10/7: Difference between revisions
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Hemifamity approximation |
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{| | {{Infobox Interval | ||
| | | Name = high tritone, greater septimal tritone, Euler's tritone | ||
| | | Color name = ry4, ruyo 4th | ||
| Sound = jid_10_7_pluck_adu_dr220.mp3 | |||
}} | |||
|} | {{Wikipedia|Septimal tritone}} | ||
'''10/7''' | In [[7-limit]] [[just intonation]], '''10/7''' is a '''high [[tritone]]''' (or '''Euler's tritone''') measuring about 617.5¢. It has a similar sound to its inversion, [[7/5]], but may sound a little edgier, less relaxed. Nonetheless, it is considered a septimal consonance. It appears in chords where a major third ([[5/4]]) appears above the harmonic seventh ([[7/4]]), such as 4:6:7:10 – This particular chord is well-approximated in [[88cET]], which has a good approximation of 10/7, but no 7/5. It's well approximated by the Pythagorean augmented fourth [[729/512]], differing by [[5120/5103]]. | ||
While in the context of the [[harmonic seventh chord]], it is rightly recognized as a type of augmented fourth, it can also be argued on the basis of the fact that 10/7 interval is larger than 600 cents that it acts more as a type of diminished fifth than an augmented fourth – an analysis that is required in cases where this interval occurs in a [[5L 2s|diatonic scale]] that demonstrates [[Rothenberg propriety]]. | |||
== Approximation == | |||
{{Interval edo approximation|10/7}} | |||
== See also == | |||
* [[7/5]] – its [[octave complement]] | |||
* [[21/20]] – its [[fifth complement]] | |||
* [[Gallery of just intervals]] | |||
[[Category:Tritone]] | |||
[[Category:Over-7 intervals]] | |||
[[ | |||
Latest revision as of 15:32, 12 December 2025
| Interval information |
greater septimal tritone,
Euler's tritone
[sound info]
In 7-limit just intonation, 10/7 is a high tritone (or Euler's tritone) measuring about 617.5¢. It has a similar sound to its inversion, 7/5, but may sound a little edgier, less relaxed. Nonetheless, it is considered a septimal consonance. It appears in chords where a major third (5/4) appears above the harmonic seventh (7/4), such as 4:6:7:10 – This particular chord is well-approximated in 88cET, which has a good approximation of 10/7, but no 7/5. It's well approximated by the Pythagorean augmented fourth 729/512, differing by 5120/5103.
While in the context of the harmonic seventh chord, it is rightly recognized as a type of augmented fourth, it can also be argued on the basis of the fact that 10/7 interval is larger than 600 cents that it acts more as a type of diminished fifth than an augmented fourth – an analysis that is required in cases where this interval occurs in a diatonic scale that demonstrates Rothenberg propriety.
Approximation
| Edo | Step size | Cents (¢) | Absolute error (¢) | Relative error (%) |
|---|---|---|---|---|
| 2 | 1\2 | 600.00 | -17.49 | -2.91 |
| 4 | 2\4 | 600.00 | -17.49 | -5.83 |
| 6 | 3\6 | 600.00 | -17.49 | -8.74 |
| 29 | 15\29 | 620.69 | +3.20 | +7.74 |
| 31 | 16\31 | 619.35 | +1.87 | +4.82 |
| 33 | 17\33 | 618.18 | +0.69 | +1.91 |
| 35 | 18\35 | 617.14 | -0.34 | -1.01 |
| 37 | 19\37 | 616.22 | -1.27 | -3.92 |
| 39 | 20\39 | 615.38 | -2.10 | -6.84 |
| 41 | 21\41 | 614.63 | -2.85 | -9.75 |
| 62 | 32\62 | 619.35 | +1.87 | +9.65 |
| 64 | 33\64 | 618.75 | +1.26 | +6.73 |
| 66 | 34\66 | 618.18 | +0.69 | +3.82 |
| 68 | 35\68 | 617.65 | +0.16 | +0.90 |
| 70 | 36\70 | 617.14 | -0.34 | -2.01 |
| 72 | 37\72 | 616.67 | -0.82 | -4.93 |
| 74 | 38\74 | 616.22 | -1.27 | -7.84 |