets treated strictly as a proper suspension were the "dissonant" fourth must resolve to a third. That's just a choice, but it makes the character of that particular harmonic style. To treat it like a consonance you could do things like play parallel 6/3 chords or maybe hit that interval as an appoggiatura, etc.

Notice that the difference between the two treatments is not about some absolute quality of a perfect fourth but rather the context in which it is used. When my 21st century ears hear a suspension figure in Palestrina I don't literally hear dissonance, but I understand in that style the suspension treatment is what casts the interval as a dissonance. It's the musical equivalent of putting a fig leaf on a Greek nude sculpture. The thing in question is not inherently offensive, but the treatment of it let's the audience know how it is regarded.

So, how to make a dissonance a consonance? Literally just do it. Modernism basically treats seconds, fourth, and seventh, etc. as intervals that do not need special handling as dissonances. That in effect makes them consonances. Personally, I think Debussy is the composer to listen to for this stuff. His music is so beautiful, so sensual, so expressive, and those moods were achieved many times with intervals that would conservatively be called dissonant. He didn't treat traditional dissonances as dissonant and so achieved new modes of harmonic expression.

Jazz is the other obvious place to look for dissonance recast as consonance. To the extend that non-chord tones would be dissonances, it's hard to identify any melody tone as a non-chord tone in jazz. Everything up to the thirteenth can easily be labeled a chord tone. The fourth is the one interval that jazz still seems to treat as a dissonance. Ironic, because the fourth as dissonant is such an old concept.

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