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Major third: Difference between revisions

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== In tempered scales ==
== In tempered scales ==
The following table lists EDOs between 5 and 26 that have intervals in the range of 370 to 415 cents ("major thirds"), as well as the tunings in 27edo, 29edo, 31edo, 34edo, 41edo, and 53edo. All EDOs larger than 26 have an interval in this range.
The following table lists the best tuning of 5/4 and 9/7*, as well as other major thirds if present, in several significant EDOs.
 
Due to the width of the range, 29edo, 41edo, and 53edo have two intervals within it.
{| class="wikitable"
|+
!EDO
!Major third
|-
|29 (flat third)
|372c
|-
|16
|375c
|-
|19
|379c
|-
|41 (flat third)
|381c
|-
|22
|382c
|-
|25
|384c
|-
|53 (flat third)
|385c
|-
|31
|387c
|-
|34
|388c
|-
|6, 9, 12, 15, 18, 21, 24, 27
|400c
|-
|53 (sharp third)
|408c
|-
|41 (sharp third)
|410c
|-
|29 (sharp third)
|414c
|}
 
 
The following table lists EDOs between 5 and 34 that have intervals in the range of 415 to 450 cents ("supermajor thirds"), as well as the tunings in 41edo and 53edo. All EDOs larger than 34 have an interval in this range.
{| class="wikitable"
!EDO
!Supermajor third
|-
|26
|415c
|-
|23
|417c
|-
|20
|420c
|-
|17, 34
|424c
|-
|31
|426c
|-
|14, 28
|429c
|-
|53
|430c
|-
|25
|432c
|-
|11, 22, 33
|436c
|-
|41
|439c
|-
|30
|440c
|-
|19
|442c
|-
|27
|444c
|-
|8, 16, 24, 32
|450c
|}
The following table lists the best tuning of 5/4 and 9/7* in several significant EDOs.


<nowiki>*</nowiki>Note that 9/7 may not always be the actual best note in the EDO, this is because of the way EDO tunings try to match how intervals in just intonation are stacked to form new intervals. See [[Val]] for more information. Essentially, this is what 9/7 should be based on the best tuning of 7 itself.
<nowiki>*</nowiki>Note that 9/7 may not always be the actual best note in the EDO, this is because of the way EDO tunings try to match how intervals in just intonation are stacked to form new intervals. See [[Val]] for more information. Essentially, this is what 9/7 should be based on the best tuning of 7 itself.
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!5/4
!5/4
!9/7
!9/7
!Other major thirds
|-
|-
|9
|9
| colspan="2" |400c
| colspan="2" |400c
|
|-
|-
|12
|12
| colspan="2" |400c
| colspan="2" |400c
|
|-
|-
|13
|13
|369c
|369c
|461c
|461c
|
|-
|14
| colspan="2" |428c
|
|-
|15
|400c
|**
|
|-
|-
|16
|16
|375c
|375c
|450c
|450c
|
|-
|-
|17
|17
|353c
|***
|424c
|424c
|
|-
|-
|19
|19
|379c
|379c
|442c
|442c
|
|-
|20
|360c
|**
|420c '''≈''' 14/11
|-
|-
|22
|22
|382c
|382c
|436c
|436c
|
|-
|-
|24
|24
|400c
|400c
|450c
|450c
|
|-
|-
|25
|25
|384c
|384c
|432c
|432c
|
|-
|-
|26
|26
|369c
|369c
|415c
|415c
|
|-
|-
|27
|27
|400c
|400c
|444c
|444c
|
|-
|28
|386c
|428c
|
|-
|-
|29
|29
|372c
|372c
|455c
|455c
|414c '''≈''' 81/64, 14/11
|-
|-
|31
|31
|388c
|388c
|426c
|426c
|
|-
|32
|375c
|**
|413c '''≈''' 14/11, 450c '''≈''' 13/10
|-
|-
|34
|34
|388c
|388c
|459c
|459c
|424c '''≈''' 14/11
|-
|-
|41
|41
|381c
|381c
|439c
|439c
|410c '''≈''' 81/64
|-
|-
|53
|53
|385c
|385c
|430c
|430c
|362c '''≈''' 21/17, 408c '''≈''' 81/64, 452c '''≈''' 13/10
|}
|}
<nowiki>**</nowiki> These edos have an approximation to 9/7, but it is not tuned to a major third interval.
<nowiki>***</nowiki> These edos have an approximation to 5/4, but it is not tuned to a major third interval.


== In regular temperaments ==
== In regular temperaments ==
Retrieved from "https://en.xen.wiki/w/Major_third"