Introductory examples in Sagittal notation: Difference between revisions
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This page lists a few elementary examples that hopefully shed some light on the philosophy (and the pitfalls!) of [[Sagittal_notation|Sagittal notation]]. For a detailed introduction into Sagittal notation the document [ | This page lists a few elementary examples that hopefully shed some light on the philosophy (and the pitfalls!) of [[Sagittal_notation|Sagittal notation]]. For a detailed introduction into Sagittal notation, see the document [https://sagittal.org/sagittal.pdf Sagittal.pdf] on Sagittal's main website, which is the latest version of the original article which introduced Sagittal to the world, that was published in Xenharmonikôn in 2006. | ||
=Just intonation: notating a harmonic scale= | =Just intonation: notating a harmonic scale= | ||
As the introduction | As the introduction to Sagittal.pdf says, Sagittal notation uses a conventional staff on which the natural notes are in a single series of fifths, i.e, in the case of just intonation, in [[3-limit|Pythagorean tuning]]. The meaning of conventional sharps and flats is Pythagorean as well, i.e. they stand for raising the corresponding note by a [[2187/2048|Pythagorean chromatic semitone (apotome)]], a "large" semitone 113.7 cents in size. | ||
For the notation of notes in higher [[Harmonic_Limit|limits]], additional symbols are introduced. The intervals these symbols stand for are mostly [[Comma|commas]] - the maybe most elementary example is the [[81/80|syntonic comma]] (ratio 81/80, 21.506 cents), the difference between a pythagorean and a just major third, necessary for just intonation in [[5-limit|5-limit]]. Other elementary commas appearing along the harmonic series are: in [[7-limit|7-limit]] the [[64/63|septimal comma or Architas' comma]] (64/63, 27.264 Cents), the difference between a minor and a harmonic seventh, and, in [[11-limit|11-limit]], the [[33/32|undecimal comma or al-Farabi quarter-tone]] (33/32, 53.2729 cents), the difference between an undecimal semi-augmented and a perfect fourth. | For the notation of notes in higher [[Harmonic_Limit|limits]], additional symbols are introduced. The intervals these symbols stand for are mostly [[Comma|commas]] - the maybe most elementary example is the [[81/80|syntonic comma]] (ratio 81/80, 21.506 cents), the difference between a pythagorean and a just major third, necessary for just intonation in [[5-limit|5-limit]]. Other elementary commas appearing along the harmonic series are: in [[7-limit|7-limit]] the [[64/63|septimal comma or Architas' comma]] (64/63, 27.264 Cents), the difference between a minor and a harmonic seventh, and, in [[11-limit|11-limit]], the [[33/32|undecimal comma or al-Farabi quarter-tone]] (33/32, 53.2729 cents), the difference between an undecimal semi-augmented and a perfect fourth. | ||
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[[File:SagittalOvertoneSeries.jpg|alt=SagittalOvertoneSeries.jpg|SagittalOvertoneSeries.jpg]] | [[File:SagittalOvertoneSeries.jpg|alt=SagittalOvertoneSeries.jpg|SagittalOvertoneSeries.jpg]] | ||
For a complete list of all comma symbols see [http://sagittal.org/ http://sagittal.org/] or | For a complete list of all comma symbols see [http://sagittal.org/ http://sagittal.org/] or Sagittal.pdf. | ||
=Equal temperaments (1): comparison of notation in different equal temperaments= | =Equal temperaments (1): comparison of notation in different equal temperaments= | ||
A special attraction of Sagittal notation is that it has been designed to notate both rational intervals (e.g. just intonation) and all kinds equal divisions of the octave. Basic guidelines for the latter, as defined in | A special attraction of Sagittal notation is that it has been designed to notate both rational intervals (e.g. just intonation) and all kinds equal divisions of the octave. Basic guidelines for the latter, as defined in Sagittal.pdf, are as follows: | ||
<ol><li>An interval in an equal temperament is to be notated in the same way as a just ratio for which the equal interval is the best approximation.</li><li>Conventional staff notation (natural notes, sharps and flats) indicates tones in a series built on the equal division’s best approximation of a fifth.</li></ol> | <ol><li>An interval in an equal temperament is to be notated in the same way as a just ratio for which the equal interval is the best approximation.</li><li>Conventional staff notation (natural notes, sharps and flats) indicates tones in a series built on the equal division’s best approximation of a fifth.</li></ol> | ||