7/4
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author Andrew_Heathwaite and made on 2010-09-23 13:51:06 UTC.
- The original revision id was 164931099.
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Original Wikitext content:
Frequency ratio 7:4, measuring approximately 968.8259064691249 cents, often gets labeled the "harmonic seventh." It represents the interval between the 4th and 7th harmonics. It is also called a "septimal subminor seventh" -- the word "septimal" referring to the presence of a 7 as the highest prime in the ratio and the word "subminor" referring to its narrowness compared with a traditional minor seventh (such as [[9_5|9:5]] or [[16_9|16:9]], 10 degrees of [[12edo]] or a minor seventh found in a meantone system). 7:4 has seen use in blues music and some musical traditions of the world, but has mostly not been recognized as a "consonance" in Western music theory. However, in most Just Intonation systems, it is treated as a consonance in its own right, with its own distinct quality. ==Otonal Tetrad== 7:4 appears in the otonal tetrad that forms the basis of much JI music: ===4:5:6:7:8=== This triad represents a sequence of overtones from the fourth to the eighth. (8, being a doubling of 4, represents an octave above the root.) The intervals between adjacent members of the chord decrease in size: [[5_4|5:4]] - approx. 386 cents - a major third [[6_5|6:5]] - approx. 316 cents - a minor third [[7_6|7:6]] - approx. 267 cents - a septimal subminor third 8:7 - approx. 231 cents - a septimal supermajor seventh This chord is similar to the "dominant seventh chord" in 12edo, the most significant difference being the mistuning of the harmonic seventh. In 12edo, the interval closest to the harmonic seventh is the minor seventh at 1000 cents. The difference of about 31 cents is striking, and especially noticable when the chords are presented next to one another. While the "dominant seventh chord" of 12edo is treated as a dissonance that needs to resolve (usually in the chord pattern V7 to I), the "otonal tetrad" has a much different flavor and is often treated by composers in Just Intonation as a consonance. Also, 12edo does not distinguish between a minor and subminor third or a major and supermajor second. Thus, the intervals between adjacent members of the chord do not have that pattern of decreasing step size: 5:4 becomes 400 cents. 6:5 becomes 300 cents. 7:6 becomes 300 cents. 8:7 becomes 200 cents.
Original HTML content:
<html><head><title>7_4</title></head><body>Frequency ratio 7:4, measuring approximately 968.8259064691249 cents, often gets labeled the "harmonic seventh." It represents the interval between the 4th and 7th harmonics. It is also called a "septimal subminor seventh" -- the word "septimal" referring to the presence of a 7 as the highest prime in the ratio and the word "subminor" referring to its narrowness compared with a traditional minor seventh (such as <a class="wiki_link" href="/9_5">9:5</a> or <a class="wiki_link" href="/16_9">16:9</a>, 10 degrees of <a class="wiki_link" href="/12edo">12edo</a> or a minor seventh found in a meantone system).<br /> <br /> 7:4 has seen use in blues music and some musical traditions of the world, but has mostly not been recognized as a "consonance" in Western music theory. However, in most Just Intonation systems, it is treated as a consonance in its own right, with its own distinct quality.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:0:<h2> --><h2 id="toc0"><a name="x-Otonal Tetrad"></a><!-- ws:end:WikiTextHeadingRule:0 -->Otonal Tetrad</h2> 7:4 appears in the otonal tetrad that forms the basis of much JI music:<br /> <!-- ws:start:WikiTextHeadingRule:2:<h3> --><h3 id="toc1"><a name="x-Otonal Tetrad-4:5:6:7:8"></a><!-- ws:end:WikiTextHeadingRule:2 -->4:5:6:7:8</h3> This triad represents a sequence of overtones from the fourth to the eighth. (8, being a doubling of 4, represents an octave above the root.) The intervals between adjacent members of the chord decrease in size:<br /> <a class="wiki_link" href="/5_4">5:4</a> - approx. 386 cents - a major third<br /> <a class="wiki_link" href="/6_5">6:5</a> - approx. 316 cents - a minor third<br /> <a class="wiki_link" href="/7_6">7:6</a> - approx. 267 cents - a septimal subminor third<br /> 8:7 - approx. 231 cents - a septimal supermajor seventh<br /> <br /> This chord is similar to the "dominant seventh chord" in 12edo, the most significant difference being the mistuning of the harmonic seventh. In 12edo, the interval closest to the harmonic seventh is the minor seventh at 1000 cents. The difference of about 31 cents is striking, and especially noticable when the chords are presented next to one another. While the "dominant seventh chord" of 12edo is treated as a dissonance that needs to resolve (usually in the chord pattern V7 to I), the "otonal tetrad" has a much different flavor and is often treated by composers in Just Intonation as a consonance.<br /> <br /> Also, 12edo does not distinguish between a minor and subminor third or a major and supermajor second. Thus, the intervals between adjacent members of the chord do not have that pattern of decreasing step size:<br /> 5:4 becomes 400 cents.<br /> 6:5 becomes 300 cents.<br /> 7:6 becomes 300 cents.<br /> 8:7 becomes 200 cents.</body></html>