The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 1241: "Pygimic"

Scale 1241: Pygimic, 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

41161837294116105072918310504116183
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
Pygimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,3,4,6,7,10}
Forte Number6-Z49
Rotational Symmetrynone
Reflection Axes5
Palindromicno
Chiralityno
Hemitonia2 (dihemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections4
Modes5
Prime?no
prime: 667
Deep Scaleno
Interval Vector224322
Interval Spectrump2m3n4s2d2t2
Distribution Spectra<1> = {1,2,3}
<2> = {3,4,5}
<3> = {4,6,8}
<4> = {7,8,9}
<5> = {9,10,11}
Spectra Variation2
Maximally Evenno
Maximal Area Setno
Interior Area2.366
Myhill Propertyno
Balancedno
Ridge Tones[10]
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}231.5
D♯{3,7,10}321.17
Minor Triadscm{0,3,7}321.17
d♯m{3,6,10}231.5
Diminished Triads{0,3,6}231.5
{4,7,10}231.5
Parsimonious Voice Leading Between Common Triads of Scale 1241. Created by Ian Ring ©2019 cm cm c°->cm d#m d#m c°->d#m C C cm->C D# D# cm->D# C->e° d#m->D# D#->e°

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.

Diameter3
Radius2
Self-Centeredno
Central Verticescm, D♯
Peripheral Verticesc°, C, d♯m, e°

Modes

Modes are the rotational transformation of this scale. Scale 1241 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 667
Scale 667: Rodimic, Ian Ring Music TheoryRodimicThis is the prime mode
3rd mode:
Scale 2381
Scale 2381: Takemitsu Linea Mode 1, Ian Ring Music TheoryTakemitsu Linea Mode 1
4th mode:
Scale 1619
Scale 1619: Prometheus Neapolitan, Ian Ring Music TheoryPrometheus Neapolitan
5th mode:
Scale 2857
Scale 2857: Stythimic, Ian Ring Music TheoryStythimic
6th mode:
Scale 869
Scale 869: Kothimic, Ian Ring Music TheoryKothimic

Prime

The prime form of this scale is Scale 667

Scale 667Scale 667: Rodimic, Ian Ring Music TheoryRodimic

Complement

The hexatonic modal family [1241, 667, 2381, 1619, 2857, 869] (Forte: 6-Z49) is the complement of the hexatonic modal family [619, 857, 1427, 1613, 2357, 2761] (Forte: 6-Z28)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1241 is 869

Scale 869Scale 869: Kothimic, Ian Ring Music TheoryKothimic

Transformations:

T0 1241  T0I 869
T1 2482  T1I 1738
T2 869  T2I 3476
T3 1738  T3I 2857
T4 3476  T4I 1619
T5 2857  T5I 3238
T6 1619  T6I 2381
T7 3238  T7I 667
T8 2381  T8I 1334
T9 667  T9I 2668
T10 1334  T10I 1241
T11 2668  T11I 2482

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 1243Scale 1243: Epylian, Ian Ring Music TheoryEpylian
Scale 1245Scale 1245: Lathian, Ian Ring Music TheoryLathian
Scale 1233Scale 1233: Ionoditonic, Ian Ring Music TheoryIonoditonic
Scale 1237Scale 1237: Salimic, Ian Ring Music TheorySalimic
Scale 1225Scale 1225: Raga Samudhra Priya, Ian Ring Music TheoryRaga Samudhra Priya
Scale 1257Scale 1257: Blues Scale, Ian Ring Music TheoryBlues Scale
Scale 1273Scale 1273: Ronian, Ian Ring Music TheoryRonian
Scale 1177Scale 1177: Garitonic, Ian Ring Music TheoryGaritonic
Scale 1209Scale 1209: Raga Bhanumanjari, Ian Ring Music TheoryRaga Bhanumanjari
Scale 1113Scale 1113: Locrian Pentatonic 2, Ian Ring Music TheoryLocrian Pentatonic 2
Scale 1369Scale 1369: Boptimic, Ian Ring Music TheoryBoptimic
Scale 1497Scale 1497: Mela Jyotisvarupini, Ian Ring Music TheoryMela Jyotisvarupini
Scale 1753Scale 1753: Hungarian Major, Ian Ring Music TheoryHungarian Major
Scale 217Scale 217, Ian Ring Music Theory
Scale 729Scale 729: Stygimic, Ian Ring Music TheoryStygimic
Scale 2265Scale 2265: Raga Rasamanjari, Ian Ring Music TheoryRaga Rasamanjari
Scale 3289Scale 3289: Lydian Sharp 2 Sharp 6, Ian Ring Music TheoryLydian Sharp 2 Sharp 6

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.