If so, why are 12 TET interval ratios for e.g. Perfect 5th 7:12 different to that of the Just Intonation which the Perfect 5th has a ratio of 3:2?

@Seery your question doesn't follow on from Tim's comment at all.. They're different, but close. That's the point of a tempered tuning. If you don't understand why we use 12TET instead of just intonation which has more consonant intervals, I suggest you post a separate question on that topic

I believe we use 12TET to be able to play different scales within a single tuning but my question doesn't quite revolve around the difference. I'm specifically looking for the consonance/dissonance levels of intervals pertaining to 12TET so I can build chord progressions and compositions with the correct levels of consonance and dissonance and I feel folks are missing what it is I'm after.. the intervals and their levels of consonance to dissonance in 12TET. If their order of consonance to dissonance are equal to Just Intonation then my query here is satisfied but it seems not to be the case.

@Some_Guy - what comment was that - I can't seem to find it.

The comment on the purpose and function of temperaments in your answer. Comment in the linguistic sense, not the digital sense; remark, observation, comment, response, utterance, point, "glob of words" if you like... I was talking about the answer you posted anyway ;)

@Seery, the 12TET is governed by the 12th root of 2. All roots of 2 are irrational so 7:12 is not the ratio of 1 to 5. ttw's answer is correct. 12TET and Just both contain consonance and dissonance. They occur approximately at the same intervals and for the same reasons. I believe I and others provided a physics based explanation in one of you previous questions. However, even that is somewhat subjective as the judgement of consonance and dissonance is a mater of taste and is really difficult to objectively quantify. Helmholtz tried but he assumed a Western definition of "good".

@ggcg Thanks for your response. During my research i encountered Helmholtz and read his stance which was included in an article which spoke on the various approaches to consonance and dissonance from different folks. I may be hard headed but even to a relative novice like myself, i feel certain intervals levels of consonance/dissonance within an octave in contrast to other intervals are undeniable, meaning there is a pattern there and i feel that some intervals are so similar in their consonance/dissonance that this is the reason people can't agree on one conclusion of the ranking.

You could just the rough estimates suggested by theorists for the last few hundred years. Perfect consonances: unison, octave, fifth, fourth*; imperfect consonances: major third, minor third, major sixth, minor sixth; dissonances: minor second, major second, minor seventh, major seventh, all augmented intervals, all diminished intervals, fourth* against the bass only. Voice leading: approach intervals by contrary motion; other notes (if possible) to nearest note in next chord (or sonority.) Usually most of my bad sounding parts of pieces occur because of violating one of these.

@Seery, but even within the standard ranking people disagree about which dissonant intervals are most or least dissonant. Also, in 12TET none of the harmonics match!!! Hence in theory none of the intervals are perfectly consonant. Folks with perfect pitch claim to be able to hear the difference and prefer to listen to Just tuned instruments. One of my physics professors in college had the problem and his wife was a professional cellist with our City's Symphony. He would "correct" her intonation by ear.

@ttw great analysis.. I read the P4 is consonant/dissonant based on context. I read that if the P4 is utilized as anything but a bass note/root note of a chord, then it is consonant and if used as a bass note/root note of a chord then it is considered dissonant.. Is this what you mean when you state "fourth against the bass only"? Cheers

@ggcg I never knew the imperfection of harmony in music until i started this project and it was very disappointing. I watched a video where they play chords in Just Intonation versus 12TET and other tuning systems and i was like wow. What a sloppy system we have going on, in aid of close to perfect compromise. I'm rather positive this will resolve in the future with A.I. tho as it seems to be an issue of practicality more than laws of nature. Also music in 440hz was made standard by Nazi Germany whilst 432hz is said to be the frequency of nature. A lot of fuckery in the world of music.

I'm not sure most people can really hear the difference but then again you can't if you are not presented with the difference. Once you hear it you cannot un-hear it. It is a compromise for convenience. But most people have a limit to pitch discrimination, which helps with tolerance.

That's what I meant about the fourth. I have seen the suggestion that the fourth over the bass sounds dissonant (implies musical motion) because it implies a 6-4 chord. However, I'm not convinced. It may be now, using CPP harmony but not necessarily some time back. In organum, fourths are used but phrases tend to end on fifths or octaves.This may not be the best place but Ludmila Ulehla has a nice ranking of chords by dissonance. (Note that the Neapolitan Sixth is dissonant but it's just a first inversion major chord in itself, context matters.)

@ttw thank you for your confirmation and reference to Ludmila Ulehla whom ill research.

@Seery A432 think is complete bunk based on misinformation (and also just logically, think about it, "hz" is an arbitrary unit based on the length of time the second, so the number 432 is meaningless and all that stuff about 432 as a magic number makes no sense. It's like talking about how many inches a guitar string should be, it's a different number if you measure in a different unit!) Not to mention, A is an arbitrary note to tune from (most music isn't in A), and that humans pitch perception is relative not absolute. I can't believe are still getting taken in by this!

@Seery This is a different question and I don't want to fill up these comments. Please feel free to ask it and I will happily answer. But yes, I am sure that there is nothing special about 432 Hz, and I can address all the points you raised in this comment. Another point you raised in that same comment was re JI: "just practicality or laws of nature?". That is another interesting question, and there are actually fundamental natural reasons why we don't tune justly (outside of practicality) which I think you might find interesting. But alas, no space here. I would love to answer though!

@Seery or, alternatively, chat me chat.stackexchange.com/rooms/96408/chat-with-seery

@Some_Guy i'm working right now but will message you shortly!