Teff - Revision history

FloraC: - parent category

2025-04-28T14:44:55Z

- parent category

← Older revision		Revision as of 14:44, 28 April 2025
Line 11:		Line 11:
	Teff, like injera, is analogous to [[12edo]] in more than one way as it tempers out both 81/80 and 50/49. It necessarily falls on the flat end of the meantone spectrum, which is a change from what 12edo listeners may be accustomed to (although tempering the timbre to reflect this difference should help). But the easy availability of a plethora of higher-limit intervals more than makes up for this. Further, the fact that the period is a half-octave means that straight-fretted teff guitars (necessarily using the {{w\|Augmented-fourths tuning\|augmented-fourths tuning}}) are a possibility.		Teff, like injera, is analogous to [[12edo]] in more than one way as it tempers out both 81/80 and 50/49. It necessarily falls on the flat end of the meantone spectrum, which is a change from what 12edo listeners may be accustomed to (although tempering the timbre to reflect this difference should help). But the easy availability of a plethora of higher-limit intervals more than makes up for this. Further, the fact that the period is a half-octave means that straight-fretted teff guitars (necessarily using the {{w\|Augmented-fourths tuning\|augmented-fourths tuning}}) are a possibility.

	[[Category:~~Temperaments~~]]		[[Category:Teff\| ]] <!-- main article -->
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	[[Category:~~Teff~~]]		[[Category:Meantone family]]

Lériendil at 00:04, 20 April 2025

2025-04-20T00:04:15Z

← Older revision		Revision as of 00:04, 20 April 2025
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	[[Category:Temperaments]]		[[Category:Temperaments]]
	[[Category:Rank-2 temperaments]]		[[Category:Rank-2 temperaments]]
	~~[[Category:Hemipyth]]~~
	[[Category:Teff]]		[[Category:Teff]]

Lériendil at 00:03, 20 April 2025

2025-04-20T00:03:43Z

← Older revision		Revision as of 00:03, 20 April 2025
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	[[Category:Temperaments]]		[[Category:Temperaments]]
			[[Category:Rank-2 temperaments]]
			[[Category:Hemipyth]]
	[[Category:Teff]]		[[Category:Teff]]

FloraC: Link to meantone family. Misc. improvements

2024-06-27T09:49:28Z

Link to meantone family. Misc. improvements

← Older revision		Revision as of 09:49, 27 June 2024
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	'''Teff''' is a temperament in which the generator is a small quarter tone of about 47 ~~cents~~, and the period is half an octave. The period itself functions as [[24/17]], [[17/12]], [[10/7]] and [[7/5]], tempering out [[50/49]] and [[289/288]]. One period up and one generator down gives [[11/8]], which is also [[18/13]] (hence tempering out the [[grossma]], [[144/143]]). One period and two generators up gives a perfect fifth ([[3/2]]), and four of these gives a [[5/1]], tempering out [[81/80]] and making this a [[meantone]] temperament. The four aforementioned commas, plus [[78/77]], suffice to define teff in the [[17-limit]].		'''Teff''' is a [[temperament]] in which the [[generator]] is a small quarter tone of about 47 [[cent]]s, and the [[period]] is half an [[octave]]. The period itself functions as [[24/17]], [[17/12]], [[10/7]] and [[7/5]], tempering out [[50/49]] and [[289/288]]. One period up and one generator down gives [[11/8]], which is also [[18/13]] (hence tempering out the [[grossma]], [[144/143]]). One period and two generators up gives a perfect fifth ([[3/2]]), and four of these gives a [[5/1]], tempering out [[81/80]] and making this a [[meantone]] temperament. The four aforementioned commas, plus [[78/77]], suffice to define teff in the [[17-limit]].

			See [[Meantone family #Teff]] for more technical data.

	Teff was named by [[Mason Green]], after the grain from which injera (the bread) is made; this is because teff is closely related to [[injera]] temperament. Teff is to injera what [[mohajira]] is to meantone; both split the generator in half in order to accommodate the 11-limit. But unlike mohajira, teff also handles the 13- and 17-limits with relative ease and low complexity. This comes at the cost of some 7-limit intervals being rather out of tune as a consequence of tempering out 50:49.		Teff was named by [[Mason Green]], after the grain from which injera (the bread) is made; this is because teff is closely related to [[injera]] temperament. Teff is to injera what [[mohajira]] is to meantone; both split the generator in half in order to accommodate the 11-limit. But unlike mohajira, teff also handles the 13- and 17-limits with relative ease and low complexity. This comes at the cost of some 7-limit intervals being rather out of tune as a consequence of tempering out 50:49.

	Teff forms ~~2MOSes~~ of 24, 26, 50, etc. [[26edo]] and [[50edo]] can both be used to tune teff (the former using the patent val, the latter using 50c). However, [[76edo]] works even better for teff, much as [[38edo]] (which is half of [[76edo]]) is an excellent tuning for injera. Here, the large and small steps of teff[26] are in ratio 3:2. Teff[26] has the structure 2(LLLLLLLLLLLLs).		Teff forms [[2mos]]es of 24, 26, 50, etc. [[26edo]] and [[50edo]] can both be used to tune teff (the former using the patent val, the latter using 50c). However, [[76edo]] works even better for teff, much as [[38edo]] (which is half of [[76edo]]) is an excellent tuning for injera. Here, the large and small steps of teff[26] are in ratio 3:2. Teff[26] has the structure 2(LLLLLLLLLLLLs).

	Using 76edo, the 7th harmonic is quite sharp and the 11th harmonic only a tiny bit so, while the 3rd, 5th, 9th, 13th, and 17th harmonics are all flat by different amounts. One might even consider teff to be a 19-limit temperament if the subminor third (which represents both [[7/6]] and [[13/11]]) is taken as representing a flat [[19/16]] as well.		Using 76edo, the 7th harmonic is quite sharp and the 11th harmonic only a tiny bit so, while the 3rd, 5th, 9th, 13th, and 17th harmonics are all flat by different amounts. One might even consider teff to be a 19-limit temperament if the subminor third (which represents both [[7/6]] and [[13/11]]) is taken as representing a flat [[19/16]] as well.

	Teff, like injera, is analogous to [[12edo]] in more than one way as it tempers out both 81/80 and 50/49. It necessarily falls on the flat end of the meantone spectrum, which is a change from what 12edo listeners may be accustomed to (although tempering the timbre to reflect this difference should help). But the easy availability of a plethora of higher-limit intervals more than makes up for this. Further, the fact that the period is a half-octave means that straight-fretted teff guitars (~~necesarily~~ using the ~~[https://en.wikipedia.org/wiki/~~Augmented-~~fourths_tuning~~ augmented-fourths tuning]) are a possibility.		Teff, like injera, is analogous to [[12edo]] in more than one way as it tempers out both 81/80 and 50/49. It necessarily falls on the flat end of the meantone spectrum, which is a change from what 12edo listeners may be accustomed to (although tempering the timbre to reflect this difference should help). But the easy availability of a plethora of higher-limit intervals more than makes up for this. Further, the fact that the period is a half-octave means that straight-fretted teff guitars (necessarily using the {{w\|Augmented-fourths tuning\|augmented-fourths tuning}}) are a possibility.

	[[Category:Temperaments]]		[[Category:Temperaments]]
	[[Category:Teff]]		[[Category:Teff]]

Xenwolf: replace {{IoT}} by plain categorization

2022-03-01T19:38:24Z

replace {{IoT}} by plain categorization

← Older revision		Revision as of 19:38, 1 March 2022
Line 9:		Line 9:
	Teff, like injera, is analogous to [[12edo]] in more than one way as it tempers out both 81/80 and 50/49. It necessarily falls on the flat end of the meantone spectrum, which is a change from what 12edo listeners may be accustomed to (although tempering the timbre to reflect this difference should help). But the easy availability of a plethora of higher-limit intervals more than makes up for this. Further, the fact that the period is a half-octave means that straight-fretted teff guitars (necesarily using the [https://en.wikipedia.org/wiki/Augmented-fourths_tuning augmented-fourths tuning]) are a possibility.		Teff, like injera, is analogous to [[12edo]] in more than one way as it tempers out both 81/80 and 50/49. It necessarily falls on the flat end of the meantone spectrum, which is a change from what 12edo listeners may be accustomed to (although tempering the timbre to reflect this difference should help). But the easy availability of a plethora of higher-limit intervals more than makes up for this. Further, the fact that the period is a half-octave means that straight-fretted teff guitars (necesarily using the [https://en.wikipedia.org/wiki/Augmented-fourths_tuning augmented-fourths tuning]) are a possibility.

			[[Category:Temperaments]]
	[[Category:Teff]]		[[Category:Teff]]
	~~{{IoT}}~~

Xenwolf: recat

2021-05-24T16:28:03Z

recat

← Older revision		Revision as of 16:28, 24 May 2021
Line 9:		Line 9:
	Teff, like injera, is analogous to [[12edo]] in more than one way as it tempers out both 81/80 and 50/49. It necessarily falls on the flat end of the meantone spectrum, which is a change from what 12edo listeners may be accustomed to (although tempering the timbre to reflect this difference should help). But the easy availability of a plethora of higher-limit intervals more than makes up for this. Further, the fact that the period is a half-octave means that straight-fretted teff guitars (necesarily using the [https://en.wikipedia.org/wiki/Augmented-fourths_tuning augmented-fourths tuning]) are a possibility.		Teff, like injera, is analogous to [[12edo]] in more than one way as it tempers out both 81/80 and 50/49. It necessarily falls on the flat end of the meantone spectrum, which is a change from what 12edo listeners may be accustomed to (although tempering the timbre to reflect this difference should help). But the easy availability of a plethora of higher-limit intervals more than makes up for this. Further, the fact that the period is a half-octave means that straight-fretted teff guitars (necesarily using the [https://en.wikipedia.org/wiki/Augmented-fourths_tuning augmented-fourths tuning]) are a possibility.

	~~[[Category:Temperament]]~~
	[[Category:Teff]]		[[Category:Teff]]
			{{IoT}}

Aura: corrected failed link

2020-12-22T22:39:49Z

corrected failed link

← Older revision		Revision as of 22:39, 22 December 2020
Line 1:		Line 1:
	'''Teff''' is a temperament in which the generator is a small quarter tone of about 47 cents, and the period is half an octave. The period itself functions as [[24/17]], [[17/12], [[10/7]] and [[7/5]], tempering out [[50/49]] and [[289/288]]. One period up and one generator down gives [[11/8]], which is also [[18/13]] (hence tempering out the [[grossma]], [[144/143]]). One period and two generators up gives a perfect fifth ([[3/2]]), and four of these gives a [[5/1]], tempering out [[81/80]] and making this a [[meantone]] temperament. The four aforementioned commas, plus [[78/77]], suffice to define teff in the [[17-limit]].		'''Teff''' is a temperament in which the generator is a small quarter tone of about 47 cents, and the period is half an octave. The period itself functions as [[24/17]], [[17/12]], [[10/7]] and [[7/5]], tempering out [[50/49]] and [[289/288]]. One period up and one generator down gives [[11/8]], which is also [[18/13]] (hence tempering out the [[grossma]], [[144/143]]). One period and two generators up gives a perfect fifth ([[3/2]]), and four of these gives a [[5/1]], tempering out [[81/80]] and making this a [[meantone]] temperament. The four aforementioned commas, plus [[78/77]], suffice to define teff in the [[17-limit]].

	Teff was named by [[Mason Green]], after the grain from which injera (the bread) is made; this is because teff is closely related to [[injera]] temperament. Teff is to injera what [[mohajira]] is to meantone; both split the generator in half in order to accommodate the 11-limit. But unlike mohajira, teff also handles the 13- and 17-limits with relative ease and low complexity. This comes at the cost of some 7-limit intervals being rather out of tune as a consequence of tempering out 50:49.		Teff was named by [[Mason Green]], after the grain from which injera (the bread) is made; this is because teff is closely related to [[injera]] temperament. Teff is to injera what [[mohajira]] is to meantone; both split the generator in half in order to accommodate the 11-limit. But unlike mohajira, teff also handles the 13- and 17-limits with relative ease and low complexity. This comes at the cost of some 7-limit intervals being rather out of tune as a consequence of tempering out 50:49.

Xenwolf: links, cats

2020-12-22T22:12:17Z

links, cats

← Older revision		Revision as of 22:12, 22 December 2020
Line 1:		Line 1:
	'''Teff''' is a temperament in which the generator is a small quarter tone of about 47 cents, and the period is half an octave. The period itself functions as 24:17, 17:12, 10:7 and 7:5, tempering out [[~~49\|~~50:49]] and [[~~288\|~~289:288]]. One period up and one generator down gives 11:8, which is also 18:13 (hence tempering out the [[~~grossma\|~~grossma]], 144:143). One period and two generators up gives a perfect fifth (3:2), and four of these gives a 5:1, tempering out 81:80 and making this a meantone temperament. The four aforementioned commas, plus 78:77, suffice to define teff in the 17-limit.		'''Teff''' is a temperament in which the generator is a small quarter tone of about 47 cents, and the period is half an octave. The period itself functions as [[24/17]], [[17/12], [[10/7]] and [[7/5]], tempering out [[50/49]] and [[289/288]]. One period up and one generator down gives [[11/8]], which is also [[18/13]] (hence tempering out the [[grossma]], [[144/143]]). One period and two generators up gives a perfect fifth ([[3/2]]), and four of these gives a [[5/1]], tempering out [[81/80]] and making this a [[meantone]] temperament. The four aforementioned commas, plus [[78/77]], suffice to define teff in the [[17-limit]].

	Teff was named by Mason Green, after the grain from which injera (the bread) is made; this is because teff is closely related to [[~~Injera\|~~injera]] temperament. Teff is to injera what [[~~Mohajira\|~~mohajira]] is to meantone; both split the generator in half in order to accommodate the 11-limit. But unlike mohajira, teff also handles the 13- and 17-limits with relative ease and low complexity. This comes at the cost of some 7-limit intervals being rather out of tune as a consequence of tempering out 50:49.		Teff was named by [[Mason Green]], after the grain from which injera (the bread) is made; this is because teff is closely related to [[injera]] temperament. Teff is to injera what [[mohajira]] is to meantone; both split the generator in half in order to accommodate the 11-limit. But unlike mohajira, teff also handles the 13- and 17-limits with relative ease and low complexity. This comes at the cost of some 7-limit intervals being rather out of tune as a consequence of tempering out 50:49.

	Teff forms 2MOSes of 24, 26, 50, etc. [[~~26edo\|~~26edo]] and [[~~50edo\|~~50edo]] can both be used to tune teff (the former using the patent val, the latter using 50c). However, [[~~76edo\|~~76edo]] works even better for teff, much as 38edo (which is half of 76edo) is an excellent tuning for injera. Here, the large and small steps of teff[26] are in ratio 3:2. Teff[26] has the structure 2(LLLLLLLLLLLLs).		Teff forms 2MOSes of 24, 26, 50, etc. [[26edo]] and [[50edo]] can both be used to tune teff (the former using the patent val, the latter using 50c). However, [[76edo]] works even better for teff, much as [[38edo]] (which is half of [[76edo]]) is an excellent tuning for injera. Here, the large and small steps of teff[26] are in ratio 3:2. Teff[26] has the structure 2(LLLLLLLLLLLLs).

	Using 76edo, the 7th harmonic is quite sharp and the 11th harmonic only a tiny bit so, while the 3rd, 5th, 9th, 13th, and 17th harmonics are all flat by different amounts. One might even consider teff to be a 19-limit temperament if the subminor third (which represents both 7:6 and 13:11) is taken as representing a flat 19:16 as well.		Using 76edo, the 7th harmonic is quite sharp and the 11th harmonic only a tiny bit so, while the 3rd, 5th, 9th, 13th, and 17th harmonics are all flat by different amounts. One might even consider teff to be a 19-limit temperament if the subminor third (which represents both [[7/6]] and [[13/11]]) is taken as representing a flat [[19/16]] as well.

	Teff, like injera, is analogous to 12edo in more than one way as it tempers out both 81:80 and 50:49. It necessarily falls on the flat end of the meantone spectrum, which is a change from what 12edo listeners may be accustomed to (although tempering the timbre to reflect this difference should help). But the easy availability of a plethora of higher-limit intervals more than makes up for this. Further, the fact that the period is a half-octave means that straight-fretted teff guitars (necesarily using the [https://en.wikipedia.org/wiki/Augmented-fourths_tuning augmented-fourths tuning]) are a possibility.		Teff, like injera, is analogous to [[12edo]] in more than one way as it tempers out both 81/80 and 50/49. It necessarily falls on the flat end of the meantone spectrum, which is a change from what 12edo listeners may be accustomed to (although tempering the timbre to reflect this difference should help). But the easy availability of a plethora of higher-limit intervals more than makes up for this. Further, the fact that the period is a half-octave means that straight-fretted teff guitars (necesarily using the [https://en.wikipedia.org/wiki/Augmented-fourths_tuning augmented-fourths tuning]) are a possibility.
	[[Category:~~teff~~]]
			[[Category:Temperament]]
			[[Category:Teff]]

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

← Older revision		Revision as of 00:00, 17 July 2018
Line 1:		Line 1:
	~~<h2>IMPORTED REVISION FROM WIKISPACES</h2>~~		'''Teff''' is a temperament in which the generator is a small quarter tone of about 47 cents, and the period is half an octave. The period itself functions as 24:17, 17:12, 10:7 and 7:5, tempering out [[49\|50:49]] and [[288\|289:288]]. One period up and one generator down gives 11:8, which is also 18:13 (hence tempering out the [[grossma\|grossma]], 144:143). One period and two generators up gives a perfect fifth (3:2), and four of these gives a 5:1, tempering out 81:80 and making this a meantone temperament. The four aforementioned commas, plus 78:77, suffice to define teff in the 17-limit.
	~~This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>~~
	~~: This revision was by author [[User:MasonGreen1\|MasonGreen1]] and made on <tt>2016-10-24 22:04:33 UTC</tt>.<br>~~
	~~: The original revision id was <tt>596770230</tt>.<br>~~
	~~: The revision comment was: <tt></tt><br>~~
	~~The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>~~
	~~<h4>Original Wikitext content:</h4>~~
	<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">Teff is a temperament in which the generator is a small quarter tone of about 47 cents, and the period is half an octave. The period itself functions as 24:17, 17:12, 10:7 and 7:5, tempering out [[49\|50:49]] and [[288\|289:288]]. One period up and one generator down gives 11:8, which is also 18:13 (hence tempering out the [[grossma]], 144:143). One period and two generators up gives a perfect fifth (3:2), and four of these gives a 5:1, tempering out 81:80 and making this a meantone temperament. The four aforementioned commas, plus 78:77, suffice to define teff in the 17-limit.

	Teff was named by Mason Green, after the grain from which injera (the bread) is made; this is because teff is closely related to [[injera]] temperament. Teff is to injera what [[mohajira]] is to meantone; both split the generator in half in order to accommodate the 11-limit. But unlike mohajira, teff also handles the 13- and 17-limits with relative ease and low complexity. This comes at the cost of some 7-limit intervals being rather out of tune as a consequence of tempering out 50:49.		Teff was named by Mason Green, after the grain from which injera (the bread) is made; this is because teff is closely related to [[Injera\|injera]] temperament. Teff is to injera what [[Mohajira\|mohajira]] is to meantone; both split the generator in half in order to accommodate the 11-limit. But unlike mohajira, teff also handles the 13- and 17-limits with relative ease and low complexity. This comes at the cost of some 7-limit intervals being rather out of tune as a consequence of tempering out 50:49.

	Teff forms 2MOSes of 24, 26, 50, etc. [[26edo]] and [[50edo]] can both be used to tune teff (the former using the patent val, the latter using 50c). However, [[76edo]] works even better for teff, much as 38edo (which is half of 76edo) is an excellent tuning for injera. Here, the large and small steps of teff[26] are in ratio 3:2. Teff[26] has the structure 2(LLLLLLLLLLLLs).		Teff forms 2MOSes of 24, 26, 50, etc. [[26edo\|26edo]] and [[50edo\|50edo]] can both be used to tune teff (the former using the patent val, the latter using 50c). However, [[76edo\|76edo]] works even better for teff, much as 38edo (which is half of 76edo) is an excellent tuning for injera. Here, the large and small steps of teff[26] are in ratio 3:2. Teff[26] has the structure 2(LLLLLLLLLLLLs).

	Using 76edo, the 7th harmonic is quite sharp and the 11th harmonic only a tiny bit so, while the 3rd, 5th, 9th, 13th, and 17th harmonics are all flat by different amounts. One might even consider teff to be a 19-limit temperament if the subminor third (which represents both 7:6 and 13:11) is taken as representing a flat 19:16 as well.		Using 76edo, the 7th harmonic is quite sharp and the 11th harmonic only a tiny bit so, while the 3rd, 5th, 9th, 13th, and 17th harmonics are all flat by different amounts. One might even consider teff to be a 19-limit temperament if the subminor third (which represents both 7:6 and 13:11) is taken as representing a flat 19:16 as well.

	Teff, like injera, is analogous to 12edo in more than one way as it tempers out both 81:80 and 50:49. It necessarily falls on the flat end of the meantone spectrum, which is a change from what 12edo listeners may be accustomed to (although tempering the timbre to reflect this difference should help). But the easy availability of a plethora of higher-limit intervals more than makes up for this. Further, the fact that the period is a half-octave means that straight-fretted teff guitars (necesarily using the [[https://en.wikipedia.org/wiki/Augmented-fourths_tuning\|augmented-fourths tuning]]) are a possibility.~~</pre></div>~~		Teff, like injera, is analogous to 12edo in more than one way as it tempers out both 81:80 and 50:49. It necessarily falls on the flat end of the meantone spectrum, which is a change from what 12edo listeners may be accustomed to (although tempering the timbre to reflect this difference should help). But the easy availability of a plethora of higher-limit intervals more than makes up for this. Further, the fact that the period is a half-octave means that straight-fretted teff guitars (necesarily using the [https://en.wikipedia.org/wiki/Augmented-fourths_tuning augmented-fourths tuning]) are a possibility.
	~~<h4>Original HTML content:</h4>~~		[[Category:teff]]
	<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Teff</title></head><body><strong>Teff</strong> is a temperament in which the generator is a small quarter tone of about 47 cents, and the period is half an octave. The period itself functions as 24:17, 17:12, 10:7 and 7:5, tempering out <a class="wiki_link" href="/49">50:49</a> and <a class="wiki_link" href="/288">289:288</a>. One period up and one generator down gives 11:8, which is also 18:13 (hence tempering out the <a class="wiki_link" href="/grossma">grossma</a>, 144:143). One period and two generators up gives a perfect fifth (3:2), and four of these gives a 5:1, tempering out 81:80 and making this a meantone temperament. The four aforementioned commas, plus 78:77, suffice to define teff in the 17-limit.<br />
	~~<br />~~
	Teff was named by Mason Green, after the grain from which injera (the bread) is made; this is because teff is closely related to <a class="wiki_link" href="/injera">injera</a> temperament. Teff is to injera what <a class="wiki_link" href="/mohajira">mohajira</a> is to meantone; both split the generator in half in order to accommodate the 11-limit. But unlike mohajira, teff also handles the 13- and 17-limits with relative ease and low complexity. This comes at the cost of some 7-limit intervals being rather out of tune as a consequence of tempering out 50:49. <br />
	~~<br />~~
	Teff forms 2MOSes of 24, 26, 50, etc. <a class="wiki_link" href="/26edo">26edo</a> and <a class="wiki_link" href="/50edo">50edo</a> can both be used to tune teff (the former using the patent val, the latter using 50c). However, <a class="wiki_link" href="/76edo">76edo</a> works even better for teff, much as 38edo (which is half of 76edo) is an excellent tuning for injera. Here, the large and small steps of teff~~[26~~] ~~are in ratio 3:2. Teff[26~~] ~~has the structure 2(LLLLLLLLLLLLs).<br />~~
	~~<br />~~
	Using 76edo, the 7th harmonic is quite sharp and the 11th harmonic only a tiny bit so, while the 3rd, 5th, 9th, 13th, and 17th harmonics are all flat by different amounts. One might even consider teff to be a 19-limit temperament if the subminor third (which represents both 7:6 and 13:11) is taken as representing a flat 19:16 as well.<br />
	~~<br />~~
	Teff, like injera, is analogous to 12edo in more than one way as it tempers out both 81:80 and 50:49. It necessarily falls on the flat end of the meantone spectrum, which is a change from what 12edo listeners may be accustomed to (although tempering the timbre to reflect this difference should help). But the easy availability of a plethora of higher-limit intervals more than makes up for this. Further, the fact that the period is a half-octave means that straight-fretted teff guitars (necesarily using the <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Augmented-fourths_tuning" rel="nofollow">augmented-fourths tuning</a>) are a possibility.</body></html></pre></div>

Wikispaces>MasonGreen1: Imported revision 596770230 - Original comment:

2016-10-24T22:04:33Z

**Imported revision 596770230 - Original comment: **

New page

<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:MasonGreen1|MasonGreen1]] and made on <tt>2016-10-24 22:04:33 UTC</tt>.<br>
: The original revision id was <tt>596770230</tt>.<br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">**Teff** is a temperament in which the generator is a small quarter tone of about 47 cents, and the period is half an octave. The period itself functions as 24:17, 17:12, 10:7 and 7:5, tempering out [[49|50:49]] and [[288|289:288]]. One period up and one generator down gives 11:8, which is also 18:13 (hence tempering out the [[grossma]], 144:143). One period and two generators up gives a perfect fifth (3:2), and four of these gives a 5:1, tempering out 81:80 and making this a meantone temperament. The four aforementioned commas, plus 78:77, suffice to define teff in the 17-limit.

Teff was named by Mason Green, after the grain from which injera (the bread) is made; this is because teff is closely related to [[injera]] temperament. Teff is to injera what [[mohajira]] is to meantone; both split the generator in half in order to accommodate the 11-limit. But unlike mohajira, teff also handles the 13- and 17-limits with relative ease and low complexity. This comes at the cost of some 7-limit intervals being rather out of tune as a consequence of tempering out 50:49.

Teff forms 2MOSes of 24, 26, 50, etc. [[26edo]] and [[50edo]] can both be used to tune teff (the former using the patent val, the latter using 50c). However, [[76edo]] works even better for teff, much as 38edo (which is half of 76edo) is an excellent tuning for injera. Here, the large and small steps of teff[26] are in ratio 3:2. Teff[26] has the structure 2(LLLLLLLLLLLLs).

Using 76edo, the 7th harmonic is quite sharp and the 11th harmonic only a tiny bit so, while the 3rd, 5th, 9th, 13th, and 17th harmonics are all flat by different amounts. One might even consider teff to be a 19-limit temperament if the subminor third (which represents both 7:6 and 13:11) is taken as representing a flat 19:16 as well.

Teff, like injera, is analogous to 12edo in more than one way as it tempers out both 81:80 and 50:49. It necessarily falls on the flat end of the meantone spectrum, which is a change from what 12edo listeners may be accustomed to (although tempering the timbre to reflect this difference should help). But the easy availability of a plethora of higher-limit intervals more than makes up for this. Further, the fact that the period is a half-octave means that straight-fretted teff guitars (necesarily using the [[https://en.wikipedia.org/wiki/Augmented-fourths_tuning|augmented-fourths tuning]]) are a possibility.</pre></div>
<h4>Original HTML content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>Teff</title></head><body><strong>Teff</strong> is a temperament in which the generator is a small quarter tone of about 47 cents, and the period is half an octave. The period itself functions as 24:17, 17:12, 10:7 and 7:5, tempering out <a class="wiki_link" href="/49">50:49</a> and <a class="wiki_link" href="/288">289:288</a>. One period up and one generator down gives 11:8, which is also 18:13 (hence tempering out the <a class="wiki_link" href="/grossma">grossma</a>, 144:143). One period and two generators up gives a perfect fifth (3:2), and four of these gives a 5:1, tempering out 81:80 and making this a meantone temperament. The four aforementioned commas, plus 78:77, suffice to define teff in the 17-limit.<br />
<br />
Teff was named by Mason Green, after the grain from which injera (the bread) is made; this is because teff is closely related to <a class="wiki_link" href="/injera">injera</a> temperament. Teff is to injera what <a class="wiki_link" href="/mohajira">mohajira</a> is to meantone; both split the generator in half in order to accommodate the 11-limit. But unlike mohajira, teff also handles the 13- and 17-limits with relative ease and low complexity. This comes at the cost of some 7-limit intervals being rather out of tune as a consequence of tempering out 50:49. <br />
<br />
Teff forms 2MOSes of 24, 26, 50, etc. <a class="wiki_link" href="/26edo">26edo</a> and <a class="wiki_link" href="/50edo">50edo</a> can both be used to tune teff (the former using the patent val, the latter using 50c). However, <a class="wiki_link" href="/76edo">76edo</a> works even better for teff, much as 38edo (which is half of 76edo) is an excellent tuning for injera. Here, the large and small steps of teff[26] are in ratio 3:2. Teff[26] has the structure 2(LLLLLLLLLLLLs).<br />
<br />
Using 76edo, the 7th harmonic is quite sharp and the 11th harmonic only a tiny bit so, while the 3rd, 5th, 9th, 13th, and 17th harmonics are all flat by different amounts. One might even consider teff to be a 19-limit temperament if the subminor third (which represents both 7:6 and 13:11) is taken as representing a flat 19:16 as well.<br />
<br />
Teff, like injera, is analogous to 12edo in more than one way as it tempers out both 81:80 and 50:49. It necessarily falls on the flat end of the meantone spectrum, which is a change from what 12edo listeners may be accustomed to (although tempering the timbre to reflect this difference should help). But the easy availability of a plethora of higher-limit intervals more than makes up for this. Further, the fact that the period is a half-octave means that straight-fretted teff guitars (necesarily using the <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Augmented-fourths_tuning" rel="nofollow">augmented-fourths tuning</a>) are a possibility.</body></html></pre></div>