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== Examples ==
== Examples ==
Here are some examples of historical temperaments. Some of these temperaments saw widespread usage, some saw limited usage, and some were discussed merely as thought experiments. Some were referred to by their modern name, while others used a different name to the modern one, but still described the same mathematical object.
Here are some examples of historical temperaments. Some of these temperaments saw widespread usage, some saw limited usage, and some were discussed merely as thought experiments. Some were referred to by their current name, while others went by a different name to the modern one, but still described the same mathematical object.


* [[Pythagorean tuning]]
* [[Pythagorean tuning]]


* [[Meantone]]
* [[Meantone]] (sorted by: tuning of [[3/2]], flattest to sharpest)
** [[1/2-comma meantone|1/2 comma]] (''Fogliano 1529)''<ref name="Monzo"> [http://www.tonalsoft.com/enc/m/meantone.aspx ''Meantone - Tonalsoft'' - Joe Monzo, 2005]</ref>*
**[[19edo]] (<small>''Costeley 1558''</small>)<ref>''Seigneur Dieu ta pitié'' - Guillaume Costeley, 1558</ref>
** [[19edo]] (''Costeley 1558'')<ref>''Seigneur Dieu ta pitié'' - Guillaume Costeley, 1558</ref>
**'''[[1/3-comma meantone|1/3 comma]]''' (<small>''Salinas 1577''</small>)<ref>''De musica libri septem'' - Francisco de Salinas, 1577</ref>
** [[1/3-comma meantone|1/3 comma]] (''Salinas 1577'')<ref>''De musica libri septem'' - Francisco de Salinas, 1577</ref>
**[[Lucy tuning|Lucy]] (<small>''Harrison 1775''</small>)<ref>''Concerning Such Mechanism'' - John Harrison, 1775</ref>
** [[Lucy tuning|Lucy]] (''Harrison 1775''<ref>''Concerning Such Mechanism'' - John Harrison, 1775</ref>
**[[2/7-comma meantone|2/7 comma]] (<small>''Zarlino 1558''</small>)<ref>''Le istitutioni harmoniche'' - Gioseffo Zarlino, 1558</ref>
** [[2/7-comma meantone|2/7 comma]] (''Zarlino 1558'')<ref>''Le istitutioni harmoniche'' - Gioseffo Zarlino, 1558</ref>
**[[5/18-comma meantone|5/18 comma]] (<small>''Smith 1749''</small>)<ref>''Harmonics, or The philosophy of musical sounds'' - Robert Smith, 1749</ref>
** [[5/18-comma meantone|5/18 comma]] (''Smith 1749''<ref>''Harmonics, or The philosophy of musical sounds'' - Robert Smith</ref>
**[[50edo]] (<small>''Henfling 1710''</small>)<ref name="Monzo"> [http://www.tonalsoft.com/enc/m/meantone.aspx ''Meantone - Tonalsoft'' - Joseph Monzo, 2005]</ref>*
** [[50edo]] (''Henfling 1710'')<ref name="Monzo" />*
**[[7/26-comma meantone|7/26 comma]] (<small>''Woolhouse 1835''</small>)<ref>''Essay on musical intervals'' - Wesley S. B. Woolhouse, 1835</ref>
** [[7/26-comma meantone|7/26 comma]] (''Woolhouse 1835'')<ref>''Essay on musical intervals'' - Wesley S. B. Woolhouse, 1835</ref>
**[[Golden meantone|Golden]] (<small>''Kornerup 1930''</small>)<ref name="Monzo" />*
** [[Golden meantone|Golden]] (''Kornerup 1930'')<ref name="Monzo" />*
**'''[[Quarter-comma meantone|1/4 comma]]''' (<small>''Aron 1523''</small>)<ref>''Toscanello de la Musica'' - Pietro Aron, 1523</ref>
** [[Quarter-comma meantone|1/4 comma]] (''Aron 1523'')<ref>''Toscanello de la Musica'' - Pietro Aron, 1523</ref>
**[[31edo]] (''<small>Vicentino 1555</small><ref>''L'Antica musica ridotta alla moderna prattica'' - Nicola Vicentino, 1555</ref><small> (possibly)</small><ref>''Theories of chromatic and Enharmonic Music in Late 16th Century Italy - Chromatic systems (or non-systems) from Vicentino to Monteverdi'' - Karol Berger, 1980</ref><small> & Huygens 1691</small>''<ref>''Lettre touchant le cycle harmonique'' - Christiaan Huygens, 1691''</ref>)
** [[31edo]] (''Vicentino 1555<ref>''L'Antica musica ridotta alla moderna prattica'' - Nicola Vicentino, 1555</ref> (possibly)<ref>''Theories of chromatic and Enharmonic Music in Late 16th Century Italy - Chromatic systems (or non-systems) from Vicentino to Monteverdi'' - Karol Berger, 1980</ref> & Christiaan Huygens 1691''<ref>''Lettre touchant le cycle harmonique'' - Christiaan Huygens, 1691''</ref>)
**[[2/9-comma meantone|2/9 comma]] (<small>''Rossi 1666''</small><ref>''Sistema musico ouero Musica speculativa'' - Lemme Rossi, 1666</ref><small> & ''Drobisch 1852''</small><ref>''Über musikalische Tonbestimmung und Temperatur'' - Moritz Wilhelm Drobisch, 1852</ref>)
** [[2/9-comma meantone|2/9 comma]] (''Rossi 1666''<ref>''Sistema musico ouero Musica speculativa'' - Lemme Rossi, 1666</ref> & ''Drobisch 1852''<ref>Über musikalische Tonbestimmung und Temperatur - Moritz Wilhelm Drobisch, 1852</ref>)
**[[74edo]] (<small>''Riccati 1762''</small>)<ref name="Monzo" />*
** [[74edo]] (''Riccati 1762'')[2]<ref name="Monzo" />*
**[[3/14-comma meantone|3/14 comma]] (<small>''Riccati 1762''</small>)<ref name="Monzo" />*
** [[3/14-comma meantone|3/14 comma]] (''Riccati 1762'')<ref name="Monzo" />*
**'''[[1/5-comma meantone|1/5 comma]]''' (<small>''Verheyen c. 1600''</small><ref>Abraham Verheyen's letter to Simon Stevin, c. 1600</ref><small> & ''Sauveur 1701''</small><ref name="Sauveur1">''Archives of the Académie des Sciences, Paris, Procès verbaux, vol. 20'', February through April 1701</ref><ref name="Sauveur2">''Mémoires de l'Académie Royale des Sciences (Paris, 1701)'', pages 299–366</ref>)
** [[1/5-comma meantone|1/5 comma]] (''Verheyen c. 1600''<ref>Abraham Verheyen's letter to Simon Stevin, c. 1600</ref> & ''Sauveur 1701''<ref name="Sauveur1">Archives of the Académie des Sciences, Paris, Procès verbaux, vol. 20, February through April 1701</ref><ref name="Sauveur2">Mémoires de l'Académie Royale des Sciences (Paris, 1701), pp. 299–366</ref>)
**[[43edo]] (<small>''Sauveur 1701''</small>)<ref name="Sauveur1" /><ref name="Sauveur2" />
** [[43edo]] (''Sauveur 1701'')<ref name="Sauveur1" /><ref name="Sauveur2" />
**[[55edo]] (<small>''Beer <1722''</small>)<ref name="Monzo" />*
** [[55edo]] (''Beer <1722'') <ref name="Monzo" />*
**'''[[1/6-comma meantone|1/6 comma]]''' (<small>''Silbermann <1748''</small>)<ref>''Gespräch zwischen einem Musico theoretico und einem Studioso Musices von der Prätorianischen, Printzischen Werkmeisterischen ... Temperatur, wie auch von dem neuen Systemate ... Telemanns zur Beförd. reiner Harmonie.'' - Georg Andreas Sorge, 1748</ref>
** [[1/6-comma meantone|1/6 comma]] (''Silbermann <1748'')<ref>Gespräch zwischen einem Musico theoretico und einem Studioso Musices von der Prätorianischen, Printzischen Werkmeisterischen ... Temperatur, wie auch von dem neuen Systemate ... Telemanns zur Beförd. reiner Harmonie. - Georg Andreas Sorge, 1748</ref>
**[[4/25-comma meantone|4/25 comma]] (<small>''Marsh 1809''</small>)<ref>''Containing the Perfection of Eighteenth-century Temperament, the Lost Art of Nineteenth-century Temperament, and the Science of Equal Temperament, Complete with Instructions for Aural and Electronic Tuning'' - Owen Jorgensen, 1991</ref>*
** [[4/25-comma meantone|4/25 comma]] (''Marsh 1809'')<ref>Containing the Perfection of Eighteenth-century Temperament, the Lost Art of Nineteenth-century Temperament, and the Science of Equal Temperament, Complete with Instructions for Aural and Electronic Tuning - Owen Jorgensen, 1991</ref>*
**'''[[1/7-comma meantone|1/7 comma]]''' (<small>''Romieu 1758''</small>)<ref>''Tuning and Temperament: A Historical Survey'' p. 126 - James Murray Barbour, 1953</ref>*
** [[1/7-comma meantone|1/7 comma]] (''Romieu 1758'')<ref>''Tuning and Temperament: A Historical Survey'' p. 126 - James Murray Barbour, 1953</ref>*
**[[12edo]] (<small>''Chu Tsai-yü 1596''</small>)<ref>''Prince Chu Tsai-Yü's Life and Work: A Re-Evaluation of His Contribution to Equal Temperament Theory'' - Fritz A. Kuttner, 1975</ref>
** [[12edo]] (''Chu Tsai-yü 1596'')<ref>''Prince Chu Tsai-Yü's Life and Work: A Re-Evaluation of His Contribution to Equal Temperament Theory'' - Fritz A. Kuttner, 1975</ref>


* [[Well temperament]]
* [[Well temperament]] (sorted by: date described, oldest to youngest)
** [[Johann Kirnberger|Kirnberger]]<ref>''Die Kunst des reinen Satzes in der Musik'' - Johaan Philipp Kirnberger, 1774</ref>
** [[Fogliano]] (<small>1529</small>)<ref>''Accurate meantone tuning based on Fogliano'' - Claudio Di Veroli, 2018 ([https://www.academia.edu/95315365/Accurate_meantone_tuning_based_on_Fogliano_2018 accessible at Academia.edu])</ref>
** Werckmeister (<small>1691</small>)<ref>''Musicalische Temperatur'' - Andreas Werckmeister, 1691</ref>
*** [[Werck3|Werckmeister III]]
*** [[Werckmeister IV]]
*** [[Werckmeister V]]
*** [[Septenarius]] (Werckmeister VI)
** [[Vallotti]] (<small>1728</small>)<ref>''Della scienza teorica e pratica della moderna musica'' - Francesco Vallotti, written 1728, published 1779</ref>
** Neidhart (<small>1732</small>)<ref>''Sectio canonis harmonici'' - Johann Georg Neidhardt, 1724</ref><ref>''Gäntzlich erschöpfte, mathematische Abtheilungen des diatonisch-chromatischen, temperirten Canonis Monochordi'' - Johann Georg Neidhardt, 1732 ([https://www.digitale-sammlungen.de/en/view/bsb10527538?q=%28G%C3%A4ntzlich+ersch%C3%B6pfte,+Mathematische+Abtheilungen+des+Diatonisch-Chromatischen,+temperirten+Canonis+Monochordi%29&page=5 digitized copy])</ref>
*** [[Hof 1732]] (<small>Name translates to ''Court''</small>)
*** [[Grosse stadt 1732]] (<small>Name translates to ''Large town''</small>)
*** [[Kleine stadt 1732]] (<small>Name translates to ''Small town''</small>)
*** [[Dorf 1732]] (<small>Name translates to ''Village''</small>)
** [[Temperament ordinaire]]
*** D'Alembert (<small>1752</small>)<ref>''Élémens de musique, theorique et pratique, suivant les principes de Monsieur Rameau'' - Jean-Baptiste le Rond d’Alembert, 1752</ref>
*** Rousseau (<small>1767</small>)<ref>''Dictionnaire de Musique'' - Jean-Jacques Rousseau, 1767</ref>
** [[Johann Kirnberger|Kirnberger]] (<small>1774</small>)<ref>''Die Kunst des reinen Satzes in der Musik'' - Johaan Philipp Kirnberger, 1774</ref>
*** [[Kirnberger I]]
*** [[Kirnberger I]]
*** [[Kirnberger II]]
*** [[Kirnberger II]]
*** [[Kirnberger III]]
*** [[Kirnberger III]]
** Neidhart<ref>''Sectio canonis harmonici'' - Johann Georg Neidhardt, 1724</ref>''Gäntzlich erschöpfte, mathematische Abtheilungen des diatonisch-chromatischen, temperirten Canonis Monochordi'' - Johann Georg Neidhardt, 1732</ref>
** Young<ref>''Philosophical Transactions'' pages 143-147 - Royal Society of London, 1800</ref>
*** [[Hof]] (''court'')
*** [[Young I]] (<small>1800</small>)
*** [[Grosse stadt]] (''large town'')
*** Young II (<small>''same as [[Vallotti]] 1728''</small>)
*** [[Kleine stadt]] (''small town'')
*** [[Dorf]] (''village'')
** [[Temperament ordinaire]]
*** D'Alembert/Rousseau 1752/67<ref>''Élémens de musique, theorique et pratique, suivant les principes de Monsieur Rameau'' - Jean-Baptiste le Rond d’Alembert, 1752</ref><ref>''Dictionnaire de Musique'' - Jean-Jacques Rousseau, 1767</ref>
** [[Vallotti]]<ref>''Della scienza teorica e pratica della moderna musica'' - Francesco Vallotti, written 1728, published 1779</ref>
** Werckmeister
*** [[Werck3|Werckmeister III]]<ref name="Werckmeister">''Musicalische Temperatur'' -Andreas Werckmeister, 1691</ref>
*** [[Werckmeister IV]]<ref name="Werckmeister" /ref>
*** [[Werckmeister V]]<ref name="Werckmeister" /ref>
*** [[Septenarius]] (Werckmeister VI)<ref name="Werckmeister" /ref>
** Young <ref>''Philosophical Transactions'' pages 143-147 - Royal Society of London, 1800</ref>
*** Young I (''see [[Vallotti]]'')
*** [[Young2|Young II]]


== See also ==
== See also ==
* ''[[Seigneur Dieu ta pitié]]'' - a historical (1558) composition for 19edo, important to the history of tuning
* ''[[Seigneur Dieu ta pitié]]'' - a historical (1558) composition for 19edo, important to the history of tuning
* [[Kellner]] - Dr Herbert Anton Kellner's approximation of Bach's well temperament, from his book ''Wie stimme ich selbst mein Cembalo'' (1975).
* [[Ancient Greek]] musical tradition
** [[Tetrachord]]s
* [[Kellner well temperament]] - Dr [[Herbert Anton Kellner]]'s approximation of Bach's well temperament, from his book ''Wie stimme ich selbst mein Cembalo'' (1975).
* Temperament extradordinaire (a modern temperament inspired by the historical ''Temperament ordinaire'')
* Temperament extradordinaire (a modern temperament inspired by the historical ''Temperament ordinaire'')
** Tempered: [[Qcmte84a]]
** Tempered: [[Qcmte84a]]
** Just: [[Secor5_23TX]]
** Just: [[Secor5_23TX]]
* Ancient Greek musical tradition
** [[Teleic scales]]
** [[Tetrachord]]s
* [[Pre-Columbian South American Music|Pre-Columbian South American musical traditions]]
* [[Pre-Columbian South American Music|Pre-Columbian South American musical traditions]]
* [[Ibo Ortgies]] - musicologist and historian focusing on historical temperaments


== External resources ==
== External resources ==
Many of these include diagrams and measurements of historical temperaments:
* [https://unm.academia.edu/FredSturm A Clear and Practical Introduction to Temperament History Parts 1-9 (Fred Sturm)]
* [https://unm.academia.edu/FredSturm A Clear and Practical Introduction to Temperament History Parts 1-9 (Fred Sturm)]
* [https://public.websites.umich.edu/~bpl/larips/lindleyortgies.html Bach-Style Keyboard Tuning (Lindley & Ortgies 2006)]
* [https://public.websites.umich.edu/~bpl/larips/lindleyortgies.html Bach-Style Keyboard Tuning (Lindley & Ortgies 2006)]
* [http://harpsichords.pbworks.com/w/page/16830827/Tuning Harpsichords Wiki - Tuning]
* [http://harpsichords.pbworks.com/w/page/16830827/Tuning Harpsichords Wiki - Tuning]
* [http://harpsichords.pbworks.com/f/Neidhardt_1732_Charts.pdf Neidhardt’s 21 temperaments of 1732]
* [http://harpsichords.pbwiki.com/f/Neidhardt_1732_Charts.pdf Neidhardt’s 21 temperaments of 1732] (alternate link in case the first one returns an error)
* [https://www.rollingball.com/images/HT.pdf rollingball.com Historical Temperaments Visualised (PDF version)]
* [https://www.rollingball.com/images/HT.pdf rollingball.com Historical Temperaments Visualised (PDF version)]


== Notes ==
== Notes ==
<nowiki>*historical source needed</nowiki>
<nowiki>*historical source needed</nowiki>{{todo|research|expand}}
 
<references />


[[Category:Lists of temperaments]]
[[Category:Lists of temperaments]]
[[Category:Historical]]
[[Category:Historical]]
[[Category:Todo:expand]]
Retrieved from "https://en.xen.wiki/w/Historical_temperaments"