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{{Editable user page}}
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  '''This page is meant to replace''' [[Xenharmonic Wiki:Introduction]]'''.'''
  '''This would hopefully replace all three of Introduction, Introduction to Xenharmonics, and Composing Powerstart.'''
If you’ve recently heard about xenharmonic music (or “xen”, or “microtonal”, which means [[Microtonal music#Terminology|roughly]] the same thing) and want to learn more about it, this is the place to start. “Xenharmonic music” (or “xen music”) is music that sounds like it was tuned differently than most Western music. (Xenharmonic music is entirely separate from the 432Hz movement.)
If you’ve recently heard about xenharmonic music (or “xen”, or “microtonal”, which means [[Microtonal music#Terminology|roughly]] the same thing) and want to learn more about it, this is the place to start. “Xenharmonic music” (or “xen music”) is music that sounds like it was tuned differently than most Western music. (Xenharmonic music is entirely separate from the 432Hz movement.)


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Here’s what you can find on this page—read the section that is most relevant to you.
Here’s what you can find on this page—read the section that is most relevant to you.


== Why have I heard claims that our dominant tuning system is out of tune? ==
== How do I find xenharmonic music to listen to? ==
 
{{todo|inline=1|explain}}
 
=== Just Intonation ===
 
==== Consonance through matching partials ====
If an instrument generates a single note, when air pressure at a given point near the instrument is graphed, the resulting graph is a sum of sine waves of various levels of frequency and amplitude. If the instrument has a harmonic timbre (as is the case with most methods of sound production, including the human voice, most instruments, and square/saw/triangle waves), these sine waves will have frequencies that are multiples of the fundamental tone (or the frequency of the perceived pitch).
 
When two notes are played at once where their frequency spectra share a high-amplitude frequency, these two notes sound concordant when played together. If these notes have a harmonic timbre, this occurs when the frequencies of the two notes have frequencies a and b where b/a is rational (i. e. the interval is within just intonation) and a and b are not too large. The two frequency spectra then share frequencies at [[Lcm|LCM]](a, b) and all multiples of it.
For example, if we take two frequencies at 100 Hz (called "Do" here) and 150 Hz ("Sol"), we see that the notes share frequencies at LCM(100, 150) = 300 and every multiple of it.<pre>Tone  Frequencies of partials (Hz)
Do    100  200  300  400  500  600  700  800  900  ...
Sol    150  300  450  600  750  900 1050 1200 1350  ...</pre>These partials will "meld" when our Do and Sol are played together. If our Sol was tuned to, for example, 148 Hz, its second harmonic component would be at 296 Hz, and the two tones played together would not meld together at 300 Hz, but would "beat". That is, we would hear a throbbing sound, the "beat rate" of which is found by reckoning the distance in Hertz between the two near-coincident partials. In this case, 300 - 296 = 4 Hz, so we'd hear a beating of four times a second (this is like a rhythm of eighth notes at a metronome marking of 120 beats per minute). This melding and beating makes it easy to sing JI intervals.
 
===Through other phenomena===
 
{{todo|inline=1| explain}}
 
=== Temperaments ===
 
{{todo|inline=1|explain}}
 
=== Limits of human hearing and playing ===
 
{{todo|inline=1|explain}}
 
== How do I find xen music to listen to? ==
Most xenharmonic works (especially on YouTube, where the most xenharmonic music is found) are usually marked with their tuning system in the title, which is usually n-edo (or n-tet or n-ed2, which mean roughly the same thing—that the octave is divided into n equal pieces).
 
=== Finding works you like by edo ===
You can use the n-edo designation to find edos you enjoy the sound of. Smaller edos in particular have a sort of flavor to them; the following groups of edos have similar flavors, and you can use this list to find other edos you might like. Some edos are in multiple groups.
 
# 8, (9,) 11, 13, (16,) 18, (23, 25,) 26. These tunings will sound the most "off" to many ears.
# 19, (26,) 31, 43, 50, 55. These tunings have very similar capabilities to 12edo with more varied colors.
# 5, 10, 15, 20, 30, 37. These are multiples of 5 (except for 37).
# 7, 14, 21, 28, 35. Similarly, multiples of 7.
# 24, 36, 48, 72. Similarly, multiples of 12. These tunings contain 12edo. The mix of unusual and usual notes can sound jarring, but these are also highly capable tunings that provide a little of the familiarity of 12edo.
# 34, 41, 46, 53, 58, 72, 99. These tunings are said to be the most "in tune," which means that they should sound more relaxed than other tuning systems.
# 17, 22, 27, 44, (46, 58)


=== Finding works you like by genre ===
=== Finding works you like by genre ===
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You can play around with tunings in Scale Workshop before you use them. Larger tunings are more difficult to work with. You might have read that some tuning system is optimal in some way; such claims mean very little and usually come attached to tuning systems that are too unwieldy (>24 notes) to start with. If you want to work within these tuning systems anyway, you might want to work with a small subset of the notes available (which is what most xenharmonic composers do)
You can play around with tunings in Scale Workshop before you use them. Larger tunings are more difficult to work with. You might have read that some tuning system is optimal in some way; such claims mean very little and usually come attached to tuning systems that are too unwieldy (>24 notes) to start with. If you want to work within these tuning systems anyway, you might want to work with a small subset of the notes available (which is what most xenharmonic composers do)


TODO: scale workshop links
{{todo|inline=1|expand|comment=scale workshop links.}}


'''10edo''' <br />This is probably the easiest edo to start with. Smaller edos can feel limiting, and larger edos can feel overwhelming.
'''10edo''' <br />This is probably the easiest edo to start with. Smaller edos can feel limiting, and larger edos can feel overwhelming.
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== How do I read and navigate the wiki? ==
== How do I read and navigate the wiki? ==
The wiki originated as a resource for [[Regular temperament theory]], so much of its material is related to that. (The wiki is steadily gaining information about alternative approaches, though!) If you're interested in reading about the mathematics of temperaments, read [[D&D's guide]].
The wiki originated as a resource for [[Regular temperament theory]], so much of its material is related to that. (The wiki is steadily gaining information about alternative approaches, though!) If you're interested in reading about the mathematics of temperaments, read [[D&D's guide]].
=== Editing the wiki ===
If you understand a concept well enough to make its article more insightful, you are welcome to improve it.
* Play in the [[SandBox]] to get the hang of editing.
* As best as possible, adhere to [[Xenharmonic Wiki: Conventions]].
* [[Help: Editing]] and [[Xenharmonic Wiki: Article guidelines]] provide some tips as well.
* [[Xenharmonic Wiki: Wikifuture]] is a wish list of sorts.
* [[Xenharmonic Wiki: Things to do]] helps you find out what community projects are currently under way.
* [[Xenharmonic Wiki: Five pillars]] summarises this wiki's fundamental principles.
* Note that “[[Special:WantedPages]]” can be deceiving. Do not blindly create pages you see there. Read [[Xenharmonic Wiki:Conventions]] first.
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