User:BudjarnLambeth/Firedance: Difference between revisions

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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)

|-

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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]]

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 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 9: @@
 Attached is [[Scale Workshop]]'s table of interval relationships in the firedance scale:
 {| class="wikitable"
-!
+|-
 ! 0 !! 1 !! 2 !! 3 !! 4 !! (5)
 |-
@@ Line 58: / Line 58: @@
 * [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]]