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Scale 1223: "Phryptimic"

Scale 1223: Phryptimic, 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
Phryptimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,1,2,6,7,10}
Forte Number6-Z17
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3173
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 TriadsF♯{6,10,1}221
Minor Triadsgm{7,10,2}221
Augmented TriadsD+{2,6,10}221
Diminished Triads{7,10,1}221
Parsimonious Voice Leading Between Common Triads of Scale 1223. Created by Ian Ring ©2019 D+ D+ F# F# D+->F# gm gm D+->gm F#->g° g°->gm

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 1223 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 2659
Scale 2659: Katynimic, Ian Ring Music TheoryKatynimic
3rd mode:
Scale 3377
Scale 3377: Phralimic, Ian Ring Music TheoryPhralimic
4th mode:
Scale 467
Scale 467: Raga Dhavalangam, Ian Ring Music TheoryRaga Dhavalangam
5th mode:
Scale 2281
Scale 2281: Rathimic, Ian Ring Music TheoryRathimic
6th mode:
Scale 797
Scale 797: Katocrimic, Ian Ring Music TheoryKatocrimic

Prime

The prime form of this scale is Scale 407

Scale 407Scale 407: Zylimic, Ian Ring Music TheoryZylimic

Complement

The hexatonic modal family [1223, 2659, 3377, 467, 2281, 797] (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 1223 is 3173

Scale 3173Scale 3173: Zarimic, Ian Ring Music TheoryZarimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1223 is chiral, and its enantiomorph is scale 3173

Scale 3173Scale 3173: Zarimic, Ian Ring Music TheoryZarimic

Transformations:

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

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 1221Scale 1221: Epyritonic, Ian Ring Music TheoryEpyritonic
Scale 1219Scale 1219, Ian Ring Music Theory
Scale 1227Scale 1227: Thacrimic, Ian Ring Music TheoryThacrimic
Scale 1231Scale 1231: Logian, Ian Ring Music TheoryLogian
Scale 1239Scale 1239: Epaptian, Ian Ring Music TheoryEpaptian
Scale 1255Scale 1255: Chromatic Mixolydian, Ian Ring Music TheoryChromatic Mixolydian
Scale 1159Scale 1159, Ian Ring Music Theory
Scale 1191Scale 1191: Pyrimic, Ian Ring Music TheoryPyrimic
Scale 1095Scale 1095: Phrythitonic, Ian Ring Music TheoryPhrythitonic
Scale 1351Scale 1351: Aeraptimic, Ian Ring Music TheoryAeraptimic
Scale 1479Scale 1479: Mela Jalarnava, Ian Ring Music TheoryMela Jalarnava
Scale 1735Scale 1735: Mela Navanitam, Ian Ring Music TheoryMela Navanitam
Scale 199Scale 199: Raga Nabhomani, Ian Ring Music TheoryRaga Nabhomani
Scale 711Scale 711: Raga Chandrajyoti, Ian Ring Music TheoryRaga Chandrajyoti
Scale 2247Scale 2247: Raga Vijayasri, Ian Ring Music TheoryRaga Vijayasri
Scale 3271Scale 3271: Mela Raghupriya, Ian Ring Music TheoryMela Raghupriya

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.