Neutral third: Difference between revisions
Rework intro to hopefully better explain this concept (it doesn't rely on a split octave) |
m Fix link |
||
| (2 intermediate revisions by the same user not shown) | |||
| Line 1: | Line 1: | ||
{{Interwiki | |||
| en = Neutral third | |||
| zh = 中三度 | |||
}} | |||
{{Infobox interval region | {{Infobox interval region | ||
| Name = Neutral third | | Name = Neutral third | ||
| Line 8: | Line 12: | ||
| MOSes = [[4L 3s]], [[3L 4s]], [[7L 3s]], [[3L 7s]] | | MOSes = [[4L 3s]], [[3L 4s]], [[7L 3s]], [[3L 7s]] | ||
| Complement = [[Neutral sixth]] | | Complement = [[Neutral sixth]] | ||
| Lower region = [[Minor | | Lower region = [[Minor third]] | ||
| Higher region = [[Major third]] | | Higher region = [[Major third]] | ||
}} | }} | ||
| Line 23: | Line 27: | ||
=== By prime limit === | === By prime limit === | ||
The [[3-limit]] and 5-limit do not have simple neutral thirds (though hemipythagorean has an irrational [[sqrt(3/2)]] interval that might be considered the "canonical" neutral third), so we start with the 7-limit: | The [[3-limit]] and 5-limit do not have simple neutral thirds (though hemipythagorean has an irrational [[sqrt(3/2)]] interval that might be considered the "canonical" neutral third), so we start with the 7-limit: | ||
* The 7-limit artoneutral and tendoneutral thirds are the ratios of [[60/49]] and [[49/40]] respectively, and they are slightly flat of and slightly sharp of 351{{c}} respectively. | |||
* The 7-limit | * The 11-limit alpharabian artoneutral and tendoneutral thirds are the ratios of [[11/9]] and [[27/22]] respectively, and they are about 347 and 355{{c}} respectively. | ||
* The 11-limit | * The 13-limit artoneutral and tendoneutral thirds are the ratios of [[39/32]] and [[16/13]] respectively, and they are about 342 and 359{{c}} respectively. | ||
* The 13-limit | * The 17-limit supraminor and submajor thirds are the ratios of [[17/14]] and [[21/17]] respectively, and they are about 336 and 366{{c}} respectively. | ||
* The 17-limit | |||
=== By delta === | === By delta === | ||
| Line 68: | Line 71: | ||
== In edos == | == In edos == | ||
The following table lists the best tuning of 39/32 and 16/13 in various significant [[edo]]s. For applicable edos, it also lists one half of the edo's perfect fifth, approximating [[ | The following table lists the best tuning of 39/32 and 16/13 in various significant [[edo]]s. For applicable edos, it also lists one half of the edo's perfect fifth, approximating [[sqrt(3/2)]], which, while not a just interval, is the "canonical" neutral third tuning, as stacking two of them gives [[3/2]]. | ||
{| class="wikitable" | {| class="wikitable" | ||
| Line 127: | Line 130: | ||
|- | |- | ||
| 60/49, 49/40 | | 60/49, 49/40 | ||
| [[Breed (temperament)|Breed]]* | | [[Breed (temperament)|Breed]] retraction* | ||
|- | |- | ||
| 11/9, 27/22 | | 11/9, 27/22 | ||