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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<span style="display: block; text-align: right;">[[de:Sagittalnotation]]</span>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
[[file:sagittal_sample.gif]]
: This revision was by author [[User:d.keenan|d.keenan]] and made on <tt>2015-08-09 07:39:23 UTC</tt>.<br>
: The original revision id was <tt>556380405</tt>.<br>
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The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<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">&lt;span style="display: block; text-align: right;"&gt;[[xenharmonie/Sagittalnotation|Deutsch]]
&lt;/span&gt;
[[image:http://sagittal.org/index_files/image005.gif align="center"]]


Sagittal [[notation]] is a universal set of microtonal accidentals, developed by Dave Keenan and George Secor with the help of numerous others. See [[http://sagittal.org/]] for the official site.
'''Sagittal notation''' is a [[musical notation]] system capable of notating almost any conceivable tuning. It was developed by [[Dave Keenan]] and [[George Secor]] with significant contributions from numerous others.  


In order for musicians to evaluate the proposal, they must adopt it enthusiastically to get a feel for what it can do. What Sagittal can notate is directly related to what we want to notate. This page, Sagittal Corner, is meant as a repository for materials which support the exploration of Sagittal notation.
== Flavors of Sagittal notation ==
Sagittal notation comes in two mutually compatible ''flavors''.


[[file:Sagittal.pdf]]
=== Evo ===
The '''Evo''' flavor (short for "evolutionary", previously called "mixed") uses only single-shaft Sagittal symbols, e.g. {{sagittal| /| }} {{sagittal| \! }} {{sagittal| |) }} {{sagittal| !) }}, alone or in combination with conventional sharps and flats and their doubles. Only the large variant of the double sharp {{sagittal| x }} (U+E47D) is considered to be stylistically-compatible with Sagittal symbols. Evo is much easier to learn, but it results in a greater number of symbols on the sheet, which can give it a more cluttered appearance, particularly with chords, and it may be confusing when two symbols alter the same note in opposite directions.


<span id="Evo-SZ"></span> A sub-flavor of Evo is '''Evo-SZ''' (Evo with Stein–Zimmermann). This is where any sagittals that are notating exactly half the alteration of a sharp or flat (most often {{sagittal| /|\ }} {{sagittal| \!/ }}) are replaced by the Stein–Zimmermann semisharp {{sagittal| > }} and narrow reversed flat {{sagittal| < }}, and the corresponding combinations (most often {{sagittal| /|\ }}{{sagittal| # }} and {{sagittal| \!/ }}{{sagittal| b }}) are replaced by {{sagittal| ># }} and {{sagittal| <b }}. The narrow variants of the fractional flats {{sagittal| < }} (U+E284) and {{sagittal| <b }} (U+E285) are preferred because they preserve the Sagittal principle that the visual size of a symbol should indicate the relative size of its alteration and they reduce left-right confusion.


===Sagibelius 2.0===  
=== Revo ===
Plugins for using Sagittal notation in Sibelius 4 and up. By [[http://www.jacobbarton.net/2011/10/sagibelius-2-0-released/|Jacob Barton]]. Hosted on this wiki. Donationware.
The '''Revo''' flavor (short for "revolutionary", previously called "pure") only requires one accidental per note. Revo therefore takes up less space on the sheet and presents a cleaner appearance, and it clearly indicates the direction of the overall alteration. It discards the conventional sharps and flats and their doubles and replaces them with these multi-shaft arrow-like symbols: {{sagittal| /||\ }} {{sagittal| \!!/ }} {{sagittal| /X\ }} {{sagittal| \Y/ }}. Adding a sharp or flat to a Sagittal is achieved by adding two more shafts, e.g. {{sagittal| /| }}{{sagittal| # }} becomes {{sagittal| /||| }} and {{sagittal| !) }}{{sagittal| b }} becomes {{sagittal| !!!) }}. When the Sagittal part alters in the opposite direction to the sharp or flat part, the rules are not so simple, e.g. {{sagittal| \! }}{{sagittal| # }} becomes {{sagittal| ||\ }} and {{sagittal| |) }}{{sagittal| b }} becomes {{sagittal| !!) }}; one must simply learn these ''[[2187/2048#Notation|apotome]] complements''.
[[file:Sagibelius_2.0.zip]]


===Support in Lilypond===  
== Notation software support ==
[[http://x31eq.com/lilypond/|Plugin for Sagitall notation in Lilypond]] by Graham Breed
=== Sibelius ===
Sagibelius 2.0 – plugins for using Sagittal notation in Sibelius 4 and up. By [http://www.jacobbarton.net/2011/10/sagibelius-2-0-released/ Jacob Barton]. Hosted on this wiki. Donationware.


===Sagittal.org problems?===
[[:File:Sagibelius_2.0.zip|Sagibelius_2.0.zip]]
Sometimes sagittal.org doesn't work. In those cases, visit http://dkeenan.com/sagittal/


===For those attending [[Xenharmonic Praxis Summer Camp]] 2011===  
=== Lilypond ===
[http://x31eq.com/lilypond/ Plugin for Sagittal notation in Lilypond] by Graham Breed


We will be attempting to use Sagittal notation during the camp! This is //not// to exclude other notations, or to mandate the use of notation at all. Please read [[http://sagittal.org/sagittal.pdf|the Sagittal introductory article]] and/or the [[http://sagittal.org/gift/GiftOfTheGods.htm|mythical introduction]] as time and interest permits. **Please make note** of any questions or desires that arise in the course of reading. If you wish, you may add comments directly to this page with the "Edit this Page" button.
=== MuseScore ===
Sagittal accidentals are available in MuseScore via the [https://www.smufl.org/fonts/ Bravura font which implements the SMuFL standard]. They can be accessed by opening the Master Palette and finding them in the Symbols section at the end.  


This page is incomplete, reflecting the finished work of an ongoing project.
=== Scala ===
Sagittal notation is available in Scala.


----
=== Dorico ===
Wish list for materials:
Because Dorico is built by Steinberg Media, the same company that maintains the SMuFL standard, it supports Sagittal.
* Example scores for notating equal tunings
* Support files for using Sagittal in Finale, Sibelius, Mus2


== Scores in Sagittal notation ==
* [[The Sagittal Songbook]]
** [http://oneforall.ytmnd.com One for All]
** [[land_urchin|Land Urchin]]
** [[Clouds_(Andrew_Heathwaite)|Clouds]]
** [[Prayer of Thanks]]


* [[:File:sunday3.pdf|Sunday Pipes]] in [[22edo]] by [[Mats Öljare]]
* Tibia in [[22edo]] by [[Paul Erlich]] ([http://www.youtube.com/watch?v=d44Lfp9lAG8 Listen]). Sagittal score [[:File:TIBIA.pdf|in F||\]] or [[:File:tibia_in_g.pdf|in G]] (contains errors in measures 9, 19 and 20)
* [[:File:Ivor_Darreg,_Suite.pdf|On the Enharmonic Tetrachord (from Suite, Op. 62)]], in [[22edo]], by [[Ivor Darreg]]. Originally printed in the Spring 1975 issue of Xenharmonikon in quarter-tone notation. Transcribed to Sagittal by [[Juhani Nuorvala]].([https://www.youtube.com/watch?v=DvHvza1vtfo Listen])


Scores in Sagittal notation -- make a page on this wiki
== The symbol sets ==
* [[Land Urchin]]
Sagittal symbols are defined in 6 "official" symbol sets, each one being defined as spliting the [[2187/2048|apotome]] in psuedoequal or equal parts (latter being '''EDA'''). It is not necessary to learn the complete Sagittal microtonal notation system. The '''Spartan''' and '''Athenian''' sets will be more than enough for most purposes.
* [[file:xenharmonic/sunday3.pdf|Sunday Pipes]] in [[22edo|22tET]] by Mats Öljare
Sagittal accidentals are not intended to be combined with one another, except in the Prime Factor JI notation, as symbols representing useful combinations and powers of primes are already provided. An accidental can often be used to represent alternative commas that differ by 2 cents or less. In such cases the intended comma ratio may be determined by the note to which it is applied, or by the musical context. Alternatively, accent marks (from the Herculean and subsequent extensions) may be added to distinguish these commas.
----
 
see also
[https://www.desmos.com/calculator/iehdworjko You can look up what the minimum precision is required to write an EDO in this Desmos graph.]
* [[http://andrewmeronek.com/music-tools/sagittal-chord-chart/|Sagittal chord chart | Andrew Meronek]]</pre></div>
 
<h4>Original HTML content:</h4>
=== Sharps/Flats ===
<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;Sagittal notation&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;span style="display: block; text-align: right;"&gt;&lt;a class="wiki_link" href="http://xenharmonie.wikispaces.com/Sagittalnotation"&gt;Deutsch&lt;/a&gt;&lt;br /&gt;
Using {{sagittal| # }} and {{sagittal| b }} (or {{sagittal|/||\}} {{sagittal|\!!/}} for Revo flavor) is still ''technically'' Sagittal notation, however, it's just a reskin.
&lt;/span&gt;&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextRemoteImageRule:26:&amp;lt;div style=&amp;quot;text-align: center&amp;quot;&amp;gt;&amp;lt;img src=&amp;quot;http://sagittal.org/index_files/image005.gif&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; /&amp;gt;&amp;lt;/div&amp;gt; --&gt;&lt;div style="text-align: center"&gt;&lt;img src="http://sagittal.org/index_files/image005.gif" alt="external image image005.gif" title="external image image005.gif" /&gt;&lt;/div&gt;&lt;!-- ws:end:WikiTextRemoteImageRule:26 --&gt;&lt;br /&gt;
=== Spartan ===
Sagittal &lt;a class="wiki_link" href="/notation"&gt;notation&lt;/a&gt; is a universal set of microtonal accidentals, developed by Dave Keenan and George Secor with the help of numerous others. See &lt;a class="wiki_link_ext" href="http://sagittal.org/" rel="nofollow"&gt;http://sagittal.org/&lt;/a&gt; for the official site.&lt;br /&gt;
It is the simplest and coarsest of the Sagittal sets. The Spartan set has a maximum resolution of 13EDA<ref>https://forum.sagittal.org/viewtopic.php?t=516</ref>, which is ''sufficient'' to notate 13-limit just intonation (if used for JI), and all EDOs which are at most sharp-13, including all EDOs from 1 up to 111, the [[Zeta peak edo|zeta peak]] [[130edo|130]], [[142edo|142]], among many others.
&lt;br /&gt;
 
In order for musicians to evaluate the proposal, they must adopt it enthusiastically to get a feel for what it can do. What Sagittal can notate is directly related to what we want to notate. This page, Sagittal Corner, is meant as a repository for materials which support the exploration of Sagittal notation.&lt;br /&gt;
The eight pairs of single-shaft accidentals [[Sagittal notation#Spartan single-shaft|shown below]] are sufficient to provide these capabilities when used alone, and to the left of the standard sharp, flat and their doubles (the Evo flavor).
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextFileRule:27:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file/Sagittal.pdf?h=52&amp;amp;w=320&amp;quot; class=&amp;quot;WikiFile&amp;quot; id=&amp;quot;wikitext@@file@@Sagittal.pdf&amp;quot; title=&amp;quot;File: Sagittal.pdf&amp;quot; width=&amp;quot;320&amp;quot; height=&amp;quot;52&amp;quot; /&amp;gt; --&gt;&lt;div class="objectEmbed"&gt;&lt;a href="/file/view/Sagittal.pdf/243193787/Sagittal.pdf" onclick="ws.common.trackFileLink('/file/view/Sagittal.pdf/243193787/Sagittal.pdf');"&gt;&lt;img src="http://www.wikispaces.com/i/mime/32/application/pdf.png" height="32" width="32" alt="Sagittal.pdf" /&gt;&lt;/a&gt;&lt;div&gt;&lt;a href="/file/view/Sagittal.pdf/243193787/Sagittal.pdf" onclick="ws.common.trackFileLink('/file/view/Sagittal.pdf/243193787/Sagittal.pdf');" class="filename" title="Sagittal.pdf"&gt;Sagittal.pdf&lt;/a&gt;&lt;br /&gt;&lt;ul&gt;&lt;li&gt;&lt;a href="/file/detail/Sagittal.pdf"&gt;Details&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a href="/file/view/Sagittal.pdf/243193787/Sagittal.pdf"&gt;Download&lt;/a&gt;&lt;/li&gt;&lt;li style="color: #666"&gt;210 KB&lt;/li&gt;&lt;/ul&gt;&lt;/div&gt;&lt;/div&gt;&lt;!-- ws:end:WikiTextFileRule:27 --&gt;&lt;br /&gt;
As an alternative, the multi-shaft Spartans provides a complete set of stand-alone accidentals to replace each of the above combinations of a single-shaft Sagittal with a standard accidental (the Revo flavor). The standard natural is used alone in both Evo and Revo variants, but only to cancel a previous accidental when a barline will not suffice.
&lt;br /&gt;
 
&lt;br /&gt;
In this set, ratios of 13 are represented by reusing the accidentals for ratios of 35 (7*5). Thusly, [[8505/8192]] (the ~13/8 interval) is only 0.4 ¢ ([[4096/4095]]) from just. Sagittal extensions following Spartan allow notation of JI ratios with primes beyond 13 (and 13 proper), and more combinations of lower primes, as well as finer tone-fractions, degrees of larger EDOs, and more complex temperaments, all with single Sagittal accidentals. The same choice of Evo versus Revo is available with each extension.
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc0"&gt;&lt;a name="x--Sagibelius 2.0"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Sagibelius 2.0&lt;/h3&gt;
 
Plugins for using Sagittal notation in Sibelius 4 and up. By &lt;a class="wiki_link_ext" href="http://www.jacobbarton.net/2011/10/sagibelius-2-0-released/" rel="nofollow"&gt;Jacob Barton&lt;/a&gt;. Hosted on this wiki. Donationware.&lt;br /&gt;
=== Athenian ===
&lt;!-- ws:start:WikiTextFileRule:28:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file/Sagibelius_2.0.zip?h=52&amp;amp;w=320&amp;quot; class=&amp;quot;WikiFile&amp;quot; id=&amp;quot;wikitext@@file@@Sagibelius_2.0.zip&amp;quot; title=&amp;quot;File: Sagibelius_2.0.zip&amp;quot; width=&amp;quot;320&amp;quot; height=&amp;quot;52&amp;quot; /&amp;gt; --&gt;&lt;div class="objectEmbed"&gt;&lt;a href="/file/view/Sagibelius_2.0.zip/263370958/Sagibelius_2.0.zip" onclick="ws.common.trackFileLink('/file/view/Sagibelius_2.0.zip/263370958/Sagibelius_2.0.zip');"&gt;&lt;img src="http://www.wikispaces.com/i/mime/32/application/zip.png" height="32" width="32" alt="Sagibelius_2.0.zip" /&gt;&lt;/a&gt;&lt;div&gt;&lt;a href="/file/view/Sagibelius_2.0.zip/263370958/Sagibelius_2.0.zip" onclick="ws.common.trackFileLink('/file/view/Sagibelius_2.0.zip/263370958/Sagibelius_2.0.zip');" class="filename" title="Sagibelius_2.0.zip"&gt;Sagibelius_2.0.zip&lt;/a&gt;&lt;br /&gt;&lt;ul&gt;&lt;li&gt;&lt;a href="/file/detail/Sagibelius_2.0.zip"&gt;Details&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a href="/file/view/Sagibelius_2.0.zip/263370958/Sagibelius_2.0.zip"&gt;Download&lt;/a&gt;&lt;/li&gt;&lt;li style="color: #666"&gt;2 MB&lt;/li&gt;&lt;/ul&gt;&lt;/div&gt;&lt;/div&gt;&lt;!-- ws:end:WikiTextFileRule:28 --&gt;&lt;br /&gt;
It is a handy symbol set, adding 10 symbol pairs to Spartan, with a total of 23 symbol pairs*, allowing for a maximum resolution of 21EDA. Early in the design of the Sagittal notation system, Secor and Keenan found that by extending the Spartan set with a further five pairs of single-shaft accidentals [[Sagittal notation#Athenian extension single-shaft|shown below]] an economical universal JI notation system could be defined, by dividing the apotome (Pythagorean sharp or flat) into 21 almost-equal divisions. This set of thirteen pairs is called the Athenian set. If the divisions were made exactly equal (5.4136 ¢), this would be an example of [[Brahmagupta]] temperament, of which the two most salient EDOs are 217 and 224.
&lt;br /&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x--Support in Lilypond"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Support in Lilypond&lt;/h3&gt;
When used for JI, it defines the ''Standard Medium Precision JI,'' capable of writing in the 17-limit.
  &lt;a class="wiki_link_ext" href="http://x31eq.com/lilypond/" rel="nofollow"&gt;Plugin for Sagitall notation in Lilypond&lt;/a&gt; by Graham Breed&lt;br /&gt;
 
&lt;br /&gt;
<nowiki>*</nowiki>There are two symbol pairs that are interchangeable in this level of precision<ref>https://sagittal.org/sagittal.pdf p.10</ref>, these being  {{sagittal|(|}} {{sagittal|(!}} / {{sagittal||\}} {{sagittal|!/}}  and  {{sagittal|)||~}} {{sagittal|)!!~}} / {{sagittal|/||}} {{sagittal|\!!}} . They will not become distinct until the next level of precision.
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x--Sagittal.org problems?"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Sagittal.org problems?&lt;/h3&gt;
 
Sometimes sagittal.org doesn't work. In those cases, visit &lt;!-- ws:start:WikiTextUrlRule:71:http://dkeenan.com/sagittal/ --&gt;&lt;a class="wiki_link_ext" href="http://dkeenan.com/sagittal/" rel="nofollow"&gt;http://dkeenan.com/sagittal/&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:71 --&gt;&lt;br /&gt;
=== Trojan (12-EDO relative) ===
&lt;br /&gt;
This is a special extension to Spartan which adds 3 more symbol sets, which is exclusively used to notate [[compton]] EDOs (12N EDOs up to [[312edo|312]]) in which the apotome is 100 cents. However, all of these EDOs lower than 168EDO can be notated using just Spartan, in which cases, depending on your needs, maybe Athenian proves to be more useful.
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="x--For those attending Xenharmonic Praxis Summer Camp 2011"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;For those attending &lt;a class="wiki_link" href="/Xenharmonic%20Praxis%20Summer%20Camp"&gt;Xenharmonic Praxis Summer Camp&lt;/a&gt; 2011&lt;/h3&gt;
 
  &lt;br /&gt;
=== Promethean ===
We will be attempting to use Sagittal notation during the camp! This is &lt;em&gt;not&lt;/em&gt; to exclude other notations, or to mandate the use of notation at all. Please read &lt;a class="wiki_link_ext" href="http://sagittal.org/sagittal.pdf" rel="nofollow"&gt;the Sagittal introductory article&lt;/a&gt; and/or the &lt;a class="wiki_link_ext" href="http://sagittal.org/gift/GiftOfTheGods.htm" rel="nofollow"&gt;mythical introduction&lt;/a&gt; as time and interest permits. &lt;strong&gt;Please make note&lt;/strong&gt; of any questions or desires that arise in the course of reading. If you wish, you may add comments directly to this page with the &amp;quot;Edit this Page&amp;quot; button.&lt;br /&gt;
It adds 20 more symbols to Athenian symbol set, allowing for a maximum resolution of 47EDA. When used for JI, it defines the ''Standard High Precision JI'' capable of writing in the 23-limit, however, this JI notation is not recommended. It instead can be used to write in EDOs such as the [[Zeta peak edo|zeta edos]] [[270edo|270]] and [[311edo|311]].
&lt;br /&gt;
 
This page is incomplete, reflecting the finished work of an ongoing project.&lt;br /&gt;
=== Herculean ===
&lt;br /&gt;
It adds the [[schisma]] diacritic to the Promethean symbol set, which can be stacked with the remaining alterations, allowing for a maximum resolution of 58EDA. When used for JI, it defines the ''Standard Ultra Precision JI'' capable of writing in the 23-limit with higher precision.
&lt;hr /&gt;
 
Wish list for materials:&lt;br /&gt;
=== Olympian ===
&lt;ul&gt;&lt;li&gt;Example scores for notating equal tunings&lt;/li&gt;&lt;li&gt;Support files for using Sagittal in Finale, Sibelius, Mus2&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
It adds the [[4096/4095|''mina'']] diacritic to the Herculean symbol set, able to be stacked up to twice with the schisma and the remaining alterations, allowing for a maximum resolution of 233EDA. When used for JI, it defines the ''Standard Extreme Precision JI'' capable of writing in the 47-limit with great precision.
&lt;br /&gt;
 
&lt;br /&gt;
=== Magrathean ===
Scores in Sagittal notation -- make a page on this wiki&lt;br /&gt;
It adds the ''tina'' diacritic (1 step of [[8539edo]]) to the Olympian symbol set, able to be stacked up to thrice with any of the symbols (three tinas make a ~mina), allowing for a whopping maximum resolution of 809EDA. When used for JI, it defines the ''Standard Insane Precision JI'' capable of writing in the 127-limit with astonishing precision. There is no level of precision higher than this, and it is unlikely that one will ever exist. Unless you want some hot sauce.<ref name=":0">https://forum.sagittal.org/viewtopic.php?p=2714&hilit=bomb#p2714  "A tina is approximately 1/809th of an apotome, 1/8539th of an octave (a [[Zeta peak edo|zeta-peak EDO]]), or 0.14 cents. The fractional-tina is generally half a tina but is intentionally arbitrary, because if you need any more precision than that, I have a bottle of Da' Bomb Beyond Insanity Hot Sauce with your name on it"</ref>
&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Land%20Urchin"&gt;Land Urchin&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a href="http://xenharmonic.wikispaces.com/file/view/sunday3.pdf/269076436/sunday3.pdf" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/sunday3.pdf/269076436/sunday3.pdf');"&gt;Sunday Pipes&lt;/a&gt; in &lt;a class="wiki_link" href="/22edo"&gt;22tET&lt;/a&gt; by Mats Öljare&lt;/li&gt;&lt;/ul&gt;&lt;hr /&gt;
 
see also&lt;br /&gt;
== Gallery ==
&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://andrewmeronek.com/music-tools/sagittal-chord-chart/" rel="nofollow"&gt;Sagittal chord chart | Andrew Meronek&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
=== Spartan single-shaft ===
<div style="margin-bottom: 20px;">
{{sge|  ¦( |  !( | n  | 5120/5103 | 7/5 kleisma }}
{{sge| /¦  | \! | p  |  81/80  | 5 comma }}
{{sge|  ¦) |  !) | t  | 64/63| 7 comma }}
{{sge|//¦  |\\! | ph  | 6561/6400 | 25 small diesis }}
{{sge| /¦) | \!) | pat |  36/35  | 35 medium diesis }}
{{sge| /¦\ | \!/ | pak |  33/32  | 11 medium diesis }}
{{sge| (¦) | (!) | jat |  729/704  | 11 large diesis }}
{{sge| (¦\ | (!/ | jak | 8505/8192 | 35 large diesis }}
</div>
 
=== Spartan multi-shaft ===
Multi-shaft sagittals are only used in the [[#Revo|Revo]] flavor of Sagittal.
<div style="margin-bottom: 20px;">
{{sge| )¦¦( | )!!( | ph  | 6561/6400 | 25S }}
{{sge|  ¦¦) |  !!) | t  |  64/63  | 7C }}
{{sge|  ¦¦\ |  !!/ | p  |  81/80  | 5C }}
{{sge| /¦¦) | \!!) | n  | 5120/5103 | 7/5k }}
{{sge| /¦¦\ | \!!/ }}
{{sge|  ¦¦¦( |  !!!( | n  | 5120/5103 | 7/5k }}
{{sge| /¦¦¦  | \!!!  | p  |  81/80  | 5C }}
{{sge|  ¦¦¦) |  !!!) | t  |  64/63  | 7C }}
{{sge|//¦¦¦  |\\!!!  | ph  | 6561/6400 | 25S }}
{{sge| /¦¦¦) | \!!!) | pat |  36/35  | 35M }}
{{sge| /¦¦¦\ | \!!!/ | pak |  33/32  | 11M }}
{{sge| (¦¦¦) | (!!!) | jat |  729/704  | 11L }}
{{sge| (¦¦¦\ | (!!!/ | jak | 8505/8192 | 35L }}
{{sge| )X( | )Y( | ph  | 6561/6400 | 25S  | mid=48px }}
{{sge|  X) |  Y) | t  |  64/63  | 7C  | mid=48px }}
{{sge|  X\ |  Y/ | p  |  81/80  | 5C  | mid=48px }}
{{sge| /X) | \Y) | n  | 5120/5103 | 7/5k | mid=48px }}
{{sge| /X\ | \Y/ | mid=48px }}
</div>
 
=== Athenian extension single-shaft ===
<div style="margin-bottom: 20px;">{{sge| )¦( | )!( | ran |  896/891  | 11/7 kleisma }}
{{sge| ~¦( | ~!( | san | 4131/4096 | 17 comma }}
{{sge|  ¦\ |  !/ | k  |  55/54  | 55 comma }}
{{sge| (¦  | (!  | j  |45927/45056| 11/7 comma }}
{{sge| (¦( | (!( | jan |  45/44  | 11/5 small diesis }}
</div>
 
=== Athenian extension multi-shaft ===
Multi-shaft sagittals are only used in the [[#Revo|Revo]] flavor of Sagittal.
<div style="margin-bottom: 20px;">
{{sge| ~¦¦( | ~!!( | jan |  45/44  | 11/5S }}
{{sge| )¦¦~ | )!!~ | j  |45927/45056| 11/7C }}
{{sge| /¦¦  | \!!  | k  |  55/54  | 55C }}
{{sge| (¦¦( | (!!( | san | 4131/4096 | 17C }}
{{sge|//¦¦  |\\!!  | ran |  896/891  | 11/7k }}
{{sge| )¦¦¦( | )!!!( | ran |  896/891  | 11/7k }}
{{sge| ~¦¦¦( | ~!!!( | san | 4131/4096 | 17C }}
{{sge|  ¦¦¦\ |  !!!/ | k  |  55/54  | 55C }}
{{sge| (¦¦¦  | (!!!  | j  |45927/45056| 11/7C }}
{{sge| (¦¦¦( | (!!!( | jan |  45/44  | 11/5S }}
{{sge| ~X( | ~Y( | jan |  45/44  | 11/5S | mid=48px }}
{{sge| )X~ | )Y~ | j  |45927/45056| 11/7C | mid=48px }}
{{sge| /X | \Y  | k  |  55/54  | 55C | mid=48px }}
{{sge| (X( | (Y( | san | 4131/4096 | 17C | mid=48px }}
{{sge|//X  |\\Y  | ran |  896/891  | 11/7k | mid=48px }}
</div>
 
=== Trojan extension ===
 
{{sge|¦~|!~|z|736/729|23CT| mid=48px }}
{{sge|)/¦|)\!|pr|41553/40960 |19/5CT| mid=48px }}
{{sge|/¦~|\!~|paz|46/45|23/5ST| mid=48px }}
{{sge|¦¦~|!!~|paz|46/45|23ST| mid=48px }}
{{sge|)¦¦)|)!!)|pr|41553/40960 |19/5CT| mid=48px }}
{{sge|/¦¦~|\!!~|z|736/729|23CT| mid=48px }}
{{sge|¦¦¦~|!!!~|z|736/729|23CT| mid=48px }}
{{sge|)/¦¦¦|)\!!!|pr|41553/40960 |19/5CT| mid=48px }}
{{sge|/¦¦¦~|\!!!~|paz|46/45|23/5ST| mid=48px }}
{{sge|X~|Y~|paz|46/45|23ST| mid=48px }}
{{sge|)X)|)Y)|pr|41553/40960 |19/5CT| mid=48px }}
{{sge|/X~|\Y~|z|736/729|23CT| mid=48px }}
 
=== Promethean extension single-shaft ===
{{sge| )¦  | )!  | r |  513/512  | 19s | mid=48px }}
{{sge| ~¦  | ~!  | s | 2187/2176  | 17k | mid=48px }}
{{sge| )~¦  | )~! | sr |  144/143  | 143C | mid=48px }}
{{sge| ~~¦  | ~~!  | sh |  99/88  | 49/11C | mid=48px }}
{{sge| )¦~  | )!~  | raz |  19683/19456  | 19C | mid=48px }}
{{sge| )¦)  | )!)  | rat |  57/56  | 19/7C | mid=48px }}
{{sge| ~¦)  | ~!)  | sat |  49/48  | 49S | mid=48px }}
{{sge| ~¦\  | ~!/  | sak |  16767/16384  | 23S | mid=48px }}
{{sge| )//¦ | )\\! | phr |  416/405  | 13/5M | mid=48px }}
{{sge| (¦~  | (!~  | jaz |  176/171  | 19/11M | mid=48px }}
{{sge| (/¦  | (\!  | jp |  4096/3969  | 49M | mid=48px }}
{{sge| )/¦\ | )\!/ | prak |  405/392  | 49/5M | mid=48px }}
{{sge| ¦\)  | !/)  | kt |  8680203/8388608  | 49L | mid=48px }}
{{sge| ¦\\  | !//  | kh |373977/360448|19/11L|| mid=48px }}
{{sge| )¦\\ | )!// | rakh |  885735/851968  | 13/5L | mid=48px }}
 
=== Promethean extension multi-shaft ===
Multi-shaft sagittals are only used in the [[#Revo|Revo]] flavor of Sagittal.
 
{{sge| )~¦¦ | )~!!    | sak |  24/23  | 23S | mid=48px }}
{{sge| ~~¦¦ | ~~!!    | sat |  6561/6272  | 49S | mid=48px }}
{{sge| )/¦¦ | )\!!    | rat |  5103/4864  | 19/7C | mid=48px }}
{{sge| (¦¦  | (!!    | raz |  19/18  | 19C | mid=48px }}
{{sge| ~¦¦) | ~!!)   | sh  |  11907/11264  | 49/11C | mid=48px }}
{{sge| ~¦¦\  | ~!!/   | sr  |  34749/32768  | 143C | mid=48px }}
{{sge| )//¦¦ | )\\!!  | s  |  17/16  | 17k | mid=48px }}
{{sge| (¦¦~ | (!!~    | r  |  81/76  | 19s | mid=48px }}
 
{{sge| )¦¦¦  | )!!!  | r |  513/512  | 19s | mid=48px }}
{{sge| ~¦¦¦  | ~!!!  | s |  2187/2176  | 17k | mid=48px }}
{{sge| )~¦¦¦  | )~!!!  | sr |  144/143  | 143C | mid=48px }}
{{sge| ~~¦¦¦  | ~~!!!  | sh |  99/88  | 49/11C | mid=48px }}
{{sge| )¦¦¦~  | )!!!~  | raz |  19683/19456  | 19C | mid=48px }}
{{sge| )¦¦¦)  | )!!!)  | rat |  57/56  | 19/7C | mid=48px }}
{{sge| ~¦¦¦)  | ~!!!)  | sat |  49/48  | 49S | mid=48px }}
{{sge| ~¦¦¦\  | ~!!!/ | sak |  16767/16384  | 23S | mid=48px }}
{{sge| )//¦¦¦ | )\\!!! | phr |  416/405  | 13/5M | mid=48px }}
{{sge| (¦¦¦~  | (!!!~  | jaz |  176/171  | 19/11M | mid=48px }}
{{sge| (/¦¦¦  | (\!!!  | jp |  4096/3969  | 49M | mid=48px }}
{{sge| )/¦¦¦\ | )\!!!/ | prak |  405/392  | 49/5M | mid=48px }}
{{sge| ¦¦¦\)  | !!!/)  | kt |  8680203/8388608  | 49L | mid=48px }}
{{sge| ¦¦¦\\  | !!!//  | kh | 373977/360448 |19/11L|| mid=48px }}
{{sge| )¦¦¦\\ | )!!!// | rakh |  885735/851968  | 13/5L | mid=48px }}
 
{{sge| )~X | )~Y    | sak |  24/23  | 23S | mid=48px }}
{{sge| ~~X | ~~Y    | sat |  6561/6272  | 49S | mid=48px }}
{{sge| )/X | )\Y    | rat |  5103/4864  | 19/7C | mid=48px }}
{{sge| (X  | (Y    | raz |  19/18  | 19C | mid=48px }}
{{sge| ~X) | ~Y)    | sh  |  11907/11264  | 49/11C | mid=48px }}
{{sge| ~X\  | ~Y/  | sr  |  34749/32768  | 143C | mid=48px }}
{{sge| )//X | )\\Y | s  |  17/16  | 17k | mid=48px }}
{{sge| (X~ | (Y~    | r  |  81/76  | 19s | mid=48px }}
 
 
=== Herculean extension diacritics ===
{| class="wikitable"
!<nowiki>|</nowiki>
!<nowiki>|</nowiki>
|-
|ai
|ao
|-
| colspan="2" |unison
|}
Ai and ao are used to write bare diacritics in the following extensions, like the schisma, schismina, and tina.
{| class="wikitable"
!{{sagittal|'}}
!{{sagittal|.}}
|-
|bi
|bo
|-
|[https://en.xen.wiki/w/Schisma 5s up]
|5s down
|}
 
=== Olympian extension diacritics ===
{| class="wikitable"
!{{sagittal|`}}
!{{sagittal|,}}
!{{sagittal|``}}
!{{sagittal|,,}}
|-
|mi
|mo
|mimi
|momo
|-
|[https://en.xen.wiki/w/4096/4095 35/13sx] up
|35/13sx down
|[https://en.xen.wiki/w/2080/2079 77/65sx] up
|77/65sx down
|}
The diacritic is called "mina".
 
=== Magrathean extension diacritics ===
{| class="wikitable"
!{{sagittal|@1}}
!{{sagittal|l1}}
!{{sagittal|@2}}
!{{sagittal|l2}}
!{{sagittal|`}}
!{{sagittal|,}}
!{{sagittal|@4}}
!{{sagittal|l4}}
!{{sagittal|@5}}
!{{sagittal|l5}}
!{{sagittal|``}}
!{{sagittal|,,}}
!{{sagittal|@7}}
!{{sagittal|l7}}
!{{sagittal|@8}}
!{{sagittal|l8}}
!{{sagittal|@8}}
!{{sagittal|l8}}
!{{sagittal|@9}}
!{{sagittal|l9}}
!{{sagittal|@.}}
!{{sagittal|l.}}
|-
|qui
|quo
|quiqui
|quoquo
|mi
|mo
|quimi
|quomo
|quiquimi
|quoquomo
|mimi
|momo
|quimimi
|quomomo
|quiquimimi
|quoquomomo
|quiquimimi
|quoquomomo
|mimimi
|momomo
|i
|o
|-
|10241/10240 up
|10241/10240 up
|5832/5831 up
|5832/5831 down
|[https://en.xen.wiki/w/4096/4095 35/13sx] up
|35/13sx down
|3025/3024 up
|3025/3024 up
|2401/2400 up
|2401/2400 down
|[https://en.xen.wiki/w/2080/2079 77/65sx] up
|77/65sx down
|1701/1700 up
|1701/1700 down
|382976/382725 up
|382976/382725 down
|382976/382725 up
|382976/382725 down
|131072/130977  up
|131072/130977  down
|1515591/1515520  up
|1515591/1515520  down
|}
The diacritic is called "tina". Notice how 3 tinas is approximately equal to one mina, so the system just equates the 3. Either way, this is an INSANE level of pitch precision, down to fractions of a cent. The "i/o" diacritic is a fraction of a tina, left arbitrary intentionally.<ref name=":0" />
 
== See also ==
* [[Sagitype]]
* [[Pain free guide to Sagittal]] by [[William Lynch]]
* [[:File:24 Edo.pdf]] – Sagittal notation guide for 24edo by William Lynch (download: [{{filepath:24 Edo.pdf}} ''24_Edo.pdf''])
* [[Introductory_examples_in_Sagittal_notation|Introductory examples]] by [[Hans Straub]]
 
== External links ==
* [http://sagittal.org/ Official site]
* [http://forum.sagittal.org Sagittal Forum]
* [http://sagittal.org/sagittal.pdf The original Xenharmonikon article (updated)]
* [http://sagittal.org/gift/GiftOfTheGods.htm Gift of the Gods: a Mythical introduction to Sagittal notation]
* [http://sagittal.org/Sagittal%20Standard%20JI%20Notation%20Calculator%20Spreadsheet.xlsx spreadsheet-based calculator for Sagittal JI notation]
* [http://sagittal.org/Sagittal-SMuFL-Map.pdf Sagittal-SMuFL-Map, a table of every Sagittal symbol]
* [https://andrewmeronek.com/music-resources/sagittal-chord-lists/ Sagittal chord chart] by [[Andrew Meronek]]
* [https://www.panix.com/~mj/tuning/EDO-Charts.html Interactive EDO Charts] by [[Mark Johnson]]
{{Navbox notation}}
 
[[Category:Notation]]
[[Category:Sagittal notation| ]] <!-- Main article -->
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