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Scale 1503: "Padygic"

Scale 1503: Padygic, 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
Padygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,1,2,3,4,6,7,8,10}
Forte Number9-8
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3957
Hemitonia6 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections3
Modes8
Prime?yes
Deep Scaleno
Interval Vector676764
Interval Spectrump6m7n6s7d6t4
Distribution Spectra<1> = {1,2}
<2> = {2,3,4}
<3> = {3,4,5}
<4> = {4,5,6}
<5> = {6,7,8}
<6> = {7,8,9}
<7> = {8,9,10}
<8> = {10,11}
Spectra Variation1.556
Maximally Evenno
Maximal Area Setyes
Interior Area2.799
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 TriadsC{0,4,7}442.2
D♯{3,7,10}442.07
F♯{6,10,1}342.47
G♯{8,0,3}242.47
Minor Triadscm{0,3,7}442.07
c♯m{1,4,8}342.47
d♯m{3,6,10}342.33
gm{7,10,2}342.33
Augmented TriadsC+{0,4,8}342.4
D+{2,6,10}342.4
Diminished Triads{0,3,6}242.47
c♯°{1,4,7}242.53
{4,7,10}242.33
{7,10,1}242.67
a♯°{10,1,4}242.53
Parsimonious Voice Leading Between Common Triads of Scale 1503. Created by Ian Ring ©2019 cm cm c°->cm d#m d#m c°->d#m C C cm->C D# D# cm->D# G# G# cm->G# C+ C+ C->C+ c#° c#° C->c#° C->e° c#m c#m C+->c#m C+->G# c#°->c#m a#° a#° c#m->a#° D+ D+ D+->d#m F# F# D+->F# gm gm D+->gm d#m->D# D#->e° D#->gm F#->g° F#->a#° g°->gm

view full size

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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 1503 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 2799
Scale 2799: Epilygic, Ian Ring Music TheoryEpilygic
3rd mode:
Scale 3447
Scale 3447: Kynygic, Ian Ring Music TheoryKynygic
4th mode:
Scale 3771
Scale 3771: Stophygic, Ian Ring Music TheoryStophygic
5th mode:
Scale 3933
Scale 3933: Ionidygic, Ian Ring Music TheoryIonidygic
6th mode:
Scale 2007
Scale 2007: Stonygic, Ian Ring Music TheoryStonygic
7th mode:
Scale 3051
Scale 3051: Stalygic, Ian Ring Music TheoryStalygic
8th mode:
Scale 3573
Scale 3573: Kaptygic, Ian Ring Music TheoryKaptygic
9th mode:
Scale 1917
Scale 1917: Sacrygic, Ian Ring Music TheorySacrygic

Prime

This is the prime form of this scale.

Complement

The nonatonic modal family [1503, 2799, 3447, 3771, 3933, 2007, 3051, 3573, 1917] (Forte: 9-8) is the complement of the tritonic modal family [69, 321, 1041] (Forte: 3-8)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1503 is 3957

Scale 3957Scale 3957: Porygic, Ian Ring Music TheoryPorygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1503 is chiral, and its enantiomorph is scale 3957

Scale 3957Scale 3957: Porygic, Ian Ring Music TheoryPorygic

Transformations:

T0 1503  T0I 3957
T1 3006  T1I 3819
T2 1917  T2I 3543
T3 3834  T3I 2991
T4 3573  T4I 1887
T5 3051  T5I 3774
T6 2007  T6I 3453
T7 4014  T7I 2811
T8 3933  T8I 1527
T9 3771  T9I 3054
T10 3447  T10I 2013
T11 2799  T11I 4026

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 1501Scale 1501: Stygyllic, Ian Ring Music TheoryStygyllic
Scale 1499Scale 1499: Bebop Locrian, Ian Ring Music TheoryBebop Locrian
Scale 1495Scale 1495: Messiaen Mode 6, Ian Ring Music TheoryMessiaen Mode 6
Scale 1487Scale 1487: Mothyllic, Ian Ring Music TheoryMothyllic
Scale 1519Scale 1519: Locrian/Aeolian Mixed, Ian Ring Music TheoryLocrian/Aeolian Mixed
Scale 1535Scale 1535: Mixodyllian, Ian Ring Music TheoryMixodyllian
Scale 1439Scale 1439: Rolyllic, Ian Ring Music TheoryRolyllic
Scale 1471Scale 1471: Radygic, Ian Ring Music TheoryRadygic
Scale 1375Scale 1375: Bothyllic, Ian Ring Music TheoryBothyllic
Scale 1247Scale 1247: Aeodyllic, Ian Ring Music TheoryAeodyllic
Scale 1759Scale 1759: Pylygic, Ian Ring Music TheoryPylygic
Scale 2015Scale 2015: Messiaen Mode 7, Ian Ring Music TheoryMessiaen Mode 7
Scale 479Scale 479: Kocryllic, Ian Ring Music TheoryKocryllic
Scale 991Scale 991: Aeolygic, Ian Ring Music TheoryAeolygic
Scale 2527Scale 2527: Phradygic, Ian Ring Music TheoryPhradygic
Scale 3551Scale 3551: Sagyllian, Ian Ring Music TheorySagyllian

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.