Major third (diatonic interval category): Difference between revisions
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Being an abstract mos degree, and not a specific interval, the diatonic major third does not have a fixed tuning, but instead has a range of ways it can be tuned, based on the tuning of the generator used in making the scale. | Being an abstract mos degree, and not a specific interval, the diatonic major third does not have a fixed tuning, but instead has a range of ways it can be tuned, based on the tuning of the generator used in making the scale. | ||
The tuning range of the diatonic major third ranges from 342.8 to 480{{c}}. The generator for a given tuning in cents, ''n'', for the diatonic major third can be found by {{ | The tuning range of the diatonic major third ranges from 342.8 to 480{{c}}. The generator for a given tuning in cents, ''n'', for the diatonic major third can be found by {{nowrap| (''n'' + 2400)/4 }}. For example, the third 384{{c}} gives us {{nowrap| (384 + 2400)/4 {{=}} 2784/4 {{=}} 696{{c}} }}, corresponding to 50edo. | ||
Several example tunings are provided below: | Several example tunings are provided below: | ||
{| class="wikitable" | {| class="wikitable center-all left-1" | ||
|+ style="font-size: 105%;" | Tunings of the major third | |+ style="font-size: 105%;" | Tunings of the major third | ||
|- | |- | ||
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If the diatonic perfect fifth is treated as [[3/2]], approximating various intervals with the diatonic major third leads to the following temperaments: | If the diatonic perfect fifth is treated as [[3/2]], approximating various intervals with the diatonic major third leads to the following temperaments: | ||
{| class="wikitable" | {| class="wikitable center-2 center-5" | ||
|- | |- | ||
! Just interval | ! Just<br>interval | ||
! Cents | ! Cents | ||
! Temperament | ! Temperament | ||
! | ! Vanishing<br>comma | ||
! Generator (eigenmonzo tuning) | ! Generator<br>(eigenmonzo tuning) | ||
|- | |- | ||
| [[27/22]] | | [[27/22]] | ||
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| [[Io]] | | [[Io]] | ||
| [[33/32]] | | [[33/32]] | ||
| {{nowrap| | | {{nowrap| P5 ≈ 689{{c}} }} | ||
|- | |- | ||
| [[16/13]] | | [[16/13]] | ||
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| [[Superflat]] | | [[Superflat]] | ||
| [[1053/1024]] | | [[1053/1024]] | ||
| {{nowrap| | | {{nowrap| P5 ≈ 690{{c}} }} | ||
|- | |- | ||
| [[21/17]] | | [[21/17]] | ||
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| Temperament of 459/448 | | Temperament of 459/448 | ||
| 459/448 | | 459/448 | ||
| {{nowrap| | | {{nowrap| P5 ≈ 692{{c}} }} | ||
|- | |- | ||
| [[5/4]] | | [[5/4]] | ||
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| [[Meantone]] | | [[Meantone]] | ||
| [[81/80]] | | [[81/80]] | ||
| {{nowrap| | | {{nowrap| P5 ≈ 697{{c}} }} | ||
|- | |- | ||
| [[81/64]] | | [[81/64]] | ||
| 408{{c}} | | 408{{c}} | ||
| [[Pythagorean tuning | | [[Pythagorean tuning]] | ||
| [[1/1]] | | [[1/1]] | ||
| {{nowrap| | | {{nowrap| P5 ≈ 702{{c}} }} | ||
|- | |- | ||
| [[14/11]] | | [[14/11]] | ||
| 418{{c}} | | 418{{c}} | ||
| [[ | | [[Pepperoni]] | ||
| [[896/891]] | | [[896/891]] | ||
| {{nowrap| | | {{nowrap| P5 ≈ 705{{c}} }} | ||
|- | |- | ||
| [[9/7]] | | [[9/7]] | ||
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| [[Superpyth|Archy/superpyth]] | | [[Superpyth|Archy/superpyth]] | ||
| [[64/63]] | | [[64/63]] | ||
| {{nowrap| | | {{nowrap| P5 ≈ 709{{c}} }} | ||
|- | |- | ||
| [[13/10]] | | [[13/10]] | ||
| 454{{c}} | | 454{{c}} | ||
| [[Oceanfront]]/ | | [[Oceanfront]] / temperament of 416/405 | ||
| [[416/405]] | | [[416/405]] | ||
| {{nowrap| | | {{nowrap| P5 ≈ 714{{c}} }} | ||
|} | |} | ||