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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{interwiki
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| en = Negri
: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2016-02-18 17:48:29 UTC</tt>.<br>
| de = Negri
: The original revision id was <tt>575224305</tt>.<br>
| es =
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<h4>Original Wikitext content:</h4>
{{Infobox regtemp
<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">See [[Marvel temperaments#Negri]].
| Title = Negri
| Subgroups = 2.3.5, 2.3.5.7, 2.3.5.7.13
| Comma basis = [[16875/16384]] (2.3.5);<br> [[49/48]], [[225/224]] (2.3.5.7);<br> [[49/48]], [[65/64]], [[91/90]] (2.3.5.7.13)
| Edo join 1 = 10 | Edo join 2 = 19
| Mapping = 1; -4 3 -2 -3
| Generators = 16/15 | Generators tuning = 125.4 | Optimization method = CWE
| MOS scales = [[1L 8s]], [[9L 1s]], [[10L 9s]]
| Pergen = (P8, P4/4)
| Color name = Laquadyoti
| Odd limit 1 = 7 | Mistuning 1 = 17.8 | Complexity 1 = 8
| Odd limit 2 = 2.3.5.7.13 15 | Mistuning 2 = 17.8 | Complexity 2 = 19
}}
'''Negri''' is a [[regular temperament]] generated by a [[generator]] of approximately 125 [[cent]]s, which can be identified with a tempered [[16/15]], such that:
* Two of them make a tempered [[7/6]]~[[8/7]]~[[15/13]];  
* Three of them make a tempered [[5/4]]~[[16/13]];  
* Four of them make a tempered [[4/3]].


[[https://soundcloud.com/sedumitr/la-multi-ani-19_edo|La Mulți Ani (negri[10], 19edo)]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Dumitrescu/__La_Mul_i_Ani__negri_10___19edo__by_Sebastian_Dumitrescu.mp3|play]] by Sebastian Dumitrescu
It is most naturally viewed as a [[2.3.5.7.13 subgroup|2.3.5.7.13-subgroup]] temperament, [[tempering out]] [[49/48]], [[65/64]] and [[91/90]]. This is sometimes called '''negra''', and it is realized consistently in [[19edo]] and [[29edo]]. Other [[edo]]s which may be usable as a negri or negra tuning include [[9edo]], [[10edo]], [[28edo]], [[47edo]], and [[48edo]], all of which are [[consistent]] through (at least) the [[5-odd-limit]], since in the broadest sense, negri is defined as tempering out the [[negri comma]] in the [[5-limit]].


[[https://soundcloud.com/gareth-hearne/negri-shmegri|Negri Shmegri]] [[http://micro.soonlabel.com/gene_ward_smith/Others/Hearne/Negri%20Shmegri.mp3|play]] by [[Gareth Hearne]] in Negri[9] symmetric mode, 19et tuning</pre></div>
The 7-limit version can also be viewed as joining with the [[marvel]] temperament family. See [[Semaphoresmic clan #Negri]] for technical data. For discussion on the various 11-limit extensions, see [[Negri extensions]].
<h4>Original HTML content:</h4>
 
<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;Negri&lt;/title&gt;&lt;/head&gt;&lt;body&gt;See &lt;a class="wiki_link" href="/Marvel%20temperaments#Negri"&gt;Marvel temperaments&lt;/a&gt;.&lt;br /&gt;
== Interval chain ==
&lt;br /&gt;
In the following table, odd harmonics and subharmonics 1–13 are in '''bold'''.
&lt;a class="wiki_link_ext" href="https://soundcloud.com/sedumitr/la-multi-ani-19_edo" rel="nofollow"&gt;La Mulți Ani (negri[10], 19edo)&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Dumitrescu/__La_Mul_i_Ani__negri_10___19edo__by_Sebastian_Dumitrescu.mp3" rel="nofollow"&gt;play&lt;/a&gt; by Sebastian Dumitrescu&lt;br /&gt;
 
&lt;br /&gt;
{| class="wikitable center-1 right-2"
&lt;a class="wiki_link_ext" href="https://soundcloud.com/gareth-hearne/negri-shmegri" rel="nofollow"&gt;Negri Shmegri&lt;/a&gt; &lt;a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Hearne/Negri%20Shmegri.mp3" rel="nofollow"&gt;play&lt;/a&gt; by &lt;a class="wiki_link" href="/Gareth%20Hearne"&gt;Gareth Hearne&lt;/a&gt; in Negri[9] symmetric mode, 19et tuning&lt;/body&gt;&lt;/html&gt;</pre></div>
|-
! #
! Cents*
! Approximate ratios
|-
| 0
| 0.0
| '''1/1'''
|-
| 1
| 125.4
| 13/12, 14/13, 15/14, 16/15
|-
| 2
| 250.7
| 7/6, '''8/7''', 15/13
|-
| 3
| 376.1
| '''5/4''', '''16/13'''
|-
| 4
| 501.4
| '''4/3'''
|-
| 5
| 626.8
| 10/7, 13/9
|-
| 6
| 752.1
| 14/9, 20/13, 32/21
|-
| 7
| 877.5
| 5/3
|-
| 8
| 1002.8
| '''16/9'''
|-
| 9
| 1128.2
| 35/18, 40/21, 52/27
|-
| 10
| 53.5
| 25/24, 28/27, 50/49, 64/63
|}
<nowiki/>* In 2.3.5.7.13-subgroup [[CWE tuning]]
 
== Scales ==
Negri forms 9-note and 10-note [[mos scale]]s, Negri[9] and Negri[10], at [[1L&nbsp;8s]] and [[9L&nbsp;1s]] respectively. In [[19edo]], the negri generator is the diatonic half-step of 2\19, which allows these mosses to be written fairly simply in conventional notation. For example, the ssssLssss mode of 19edo could be written as E F Gb G# A B C Db D# E. This mode is particularly useful as it has identical ssss pentachords (analogous to the [[tetrachord]]s of classical Greek music theory) on the 1/1 and 3/2. It is also notable in that a subset of these notes form the E double harmonic major scale, E F G# A B C D# E, which features in a wide variety of world musical traditions. In fact, all modes of Negri[9] and Negri[10] contain at least one mode of the double harmonic scale as a subset.
 
Another useful mode of Negri[9] is Lssssssss, which in 19edo would be A B C Db D# E F Gb G# A. This has a minor triad (A–C–E) for a tonic chord, which can be extended to a 7-limit utonal tetrad (A–C–E–Gb), as well as 7-limit otonal tetrads on E and F that can function as, respectively, a dominant seventh chord and a German augmented sixth chord. This scale also contains the popular Hungarian minor mode of the double harmonic scale, A B C D# E F G# A.
 
4 of the 9 modes of Negri[9] are like the Locrian mode of the diatonic major scale in that they do not have a note a perfect 5th above the tonic. These are more difficult to apply conventional music theory to. However even in these modes there are a number of chords built on the tonic that can provide a measure of consonance and stability, such as 13:16:20:24 and 6:7:8.
 
Negri[10] also has a number of useful features. One of these features is the fact that it makes 4:5:6 and 10:12:15 share the same "shape" of generic intervals in the scale (as in other rank-2 decatonic scales such as [[pajara]] and [[blackwood]] scales; this is because 5/4 and 6/5 get tempered to the same interval in [[10edo]]).
 
== History and terminology ==
Negri was named by [[Paul Erlich]] in 2001<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_31054.html#31065 Yahoo! Tuning Group | ''The grooviest linear temperaments for 7-limit music'']</ref> after John Negri's 10-out-of-19 maximally even scale<ref>"The Nineteen-Tone System as Ten Plus Nine". [https://interval.xentonic.org/tables-of-contents.html ''Interval, Journal of Music Research and Development''], pp. 11–13 of Volume 5, Number 3 (Winter 1986–1987). John Negri.</ref>. It used to be known by distinct names in the 5- and 7-limit as ''negripent'' and ''negrisept'', respectively (for more information on this, see [[Temperament names#Diminished and dimipent]]). It was also earlier known as "quadrafourths" and "tertiathirds".<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_3774#3780 Yahoo! Tuning Group | ''25 best weighted generator steps 5-limit temperaments''] – "I'm calling this tertiathirds (was quadrafourths)." —Dave Keenan</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_41392#41396 Yahoo! Tuning Group | ''! middle-path 7-limit tetradic scales for kalle''] – "Negri [is the new name for quadrafourths]." —Gene Ward Smith</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12957.html#12970 Yahoo! Tuning Group | ''98 named 7-limit temperaments''] – "[Negri] aka 'tertiathirds', 'negrisept' (MP)" —Herman Miller</ref>
 
== Tunings ==
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 7-limit norm-based tunings
|-
! rowspan="2" |
! colspan="3" | Euclidean
|-
! Constrained
! Constrained & skewed
! Destretched
|-
! Equilateral
| CEE: ~15/14 = 124.602{{c}}
| CSEE: ~15/14 = 125.284{{c}}
| POEE: ~15/14 = 125.468{{c}}
|-
! Tenney
| CTE: ~15/14 = 124.813{{c}}
| CWE: ~15/14 = 125.435{{c}}
| POTE: ~15/14 = 125.608{{c}}
|-
! Benedetti, <br>Wilson
| CBE: ~15/14 = 124.874{{c}}
| CSBE: ~15/14 = 125.429{{c}}
| POBE: ~15/14 = 125.629{{c}}
|}
 
{| class="wikitable mw-collapsible mw-collapsed"
|+ style="font-size: 105%; white-space: nowrap;" | 2.3.5.7.13-subgroup norm-based tunings
|-
! rowspan="2" |
! colspan="3" | Euclidean
|-
! Constrained
! Constrained & skewed
! Destretched
|-
! Equilateral
| CEE: ~14/13 = 123.471{{c}}
| CSEE: ~14/13 = 124.672{{c}}
| POEE: ~14/13 = 125.528{{c}}
|-
! Tenney
| CTE: ~14/13 = 124.457{{c}}
| CWE: ~14/13 = 125.354{{c}}
| POTE: ~14/13 = 125.567{{c}}
|-
! Benedetti, <br>Wilson
| CBE: ~14/13 = 124.756{{c}}
| CSBE: ~14/13 = 125.428{{c}}
| POBE: ~14/13 = 125.616{{c}}
|}
 
=== Tuning spectrum ===
{| class="wikitable center-all left-4"
|-
! Edo<br>generator
! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]]
! Generator (¢)
! Comments
|-
|
| 15/8
| 111.731
|
|-
|
| 7/4
| 115.587
|
|-
|
| 15/14
| 119.443
|
|-
|
| 13/8
| 119.824
|
|-
| 1\10
|
| 120.000
| Lower bound of 7-, 9-odd-limit, <br>and 2.3.5.7.13-subgroup 13-odd-limit diamond monotone
|-
|
| 7/5
| 123.498
|
|-
|
| 15/13
| 123.871
|
|-
| 3\29
|
| 124.138
|
|-
|
| 13/10
| 124.298
|
|-
|
| 3/2
| 124.511
| 7- and 9-odd-limit minimax
|-
| 5\48
|
| 125.000
| 48df val
|-
|
| 10/9
| 125.673
|
|-
| 2\19
|
| 126.316
| Upper bound of 9-odd-limit<br>and 2.3.5.7.13-subgroup 13-odd-limit diamond monotone
|-
|
| 5/3
| 126.337
| 5-odd-limit minimax
|-
|
| 13/9
| 127.324
|
|-
|
| 9/7
| 127.486
|
|-
| 5\47
|
| 127.660
| 47df val
|-
|
| 13/7
| 128.298
|
|-
| 3\28
|
| 128.571
| 28df val
|-
|
| 5/4
| 128.771
|
|-
| 1\9
|
| 133.333
| Upper bound of 7-odd-limit diamond monotone
|-
|
| 7/6
| 133.435
|
|-
|
| 13/12
| 138.573
|
|}
 
== See also ==
* [[Intervals of Negri-9]]
* [[Modes of Negri-9]]
 
== Music ==
; [[Mike Battaglia]]
* [https://youtu.be/bCLZChG6U6c ''Negri Comma Pump'']
 
; [[Sebastian Dumitrescu]]
* [https://soundcloud.com/sedumitr/la-multi-ani-19_edo ''La Mulți Ani''] ([http://micro.soonlabel.com/gene_ward_smith/Others/Dumitrescu/__La_Mul_i_Ani__negri_10___19edo__by_Sebastian_Dumitrescu.mp3 play]{{dead link}}) – Negri[10] in 19edo tuning
 
; [[Lillian Hearne]]
* [https://soundcloud.com/lillianhearne/negri-shmegri ''Negri Shmegri''] ([http://micro.soonlabel.com/gene_ward_smith/Others/Hearne/Negri%20Shmegri.mp3 play]{{dead link}}) – Negri[9] symmetric mode in 19edo
 
; [[Herman Miller]]
* [https://soundcloud.com/morphosyntax-1/without-a-clue ''Without a Clue''] (2024)
 
; [[Ray Perlner]]
* [https://www.youtube.com/playlist?list=PLkW9S8bpltfy3qYhWKO2vyloaMGiH4JtN ''Negri-9 Modal Fugues''] (YouTube playlist)
 
== References ==
<references/>
 
[[Category:Negri| ]] <!-- main article -->
[[Category:Rank-2 temperaments]]
[[Category:Semaphoresmic clan]]
[[Category:Marvel temperaments]]
[[Category:Avicennmic temperaments]]

Latest revision as of 22:05, 13 April 2026

Negri
Subgroups 2.3.5, 2.3.5.7, 2.3.5.7.13
Comma basis 16875/16384 (2.3.5);
49/48, 225/224 (2.3.5.7);
49/48, 65/64, 91/90 (2.3.5.7.13)
Reduced mapping ⟨1; -4 3 -2 -3]
ET join 10 & 19
Generators (CWE) ~16/15 = 125.4 ¢
MOS scales 1L 8s, 9L 1s, 10L 9s
Ploidacot omega-tetracot
Pergen (P8, P4/4)
Color name Laquadyoti
Minimax error 7-odd-limit: 17.8 ¢;
2.3.5.7.13 15-odd-limit: 17.8 ¢
Target scale size 7-odd-limit: 8 notes;
2.3.5.7.13 15-odd-limit: 19 notes

Negri is a regular temperament generated by a generator of approximately 125 cents, which can be identified with a tempered 16/15, such that:

  • Two of them make a tempered 7/6~8/7~15/13;
  • Three of them make a tempered 5/4~16/13;
  • Four of them make a tempered 4/3.

It is most naturally viewed as a 2.3.5.7.13-subgroup temperament, tempering out 49/48, 65/64 and 91/90. This is sometimes called negra, and it is realized consistently in 19edo and 29edo. Other edos which may be usable as a negri or negra tuning include 9edo, 10edo, 28edo, 47edo, and 48edo, all of which are consistent through (at least) the 5-odd-limit, since in the broadest sense, negri is defined as tempering out the negri comma in the 5-limit.

The 7-limit version can also be viewed as joining with the marvel temperament family. See Semaphoresmic clan #Negri for technical data. For discussion on the various 11-limit extensions, see Negri extensions.

Interval chain

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

# Cents* Approximate ratios
0 0.0 1/1
1 125.4 13/12, 14/13, 15/14, 16/15
2 250.7 7/6, 8/7, 15/13
3 376.1 5/4, 16/13
4 501.4 4/3
5 626.8 10/7, 13/9
6 752.1 14/9, 20/13, 32/21
7 877.5 5/3
8 1002.8 16/9
9 1128.2 35/18, 40/21, 52/27
10 53.5 25/24, 28/27, 50/49, 64/63

* In 2.3.5.7.13-subgroup CWE tuning

Scales

Negri forms 9-note and 10-note mos scales, Negri[9] and Negri[10], at 1L 8s and 9L 1s respectively. In 19edo, the negri generator is the diatonic half-step of 2\19, which allows these mosses to be written fairly simply in conventional notation. For example, the ssssLssss mode of 19edo could be written as E F Gb G# A B C Db D# E. This mode is particularly useful as it has identical ssss pentachords (analogous to the tetrachords of classical Greek music theory) on the 1/1 and 3/2. It is also notable in that a subset of these notes form the E double harmonic major scale, E F G# A B C D# E, which features in a wide variety of world musical traditions. In fact, all modes of Negri[9] and Negri[10] contain at least one mode of the double harmonic scale as a subset.

Another useful mode of Negri[9] is Lssssssss, which in 19edo would be A B C Db D# E F Gb G# A. This has a minor triad (A–C–E) for a tonic chord, which can be extended to a 7-limit utonal tetrad (A–C–E–Gb), as well as 7-limit otonal tetrads on E and F that can function as, respectively, a dominant seventh chord and a German augmented sixth chord. This scale also contains the popular Hungarian minor mode of the double harmonic scale, A B C D# E F G# A.

4 of the 9 modes of Negri[9] are like the Locrian mode of the diatonic major scale in that they do not have a note a perfect 5th above the tonic. These are more difficult to apply conventional music theory to. However even in these modes there are a number of chords built on the tonic that can provide a measure of consonance and stability, such as 13:16:20:24 and 6:7:8.

Negri[10] also has a number of useful features. One of these features is the fact that it makes 4:5:6 and 10:12:15 share the same "shape" of generic intervals in the scale (as in other rank-2 decatonic scales such as pajara and blackwood scales; this is because 5/4 and 6/5 get tempered to the same interval in 10edo).

History and terminology

Negri was named by Paul Erlich in 2001[1] after John Negri's 10-out-of-19 maximally even scale[2]. It used to be known by distinct names in the 5- and 7-limit as negripent and negrisept, respectively (for more information on this, see Temperament names#Diminished and dimipent). It was also earlier known as "quadrafourths" and "tertiathirds".[3][4][5]

Tunings

7-limit norm-based tunings
Euclidean
Constrained Constrained & skewed Destretched
Equilateral CEE: ~15/14 = 124.602 ¢ CSEE: ~15/14 = 125.284 ¢ POEE: ~15/14 = 125.468 ¢
Tenney CTE: ~15/14 = 124.813 ¢ CWE: ~15/14 = 125.435 ¢ POTE: ~15/14 = 125.608 ¢
Benedetti,
Wilson 		CBE: ~15/14 = 124.874 ¢ CSBE: ~15/14 = 125.429 ¢ POBE: ~15/14 = 125.629 ¢
2.3.5.7.13-subgroup norm-based tunings
Euclidean
Constrained Constrained & skewed Destretched
Equilateral CEE: ~14/13 = 123.471 ¢ CSEE: ~14/13 = 124.672 ¢ POEE: ~14/13 = 125.528 ¢
Tenney CTE: ~14/13 = 124.457 ¢ CWE: ~14/13 = 125.354 ¢ POTE: ~14/13 = 125.567 ¢
Benedetti,
Wilson 		CBE: ~14/13 = 124.756 ¢ CSBE: ~14/13 = 125.428 ¢ POBE: ~14/13 = 125.616 ¢

Tuning spectrum

Edo
generator 		Unchanged interval
(eigenmonzo) 		Generator (¢) Comments
15/8 111.731
7/4 115.587
15/14 119.443
13/8 119.824
1\10 120.000 Lower bound of 7-, 9-odd-limit,
and 2.3.5.7.13-subgroup 13-odd-limit diamond monotone
7/5 123.498
15/13 123.871
3\29 124.138
13/10 124.298
3/2 124.511 7- and 9-odd-limit minimax
5\48 125.000 48df val
10/9 125.673
2\19 126.316 Upper bound of 9-odd-limit
and 2.3.5.7.13-subgroup 13-odd-limit diamond monotone
5/3 126.337 5-odd-limit minimax
13/9 127.324
9/7 127.486
5\47 127.660 47df val
13/7 128.298
3\28 128.571 28df val
5/4 128.771
1\9 133.333 Upper bound of 7-odd-limit diamond monotone
7/6 133.435
13/12 138.573

See also

Music

Mike Battaglia
Sebastian Dumitrescu
Lillian Hearne
Herman Miller
Ray Perlner

References

  1. ↑ Yahoo! Tuning Group | The grooviest linear temperaments for 7-limit music
  2. ↑ "The Nineteen-Tone System as Ten Plus Nine". Interval, Journal of Music Research and Development, pp. 11–13 of Volume 5, Number 3 (Winter 1986–1987). John Negri.
  3. ↑ Yahoo! Tuning Group | 25 best weighted generator steps 5-limit temperaments – "I'm calling this tertiathirds (was quadrafourths)." —Dave Keenan
  4. ↑ Yahoo! Tuning Group | ! middle-path 7-limit tetradic scales for kalle – "Negri [is the new name for quadrafourths]." —Gene Ward Smith
  5. ↑ Yahoo! Tuning Group | 98 named 7-limit temperaments – "[Negri] aka 'tertiathirds', 'negrisept' (MP)" —Herman Miller
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