Just intonation: Difference between revisions

Just Intonation (JI) describes [[Gallery_of_Just_Intervals|intervals]] between pitches by specifying ratios (of [http://en.wikipedia.org/wiki/Rational_number rational numbers]) between the frequencies of pitches.<ref>Just Intonation is sometimes distinguished from ''rational intonation,'' by requiring that the ratios be lower than some arbitrary complexity (as for example measured by [[Tenney Height|Tenney height]], [[Benedetti height]], etc.) but there is no clear dividing line. The matter is partially a question of intent. The rank two tuning system in which all intervals are given as combinations of the just perfect fourth, 4/3, and the just minor third, 6/5, would seem to be a nonoctave 5-limit just intonation system by definition. In practice however, it casually suggests a rank two 7-limit [[microtempering]] system because of very accurate approximations to the octave and to seven limit intervals: (6/5)^2/(4/3) = 27/25, the semitone maximus or just minor second; and (27/25)^9 is less than a cent short of an octave, while (27/25)^2 is almost precisely 7/6, the [http://en.wikipedia.org/wiki/Septimal_minor_third septimal minor third].</ref>

There is more to it than this, of course, but the basic principles of Just Intonation are very simple. Hundreds of years ago, when the intonation of a few well-known intervals was the concern, understanding and defining "Just" was not difficult. These days, though, and going on from these basics, it can get a bit more complicated...

To start off your exploration of just intonation scales, the [[Gallery_of_12-tone_Just_Intonation_Scales|Gallery of 12-tone Just Intonation Scales]] is a good place to start.

The use of just intonation could be divided into these two flavors:

[[Lou_Harrison|Lou Harrison]] used this term; it means that you choose just-intonation pitches from the set of all possible just intervals (not from a mode or scale) as you use them in music. Dedicated page -&gt; [[FreeStyleJI|FreeStyleJI]]

(In need of a better name maybe) Here are six ways that musicians and theorists have constrained the field of potential just ratios (from Jacques Dudon, "Differential Coherence", ''1/1'' vol. 11, no. 2: p.1):

''8. While related to the above, the use of recurrent sequences is by some included under JI as it involves whole numbers. Wilson's [http://anaphoria.com/wilsonintroMERU.html Meru scales] are a good example.''

[[Regular_Temperaments|Regular Temperaments]] are just intonation systems of various [[harmonic_limits|harmonic limits]] with certain commas 'tempered out'

[[AdaptiveJI|Adaptive JI]]

[[Gallery_of_Just_Intervals|Gallery of Just Intervals]]

[[boogiewoogiescale|Boogie woogie scale]]

<ul><li>[http://en.wikipedia.org/wiki/Just_intonation Wikipedia article on just intonation]</li><li>[http://nowitzky.hostwebs.com/justint/ Just Intonation] by Mark Nowitzky [http://www.webcitation.org/5xeAm2lPL Permalink]</li><li>[http://www.kylegann.com/tuning.html Just Intonation Explained] by Kyle Gann [http://www.webcitation.org/5xe2iC7Nq Permalink]</li><li>[http://www.kylegann.com/Octave.html Anatomy of an Octave] by Kyle Gann [http://www.webcitation.org/5xe30LCev Permalink]</li><li>[http://www.dbdoty.com/Words/What-is-Just-Intonation.html What is Just Intonation?] by David B. Doty [http://www.webcitation.org/5xe3MeWVq Permalink]</li><li>[http://lumma.org/tuning/faq/#whatisJI What is "just intonation"?] by Carl Lumma [http://www.webcitation.org/65NwFAKLh Permalink]</li><li>[http://www.dbdoty.com/Words/werntz.html A Response to Julia Werntz] by David B. Doty [http://www.webcitation.org/5xe38KWx4 Permalink]</li><li>[http://lumma.org/tuning/gws/commaseq.htm Comma Sequences] by Gene Ward Smith [http://www.webcitation.org/5xe4rPLZ0 Permalink]</li><li>[https://casfaculty.case.edu/ross-duffin/just-intonation-in-renaissance-theory-practice/ Just Intonation in Renaissance Theory & Practice] by Ross W. Duffin

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