Minor third: Difference between revisions
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This article covers intervals between 240 and 340{{c}}. The outer range of this might be too extreme to call "minor thirds", but this is done so that one can find what they're looking for easily. | This article covers intervals between 240 and 340{{c}}. The outer range of this might be too extreme to call "minor thirds", but this is done so that one can find what they're looking for easily. | ||
==In just intonation== | == In just intonation == | ||
===By prime limit=== | === By prime limit === | ||
3-limit intervals in the range of minor thirds include the '''Pythagorean minor third''' of [[32/27]], 294.1{{c}} in size, which corresponds to the mos-based interval category of the diatonic minor third and is generated by [[stacking]] three just perfect fourths of [[4/3]], and the '''Pythagorean augmented second''' of [[19683/16384]], which is sharp of 32/27 by one Pythagorean comma, and is about 318{{c}} in size. | 3-limit intervals in the range of minor thirds include the '''Pythagorean minor third''' of [[32/27]], 294.1{{c}} in size, which corresponds to the mos-based interval category of the diatonic minor third and is generated by [[stacking]] three just perfect fourths of [[4/3]], and the '''Pythagorean augmented second''' of [[19683/16384]], which is sharp of 32/27 by one Pythagorean comma, and is about 318{{c}} in size. | ||
Much [[odd limit|simpler]] minor thirds exist in higher [[prime limit|limits]], however, for example: | Much [[odd limit|simpler]] minor thirds exist in higher [[prime limit|limits]], however, for example: | ||
*The 5-limit '''classical minor third''' is a ratio of [[6/5]], and is about 316{{c}}. | * The 5-limit '''classical minor third''' is a ratio of [[6/5]], and is about 316{{c}}. | ||
*The 7-limit '''(septimal) subminor third''' is a ratio of [[7/6]], and is about 267{{c}}. | * The 7-limit '''(septimal) subminor third''' is a ratio of [[7/6]], and is about 267{{c}}. | ||
*The 11-limit '''neogothic minor third''' is a ratio of [[13/11]], and is about 290{{c}}. | * The 11-limit '''neogothic minor third''' is a ratio of [[13/11]], and is about 290{{c}}. | ||
**Note that this is '''not''' the fifth complement to the neogothic [[major third]], which is actually a ratio of 33/28, and is about 284{{c}}. | ** Note that this is '''not''' the fifth complement to the neogothic [[major third]], which is actually a ratio of 33/28, and is about 284{{c}}. | ||
*The 13-limit '''(tridecimal) inframinor third''' is a ratio of [[15/13]], and is about 248{{c}}. | * The 13-limit '''(tridecimal) inframinor third''' is a ratio of [[15/13]], and is about 248{{c}}. | ||
**There is also a 13-limit '''(tridecimal) supraminor third''', which is a ratio of [[63/52]], and is about 332{{c}}. | ** There is also a 13-limit '''(tridecimal) supraminor third''', which is a ratio of [[63/52]], and is about 332{{c}}. | ||
*The 17-limit '''(septendecimal) submajor third''' is a ratio of [[17/14]], and is about 336{{c}}. | * The 17-limit '''(septendecimal) submajor third''' is a ratio of [[17/14]], and is about 336{{c}}. | ||
===By delta=== | |||
=== By delta === | |||
See [[Delta-N ratio]]. | See [[Delta-N ratio]]. | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
|6/5 | ! colspan="2" | Delta-1 | ||
|316{{C}} | ! colspan="2" | Delta-2 | ||
|13/11 | ! colspan="2" | Delta-3 | ||
|290{{C}} | ! colspan="2" | Delta-4 | ||
|17/14 | |- | ||
|336{{C}} | | 6/5 | ||
|23/19 | | 316{{C}} | ||
|331{{C}} | | 13/11 | ||
| 290{{C}} | |||
| 17/14 | |||
| 336{{C}} | |||
| 23/19 | |||
| 331{{C}} | |||
|- | |- | ||
|7/6 | | 7/6 | ||
|267{{C}} | | 267{{C}} | ||
|15/13 | | 15/13 | ||
|248{{C}} | | 248{{C}} | ||
|19/16 | | 19/16 | ||
|298{{C}} | | 298{{C}} | ||
|25/21 | | 25/21 | ||
|302{{C}} | | 302{{C}} | ||
|- | |- | ||
| | | | ||
| | | | ||
| | | | ||
| | | | ||
|20/17 | | 20/17 | ||
|281{{C}} | | 281{{C}} | ||
|27/23 | | 27/23 | ||
|278{{C}} | | 278{{C}} | ||
|- | |- | ||
| | | | ||
| | | | ||
| | | | ||
| | | | ||
|22/19 | | 22/19 | ||
|254{{C}} | | 254{{C}} | ||
|29/25 | | 29/25 | ||
|257{{C}} | | 257{{C}} | ||
|- | |- | ||
| | | | ||
| | | | ||
| | | | ||
| | | | ||
|23/20 | | 23/20 | ||
|242{{C}} | | 242{{C}} | ||
| | | | ||
| | | | ||
|} | |} | ||
==In edos== | == In edos == | ||
The following table lists the best tuning of 7/6 and 6/5, as well as other minor thirds if present, in various significant [[edos]]. | The following table lists the best tuning of 7/6 and 6/5, as well as other minor thirds if present, in various significant [[edos]]. | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
!EDO | ! EDO | ||
!7/6 | ! 7/6 | ||
!6/5 | ! 6/5 | ||
!Other minor thirds | ! Other minor thirds | ||
|- | |- | ||
|12 | | 12 | ||
| colspan="2" |300{{c}} | | colspan="2" | 300{{c}} | ||
| | | | ||
|- | |- | ||
|15 | | 15 | ||
|240{{c}} | | 240{{c}} | ||
|320{{c}} | | 320{{c}} | ||
| | | | ||
|- | |- | ||
|16 | | 16 | ||
| colspan="2" |300{{c}} | | colspan="2" | 300{{c}} | ||
| | | | ||
|- | |- | ||
|17 | | 17 | ||
| colspan="2" |282{{c}} | | colspan="2" | 282{{c}} | ||
| | | | ||
|- | |- | ||
|19 | | 19 | ||
|253{{c}} | | 253{{c}} | ||
|316{{c}} | | 316{{c}} | ||
| | | | ||
|- | |- | ||
|22 | | 22 | ||
|273{{c}} | | 273{{c}} | ||
|327{{c}} | | 327{{c}} | ||
| | | | ||
|- | |- | ||
|24 | | 24 | ||
|250{{c}} | | 250{{c}} | ||
|300{{c}} | | 300{{c}} | ||
| | | | ||
|- | |- | ||
|25 | | 25 | ||
|288{{c}} | | 288{{c}} | ||
|336{{c}} | | 336{{c}} | ||
|240{{c}} ≈ 15/13 | | {{nowrap|240{{c}} ≈ 15/13}} | ||
|- | |- | ||
|26 | | 26 | ||
|277{{c}} | | 277{{c}} | ||
|323{{c}} | | 323{{c}} | ||
| | | | ||
|- | |- | ||
|27 | | 27 | ||
|267{{c}} | | 267{{c}} | ||
|311{{c}} | | 311{{c}} | ||
| | | | ||
|- | |- | ||
|29 | | 29 | ||
|248{{c}} | | 248{{c}} | ||
|331{{c}} | | 331{{c}} | ||
|290{{c}} ≈ 32/27, 13/11 | | {{nowrap|290{{c}} ≈ 32/27, 13/11}} | ||
|- | |- | ||
|31 | | 31 | ||
|271{{c}} | | 271{{c}} | ||
|310{{c}} | | 310{{c}} | ||
| | | | ||
|- | |- | ||
|34 | | 34 | ||
|282{{c}} | | 282{{c}} | ||
|318{{c}} | | 318{{c}} | ||
|247{{c}} ≈ 15/13 | | {{nowrap|247{{c}} ≈ 15/13}} | ||
|- | |- | ||
|41 | | 41 | ||
|263{{c}} | | 263{{c}} | ||
|322{{c}} | | 322{{c}} | ||
|293{{c}} ≈ 32/27 | | {{nowrap|293{{c}} ≈ 32/27}} | ||
|- | |- | ||
|53 | | 53 | ||
|272{{c}} | | 272{{c}} | ||
|317{{c}} | | 317{{c}} | ||
|340{{c}} ≈ 17/14 | | {{nowrap|340{{c}} ≈ 17/14|294{{c}} ≈ 32/27|249{{c}} ≈ 15/13}} | ||
|} | |} | ||
==In regular temperaments== | |||
== In regular temperaments == | |||
The two simplest minor third ratios are 7/6 and 6/5. The following notable temperaments are generated by them:{{Todo|complete list|inline=1}} | The two simplest minor third ratios are 7/6 and 6/5. The following notable temperaments are generated by them:{{Todo|complete list|inline=1}} | ||
{{Navbox intervals}} | {{Navbox intervals}} | ||