7-limit: Difference between revisions

The '''7-limit''' or 7-prime-limit consists of rational intervals where 7 is the highest allowable [[prime]] factor, so that every such interval may be written as a ratio of integers which are products of 2, 3, 5 and 7. This is an infinite set and still infinite even if we restrict consideration to a single octave. Some examples within the octave include [[7/4]], [[7/5]], [[7/6]], [[9/7]], [[15/14]], [[21/16]], [[21/20]], [[35/27]], [[49/36]], and so on.

The [[7-odd-limit]] refers to a constraint on the selection of [[Just intonation|just]] [[Interval class|intervals]] for a scale or composition such that 7 is the highest allowable odd number, either for the intervals of the scale, or the ratios between successive or simultaneously sounding notes of the composition. The complete list of 7 odd-limit intervals within the octave is [[1/1]], [[8/7]], [[7/6]], [[6/5]], [[5/4]], [[4/3]], [[7/5]], [[10/7]], [[3/2]], [[8/5]], [[5/3]], [[12/7]], [[7/4]], [[2/1]], which is known as the [[Wikipedia:Tonality diamond|7-limit tonality diamond]].

The phrase "7-limit just intonation" usually refers to the 7-prime-limit and includes primes 2, 3, 5, and 7. When octave equivalence is assumed, an interval can be taken as representing that interval in every possible voicing. This leaves primes 3, 5, and 7, which can be represented in [[The Seven Limit Symmetrical Lattices|3-dimensional lattice diagrams]], each prime represented by a different dimension. Lattices describing scales beyond the 7-limit require more than three dimensions, and in the 7-limit, such lattices have unique features which simplify the relations between 7-limit chords.

For a variety of reasons, common-practice music has been somewhat stuck at the 5-limit for centuries, though 7-limit intervals have a characteristic jazzy sound which is at least partially familiar. Music in the 7-limit thus represents a large step forward, although not as much as [[11-limit|11-]] or [[13-limit]], which usually sound much more exotic.

A list of [[edo]]s which tunes the 7-limit with more accuracy: {{EDOs| 5, 9, 10, 12, 19, 27, 31, 41, 53, 72, 99, 171, 441, 612 }} and so on. Another list of edos which tunes the 7-limit well relative to their size ([[TE relative error|relative error]] < 5%): {{EDOs| 12, 19, 31, 41, 53, 72, 99, 118, 130, 140, 152, 171, 183, 202, 212, 217, 224, 229, 239, 243, 251, 270, 282, 289, 301, 311, 323, 354, 369, 373, 383, 388, 395, 400, 410, 414, 422, 441, 453, 460, 472, 482, 494, 525, 544, 566, 571, 581, 593, 612 }} and so on.  

== List of intervals in the 7-prime-limit and 81-odd-limit ==

| {{Monzo| 1 0 2 -2 }}

* [http://micro.soonlabel.com/0-praxis/audio/August/august_12_Ruckus.mp3 Ruckus From the Quiet Zone] by [[Ralph Lewis]]

* [http://micro.soonlabel.com/blue-tuning/blue-ji-excluded-by-peers.mp3 Excluded by Peers] by [[Chris Vaisvil]]

* [http://micro.soonlabel.com/centaur_tuning/Prelude_For_Centaur_Tuned_Piano.mp3 Prelude for Centaur Tuned Piano] by Chris Vaisvil

* [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Prelude%20%231%20for%207-limit%20JI.mp3 Prelude #1 in 7-limit JI] by [[Ivor Darreg]] &larr; are there any notations for it?

* [http://www.archive.org/details/ClintonVariations Clinton Variations] [http://www.archive.org/download/ClintonVariations/clinton.mp3 play] by [[Gene Ward Smith]]

* [http://www.youtube.com/watch?v=HzQmaxDIxnc&feature=channel_video_title Pachelbel's Canon in D in 7-limit JI] [http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Meneghin/Pachelbel_s%20Canon%20in%20D%20-%20Relaxing%20music,%20with%20mountain%20views.mp3 play]

* [http://clones.soonlabel.com/public/classical-music/mars-7-limit-kontakt5.mp3 Mars in 7-Limit JI] from [http://en.wikipedia.org/wiki/The_Planets The Planets] the orchestral suite by Gustav Holst arranged by [[Chris Vaisvil]] (Blog entry: [http://chrisvaisvil.com/gustav-holsts-mars-arranged-for-7-limit-ji-orchestra/ Gustav Holst’s Mars arranged for 7-limit JI Orchestra « Music &amp; Techniques by Chris Vaisvil])

* [http://micro.soonlabel.com/gene_ward_smith/Others/Kite/Consolation%20%233%20by%20Ken%20Stillwell%20retuned.mp3 Liszt Consolation #3] Ken Stillwell performance, retuned by [[Kite Giedraitis]] to the [[kite33]] 7-limit JI scale

* [http://tallkite.com/music/IHearNumbers.html I Hear Numbers] by [[Kite Giedraitis]]

* [[Harmonic limit]]

* [[7-odd-limit]]

* [[Wikipedia: Highly composite number]]

[[Category:Interval collection]]