357/256: Difference between revisions
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Created page with "{{Infobox Interval | Name = merry tritone, octave-reduced 357th harmonic | Color name = 17oz5, sozo 5th }} The '''merry tritone''', '''357/256''', is a close approximation to..." |
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The '''merry tritone''', '''357/256''', is a close approximation to 12\25, hence the name. It is also a rather good approximation to [[32/23]] at about four cents ( | The '''merry tritone''', '''357/256''', is a close approximation to [[25edo#Intervals|12\25]], hence the name. It is also a rather good approximation to [[32/23]] at [[8211/8192]] (about four cents) away. In the same region ('flat [[tritone]]'), we have [[25/18]] at [[3213/3200]] down and [[7/5]] at [[256/255]] up. | ||
== Terminology and notation == | |||
Conceptualization systems disagree on whether [[17/16]] should be a [[diatonic semitone]] or a [[chromatic semitone]], and as a result the disagreement propagates to all intervals of [[harmonic class|HC17]]. See [[17-limit]] for a detailed discussion. | |||
For 357/256 specifically: | |||
* In [[Functional Just System]], it is a diminished fifth, separated by [[4131/4096]] from the [[1024/729|Pythagorean diminished fifth (1024/729)]] less a [[64/63]]. | |||
* In [[Helmholtz-Ellis notation]], it is an augmented fourth, separated by [[2187/2176]] from the [[729/512|Pythagorean augmented fourth (729/512)]] less a [[64/63]]. | |||
The term ''merry tritone'' omits the distinction and only describes its melodic property i.e. the size. | |||
[[Category:Tritone]] | [[Category:Tritone]] | ||
[[Category:Octave-reduced harmonics]] | [[Category:Octave-reduced harmonics]] | ||
[[Category:25edo]] | |||
Latest revision as of 11:01, 20 April 2025
| Interval information |
octave-reduced 357th harmonic
reduced harmonic
The merry tritone, 357/256, is a close approximation to 12\25, hence the name. It is also a rather good approximation to 32/23 at 8211/8192 (about four cents) away. In the same region ('flat tritone'), we have 25/18 at 3213/3200 down and 7/5 at 256/255 up.
Terminology and notation
Conceptualization systems disagree on whether 17/16 should be a diatonic semitone or a chromatic semitone, and as a result the disagreement propagates to all intervals of HC17. See 17-limit for a detailed discussion.
For 357/256 specifically:
- In Functional Just System, it is a diminished fifth, separated by 4131/4096 from the Pythagorean diminished fifth (1024/729) less a 64/63.
- In Helmholtz-Ellis notation, it is an augmented fourth, separated by 2187/2176 from the Pythagorean augmented fourth (729/512) less a 64/63.
The term merry tritone omits the distinction and only describes its melodic property i.e. the size.