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.
+{{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.}}
-Zeta-stretched 15edo (also known as [[47zpi]], the 47th [[zeta peak index]]), is 15edo with octaves stretched according to this process: [[The Riemann Zeta Function and Tuning#Optimal octave stretch|Optimal octave stretch]].
+[[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]].
 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.
 The firedance scale was designed by starting with [[5edo]], and then just tweaking intervals up and down by individual edo-steps of 15edo, by ear, until it sounded good.
 Attached is [[Scale Workshop]]'s table of interval relationships in the firedance scale:
 {| class="wikitable"
-!
-!0
-!1
-!2
-!3
-!4
-!(5)
 |-
-!0.
+! !! 0 !! 1 !! 2 !! 3 !! 4 !! (5)
-|0.
+|-
-|239.147
+! 0
-|558.010
+| 0 || 239.147 || 558.010 || 717.441 || 956.588 || 1195.7
-|717.441
-|956.588
-|1195.7
 |-
-!239.147
+! 239.147
-|0.
+| 0 || 318.9 || 478.3 || 717.4 || 956.6 || 1195.7
-|318.9
-|478.3
-|717.4
-|956.6
-|1195.7
 |-
-!558.010
+! 558.010
-|0.
+| 0 || 159.4 || 398.6 || 637.7 || 876.9 || 1195.7
-|159.4
-|398.6
-|637.7
-|876.9
-|1195.7
 |-
-!717.441
+! 717.441
-|0.
+| 0 || 239.1 || 478.3 || 717.4 || 1036.3 || 1195.7
-|239.1
-|478.3
-|717.4
-|1036.3
-|1195.7
 |-
-!956.588
+! 956.588
-|0.
+| 0 || 239.1 ||478.3 || 797.2 || 956.6 || 1195.7
-|239.1
-|478.3
-|797.2
-|956.6
-|1195.7
 |}
-Although it wasn't consciously designed this way, you can see that a lot of warm septimal harmonies occur in the intervals between the intervals. Most notably, all those 717's are decent approximations of [[3/2]], all those 239's are decent approximations of [[8/7]], and all those 956's are decent approximations of [[7/4]].
+Although it wasn't consciously designed this way, you can see that a lot of septimal harmonies occur in the intervals between the intervals. Most notably, all those 717's are decent approximations of [[3/2]], all those 239's are decent approximations of [[8/7]], and all those 956's are decent approximations of [[7/4]].
 On top of that, the firedance scale is a very close approximation to this [[primodal]] over-7 scale. A subset of [[56afdo]]:
-*64/56
+* 64/56
-*77/56
+* 77/56
-*84/56
+* 84/56
-*98/56
+* 98/56
-*112/56
+* 112/56
 just being a higher octave of 7 in the [[harmonic series]].
 So from both a [[regular temperament theory]] point of view and also a primodality point of view, it's quite a nifty little scale with lots of xen harmonies baked into it.
@@ Line 91: / Line 59: @@
 </pre>
-[[Category:5-tone scales]][[Category:Tempered scales]][[Category:15edo]][[Category:11-limit]][[Category:Pages with Scala files]]
+== Music ==
+* [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]]