Irregular vs. regular temperaments

Margo>"Secondly, irregular temperaments can be very attractive for beginners as well as more experienced students of alternative tunings, with George Secor's 17-note well-temperament (17-WT) as a fine example."

   This always got me.  Regular temperaments are defined as temperaments where "each frequency ratio is obtainable as a product of powers of a finite number of generators".  So then, as I understand it, rank one is an EDO and rank two is a combination of two EDOs (multiple generators)..and systems like quarter comma meantone (with a flat fifth and octave as generators) fall under this.

  Thus in such systems you get properties you get advantages such as consistent mapping of primes and ratios (shouldn't that be obvious>...everything is
equally spaced).
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   Then you get something like a strictly proper scales...which can exist in irregular temperaments.  So two steps of the scale, for example, can never be smaller than one step...even though it's not an EDO.  And you often get other consistencies along with this, such as that no fourth is smaller than a third.
  And, as Erv Wilson has spoken of, there are two ideals in scales: adherence to the harmonic series (often forming oddly spaced intervals) and adherence to consistent, predictable interval size (IE in EDOs).  His middle ground (of course) was MOS scales.  But you need not use EDOs to get subsets that are MOS scales...

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   I believe it's a common misconception that the obvious "best standards" way to get a scale that's easy to play is to use a regular tempered EDO.  Sure,
you can get some bizarrely hard to play irregular temperaments...but if you get a strictly proper scale with very "regular" properties...I am confident there are tons of (and not just rare exceptions) irregular tempered scales that would work well musically and, yes, regarding music involving chords or full-on polyphony with multiple instruments being used..

 
>"Third, focusing on the types or "families" of intervals a tuning supports may often be more easily and quickly comprehensible than starting with a list of the commas tempered out or observed == although both, naturally, may be of some interest."

   And this all seems to go back to interval classes as a focal point.  And much as I think it's very elegant someone can take a list of commas generated for errors of powers of one prime-based ratio vs. another and automatically find the best matching EDO...sometimes it seems like overkill.  Especially
considering what you are mapping, considering it's based on powers of a few numbers, is equally spaced.  Predictable interval classes on the average seem, more or less, the greater "point" of all these things...and it amazes me how all this talk of tempering commas can't, in some way, be fairly well "reduced" to interval classes for "beginners" (read...almost any musician...including my profession jazz guitarist brother who freaked out when I showed him a few notes off the list about how mapping in regular temperaments works).

   Personally I usually look at a few steps of a scale from a few different places and think "what intervals does this scale have and what kinds of error does it have on them?".  Then I look for information if it's strictly proper or not....and, if it succeeds on both grounds, I usually try and compose with it.

   And far as EDOs...I usually map the EDO in SCALA and just look at the ratios to get an idea of the types of ratios/chords and degrees of error I'm dealing with. While I wish I did know and have practice with quickly finding EDOs according to desired intervals using Vals and Monzos...often I find the above method fairly adequate...and much much easier to quickly understand than the "Monzo fractions of a Val prime mapping" lingo behind regular temperaments.