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| Odd limit 2 = 13-limit 21 | Mistuning 2 = 26.3 | Complexity 2 = 17
| Odd limit 2 = 13-limit 21 | Mistuning 2 = 26.3 | Complexity 2 = 17
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'''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).
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).
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== Intervals ==
== Intervals ==
{| class="wikitable center-1 right-2"
In the following table, odd harmonics 1–13 are in '''bold'''.
 
{| class="wikitable center-1 right-2 center-3"
! #
! #
! Cents*
! Cents*
! Ratios
! Category
! Name
! Approximate ratios
|-
|-
| 0
| 0
| 0.0
| 0.0
| 1/1
| P1
| Perfect 1sn
| '''1/1'''
|-
|-
| 1
| 1
| 350.7
| 350.7
| 11/9, 16/13
| n3
| Neutral 3rd
| 11/9, '''16/13'''
|-
|-
| 2
| 2
| 701.3
| 701.3
| 3/2
| P5
| Perfect 5th
| '''3/2'''
|-
|-
| 3
| 3
| 1052.0
| 1052.0
| 20/11, 11/6, 24/13, 13/7
| n7
| Neutral 7th
| 11/6, 13/7, 20/11, 24/13
|-
|-
| 4
| 4
| 202.6
| 202.6
| 8/7, 9/8, 10/9
| M2
| Major 2nd
| '''8/7''', '''9/8''', 10/9
|-
|-
| 5
| 5
| 553.3
| 553.3
| 11/8, 18/13
| ½A4
| Semi-aug 4th
| '''11/8''', 18/13
|-
|-
| 6
| 6
| 903.9
| 903.9
| 5/3, 27/16, 22/13, 12/7
| M6
| Major 6th
| 5/3, 12/7, 22/13, 27/16
|-
|-
| 7
| 7
| 54.6
| 54.6
| 40/39, 33/32, 27/26, 22/21
| ½A1
| Semi-aug 1sn
| 22/21, 27/26, 33/32, 40/39
|-
|-
| 8
| 8
| 405.3
| 405.3
| 5/4, 9/7
| M3
| Major 3rd
| '''5/4''', 9/7
|-
|-
| 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
 
== Tunings ==
=== Norm-based tunings ===
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 11-limit norm-based tunings
|-
! rowspan="2" |
! colspan="3" | Euclidean
|-
! Constrained
! Constrained & skewed
! Destretched
|-
! Tenney
| CTE: ~11/9 = 349.8647{{c}}
| CWE: ~11/9 = 350.7031{{c}}
| POTE: ~11/9 = 350.9340{{c}}
|}
 
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 13-limit norm-based tunings
|-
! rowspan="2" |
! colspan="3" | Euclidean
|-
! Constrained
! Constrained & skewed
! Destretched
|-
! Tenney
| CTE: ~11/9 = 349.9044{{c}}
| CWE: ~11/9 = 350.6573{{c}}
| POTE: ~11/9 = 350.8162{{c}}
|}


== History ==
== Notes ==
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.
<references group="note"/>


[[Category:Neutrominant| ]] <!-- main article -->
[[Category:Neutrominant| ]] <!-- main article -->
[[Category:Dominant]]
[[Category:Dominant]]
Retrieved from "https://en.xen.wiki/w/Neutrominant"