Interval size measure: Difference between revisions
m Removing from Category:Theory using Cat-a-lot |
→Logarithmic: rid of "PRIME" in favor of "[#] (prime)" |
||
| Line 30: | Line 30: | ||
| [[Normal diesis]] | | [[Normal diesis]] | ||
| [[31edo|31]] | | [[31edo|31]] | ||
| | | 31 (prime) | ||
| See the dedicated page. | | See the dedicated page. | ||
|- | |- | ||
| [[Méride]] | | [[Méride]] | ||
| [[43edo|43]] | | [[43edo|43]] | ||
| | | 43 (prime) | ||
| Proposed by [[Joseph Sauveur]], as 7 heptaméride units<ref name="measure">[http://www.huygens-fokker.org/docs/measures.html Stichting Huygens-Fokker: Logarithmic Interval Measures]</ref><ref>[http://tonalsoft.com/enc/m/meride.aspx Tonalsoft | ''Méride / 43-ed2 / 43-edo / 43-ET / 43-tone equal-temperament'']</ref>. | | Proposed by [[Joseph Sauveur]], as 7 heptaméride units<ref name="measure">[http://www.huygens-fokker.org/docs/measures.html Stichting Huygens-Fokker: Logarithmic Interval Measures]</ref><ref>[http://tonalsoft.com/enc/m/meride.aspx Tonalsoft | ''Méride / 43-ed2 / 43-edo / 43-ET / 43-tone equal-temperament'']</ref>. | ||
|- | |- | ||
| [[Holdrian comma]] | | [[Holdrian comma]] | ||
| [[53edo|53]] | | [[53edo|53]] | ||
| | | 53 (prime) | ||
| <ref name="measure"/> | | <ref name="measure"/> | ||
|- | |- | ||
| Line 75: | Line 75: | ||
| [[Gene]] | | [[Gene]] | ||
| [[311edo|311]] | | [[311edo|311]] | ||
| | | 311 (prime) | ||
| Proposed by Joe Monzo (2007)<ref>[http://tonalsoft.com/enc/g/gene.aspx Tonalsoft | ''Gene, 311-edo'']</ref>. | | Proposed by Joe Monzo (2007)<ref>[http://tonalsoft.com/enc/g/gene.aspx Tonalsoft | ''Gene, 311-edo'']</ref>. | ||
|- | |- | ||
| Line 199: | Line 199: | ||
|- | |- | ||
| [[Iota]] | | [[Iota]] | ||
| [[ | | [[1700edo|1700]] | ||
| 2<sup>2</sup> × 5<sup>2</sup> × 17 | | 2<sup>2</sup> × 5<sup>2</sup> × 17 | ||
| [[Relative cent]] of [[17edo]]; proposed by [[Margo Schulter]] (2002) and [[George Secor]]<ref name="measure"/>. | | [[Relative cent]] of [[17edo]]; proposed by [[Margo Schulter]] (2002) and [[George Secor]]<ref name="measure"/>. | ||
| Line 230: | Line 230: | ||
| [[Tina]] | | [[Tina]] | ||
| [[8539edo|8539]] | | [[8539edo|8539]] | ||
| | | 8539 (prime) | ||
| Provides good approximations for 41-limit primes except 37; named by [[Dave Keenan]] and [[George Secor]]; edo representation of [[Sagittal notation|Sagittal]]'s Insane (Magrathean) precision level JI notation (809eda)<ref name="measure"/><ref>[http://tonalsoft.com/enc/t/tina.aspx Tonalsoft | ''Tina'']</ref>. | | Provides good approximations for 41-limit primes except 37; named by [[Dave Keenan]] and [[George Secor]]; edo representation of [[Sagittal notation|Sagittal]]'s Insane (Magrathean) precision level JI notation (809eda)<ref name="measure"/><ref>[http://tonalsoft.com/enc/t/tina.aspx Tonalsoft | ''Tina'']</ref>. | ||
|- | |- | ||
| Line 255: | Line 255: | ||
| [[Jot]] | | [[Jot]] | ||
| [[30103edo|30103]] | | [[30103edo|30103]] | ||
| | | 30103 (prime) | ||
| 30103 ≃ 100,000 × log<sub>10</sub>2; Proposed by [[Augustus de Morgan]] (1864)<ref name="measure"/><ref>[http://www.tonalsoft.com/enc/j/jot.aspx Tonalsoft | ''Jot'']</ref><ref name="equal"/>. | | 30103 ≃ 100,000 × log<sub>10</sub>2; Proposed by [[Augustus de Morgan]] (1864)<ref name="measure"/><ref>[http://www.tonalsoft.com/enc/j/jot.aspx Tonalsoft | ''Jot'']</ref><ref name="equal"/>. | ||
|- | |- | ||
| Line 319: | Line 319: | ||
Within a given [[Equal-step tuning|equal-stepped]] tonal system, the [[relative cent]] (rct, r¢) can be used to describe properties of pitches (for instance the approximation of [[Just intonation|JI]] intervals). It is defined as on 100th (or 1 percent) of the interval between two neighbouring pitches in the used equal tuning. | Within a given [[Equal-step tuning|equal-stepped]] tonal system, the [[relative cent]] (rct, r¢) can be used to describe properties of pitches (for instance the approximation of [[Just intonation|JI]] intervals). It is defined as on 100th (or 1 percent) of the interval between two neighbouring pitches in the used equal tuning. | ||
See also: [http://arxiv.org/abs/0907.5249 ''Why the Kirnberger Kernel Is So Small''] by [[Don N. Page]] | |||
== Ratio == | == Ratio == | ||