Chromatic pairs: Difference between revisions

{{Redirect|Terrain|the scale|Terrain (scale)}}

 

 

 

 

 

 

 

 

 

* [[terrain9]] – 9-tone albitonic scale

* [[terrain15]] – 15-tone chromatic scale

 

 

 

{{Mapping|legend=2| 1 0 1| 0 3 1 }}

 

 

 

 

 

* [[petrtri5]] – 5-tone haplotonic scale

* [[petrtri8]] – 8-tone albitonic scale

* [[petrtri13]] – 13-tone chromatic scale

Barton may be described as the 11 &amp; 13 temperament in the 2.5.11.13 subgroup. It was named after [[Jacob Barton]] by [[Gene Ward Smith]] and [[Carl Lumma]] in 2006<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_14632.html Yahoo! Tuning Group | "father" variant?]</ref>.

 

 

 

{{Mapping|legend=2| 1 6 3 6 | 0 -8 1 -5 }}

 

{{Mapping|legend=3| 1 0 6 0 3 6 | 0 0 -8 0 1 -5 }}

 

 

 

{{Optimal ET sequence|legend=1| 11, 13, 24, 37, 50, 87, 298, 385, 472, 559, 1590cd }}

 

 

 

 

{{Mapping|legend=2| 1 2 0 1 | 0 -4 3 1 }}

 

 

 

 

 

* [[nestoria7]] – 7-tone albitonic scale

* [[nestoria12]] – 12-tone chromatic scale

* [[nestoria17]] – 17-tone mega chromatic scale

{{See also| Orgonia }}

 

Orgone, the 4 &amp; 7 temperament in the 2.7.11 subgroup, is related to [[superkleismic]].

 

 

 

 

 

 

 

{{Optimal ET sequence|legend=1| 4, 7, 11, 15, 26, 89, 115, 141, 167, 308, 475bc, 783bc }}

 

* [[orgone7]] – 7-tone albitonic scale

* [[orgone11]] – 11-tone chromatic scale

* [[orgone15]] – 15-tone mega chromatic scale

 

 

 

{{Mapping|legend=2| 1 0 2 | 0 1 -2 }}

 

 

 

 

 

* [[marveltwintri7]] – 7-tone albitonic scale

* [[marveltwintri11]] – 11-tone chromatic scale

* [[marveltwintri15]] – 15-tone mega chromatic scale

{{Main| Hanson and cata }}

 

 

 

{{Mapping|legend=2| 1 0 -6 -1 | 0 2 9 3 }}

 

 

 

 

 

* [[bridgetown9]] – 9-tone albitonic scale

* [[bridgetown14]] – 14-tone chromatic scale

* [https://web.archive.org/web/20201127012744/http://micro.soonlabel.com/tuning-survey/daily20111026-bridgetown-14.mp3 ''Route 14 in Bridgetown''] (archived 2020) by [[Chris Vaisvil]]

 

 

 

{{Mapping|legend=2| 1 0 10 -6 -1 | 0 2 -12 9 3 }}

 

 

 

 

 

* [[haumea5]] – 5-tone haplotonic scale

* [[haumea9]] – 9-tone albitonic scale

* [[haumea14]] – 14-tone chromatic scale

* [[haumea19]] – 19-tone mega chromatic scale

* [[neutral7]] – 7-tone albitonic scale

* [[neutral10]] – 10-tone chromatic scale

* [[neutral17]] – 17-tone mega-chromatic scale

 

 

 

{{Mapping|legend=2| 1 5 4 4 | 0 -9 -4 -1 }}

 

 

 

 

 

* [[huntington7]] – 7-tone haplotonic scale

* [[huntington10]] – 10-tone albitonic scale

* [[huntington17]] – 17-tone chromatic scale

 

 

 

{{Mapping|legend=2| 2 0 -1 -2 | 0 2 5 3 }}

 

 

 

 

 

* [[tobago6]] – 6-tone haplotonic scale

* [[tobago10]] – 10-tone albitonic scale

* [[tobago14]] – 14-tone chromatic scale

* [[tobago24]] – 24-tone quatertone scale

 

 

 

 

{{Mapping|legend=2| 1 0 7 12 | 0 1 -4 -7 }}

 

 

 

 

{{Optimal ET sequence|legend=1| 5, 7, 12, 17, 29, 46, 58, 75, 80, 87, 104, 121, 167, 196, 208, 271, 595bcd }}

 

* [[pepperoni7]] – 7-tone albitonic scale

* [[pepperoni12]] – 12-tone chromatic scale

 

 

 

{{Mapping|legend=2| 2 0 -7 | 0 1 3 }}

 

{{Mapping|legend=3| 2 0 4 0 5 | 0 0 1 0 3 }}

 

 

 

 

* [[wizz6]] – 6-tone haplotonic scale

* [[wizz10]] – 10-tone albitonic scale

* [[wizz16]] – 16-tone chromatic scale

 

 

 

{{Mapping|legend=2| 1 0 1 3 | 0 8 7 2 }}

 

{{Mapping|legend=3| 1 0 0 0 1 3 | 0 0 0 8 7 2 }}

 

 

 

 

* [[bossier8]] – 8-tone albitonic scale

* [[bossier11]] – 11-tone chromatic scale

* [[bossier14]] – 14-tone mega-chromatic scale

* [[penta5]] – 5-tone haplotonic scale

* [[penta8]] – 8-tone albitonic scale

* [[penta11]] – 11-tone chromatic scale

* [[penta19]] – 19-tone mega-chromatic scale

 

 

{{Mapping|legend=2| 1 0 6 | 0 3 -2 }}

 

 

 

 

 

* [[bluebirds6]] – 6-tone haplotonic scale

* [[bluebirds7]] – 7-tone albitonic scale

* [[bluebirds13]] – 13-tone chromatic scale

 

 

 

{{Mapping|legend=2| 1 0 5 | 0 1 -2 }}

 

 

 

 

 

* [[marveltri7]] – 7-tone albitonic scale

* [[marveltri10]] – 10-tone chromatic scale

* [[marveltri13]] – 13-tone mega-chromatic scale

 

 

[[Comma list]]: 196/195 = {{monzo| 2 -1 2 0 -1 }}, 352/351 = {{monzo| 5 -3 0 1 -1 }}, 364/363 = {{monzo| 2 -1 1 -2 1 }}

 

 

 

 

 

 

 

* [[edson5]] – 5-tone haplotonic scale

* [[edson7]] – 7-tone albitonic scale

* [[edson12]] – 12-tone chromatic scale

* [[edson17]] – 17-tone mega-chromatic scale

* [[photia7]] – 7-tone albitonic scale

* [[photia12]] – 12-tone chromatic scale

* [[shoe5]] – 5-tone mini-haplotonic scale

* [[shoe6]] – 6-tone haplotonic scale

* [[shoe11]] – 11-tone albitonic scale

* [[shoe16]] – 16-tone chromatic scale

* [[roulette6]] – 6-tone haplotonic scale

* [[roulette7]] – 7-tone albitonic scale

* [[roulette13]] – 13-tone chromatic scale

* [[roulette19]] – 19-tone mega-chromatic scale

 

 

 

{{Mapping|legend=2| 1 5 4 4 2 | 0 -9 -4 -1 7 }}

 

{{Mapping|legend=3| 1 0 -4 0 0 3 9 | 0 0 9 4 0 1 -7 }}

 

 

 

 

* [[silver7]] – 7-tone haplotonic scale

* [[silver10]] – 10-tone albitonic scale

* [[silver17]] – 17-tone chromatic scale

* [[baldy6]] – 6-tone haplotonic scale

* [[baldy11]] – 11-tone albitonic scale

* [[baldy17]] – 17-tone chromatic scale

 

 

 

{{Mapping|legend=2| 1 0 2 -2 | 0 3 -1 5 }}

 

 

 

 

 

* [[guanyintet5]] – 5-tone haplotonic scale

* [[guanyintet9]] – 9-tone albitonic scale

* [[guanyintet13]] – 13-tone chromatic scale

 

 

 

{{Mapping|legend=2| 1 0 0 0 | 0 3 5 1 }}

 

 

 

 

 

* [[gariberttet5]] – 5-tone haplotonic scale

* [[gariberttet9]] – 9-tone albitonic scale

* [[gariberttet13]] – 13-tone chromatic scale

* [[namo7]] – 7-tone haplotonic scale

* [[namo10]] – 10-tone albitonic scale

* [[namo17]] – 17-tone chromatic scale

 

 

 

{{Mapping|legend=2| 1 0 0 | 0 2 1 }}

 

 

 

 

 

* [[sentry5]] – 5-tone haplotonic scale

* [[sentry8]] – 8-tone albitonic scale

* [[sentry11]] – 11-tone chromatic scale

* [[hemif7]] – 7-tone haplotonic scale

* [[hemif10]] – 10-tone albitonic scale

* [[hemif17]] – 17-tone chromatic scale

== Mabila ==

Given below is the no-3 version of mabila, the 7 &amp; 9 temperament.

 

 

 

 

 

 

 

 

[[File:mabila_66edo.jpg|right|alt=mabila_66edo.jpg|Mabila in 66edo]]

* [[mabila7]] – 7-tone haplotonic scale

* [[mabila9]] – 9-tone albitonic scale

* [[mabila16]] – 16-tone chromatic scale

 

 

 

{{Mapping|legend=2| 1 0 0 2 | 0 6 10 -1 }}

 

 

 

 

 

* [[indium8]] – 8-tone albitonic scale

* [[indium17]] – 17-tone chromatic scale

* ''The Cry of Indium'' (2011) by [[Chris Vaisvil]] [https://www.chrisvaisvil.com/the-cry-of-indium/ blog] | [https://web.archive.org/web/20201127012551/http://micro.soonlabel.com/chromatic_pairs/indium17/daily20111101-indium17.mp3 play] – in Indium[17]

Related temperaments: starling; becomes myna

 

 

 

 

[[Gencom|Gencom]]: [2 6/5; 126/125]

 

Gencom mapping: [&lt;1 -1 0 1|, &lt;0 4/3 1/3 -5/3|]

 

 

 

[[Tp tuning #T2 tuning|RMS error]]: 0.8398 cents

 

[[starlingtet4|Four note haplotonic scale]]

 

[[starlingtet7|Seven note albitonic scale]]

 

[[starlingtet11|Eleven note chromatic scale]]

[[Comma list]]: 1352/1331

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~13/11 = 279.318

 

[[Gencom|Gencom]]: [2 13/11; 1352/1331]

 

 

 

 

[[Tp tuning #T2 tuning|RMS error]]: 0.8449 cents

 

 

[[lovecraft5|Five note haplotonic scale]]

 

[[lovecraft9|Nine note albitonic scale]]

 

[[lovecraft13|Thirteen note chromatic scale]]

[[Comma list]]: 29282/28561

 

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/8 = 546.660

 

Gencom: [13/11 11/8; 29282/28561]

 

Gencom mapping: [&lt;4 0 0 0 12 13|, &lt;0 0 0 0 1 1|]

 

Mapping: [&lt;4 0 1|, &lt;0 1 1|]

 

 

 

[[blackbirds8|Eight note albitonic scale]]

 

[[blackbirds12|Twelve note chromatic scale]]

 

[[blackbirds16|Sixteen note mega chromatic scale]]

Related temperaments: [[Orwellismic_family#Guanyin-Georgian|georgian]], winston

 

 

[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~7/6 = 269.300

 

[[Gencom|Gencom]]: [2 7/6; 144/143 176/175 196/195]

 

Gencom mapping: [&lt;1 -5/4 3 -1/4 7/4 -1/4|, &lt;0 -1/4 -3 3/4 -21/4 19/4|]

 

 

 

[[Tp tuning #T2 tuning|RMS error]]: 0.8790 cents

 

[[laz5|Five note haplotonic scale]]

 

[[laz9|Nine note albitonic scale]]

 

[[laz13|Thirteen note chromatic scale]]

* [[Myna7]] – 7-tone [[haplotonic scale]]

* [[Myna11]] – 11-tone [[albitonic scale]]

* [[Myna15]] – 15-tone [[chromatic scale]]

Related temperament: [[Porcupine_family#Opossum|Opossum]], [[Starling_temperaments#Nusecond temperament|Nusecond]]

[[Subgroup]]: 2.5/3.7/3.11/3

[[Comma list]]: 121/120, 126/125

[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~11/10 = 155.776

[[Gencom|Gencom]]: [2 11/10; 121/120 126/125]

Gencom mapping: &lt;1 -5/4 -1/4 3/4 3/4|, &lt;0 9/4 1/4 -15/4 5/4|]

Mapping: [&lt;1 1 2 2|, &lt;0 -2 -6 -1|]

 

 

[[Tp tuning #T2 tuning|RMS error]]: 1.034 cents

 

 

[[greeley8|Eight note albitonic scale]]

 

 

 

 

 

 

[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~13/10 = 453.242

 

[[Gencom|Gencom]]: [2 13/10; 121/120 169/168 275/273]

 

 

Mapping: [&lt;1 3 5 3 4|, &lt;0 -6 -10 -3 -5|]

 

 

 

 

 

[[semidim13|Thirteen note chromatic scale]]

Related temperament: Orwell

 

[[Subgroup]]: 2.7/3.11

 

[[Comma list]]: 99/98

 

 

 

Gencom mapping: [&lt;1 -1/2 0 1/2 3|, &lt;0 -1/2 0 1/2 2|]

 

 

 

 

[[mothwelltri5|Five note haplotonic scale]]

 

[[mothwelltri9|Nine note albitonic scale]]

 

[[mothwelltri13|Thirteen note chromatic scale]]

Related temperament: [[Marvel_family#Minerva|minerva]], würschmidt

[[Subgroup]]: 2.5.9/7.11/9

 

[[Comma list]]: 99/98, 176/175

 

 

[[Gencom|Gencom]]: [2 5/4; 99/98 176/175]

 

Gencom mapping: [&lt;1 4/9 2 -1/9 -1/9|, &lt;0 -4/3 1 -2/3 4/3|]

 

 

 

 

[[sulis7|Seven note haplotonic scale]]

 

[[sulis10|Ten note albitonic scale]]

 

[[sulis13|Thirteen note chromatic scale]]

Related temperament: [[Meantone_family|squares]]

[[Subgroup]]: 2.3.7.11

[[Comma list]]: 99/98, 243/242

 

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~9/7 = 425.244

 

[[Gencom|Gencom]]: [2 9/7; 99/98 243/242]

 

Gencom mapping: [&lt;1 3 0 6 7|, &lt;0 -4 0 -9 -10|]

 

Mapping: [&lt;1 3 6 7|, &lt;0 -4 -9 -10|]

 

 

 

 

[[skwares8|Eight note albitonic scale]]

 

[[skwares11|Eleven note mega albitonic scale]]

 

[[skwares14|Fourteen note chromatic scale]]

* [[Orwell5]] – 5-tone [[haplotonic scale]]

* [[Orwell9]] – 9-tone [[albitonic scale]]

* [[Orwell13]] – 13-tone [[chromatic scale]]

 

[[Comma list]]: 100/99 = {{monzo| 2 2 0 -1 }}, 385/384 = {{monzo| -7 1 1 1 }}

 

{{Mapping|legend=2| 1 0 5 2 | 0 1 -3 2 }}

 

 

{{Mapping|legend=3| 1 -1/2 1/2 2 4 | 0 1/2 -1/2 3 -2 }}

 

 

 

 

 

 

* [[magicaltet7]] – 7-tone [[albitonic scale]]

* [[magicaltet11]] – 11-tone [[chromatic scale]]

* [[magicaltet15]] – 15-tone [[mega-chromatic scale]]

* [[Magic7]] – 7-tone [[haplotonic scale]]

* [[Magic10]] – 10-tone [[albitonic scale]]

* [[Magic13]] – 13-tone [[chromatic scale]]

* [[Magic16]] – 16-tone [[mega-chromatic scale]]

Related temperament: [[Octagar_family|nakika]], octacot

[[Subgroup]]: 2.9/5.7/3.11/9

 

[[Comma list]]: 100/99, 245/242

 

[[Optimal tuning]] ([[Tp tuning|subgroup]] [[POTE]]): ~2 = 1\1, ~21/20 = 87.892

 

 

Gencom mapping: [&lt;1 1/10 -4/5 11/10 1/5|, &lt;0 -3/2 -1 3/2 1|]

 

 

 

 

[[kiribati13|Thirteen note chromatic scale]]

 

[[Comma list]]: 343/338, 847/832

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/8 = 540.099

 

[[Gencom|Gencom]]: [2 11/8; 343/338 847/832]

 

 

 

{{Optimal ET sequence|legend=1| 5, 7, 9, 11, 20 }}

 

[[Tp tuning #T2 tuning|RMS error]]: 1.282 cents

 

[[File:score_20edo.jpg|alt=score_20edo.jpg|score_20edo.jpg]]

 

 

[[score7|Seven note albitonic scale]]

 

[[score9|Nine note mega albitonic scale]]

 

[[score11|Eleven note chromatic scale]]

* [[Sensi5]] – 5-tone [[haplotonic scale]]

* [[Sensi8]] – 8-tone [[albitonic scale]]

* [[Sensi11]] – 11-tone [[mega-albitonic scale]]

* [[Sensi19]] – 19-tone [[chromatic scale]]

* [[Sensi5]] – 5-tone [[haplotonic scale]]

* [[Sensi8]] – 8-tone [[albitonic scale]]

* [[Sensi11]] – 11-tone [[mega-albitonic scale]]

* [[Sensi19]] – 19-tone [[chromatic scale]]

* [[Meantone5]] – 5-tone [[haplotonic scale]]

* [[Meantone7]] – 7-tone [[albitonic scale]]

* [[Meantone12]] – 12-tone [[chromatic scale]]

* [[Mohaha7]] – 7-tone [[albitonic scale]]

* [[Mohaha10]] – 10-tone [[chromatic scale]]

Related temperaments: casablanca, orwell

[[Subgroup]]: 2.9.7.11

 

[[Comma list]]: 99/98, 9317/9216

 

[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~11/8 = 542.672 cents

 

 

Gencom mapping: [&lt;1 0 0 1 3|, &lt;0 7/2 0 4 1|]

 

Mapping: [&lt;1 0 1 3|, &lt;0 7 4 1|]

 

 

[[Tp tuning #T2 tuning|RMS error]]: 1.424 cents

 

 

[[joan7|Seven note albitonic scale]]

 

[[joan9|Nine note mega albitonic scale]]

 

[[joan11|Eleven note chromatic scale]]

* [[Tutone6]] – 6-tone [[haplotonic scale]]

* [[Tutone7]] – 7-tone [[albitonic scale]]

* [[Tutone13]] – 13-tone [[chromatic scale]]

Related temperament: [[Magic_family#Magic-13-limit|magic]]

Svalname: 11&amp;30

 

 

[[Comma list]]: 100/99, 105/104, 144/143, 196/195

 

 

 

Gencom mapping: [&lt;1 5/2 5/2 5 2 7|, &lt;0 -5/2 -1/2 -6 4 -9|]

 

 

 

[[Tp tuning #T2 tuning|RMS error]]: 1.540 cents

 

[[stacks5|Five note haplotonic scale]]

 

[[stacks8|Eight note albitonic scale]]

 

[[stacks11|Eleven note note chromatic scale]]

 

[[stacks19|Nineteen note note mega chromatic scale]]

 

 

 

 

 

 

 

[[Tp tuning #T2 tuning|RMS error]]: 1.752 cents

 

[[File:blue_60edo.png|alt=blue_60edo.png|blue_60edo.png]]

 

[[bleu8|bleu8]] - Eight note [[haplotonic_scale|haplotonic scale]]

 

[[bleu9|bleu9]] - Nine note [[albitonic_scale|albitonic scale]]

 

[[bleu17|bleu17]] - Seventeen note [[chromatic_scale|chromatic scale]]