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Scale 1627: "Zyptian"

Scale 1627: Zyptian, 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
Zyptian

Analysis

Cardinality7 (heptatonic)
Pitch Class Set{0,1,3,4,6,9,10}
Forte Number7-31
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2893
Hemitonia3 (trihemitonic)
Cohemitonia0 (ancohemitonic)
Imperfections4
Modes6
Prime?no
prime: 731
Deep Scaleno
Interval Vector336333
Interval Spectrump3m3n6s3d3t3
Distribution Spectra<1> = {1,2,3}
<2> = {3,4,5}
<3> = {4,5,6}
<4> = {6,7,8}
<5> = {7,8,9}
<6> = {9,10,11}
Spectra Variation1.714
Maximally Evenno
Maximal Area Setno
Interior Area2.549
Myhill Propertyno
Balancedno
Ridge Tonesnone
ProprietyImproper
Heliotonicyes

Harmonic Chords

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}331.7
A{9,1,4}331.7
Minor Triadsd♯m{3,6,10}331.8
f♯m{6,9,1}431.6
am{9,0,4}331.8
Diminished Triads{0,3,6}232
d♯°{3,6,9}231.9
f♯°{6,9,0}231.9
{9,0,3}232
a♯°{10,1,4}232
Parsimonious Voice Leading Between Common Triads of Scale 1627. Created by Ian Ring ©2019 d#m d#m c°->d#m c°->a° d#° d#° d#°->d#m f#m f#m d#°->f#m F# F# d#m->F# f#° f#° f#°->f#m am am f#°->am f#m->F# A A f#m->A a#° a#° F#->a#° a°->am am->A A->a#°

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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
Radius3
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 1627 can be rotated to make 6 other scales. The 1st mode is itself.

2nd mode:
Scale 2861
Scale 2861: Katothian, Ian Ring Music TheoryKatothian
3rd mode:
Scale 1739
Scale 1739: Mela Sadvidhamargini, Ian Ring Music TheoryMela Sadvidhamargini
4th mode:
Scale 2917
Scale 2917: Nohkan Flute Scale, Ian Ring Music TheoryNohkan Flute Scale
5th mode:
Scale 1753
Scale 1753: Hungarian Major, Ian Ring Music TheoryHungarian Major
6th mode:
Scale 731
Scale 731: Ionorian, Ian Ring Music TheoryIonorianThis is the prime mode
7th mode:
Scale 2413
Scale 2413: Locrian Natural 2, Ian Ring Music TheoryLocrian Natural 2

Prime

The prime form of this scale is Scale 731

Scale 731Scale 731: Ionorian, Ian Ring Music TheoryIonorian

Complement

The heptatonic modal family [1627, 2861, 1739, 2917, 1753, 731, 2413] (Forte: 7-31) is the complement of the pentatonic modal family [587, 601, 713, 1609, 2341] (Forte: 5-31)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 1627 is 2893

Scale 2893Scale 2893: Lylian, Ian Ring Music TheoryLylian

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1627 is chiral, and its enantiomorph is scale 2893

Scale 2893Scale 2893: Lylian, Ian Ring Music TheoryLylian

Transformations:

T0 1627  T0I 2893
T1 3254  T1I 1691
T2 2413  T2I 3382
T3 731  T3I 2669
T4 1462  T4I 1243
T5 2924  T5I 2486
T6 1753  T6I 877
T7 3506  T7I 1754
T8 2917  T8I 3508
T9 1739  T9I 2921
T10 3478  T10I 1747
T11 2861  T11I 3494

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 1625Scale 1625: Lythimic, Ian Ring Music TheoryLythimic
Scale 1629Scale 1629: Synian, Ian Ring Music TheorySynian
Scale 1631Scale 1631: Rynyllic, Ian Ring Music TheoryRynyllic
Scale 1619Scale 1619: Prometheus Neapolitan, Ian Ring Music TheoryPrometheus Neapolitan
Scale 1623Scale 1623: Lothian, Ian Ring Music TheoryLothian
Scale 1611Scale 1611: Dacrimic, Ian Ring Music TheoryDacrimic
Scale 1643Scale 1643: Locrian Natural 6, Ian Ring Music TheoryLocrian Natural 6
Scale 1659Scale 1659: Maqam Shadd'araban, Ian Ring Music TheoryMaqam Shadd'araban
Scale 1563Scale 1563, Ian Ring Music Theory
Scale 1595Scale 1595: Dacrian, Ian Ring Music TheoryDacrian
Scale 1691Scale 1691: Kathian, Ian Ring Music TheoryKathian
Scale 1755Scale 1755: Octatonic, Ian Ring Music TheoryOctatonic
Scale 1883Scale 1883, Ian Ring Music Theory
Scale 1115Scale 1115: Superlocrian Hexamirror, Ian Ring Music TheorySuperlocrian Hexamirror
Scale 1371Scale 1371: Superlocrian, Ian Ring Music TheorySuperlocrian
Scale 603Scale 603: Aeolygimic, Ian Ring Music TheoryAeolygimic
Scale 2651Scale 2651: Panian, Ian Ring Music TheoryPanian
Scale 3675Scale 3675: Monyllic, Ian Ring Music TheoryMonyllic

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.