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Scale 1787: "Mycrygic"

Scale 1787: Mycrygic, 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
Mycrygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,1,3,4,5,6,7,9,10}
Forte Number9-10
Rotational Symmetrynone
Reflection Axes5
Palindromicno
Chiralityno
Hemitonia6 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections3
Modes8
Prime?no
prime: 1759
Deep Scaleno
Interval Vector668664
Interval Spectrump6m6n8s6d6t4
Distribution Spectra<1> = {1,2}
<2> = {2,3}
<3> = {3,4,5}
<4> = {4,5,6}
<5> = {6,7,8}
<6> = {7,8,9}
<7> = {9,10}
<8> = {10,11}
Spectra Variation1.333
Maximally Evenno
Maximal Area Setyes
Interior Area2.799
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}442.37
D♯{3,7,10}442.42
F{5,9,0}342.47
F♯{6,10,1}442.32
A{9,1,4}442.37
Minor Triadscm{0,3,7}442.42
d♯m{3,6,10}442.37
f♯m{6,9,1}442.37
am{9,0,4}442.32
a♯m{10,1,5}342.47
Augmented TriadsC♯+{1,5,9}442.32
Diminished Triads{0,3,6}242.63
c♯°{1,4,7}242.63
d♯°{3,6,9}242.63
{4,7,10}242.63
f♯°{6,9,0}242.74
{7,10,1}242.58
{9,0,3}242.58
a♯°{10,1,4}242.74
Parsimonious Voice Leading Between Common Triads of Scale 1787. Created by Ian Ring ©2019 cm cm c°->cm d#m d#m c°->d#m C C cm->C D# D# cm->D# cm->a° c#° c#° C->c#° C->e° am am C->am A A c#°->A C#+ C#+ F F C#+->F f#m f#m C#+->f#m C#+->A a#m a#m C#+->a#m d#° d#° d#°->d#m d#°->f#m d#m->D# F# F# d#m->F# D#->e° D#->g° f#° f#° F->f#° F->am f#°->f#m f#m->F# F#->g° F#->a#m a°->am am->A a#° a#° A->a#° a#°->a#m

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 1787 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 2941
Scale 2941: Laptygic, Ian Ring Music TheoryLaptygic
3rd mode:
Scale 1759
Scale 1759: Pylygic, Ian Ring Music TheoryPylygicThis is the prime mode
4th mode:
Scale 2927
Scale 2927: Rodygic, Ian Ring Music TheoryRodygic
5th mode:
Scale 3511
Scale 3511: Epolygic, Ian Ring Music TheoryEpolygic
6th mode:
Scale 3803
Scale 3803: Epidygic, Ian Ring Music TheoryEpidygic
7th mode:
Scale 3949
Scale 3949: Koptygic, Ian Ring Music TheoryKoptygic
8th mode:
Scale 2011
Scale 2011: Raphygic, Ian Ring Music TheoryRaphygic
9th mode:
Scale 3053
Scale 3053: Zycrygic, Ian Ring Music TheoryZycrygic

Prime

The prime form of this scale is Scale 1759

Scale 1759Scale 1759: Pylygic, Ian Ring Music TheoryPylygic

Complement

The nonatonic modal family [1787, 2941, 1759, 2927, 3511, 3803, 3949, 2011, 3053] (Forte: 9-10) is the complement of the tritonic modal family [73, 521, 577] (Forte: 3-10)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1787 is 3053

Scale 3053Scale 3053: Zycrygic, Ian Ring Music TheoryZycrygic

Transformations:

T0 1787  T0I 3053
T1 3574  T1I 2011
T2 3053  T2I 4022
T3 2011  T3I 3949
T4 4022  T4I 3803
T5 3949  T5I 3511
T6 3803  T6I 2927
T7 3511  T7I 1759
T8 2927  T8I 3518
T9 1759  T9I 2941
T10 3518  T10I 1787
T11 2941  T11I 3574

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 1785Scale 1785: Tharyllic, Ian Ring Music TheoryTharyllic
Scale 1789Scale 1789: Blues Enneatonic II, Ian Ring Music TheoryBlues Enneatonic II
Scale 1791Scale 1791: Aerygyllian, Ian Ring Music TheoryAerygyllian
Scale 1779Scale 1779: Zynyllic, Ian Ring Music TheoryZynyllic
Scale 1783Scale 1783: Youlan Scale, Ian Ring Music TheoryYoulan Scale
Scale 1771Scale 1771, Ian Ring Music Theory
Scale 1755Scale 1755: Octatonic, Ian Ring Music TheoryOctatonic
Scale 1723Scale 1723: JG Octatonic, Ian Ring Music TheoryJG Octatonic
Scale 1659Scale 1659: Maqam Shadd'araban, Ian Ring Music TheoryMaqam Shadd'araban
Scale 1915Scale 1915: Thydygic, Ian Ring Music TheoryThydygic
Scale 2043Scale 2043: Maqam Tarzanuyn, Ian Ring Music TheoryMaqam Tarzanuyn
Scale 1275Scale 1275: Stagyllic, Ian Ring Music TheoryStagyllic
Scale 1531Scale 1531: Styptygic, Ian Ring Music TheoryStyptygic
Scale 763Scale 763: Doryllic, Ian Ring Music TheoryDoryllic
Scale 2811Scale 2811: Barygic, Ian Ring Music TheoryBarygic
Scale 3835Scale 3835, Ian Ring Music Theory

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. Tons of background resources contributed to the production of this summary; for a list of these peruse this Bibliography.