Microtone: Difference between revisions
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The '''Microtone''' is an [[interval measure]] that | The '''Microtone''' is an [[interval measure]] that can be considered as sufficiently precise for all thinkable musical and music-science purposes. Besides its high accuracy, it is of high neutrality since it favors neither twelve-tonality nor even the [[octave]]. Nevertheless its relevance for practical application in music is low due to the incompatibility with "[[human scale]]". Humans are not good at big numbers and have only limited pitch perception (the [[Just-noticeable difference]] (JND) is around 6 cents). | ||
One actual microtone ('''1µt''') would be defined as one millionth of the [[tone]]: | One actual microtone ('''1µt''') would be defined as one millionth of the [[tone]]: | ||
{| class="wikitable" | {| class="wikitable right-3" | ||
|+ | |+ Some numerical impressions (laughter permitted) | ||
! Name | ! Name | ||
! Size in [[ | ! Size | ||
! Size ([[cents|¢]], 12 decimals) | |||
! Size (in [[cents|cents (¢)]], scientific notation)<ref>The values were produced by [https://keisan.casio.com/calculator High precision calculator].</ref> | |||
|- | |- | ||
| | | Tone (=[[9/8]]) | ||
| | | 204¢ | ||
| <tt>203.910,001,730,775</tt> | |||
| <tt>2.03910001730774835488973465474759621023555E+2</tt> | |||
|- | |- | ||
| Millitone | | Millitone | ||
| | | 204m¢ | ||
| <tt>0.203,910,001,731</tt> | |||
| <tt>2.03910001730774835488973465474759621023555E-1</tt> | |||
|- | |- | ||
| | | Microtone | ||
| | | 204µ¢ | ||
| <tt>0.000,203,910,002</tt> | |||
| <tt>2.03910001730774835488973465474759621023555E-4</tt> | |||
|} | |} | ||
<references/> | |||
== The Microtone Challenge == | == The Microtone Challenge == | ||
Two sounds different only by 1µt produce a very slow [[beat]]; depending on the frequency one have to wait more or less to | A microtone is indeed a very small interval: 4,904 microtones make one [[cent]], and 5,884,949 an octave. | ||
Two sounds different only by 1µt produce a very slow [[beat]]; depending on the frequency one have to wait more or less to recognize it. The beat frequency is | |||
* at the upper limit of the hearing range (20 kHz) 7 minutes | * at the upper limit of the hearing range (20 kHz) 7 minutes | ||
| Line 34: | Line 45: | ||
Given this, will it be ever possible to make a ''microtone experience'' at all? | Given this, will it be ever possible to make a ''microtone experience'' at all? | ||
== External links == | |||
* [http://musictheory.zentral.zone/huntsystem2.html#2 H-Pi Instruments | Hunt System Scale] - section "The JND" | |||
* [https://en.wikipedia.org/wiki/Pitch_(music)#Just-noticeable_difference Pitch (music) - Wikipedia] - section "Just-noticeable difference" | |||
[[Category:Interval measure]] | [[Category:Interval measure]] | ||
Revision as of 17:05, 15 June 2020
The Microtone is an interval measure that can be considered as sufficiently precise for all thinkable musical and music-science purposes. Besides its high accuracy, it is of high neutrality since it favors neither twelve-tonality nor even the octave. Nevertheless its relevance for practical application in music is low due to the incompatibility with "human scale". Humans are not good at big numbers and have only limited pitch perception (the Just-noticeable difference (JND) is around 6 cents).
One actual microtone (1µt) would be defined as one millionth of the tone:
| Name | Size | Size (¢, 12 decimals) | Size (in cents (¢), scientific notation)[1] |
|---|---|---|---|
| Tone (=9/8) | 204¢ | 203.910,001,730,775 | 2.03910001730774835488973465474759621023555E+2 |
| Millitone | 204m¢ | 0.203,910,001,731 | 2.03910001730774835488973465474759621023555E-1 |
| Microtone | 204µ¢ | 0.000,203,910,002 | 2.03910001730774835488973465474759621023555E-4 |
- ↑ The values were produced by High precision calculator.
The Microtone Challenge
A microtone is indeed a very small interval: 4,904 microtones make one cent, and 5,884,949 an octave.
Two sounds different only by 1µt produce a very slow beat; depending on the frequency one have to wait more or less to recognize it. The beat frequency is
- at the upper limit of the hearing range (20 kHz) 7 minutes
- in the range of the highest acoustic sensibility (4 kHz) 35 minutes
- at the lower limit of the hearing range (16 Hz) 7 days
Given this, will it be ever possible to make a microtone experience at all?
External links
- H-Pi Instruments | Hunt System Scale - section "The JND"
- Pitch (music) - Wikipedia - section "Just-noticeable difference"