30edt - Revision history

Squib: 3/2 is not just in 30edt

2025-12-26T18:37:59Z

3/2 is not just in 30edt

← Older revision		Revision as of 18:37, 26 December 2025
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	Because [[19edo]] has the [[3/1\|3rd]], [[5/1\|5th]], [[7/1\|7th]], and [[13/1\|13th]] [[harmonic]]s all flat (the latter two very flat), it benefits greatly from octave stretching. 30edt is one possible alternative; at the cost of sharpening the octave, it achieves much better matches to the odd harmonics; the 3 (tritave) is by definition just, the 5 slightly sharp, and the 7 and 13 slightly flat.		Because [[19edo]] has the [[3/1\|3rd]], [[5/1\|5th]], [[7/1\|7th]], and [[13/1\|13th]] [[harmonic]]s all flat (the latter two very flat), it benefits greatly from octave stretching. 30edt is one possible alternative; at the cost of sharpening the octave, it achieves much better matches to the odd harmonics; the 3 (tritave) is by definition just, the 5 slightly sharp, and the 7 and 13 slightly flat.

	While the fifth is just, the fourth is noticeably sharper and less accurate than in 19edo, being close to that of [[26edo]].		While the fifth is closer to just than in 19edo, the fourth is noticeably sharper and less accurate than in 19edo, being close to that of [[26edo]].

	=== Harmonics ===		=== Harmonics ===

FloraC: Cleanup; +see also

2025-03-30T11:19:22Z

Cleanup; +see also

← Older revision		Revision as of 11:19, 30 March 2025
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	== Theory ==		== Theory ==
	30edt is related to [[19edo]], but with the [[3/1]] rather than the [[2/1]] being [[just]], which results in octaves being is [[stretched and compressed tuning\|stretched]] by about 4.5715{{cent}}. It is [[consistent]] to the 10-[[integer-limit]].		30edt is related to [[19edo]], but with the [[3/1]] rather than the [[2/1]] being [[just]], which results in octaves being is [[stretched and compressed tuning\|stretched]] by about 4.5715{{cent}}. Like 19edo, 30edt is [[consistent]] to the [[integer-limit\|10-integer-limit]].

	Because [[19edo]] has the 3rd, 5th, 7th, and 13th [[harmonic]]s all flat (the latter two very flat), it benefits greatly from octave stretching. 30edt is one possible alternative; at the cost of sharpening the octave, it achieves much better matches to the odd harmonics; the 3 (tritave) is by definition just, the 5 slightly sharp, and the 7 and 13 slightly flat.		Because [[19edo]] has the [[3/1\|3rd]], [[5/1\|5th]], [[7/1\|7th]], and [[13/1\|13th]] [[harmonic]]s all flat (the latter two very flat), it benefits greatly from octave stretching. 30edt is one possible alternative; at the cost of sharpening the octave, it achieves much better matches to the odd harmonics; the 3 (tritave) is by definition just, the 5 slightly sharp, and the 7 and 13 slightly flat.

	While the fifth is just, the fourth is noticeably sharper and less accurate than in 19edo, being close to that of [[26edo]].		While the fifth is just, the fourth is noticeably sharper and less accurate than in 19edo, being close to that of [[26edo]].
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	; [[Ray Perlner]]		; [[Ray Perlner]]
	* [https://www.youtube.com/watch?v=fEQ13hzs3fY ''Fugue for Piano in 30EDT Bohlen-Pierce-Stearns{{lbrack}}9{{rbrack}} sLsLssLsL "Dur I"''] (2024)		* [https://www.youtube.com/watch?v=fEQ13hzs3fY ''Fugue for Piano in 30EDT Bohlen-Pierce-Stearns{{lbrack}}9{{rbrack}} sLsLssLsL "Dur I"''] (2024)

			== See also ==
			* [[11edf]] – relative edf
			* [[19edo]] – relative edo
			* [[49ed6]] – relative ed6
			* [[53ed7]] – relative ed7
			* [[68ed12]] – relative ed12
			* [[93ed30]] – relative ed30

	[[Category:Listen]]		[[Category:Listen]]

BudjarnLambeth: /* Theory */ It is not a phoenix tuning, I was wrong about that.

2025-03-25T01:12:04Z

Theory: It is not a phoenix tuning, I was wrong about that.

← Older revision		Revision as of 01:12, 25 March 2025
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	While the fifth is just, the fourth is noticeably sharper and less accurate than in 19edo, being close to that of [[26edo]].		While the fifth is just, the fourth is noticeably sharper and less accurate than in 19edo, being close to that of [[26edo]].

	~~30edt is a [[Phoenix]] tuning and exhibits all the benefits of such tunings.~~

	=== Harmonics ===		=== Harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 30 factors into primes as 2 × 3 × 5, 30edt has subset edts {{EDs\|equave=t\| 2, 3, 5, 6, 10, and 15 }}.		Since 30 factors into primes as 2 × 3 × 5, 30edt has subset edts {{EDs\|equave=t\| 2, 3, 5, 6, 10, and 15 }}.

	== Intervals ==		== Intervals ==

ArrowHead294: Replace {{scale link}} with {{mos scalesig}}

2025-03-08T00:28:48Z

Replace {{scale link}} with {{mos scalesig}}

← Older revision		Revision as of 00:28, 8 March 2025
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	30edt contains all [[19edo]] intervals within 3/1, all tempered progressively sharper. The accumulation of the 0.241{{c}} sharpening of the unit step relative to 19edo leads to the excellent 6edt approximations of 6/5 and 5/2. Non-redundantly with simpler edts, the 41 degree ~9/2 is only .6615{{c}} flatter than that in 6edo.		30edt contains all [[19edo]] intervals within 3/1, all tempered progressively sharper. The accumulation of the 0.241{{c}} sharpening of the unit step relative to 19edo leads to the excellent 6edt approximations of 6/5 and 5/2. Non-redundantly with simpler edts, the 41 degree ~9/2 is only .6615{{c}} flatter than that in 6edo.

	30edt also contains all the mos contained in 15edt, being the double of this equal division. Being even, 30edt introduces mos with an even number of periods per tritave such as a {{sl\|6L 6s}} similar to Hexe Dodecatonic. This mos has a period of 1/6 of the tritave and the generator is a single or double step. The major scale is sLsLsLsLsLsL, and the minor scale is LsLsLsLsLsLs. Being a "real" 3/2, the interval of 11 degrees generates an [[unfair]] [[Sigma]] scale of {{sl\|8L 3s}} and the major scale is LLLsLLLsLLs. The sharp 9/7 of 7 degrees, in addition to generating a Lambda mos will generate a {{sl\|4L 9s}} unfair "Superlambda" mos which does not border on being atonal as the 17edt rendition does.		30edt also contains all the mos contained in 15edt, being the double of this equal division. Being even, 30edt introduces mos with an even number of periods per tritave such as a {{mos scalesig\|6L 6s<3/1>\|link=1}} similar to Hexe Dodecatonic. This mos has a period of 1/6 of the tritave and the generator is a single or double step. The major scale is sLsLsLsLsLsL, and the minor scale is LsLsLsLsLsLs. Being a "real" 3/2, the interval of 11 degrees generates an [[unfair]] [[Sigma]] scale of {{mos scalesig\|8L 3s<3/1>\|link=1}} and the major scale is LLLsLLLsLLs. The sharp 9/7 of 7 degrees, in addition to generating a Lambda mos will generate a {{mos scalesig\|4L 9s<3/1>\|link=1}} unfair "Superlambda" mos which does not border on being atonal as the 17edt rendition does.

	== Music ==		== Music ==

FloraC: Fix unfinished sentence

2025-02-16T16:41:30Z

Fix unfinished sentence

← Older revision		Revision as of 16:41, 16 February 2025
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	== Theory ==		== Theory ==
	30edt is related to [[19edo]], but with the [[3/1]] rather than the [[2/1]] being [[just]], which results in octaves being is [[stretched and compressed tuning\|stretched]] by about 4.5715{{cent}} ~~and the step size is about~~. It is [[consistent]] to the 10-[[integer-limit]].		30edt is related to [[19edo]], but with the [[3/1]] rather than the [[2/1]] being [[just]], which results in octaves being is [[stretched and compressed tuning\|stretched]] by about 4.5715{{cent}}. It is [[consistent]] to the 10-[[integer-limit]].

	Because [[19edo]] has the 3rd, 5th, 7th, and 13th [[harmonic]]s all flat (the latter two very flat), it benefits greatly from octave stretching. 30edt is one possible alternative; at the cost of sharpening the octave, it achieves much better matches to the odd harmonics; the 3 (tritave) is by definition just, the 5 slightly sharp, and the 7 and 13 slightly flat.		Because [[19edo]] has the 3rd, 5th, 7th, and 13th [[harmonic]]s all flat (the latter two very flat), it benefits greatly from octave stretching. 30edt is one possible alternative; at the cost of sharpening the octave, it achieves much better matches to the odd harmonics; the 3 (tritave) is by definition just, the 5 slightly sharp, and the 7 and 13 slightly flat.

ArrowHead294: /* Intervals */ Link

2025-02-16T14:56:29Z

Intervals: Link

← Older revision		Revision as of 14:56, 16 February 2025
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	! rowspan="2" \| #		! rowspan="2" \| #
	! rowspan="2" \| Cents		! rowspan="2" \| Cents
	! rowspan="2" \| ~~Hekts~~		! rowspan="2" \| [[Hekt]]s
	! rowspan="2" \| Approximate ratios		! rowspan="2" \| Approximate ratios
	! colspan="2" \| Scale name		! colspan="2" \| Scale name

FloraC: Fix a parameter

2025-01-23T12:05:41Z

Fix a parameter

← Older revision		Revision as of 12:05, 23 January 2025
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	=== Harmonics ===		=== Harmonics ===
	{{Harmonics in equal\|30\|3\|1\|intervals=integer}}		{{Harmonics in equal\|30\|3\|1\|intervals=integer}}
	{{Harmonics in equal\|30\|3\|1\|intervals=integer\|columns=12\|start=12\|collapsed=1\|Approximation of harmonics in 30edt (continued)}}		{{Harmonics in equal\|30\|3\|1\|intervals=integer\|columns=12\|start=12\|collapsed=1\|title=Approximation of harmonics in 30edt (continued)}}

	=== Subsets and supersets ===		=== Subsets and supersets ===

FloraC: +subsets and supersets

2025-01-23T11:59:56Z

+subsets and supersets

← Older revision		Revision as of 11:59, 23 January 2025
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	{{Harmonics in equal\|30\|3\|1\|intervals=integer}}		{{Harmonics in equal\|30\|3\|1\|intervals=integer}}
	{{Harmonics in equal\|30\|3\|1\|intervals=integer\|columns=12\|start=12\|collapsed=1\|Approximation of harmonics in 30edt (continued)}}		{{Harmonics in equal\|30\|3\|1\|intervals=integer\|columns=12\|start=12\|collapsed=1\|Approximation of harmonics in 30edt (continued)}}

			=== Subsets and supersets ===
			Since 30 factors into primes as 2 × 3 × 5, 30edt has subset edts {{EDs\|equave=t\| 2, 3, 5, 6, 10, and 15 }}.

	== Intervals ==		== Intervals ==
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	30edt contains all [[19edo]] intervals within 3/1, all tempered progressively sharper. The accumulation of the 0.241{{c}} sharpening of the unit step relative to 19edo leads to the excellent 6edt approximations of 6/5 and 5/2. Non-redundantly with simpler edts, the 41 degree ~9/2 is only .6615{{c}} flatter than that in 6edo.		30edt contains all [[19edo]] intervals within 3/1, all tempered progressively sharper. The accumulation of the 0.241{{c}} sharpening of the unit step relative to 19edo leads to the excellent 6edt approximations of 6/5 and 5/2. Non-redundantly with simpler edts, the 41 degree ~9/2 is only .6615{{c}} flatter than that in 6edo.

	30edt also contains all the mos contained in [[15edt]], being the double of this equal division. Being even, 30edt introduces mos with an even number of periods per tritave such as a {{sl\|6L 6s}} similar to Hexe Dodecatonic. This mos has a period of 1/6 of the tritave and the generator is a single or double step. The major scale is sLsLsLsLsLsL, and the minor scale is LsLsLsLsLsLs. Being a "real" 3/2, the interval of 11 degrees generates an [[unfair]] [[Sigma]] scale of {{sl\|8L 3s}} and the major scale is LLLsLLLsLLs. The sharp 9/7 of 7 degrees, in addition to generating a Lambda mos will generate a {{sl\|4L 9s}} unfair "Superlambda" mos which does not border on being atonal as the 17edt rendition does.		30edt also contains all the mos contained in 15edt, being the double of this equal division. Being even, 30edt introduces mos with an even number of periods per tritave such as a {{sl\|6L 6s}} similar to Hexe Dodecatonic. This mos has a period of 1/6 of the tritave and the generator is a single or double step. The major scale is sLsLsLsLsLsL, and the minor scale is LsLsLsLsLsLs. Being a "real" 3/2, the interval of 11 degrees generates an [[unfair]] [[Sigma]] scale of {{sl\|8L 3s}} and the major scale is LLLsLLLsLLs. The sharp 9/7 of 7 degrees, in addition to generating a Lambda mos will generate a {{sl\|4L 9s}} unfair "Superlambda" mos which does not border on being atonal as the 17edt rendition does.

	== Music ==		== Music ==

FloraC: Cleanup (2/2)

2025-01-23T11:50:21Z

Cleanup (2/2)

Show changes

FloraC: Cleanup (1/2)

2025-01-23T11:44:20Z

Cleanup (1/2)

← Older revision		Revision as of 11:44, 23 January 2025
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	{{ED intro}}		{{ED intro}}

			== Theory ==
	30edt is related to [[19edo]], but with the [[3/1]] rather than the [[2/1]] being [[just]], which results in octaves being is [[stretched and compressed tuning\|stretched]] by about 4.5715{{cent}} and the step size is about. It is [[consistent]] to the 10-[[integer-limit]].		30edt is related to [[19edo]], but with the [[3/1]] rather than the [[2/1]] being [[just]], which results in octaves being is [[stretched and compressed tuning\|stretched]] by about 4.5715{{cent}} and the step size is about. It is [[consistent]] to the 10-[[integer-limit]].

Line 10:		Line 11:
	30edt is a [[Phoenix]] tuning and exhibits all the benefits of such tunings.		30edt is a [[Phoenix]] tuning and exhibits all the benefits of such tunings.

	== Harmonics ==		=== Harmonics ===
	{{Harmonics in equal		{{Harmonics in equal\|30\|3\|1\|intervals=integer}}
	\| ~~steps =~~ 30		{{Harmonics in equal\|30\|3\|1\|intervals=integer\|columns=12\|start=12\|collapsed=1\|Approximation of harmonics in 30edt (continued)}}
	\| ~~num =~~ 3
	\| ~~denom =~~ 1
	\| intervals = integer
	}}
	{{Harmonics in equal
	\| ~~steps =~~ 30
	\| ~~num~~ = 3
	\| ~~denom~~ = 1
	\| start = 12
	\| collapsed = 1
	\| ~~intervals = integer~~
	}}

	== Intervals of 30edt ==		== Intervals of 30edt ==
	{\| class="wikitable center-all"		{\| class="wikitable center-all right-2 right-3 left-4"
	\|-		\|-
	! rowspan="2" \| ~~Degrees~~		! rowspan="2" \| #
	! rowspan="2" \| Cents		! rowspan="2" \| Cents
	! rowspan="2" \| Hekts		! rowspan="2" \| Hekts
	! rowspan="2" \| Approximate ~~Ratios~~		! rowspan="2" \| Approximate ratios
	! colspan="2" \| Scale name		! colspan="2" \| Scale name
	\|-		\|-
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	\| 0		\| 0
	\| 0		\| 0
	\| ~~<span style="color: #660000;">~~[[1/1]]~~</span>~~		\| [[1/1]]
	\| colspan="2" \| C		\| colspan="2" \| C
	\|-		\|-
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	\| 63.3985		\| 63.3985
	\| 43.333		\| 43.333
	\| 28/27~~, 27/26~~		\| 27/26, 28/27
	\| C^/Dbv		\| C^/Dbv
	\| C#/Dbb		\| C#/Dbb
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	\| 126.797		\| 126.797
	\| 86.667		\| 86.667
	\| [[14/13]], [[15/14]], [[16/15]], 29/27		\| [[14/13]], [[15/14]], [[16/15]], [[29/27]]
	\| Db		\| Db
	\| Cx/Db		\| Cx/Db
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	\| 190.1955		\| 190.1955
	\| 130		\| 130
	\| 10/9~~~9/8~~		\| 9/8, 10/9
	\| C#		\| C#
	\| D		\| D
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	\| 380.391		\| 380.391
	\| 260		\| 260
	\| ~~<span style="color: #660000;">~~[[5/4]]~~</span>~~		\| [[5/4]]
	\| D^/Ev		\| D^/Ev
	\| E		\| E
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	\| 760.782		\| 760.782
	\| 520		\| 520
	\| ~~<span style="color: #660000;">~~[[14/9]]~~</span>~~		\| [[14/9]]
	\| F		\| F
	\| G#/Hbb		\| G#/Hbb
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	\| 1141.173		\| 1141.173
	\| 780		\| 780
	\| ~~<span style="color: #660000;">~~[[27/14]]~~</span>~~		\| [[27/14]]
	\| G#^/Hv		\| G#^/Hv
	\| J#/Kbb		\| J#/Kbb
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	\| 1394.767		\| 1394.767
	\| 953.333		\| 953.333
	\| [[9/4]] ~~([[9/8]] plus an octave)~~		\| [[9/4]]
	\| J^/Av		\| J^/Av
	\| L		\| L
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	\| 1521.564		\| 1521.564
	\| 1040		\| 1040
	\| [[12/5]] ~~(<span style="color: #660000;">[[6/5]]</span> plus an octave)~~		\| [[12/5]]
	\| A^/Bbv		\| A^/Bbv
	\| Lx/Ab		\| Lx/Ab
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	\| 1648.361		\| 1648.361
	\| 1126.667		\| 1126.667
	\| [[13/5]] ~~([[13/10]] plus an octave)~~		\| [[13/5]]
	\| A#		\| A#
	\| A#/Bbb		\| A#/Bbb
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	\| 1775.158		\| 1775.158
	\| 1213.333		\| 1213.333
	\| [[14/5]] ~~([[7/5]] plus an octave)~~		\| [[14/5]]
	\| B		\| B
	\|-		\|-
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	\|}		\|}

	30edt contains all [[19edo]] intervals within 3/1, all ~~temepered~~ progressively sharper. The accumulation of the 0.241{{c}} sharpening of the unit step relative to 19edo leads to the excellent 6edt approximations of 6/5 and 5/2. Non-redundantly with simpler edts, the 41 degree ~9/2 is only .6615{{c}} flatter than that in 6edo.		30edt contains all [[19edo]] intervals within 3/1, all tempered progressively sharper. The accumulation of the 0.241{{c}} sharpening of the unit step relative to 19edo leads to the excellent 6edt approximations of 6/5 and 5/2. Non-redundantly with simpler edts, the 41 degree ~9/2 is only .6615{{c}} flatter than that in 6edo.

	30edt also contains all the ~~MOS~~ contained in 15edt, being the double of this equal division. Being even, 30edt introduces ~~MOS~~ with an even number of periods per tritave such as a {{sl\|6L 6s}} similar to Hexe Dodecatonic. This ~~MOS~~ has a period of 1/6 of the tritave and the generator is a single or double step. The major scale is sLsLsLsLsLsL, and the minor scale is LsLsLsLsLsLs. Being a "real" 3/2, the interval of 11 degrees generates an unfair Sigma scale of {{sl\|8L 3s}} and the major scale is LLLsLLLsLLs. The sharp 9/7 of 7 degrees, in addition to generating a Lambda ~~MOS~~ will generate a {{sl\|4L 9s}} unfair "Superlambda" ~~MOS~~ which does not border on being atonal as the 17edt rendition does.		30edt also contains all the mos contained in [[15edt]], being the double of this equal division. Being even, 30edt introduces mos with an even number of periods per tritave such as a {{sl\|6L 6s}} similar to Hexe Dodecatonic. This mos has a period of 1/6 of the tritave and the generator is a single or double step. The major scale is sLsLsLsLsLsL, and the minor scale is LsLsLsLsLsLs. Being a "real" 3/2, the interval of 11 degrees generates an [[unfair]] [[Sigma]] scale of {{sl\|8L 3s}} and the major scale is LLLsLLLsLLs. The sharp 9/7 of 7 degrees, in addition to generating a Lambda mos will generate a {{sl\|4L 9s}} unfair "Superlambda" mos which does not border on being atonal as the 17edt rendition does.

	== Music ==		== Music ==
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	* [https://www.youtube.com/watch?v=fEQ13hzs3fY ''Fugue for Piano in 30EDT Bohlen-Pierce-Stearns{{lbrack}}9{{rbrack}} sLsLssLsL "Dur I"''] (2024)		* [https://www.youtube.com/watch?v=fEQ13hzs3fY ''Fugue for Piano in 30EDT Bohlen-Pierce-Stearns{{lbrack}}9{{rbrack}} sLsLssLsL "Dur I"''] (2024)

	~~[[Category:Edt]]~~
	[[Category:Listen]]		[[Category:Listen]]

← Older revision		Revision as of 14:56, 16 February 2025
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	! rowspan="2" \| #		! rowspan="2" \| #
	! rowspan="2" \| Cents		! rowspan="2" \| Cents
	! rowspan="2" \| ~~Hekts~~		! rowspan="2" \| [[Hekt]]s
	! rowspan="2" \| Approximate ratios		! rowspan="2" \| Approximate ratios
	! colspan="2" \| Scale name		! colspan="2" \| Scale name