Maeve Gutierrez: Difference between revisions

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 {{Idiosyncratic terms|Names of scales made up by [[Budjarn Lambeth]] for the purpose of documentation; if Gutierrez names the scales at some point, Gutierrez's names should be used instead.}}
-=== Reduced 3ed7/3 subminor pentatonic scale ===
+=== 4:5:6:7-to-30:35:40:44 double delta scale ===
-In a public post on the [[Xenharmonic Alliance]] Discord server, in October 2025, Gutierrez described the following [[pentatonic]] tempered scale:
+This scale was described by Gutierrez in October 2025, on the [[Xenharmonic Alliance]] Discord server. In [[cents]], its intervals are:
-* 266.9
+* 266.87
-* 489.0
+* 484.92
-* 755.8
+* 669.28
-* 977.9
+* 936.15
-* 1200.0
+* 1154.20
-It is all the intervals in 3ed7/3 up to its sharp tritave, but [[octave-reduced]]. It creates a subminor pentatonic scale near 5edo with a better 4/3 and 7/6, but with a 14/9 instead of a 3/2. (Which is quite a bit more [[xenharmonic]].)
+* 1338.56
+* 1466.87
+; Creation of the scale
+If you start with the [[JI]] chord:
+* 1/1 - 5/4 - 3/2 - 7/4
+Then compress it logarithmically such that 5/4 becomes 7/6, you get the [[delta-rational]] chord:
+* 0¢ - 266.9¢ - 484.9¢ - 669.3¢
+If you stack a second copy of the same chord on top of itself you get the scale:
+* 266.87
+* 484.92
+* 669.28
+* 936.15
+* 1154.20
+* 1338.56
+Then you can add a 7/3 to the end to act as a [[period]] and you get Gutierrez scale.
+; Approximation of JI
+Here are the [[17-limit]] JI intervals approximated by the first 3 periods of the scale:
+* 266.87 (7/6)
+* 484.92 (4/3)
+* 669.28 (22/15, 25/17)
+* 936.15 (12/7)
+* 1154.20 (33/17, 35/18)
+* 1338.56 (13/6)
+* 1605.43 (5/2)
+* 1823.48 (20/7)
+* 2007.84 (16/5)
+* 2274.71 (15/4, 26/7)
+* 2492.76 (17/4, 21/5)
+* 2677.12 (14/3)
+* 2943.99 (11/2)
+* 3162.04 (25/4)
+* 3346.4 (7/1)
+* 3613.27 (8/1)
+* 3831.32 (55/6, 64/7)
+* 4015.68 (51/5)
 === 6ed7/3''+''7edo scale ===
@@ Line 147: / Line 187: @@
 * 3 17 22 3 20 5 17 25 5 14 22 5 3 16 18 4 19 5 5 12 2 6 17 5
 * (identical to original scale within 1{{c}})
+=== Reduced 3ed7/3 subminor pentatonic scale ===
+In a public post on the [[Xenharmonic Alliance]] Discord server, in October 2025, Gutierrez described the following [[pentatonic]] tempered scale:
+* 266.9
+* 489.0
+* 755.8
+* 977.9
+* 1200.0
+It is all the intervals in 3ed7/3 up to its sharp tritave, but [[octave-reduced]]. It creates a subminor pentatonic scale near 5edo with a better 4/3 and 7/6, but with a 14/9 instead of a 3/2. (Which is quite a bit more [[xenharmonic]].)
 === Sun-after-a-storm pentachord ===