A few issues with "JI worship" and a few proposed alternatives

I think this is worth bringing up as so many people believe JI is the be and end all of tuning theories.

As I understand it

A) JI somewhat assume periodicity is the primary determinate of consonance...as opposed to theories of critical band roughness.
B) It follows that "tonality" is the basis by which JI chords point toward a root tone. IE in the 2:3:4 chord of 200hz, 300hz, 400hz...all tones point at a root of 100hz...which happens to be the difference tone between 300-200hz and 400-300hz.
C) JI scales are built largely to enable as many chords that optimize both A and B as possible and, indirectly, enable (among those many chords) certain special chords (often not available in 12TET) that target a composer's desired mood more effectively.
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I will agree on this much:
2A) Periodicity means a lot. In general a waveform composed of multiple tones that takes too long to repeat sounds unstable to the ear and even "looks" unstable in a time-domain graph of the waveform to the point you can't readily look at it and identify the points of periodicity IE "perfect sample loop points".
In general, I've found that a chord which more-or-less repeats exactly the same pattern in every 10th of a second or less is good enough to feel "balanced". Coincidentally, the mp3 audio format assumes the ear has a time resolution of about a tenth of a second (no coincidence, I'm betting).
2B) Chords need to show at least some tonality to feel resolved. Any chord I've tried that doesn't summarize to about x/18 or lower IE 18:20:24 sounds unstable to me.
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However I see problems in "perfect" low-limit JI with

A) Roughness ALSO means a lot. The so-called "perfect" minor second is virtually never used in chords, and I strongly suspect it is due to roughness. IMVHO any two tones closer than about 1.08 or 13/12 (such as half-steps in diatonic scales) are too rough to be used in chords, thus making the goal of maximum chords much harder to achieve. What do you believe is about the minimum interval that can be used in a chord?

C)......as I've found that trying to get "perfectly" pure intervals (especially 7-odd-limit or lower) severely limits the number of chords possible.
2C) The alternative? Why, tempering off JI scales...of course. Personally I've found up to 12 cents or so off JI can often double or triple the number of chords that meet A) and B) while feeling close enough to perfect that most people don't notice it much. Another alternative: make a scale that's not JI (IE an irrational number generated scale) and round it to JI...I've found using a common denominator of no more than 36 (between all notes) works best for that. What are your beliefs about tempering and what a good margin of error for tempering off JI is?
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A few things that really get my goat, though, are
1) How complicated academics make JI...to the point I swear they scare off most people.
Here is something I swear you could use to teach even teach 5th graders how to make their own JI scales
A) Take any x/y fraction where y is a fixed number IE 8/8 9/8 11/8 (8:9:11)...and you have a JI chord.
B) Take a few JI chords and link them together to make a JI scale...preferably keeping the least common factor denominator at a small number (IE x/36 or under...note diatonic JI fits in x/24 format).

Sure you can go into more detail about difference tones, how/why the chords match the harmonic series, the acoustics of periodicity, periodicity blocks, tonality in relation to difference tones, sub-harmonics... But wouldn't it be nice to give people the tools to at least start making their own JI scales before we shoot them over the head about all the technical details they "missed" and give them a "this is why you aren't a PHD" essay?
Also isn't it true that, no matter how good a scale looks on paper, if most people can't tell a positive emotional difference in the sounds possible with it, it largely defeats the purpose (music ultimately is about emotion, right)?

2) This idea that anything new that tempers off JI or originates from a non-JI generation method must somehow be the simple product of a lack of academic understanding and/or effort. Often it doesn't cross people's minds that the scale creator may have not intended for the scale to sound like low-limit Just-Intonation, that it may have been intended for use with alternative timbres, and so on. 22TET and Bill Sethares' use of 10TET and 11TET are two obvious examples of this, in my book.
Shouldn't we be offering advice in terms of alternatives to "fine-tune" or at least elaborate on valuable parts from ideas instead of telling each other what the other person makes must be either 100% rubbish or 100% perfect?

Whoa, wall of text. Some points I'd like to respond to:

> A) JI somewhat assume periodicity is the primary determinate of consonance...as opposed to theories of critical band roughness.

JI doesn't make any assumptions about consonance. It's just a system
of tuning based entirely on creating integer-ratio relationships with
different notes.

> B) It follows that "tonality" is the basis by which JI chords point toward a root tone. IE in the 2:3:4 chord of 200hz, 300hz, 400hz...all tones point at a root of 100hz...which happens to be the difference tone between 300-200hz and 400-300hz.

I definitely don't think that JI makes that claim. I am of the
personal viewpoint that one must consider all of the sub-dyads and
sub-triads in a chord separately, as well as consider the chord as a
whole, to figure out what is going on tonally. I've been calling this
a chord's "harmonic profile," and I'm trying to find a good way to
model it atm.

> A) Roughness ALSO means a lot. The so-called "perfect" minor second is virtually never used in chords, and I strongly suspect it is due to roughness. IMVHO any two tones closer than about 1.08 or 13/12 (such as half-steps in diatonic scales) are too rough to be used in chords, thus making the goal of maximum chords much harder to achieve. What do you believe is about the minimum interval that can be used in a chord?

I don't know why you'd say this. I use 100-cent intervals in chords
all the time. Here's a beautiful voicing for mixolydian: G E F B C' G'
A'. As you can see it's made mostly of stacked seconds and fifths. The
seconds carry the weight of the information (entropy) in the chord,
and the fifths not so much. I'm not entirely sure if the entropy I'm
referring to here is the same as Erlich's model of Harmonic Entropy,
though.

-Mike

Hi Michael,

I think this is worth bringing up as so many people believe JI is the be and
> end all of tuning theories.
>

Well I'll reply to this as I think you're refering to me.
But I think I'm about the only person who thinks what you're saying above :)
I don't know where you've gotten the impression that many people believe
this as it's fairly easy to tell that my theories aren't exactly popular to
say the least haha.
And the other people who are involved in JI have not made a claim that they
think JI is the be and end all of tuning theories as far as I read.

As for the other things.
I'm into 5-limit JI so not much of a point to reply to the extended JI
questions you have.

I can say the following, that my JI is as much about "roughness" as it is
about consonance. Both are used and both are greatly exadurated compared to
12tet.

Marcel

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