Neutrominant - Revision history

FloraC: + tunings

2026-04-08T08:46:15Z

+ tunings

@@ Line 16: / Line 16: @@
 | Odd limit 2 = 13-limit 21 | Mistuning 2 = 26.3 | Complexity 2 = 17
 }}
-'''Neutrominant''' (formerly maqamic) is a linear mimicry of [[Middle-Eastern music|maqam music]] within the [[regular temperament|regular mapping paradigm]], much as [[pelogic]] is a linear mimicry of the gamelan pelog scale. It is the temperament that you get if you take, at face value, the simplest harmonic mapping consistent with the scalar structure of the maqamat. It deliberately ignores the issue of whether or not those dyads are resolved by the auditory system as such when played melodically (as maqam music is generally a melodic art form), intending instead to serve as a vehicle for the adventurous microtonalist who wants to explore a harmonic context for maqam music.
+'''Neutrominant''' (formerly maqamic<ref group="note">The temperament was originally named ''maqamic'' by [[Mike Battaglia]], who later commented "it was a dumb name". It was thus changed to ''neutrominant'' following a community decision, reasoning that it was best viewed as an extension of [[neutral]] temperament. </ref>) is a linear mimicry of [[Middle-Eastern music|maqam music]] within the [[regular temperament|regular mapping paradigm]], much as [[pelogic]] is a linear mimicry of the gamelan pelog scale. It is the temperament that you get if you take, at face value, the simplest harmonic mapping consistent with the scalar structure of the maqamat. It deliberately ignores the issue of whether or not those dyads are resolved by the auditory system as such when played melodically (as maqam music is generally a melodic art form), intending instead to serve as a vehicle for the adventurous microtonalist who wants to explore a harmonic context for maqam music.
 Melodically, it is a "linearized" version of the maqam modal system; it elevates the notion of "the diatonic scale with quartertones" out of the realm of [[24edo|24-equal]] into a higher-dimensional [[rank-2 temperament]]. If the maqamat are taken to be rank 2, they all end up being [[modmos]]'s of the proper [[3L 4s]] [[mos]]. This mos takes a neutral third as a [[generator]], and the usual [[5L 2s]] diatonic scale is itself a modmos. The [[quartertone]] [[chroma]] in this setup is exactly half of the usual [[chromatic semitone]] from 5L 2s (regardless of how it is intonated).
@@ Line 108: / Line 108: @@
 <nowiki>*</nowiki> In 13-limit CWE tuning
-== History ==
+== Tunings ==
-The temperament was originally named ''maqamic'' by [[Mike Battaglia]], who later commented "it was a dumb name". It was thus changed to ''neutrominant'' following a community decision, reasoning that it is best viewed as an extension of [[neutral]] temperament.
+=== Norm-based tunings ===
 [[Category:Neutrominant| ]] <!-- main article -->
 [[Category:Dominant]]

FloraC: /* Intervals */ adopt abbreviations for diatonic categories

2026-04-08T08:40:50Z

Intervals: adopt abbreviations for diatonic categories

← Older revision		Revision as of 08:40, 8 April 2026
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	In the following table, odd harmonics 1–13 are in '''bold'''.		In the following table, odd harmonics 1–13 are in '''bold'''.

	{\| class="wikitable center-1 right-2"		{\| class="wikitable center-1 right-2 center-3"
	! #		! #
	! Cents*		! Cents*
			! Category
	! Approximate ratios		! Approximate ratios
	~~! Name~~
	\|-		\|-
	\| 0		\| 0
	\| 0.0		\| 0.0
			\| P1
	\| '''1/1'''		\| '''1/1'''
	~~\| Perfect 1sn~~
	\|-		\|-
	\| 1		\| 1
	\| 350.7		\| 350.7
			\| n3
	\| 11/9, '''16/13'''		\| 11/9, '''16/13'''
	~~\| Neutral 3rd~~
	\|-		\|-
	\| 2		\| 2
	\| 701.3		\| 701.3
			\| P5
	\| '''3/2'''		\| '''3/2'''
	~~\| Perfect 5th~~
	\|-		\|-
	\| 3		\| 3
	\| 1052.0		\| 1052.0
			\| n7
	\| 11/6, 13/7, 20/11, 24/13		\| 11/6, 13/7, 20/11, 24/13
	~~\| Neutral 7th~~
	\|-		\|-
	\| 4		\| 4
	\| 202.6		\| 202.6
			\| M2
	\| '''8/7''', '''9/8''', 10/9		\| '''8/7''', '''9/8''', 10/9
	~~\| Major 2nd~~
	\|-		\|-
	\| 5		\| 5
	\| 553.3		\| 553.3
			\| ½A4
	\| '''11/8''', 18/13		\| '''11/8''', 18/13
	~~\| Semi-aug 4th~~
	\|-		\|-
	\| 6		\| 6
	\| 903.9		\| 903.9
			\| M6
	\| 5/3, 12/7, 22/13, 27/16		\| 5/3, 12/7, 22/13, 27/16
	~~\| Major 6th~~
	\|-		\|-
	\| 7		\| 7
	\| 54.6		\| 54.6
			\| ½A1
	\| 22/21, 27/26, 33/32, 40/39		\| 22/21, 27/26, 33/32, 40/39
	~~\| Semi-aug 1sn~~
	\|-		\|-
	\| 8		\| 8
	\| 405.3		\| 405.3
			\| M3
	\| '''5/4''', 9/7		\| '''5/4''', 9/7
	~~\| Major 3rd~~
	\|-		\|-
	\| 9		\| 9
	\| 755.9		\| 755.9
			\| ½A5
	\| 11/7, 20/13		\| 11/7, 20/13
	~~\| Semi-aug 5th~~
	\|-		\|-
	\| 10		\| 10
	\| 1106.6		\| 1106.6
			\| M7
	\| 15/8, 27/14		\| 15/8, 27/14
	~~\| Major 7th~~
	\|-		\|-
	\| 11		\| 11
	\| 257.2		\| 257.2
			\| ½A2
	\| 15/13		\| 15/13
	~~\| Semi-aug 2nd~~
	\|-		\|-
	\| 12		\| 12
	\| 607.9		\| 607.9
			\| A4
	\| 10/7		\| 10/7
	~~\| Aug 4th~~
	\|}		\|}
	<nowiki>*</nowiki> In 13-limit CWE tuning		<nowiki>*</nowiki> In 13-limit CWE tuning

FloraC: /* Intervals */ sort by complexity. + bold

2026-03-10T08:11:29Z

Intervals: sort by complexity. + bold

← Older revision		Revision as of 08:11, 10 March 2026
Line 33:		Line 33:

	== Intervals ==		== Intervals ==
			In the following table, odd harmonics 1–13 are in '''bold'''.

	{\| class="wikitable center-1 right-2"		{\| class="wikitable center-1 right-2"
	! #		! #
	! Cents*		! Cents*
	! ~~Ratios~~		! Approximate ratios
	! Name		! Name
	\|-		\|-
	\| 0		\| 0
	\| 0.0		\| 0.0
	\| 1/1		\| '''1/1'''
	\| Perfect 1sn		\| Perfect 1sn
	\|-		\|-
	\| 1		\| 1
	\| 350.7		\| 350.7
	\| 11/9, 16/13		\| 11/9, '''16/13'''
	\| Neutral 3rd		\| Neutral 3rd
	\|-		\|-
	\| 2		\| 2
	\| 701.3		\| 701.3
	\| 3/2		\| '''3/2'''
	\| Perfect 5th		\| Perfect 5th
	\|-		\|-
	\| 3		\| 3
	\| 1052.0		\| 1052.0
	\| 20/11~~, 11/6~~, 24/13~~, 13/7~~		\| 11/6, 13/7, 20/11, 24/13
	\| Neutral 7th		\| Neutral 7th
	\|-		\|-
	\| 4		\| 4
	\| 202.6		\| 202.6
	\| 8/7, 9/8, 10/9		\| '''8/7''', '''9/8''', 10/9
	\| Major 2nd		\| Major 2nd
	\|-		\|-
	\| 5		\| 5
	\| 553.3		\| 553.3
	\| 11/8, 18/13		\| '''11/8''', 18/13
	\| Semi-aug 4th		\| Semi-aug 4th
	\|-		\|-
	\| 6		\| 6
	\| 903.9		\| 903.9
	\| 5/3, 27/16, 22/13, 12/7		\| 5/3, 12/7, 22/13, 27/16
	\| Major 6th		\| Major 6th
	\|-		\|-
	\| 7		\| 7
	\| 54.6		\| 54.6
	\| 40/39, 33/32, 27/~~26, 22/21~~		\| 22/21, 27/26, 33/32, 40/39
	\| Semi-aug 1sn		\| Semi-aug 1sn
	\|-		\|-
	\| 8		\| 8
	\| 405.3		\| 405.3
	\| 5/4, 9/7		\| '''5/4''', 9/7
	\| Major 3rd		\| Major 3rd
	\|-		\|-
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	\| Aug 4th		\| Aug 4th
	\|}		\|}
	<nowiki>*</nowiki>In 13-limit CWE tuning		<nowiki>*</nowiki> In 13-limit CWE tuning

	== History ==		== History ==

FloraC: + infobox. Style

2026-03-10T08:05:27Z

+ infobox. Style

Show changes

FloraC: Recategorize (dominant extension)

2026-03-10T07:39:20Z

Recategorize (dominant extension)

← Older revision		Revision as of 07:39, 10 March 2026
Line 99:		Line 99:
	[[Category:Neutrominant\| ]] <!-- main article -->		[[Category:Neutrominant\| ]] <!-- main article -->
	[[Category:Dominant]]		[[Category:Dominant]]
	~~[[Category:Rank-2 temperaments]]~~
	~~[[Category:Meantone family]]~~
	~~[[Category:Archytas clan]]~~
	~~[[Category:Mint temperaments]]~~

Overthink: /* Intervals */ added more for 7 gens

2025-10-09T22:10:33Z

Intervals: added more for 7 gens

← Older revision		Revision as of 22:10, 9 October 2025
Line 64:		Line 64:
	\|7		\|7
	\|54.6		\|54.6
	\|33/32		\|40/39, 33/32, 27/26, 22/21
	\|Semi-aug 1sn		\|Semi-aug 1sn
	\|-		\|-

Overthink: /* Intervals */ added a few more ratios

2025-10-09T17:08:39Z

Intervals: added a few more ratios

← Older revision		Revision as of 17:08, 9 October 2025
Line 49:		Line 49:
	\|4		\|4
	\|202.6		\|202.6
	\|9/8		\|8/7, 9/8, 10/9
	\|Major 2nd		\|Major 2nd
	\|-		\|-
Line 59:		Line 59:
	\|6		\|6
	\|903.9		\|903.9
	\|27/16, 22/13		\|5/3, 27/16, 22/13, 12/7
	\|Major 6th		\|Major 6th
	\|-		\|-

Overthink: added ratios

2025-10-09T17:07:36Z

added ratios

← Older revision		Revision as of 17:07, 9 October 2025
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	\|0		\|0
	\|0.0		\|0.0
	\|		\|1/1
	\|Perfect 1sn		\|Perfect 1sn
	\|-		\|-
	\|1		\|1
	\|350.7		\|350.7
	\|		\|11/9, 16/13
	\|Neutral 3rd		\|Neutral 3rd
	\|-		\|-
	\|2		\|2
	\|701.3		\|701.3
	\|		\|3/2
	\|Perfect 5th		\|Perfect 5th
	\|-		\|-
	\|3		\|3
	\|1052.0		\|1052.0
	\|		\|20/11, 11/6, 24/13, 13/7
	\|Neutral 7th		\|Neutral 7th
	\|-		\|-
	\|4		\|4
	\|202.6		\|202.6
	\|		\|9/8
	\|Major 2nd		\|Major 2nd
	\|-		\|-
	\|5		\|5
	\|553.3		\|553.3
	\|		\|11/8, 18/13
	\|Semi-aug 4th		\|Semi-aug 4th
	\|-		\|-
	\|6		\|6
	\|903.9		\|903.9
	\|		\|27/16, 22/13
	\|Major 6th		\|Major 6th
	\|-		\|-
	\|7		\|7
	\|54.6		\|54.6
	\|		\|33/32
	\|Semi-aug 1sn		\|Semi-aug 1sn
	\|-		\|-
	\|8		\|8
	\|405.3		\|405.3
	\|		\|5/4, 9/7
	\|Major 3rd		\|Major 3rd
	\|-		\|-
	\|9		\|9
	\|755.9		\|755.9
	\|		\|11/7, 20/13
	\|Semi-aug 5th		\|Semi-aug 5th
	\|-		\|-
	\|10		\|10
	\|1106.6		\|1106.6
	\|		\|15/8, 27/14
	\|Major 7th		\|Major 7th
	\|-		\|-
	\|11		\|11
	\|257.2		\|257.2
	\|		\|15/13
	\|Semi-aug 2nd		\|Semi-aug 2nd
	\|-		\|-
	\|12		\|12
	\|607.9		\|607.9
	\|		\|10/7
	\|Aug 4th		\|Aug 4th
	\|}		\|}

Overthink at 06:57, 9 October 2025

2025-10-09T06:57:54Z

@@ Line 7: / Line 7: @@
 Melodically, it is a "linearized" version of the maqam modal system; it elevates the notion of "the diatonic scale with quartertones" out of the realm of 24-equal into a higher-dimensional rank 2 temperament. If the maqamat are taken to be rank 2, they all end up being [[MODMOS]]'s of the proper 3L4s MOS. This MOS takes a neutral third as a generator, and the usual 5L2s diatonic scale is itself a MODMOS. The "quarter-tone" chroma in this setup is exactly half of the usual chromatic semitone from 5L2s (regardless of how it's intonated).
-Harmonically, intervals in this temperament are mapped to reflect some of the intonational choices that actual Arabic maqam musicians make when playing maqam music on a fretless instrument such as an oud. Sometimes notes that share the same notational representation are intoned very differently under different circumstances; for example, while the fourths are generally intoned very close to 4/3, it's common to adaptively intone the minor 7th closer to 7/4. When this happens, the two notes are said to share a tempered equivalence class, and the comma between the two versions of the note is said to vanish, no matter how large it is. Real-life intonational differences existing within these equivalence classes can then be viewed as a form of adaptive intonation within this temperament, paralleling how western string quartets will often intone their major chords to be as close to 4:5:6 as possible, despite that 81/80 vanishes over the larger structure of the music.
+Harmonically, intervals in this temperament are mapped to reflect some of the intonational choices that actual Arabic maqam musicians make when playing maqam music on a fretless instrument such as an oud. Sometimes notes that share the same notational representation are intoned very differently under different circumstances; for example, while the fourths are generally intoned very close to [[4/3]], it's common to adaptively intone the minor 7th closer to [[7/4]]. When this happens, the two notes are said to share a tempered equivalence class, and the comma between the two versions of the note is said to vanish, no matter how large it is. Real-life intonational differences existing within these equivalence classes can then be viewed as a form of adaptive intonation within this temperament, paralleling how western string quartets will often intone their major chords to be as close to [[4:5:6]] as possible, despite that [[81/80]] vanishes over the larger structure of the music.
 This temperament will hence appear less accurate than it really is, due to the fact that it approximates the performance of highly adaptive fretless instruments, and equivalence classes should be understood as reflecting a cognitive grouping of intervals rather than demanding any particular "middle of the road" intonational ideal. For fixed pitch instruments, 17-equal and 24-equal support this temperament about as well as can be done, but it should be noted that this temperament was designed particularly with adaptive intonation in mind.
-Like [[mohajira]], neutrominant tempers out 121/120 and 81/80; unlike it, it eliminates 36/35 (and hence 64/63) instead of 176/175. Harmonically, neutrominant temperament maps two whole tones to 5/4, which is an intonational choice sometimes made by actual Arabic maqam performers, and which indicates that 81/80 vanishes. It also maps two fourths to 7/4, which is likewise an intonational choice often made by maqam performers, although they tend to do this adaptively rather than optimizing their 4/3's around this ideal. Finally, we find the simplest harmonic intervals approximating the neutral second and neutral third, which are 11/10 and 11/9. These, when doubled, yield 6/5 and 3/2, respectively, thus indicating that 121/120 and 243/242 vanish in this tuning.
+Like [[mohajira]], neutrominant tempers out [[121/120]] and 81/80; unlike it, it eliminates [[36/35]] (and hence [[64/63]]) instead of 176/175. Harmonically, neutrominant temperament maps two whole tones to 5/4, which is an intonational choice sometimes made by actual Arabic maqam performers, and which indicates that 81/80 vanishes. It also maps two fourths to 7/4, which is likewise an intonational choice often made by maqam performers, although they tend to do this adaptively rather than optimizing their 4/3's around this ideal. Finally, we find the simplest harmonic intervals approximating the neutral second and neutral third, which are 11/10 and 11/9. These, when doubled, yield 6/5 and 3/2, respectively, thus indicating that 121/120 and [[243/242]] vanish in this tuning.
 Other attempts to mimic the structure of maqam music within the regular mapping paradigm may exist; this temperament is meant to be the simplest harmonic template possible that is consistent with the scalar structure of maqam music. For example, if one wanted to consider the two neutral thirds and neutral seconds as being different sizes, that would correspond to some sort of rank-3 temperament, and if one wanted to consider the 7/4 as being a "quarter tone" flat of 9/5 (where the quarter tone is the chroma for the 7-note MOS), that would correspond to mohajira temperament.
 See [[Rastmic clan #Neutrominant]] for more technical details.
 == History ==

FloraC: - parent category

2025-04-28T14:28:06Z

- parent category

← Older revision		Revision as of 14:28, 28 April 2025
Line 20:		Line 20:
	The temperament was originally named ''maqamic'' by [[Mike Battaglia]], who later commented "it was a dumb name". It was thus changed to ''neutrominant'' following a community decision, reasoning that it is best viewed as an extension of [[neutral]] temperament.		The temperament was originally named ''maqamic'' by [[Mike Battaglia]], who later commented "it was a dumb name". It was thus changed to ''neutrominant'' following a community decision, reasoning that it is best viewed as an extension of [[neutral]] temperament.

	[[Category:~~Temperaments~~]]		[[Category:Neutrominant\| ]] <!-- main article -->
			[[Category:Dominant]]
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	[[Category:Meantone family]]		[[Category:Meantone family]]
	[[Category:Archytas clan]]		[[Category:Archytas clan]]
	[[Category:Mint temperaments]]		[[Category:Mint temperaments]]
	~~[[Category:Dominant]]~~
	~~[[Category:Neutrominant\| ]] <!-- main article -->~~