Singtervals: Difference between revisions

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'''Singtervals''' is a series of [[Ear training|ear-training]] exercises originated by [[Andrew Heathwaite]] ~~'round~~ 2011.

'''Singtervals''' is a series of [[Ear training|ear-training]] exercises originated by [[Andrew Heathwaite]] around 2011.

[[File:9-limit Singtervals.png|thumb]]

== A rundown of 9-odd-limit Singtervals ==

* The order of [[interval]]s as they correspond to the chart begin going down the left column, and back up from the bottom of the right column. This way, octave inversions of intervals are lined up next to one another.

* The order of [[~~Interval|intervals~~]] as they correspond to the chart begin going down the left column, and back up from the bottom of the right column. This way, octave inversions of intervals are lined up next to one another.

* Whenever the [[solfege]] appears, that is referring to a transposition of the harmonic series. do = 1/1, re = 9/8, mi = 5/4, so = 3/2, ta = 7/4.

* The transpositions of do are by ~~sub-harmonic~~ intervals. (The [[subharmonic series]] is the harmonic series turned upside down i.e. 1/1, 1/2, 1/3, 1/4, etc.)

* The transpositions of do are by subharmonic intervals. (The [[subharmonic series]] is the harmonic series turned upside down i.e. 1/1, 1/2, 1/3, 1/4, etc.)

* This is to facilitate changes of function of the 1/1. For example, in the first singterval, labeled [[10/9]], the tonic of the harmonic series is transposed to the 9th subharmonic, or 16/9, so that 1/1 functions as 9/8 (re) and 10/9 functions as 5/4 (mi).

* This exercise is exhaustive of the [[9-odd-limit]], i.e. it contains every possible (octave-reduced) interval that can be expressed by a fraction between whole numbers 1 through 9.

* The resulting intervals ''between'' the intervals being sung can be calculated by dividing the consecutive fractions. For example, the microtone between 10/9 and 9/8 is [[81/80]]. Other intervals encountered include 64/63, 36/35, 25/24, 28/27, 21/20, and 49/48. Since all of these intervals are of the form n+1/n, they fall within the category of [[~~Superparticular~~ interval~~|Superparticular intervals~~]].

* The resulting intervals ''between'' the intervals being sung can be calculated by dividing the consecutive fractions. For example, the microtone between 10/9 and 9/8 is [[81/80]]. Other intervals encountered include 64/63, 36/35, 25/24, 28/27, 21/20, and 49/48. Since all of these intervals are of the form (''n'' + 1)/''n'', they fall within the category of [[superparticular interval]]s.

* A handy way to convert a ratio a/b to cents is to Google "log(a/b)/log(2)*1200." For example, typing "log(10/9)/log(2)*1200" into Google yields 182.403712134!

* A handy way to convert a ratio ''a''/''b'' to cents is to Google <code>log(a/b)/log(2)*1200</code>. For example, typing <code>log(10/9)/log(2)*1200</code> into Google yields 182.403712134!

== 9-limit ~~Singtervals~~ ==

== 9-odd-limit singtervals ==

<soundcloud>https://soundcloud.com/andrew_heathwaite/9-limit-singtervals</soundcloud>

@@ Line 1: / Line 1: @@
-'''Singtervals''' is a series of [[Ear training|ear-training]] exercises originated by [[Andrew Heathwaite]] 'round 2011.
+'''Singtervals''' is a series of [[Ear training|ear-training]] exercises originated by [[Andrew Heathwaite]] around 2011.
 [[File:9-limit Singtervals.png|thumb]]
 == A rundown of 9-odd-limit Singtervals ==
+* The order of [[interval]]s as they correspond to the chart begin going down the left column, and back up from the bottom of the right column. This way, octave inversions of intervals are lined up next to one another.
-* The order of [[Interval|intervals]] as they correspond to the chart begin going down the left column, and back up from the bottom of the right column. This way, octave inversions of intervals are lined up next to one another.
 * Whenever the [[solfege]] appears, that is referring to a transposition of the harmonic series. do = 1/1, re = 9/8, mi = 5/4, so = 3/2, ta = 7/4.
-* The transpositions of do are by sub-harmonic intervals. (The [[subharmonic series]] is the harmonic series turned upside down i.e. 1/1, 1/2, 1/3, 1/4, etc.)
+* The transpositions of do are by subharmonic intervals. (The [[subharmonic series]] is the harmonic series turned upside down i.e. 1/1, 1/2, 1/3, 1/4, etc.)
 * This is to facilitate changes of function of the 1/1. For example, in the first singterval, labeled [[10/9]], the tonic of the harmonic series is transposed to the 9th subharmonic, or 16/9, so that 1/1 functions as 9/8 (re) and 10/9 functions as 5/4 (mi).
 * This exercise is exhaustive of the [[9-odd-limit]], i.e. it contains every possible (octave-reduced) interval that can be expressed by a fraction between whole numbers 1 through 9.
-* The resulting intervals ''between'' the intervals being sung can be calculated by dividing the consecutive fractions. For example, the microtone between 10/9 and 9/8 is [[81/80]]. Other intervals encountered include 64/63, 36/35, 25/24, 28/27, 21/20, and 49/48. Since all of these intervals are of the form n+1/n, they fall within the category of [[Superparticular interval|Superparticular intervals]].
+* The resulting intervals ''between'' the intervals being sung can be calculated by dividing the consecutive fractions. For example, the microtone between 10/9 and 9/8 is [[81/80]]. Other intervals encountered include 64/63, 36/35, 25/24, 28/27, 21/20, and 49/48. Since all of these intervals are of the form (''n'' + 1)/''n'', they fall within the category of [[superparticular interval]]s.
-* A handy way to convert a ratio a/b to cents is to Google "log(a/b)/log(2)*1200." For example, typing "log(10/9)/log(2)*1200" into Google yields 182.403712134!
+* A handy way to convert a ratio ''a''/''b'' to cents is to Google <code>log(a/b)/log(2)*1200</code>. For example, typing <code>log(10/9)/log(2)*1200</code> into Google yields 182.403712134!
-== 9-limit Singtervals ==
+== 9-odd-limit singtervals ==
 <soundcloud>https://soundcloud.com/andrew_heathwaite/9-limit-singtervals</soundcloud>