Meantone: Difference between revisions
m →Tunings: cleanup |
- 25/21 and 42/25 (totally overshadowed by 5/3 and 6/5). + 28/27 and 27/14. Misc. cleanup +1 |
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== History == | == History == | ||
{{See also|Historical temperaments}} | {{See also| Historical temperaments }} | ||
Meantone with fifths flatter than 700{{cent}} were the dominant tuning used in Europe from around late 15th century to around early 18th century, after which various [[well temperament]]s and eventually [[12edo|12-tone equal temperament]] won in popularity. However, even today, the vast majority of common-practice Western music theory is based exclusively on meantone, as 12-tone equal temperament is itself a meantone tuning. | Meantone with fifths flatter than 700{{cent}} were the dominant tuning used in Europe from around late 15th century to around early 18th century, after which various [[well temperament]]s and eventually [[12edo|12-tone equal temperament]] won in popularity. However, even today, the vast majority of common-practice Western music theory is based exclusively on meantone, as 12-tone equal temperament is itself a meantone tuning. | ||
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== Intervals == | == Intervals == | ||
{{ | {{Main| Meantone intervals }} | ||
In the following tables, odd harmonics 1–15 are labeled in '''bold'''. | In the following tables, odd harmonics 1–15 are labeled in '''bold'''. | ||
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{| class="wikitable sortable center-1 right-2" | {| class="wikitable sortable center-1 right-2" | ||
|- | |- | ||
! | ! # | ||
! Cents* | ! Cents* | ||
! class="unsortable" | Approximate ratios | ! class="unsortable" | Approximate ratios | ||
| Line 76: | Line 76: | ||
| 3 | | 3 | ||
| 890.0 | | 890.0 | ||
| 5/3 | | 5/3 | ||
|- | |- | ||
| 4 | | 4 | ||
| Line 92: | Line 92: | ||
| 7 | | 7 | ||
| 76.6 | | 76.6 | ||
| 21/20, 25/24 | | 21/20, 25/24, 28/27 | ||
|- | |- | ||
| 8 | | 8 | ||
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{| class="wikitable sortable center-1 right-2" | {| class="wikitable sortable center-1 right-2" | ||
|- | |- | ||
! | ! # | ||
! Cents* | ! Cents* | ||
! class="unsortable" | Approximate ratios | ! class="unsortable" | Approximate ratios | ||
| Line 136: | Line 136: | ||
| −3 | | −3 | ||
| 310.0 | | 310.0 | ||
| 6/5 | | 6/5 | ||
|- | |- | ||
| −4 | | −4 | ||
| Line 152: | Line 152: | ||
| −7 | | −7 | ||
| 1123.4 | | 1123.4 | ||
| 40/21, 48/25 | | 27/14, 40/21, 48/25 | ||
|- | |- | ||
| −8 | | −8 | ||
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|} | |} | ||
</div> | </div> | ||
<nowiki/>* In [[CWE]] | <nowiki/>* In 7-limit [[CWE]] tuning, octave reduced | ||
== Chords == | == Chords == | ||
Meantone induces [[didymic chords]], the [[essentially tempered chord]]s and associated progressions which are not found in other temperaments. Notably, the roots of the common chord progression | Meantone induces [[didymic chords]], the [[essentially tempered chord]]s and associated progressions which are not found in other temperaments. Notably, the roots of the common chord progression vi–ii–V–I make up such a tetrad. Moreover, the dominant seventh chord and the half-diminished seventh chord can be seen as essentially tempered by septimal meantone. | ||
== Scales == | == Scales == | ||
{{Main| Meantone scales }} | {{Main| Meantone scales }} | ||
; | ; Edo tunings | ||
* [[Meantone5]] – pentic scale in 31edo | * [[Meantone5]] – pentic scale in 31edo | ||
* [[Meantone7]] – diatonic scale in 31edo | * [[Meantone7]] – diatonic scale in 31edo | ||
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== See also == | == See also == | ||
* [[Angel]] | * [[Angel]] – fifth-equivalent or 5/1-equivalent meantone | ||
== External links == | == External links == | ||