Carlos Alpha - Revision history

Inthar at 00:58, 25 February 2026

2026-02-25T00:58:35Z

← Older revision		Revision as of 00:58, 25 February 2026
Line 1:		Line 1:
	'''Carlos Alpha''' is a tuning system conceptualized as a chain of steps between a [[15edo]] and [[16edo]] semitone in size, which reach a [[Perfect fifth\|fifth]] after nine steps, [[5/4]] after five steps, and [[8/7]] after three steps. Originally, Carlos Alpha was conceptualized as multiple of these chains offset by [[Octave\|octaves]], but is also often used as a [[non-octave tuning system]].		'''Carlos Alpha''' is a tuning system conceptualized as a chain of steps between a [[15edo]] and [[16edo]] semitone in size, which reach a [[Perfect fifth\|fifth]] after nine steps, [[5/4]] after five steps, and [[8/7]] after three steps. Originally, Carlos Alpha was conceptualized as multiple of these chains offset by [[Octave\|octaves]], but is also often used as a [[non-octave tuning system]].

	In regular temperament theory, Carlos Alpha corresponds to the '''~~valentine~~''' temperament, which has an octave as a period and a semitone of about 78 cents as a generator. It also easily admits an extension to the 2.3.5.7.11.17.23 subgroup to a high degree of accuracy.		In regular temperament theory, Carlos Alpha corresponds to the '''Valentine''' temperament, which has an octave as a period and a semitone of about 78 cents as a generator. It also easily admits an extension to the 2.3.5.7.11.17.23 subgroup to a high degree of accuracy.

	It can be seen as equalizing the steps between 20:21:22:23:24:25, which suggests a perhaps somewhat inaccurate extension to the full 23-limit which equalizes 19:20:21:22:23:24:25:26; this is the most accurately tuned around 31edo. Valentine tempers out the [[Slendric\|gamelisma]] and can thus be seen as an extension splitting each step of [[~~slendric~~]] into three parts. In this way, it is a counterpart to [[~~miracle~~]], which splits the ~~slendric~~ generator into two parts.		It can be seen as equalizing the steps between 20:21:22:23:24:25, which suggests a perhaps somewhat inaccurate extension to the full 23-limit which equalizes 19:20:21:22:23:24:25:26; this is the most accurately tuned around 31edo. Valentine tempers out the [[Slendric\|gamelisma]] and can thus be seen as an extension splitting each step of [[Slendric]] into three parts. In this way, it is a counterpart to [[Miracle]], which splits the Slendric generator into two parts.

	{\| class="wikitable"		{\| class="wikitable"

Vector at 11:34, 22 February 2026

2026-02-22T11:34:00Z

← Older revision		Revision as of 11:34, 22 February 2026
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	''Note: Due to a bug with the template, the step counts are octave-reduced instead of'' ''fifth-reduced.''		''Note: Due to a bug with the template, the step counts are octave-reduced instead of'' ''fifth-reduced.''

	{{Navbox EDO}}		{{Navbox EDO}}{{Navbox regtemp}}

Vector at 04:17, 22 February 2026

2026-02-22T04:17:09Z

← Older revision		Revision as of 04:17, 22 February 2026
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	\|}		\|}
	As a non-octave temperament, it is essentially 9edf, in which case the second column of this table can be ignored and an in-tune 4/1 may be found at 31 generators up; 9edf can be seen as a 4.3.5.(8/7).11 temperament.		As a non-octave temperament, it is essentially 9edf, in which case the second column of this table can be ignored and an in-tune 4/1 may be found at 31 generators up; 9edf can be seen as a 4.3.5.(8/7).11 temperament.

			{{Harmonics in ED\|15.3856\|31\|0}}

			''Note: Due to a bug with the template, the step counts are octave-reduced instead of'' ''fifth-reduced.''

			{{Navbox EDO}}

Lériendil at 20:43, 21 January 2026

2026-01-21T20:43:02Z

← Older revision		Revision as of 20:43, 21 January 2026
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	In regular temperament theory, Carlos Alpha corresponds to the '''valentine''' temperament, which has an octave as a period and a semitone of about 78 cents as a generator. It also easily admits an extension to the 2.3.5.7.11.17.23 subgroup to a high degree of accuracy.		In regular temperament theory, Carlos Alpha corresponds to the '''valentine''' temperament, which has an octave as a period and a semitone of about 78 cents as a generator. It also easily admits an extension to the 2.3.5.7.11.17.23 subgroup to a high degree of accuracy.

	It can be seen as equalizing the steps between 20:21:22:23:24:25, which suggests a perhaps somewhat inaccurate extension to the full 23-limit which equalizes 19:20:21:22:23:24:25:26; this is the most accurately tuned around 31edo. Valentine tempers out the [[Slendric\|~~slendrisma~~]] and can thus be seen as an extension splitting each step of [[slendric]] into three parts. In this way, it is a counterpart to [[miracle]], which splits the slendric generator into two parts.		It can be seen as equalizing the steps between 20:21:22:23:24:25, which suggests a perhaps somewhat inaccurate extension to the full 23-limit which equalizes 19:20:21:22:23:24:25:26; this is the most accurately tuned around 31edo. Valentine tempers out the [[Slendric\|gamelisma]] and can thus be seen as an extension splitting each step of [[slendric]] into three parts. In this way, it is a counterpart to [[miracle]], which splits the slendric generator into two parts.

	{\| class="wikitable"		{\| class="wikitable"

Vector: Created page with "'''Carlos Alpha''' is a tuning system conceptualized as a chain of steps between a 15edo and 16edo semitone in size, which reach a fifth after nine steps, 5/4 after five steps, and 8/7 after three steps. Originally, Carlos Alpha was conceptualized as multiple of these chains offset by octaves, but is also often used as a non-octave tuning system. In regular temperament theory, Carlos Alpha corresponds to the '''valentine'..."

2026-01-21T00:55:19Z

Created page with "'''Carlos Alpha''' is a tuning system conceptualized as a chain of steps between a 15edo and 16edo semitone in size, which reach a fifth after nine steps, 5/4 after five steps, and 8/7 after three steps. Originally, Carlos Alpha was conceptualized as multiple of these chains offset by octaves, but is also often used as a non-octave tuning system. In regular temperament theory, Carlos Alpha corresponds to the '''valentine'..."

New page

'''Carlos Alpha''' is a tuning system conceptualized as a chain of steps between a [[15edo]] and [[16edo]] semitone in size, which reach a [[Perfect fifth|fifth]] after nine steps, [[5/4]] after five steps, and [[8/7]] after three steps. Originally, Carlos Alpha was conceptualized as multiple of these chains offset by [[Octave|octaves]], but is also often used as a [[non-octave tuning system]].

In regular temperament theory, Carlos Alpha corresponds to the '''valentine''' temperament, which has an octave as a period and a semitone of about 78 cents as a generator. It also easily admits an extension to the 2.3.5.7.11.17.23 subgroup to a high degree of accuracy.

It can be seen as equalizing the steps between 20:21:22:23:24:25, which suggests a perhaps somewhat inaccurate extension to the full 23-limit which equalizes 19:20:21:22:23:24:25:26; this is the most accurately tuned around 31edo. Valentine tempers out the [[Slendric|slendrisma]] and can thus be seen as an extension splitting each step of [[slendric]] into three parts. In this way, it is a counterpart to [[miracle]], which splits the slendric generator into two parts.

{| class="wikitable"
|+Intervals of Carlos Alpha
!Note
!Up from the unison
!Interpretation
!Down from the octave
!Interpretation
|-
|0
|0c
|1/1
|1200c
|2/1
|-
|1
|78c
|21/20, 25/24
|1122c
|48/25, 40/21
|-
|2
|156c
|11/10, 12/11
|1044c
|20/11, 11/6
|-
|3
|234c
|8/7
|966c
|7/4
|-
|4
|312c
|6/5
|888c
|5/3
|-
|5
|390c
|5/4
|810c
|8/5
|-
|6
|468c
|21/16
|732c
|32/21
|-
|7
|546c
|11/8
|654c
|16/11
|-
|8
|624c
|23/16
|576c
|32/23
|-
|9
|702c
|3/2
|498c
|4/3
|-
|10
|780c
|11/7
|420c
|14/11
|-
|11
|858c
|18/11
|342c
|11/9
|-
|12
|936c
|12/7
|264c
|7/6
|-
|13
|1014c
|9/5
|186c
|10/9
|-
|14
|1092c
|15/8, 32/17
|108c
|16/15, 17/16
|-
|15
|1170c
|96/49
|30c
|49/48
|}
As a non-octave temperament, it is essentially 9edf, in which case the second column of this table can be ignored and an in-tune 4/1 may be found at 31 generators up; 9edf can be seen as a 4.3.5.(8/7).11 temperament.