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Scale 1917: "Sacrygic"

Scale 1917: Sacrygic, 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
Sacrygic

Analysis

Cardinality9 (nonatonic)
Pitch Class Set{0,2,3,4,5,6,8,9,10}
Forte Number9-8
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 2013
Hemitonia6 (multihemitonic)
Cohemitonia4 (multicohemitonic)
Imperfections3
Modes8
Prime?no
prime: 1503
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 TriadsD{2,6,9}442.2
F{5,9,0}442.07
G♯{8,0,3}342.47
A♯{10,2,5}242.47
Minor Triadsdm{2,5,9}442.07
d♯m{3,6,10}342.47
fm{5,8,0}342.33
am{9,0,4}342.33
Augmented TriadsC+{0,4,8}342.4
D+{2,6,10}342.4
Diminished Triads{0,3,6}242.53
{2,5,8}242.47
d♯°{3,6,9}242.53
f♯°{6,9,0}242.33
{9,0,3}242.67
Parsimonious Voice Leading Between Common Triads of Scale 1917. Created by Ian Ring ©2019 d#m d#m c°->d#m G# G# c°->G# C+ C+ fm fm C+->fm C+->G# am am C+->am dm dm d°->dm d°->fm D D dm->D F F dm->F A# A# dm->A# D+ D+ D->D+ d#° d#° D->d#° f#° f#° D->f#° D+->d#m D+->A# d#°->d#m fm->F F->f#° F->am G#->a° a°->am

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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.

Diameter4
Radius4
Self-Centeredyes

Modes

Modes are the rotational transformation of this scale. Scale 1917 can be rotated to make 8 other scales. The 1st mode is itself.

2nd mode:
Scale 1503
Scale 1503: Padygic, Ian Ring Music TheoryPadygicThis is the prime mode
3rd mode:
Scale 2799
Scale 2799: Epilygic, Ian Ring Music TheoryEpilygic
4th mode:
Scale 3447
Scale 3447: Kynygic, Ian Ring Music TheoryKynygic
5th mode:
Scale 3771
Scale 3771: Stophygic, Ian Ring Music TheoryStophygic
6th mode:
Scale 3933
Scale 3933: Ionidygic, Ian Ring Music TheoryIonidygic
7th mode:
Scale 2007
Scale 2007: Stonygic, Ian Ring Music TheoryStonygic
8th mode:
Scale 3051
Scale 3051: Stalygic, Ian Ring Music TheoryStalygic
9th mode:
Scale 3573
Scale 3573: Kaptygic, Ian Ring Music TheoryKaptygic

Prime

The prime form of this scale is Scale 1503

Scale 1503Scale 1503: Padygic, Ian Ring Music TheoryPadygic

Complement

The nonatonic modal family [1917, 1503, 2799, 3447, 3771, 3933, 2007, 3051, 3573] (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 1917 is 2013

Scale 2013Scale 2013: Mocrygic, Ian Ring Music TheoryMocrygic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 1917 is chiral, and its enantiomorph is scale 2013

Scale 2013Scale 2013: Mocrygic, Ian Ring Music TheoryMocrygic

Transformations:

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

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 1919Scale 1919: Rocryllian, Ian Ring Music TheoryRocryllian
Scale 1913Scale 1913, Ian Ring Music Theory
Scale 1915Scale 1915: Thydygic, Ian Ring Music TheoryThydygic
Scale 1909Scale 1909: Epicryllic, Ian Ring Music TheoryEpicryllic
Scale 1901Scale 1901: Ionidyllic, Ian Ring Music TheoryIonidyllic
Scale 1885Scale 1885: Saptyllic, Ian Ring Music TheorySaptyllic
Scale 1853Scale 1853: Maryllic, Ian Ring Music TheoryMaryllic
Scale 1981Scale 1981: Houseini, Ian Ring Music TheoryHouseini
Scale 2045Scale 2045: Katogyllian, Ian Ring Music TheoryKatogyllian
Scale 1661Scale 1661: Gonyllic, Ian Ring Music TheoryGonyllic
Scale 1789Scale 1789: Blues Enneatonic II, Ian Ring Music TheoryBlues Enneatonic II
Scale 1405Scale 1405: Goryllic, Ian Ring Music TheoryGoryllic
Scale 893Scale 893: Dadyllic, Ian Ring Music TheoryDadyllic
Scale 2941Scale 2941: Laptygic, Ian Ring Music TheoryLaptygic
Scale 3965Scale 3965: Messiaen Mode 7 Inverse, Ian Ring Music TheoryMessiaen Mode 7 Inverse

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.