The term pentatonic literally means five tones. Quick audio of the octatonic (or octotonic) scale played starting on C. There are two versions...one starting with a semitone jump, and the other with the tone jump. Some scales have rotational symmetry, sometimes known as "limited transposition". Pitch spelling algorithm employed here is adapted from a method by Uzay Bora, Baris Tekin Tezel, and Alper Vahaplar. This blog makes use of third party services that track user information. All other diagrams and visualizations are © Ian Ring. The Octatonic Scale is a scale that has eight notes that is constructed from alternating half-steps (H) and whole-steps (W). These are other scales that are similar to this one, created by adding a tone, removing a tone, or moving one note up or down a semitone. These services may also be using web beacons to collect information. Defines the scale as the sequence of intervals between one tone and the next. These are the common triads (major, minor, augmented and diminished) that you can create from members of this scale. The "i" icon marks. This value is the quantity of imperfections in this scale. Scale notation generated by VexFlow, graph visualization by Graphviz, and MIDI playback by MIDI.js. A scale is balanced if the distribution of its tones would satisfy the "centrifuge problem", ie are placed such that it would balance on its centre point. A scale is a maximal area set if a polygon described by vertices dodecimetrically placed around a circle produces the maximal interior area for scales of the same cardinality. The bracelet shows tones that are in this scale, starting from the top (12 o'clock), going clockwise in ascending semitones. 8 (octatonic) Pitch Class Set. 6 – Play a vertical A major scale on the spot using your memorized major scale formula. The Spectrum Width is the difference between the highest and lowest values in each spectrum. Describes the specific interval sizes that exist for each generic interval size. Here is an example of a octatonic scale starting on D: An octatonic scale may also begin with a whole-step: W-H-W-H-W-H-W-H . Scale 1723 can be rotated to make 7 other scales. This number does not include the scale itself, so the number is usually one less than its cardinality; unless there are rotational symmetries then there are even fewer modes. Tonnetz diagrams are popular in Neo-Riemannian theory. A cohemitone is an instance of two adjacent hemitones. A C Minor scale, for comparison, is structured like so: Notes: C, D, Eb, F, G, Ab, Bb Scale Formula: 1 2 b3 4 5 b6 b7 Scale Intervals: W H W W H W W The Natural Minor scale of C flattens the third, sixth and seventh of the scale… These services may be placing and reading cookies on your browser in order to serve ads or analyze website statistics. Above is a graph showing opportunities for parsimonious voice leading between triads*. Propriety describes whether every specific interval is uniquely mapped to a generic interval. This structure creates a Major scale from any starting note. An algorithm for spelling the pitches of any musical scale. If needed, cookies can usually be managed or disabled through the privacy settings in your web browser. This diagram helps to visualize common triads (they're triangles) and circle-of-fifth relationships (horizontal lines). Operation is an identical way to express the same thing; the syntax is where each tone of the set x is transformed by the equation y = ax + b, The transformations that map this set to itself are: T0. When c is zero, the scale is Proper. If a scale has an axis of reflective symmetry, then it can transform into itself by inversion. The Octatonic Scale consists, as the name implies, of eight notes. Each line connects two triads that have two common tones, while the third tone changes by one generic scale step. It also implies that the scale has Ridge Tones. Indicates if the scale can be constructed using a generator, and an origin. Notably an axis of reflection can occur directly on a tone or half way between two tones. Hemitonia describes how many such hemitones exist. Describes if this scale is in prime form, using the Rahn/Ring formula. Determined by the Distribution Spectra; this is the sum of all spectrum widths divided by the scale cardinality. The same as the Interval Vector, but expressed in a syntax used by Howard Hanson. All maximally even sets have maximal area, but not all maximal area sets are maximally even. The pentatonic scale is a class of scale that has five tones per octave. The inverse of 1723 is 2989, Only scales that are chiral will have an enantiomorph. Special thanks to Richard Repp for helping with technical accuracy, and George Howlett for assistance with the Carnatic ragas. Cohemitonia describes how many such cohemitones exist. Cardinality is the count of how many pitches are in the scale. In the melodic minor scale ascending, the half steps occur between 2-3 and 7-8. A scale is either "Proper", "Strictly Proper", or "Improper". Describes if this scale is in prime form, using the Starr/Rahn algorithm. An octatonic scale is also used as a term that describe a scale with eight notes in it. Describes the intervallic content of the scale, read from left to right as the number of occurences of each interval size from semitone, up to six semitones. A code assigned by theorist Allen Forte, for this pitch class set and all of its transpositional (rotation) and inversional (reflection) transformations.

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