Bohlen-Pierce - Revision history

Hotcrystal0: more accurate

2026-04-11T12:21:24Z

more accurate

← Older revision		Revision as of 12:21, 11 April 2026
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	{{Harmonics in ED\|24.606\|31\|0}}		{{Harmonics in ED\|24.606\|31\|0}}

	=== ~~41edo~~ ===		=== 65edt ===
	13edt is approximately 8.2edo. Dividing each step into fifths to obtain a more accurate octave results in a slightly detuned version of [[41edo]].		13edt is approximately 8.2edo. Dividing each step into fifths to obtain a more accurate octave results in a slightly detuned version of [[41edo]].

Vector at 08:02, 11 April 2026

2026-04-11T08:02:10Z

← Older revision		Revision as of 08:02, 11 April 2026
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	{{Harmonics in ED\|24.606\|31\|0}}		{{Harmonics in ED\|24.606\|31\|0}}

	=== ~~65edt~~ ===		=== 41edo ===
	~~See~~ [[41edo]].		13edt is approximately 8.2edo. Dividing each step into fifths to obtain a more accurate octave results in a slightly detuned version of [[41edo]].

	== Bohpier temperament ==		== Bohpier temperament ==

Overthink: /* Multiples */ add 39edt

2026-03-27T00:21:57Z

Multiples: add 39edt

← Older revision		Revision as of 00:21, 27 March 2026
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	== Multiples ==		== Multiples ==
			=== 39edt ===
			39edt, sometimes known as Triple Bohlen-Pierce, additionally adds approximations of the 11th and 13th harmonics to 13edt.
			{{Harmonics in ED\|24.606\|31\|0}}

	=== 65edt ===		=== 65edt ===

Vector at 04:15, 22 February 2026

2026-02-22T04:15:18Z

← Older revision		Revision as of 04:15, 22 February 2026
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	== Bohpier temperament ==		== Bohpier temperament ==
	Bohpier temperament is somewhat analogous to [[blackwood]] or [[compton]] temperament, but based on 13edt, adding the [[octave]] as a separate generator (in this case, the period). It is supported by 41edo.		Bohpier temperament is somewhat analogous to [[blackwood]] or [[compton]] temperament, but based on 13edt, adding the [[octave]] as a separate generator (in this case, the period). It is supported by 41edo.

			{{Navbox EDO}}

Vector at 04:14, 22 February 2026

2026-02-22T04:14:24Z

← Older revision		Revision as of 04:14, 22 February 2026
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	=== 65edt ===		=== 65edt ===
	See [[41edo]].		See [[41edo]].

			== Bohpier temperament ==
			Bohpier temperament is somewhat analogous to [[blackwood]] or [[compton]] temperament, but based on 13edt, adding the [[octave]] as a separate generator (in this case, the period). It is supported by 41edo.

Vector at 04:12, 22 February 2026

2026-02-22T04:12:53Z

@@ Line 12: / Line 12: @@
 * 49/45
 * 27/25
 == Multiples ==

Vector: Created page with "The '''Bohlen-Pierce''' system is a non-octave tuning system of (exact or well-tempered) '''13 equal divisions of the perfect twelfth''' (or tritave). In the Bohlen-Pierce system, the tritave is generally seen as the interval of equivalence, and harmony emphasizes the odd harmonics (such as the chord 3:5:7:9). It is the smallest EDT that has a tuning of lambda, the 9-note scale of the sensamagic temperament (which serves an analogous role to meantone..."

2026-02-22T04:02:06Z

Created page with "The '''Bohlen-Pierce''' system is a non-octave tuning system of (exact or well-tempered) '''13 equal divisions of the perfect twelfth''' (or tritave). In the Bohlen-Pierce system, the tritave is generally seen as the interval of equivalence, and harmony emphasizes the odd harmonics (such as the chord 3:5:7:9). It is the smallest EDT that has a tuning of lambda, the 9-note scale of the sensamagic temperament (which serves an analogous role to meantone..."

New page

The '''Bohlen-Pierce''' system is a non-octave tuning system of (exact or well-tempered) '''13 equal divisions of the [[3/1|perfect twelfth]]''' (or tritave). In the Bohlen-Pierce system, the tritave is generally seen as the interval of equivalence, and harmony emphasizes the odd harmonics (such as the chord 3:5:7:9). It is the smallest EDT that has a tuning of [[lambda]], the 9-note scale of the [[sensamagic]] temperament (which serves an analogous role to [[meantone]] in tritave-based harmony).

== General theory ==

=== JI approximation ===
13edt's 2/1 is flat about 30 cents, making it most prominently a 3.5.7 subgroup temperament, although it also contains approximations of 19, 23, and 29. 7/3 (the tritave-reduced 7th harmonic) is flattened by a small amount, so that a sharpened 9/7 stacks twice to a flattened 5/3, as in [[sensamagic]] temperament. As a full 7-limit temperament, it supports [[sensi]], albeit with a severely flattened octave.{{Harmonics in ED|8.202|31|0}}''Note: Due to a bug with the template, the step counts are octave-reduced instead of tritave-reduced.''
{{Wip}}

=== Edtstep interpretations ===
The step of 13edt can be interpreted as the following ratios in the 3.5.7 subgroup.

* 49/45
* 27/25

== Multiples ==

=== 65edt ===
See [[41edo]].