It just seems to be that when I strike a I and then V they are simply not dissonant whereas the I & II are far more. WWWH

@leftaroundabout- what do you mean by a "high-intonated" third? I find the resolution of a just dominant chord to its tonic- say 12/15/18 to 8/16/20, to be just as convincing, and with less cringeworthy dissonance. But maybe that's just me....

This answer is wrong. To be clear: I'm not saying this answer is wrong due to logarithmic perception. I'm saying it is flat out wrong. The ratio between the dominant and the tonic frequency is not 3/2 as this answer assumes. The actual ratio in 12-tone music is 2 raised to the power of (7/12). A3 is 220Hz, A4 is 440Hz, but E4 is not 330Hz; E4 is 329.6275569...Hz

See the discussion of Equal Temperament on page 10 of the PDF here: arxiv.org/pdf/1209.3767.pdf

@hft while we can well discuss whether the major third is ⁵⁄₄ or 2⁴'¹², that discussion is pretty much completely irrelevant for the fifth because ³⁄₂ and 2⁷'¹² are so close to each other that they're in almost all contexts indistinguishable to the ear. You may say that 2⁷'¹² is the “conceptually better” definition (which would a valid, if obnoxious, opinion), but that wouldn't change anything about whether or not the fifth is in the middle of the octave.

Added a footnote anyway...

The new footnote is appropriate because the answer is technically wrong for most music and instruments.

@hft I might just as well make that statement for your answer. Most music is in fact neither exactly 12-edo nor 5-limit, and deviates from both by more than the 2ct difference between the JI- and 12-edo fifths. The only music that sticks pretty consistently to 12-edo is pure keyboard music, and even those weren't generally equal-tempered until mid-19th century.

...and of course most pop music of this century, but that's just because of the ongoing autotune epidemic.

This is why I prefer a 53-tone scale where 31 half notes get you even closer to the ratio 3/2 than do 7 half notes in the 12-tone scale. But the instruments are hard to play without 50 fingers.

@hft: Before going around telling everyone that they are are "flat out wrong," please listen to my two cents. No, that's actually the whole argument. Two cents. That's what you're literally arguing about here. Actual studies of actual intonation of performers clearly show that most instruments are not played consistently played within the level of accuracy of two cents, with the exception of things like pianos that are often tuned by professionals and can hold a tuning for a long time. From a practical standpoint, "technically wrong for most music and instruments" is actually incorrect.

What is the difference between "actually incorrect" and "flat out wrong"?

@hft: Please re-read my comment (and yours). I was quoting your comment about 3:2 being "technically wrong for most music and instruments" and noting that statement was incorrect from a practical standpoint, given practical limits for tuning precision. In other words, you're wrong about saying it's wrong. Not sure if that addresses your question.

Nope, not going to re-read your comment.

@hft this is like arguing about whether someone is halfway down a football field depending on whether they're standing on the near edge of the center line or at the center of the center line. You're trying to measure more accurately than the precision.

Furthermore, the idea that any particular tuning system is more correct than the acoustical intervals it approximates is puzzling. It's rather more common to say that equal temperament is slightly incorrect.

Consider an ensemble that plays a chord in just intonation with frequencies of 220, 330, 440, and 550 Hz. Would you say that they were wrong? I certainly wouldn't.

@phoog The question was "Is the dominant tone of a major scale halfway in frequency between the tonic and octave?"

I would argue that the correct answer is "no." This is because if you were to ask me to describe a major scale I would start off by describing the 12 equally spaced half steps. Then I was say that a major scale is: "whole step, whole step, half step, whole step, whole step, whole step, half step." This is what I consider a major scale to be. This is what the OP asked about. The Sol is 7 "equally spaced" half steps above the Do.

This means that I consider it incorrect to say that the Sol frequency is 3/2 times the Do frequency. I don't really care about other tunings. I'm answering the question the OP asked in the way that I feel is most broadly applicable and correct.