33ed8/3 - Revision history

BudjarnLambeth at 04:15, 12 October 2026

2026-10-12T04:15:18Z

← Older revision		Revision as of 04:15, 12 October 2026
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	== Music ==		== Music ==
	* [https://www.youtube.com/watch?v=MArLmzWrx5I ''Improvisation in 33ed8/3''] - [[Budjarn Lambeth]] (2026)		* [https://www.youtube.com/watch?v=MArLmzWrx5I ''Improvisation in 33ed8/3''] - [[Budjarn Lambeth]] (2026)

			== See also ==
			* [[23edo and octave stretching]]
			* [[36edt]]

BudjarnLambeth at 03:43, 12 October 2026

2026-10-12T03:43:39Z

← Older revision		Revision as of 03:43, 12 October 2026
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	{{Harmonics in equal\|23\|2\|1\|intervals=integer}}		{{Harmonics in equal\|23\|2\|1\|intervals=integer}}
	{{Harmonics in equal\|23\|2\|1\|intervals=integer\|start=12}}		{{Harmonics in equal\|23\|2\|1\|intervals=integer\|start=12}}

			== Scales ==
			* Lambeth's 4-tone [[MOS scale]]: 10 10 3 10

	== Music ==		== Music ==
	* [https://www.youtube.com/watch?v=MArLmzWrx5I ''Improvisation in 33ed8/3''] - [[Budjarn Lambeth]] (2026)		* [https://www.youtube.com/watch?v=MArLmzWrx5I ''Improvisation in 33ed8/3''] - [[Budjarn Lambeth]] (2026)

BudjarnLambeth: /* Harmonics */

2026-10-12T03:39:45Z

Harmonics

← Older revision		Revision as of 03:39, 12 October 2026
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	{{Harmonics in equal\|33\|8\|3\|intervals=integer}}		{{Harmonics in equal\|33\|8\|3\|intervals=integer}}
	{{Harmonics in equal\|33\|8\|3\|intervals=integer\|start=12}}		{{Harmonics in equal\|33\|8\|3\|intervals=integer\|start=12}}

			=== [[36edt]] for comparison ===
			{{Harmonics in equal\|36\|3\|1\|intervals=integer}}
			{{Harmonics in equal\|36\|3\|1\|intervals=integer\|start=12}}

	=== [[23edo]] for comparison ===		=== [[23edo]] for comparison ===
	{{Harmonics in equal\|23\|2\|1\|intervals=integer}}		{{Harmonics in equal\|23\|2\|1\|intervals=integer}}
	{{Harmonics in equal\|23\|2\|1\|intervals=integer\|start=12}}		{{Harmonics in equal\|23\|2\|1\|intervals=integer\|start=12}}

	~~=== [[36edt]] for comparison ===~~
	~~{{Harmonics in equal\|36\|3\|1\|intervals=integer}}~~
	~~{{Harmonics in equal\|36\|3\|1\|intervals=integer\|start=12}}~~

	== Music ==		== Music ==
	* [https://www.youtube.com/watch?v=MArLmzWrx5I ''Improvisation in 33ed8/3''] - [[Budjarn Lambeth]] (2026)		* [https://www.youtube.com/watch?v=MArLmzWrx5I ''Improvisation in 33ed8/3''] - [[Budjarn Lambeth]] (2026)

BudjarnLambeth: Document scale I stumbled upon that was so good I immediately made music with it

2026-10-12T03:37:42Z

Document scale I stumbled upon that was so good I immediately made music with it

New page

{{Infobox ET}}
{{ED intro}}

33ed8/3 was first explored by [[Budjarn Lambeth]] in his 2026 piece [https://www.youtube.com/watch?v=MArLmzWrx5I ''Improvisation in 33ed8/3'']. Below his music video, he gave the following description of the tuning and why he used it:

"''33ed8/3 is a very [[octave shrinking|squished]] version of [[23edo]] such that the [[2/1|octave]] equals 1183.5 [[cents]] instead of the usual 1200.0.

''I came across 33ed8/3 because I tried out the 10 10 3 [[MOS scale]] from 23edo using the "platinum" [[timbre]] in [[Scale Workshop]], and I realized that the [[interval]] near [[8/3]] was sounding more like an [[equivalence]] to my ear than the octave was!

''The 8/3 interval was 33 steps of 23edo, so I decided to change tuning to 33ed8/3, and it worked perfectly, the equivalence became even stronger and everything overall sounded "more in-tune".

''Before today, I would never have thought that 8/3 could sound like an equivalence. If I had to guess, the platinum timbre is the reason. It has a stretched [[overtone]] spectrum, so perhaps it is stretched just the right amount such that the overtone that occurs at 2/1 for a harmonic instrument, occurs at 8/3 for struck platinum?

''That's just a guess, I have no idea whether it's true.''"

Besides 23edo, a closer lookalike to 33ed8/3 is actually [[36edt]], although it still has significant enough differences to be an audibly different scale - its mappings of every [[harmonic]] after the first are different (a different number of steps).

== Interval table ==
{{Interval table}}

== Harmonics ==
In the [[11-odd-limit]], 33ed8/3 improves 23edo's tuning of most odd harmonics at the expense of most even harmonics. This makes it potentially a good no-twos [[subgroup]] tuning (eg for the [[3.5.7 subgroup|3.5.7.11 subgroup]]).
{{Harmonics in equal|33|8|3|intervals=integer}}
{{Harmonics in equal|33|8|3|intervals=integer|start=12}}

=== [[23edo]] for comparison ===
{{Harmonics in equal|23|2|1|intervals=integer}}
{{Harmonics in equal|23|2|1|intervals=integer|start=12}}

=== [[36edt]] for comparison ===
{{Harmonics in equal|36|3|1|intervals=integer}}
{{Harmonics in equal|36|3|1|intervals=integer|start=12}}

== Music ==
* [https://www.youtube.com/watch?v=MArLmzWrx5I ''Improvisation in 33ed8/3''] - [[Budjarn Lambeth]] (2026)