Xenharmonic Wiki

Just intonation: Difference between revisions

← Older edit
VisualWikitext
Wikispaces>hstraub
**Imported revision 9120421 - Original comment: Pages for compositions in JI**
Hkm (talk | contribs)
934 edits
clarified relation between JI and harmonic series
 
(124 intermediate revisions by 33 users not shown)
Line 1: Line 1:
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{interwiki
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| en = Just intonation
: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2007-10-08 06:15:52 UTC</tt>.<br>
| de = Reine Stimmungen
: The original revision id was <tt>9120421</tt>.<br>
| es = Entonación Justa
: The revision comment was: <tt>Pages for compositions in JI</tt><br>
| ja = 純正律
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
| ko = 순정률
<h4>Original Wikitext content:</h4>
| ro = Intervale raționale
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">=Just Intonation defined=
}}
Describe intervals between pitches by specifying ratios (of [[http://en.wikipedia.org/wiki/Rational_number|rational numbers]]) between the frequencies of pitches, and you will be speaking Just Intonation.
{{Wikipedia}}


=Overtone Series=
'''Just intonation''' ('''JI''') is an approach to [[musical tuning]] which uses tones whose frequencies are whole-number ratios of a given fundamental [[frequency]]. Just intonation includes the [[harmonic series]], which is the collection of tones found at integer multiples of a fundamental frequency; all just intervals can be found as the interval between two notes in the harmonic series. Just ratios of small numbers, called '''Low-complexity just intonation (LCJI)''' intervals, tend to be the most [[concordant|consonant]] in the sense that their sounds meld together.  
(Insert theory/description here...)


==[[OverToneSeries|Compositions]]==
In the context of Western music theory prior to the 20th century, the term ''just intonation'' used alone usually refers to [[5-limit]] tuning--intervals where the numerators and denominators of any ratio used have no prime factors greater than 5. ''Extended just intonation'', a term coined by [[Ben Johnston]], refers to any tuning in the harmonic series regardless of [[prime limit]].<ref>From Ben Johnston "A Notation System for Extended Just Intonation." ''Maximum Clarity'', 2006, p. 77</ref> In current usage, just intonation typically refers to extended just intonation. The practice of just intonation without any particular constraint is sometimes referred to as '''rational intonation''' ('''RI''') or as [[free style JI]].


=Freestyle Just/Adaptive Just Intonation=
The structure of just intonation has several implications on music composition. [[Wolf interval|Wolf intervals]] and [[Comma|commas]], two kinds of dissonant intervals, may appear between distantly-related pitches. In addition, certain chord progressions are [[Comma pump|comma pumps]], which may cause the [[tonal center]] of a piece to drift up or down in pitch over time. These effects can be treated either as tools to use or as problems to be solved. Examples of approaches that try to solve these problems without greatly restricting the set of available ratios include pitch shifts, [[adaptive just intonation]] and [[temperament]]. Other approaches restrict the space of usable JI intervals in a way that makes these problems arise less frequently.
Compose music such that each pitch you choose is chosen from the infinitely large pool of rational numbers. Daunting!


==Software==  
== Consonance ==
* Chuckk Hubbard's [[http://www.badmuthahubbard.com/jisequencer.html|No-scale JI Sequencer]]
LCJI intervals achieve consonance through alignment of [[Partial|partials]] if the interval has [[Harmonic timbre|harmonic timbre]]. In fact, alignment of partials is a stronger effect with harmonic timbre: if partials align at frequency n, they will also align at every multiple of n; and in addition, two notes whose partials align with the same root note will also have partials aligning with each other. This allows for the construction of just-intonation chords of more than two notes where every comprising interval is a consonance.  
* [[http://www.math.tu-dresden.de/%7Emutabor/|Mutabor]]


== ==
Low-complexity JI intervals and chords also achieve consonance by being the ratios between harmonics of a (possibly unplayed) fundamental even if they do not have harmonic timbre.
==[[AdaptiveJI|Compositions]]==


=Constraints=  
==Ways of using JI==
Create subsets of the infinitely large pool of ratios.
Here are multiple ways in which musicians and theorists have used just intonation.


(insert Jacques Dudon article quote here)
[[Free style JI|'''Free style JI''']] <br />
[[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.


==JI theory==
'''Harmonic limits and subgroups'''<br />
Links to JI theory pages on [[http://moinmoin.riters.com/microtonal|another microtonal wiki]], pending transfer to this wiki:
[[Harmonic limit|Harmonic limits]] set a limit for the highest prime number in the factorization of any ratio used. [[Subgroup|Subgroups]] name a list of allowable prime numbers used.
[[http://moinmoin.riters.com/microtonal/index.cgi/58Note11LimitJI|58 note 11 limit JI]] - hyper-Partchian!
[[http://moinmoin.riters.com/microtonal/index.cgi/Reduction|Reduction]]
[[http://moinmoin.riters.com/microtonal/index.cgi/Comma_20sequences|Comma sequences]]
[[http://moinmoin.riters.com/microtonal/index.cgi/Hahn_20distance|Hahn distance]]


==Scales==
'''Restrictions on the denominator or numerator'''<br />
[[boogiewoogiescale|Boogie woogie scale]]
Some approaches restrict "the denominator to one or very few values"<ref name=":0">From Jacques Dudon, "Differential Coherence", ''1/1'' vol. 11, no. 2: p.1).</ref> (the [[harmonic series]], [[isoharmonic chord]]s, [[AFDO]]s/[[overtone scale]]s, [[primodality]], [[Ringer scale|ringer scales]]), the "numerator to one or a very few values" (the [[subharmonic series]],  [[IFDO]]s/undertone scales), or both ([[Tonality diamond|tonality diamonds]])
[[Arnold Dreyblatt]]
Gallery of pentatonics


==[[FiniteSubsetJI|Compositions]]== </pre></div>
'''Mediants'''<br />
<h4>Original HTML content:</h4>
The use of harmonic and arithmetic [[Mediant (operation)|mediants]] as was common with the Ancient Greeks. This can also involve further divisions besides two parts as seen with Ptolemy sometimes using 3 parts. The Chinese have historically used as many as 10 parts.
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Just intonation&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Just Intonation defined"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Just Intonation defined&lt;/h1&gt;
 
Describe intervals between pitches by specifying ratios (of &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Rational_number" rel="nofollow"&gt;rational numbers&lt;/a&gt;) between the frequencies of pitches, and you will be speaking Just Intonation.&lt;br /&gt;
'''Approximations/alterations of tempered tunings''' <br />
&lt;br /&gt;
These are [[Detempering|detemperings]], including [[NEJI]] systems.
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Overtone Series"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Overtone Series&lt;/h1&gt;
 
(Insert theory/description here...)&lt;br /&gt;
'''Other approaches'''<br />
&lt;br /&gt;
Other approaches include [http://anaphoria.com/wilsonintroMERU.html Meru scales], [[Tritriadic scale|titriadic scales]], and [[combination product sets|product sets]].
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Overtone Series-Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;&lt;a class="wiki_link" href="/OverToneSeries"&gt;Compositions&lt;/a&gt;&lt;/h2&gt;
 
&lt;br /&gt;
==Instruments==
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Freestyle Just/Adaptive Just Intonation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Freestyle Just/Adaptive Just Intonation&lt;/h1&gt;
{{todo|expand|comment=Expand the instruments section with more examples}}
Compose music such that each pitch you choose is chosen from the infinitely large pool of rational numbers. Daunting!&lt;br /&gt;
*The [[Kalimba#Array mbira|array mbira]] was designed by [[Bill Wesley]] as a versatile just intonation instrument, covering a 5 octave range.
&lt;br /&gt;
*Most of [[Harry Partch]]'s instruments were designed to be for just intonation.
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Freestyle Just/Adaptive Just Intonation-Software"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Software&lt;/h2&gt;
==Music==
&lt;ul&gt;&lt;li&gt;Chuckk Hubbard's &lt;a class="wiki_link_ext" href="http://www.badmuthahubbard.com/jisequencer.html" rel="nofollow"&gt;No-scale JI Sequencer&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://www.math.tu-dresden.de/%7Emutabor/" rel="nofollow"&gt;Mutabor&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
{{Main|Music in just intonation}}
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt; &lt;/h2&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Freestyle Just/Adaptive Just Intonation-Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;&lt;a class="wiki_link" href="/AdaptiveJI"&gt;Compositions&lt;/a&gt;&lt;/h2&gt;
== Notation ==
&lt;br /&gt;
There are various [[Musical notation|notation systems]] for just intonation.
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Constraints"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Constraints&lt;/h1&gt;
==See also==
Create subsets of the infinitely large pool of ratios.&lt;br /&gt;
{{todo|cleanup|inline=1}}
&lt;br /&gt;
*[[List of approaches to musical tuning]]
(insert Jacques Dudon article quote here)&lt;br /&gt;
*[[Gallery of just intervals]]
&lt;br /&gt;
*[[Gallery of 12-tone just intonation scales]]
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="Constraints-JI theory"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;JI theory&lt;/h2&gt;
*[[Families of scales]]
Links to JI theory pages on &lt;a class="wiki_link_ext" href="http://moinmoin.riters.com/microtonal" rel="nofollow"&gt;another microtonal wiki&lt;/a&gt;, pending transfer to this wiki:&lt;br /&gt;
*[[boogiewoogiescale|Boogie woogie scale]]
&lt;a class="wiki_link_ext" href="http://moinmoin.riters.com/microtonal/index.cgi/58Note11LimitJI" rel="nofollow"&gt;58 note 11 limit JI&lt;/a&gt; - hyper-Partchian!&lt;br /&gt;
*[[:Category:Just intonation]]
&lt;a class="wiki_link_ext" href="http://moinmoin.riters.com/microtonal/index.cgi/Reduction" rel="nofollow"&gt;Reduction&lt;/a&gt;&lt;br /&gt;
==References==
&lt;a class="wiki_link_ext" href="http://moinmoin.riters.com/microtonal/index.cgi/Comma_20sequences" rel="nofollow"&gt;Comma sequences&lt;/a&gt;&lt;br /&gt;
<references />
&lt;a class="wiki_link_ext" href="http://moinmoin.riters.com/microtonal/index.cgi/Hahn_20distance" rel="nofollow"&gt;Hahn distance&lt;/a&gt;&lt;br /&gt;
 
&lt;br /&gt;
==Further reading==
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Constraints-Scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Scales&lt;/h2&gt;
*[http://www.tonalsoft.com/enc/j/just.aspx Just intonation] on the [[Tonalsoft Encyclopedia]]
&lt;a class="wiki_link" href="/boogiewoogiescale"&gt;Boogie woogie scale&lt;/a&gt;&lt;br /&gt;
*[http://nowitzky.hostwebs.com/justint/ Just Intonation] by Mark Nowitzky
&lt;a class="wiki_link" href="/Arnold%20Dreyblatt"&gt;Arnold Dreyblatt&lt;/a&gt;&lt;br /&gt;
*[http://www.kylegann.com/tuning.html Just Intonation Explained] by Kyle Gann
Gallery of pentatonics&lt;br /&gt;
*[http://www.kylegann.com/Octave.html Anatomy of an Octave] by Kyle Gann
&lt;br /&gt;
*[http://www.dbdoty.com/Words/What-is-Just-Intonation.html What is Just Intonation?] by David B. Doty
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="Constraints-Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;&lt;a class="wiki_link" href="/FiniteSubsetJI"&gt;Compositions&lt;/a&gt;&lt;/h2&gt;
*[http://lumma.org/tuning/faq/#whatisJI What is "just intonation"?] by Carl Lumma
&lt;/body&gt;&lt;/html&gt;</pre></div>
*[http://www.dbdoty.com/Words/werntz.html A Response to Julia Werntz] by David B. Doty
*[http://lumma.org/tuning/gws/commaseq.htm Comma Sequences] by Gene Ward Smith
*[https://casfaculty.case.edu/ross-duffin/just-intonation-in-renaissance-theory-practice/ Just Intonation in Renaissance Theory & Practice] by Ross W. Duffin
Retrieved from "https://en.xen.wiki/w/Just_intonation"