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Scale 825: "Thyptimic"

Scale 825: Thyptimic, 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
Thyptimic

Analysis

Cardinality6 (hexatonic)
Pitch Class Set{0,3,4,5,8,9}
Forte Number6-Z44
Rotational Symmetrynone
Reflection Axesnone
Palindromicno
Chiralityyes
enantiomorph: 921
Hemitonia3 (trihemitonic)
Cohemitonia1 (uncohemitonic)
Imperfections3
Modes5
Prime?no
prime: 615
Deep Scaleno
Interval Vector313431
Interval Spectrump3m4n3sd3t
Distribution Spectra<1> = {1,3}
<2> = {2,4,6}
<3> = {5,7}
<4> = {6,8,10}
<5> = {9,11}
Spectra Variation2.333
Maximally Evenno
Maximal Area Setno
Interior Area2.25
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 TriadsF{5,9,0}231.5
G♯{8,0,3}231.5
Minor Triadsfm{5,8,0}231.5
am{9,0,4}321.17
Augmented TriadsC+{0,4,8}321.17
Diminished Triads{9,0,3}231.5
Parsimonious Voice Leading Between Common Triads of Scale 825. Created by Ian Ring ©2019 C+ C+ fm fm C+->fm G# G# C+->G# am am C+->am F F fm->F F->am G#->a° a°->am

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 VerticesC+, am
Peripheral Verticesfm, F, G♯, a°

Modes

Modes are the rotational transformation of this scale. Scale 825 can be rotated to make 5 other scales. The 1st mode is itself.

2nd mode:
Scale 615
Scale 615: Phrothimic, Ian Ring Music TheoryPhrothimicThis is the prime mode
3rd mode:
Scale 2355
Scale 2355: Raga Lalita, Ian Ring Music TheoryRaga Lalita
4th mode:
Scale 3225
Scale 3225: Ionalimic, Ian Ring Music TheoryIonalimic
5th mode:
Scale 915
Scale 915: Raga Kalagada, Ian Ring Music TheoryRaga Kalagada
6th mode:
Scale 2505
Scale 2505: Mydimic, Ian Ring Music TheoryMydimic

Prime

The prime form of this scale is Scale 615

Scale 615Scale 615: Phrothimic, Ian Ring Music TheoryPhrothimic

Complement

The hexatonic modal family [825, 615, 2355, 3225, 915, 2505] (Forte: 6-Z44) is the complement of the hexatonic modal family [411, 867, 1587, 2253, 2481, 2841] (Forte: 6-Z19)

Inverse

The inverse of a scale is a reflection using the root as its axis. The inverse of 825 is 921

Scale 921Scale 921: Bogimic, Ian Ring Music TheoryBogimic

Enantiomorph

Only scales that are chiral will have an enantiomorph. Scale 825 is chiral, and its enantiomorph is scale 921

Scale 921Scale 921: Bogimic, Ian Ring Music TheoryBogimic

Transformations:

T0 825  T0I 921
T1 1650  T1I 1842
T2 3300  T2I 3684
T3 2505  T3I 3273
T4 915  T4I 2451
T5 1830  T5I 807
T6 3660  T6I 1614
T7 3225  T7I 3228
T8 2355  T8I 2361
T9 615  T9I 627
T10 1230  T10I 1254
T11 2460  T11I 2508

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 827Scale 827: Mixolocrian, Ian Ring Music TheoryMixolocrian
Scale 829Scale 829: Lygian, Ian Ring Music TheoryLygian
Scale 817Scale 817: Zothitonic, Ian Ring Music TheoryZothitonic
Scale 821Scale 821: Aeranimic, Ian Ring Music TheoryAeranimic
Scale 809Scale 809: Dogitonic, Ian Ring Music TheoryDogitonic
Scale 793Scale 793: Mocritonic, Ian Ring Music TheoryMocritonic
Scale 857Scale 857: Aeolydimic, Ian Ring Music TheoryAeolydimic
Scale 889Scale 889: Borian, Ian Ring Music TheoryBorian
Scale 953Scale 953: Mela Yagapriya, Ian Ring Music TheoryMela Yagapriya
Scale 569Scale 569: Mothitonic, Ian Ring Music TheoryMothitonic
Scale 697Scale 697: Lagimic, Ian Ring Music TheoryLagimic
Scale 313Scale 313: Goritonic, Ian Ring Music TheoryGoritonic
Scale 1337Scale 1337: Epogimic, Ian Ring Music TheoryEpogimic
Scale 1849Scale 1849: Chromatic Hypodorian Inverse, Ian Ring Music TheoryChromatic Hypodorian Inverse
Scale 2873Scale 2873: Ionian Augmented Sharp 2, Ian Ring Music TheoryIonian Augmented Sharp 2

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.