Extended-diatonic interval names: Difference between revisions

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''tonos'' referred both to the interval of a whole tone, and something more akin to [[mode]] or key in the modern sense ([http://lumma.org/tuning/chalmers/DivisionsOfTheTetrachord.pdf Chalmers, 1993])

''ditone'' referred to the interval made by stacking two [[9/8]] whole tones, resulting in [[81/64]], the Pythagorean major third. ([[~~Joe~~ Monzo|Monzo]], [http://www.tonalsoft.com/ http://www.tonalsoft.com])

''ditone'' referred to the interval made by stacking two [[9/8]] whole tones, resulting in [[81/64]], the Pythagorean major third. ([[Joseph Monzo|Monzo]], [http://www.tonalsoft.com/ http://www.tonalsoft.com])

[[256/243]] - the ''limma'', which is the ratio between left over after subtracting two 9/8 tones (together making a ditone) a perfect fourth, the ''diatonic semitone'' of the Pythagorean diatonic scale

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|}Each interval name has two sizes that differ by the comma 243/242. The notation included in the table is from HEWM notation, developed as an extension to the Helmholtz-Ellis use of '+' and '-' by ~~Joe~~ Monzo (http://www.tonalsoft.com/enc/h/hewm.aspx<nowiki/>).'^' indicates raising 'v' a lowered of [[33/32]]. In HEWM notation '+' and '-' are refined to mean raising and lowering of 81/80 respectively and '>' and '<' are added instead to indicate raising and lowering of 64/63. Letter names correspond instead of the Ptolemaic sequence, as in Smith's and Helmholtz' descriptions, but to a Pythagorean tuning of the diatonic scale, where '#' and '♭' and respectively raise and lower the apotome, 2187/2048. HEWM notation is not accompanied by an interval naming system.

|}Each interval name has two sizes that differ by the comma 243/242. The notation included in the table is from HEWM notation, developed as an extension to the Helmholtz-Ellis use of '+' and '-' by Joseph Monzo (http://www.tonalsoft.com/enc/h/hewm.aspx<nowiki/>).'^' indicates raising 'v' a lowered of [[33/32]]. In HEWM notation '+' and '-' are refined to mean raising and lowering of 81/80 respectively and '>' and '<' are added instead to indicate raising and lowering of 64/63. Letter names correspond instead of the Ptolemaic sequence, as in Smith's and Helmholtz' descriptions, but to a Pythagorean tuning of the diatonic scale, where '#' and '♭' and respectively raise and lower the apotome, 2187/2048. HEWM notation is not accompanied by an interval naming system.

== Common interval names today ==

@@ Line 25: / Line 25: @@
 ''tonos'' referred both to the interval of a whole tone, and something more akin to [[mode]] or key in the modern sense ([http://lumma.org/tuning/chalmers/DivisionsOfTheTetrachord.pdf Chalmers, 1993])
-''ditone'' referred to the interval made by stacking two [[9/8]] whole tones, resulting in [[81/64]], the Pythagorean major third. ([[Joe Monzo|Monzo]], [http://www.tonalsoft.com/ http://www.tonalsoft.com])
+''ditone'' referred to the interval made by stacking two [[9/8]] whole tones, resulting in [[81/64]], the Pythagorean major third. ([[Joseph Monzo|Monzo]], [http://www.tonalsoft.com/ http://www.tonalsoft.com])
 [[256/243]] - the ''limma'', which is the ratio between left over after subtracting two 9/8 tones (together making a ditone) a perfect fourth, the ''diatonic semitone'' of the Pythagorean diatonic scale
@@ Line 167: / Line 167: @@
 |44:81
 |1057
-|}Each interval name has two sizes that differ by the comma 243/242. The notation included in the table is from HEWM notation, developed as an extension to the Helmholtz-Ellis use of '+' and '-' by Joe Monzo (http://www.tonalsoft.com/enc/h/hewm.aspx<nowiki/>).'^' indicates raising 'v' a lowered of [[33/32]]. In HEWM notation '+' and '-' are refined to mean raising and lowering of 81/80 respectively and '>' and '<' are added instead to indicate raising and lowering of 64/63. Letter names correspond instead of the Ptolemaic sequence, as in Smith's and Helmholtz' descriptions, but to a Pythagorean tuning of the diatonic scale, where '#' and '♭' and respectively raise and lower the apotome, 2187/2048. HEWM notation is not accompanied by an interval naming system.
+|}Each interval name has two sizes that differ by the comma 243/242. The notation included in the table is from HEWM notation, developed as an extension to the Helmholtz-Ellis use of '+' and '-' by Joseph Monzo (http://www.tonalsoft.com/enc/h/hewm.aspx<nowiki/>).'^' indicates raising 'v' a lowered of [[33/32]]. In HEWM notation '+' and '-' are refined to mean raising and lowering of 81/80 respectively and '>' and '<' are added instead to indicate raising and lowering of 64/63. Letter names correspond instead of the Ptolemaic sequence, as in Smith's and Helmholtz' descriptions, but to a Pythagorean tuning of the diatonic scale, where '#' and '♭' and respectively raise and lower the apotome, 2187/2048. HEWM notation is not accompanied by an interval naming system.
 == Common interval names today ==