Young temperament

In his first temperament, {{harvp|Young|1800}} chose to make the major third C-E wider than just by {{sfrac|1|4}} of a syntonic comma (about 5 cents, {{Audio|Young temperament major third on C.mid|Play}}), and the major third F{{sup|{{music|#}}}}-A{{sup|{{music|#}}}} (≈ B{{sup|{{music|b}}}}) wider than just by a full syntonic comma (about 22 cents, {{Audio|Young temperament widest major third on C.mid|Play}}). He achieved the first by making each of the fifths C-G, G-D, D-A and A-E narrower than just by {{sfrac|3|16}} of a syntonic comma, and the second by making each of the fifths F{{sup|{{music|#}}}}-C{{sup|{{music|#}}}}, C{{sup|{{music|#}}}}-G{{sup|{{music|#}}}}, G{{sup|{{music|#}}}}-D{{sup|{{music|#}}}} (E{{sup|{{music|b}}}}) and E{{sup|{{music|b}}}}-B{{sup|{{music|b}}}} perfectly just.{{sfnp|Barbour|2004|pp=[https://archive.org/stream/tuningtemperamen00barb#page/167/mode/1up 167-168]}}{{efn|

This article follows {{harvp|Barbour|2004}} in labelling the notes of the chromatic scale as E{{sup|{{music|b}}}}, B{{sup|{{music|b}}}}, F, C, G, D, A, E, B, F{{music|#}}, C{{sup|{{music|#}}}}, and G{{sup|{{music|#}}}}. In both of Young's temperaments all 12 notes on the circle of fifths are by definition intended to be used as replacements for their enharmonic equivalents: D{{sup|{{music|#}}}} {{math|↦}} E{{sup|{{music|b}}}} , A{{sup|{{music|#}}}} {{math|↦}} B{{sup|{{music|b}}}} , E{{sup|{{music|#}}}} {{math|↦}} F{{sup|{{music|b}}}} , B{{sup|{{music|#}}}} {{math|↦}} C , F{{sup|{{music|b}}}} {{math|↦}} E , C{{sup|{{music|b}}}} {{math|↦}} B , G{{sup|{{music|b}}}} {{math|↦}} F{{sup|{{music|#}}}} , D{{sup|{{music|b}}}} {{math|↦}} C{{sup|{{music|#}}}} , and A{{sup|{{music|b}}}} {{math|↦}} G{{sup|{{music|#}}}} .

}}

The remaining fifths, E-B, B-F{{sup|{{music|#}}}}, B{{sup|{{music|b}}}}-F and F-C were all made the same size, chosen so that the circle of fifths would close – that is, so that the total span of all twelve fifths would be exactly seven octaves. The resulting fifths are narrower than just by about {{sfrac|1|12}} of a syntonic comma, or 1.8 cents.{{sfnp|Barbour|2004|p=[https://archive.org/stream/tuningtemperamen00barb#page/168/mode/1up 168]}} The precise difference is {{sfrac|3|16}} of a syntonic comma less than {{sfrac|1|4}} of a Pythagorean comma, differing from an equal temperament fifth by only about {{sfrac|1|8}} of a cent. The exact and approximate numerical sizes of the three types of fifth, in cents, are as follows:

:

Each of the major thirds in the resulting scale comprises four of these fifths less two octaves. {{nobr| If {{math|s_j {{overset|Def|{{small|══}}}} f_j − 600 }} }} {{nobr|( for {{math| j {{=}} 1, 2, 3 )}} ,}} the sizes of the major thirds can be conveniently expressed as in the second row of the table in {{harvp|Jorgensen |1991|at=Table 71-2, pp. 264-265}}. In these temperaments the intervals B-E{{sup|{{music|b}}}}, F{{sup|{{music|#}}}}-B{{sup|{{music|b}}}}, C{{sup|{{music|#}}}}-F, and G{{sup|{{music|#}}}}-C, here written as diminished fourths, are identical to the major thirds B-D{{sup|{{music|#}}}}, F{{sup|{{music|#}}}}-A{{sup|{{music|#}}}}, C{{sup|{{music|#}}}}-E{{sup|{{music|#}}}}, and G{{sup|{{music|#}}}}-B{{sup|{{music|#}}}}, respectively.

:

As can be seen from the third row of the table, the widths of the tonic major thirds of successive major keys around the circle of fifths increase by about 2 cents {{nobr|{{math|( s{{sub|2}} − s{{sub|1}} }} }} or {{nobr|{{math| s{{sub|3}} − s{{sub|2}} )}} }} to 4 cents

{{nobr|{{math|( s{{sub|3}} − s{{sub|1}} ) }} }} per step in either direction from the narrowest, in C major, to the widest, in F{{sup|{{music|#}}}} major.

The following table gives the pitch differences in cents between the notes of a chromatic scale tuned with Young's first temperament and those of one tuned with equal temperament, when the note A of each scale is assigned the same pitch.{{sfnp|Jorgensen |1991|at=Table 71-1, p. 264}}

:

In the second temperament, {{harvp|Young|1802}} made each of the fifths F{{music|#}}-C{{music|#}}, C{{music|#}}-G{{music|#}}, G{{music|#}}-E{{music|b}},

E{{music|b}}-B{{music|b}}, B{{music|b}}-F, and F-C perfectly just, while the fifths C-G, G-D, D-A, A-E, E-B, and B-F{{music|#}} are each {{sfrac|1|6}} of a

Pythagorean (ditonic) comma narrower than just.{{sfnp|Barbour|2004|p=[https://archive.org/stream/tuningtemperamen00barb#page/163/mode/1up 163]}} The exact and approximate numerical sizes of these latter fifths, in cents, are given by:

If {{math| f₃ }} and {{math| s₃ }} are the same as in the previous section, and {{nobr|{{math| s₄ {{overset|Def|{{small|══}}}} f₄ − 600 }} ,}} the sizes of the major thirds in the temperament are as given in the second row of the following table:{{sfnp|Jorgensen|1991|at=Table 69-1, p. 254}}

The following table gives the pitch differences in cents between the notes of a chromatic scale tuned with Young's second temperament and those of one tuned with equal temperament, when the note A of each scale is given the same pitch.{{sfnp|Jorgensen|1991|at=Table 70-1, p. 259}}

Young's 2nd temperament is very similar to the Vallotti temperament which also has six consecutive pure fifths and six tempered by {{sfrac|1|6}} of a Pythagorean comma. Young's temperament is shifted one note around the circle of fifths, with the first tempered fifth beginning on C instead of F.{{sfnp|Donahue |2005|p=[https://books.google.com/books?id=FTRADRMfld4C&pg=PA28 28–29 ]}} For this reason it is sometimes called "Vallotti-Young" or "shifted Vallotti".

{{notelist|199em}}

{{reflist|25em}}

{{refbegin|25em}}

• {{cite book

| last = Barbour | first = James Murray | author-link = James Murray Barbour

| year = 2004 | orig-year = 1951

| title = Tuning and Temperament: A historical survey

| publisher = Dover Publications

| location = Minneola, NY

| isbn = 978-0-486-43406-3

| url = https://archive.org/stream/tuningtemperamen00barb

}}

• {{cite book

| last = Donahue | first = Thomas

| year = 2005

| title = A Guide to Musical Temperament

| publisher = Scarecrow Press

| location = Lanham, MD

| isbn = 978-0-8108-5438-3

| url = https://books.google.com/books?id=FTRADRMfld4C

}}

• {{cite book

| last = Jorgensen | first = Owen

| year = 1991

| title = Tuning

| publisher = Michigan State University Press

| location = East Lansing, MI

| isbn = 978-0-87013-290-2

| quote = 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.

}}

• {{cite journal

| last = Young | first = Thomas | author-link = Thomas Young (scientist)

| year = 1800

| title = Outlines of experiments and inquiries respecting sound and light in a letter to Edward Whitaker Gray, M.D. Sec. R.S.

| journal = Philosophical Transactions of the Royal Society of London

| volume = 90 | pages = 106–150

| doi = 10.1098/rstl.1800.0008 | doi-access= free

}}

• {{cite journal

| last = Young | first = Thomas | author-link = Thomas Young (scientist)

| year = 1802

| title = Outlines of experiments and inquiries respecting sound and light

| journal = Journal of Natural Philosophy, Chemistry and the Arts

| volume = 5

| pages = [https://books.google.com/books?id=t4tEAAAAcAAJ&pg=PA72 72-78], [https://books.google.com/books?id=t4tEAAAAcAAJ&pg=PA81 81-91], [https://books.google.com/books?id=t4tEAAAAcAAJ&pg=PA121 121-130], [https://books.google.com/books?id=t4tEAAAAcAAJ&pg=PA168 167]

| url = https://books.google.com/books?id=t4tEAAAAcAAJ&pg=PA72

}}

• {{cite book

| last = Young | first = Thomas | author-link = Thomas Young (scientist)

| year = 1807

| title = A Course of Lectures on Natural Philosophy and the Mechanical Arts

| volume = 2

| publisher = Joseph Johnson

| location = London, UK

| url = https://archive.org/stream/lecturescourseof02younrich

}}

{{refend}}

{{musical tuning}}

Category:Musical temperaments