Negri: Difference between revisions

* Two of them make a tempered [[7/6]]~[[8/7]]~[[15/13]];

* Three of them make a tempered [[5/4]]~[[16/13]];

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]].  

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]].  

| 13/12, 14/13, 15/14, 16/15

| 7/6, '''8/7''', 15/13

| 14/9, 20/13, 32/21

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>

|+ style="font-size: 105%; white-space: nowrap;" | 7-limit norm-based tunings

! rowspan="2" |  

! colspan="3" | Euclidean

! Equilateral

| CEE: ~15/14 = 124.602{{c}}

| CSEE: ~15/14 = 125.284{{c}}

| POEE: ~15/14 = 125.468{{c}}

| 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}}

|+ style="font-size: 105%; white-space: nowrap;" | 2.3.5.7.13-subgroup norm-based tunings

! rowspan="2" |

! colspan="3" | Euclidean

| CEE: ~14/13 = 123.471{{c}}

| CSEE: ~14/13 = 124.672{{c}}

| POEE: ~14/13 = 125.528{{c}}

| CTE: ~14/13 = 124.457{{c}}

| CWE: ~14/13 = 125.354{{c}}

| POTE: ~14/13 = 125.567{{c}}

| CBE: ~14/13 = 124.756{{c}}

| CSBE: ~14/13 = 125.428{{c}}

| POBE: ~14/13 = 125.616{{c}}

! [[Eigenmonzo|Unchanged interval<br>(eigenmonzo)]]

* [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

* [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

* [https://soundcloud.com/morphosyntax-1/without-a-clue ''Without a Clue''] (2024)

== References ==