Neutrominant: Difference between revisions

Neutrominant
Subgroups	2.3.5.7.11, 2.3.5.7.11.13
Comma basis	36/35, 64/63, 121/120 (11-limit); ; 36/35, 64/63, 66/65, 121/120 (13-limit)
Reduced mapping	⟨1; 2 8 -4 5 -1]
ET join	17c & 24d
Generators (CWE)	~11/9 = 350.7 ¢
MOS scales	3L 4s, 7L 3s, 7L 10s
Ploidacot	dicot
Minimax error	11-odd-limit: 25.3 ¢; ; 13-limit 21-odd-limit: 26.3 ¢
Target scale size	11-odd-limit: 17 notes; ; 13-limit 21-odd-limit: 17 notes

← Older edit

VisualWikitext

Latest revision as of 08:46, 8 April 2026

Neutrominant (formerly maqamic^{[note 1]}) is a linear mimicry of maqam music within the 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 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).

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 is common to adaptively intone the minor seventh 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 considered 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.

It can be extended to the 13-limit by setting 16/13 to the neutral third and equating it with 11/9, tempering out 144/143.

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 quartertone flat of 9/5 (where the quartertone is the chroma for the 7-note mos), that would correspond to mohajira temperament.

See Rastmic clan #Neutrominant for more technical details.

Intervals

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

#	Cents*	Category	Approximate ratios
0	0.0	P1	1/1
1	350.7	n3	11/9, 16/13
2	701.3	P5	3/2
3	1052.0	n7	11/6, 13/7, 20/11, 24/13
4	202.6	M2	8/7, 9/8, 10/9
5	553.3	½A4	11/8, 18/13
6	903.9	M6	5/3, 12/7, 22/13, 27/16
7	54.6	½A1	22/21, 27/26, 33/32, 40/39
8	405.3	M3	5/4, 9/7
9	755.9	½A5	11/7, 20/13
10	1106.6	M7	15/8, 27/14
11	257.2	½A2	15/13
12	607.9	A4	10/7

* In 13-limit CWE tuning

Tunings

Norm-based tunings

11-limit norm-based tunings
	Euclidean
	Constrained	Constrained & skewed	Destretched
Tenney	CTE: ~11/9 = 349.8647 ¢	CWE: ~11/9 = 350.7031 ¢	POTE: ~11/9 = 350.9340 ¢

13-limit norm-based tunings
	Euclidean
	Constrained	Constrained & skewed	Destretched
Tenney	CTE: ~11/9 = 349.9044 ¢	CWE: ~11/9 = 350.6573 ¢	POTE: ~11/9 = 350.8162 ¢

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 was best viewed as an extension of neutral temperament.

[1] 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.

[note 1]

@@ Line 1: / Line 1: @@
-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+{{Interwiki|
-This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
+| en = Neutrominant
-: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2013-09-05 10:42:16 UTC</tt>.<br>
+| de = Neutrominant
-: The original revision id was <tt>448782362</tt>.<br>
+}}
-: The revision comment was: <tt></tt><br>
+{{Infobox regtemp
-The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
+| Title = Neutrominant
-<h4>Original Wikitext content:</h4>
+| Subgroups = 2.3.5.7.11, 2.3.5.7.11.13
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">&lt;span style="display: block; text-align: right;"&gt;Other languages: [[xenharmonie/maqamisch|Deutsch]]
+| Comma basis = [[36/35]], [[64/63]], [[121/120]] (11-limit); <br>[[36/35]], [[64/63]], [[66/65]], [[121/120]] (13-limit)
-&lt;/span&gt;
+| Edo join 1 = 17c | Edo join 2 = 24d
-[[Comma]]s: 81/80, 36/35, 121/120
+| Mapping = 1; 2 8 -4 5 -1
+| Generators = 11/9
+| Generators tuning = 350.7
+| Optimization method = CWE
+| MOS scales = [[3L 4s]], [[7L 3s]], [[7L 10s]]
+| Odd limit 1 = 11 | Mistuning 1 = 25.3 | Complexity 1 = 17
+| Odd limit 2 = 13-limit 21 | Mistuning 2 = 26.3 | Complexity 2 = 17
+}}
+'''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.
-Maqamic temperament is a linear mimicry of [[Arabic, Turkish, Persian|maqam music]] within the [[Regular Temperaments|regular mapping paradigm]], much as [[Pelogic family|pelogic temperament]] 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 24-equal into a higher-dimensional rank 2 temperament. If the maqamat are taken to be rank 2, they all end up being [[MODMOS Scales|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 {{w|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 is common to adaptively intone the minor seventh 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, [[17edo|17-equal]] and 24-equal support this temperament about as well as can be done, but it should be noted that this temperament was considered particularly with adaptive intonation in mind.
-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|mohajira]], maqamic tempers out 121/120 and 81/80; unlike it, it eliminates 36/35 (and hence 64/63) instead of 176/175. Harmonically, maqamic 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.
+It can be extended to the [[13-limit]] by setting [[16/13]] to the neutral third and equating it with 11/9, tempering out [[144/143]].
-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|Mohajira temperament]].
+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 quartertone flat of [[9/5]] (where the quartertone is the chroma for the 7-note mos), that would correspond to mohajira temperament.
-[[POTE tuning|POTE generator]]: 350.934
+See [[Rastmic clan #Neutrominant]] for more technical details.
-Map: [&lt;1 1 0 4 2|, &lt;0 2 8 -4 5|]
+== Intervals ==
-[[Generator]]s: 2, 11/9
+In the following table, odd harmonics 1–13 are in '''bold'''.
-EDOs: [[7edo|7]], [[10edo|10c]], [[17edo|17c]], [[24edo|24d]], [[31edo|31d]]
-==13-limit==
+{| class="wikitable center-1 right-2 center-3"
-The 13-limit version of this temperament eliminates 144/143 and hence 169/168 as well; this signifies that the generator could also be taken as (or intoned as) 16/13, and also that the 6/5's, which are also 7/6's, are evenly divided into two equal 13/12's.
+! #
+! Cents*
+! Category
+! Approximate ratios
+|-
+| 0
+| 0.0
+| P1
+| '''1/1'''
+|-
+| 1
+| 350.7
+| n3
+| 11/9, '''16/13'''
+|-
+| 2
+| 701.3
+| P5
+| '''3/2'''
+|-
+| 3
+| 1052.0
+| n7
+| 11/6, 13/7, 20/11, 24/13
+|-
+| 4
+| 202.6
+| M2
+| '''8/7''', '''9/8''', 10/9
+|-
+| 5
+| 553.3
+| ½A4
+| '''11/8''', 18/13
+|-
+| 6
+| 903.9
+| M6
+| 5/3, 12/7, 22/13, 27/16
+|-
+| 7
+| 54.6
+| ½A1
+| 22/21, 27/26, 33/32, 40/39
+|-
+| 8
+| 405.3
+| M3
+| '''5/4''', 9/7
+|-
+| 9
+| 755.9
+| ½A5
+| 11/7, 20/13
+|-
+| 10
+| 1106.6
+| M7
+| 15/8, 27/14
+|-
+| 11
+| 257.2
+| ½A2
+| 15/13
+|-
+| 12
+| 607.9
+| A4
+| 10/7
+|}
+<nowiki>*</nowiki> In 13-limit CWE tuning
-[[Comma]]s: 81/80, 36/35, 121/120, 144/143
+== 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}}
+|}
-[[POTE tuning|POTE generator]]: 350.816
+{| 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}}
+|}
-Map: [&lt;1 1 0 4 2 4|, &lt;0 2 8 -4 5 -1|]
+== Notes ==
-Generators: 2, 11/9
+<references group="note"/>
-EDOs: [[7edo|7]], [[10edo|10c]], [[17edo|17c]], [[24edo|24d]],[[31edo| 31d]]</pre></div>
-<h4>Original HTML content:</h4>
+[[Category:Neutrominant| ]] <!-- main article -->
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;maqamic&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;span style="display: block; text-align: right;"&gt;Other languages: &lt;a class="wiki_link" href="http://xenharmonie.wikispaces.com/maqamisch"&gt;Deutsch&lt;/a&gt;&lt;br /&gt;
+[[Category:Dominant]]
-&lt;/span&gt;&lt;br /&gt;
-&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 81/80, 36/35, 121/120&lt;br /&gt;
-&lt;br /&gt;
-Maqamic temperament is a linear mimicry of &lt;a class="wiki_link" href="/Arabic%2C%20Turkish%2C%20Persian"&gt;maqam music&lt;/a&gt; within the &lt;a class="wiki_link" href="/Regular%20Temperaments"&gt;regular mapping paradigm&lt;/a&gt;, much as &lt;a class="wiki_link" href="/Pelogic%20family"&gt;pelogic temperament&lt;/a&gt; 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.&lt;br /&gt;
-&lt;br /&gt;
-Melodically, it is a &amp;quot;linearized&amp;quot; version of the maqam modal system; it elevates the notion of &amp;quot;the diatonic scale with quartertones&amp;quot; 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 &lt;a class="wiki_link" href="/MODMOS%20Scales"&gt;MODMOS&lt;/a&gt;'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 &amp;quot;quarter-tone&amp;quot; chroma in this setup is exactly half of the usual chromatic semitone from 5L2s (regardless of how it's intonated).&lt;br /&gt;
-&lt;br /&gt;
-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.&lt;br /&gt;
-&lt;br /&gt;
-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 &amp;quot;middle of the road&amp;quot; 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.&lt;br /&gt;
-&lt;br /&gt;
-Like &lt;a class="wiki_link" href="/Mohajira"&gt;mohajira&lt;/a&gt;, maqamic tempers out 121/120 and 81/80; unlike it, it eliminates 36/35 (and hence 64/63) instead of 176/175. Harmonically, maqamic 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.&lt;br /&gt;
-&lt;br /&gt;
-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 &amp;quot;quarter tone&amp;quot; flat of 9/5 (where the quarter tone is the chroma for the 7-note MOS), that would correspond to &lt;a class="wiki_link" href="/Mohajira"&gt;Mohajira temperament&lt;/a&gt;.&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 350.934&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 1 0 4 2|, &amp;lt;0 2 8 -4 5|]&lt;br /&gt;
-&lt;a class="wiki_link" href="/Generator"&gt;Generator&lt;/a&gt;s: 2, 11/9&lt;br /&gt;
-EDOs: &lt;a class="wiki_link" href="/7edo"&gt;7&lt;/a&gt;, &lt;a class="wiki_link" href="/10edo"&gt;10c&lt;/a&gt;, &lt;a class="wiki_link" href="/17edo"&gt;17c&lt;/a&gt;, &lt;a class="wiki_link" href="/24edo"&gt;24d&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31d&lt;/a&gt;&lt;br /&gt;
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;13-limit&lt;/h2&gt;
- The 13-limit version of this temperament eliminates 144/143 and hence 169/168 as well; this signifies that the generator could also be taken as (or intoned as) 16/13, and also that the 6/5's, which are also 7/6's, are evenly divided into two equal 13/12's.&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 81/80, 36/35, 121/120, 144/143&lt;br /&gt;
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: 350.816&lt;br /&gt;
-&lt;br /&gt;
-Map: [&amp;lt;1 1 0 4 2 4|, &amp;lt;0 2 8 -4 5 -1|]&lt;br /&gt;
-Generators: 2, 11/9&lt;br /&gt;
-EDOs: &lt;a class="wiki_link" href="/7edo"&gt;7&lt;/a&gt;, &lt;a class="wiki_link" href="/10edo"&gt;10c&lt;/a&gt;, &lt;a class="wiki_link" href="/17edo"&gt;17c&lt;/a&gt;, &lt;a class="wiki_link" href="/24edo"&gt;24d&lt;/a&gt;,&lt;a class="wiki_link" href="/31edo"&gt; 31d&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>

Neutrominant: Difference between revisions

Latest revision as of 08:46, 8 April 2026

Contents

Intervals

Tunings

Norm-based tunings

Notes

Navigation menu

Neutrominant: Difference between revisions

Latest revision as of 08:46, 8 April 2026

Intervals

Tunings

Norm-based tunings

Notes

Navigation menu

Search