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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | '''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]]. |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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| : This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2016-10-24 22:04:33 UTC</tt>.<br>
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| : The original revision id was <tt>596770230</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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| <h4>Original Wikitext content:</h4>
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| <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.
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| 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.
| | See [[Meantone family #Teff]] for more technical data. |
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| 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 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. |
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| 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 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). |
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| 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>
| | 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. |
| <h4>Original HTML content:</h4>
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| <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 />
| | 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. |
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| 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 />
| | [[Category:Teff| ]] <!-- main article --> |
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| | [[Category:Rank-2 temperaments]] |
| 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 />
| | [[Category:Meantone family]] |
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| 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 /> | |
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| 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> | |