User:TromboneBoi9: Difference between revisions

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== Irrational HEJI Extensions ==

I've heard [[Golden ratio|phi]] is somewhat ~~usefu~~ in xen areas, as well as other popular irrational numbers, so what would it look like if I extended [[Helmholtz-Ellis notation|HEJI]] (my go-to Just Intonation notation) to support these numbers like factors?

I've heard [[Golden ratio|phi]] is somewhat useful in xen areas, as well as other popular irrational numbers, so what would it look like if I extended [[Helmholtz-Ellis notation|HEJI]] (my go-to Just Intonation notation) to support these numbers like factors?

=== Commas ===

===Commas===

==== Golden Ratio ====

====Golden Ratio====

The ratio [[Acoustic phi|phi]] adds up to 833.0903 cents, a sharp minor sixth. The Pythagorean minor sixth is [[128/81]], about 792.1800 cents. This leaves a comma of (81*phi)/128, about 40.9103 cents. I dub this interval the '''Golden quartertone'''.

==== Pi ====

====Pi====

The ratio pi/2 adds up to 781.7954 cents, an okay minor sixth. The Pythagorean minor sixth is [[128/81]], about 792.1800 cents. This leaves a comma of 256/(81*pi), about 10.3846 cents. I dub this interval the '''Circular comma'''.

==== Euler's constant ====

====Euler's constant====

The ratio e/2 adds up to 531.2340 cents, a pretty sharp fourth. The Pythagorean perfect fourth is, of course, [[4/3]], 498.0450 cents. This leaves a comma of (3*e)/8, about 33.1890 cents. I dub this interval the '''Eulerian comma'''.

=== Notation ===

===Notation===

For the golden quartertone, I plan to use the symbol Blackwood used in his microtonal notation, because it already resembles a phi symbol (ϕ). For pi, I designed a symbol similar to [https://en.xen.wiki/images/c/cf/Sagittal_sharp_kao.png the 55-comma symbol in Sagittal], but the "arrowhead" is replaced with a circular cap, making the symbol resemble a ''J'' with an extra shaft.

I'm yet to design a symbol for e.

@@ Line 562: / Line 562: @@
 == Irrational HEJI Extensions ==
-I've heard [[Golden ratio|phi]] is somewhat usefu in xen areas, as well as other popular irrational numbers, so what would it look like if I extended [[Helmholtz-Ellis notation|HEJI]] (my go-to Just Intonation notation) to support these numbers like factors?
+I've heard [[Golden ratio|phi]] is somewhat useful in xen areas, as well as other popular irrational numbers, so what would it look like if I extended [[Helmholtz-Ellis notation|HEJI]] (my go-to Just Intonation notation) to support these numbers like factors?
-=== Commas ===
+===Commas===
-==== Golden Ratio ====
+====Golden Ratio====
 The ratio [[Acoustic phi|phi]] adds up to 833.0903 cents, a sharp minor sixth. The Pythagorean minor sixth is [[128/81]], about 792.1800 cents. This leaves a comma of (81*phi)/128, about 40.9103 cents. I dub this interval the '''Golden quartertone'''.
-==== Pi ====
+====Pi====
 The ratio pi/2 adds up to 781.7954 cents, an okay minor sixth. The Pythagorean minor sixth is [[128/81]], about 792.1800 cents. This leaves a comma of 256/(81*pi), about 10.3846 cents. I dub this interval the '''Circular comma'''.
-==== Euler's constant ====
+====Euler's constant====
 The ratio e/2 adds up to 531.2340 cents, a pretty sharp fourth. The Pythagorean perfect fourth is, of course, [[4/3]], 498.0450 cents. This leaves a comma of (3*e)/8, about 33.1890 cents. I dub this interval the '''Eulerian comma'''.
-=== Notation ===
+===Notation===
 For the golden quartertone, I plan to use the symbol Blackwood used in his microtonal notation, because it already resembles a phi symbol (ϕ). For pi, I designed a symbol similar to [https://en.xen.wiki/images/c/cf/Sagittal_sharp_kao.png the 55-comma symbol in Sagittal], but the "arrowhead" is replaced with a circular cap, making the symbol resemble a ''J'' with an extra shaft.
 I'm yet to design a symbol for e.