Singtervals - Revision history

FloraC: Style

2025-03-20T13:57:48Z

Style

Xenjacob at 09:53, 20 March 2025

2025-03-20T09:53:12Z

← Older revision		Revision as of 09:53, 20 March 2025
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	[[Category:todo:intro]]		[[Category:todo:intro]]
	[[File:Singtervals9 visualization.pdf\|thumb]]		[[File:Singtervals9 visualization.pdf\|thumb]]
			[https://soundcloud.com/metaclown/jacob-barton-singing-andrew-heathwaites-singtervals-9limit Jacob Barton singing 9-limit singtervals]

			== And beyond ==
			<soundcloud>https://soundcloud.com/andrew_heathwaite/11-limit-singtervals</soundcloud>
			[https://archive.org/details/singtervals-through-15-limit-pure Casey Hale's 15-odd-limit Singtervals notated in Revo Sagittal]

Xenjacob at 09:47, 20 March 2025

2025-03-20T09:47:35Z

← Older revision		Revision as of 09:47, 20 March 2025
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			'''Singtervals''' is a series of [[Ear training\|ear-training]] exercises originated by [[Andrew Heathwaite]] 'round 2011.
			[[File:9-limit Singtervals.png\|thumb]]

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

			* 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.)
			* 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]].
			* 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!

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

	~~[[:File:singtervals9_visualization.pdf\|singtervals9 visualization.pdf]]~~

	[[Category:todo:intro]]		[[Category:todo:intro]]
			[[File:Singtervals9 visualization.pdf\|thumb]]

Spt3125: Category:todo:intro

2018-12-08T17:52:25Z

Category:todo:intro

← Older revision		Revision as of 17:52, 8 December 2018
Line 1:		Line 1:
	<soundcloud>https://soundcloud.com/andrew_heathwaite/9-limit-singtervals</soundcloud>		<soundcloud>https://soundcloud.com/andrew_heathwaite/9-limit-singtervals</soundcloud>

	[[:File:singtervals9_visualization.pdf\|singtervals9 visualization.pdf]]		[[:File:singtervals9_visualization.pdf\|singtervals9 visualization.pdf]]

			[[Category:todo:intro]]

PreImportHandFixes>Battaglia01: Mike - added SoundCloud player (EmbedVideo plugin)

2018-08-19T19:43:40Z

Mike - added SoundCloud player (EmbedVideo plugin)

← Older revision		Revision as of 19:43, 19 August 2018
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			<soundcloud>https://soundcloud.com/andrew_heathwaite/9-limit-singtervals</soundcloud>
	[[:File:singtervals9_visualization.pdf\|singtervals9 visualization.pdf]]		[[:File:singtervals9_visualization.pdf\|singtervals9 visualization.pdf]]

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

← Older revision		Revision as of 00:00, 17 July 2018
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	~~<h2>IMPORTED REVISION FROM WIKISPACES</h2>~~		[[:File:singtervals9_visualization.pdf\|singtervals9 visualization.pdf]]
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Wikispaces>xenjacob: Imported revision 533247350 - Original comment:

2014-11-30T22:32:14Z

**Imported revision 533247350 - Original comment: **

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:xenjacob|xenjacob]] and made on <tt>2014-11-30 22:32:14 UTC</tt>.<br>
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← Older revision		Revision as of 13:57, 20 March 2025
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]]		[[File:9-limit Singtervals.png\|thumb]]

	== A rundown of 9-odd-limit Singtervals ==		== 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.		* 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 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.		* 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>		<soundcloud>https://soundcloud.com/andrew_heathwaite/9-limit-singtervals</soundcloud>