Xenharmonic Wiki

Negri: Difference between revisions

← Older edit
VisualWikitext
Xenwolf (talk | contribs)
autopatrolled, Bureaucrats, confirmaccount-notify, Interface administrators, Sysops
8,705 edits
m simplify link (this kind of simplification is the reason why page names should be in singular if possible)
Overthink (talk | contribs)
autopatrolled
2,672 edits
→Scales: correction
 
(47 intermediate revisions by 12 users not shown)
Line 1: Line 1:
{{interwiki
{{interwiki
| en = Negri
| de = Negri
| de = Negri
| en = Negri
| es =  
| es =  
| ja =  
| ja =  
}}
}}
{{See also|Marvel temperaments #Negri}}
{{Infobox regtemp
'''Negri''' is a temperament generated by a generator of approximately 125.7549 cents, which can be identified with a tempered [[16/15]], such that:
| Title = Negri
 
| Subgroups = 2.3.5, 2.3.5.7, 2.3.5.7.13
* Two of them make a tempered [[7/6]]~[[8/7]]~[[15/13]]
| 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)
* Three of them make a tempered [[5/4]]~[[16/13]]
| 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]].
* 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 called '''negra'''.  
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]].  


It is an important temperament which is most notable for being in [[19edo]], where it is generated by the "diatonic half step" of 2\19, but can also be found (albeit not very accurately) in [[9edo]] and [[10edo]].
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]].  


It forms 9-note MOS's at [[1L 8s]], with the mode ssssLssss being 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 , as well as 10-note MOS's at [[9L 1s]], which is also useful in 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 thing in [[10edo]]).
== Interval chain ==
 
In the following table, odd harmonics and subharmonics 1–13 are in '''bold'''.  
The 7-limit extension can also be viewed as joining with the [[Marvel temperaments #Negri|Marvel temperament family]]; the tuning information below is also located there. For the various 11-limit extensions, see [[negri extensions]].  


== Interval chain ==
{| class="wikitable center-1 right-2"
{| class="wikitable center-1 right-2"
|-
! #
! #
! Cents*
! Cents*
! Approximate Ratios
! Approximate ratios
|-
|-
| 0
| 0
| 0.0
| 0.0
| 1/1
| '''1/1'''
|-
|-
| 1
| 1
| 125.6
| 125.4
| 16/15, 15/14, 14/13, 13/12
| 13/12, 14/13, 15/14, 16/15
|-
|-
| 2
| 2
| 251.1
| 250.7
| 8/7, 7/6, 15/13
| 7/6, '''8/7''', 15/13
|-
|-
| 3
| 3
| 376.7
| 376.1
| 5/4, 16/13
| '''5/4''', '''16/13'''
|-
|-
| 4
| 4
| 502.3
| 501.4
| 4/3
| '''4/3'''
|-
|-
| 5
| 5
| 627.8
| 626.8
| 10/7, 13/9
| 10/7, 13/9
|-
|-
| 6
| 6
| 753.4
| 752.1
| 14/9, 32/21, 20/13
| 14/9, 20/13, 32/21
|-
|-
| 7
| 7
| 879.0
| 877.5
| 5/3
| 5/3
|-
|-
| 8
| 8
| 1004.5
| 1002.8
| 16/9
| '''16/9'''
|-
|-
| 9
| 9
| 1130.1
| 1128.2
| 35/18, 40/21, 52/27
| 35/18, 40/21, 52/27
|-
|-
| 10
| 10
| 55.7
| 53.5
| 25/24, 28/27, 50/49, 64/63
| 25/24, 28/27, 50/49, 64/63
|}
|}
<nowiki>*</nowiki> In 2.3.5.7.13 POTE tuning
<nowiki/>* In 2.3.5.7.13-subgroup [[CWE tuning]]


== Temperament data ==
== Scales ==
{{main| Marvel temperaments #Negri }}
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.


; 5-limit
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.


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
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.  
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">


Subgroup: 2.3.5
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]]).


[[Comma list]]: 16875/16384
== 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>


[[Mapping]]: [{{val| 1 2 2 }}, {{val| 0 -4 3 }}]
== 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}}
|}


[[Wedgie]]: {{wedgie| 4 -3 -14 }}
{| 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}}
|}


{{Val list|legend=1| 9, 10, 19, 67c, 86c, 105c }}
=== 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
|
|}


</div></div>
== See also ==
* [[Intervals of Negri-9]]
* [[Modes of Negri-9]]


; 7-limit
== Music ==
; [[Mike Battaglia]]
* [https://youtu.be/bCLZChG6U6c ''Negri Comma Pump'']


<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
; [[Sebastian Dumitrescu]]
<div style="line-height:1.6;">Technical data</div>
* [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
<div class="mw-collapsible-content">


Subgroup: 2.3.5.7
; [[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


[[Comma list]]: 49/48, 225/224
; [[Herman Miller]]
* [https://soundcloud.com/morphosyntax-1/without-a-clue ''Without a Clue''] (2024)


[[Mapping]]: [{{val| 1 2 2 3 }}, {{val| 0 -4 3 -2 }}]
; [[Ray Perlner]]
* [https://www.youtube.com/playlist?list=PLkW9S8bpltfy3qYhWKO2vyloaMGiH4JtN ''Negri-9 Modal Fugues''] (YouTube playlist)


[[Wedgie]]: {{wedgie| 4 -3 2 -14 -8 13 }}
== References ==
 
<references/>
{{Val list|legend=1| 9, 10, 19, 48d, 67cdd, 86cdd }}
 
</div></div>
 
; 2.3.5.7.13 (negra)
 
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;">
<div style="line-height:1.6;">Technical data</div>
<div class="mw-collapsible-content">
 
Subgroup: 2.3.5.7.13
 
[[Comma list]]: 49/48, 65/64, 91/90
 
[[Mapping]]: [{{val| 1 2 2 3 4 }}, {{val| 0 -4 3 -2 -3 }}]
 
Gencom map: [{{val| 1 2 2 3 0 4 }}, {{val| 0 -4 3 -2 0 -3 }}]
 
Gencom: [2 14/13; 49/48 65/64 91/90]
 
{{Val list|legend=1| 9, 10, 19, 48df, 67cddf, 86cddff }}
 
</div></div>
 
== Examples ==
 
* [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]]
* [https://soundcloud.com/gareth-hearne/negri-shmegri Negri Shmegri] {{dead link}} - [http://micro.soonlabel.com/gene_ward_smith/Others/Hearne/Negri%20Shmegri.mp3 play] by [[Gareth Hearne]] in Negri[9] symmetric mode, 19et tuning
* [https://youtu.be/bCLZChG6U6c Negri Comma Pump] played by [[Mike Battaglia]]
* [https://www.youtube.com/playlist?list=PLkW9S8bpltfy3qYhWKO2vyloaMGiH4JtN Negri-9 Modal Fugues] (YouTube playlist, 2 of 9 complete) by [[Ray Perlner]]


[[Category:Negri| ]] <!-- main article -->
[[Category:Rank-2 temperaments]]
[[Category:Semaphoresmic clan]]
[[Category:Marvel temperaments]]
[[Category:Marvel temperaments]]
[[Category:Negri| ]] <!-- main article -->
[[Category:Avicennmic temperaments]]
 
{{IoT}}
Retrieved from "https://en.xen.wiki/w/Negri"