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| | {{#invoke:Diatonic interval category|diatonic_interval_category|{{{1|4}}}|{{{2|0}}}}} |
| As a diatonic interval category, a {{#ifeq: {{#expr: {{{ordinal}}} mod 7}}|0|perfect|{{#ifeq: {{{quality}}}|m|{{#ifeq: {{{ordinal}}}|3|perfect|{{#ifeq: {{{ordinal}}}|4|diminished|minor}}}}|{{#ifeq: {{{ordinal}}}|3|augmented|{{#ifeq: {{{ordinal}}}|4|perfect|major}}}}}}}} {{#ifeq: {{{ordinal}}}|0|unison|}} {{#ifeq: {{{ordinal}}}|1|second|}}{{#ifeq: {{{ordinal}}}|2|third|}}{{#ifeq: {{{ordinal}}}|3|fourth|}}{{#ifeq: {{{ordinal}}}|4|fifth|}}{{#ifeq: {{{ordinal}}}|5|sixth|}}{{#ifeq: {{{ordinal}}}|6|seventh|}}{{#ifeq: {{{ordinal}}}|7|octave|}} is an interval that spans {{{ordinal}}} scale step{{#ifeq: {{{ordinal}}}|1||s}} in the [[diatonic]] scale with the {{#ifeq: {{{ordinal}}}|0|perfect|{{#ifeq: {{{quality}}}|m|{{#ifeq: {{{ordinal}}}|3|perfect (narrower)|{{#ifeq: {{{ordinal}}}|4|diminished (narrower)|minor (narrower)}}}}|{{#ifeq: {{{ordinal}}}|3|augmented (wider)|{{#ifeq: {{{ordinal}}}|4|perfect (wider)|major (wider)}}}}}}}} quality. It is generated by stacking {{#ifeq: {{#expr: {{{ordinal}}} mod 7}}|0|no fifths|{{
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| #ifeq: {{{quality}}}|M|{{#ifeq: {{{ordinal}}}|1|two fifths|}}{{#ifeq: {{{ordinal}}}|2|four fifths|}}{{#ifeq: {{{ordinal}}}|3|six fifths|}}{{#ifeq: {{{ordinal}}}|4|one fifth|}}{{#ifeq: {{{ordinal}}}|5|three fifths|}}{{#ifeq: {{{ordinal}}}|6|five fifths|}}{{#ifeq: {{{ordinal}}}|7|no fifths|}}|{{#ifeq: {{{ordinal}}}|1|five fourths|}}{{#ifeq: {{{ordinal}}}|2|three fourths|}}{{#ifeq: {{{ordinal}}}|3|one fourth|}}{{#ifeq: {{{ordinal}}}|4|six fourths|}}{{#ifeq: {{{ordinal}}}|5|four fourths|}}{{#ifeq: {{{ordinal}}}|6|two fourths|}}{{#ifeq: {{{ordinal}}}|7|no fifths|}}}}}} octave reduced, and depending on the specific tuning, it ranges from ##### to ##### ¢ (##### to #####).
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| The ##### is enharmonic with the #####, ranging from ##### to ##### ¢. It is generated by stacking ##### octave reduced, and is as such not found in the diatonic scale. | | <noinclude> |
| | <hr> |
| | The first parameter of the template is the fifthspan of the diatonic interval. Currently this only supports fifthspans within [-12, 12]. |
| | The second parameter is whether the interval of 0 fifths should be interpreted as a unison or an octave. |
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| The diatonic scale contains ##### #####
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| {{#ifeq: yes | yes | Hooray...! | Darn...! }}
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| <noinclude>{{Diatonic interval category|ordinal=7|quality=M}}</noinclude>
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| | </noinclude> |
Latest revision as of 09:02, 16 December 2025
The major third (M3), as a diatonic interval category, is an interval that spans 2 steps of the diatonic scale with the major (wider) quality. It is generated by stacking 4 fifths octave-reduced, and depending on the specific tuning it ranges from 343 to 480 cents (2\7 to 2\5).
An interval in just intonation may be labeled "major third" if it is reasonably mapped to 2 steps of the diatonic scale and 4 steps of the dodecatonic chromatic scale.
The diminished fourth (d4) is enharmonic with the major third, ranging from 240 to 514 cents (1\5 to 3\7). It is generated by stacking 8 fourths octave-reduced (and as such is not found in the diatonic scale).
An interval in just intonation may be labeled "diminished fourth" if it is reasonably mapped to 3 steps of the diatonic scale and 4 steps of the dodecatonic chromatic scale.
The first parameter of the template is the fifthspan of the diatonic interval. Currently this only supports fifthspans within [-12, 12].
The second parameter is whether the interval of 0 fifths should be interpreted as a unison or an octave.
