User:BudjarnLambeth/Firedance: Difference between revisions

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{{Editable user page|Don't remove anything (unless it's offensive or factually incorrect), but feel free to add any observations about the scale, subsets, music examples, etc., and feel free to improve the formatting or layout as long as you don't remove information.}}

[[File:Firedance.png|thumb|Firedance scale (circle diagram).]]

The '''firedance scale''' is a subset of zeta-stretched 15edo described by [[Budjarn Lambeth]] in 2023.

Zeta-stretched 15edo (also known as [[47zpi]], the 47th [[zeta peak index]]), is 15edo with octaves compressed according to this process: [[~~The~~ Riemann ~~Zeta Function~~ and ~~Tuning~~#Optimal octave stretch|Optimal octave stretch]].

Zeta-stretched 15edo (also known as [[47zpi]], the 47th [[zeta peak index]]), is 15edo with octaves compressed according to this process: [[the Riemann zeta function and tuning#Optimal octave stretch|Optimal octave stretch]].

You can also stretch 15edo using [[Paul Erlich]]'s [[TOP]] tuning, or using [[TE]] tuning, and get a very similar (but not exactly identical) result. Or even just use plain old pure-octaves [[15edo]]. All are considered acceptable tunings.

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Attached is [[Scale Workshop]]'s table of interval relationships in the firedance scale:

{| class="wikitable"

!

|-

! 0 !! 1 !! 2 !! 3 !! 4 !! (5)

! !! 0 !! 1 !! 2 !! 3 !! 4 !! (5)

|-

! 0

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* [https://www.youtube.com/watch?v=eSXomnrP7O8 Improvisation in Zeta-Stretched 15-Tone Equal Temperament (15 EDO)] - [[Budjarn Lambeth]] (2024)

[[Category:5-tone scales]][[Category:Tempered scales]][[Category:15edo]][[Category:11-limit]][[Category:Pages with Scala files]]

[[Category:5-tone scales]]

[[Category:Tempered scales]]

[[Category:15edo]]

[[Category:11-limit]]

[[Category:Pages with Scala files]]

@@ Line 1: / Line 1: @@
+{{Editable user page|Don't remove anything (unless it's offensive or factually incorrect), but feel free to add any observations about the scale, subsets, music examples, etc., and feel free to improve the formatting or layout as long as you don't remove information.}}
+[[File:Firedance.png|thumb|Firedance scale (circle diagram).]]
 The '''firedance scale''' is a subset of zeta-stretched 15edo described by [[Budjarn Lambeth]] in 2023.
-Zeta-stretched 15edo (also known as [[47zpi]], the 47th [[zeta peak index]]), is 15edo with octaves compressed according to this process: [[The Riemann Zeta Function and Tuning#Optimal octave stretch|Optimal octave stretch]].
+Zeta-stretched 15edo (also known as [[47zpi]], the 47th [[zeta peak index]]), is 15edo with octaves compressed according to this process: [[the Riemann zeta function and tuning#Optimal octave stretch|Optimal octave stretch]].
 You can also stretch 15edo using [[Paul Erlich]]'s [[TOP]] tuning, or using [[TE]] tuning, and get a very similar (but not exactly identical) result. Or even just use plain old pure-octaves [[15edo]]. All are considered acceptable tunings.
@@ Line 9: / Line 13: @@
 Attached is [[Scale Workshop]]'s table of interval relationships in the firedance scale:
 {| class="wikitable"
-!
+|-
-! 0 !! 1 !! 2 !! 3 !! 4 !! (5)
+! !! 0 !! 1 !! 2 !! 3 !! 4 !! (5)
 |-
 ! 0
@@ Line 58: / Line 62: @@
 * [https://www.youtube.com/watch?v=eSXomnrP7O8 Improvisation in Zeta-Stretched 15-Tone Equal Temperament (15 EDO)] - [[Budjarn Lambeth]] (2024)
-[[Category:5-tone scales]][[Category:Tempered scales]][[Category:15edo]][[Category:11-limit]][[Category:Pages with Scala files]]
+[[Category:5-tone scales]]
+[[Category:Tempered scales]]
+[[Category:15edo]]
+[[Category:11-limit]]
+[[Category:Pages with Scala files]]