Nick Vuci's Fundamentals of Xen: Difference between revisions

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== Just Intonation (JI) ==

If the pitch or frequency of a note is the number of times per second it causes the air to vibrate, and an interval is when two notes play at the same time, then Just Intonation (JI) is where the frequencies of the notes form whole-number ratios with each other. [[ji_intro.mp4]] (non-essential video) ~~###~~ Harmonic Series A fundamental aspect of JI is the harmonic series. The harmonic series is the series that happens when you keep adding the first frequency over and over, ad infinitum. Which is 1:2:3:4:5:6:7… If we take a segment of it, we get different intervals and chords. For example, 4:5:6 is the major triad. ''Try it out in'' [https://scaleworkshop.plainsound.org Scale Workshop] ''by creating a new scale from the ‘harmonic series segment’''!

If the pitch or frequency of a note is the number of times per second it causes the air to vibrate, and an interval is when two notes play at the same time, then Just Intonation (JI) is where the frequencies of the notes form whole-number ratios with each other. [[ji_intro.mp4]] (non-essential video)

=== Harmonic Series ===

A fundamental aspect of JI is the harmonic series. The harmonic series is the series that happens when you keep adding the first frequency over and over, ad infinitum. Which is 1:2:3:4:5:6:7… If we take a segment of it, we get different intervals and chords. For example, 4:5:6 is the major triad. ''Try it out in'' [https://scaleworkshop.plainsound.org Scale Workshop] ''by creating a new scale from the ‘harmonic series segment’''!

''Clarifaction: something that confused me when I was learning about Just Intonation is the conflation I made between JI intervals and divisions of string vibrations. That’s because it’s two ways of looking at the same thing. See the physics forumla wavelength is proportionate to the speed of sound (or light) over frequency: lambda equals v over f.''

=== Primes ===

Sometimes intervals can be reduced, for example 6/3 is the same as 2/1, but sometimes they cannot if they include primes. Primes are important because they introduce new flavours of intervals. When we have collections of JI intervals, because they can theoretically go on forever, we use conceptual limits to make things finite and usable.

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''Try it out with Nick Vuci’s'' [https://tonalitydiamondapplet.nickvuci.com/ Tonality Diamond Explorer]!

[[5-Limit_Tonality_Diamond.mp4]] [https://us-east-1.linodeobjects.com/xenwiki/xenwiki_en/files/5-Limit_Tonality_Diamond_original_format.mp4 5-limit tonality diamond] ~~###~~ Lattices Lattices are another way to visualize JI: [[Wilsonic lattice.mp4]] [https://cdn.discordapp.com/attachments/1404347667076874281/1469142815543136499/Wilsonic_lattice.mp4?ex=699da79e&is=699c561e&hm=363e4c60e5983cab0f83dbe94d98c2786b64436dbb557750dc67feee706de815& Lattice] ~~###~~ Conclusion In essence, JI is when intervals can be defined as frequencies that align and form whole number ratios. The tonality diamond is the conceptual layout of an odd-limit.

[[5-Limit_Tonality_Diamond.mp4]] [https://us-east-1.linodeobjects.com/xenwiki/xenwiki_en/files/5-Limit_Tonality_Diamond_original_format.mp4 5-limit tonality diamond]

=== Lattices ===

Lattices are another way to visualize JI: [[Wilsonic lattice.mp4]] [https://cdn.discordapp.com/attachments/1404347667076874281/1469142815543136499/Wilsonic_lattice.mp4?ex=699da79e&is=699c561e&hm=363e4c60e5983cab0f83dbe94d98c2786b64436dbb557750dc67feee706de815& Lattice]

=== Conclusion ===

In essence, JI is when intervals can be defined as frequencies that align and form whole number ratios. The tonality diamond is the conceptual layout of an odd-limit.

Some extra things on Just Intonation is that there are other approaches to Just-Intonation besides the basic tonality diamonds. You have [https://en.xen.wiki/w/Primodality primodality] that exploits prime modes of the harmonic series and incorporates commas, which are usually seen as a musical inconvience or blight, and then you have Hexany by Erv Wilson which is a way to make JI without a tonal-center using Combination Product Sets. The [https://www.wilsonic.co/ Wilsonic software] makes all these things accessible.

@@ Line 5: / Line 5: @@
 == Just Intonation (JI) ==
-If the pitch or frequency of a note is the number of times per second it causes the air to vibrate, and an interval is when two notes play at the same time, then Just Intonation (JI) is where the frequencies of the notes form whole-number ratios with each other. [[ji_intro.mp4]] (non-essential video) ### Harmonic Series A fundamental aspect of JI is the harmonic series. The harmonic series is the series that happens when you keep adding the first frequency over and over, ad infinitum. Which is 1:2:3:4:5:6:7… If we take a segment of it, we get different intervals and chords. For example, 4:5:6 is the major triad. ''Try it out in'' [https://scaleworkshop.plainsound.org Scale Workshop] ''by creating a new scale from the ‘harmonic series segment’''!
+If the pitch or frequency of a note is the number of times per second it causes the air to vibrate, and an interval is when two notes play at the same time, then Just Intonation (JI) is where the frequencies of the notes form whole-number ratios with each other. [[ji_intro.mp4]] (non-essential video)
+=== Harmonic Series ===
+A fundamental aspect of JI is the harmonic series. The harmonic series is the series that happens when you keep adding the first frequency over and over, ad infinitum. Which is 1:2:3:4:5:6:7… If we take a segment of it, we get different intervals and chords. For example, 4:5:6 is the major triad. ''Try it out in'' [https://scaleworkshop.plainsound.org Scale Workshop] ''by creating a new scale from the ‘harmonic series segment’''!
 ''Clarifaction: something that confused me when I was learning about Just Intonation is the conflation I made between JI intervals and divisions of string vibrations. That’s because it’s two ways of looking at the same thing. See the physics forumla wavelength is proportionate to the speed of sound (or light) over frequency: lambda equals v over f.''
 === Primes ===
 Sometimes intervals can be reduced, for example 6/3 is the same as 2/1, but sometimes they cannot if they include primes. Primes are important because they introduce new flavours of intervals. When we have collections of JI intervals, because they can theoretically go on forever, we use conceptual limits to make things finite and usable.
@@ Line 35: / Line 37: @@
 ''Try it out with Nick Vuci’s'' [https://tonalitydiamondapplet.nickvuci.com/ Tonality Diamond Explorer]!
-[[5-Limit_Tonality_Diamond.mp4]] [https://us-east-1.linodeobjects.com/xenwiki/xenwiki_en/files/5-Limit_Tonality_Diamond_original_format.mp4 5-limit tonality diamond] ### Lattices Lattices are another way to visualize JI: [[Wilsonic lattice.mp4]] [https://cdn.discordapp.com/attachments/1404347667076874281/1469142815543136499/Wilsonic_lattice.mp4?ex=699da79e&amp;is=699c561e&amp;hm=363e4c60e5983cab0f83dbe94d98c2786b64436dbb557750dc67feee706de815&amp; Lattice] ### Conclusion In essence, JI is when intervals can be defined as frequencies that align and form whole number ratios. The tonality diamond is the conceptual layout of an odd-limit.
+[[5-Limit_Tonality_Diamond.mp4]] [https://us-east-1.linodeobjects.com/xenwiki/xenwiki_en/files/5-Limit_Tonality_Diamond_original_format.mp4 5-limit tonality diamond]
+=== Lattices ===
+Lattices are another way to visualize JI: [[Wilsonic lattice.mp4]] [https://cdn.discordapp.com/attachments/1404347667076874281/1469142815543136499/Wilsonic_lattice.mp4?ex=699da79e&amp;is=699c561e&amp;hm=363e4c60e5983cab0f83dbe94d98c2786b64436dbb557750dc67feee706de815&amp; Lattice]
+=== Conclusion ===
+In essence, JI is when intervals can be defined as frequencies that align and form whole number ratios. The tonality diamond is the conceptual layout of an odd-limit.
 Some extra things on Just Intonation is that there are other approaches to Just-Intonation besides the basic tonality diamonds. You have [https://en.xen.wiki/w/Primodality primodality] that exploits prime modes of the harmonic series and incorporates commas, which are usually seen as a musical inconvience or blight, and then you have Hexany by Erv Wilson which is a way to make JI without a tonal-center using Combination Product Sets. The [https://www.wilsonic.co/ Wilsonic software] makes all these things accessible.