The Exciting Universe Of Music Theory
presents

more than you ever wanted to know about...

Scale 1975: "Ionocrygic"

Scale 1975: Ionocrygic, 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
Ionocrygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,1,2,4,5,7,8,9,10}
Forte Number9-11
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 3517
Hemitonia6 (multihemitonic)
Cohemitonia3 (tricohemitonic)
Imperfections2
Modes8
Prime?no
prime: 1775
Deep Scaleno
Interval Vector667773
Interval Spectrump7m7n7s6d6t3
Distribution Spectra<1> = {1,2}
<2> = {2,3}
<3> = {3,4,5}
<4> = {5,6}
<5> = {6,7}
<6> = {7,8,9}
<7> = {9,10}
<8> = {10,11}
Spectra Variation1.111
Maximally Evenno
Maximal Area Setyes
Interior Area2.799
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyProper
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}342.56
C♯{1,5,8}442.17
F{5,9,0}342.39
A{9,1,4}442.17
A♯{10,2,5}342.5
Minor Triadsc♯m{1,4,8}442.22
dm{2,5,9}342.39
fm{5,8,0}342.44
gm{7,10,2}342.67
am{9,0,4}342.44
a♯m{10,1,5}442.28
Augmented TriadsC+{0,4,8}442.33
C♯+{1,5,9}542
Diminished Triadsc♯°{1,4,7}242.67
{2,5,8}242.67
{4,7,10}242.72
{7,10,1}242.72
a♯°{10,1,4}242.56
Parsimonious Voice Leading Between Common Triads of Scale 1975. Created by Ian Ring ©2019 C C C+ C+ C->C+ c#° c#° C->c#° C->e° c#m c#m C+->c#m fm fm C+->fm am am C+->am c#°->c#m C# C# c#m->C# A A c#m->A C#+ C#+ C#->C#+ C#->d° C#->fm dm dm C#+->dm F F C#+->F C#+->A a#m a#m C#+->a#m d°->dm A# A# dm->A# gm gm e°->gm fm->F F->am g°->gm g°->a#m gm->A# am->A a#° a#° A->a#° a#°->a#m a#m->A#

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 1975 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 3035
Scale 3035: Gocrygic, Ian Ring Music TheoryGocrygic
3rd mode:
Scale 3565
Scale 3565: Aeolorygic, Ian Ring Music TheoryAeolorygic
4th mode:
Scale 1915
Scale 1915: Thydygic, Ian Ring Music TheoryThydygic
5th mode:
Scale 3005
Scale 3005: Gycrygic, Ian Ring Music TheoryGycrygic
6th mode:
Scale 1775
Scale 1775: Lyrygic, Ian Ring Music TheoryLyrygicThis is the prime mode
7th mode:
Scale 2935
Scale 2935: Modygic, Ian Ring Music TheoryModygic
8th mode:
Scale 3515
Scale 3515: Moorish Phrygian, Ian Ring Music TheoryMoorish Phrygian
9th mode:
Scale 3805
Scale 3805: Moptygic, Ian Ring Music TheoryMoptygic

Prime

The prime form of this scale is Scale 1775

Scale 1775Scale 1775: Lyrygic, Ian Ring Music TheoryLyrygic

Complement

The nonatonic modal family [1975, 3035, 3565, 1915, 3005, 1775, 2935, 3515, 3805] (Forte: 9-11) is the complement of the tritonic modal family [137, 289, 529] (Forte: 3-11)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1975 is 3517

Scale 3517Scale 3517: Epocrygic, Ian Ring Music TheoryEpocrygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1975 is chiral, and its enantiomorph is scale 3517

Scale 3517Scale 3517: Epocrygic, Ian Ring Music TheoryEpocrygic

Transformations:

T0 1975  T0I 3517
T1 3950  T1I 2939
T2 3805  T2I 1783
T3 3515  T3I 3566
T4 2935  T4I 3037
T5 1775  T5I 1979
T6 3550  T6I 3958
T7 3005  T7I 3821
T8 1915  T8I 3547
T9 3830  T9I 2999
T10 3565  T10I 1903
T11 3035  T11I 3806

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 1973Scale 1973: Zyryllic, Ian Ring Music TheoryZyryllic
Scale 1971Scale 1971: Aerynyllic, Ian Ring Music TheoryAerynyllic
Scale 1979Scale 1979: Aeradygic, Ian Ring Music TheoryAeradygic
Scale 1983Scale 1983: Soryllian, Ian Ring Music TheorySoryllian
Scale 1959Scale 1959: Katolyllic, Ian Ring Music TheoryKatolyllic
Scale 1967Scale 1967: Diatonic Dorian Mixed, Ian Ring Music TheoryDiatonic Dorian Mixed
Scale 1943Scale 1943, Ian Ring Music Theory
Scale 2007Scale 2007: Stonygic, Ian Ring Music TheoryStonygic
Scale 2039Scale 2039: Danyllian, Ian Ring Music TheoryDanyllian
Scale 1847Scale 1847: Thacryllic, Ian Ring Music TheoryThacryllic
Scale 1911Scale 1911: Messiaen Mode 3, Ian Ring Music TheoryMessiaen Mode 3
Scale 1719Scale 1719: Lyryllic, Ian Ring Music TheoryLyryllic
Scale 1463Scale 1463, Ian Ring Music Theory
Scale 951Scale 951: Thogyllic, Ian Ring Music TheoryThogyllic
Scale 2999Scale 2999: Chromatic and Permuted Diatonic Dorian Mixed, Ian Ring Music TheoryChromatic and Permuted Diatonic Dorian Mixed
Scale 4023Scale 4023: Styptyllian, Ian Ring Music TheoryStyptyllian

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.