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Scale 1817: "Phrythimic"

Scale 1817: Phrythimic, Ian Ring Music Theory

Bracelet Diagram

The bracelet shows tones that are in this scale, starting from the top (12 o'clock), going clockwise in ascending semitones. The "i" icon marks imperfect tones that do not have a tone a fifth above. Dotted lines indicate axes of symmetry.

Tonnetz Diagram

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Tonnetz diagrams are popular in Neo-Riemannian theory. Notes are arranged in a lattice where perfect 5th intervals are from left to right, major third are northeast, and major 6th intervals are northwest. Other directions are inverse of their opposite. This diagram helps to visualize common triads (they're triangles) and circle-of-fifth relationships (horizontal lines).

Common Names

Zeitler
Phrythimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,3,4,8,9,10}
Forte Number6-Z17
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 797
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes5
Prime?no
prime: 407
Deep Scaleno
Interval Vector322332
Interval Spectrump3m3n2s2d3t2
Distribution Spectra<1> = {1,2,3,4}
<2> = {2,3,4,5}
<3> = {4,6,8}
<4> = {7,8,9,10}
<5> = {8,9,10,11}
Spectra Variation2.667
Maximally Evenno
Maximal Area Setno
Interior Area2.116
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicno

Common Triads

These are the common triads (major, minor, augmented and diminished) that you can create from members of this scale.

* Pitches are shown with C as the root

Triad TypeTriad*Pitch ClassesDegreeEccentricityCloseness Centrality
Major TriadsG♯{8,0,3}221
Minor Triadsam{9,0,4}221
Augmented TriadsC+{0,4,8}221
Diminished Triads{9,0,3}221
Parsimonious Voice Leading Between Common Triads of Scale 1817. Created by Ian Ring ©2019 C+ C+ G# G# C+->G# am am C+->am G#->a° a°->am

Above is a graph showing opportunities for parsimonious voice leading between triads*. Each line connects two triads that have two common tones, while the third tone changes by one generic scale step.

Diameter2
Radius2
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 1817 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 739
Scale 739: Rorimic, Ian Ring Music TheoryRorimic
3rd mode:
Scale 2417
Scale 2417: Kanimic, Ian Ring Music TheoryKanimic
4th mode:
Scale 407
Scale 407: Zylimic, Ian Ring Music TheoryZylimicThis is the prime mode
5th mode:
Scale 2251
Scale 2251: Zodimic, Ian Ring Music TheoryZodimic
6th mode:
Scale 3173
Scale 3173: Zarimic, Ian Ring Music TheoryZarimic

Prime

The prime form of this scale is Scale 407

Scale 407Scale 407: Zylimic, Ian Ring Music TheoryZylimic

Complement

The hexatonic modal family [1817, 739, 2417, 407, 2251, 3173] (Forte: 6-Z17) is the complement of the hexatonic modal family [359, 907, 1649, 2227, 2501, 3161] (Forte: 6-Z43)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1817 is 797

Scale 797Scale 797: Katocrimic, Ian Ring Music TheoryKatocrimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1817 is chiral, and its enantiomorph is scale 797

Scale 797Scale 797: Katocrimic, Ian Ring Music TheoryKatocrimic

Transformations:

T0 1817  T0I 797
T1 3634  T1I 1594
T2 3173  T2I 3188
T3 2251  T3I 2281
T4 407  T4I 467
T5 814  T5I 934
T6 1628  T6I 1868
T7 3256  T7I 3736
T8 2417  T8I 3377
T9 739  T9I 2659
T10 1478  T10I 1223
T11 2956  T11I 2446

Nearby Scales:

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.

Scale 1819Scale 1819: Pydian, Ian Ring Music TheoryPydian
Scale 1821Scale 1821: Aeradian, Ian Ring Music TheoryAeradian
Scale 1809Scale 1809: Ranitonic, Ian Ring Music TheoryRanitonic
Scale 1813Scale 1813: Katothimic, Ian Ring Music TheoryKatothimic
Scale 1801Scale 1801, Ian Ring Music Theory
Scale 1833Scale 1833: Ionacrimic, Ian Ring Music TheoryIonacrimic
Scale 1849Scale 1849: Chromatic Hypodorian Inverse, Ian Ring Music TheoryChromatic Hypodorian Inverse
Scale 1881Scale 1881: Katorian, Ian Ring Music TheoryKatorian
Scale 1945Scale 1945: Zarian, Ian Ring Music TheoryZarian
Scale 1561Scale 1561, Ian Ring Music Theory
Scale 1689Scale 1689: Lorimic, Ian Ring Music TheoryLorimic
Scale 1305Scale 1305: Dynitonic, Ian Ring Music TheoryDynitonic
Scale 793Scale 793: Mocritonic, Ian Ring Music TheoryMocritonic
Scale 2841Scale 2841: Sothimic, Ian Ring Music TheorySothimic
Scale 3865Scale 3865: Starian, Ian Ring Music TheoryStarian

This scale analysis was created by Ian Ring, Canadian Composer of works for Piano, and total music theory nerd. The software used to generate this analysis is an open source project at GitHub. Scale notation generated by VexFlow, graph visualization by Graphviz, and MIDI playback by MIDI.js. Some scale names used on this and other pages are ©2005 William Zeitler (http://allthescales.org) used with permission.

Pitch spelling algorithm employed here is adapted from a method by Uzay Bora, Baris Tekin Tezel, and Alper Vahaplar. (An algorithm for spelling the pitches of any musical scale) Contact authors Patent owner: Dokuz Eylül University, Used with Permission. Contact TTO

Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography. Special thanks to Richard Repp for helping with technical accuracy.