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Negri: Difference between revisions

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| 1
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| 125.4
| 125.4
| 16/15, 15/14, 14/13, 13/12
| 13/12, 14/13, 15/14, 16/15
|-
|-
| 2
| 2
| 250.7
| 250.7
| '''8/7''', 7/6, 15/13
| 7/6, '''8/7''', 15/13
|-
|-
| 3
| 3
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| 6
| 6
| 752.1
| 752.1
| 14/9, 32/21, 20/13
| 14/9, 20/13, 32/21
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|-
| 7
| 7
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== History and terminology ==
== 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".
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>
<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 ==
== Tunings ==
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|+ style="font-size: 105%; white-space: nowrap;" | 7-limit prime-optimized tunings
|+ style="font-size: 105%; white-space: nowrap;" | 7-limit prime-optimized tunings
|-
|-
! Weight-skew\order !! Euclidean
! rowspan="2" |
! colspan="2" | Euclidean
|-
|-
| Tenney || CTE: ~14/13 = 124.8134¢
! Unskewed
! Skewed
|-
|-
| Weil || CWE: ~14/13 = 125.4347¢
! Equilateral
| CEE: ~15/14 = 124.602¢
| CSEE: ~15/14 = 125.284¢
|-
|-
| Equilateral || CEE: ~14/13 = 124.6024¢
! Tenney
| CTE: ~15/14 = 124.813¢
| CWE: ~15/14 = 125.435¢
|-
|-
| Skewed-equilateral || CSEE: ~14/13 = 125.2840¢
! Benedetti, <br>Wilson
|-
| CBE: ~15/14 = 124.874¢
| Benedetti/Wilson || CBE: ~14/13 = 124.8740¢
| CSBE: ~15/14 = 125.429¢
|-
| Skewed-Benedetti/Wilson || CSBE: ~14/13 = 125.4287¢
|}
|}


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|+ style="font-size: 105%; white-space: nowrap;" | 2.3.5.7.13-subgroup prime-optimized tunings
|+ style="font-size: 105%; white-space: nowrap;" | 2.3.5.7.13-subgroup prime-optimized tunings
|-
|-
! Weight-skew\order !! Euclidean
! rowspan="2" |  
|-
! colspan="2" | Euclidean
| Tenney || CTE: ~14/13 = 124.4571¢
|-
| Weil || CWE: ~14/13 = 125.3543¢
|-
|-
| Equilateral || CEE: ~14/13 = 123.4707¢
! Unskewed
! Skewed
|-
|-
| Skewed-equilateral || CSEE: ~14/13 = 124.6721¢
! Equilateral
| CEE: ~14/13 = 123.471¢
| CSEE: ~14/13 = 124.672¢
|-
|-
| Benedetti/Wilson || CBE: ~14/13 = 124.7557¢
! Tenney
| CTE: ~14/13 = 124.457¢
| CWE: ~14/13 = 125.354¢
|-
|-
| Skewed-Benedetti/Wilson || CSBE: ~14/13 = 125.4278¢
! Benedetti, <br>Wilson
| CBE: ~14/13 = 124.756¢
| CSBE: ~14/13 = 125.428¢
|}
|}


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