17/15: Difference between revisions

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'''17/15'''
{{Infobox Interval
|0 -1 -1 0 0 0 1>
| Icon =
| Ratio = 17/15
| Monzo = 0 -1 -1 0 0 0 1
| Cents = 216.68669
| Name = septendecimal whole tone
| Color name = 17og3, sogu 3rd
| Sound = jid_17_15_pluck_adu_dr220.mp3
}}


216.6867 cents
In [[17-limit]] [[just intonation]], '''17/15''' is the "septendecimal whole tone" measuring about 216.7¢. It is the [[mediant]] between [[9/8]] and [[8/7]], as it is (9+8)/(8+7). It is found in the [[OverToneSeries|harmonic series]] between the 17th and 15th overtones. [[11edo]]'s second degree, measuring approximately 218.2¢, is close in size to 17/15 -- indeed, the 11edo system has excellent approximations of the 15th and 17th harmonics, and so this harmonic function is plausible in 11edo.


[[File:jid_17_15_pluck_adu_dr220.mp3]] [[:File:jid_17_15_pluck_adu_dr220.mp3|sound sample]]
√2/(17/15) is three cents flat of a 5/4 major third, and this or 17/15 itself can be used for a tuning for wizard and its various relatives (lizard, gizzard, etc.).


In [[17-limit|17-limit]] [[Just_intonation|Just Intonation]], 17/15 is the "septendecimal whole tone" measuring about 216.7¢. It is the [[mediant|mediant]] between [[9/8|9/8]] and [[8/7|8/7]], as it is (9+8)/(8+7). It is found in the [[OverToneSeries|harmonic series]] between the 17th and 15th overtones. [[11edo|11edo]]'s second degree, measuring approximately 218.2¢, is close in size to 17/15 -- indeed, the 11edo system has excellent approximations of the 15th and 17th harmonics, and so this harmonic function is plausible in 11edo.
== See also ==
 
* [[30/17]] its [[inverse interval]]
√2/(17/15) is three cents flat of a 5/4 major third, and this or 17/15 itself can be used for a tuning for wizard and its various relatives (lizard, gizzard, etc.).
* [[Gallery of Just Intervals]]


See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]     [[Category:17-limit]]
[[Category:17-limit]]
[[Category:just_interval]]
[[Category:Interval]]
[[Category:sound_example]]
[[Category:Ratio]]
[[Category:Just interval]]
[[Category:Sound example]]

Revision as of 22:46, 26 October 2018

Interval information
Ratio 17/15
Factorization 3-1 × 5-1 × 17
Monzo [0 -1 -1 0 0 0 1⟩
Size in cents 216.6867¢
Name septendecimal whole tone
Color name 17og3, sogu 3rd
FJS name [math]\displaystyle{ \text{d3}^{17}_{5} }[/math]
Special properties reduced
Tenney norm (log2 nd) 7.99435
Weil norm (log2 max(n, d)) 8.17493
Wilson norm (sopfr(nd)) 25

[sound info]
Open this interval in xen-calc

In 17-limit just intonation, 17/15 is the "septendecimal whole tone" measuring about 216.7¢. It is the mediant between 9/8 and 8/7, as it is (9+8)/(8+7). It is found in the harmonic series between the 17th and 15th overtones. 11edo's second degree, measuring approximately 218.2¢, is close in size to 17/15 -- indeed, the 11edo system has excellent approximations of the 15th and 17th harmonics, and so this harmonic function is plausible in 11edo.

√2/(17/15) is three cents flat of a 5/4 major third, and this or 17/15 itself can be used for a tuning for wizard and its various relatives (lizard, gizzard, etc.).

See also

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