17/16: Difference between revisions
m fixed erroneous 17th "overtone", this is the 17th harmonic |
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{{Infobox Interval | {{Infobox Interval | ||
| Name = large septendecimal semitone <br>minor diatonic semitone | |||
| Name = large septendecimal semitone | |||
| Color name = 17o2, iso 2nd | | Color name = 17o2, iso 2nd | ||
| Sound = jid_17_16_pluck_adu_dr220.mp3 | | Sound = jid_17_16_pluck_adu_dr220.mp3 | ||
}} | }} | ||
{{Wikipedia|Minor diatonic semitone}} | |||
In [[17-limit]] [[just intonation]], '''17/16''' is the 17th [[harmonic]], [[octave reduced]], and may be called the '''large septendecimal semitone'''. Measuring about 105{{cent}}, it is close to the [[12edo]] semitone of 100{{cent}}, and thus 12edo can be said to approximate it closely, although an even better approximation is available in [[23edo]]. In a chord, it can function similarly to a jazz "minor ninth"—for instance, 8:10:12:14:17 (although here the interval is [[17/8]], which is a little less harsh sounding than 17/16). In 17-limit JI, [[17/1]] is treated as the next basic consonance after [[13/1|13]] and [[15/1|15]]. | |||
17/16 is one of two [[superparticular]] semitones in the 17-limit; the other is [[18/17]], the small septendecimal semitone, which measures about 99{{c}}. The difference between them is [[289/288]], about 6{{c}}. If 12edo is treated as a harmonic system approximating 9 and 17, then 289/288 is tempered out. | |||
17/16 is | 17/16 is almost exactly 1/3 of the [[6/5]] minor third. The difference between 6/5 and three 17/16 semitones is [[24576/24565]], an interval of approximately 0.8{{c}}. 17/16 is also almost exactly 1/8 of [[13/8]], with the difference between 13/8 and (17/16)<sup>8</sup> being approximately 0.9{{c}}. The difference between ten 17/16's and [[11/6]] is approximately 0.2{{c}}, while the difference between thirteen 17/16's and [[11/5]] is approximately 0.6{{c}}. | ||
== 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 17/16 specifically: | |||
* In [[Functional Just System]], it is a diatonic semitone, separated by [[4131/4096]] from the [[256/243|Pythagorean minor second (256/243)]]. It is also called the '''minor diatonic semitone''', which contrasts the [[5-limit]] major diatonic semitone of [[16/15]] by [[256/255]], about 6.8{{c}}. | |||
* In [[Helmholtz–Ellis notation]], it is a chromatic semitone, separated by [[2187/2176]] from the [[2187/2048|Pythagorean augmented unison (2187/2048)]]. | |||
It could also be reasonable to treat 17/16 as the formal comma for prime 17 in its own right, as it is roughly the same size as the 3-limit accidental 2187/2048. | |||
The term ''large septendecimal semitone'' omits the diatonic/chromatic part and only describes its melodic property i.e. the size. It is said in contrast to the small septendecimal semitone of 18/17. | |||
== See also == | == See also == | ||
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* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
[[Category:Second]] | [[Category:Second]] | ||
[[Category:Semitone]] | |||
[[Category:Chroma]] | [[Category:Chroma]] | ||